The OCaml system release 5.2 Documentation and user’s manual Xavier Leroy, Damien Doligez, Alain Frisch, Jacques Garrigue, Didier Rémy, KC Sivaramakrishnan and Jérôme Vouillon 13^thMay, 2024 Copyright © 2013 Institut National de Recherche en Informatique et en Automatique This manual is also available in PDF (1), plain text (2), as a bundle of HTML files (3), and as a bundle of Emacs Info files (4). --------------------------------------- (1) https://ocaml.org/releases/5.2/ocaml-5.2-refman.pdf (2) https://ocaml.org/releases/5.2/ocaml-5.2-refman.txt (3) https://ocaml.org/releases/5.2/ocaml-5.2-refman-html.tar.gz (4) https://ocaml.org/releases/5.2/ocaml-5.2-refman.info.tar.gz Contents ******** - Part: I An introduction to OCaml - Chapter 1 The core language - 1.1 Basics - 1.2 Data types - 1.3 Functions as values - 1.4 Records and variants - 1.4.1 Record and variant disambiguation - 1.5 Imperative features - 1.6 Exceptions - 1.7 Lazy expressions - 1.8 Symbolic processing of expressions - 1.9 Pretty-printing - 1.10 Printf formats - 1.11 Standalone OCaml programs - Chapter 2 The module system - 2.1 Structures - 2.2 Signatures - 2.3 Functors - 2.4 Functors and type abstraction - 2.5 Modules and separate compilation - Chapter 3 Objects in OCaml - 3.1 Classes and objects - 3.2 Immediate objects - 3.3 Reference to self - 3.4 Initializers - 3.5 Virtual methods - 3.6 Private methods - 3.7 Class interfaces - 3.8 Inheritance - 3.9 Multiple inheritance - 3.10 Parameterized classes - 3.11 Polymorphic methods - 3.12 Using coercions - 3.13 Functional objects - 3.14 Cloning objects - 3.15 Recursive classes - 3.16 Binary methods - 3.17 Friends - Chapter 4 Labeled arguments - 4.1 Optional arguments - 4.2 Labels and type inference - 4.3 Suggestions for labeling - Chapter 5 Polymorphic variants - 5.1 Basic use - 5.2 Advanced use - 5.3 Weaknesses of polymorphic variants - Chapter 6 Polymorphism and its limitations - 6.1 Weak polymorphism and mutation - 6.1.1 Weakly polymorphic types - 6.1.2 The value restriction - 6.1.3 The relaxed value restriction - 6.1.4 Variance and value restriction - 6.1.5 Abstract data types - 6.2 Polymorphic recursion - 6.2.1 Explicitly polymorphic annotations - 6.2.2 More examples - 6.3 Higher-rank polymorphic functions - Chapter 7 Generalized algebraic datatypes - 7.1 Recursive functions - 7.2 Type inference - 7.3 Refutation cases - 7.4 Advanced examples - 7.5 Existential type names in error messages - 7.6 Explicit naming of existentials - 7.7 Equations on non-local abstract types - Chapter 8 Advanced examples with classes and modules - 8.1 Extended example: bank accounts - 8.2 Simple modules as classes - 8.2.1 Strings - 8.2.2 Hashtbl - 8.2.3 Sets - 8.3 The subject/observer pattern - Chapter 9 Parallel programming - 9.1 Domains - 9.1.1 Joining domains - 9.2 Domainslib: A library for nested-parallel programming - 9.2.1 Parallelising Fibonacci using domainslib - 9.2.2 Parallel iteration constructs - 9.3 Parallel garbage collection - 9.4 Memory model: The easy bits - 9.5 Blocking synchronisation - 9.5.1 Interaction with systhreads - 9.6 Interaction with C bindings - 9.7 Atomics - 9.7.1 Lock-free stack - Chapter 10 Memory model: The hard bits - 10.1 Why weakly consistent memory? - 10.1.1 Compiler optimisations - 10.1.2 Hardware optimisations - 10.2 Data race freedom implies sequential consistency - 10.2.1 Memory locations - 10.2.2 Happens-before relation - 10.2.3 Data race - 10.2.4 DRF-SC - 10.3 Reasoning with DRF-SC - 10.4 Local data race freedom - 10.5 An operational view of the memory model - 10.5.1 Non-atomic locations - 10.5.2 Domains - 10.5.3 Non-atomic accesses - 10.5.4 Atomic accesses - 10.5.5 Reasoning with the semantics - 10.6 Non-compliant operations - Part: II The OCaml language - Chapter 11 The OCaml language - 11.1 Lexical conventions - 11.2 Values - 11.2.1 Base values - 11.2.2 Tuples - 11.2.3 Records - 11.2.4 Arrays - 11.2.5 Variant values - 11.2.6 Polymorphic variants - 11.2.7 Functions - 11.2.8 Objects - 11.3 Names - 11.4 Type expressions - 11.5 Constants - 11.6 Patterns - 11.7 Expressions - 11.7.1 Precedence and associativity - 11.7.2 Basic expressions - 11.7.3 Control structures - 11.7.4 Operations on data structures - 11.7.5 Operators - 11.7.6 Objects - 11.7.7 Coercions - 11.7.8 Other - 11.8 Type and exception definitions - 11.8.1 Type definitions - 11.8.2 Exception definitions - 11.9 Classes - 11.9.1 Class types - 11.9.2 Class expressions - 11.9.3 Class definitions - 11.9.4 Class specifications - 11.9.5 Class type definitions - 11.10 Module types (module specifications) - 11.10.1 Simple module types - 11.10.2 Signatures - 11.10.3 Functor types - 11.10.4 The with operator - 11.11 Module expressions (module implementations) - 11.11.1 Simple module expressions - 11.11.2 Structures - 11.11.3 Functors - 11.12 Compilation units - Chapter 12 Language extensions - 12.1 Recursive definitions of values - 12.2 Recursive modules - 12.3 Private types - 12.3.1 Private variant and record types - 12.3.2 Private type abbreviations - 12.3.3 Private row types - 12.4 Locally abstract types - 12.5 First-class modules - 12.6 Recovering the type of a module - 12.7 Substituting inside a signature - 12.7.1 Destructive substitutions - 12.7.2 Local substitution declarations - 12.7.3 Module type substitutions - 12.8 Type-level module aliases - 12.9 Overriding in open statements - 12.10 Generalized algebraic datatypes - 12.11 Syntax for Bigarray access - 12.12 Attributes - 12.12.1 Built-in attributes - 12.13 Extension nodes - 12.13.1 Built-in extension nodes - 12.14 Extensible variant types - 12.14.1 Private extensible variant types - 12.15 Generative functors - 12.16 Extension-only syntax - 12.16.1 Extension operators - 12.16.2 Extension literals - 12.17 Inline records - 12.18 Documentation comments - 12.18.1 Floating comments - 12.18.2 Item comments - 12.18.3 Label comments - 12.19 Extended indexing operators - 12.19.1 Multi-index notation - 12.20 Empty variant types - 12.21 Alerts - 12.22 Generalized open statements - 12.23 Binding operators - 12.23.1 Examples - 12.23.2 Conventions - 12.23.3 General desugaring rules - 12.23.4 Short notation for variable bindings (let-punning) - 12.24 Effect handlers - 12.24.1 Basics - 12.24.2 Concurrency - 12.24.3 User-level threads - 12.24.4 Control inversion - 12.24.5 Semantics - 12.24.6 Shallow handlers - Part: III The OCaml tools - Chapter 13 Batch compilation (ocamlc) - 13.1 Overview of the compiler - 13.2 Options - 13.3 Modules and the file system - 13.4 Common errors - 13.5 Warning reference - 13.5.1 Warning 6: Label omitted in function application - 13.5.2 Warning 9: missing fields in a record pattern - 13.5.3 Warning 52: fragile constant pattern - 13.5.4 Warning 57: Ambiguous or-pattern variables under guard - Chapter 14 The toplevel system or REPL (ocaml) - 14.1 Options - 14.2 Toplevel directives - 14.3 The toplevel and the module system - 14.4 Common errors - 14.5 Building custom toplevel systems: ocamlmktop - 14.5.1 Options - 14.6 The native toplevel: ocamlnat (experimental) - Chapter 15 The runtime system (ocamlrun) - 15.1 Overview - 15.2 Options - 15.3 Dynamic loading of shared libraries - 15.4 Common errors - Chapter 16 Native-code compilation (ocamlopt) - 16.1 Overview of the compiler - 16.2 Options - 16.3 Common errors - 16.4 Running executables produced by ocamlopt - 16.5 Compatibility with the bytecode compiler - Chapter 17 Lexer and parser generators (ocamllex, ocamlyacc) - 17.1 Overview of ocamllex - 17.1.1 Options - 17.2 Syntax of lexer definitions - 17.2.1 Header and trailer - 17.2.2 Naming regular expressions - 17.2.3 Entry points - 17.2.4 Regular expressions - 17.2.5 Actions - 17.2.6 Variables in regular expressions - 17.2.7 Refill handlers - 17.2.8 Reserved identifiers - 17.3 Overview of ocamlyacc - 17.4 Syntax of grammar definitions - 17.4.1 Header and trailer - 17.4.2 Declarations - 17.4.3 Rules - 17.4.4 Error handling - 17.5 Options - 17.6 A complete example - 17.7 Common errors - Chapter 18 Dependency generator (ocamldep) - 18.1 Options - 18.2 A typical Makefile - Chapter 19 The documentation generator (ocamldoc) - 19.1 Usage - 19.1.1 Invocation - 19.1.2 Merging of module information - 19.1.3 Coding rules - 19.2 Syntax of documentation comments - 19.2.1 Placement of documentation comments - 19.2.2 The Stop special comment - 19.2.3 Syntax of documentation comments - 19.2.4 Text formatting - 19.2.5 Documentation tags (@-tags) - 19.3 Custom generators - 19.3.1 The generator modules - 19.3.2 Handling custom tags - 19.4 Adding command line options - 19.4.1 Compilation and usage - Chapter 20 The debugger (ocamldebug) - 20.1 Compiling for debugging - 20.2 Invocation - 20.2.1 Starting the debugger - 20.2.2 Initialization file - 20.2.3 Exiting the debugger - 20.3 Commands - 20.3.1 Getting help - 20.3.2 Accessing the debugger state - 20.4 Executing a program - 20.4.1 Events - 20.4.2 Starting the debugged program - 20.4.3 Running the program - 20.4.4 Time travel - 20.4.5 Killing the program - 20.5 Breakpoints - 20.6 The call stack - 20.7 Examining variable values - 20.8 Controlling the debugger - 20.8.1 Setting the program name and arguments - 20.8.2 How programs are loaded - 20.8.3 Search path for files - 20.8.4 Working directory - 20.8.5 Turning reverse execution on and off - 20.8.6 Behavior of the debugger with respect to fork - 20.8.7 Stopping execution when new code is loaded - 20.8.8 Communication between the debugger and the program - 20.8.9 Fine-tuning the debugger - 20.8.10 User-defined printers - 20.9 Miscellaneous commands - 20.10 Running the debugger under Emacs - Chapter 21 Profiling (ocamlprof) - 21.1 Compiling for profiling - 21.2 Profiling an execution - 21.3 Printing profiling information - 21.4 Time profiling - Chapter 22 Interfacing C with OCaml - 22.1 Overview and compilation information - 22.1.1 Declaring primitives - 22.1.2 Implementing primitives - 22.1.3 Statically linking C code with OCaml code - 22.1.4 Dynamically linking C code with OCaml code - 22.1.5 Choosing between static linking and dynamic linking - 22.1.6 Building standalone custom runtime systems - 22.2 The value type - 22.2.1 Integer values - 22.2.2 Blocks - 22.2.3 Pointers outside the heap - 22.3 Representation of OCaml data types - 22.3.1 Atomic types - 22.3.2 Tuples and records - 22.3.3 Arrays - 22.3.4 Concrete data types - 22.3.5 Objects - 22.3.6 Polymorphic variants - 22.4 Operations on values - 22.4.1 Kind tests - 22.4.2 Operations on integers - 22.4.3 Accessing blocks - 22.4.4 Allocating blocks - 22.4.5 Raising exceptions - 22.5 Living in harmony with the garbage collector - 22.5.1 Simple interface - 22.5.2 Low-level interface - 22.5.3 Pending actions and asynchronous exceptions - 22.6 A complete example - 22.7 Advanced topic: callbacks from C to OCaml - 22.7.1 Applying OCaml closures from C - 22.7.2 Obtaining or registering OCaml closures for use in C functions - 22.7.3 Registering OCaml exceptions for use in C functions - 22.7.4 Main program in C - 22.7.5 Embedding the OCaml code in the C code - 22.8 Advanced example with callbacks - 22.9 Advanced topic: custom blocks - 22.9.1 The struct custom_operations - 22.9.2 Allocating custom blocks - 22.9.3 Accessing custom blocks - 22.9.4 Writing custom serialization and deserialization functions - 22.9.5 Choosing identifiers - 22.9.6 Finalized blocks - 22.10 Advanced topic: Bigarrays and the OCaml-C interface - 22.10.1 Include file - 22.10.2 Accessing an OCaml bigarray from C or Fortran - 22.10.3 Wrapping a C or Fortran array as an OCaml Bigarray - 22.11 Advanced topic: cheaper C call - 22.11.1 Passing unboxed values - 22.11.2 Direct C call - 22.11.3 Example: calling C library functions without indirection - 22.12 Advanced topic: multithreading - 22.12.1 Registering threads created from C - 22.12.2 Parallel execution of long-running C code with systhreads - 22.13 Advanced topic: interfacing with Windows Unicode APIs - 22.14 Building mixed C/OCaml libraries: ocamlmklib - 22.15 Cautionary words: the internal runtime API - 22.15.1 Internal variables and CAML_INTERNALS - 22.15.2 OCaml version macros - Chapter 23 Optimisation with Flambda - 23.1 Overview - 23.2 Command-line flags - 23.2.1 Specification of optimisation parameters by round - 23.3 Inlining - 23.3.1 Classic inlining heuristic - 23.3.2 Overview of “Flambda” inlining heuristics - 23.3.3 Handling of specific language constructs - 23.3.4 Inlining reports - 23.3.5 Assessment of inlining benefit - 23.3.6 Control of speculation - 23.4 Specialisation - 23.4.1 Assessment of specialisation benefit - 23.5 Default settings of parameters - 23.5.1 Settings at -O2 optimisation level - 23.5.2 Settings at -O3 optimisation level - 23.6 Manual control of inlining and specialisation - 23.7 Simplification - 23.8 Other code motion transformations - 23.8.1 Lifting of constants - 23.8.2 Lifting of toplevel let bindings - 23.9 Unboxing transformations - 23.9.1 Unboxing of closure variables - 23.9.2 Unboxing of specialised arguments - 23.9.3 Unboxing of closures - 23.10 Removal of unused code and values - 23.10.1 Removal of redundant let expressions - 23.10.2 Removal of redundant program constructs - 23.10.3 Removal of unused arguments - 23.10.4 Removal of unused closure variables - 23.11 Other code transformations - 23.11.1 Transformation of non-escaping references into mutable variables - 23.11.2 Substitution of closure variables for specialised arguments - 23.12 Treatment of effects - 23.13 Compilation of statically-allocated modules - 23.14 Inhibition of optimisation - 23.15 Use of unsafe operations - 23.16 Glossary - Chapter 24 Fuzzing with afl-fuzz - 24.1 Overview - 24.2 Generating instrumentation - 24.2.1 Advanced options - 24.3 Example - Chapter 25 Runtime tracing with runtime events - 25.1 Overview - 25.2 Architecture - 25.2.1 Event sources - 25.2.2 Events transport - 25.3 Usage - 25.3.1 With OCaml APIs - 25.3.2 With tooling - 25.4 Custom events - 25.4.1 Overview - 25.4.2 Tracing custom events: an example - Chapter 26 The “Tail Modulo Constructor” program transformation - 26.1 Disambiguation - 26.2 Danger: getting out of tail-mod-cons - 26.3 Details on the transformation - 26.4 Current limitations - Chapter 27 Runtime detection of data races with ThreadSanitizer - 27.1 Overview and usage - 27.2 Performance implications - 27.3 False negatives and false positives - 27.4 Runtime options - 27.5 Guidelines for linking - 27.6 Changes in the delivery of signals - Part: IV The OCaml library - Chapter 28 The core library - 28.1 Built-in types and predefined exceptions - 28.2 Module Stdlib : The OCaml Standard library. - Chapter 29 The standard library - 29.1 Module Arg : Parsing of command line arguments. - 29.2 Module Array : Array operations. - 29.3 Module ArrayLabels : Array operations. - 29.4 Module Atomic : Atomic references. - 29.5 Module Bigarray : Large, multi-dimensional, numerical arrays. - 29.6 Module Bool : Boolean values. - 29.7 Module Buffer : Extensible buffers. - 29.8 Module Bytes : Byte sequence operations. - 29.9 Module BytesLabels : Byte sequence operations. - 29.10 Module Callback : Registering OCaml values with the C runtime. - 29.11 Module Char : Character operations. - 29.12 Module Complex : Complex numbers. - 29.13 Module Condition : Condition variables. - 29.14 Module Domain - 29.15 Module Digest : Message digest. - 29.16 Module Dynarray : Dynamic arrays. - 29.17 Module Effect - 29.18 Module Either : Either type. - 29.19 Module Ephemeron : Ephemerons and weak hash tables. - 29.20 Module Filename : Operations on file names. - 29.21 Module Float : Floating-point arithmetic. - 29.22 Module Format : Pretty-printing. - 29.23 Module Fun : Function manipulation. - 29.24 Module Gc : Memory management control and statistics; finalised values. - 29.25 Module Hashtbl : Hash tables and hash functions. - 29.26 Module In_channel : Input channels. - 29.27 Module Int : Integer values. - 29.28 Module Int32 : 32-bit integers. - 29.29 Module Int64 : 64-bit integers. - 29.30 Module Lazy : Deferred computations. - 29.31 Module Lexing : The run-time library for lexers generated by ocamllex. - 29.32 Module List : List operations. - 29.33 Module ListLabels : List operations. - 29.34 Module Map : Association tables over ordered types. - 29.35 Module Marshal : Marshaling of data structures. - 29.36 Module MoreLabels : Extra labeled libraries. - 29.37 Module Mutex : Locks for mutual exclusion. - 29.38 Module Nativeint : Processor-native integers. - 29.39 Module Oo : Operations on objects - 29.40 Module Option : Option values. - 29.41 Module Out_channel : Output channels. - 29.42 Module Parsing : The run-time library for parsers generated by ocamlyacc. - 29.43 Module Printexc : Facilities for printing exceptions and inspecting current call stack. - 29.44 Module Printf : Formatted output functions. - 29.45 Module Queue : First-in first-out queues. - 29.46 Module Random : Pseudo-random number generators (PRNG). - 29.47 Module Result : Result values. - 29.48 Module Scanf : Formatted input functions. - 29.49 Module Seq : Sequences. - 29.50 Module Set : Sets over ordered types. - 29.51 Module Semaphore : Semaphores - 29.52 Module Stack : Last-in first-out stacks. - 29.53 Module StdLabels : Standard labeled libraries. - 29.54 Module String : Strings. - 29.55 Module StringLabels : Strings. - 29.56 Module Sys : System interface. - 29.57 Module Type : Type introspection. - 29.58 Module Uchar : Unicode characters. - 29.59 Module Unit : Unit values. - 29.60 Module Weak : Arrays of weak pointers and hash sets of weak pointers. - 29.61 Ocaml_operators : Precedence level and associativity of operators - Chapter 30 The compiler front-end - 30.1 Module Ast_mapper : The interface of a -ppx rewriter - 30.2 Module Asttypes : Auxiliary AST types used by parsetree and typedtree. - 30.3 Module Location : Source code locations (ranges of positions), used in parsetree. - 30.4 Module Longident : Long identifiers, used in parsetree. - 30.5 Module Parse : Entry points in the parser - 30.6 Module Parsetree : Abstract syntax tree produced by parsing - 30.7 Module Pprintast : Pretty-printers for Parsetree[30.6] - Chapter 31 The unix library: Unix system calls - Chapter 32 The str library: regular expressions and string processing - 32.1 Module Str : Regular expressions and high-level string processing - Chapter 33 The runtime_events library - 33.1 Module Runtime_events : Runtime events - ring buffer-based runtime tracing - Chapter 34 The threads library - 34.1 Module Thread : Lightweight threads for Posix 1003.1c and Win32. - 34.2 Module Event : First-class synchronous communication. - Chapter 35 The dynlink library: dynamic loading and linking of object files - 35.1 Module Dynlink : Dynamic loading of .cmo, .cma and .cmxs files. - Chapter 36 Recently removed or moved libraries (Graphics, Bigarray, Num, LablTk) - 36.1 The Graphics Library - 36.2 The Bigarray Library - 36.3 The Num Library - 36.4 The Labltk Library and OCamlBrowser - Part: V Indexes - Chapter 37 Index to the library - Chapter 38 Index of keywords Foreword ******** This manual documents the release 5.2 of the OCaml system. It is organized as follows. - Part I, “An introduction to OCaml”, gives an overview of the language. - Part II, “The OCaml language”, is the reference description of the language. - Part III, “The OCaml tools”, documents the compilers, toplevel system, and programming utilities. - Part IV, “The OCaml library”, describes the modules provided in the standard library. Conventions *=*=*=*=*=* OCaml runs on several operating systems. The parts of this manual that are specific to one operating system are presented as shown below:  Unix: This is material specific to the Unix family of operating systems, including Linux and macOS.  Windows: This is material specific to Microsoft Windows (Vista, 7, 8, 10, 11). License *=*=*=* The OCaml system is copyright © 1996–2013 Institut National de Recherche en Informatique et en Automatique (INRIA). INRIA holds all ownership rights to the OCaml system. The OCaml system is open source and can be freely redistributed. See the file LICENSE in the distribution for licensing information. The OCaml documentation and user’s manual is copyright © 2013 Institut National de Recherche en Informatique et en Automatique (INRIA). Availability *=*=*=*=*=*= The complete OCaml distribution can be accessed via the ocaml.org website (5). This site contains a lot of additional information on OCaml. --------------------------------------- (5) https://ocaml.org/ Part: I ******* An introduction to OCaml ************************ Chapter 1  The core language ******************************** This part of the manual is a tutorial introduction to the OCaml language. A good familiarity with programming in a conventional languages (say, C or Java) is assumed, but no prior exposure to functional languages is required. The present chapter introduces the core language. Chapter 2 deals with the module system, chapter 3 with the object-oriented features, chapter 4 with labeled arguments, chapter 5 with polymorphic variants, chapter 6 with the limitations of polymorphism, and chapter 8 gives some advanced examples. 1.1 Basics *=*=*=*=*=*= For this overview of OCaml, we use the interactive system, which is started by running ocaml from the Unix shell or Windows command prompt. This tutorial is presented as the transcript of a session with the interactive system: lines starting with # represent user input; the system responses are printed below, without a leading #. Under the interactive system, the user types OCaml phrases terminated by ;; in response to the # prompt, and the system compiles them on the fly, executes them, and prints the outcome of evaluation. Phrases are either simple expressions, or let definitions of identifiers (either values or functions). << # 1 + 2 * 3;; - : int = 7 >> << # let pi = 4.0 *. atan 1.0;; val pi : float = 3.14159265358979312 >> << # let square x = x *. x;; val square : float -> float = >> << # square (sin pi) +. square (cos pi);; - : float = 1. >> The OCaml system computes both the value and the type for each phrase. Even function parameters need no explicit type declaration: the system infers their types from their usage in the function. Notice also that integers and floating-point numbers are distinct types, with distinct operators: + and * operate on integers, but +. and *. operate on floats. << # 1.0 * 2;; Error: This expression has type float but an expression was expected of type int >> Recursive functions are defined with the let rec binding: << # let rec fib n = if n < 2 then n else fib (n - 1) + fib (n - 2);; val fib : int -> int = >> << # fib 10;; - : int = 55 >> 1.2 Data types *=*=*=*=*=*=*=*= In addition to integers and floating-point numbers, OCaml offers the usual basic data types: - booleans << # (1 < 2) = false;; - : bool = false >> << # let one = if true then 1 else 2;; val one : int = 1 >> - characters << # 'a';; - : char = 'a' >> << # int_of_char '\n';; - : int = 10 >> - immutable character strings << # "Hello" ^ " " ^ "world";; - : string = "Hello world" >> << # {|This is a quoted string, here, neither \ nor " are special characters|};; - : string = "This is a quoted string, here, neither \\ nor \" are special characters" >> << # {|"\\"|}="\"\\\\\"";; - : bool = true >> << # {delimiter|the end of this|}quoted string is here|delimiter} = "the end of this|}quoted string is here";; - : bool = true >> Predefined data structures include tuples, arrays, and lists. There are also general mechanisms for defining your own data structures, such as records and variants, which will be covered in more detail later; for now, we concentrate on lists. Lists are either given in extension as a bracketed list of semicolon-separated elements, or built from the empty list [] (pronounce “nil”) by adding elements in front using the :: (“cons”) operator. << # let l = ["is"; "a"; "tale"; "told"; "etc."];; val l : string list = ["is"; "a"; "tale"; "told"; "etc."] >> << # "Life" :: l;; - : string list = ["Life"; "is"; "a"; "tale"; "told"; "etc."] >> As with all other OCaml data structures, lists do not need to be explicitly allocated and deallocated from memory: all memory management is entirely automatic in OCaml. Similarly, there is no explicit handling of pointers: the OCaml compiler silently introduces pointers where necessary. As with most OCaml data structures, inspecting and destructuring lists is performed by pattern-matching. List patterns have exactly the same form as list expressions, with identifiers representing unspecified parts of the list. As an example, here is insertion sort on a list: << # let rec sort lst = match lst with [] -> [] | head :: tail -> insert head (sort tail) and insert elt lst = match lst with [] -> [elt] | head :: tail -> if elt <= head then elt :: lst else head :: insert elt tail ;; val sort : 'a list -> 'a list = val insert : 'a -> 'a list -> 'a list = >> << # sort l;; - : string list = ["a"; "etc."; "is"; "tale"; "told"] >> The type inferred for sort, 'a list -> 'a list, means that sort can actually apply to lists of any type, and returns a list of the same type. The type 'a is a type variable, and stands for any given type. The reason why sort can apply to lists of any type is that the comparisons (=, <=, etc.) are polymorphic in OCaml: they operate between any two values of the same type. This makes sort itself polymorphic over all list types. << # sort [6; 2; 5; 3];; - : int list = [2; 3; 5; 6] >> << # sort [3.14; 2.718];; - : float list = [2.718; 3.14] >> The sort function above does not modify its input list: it builds and returns a new list containing the same elements as the input list, in ascending order. There is actually no way in OCaml to modify a list in-place once it is built: we say that lists are immutable data structures. Most OCaml data structures are immutable, but a few (most notably arrays) are mutable, meaning that they can be modified in-place at any time. The OCaml notation for the type of a function with multiple arguments is arg1_type -> arg2_type -> ... -> return_type. For example, the type inferred for insert, 'a -> 'a list -> 'a list, means that insert takes two arguments, an element of any type 'a and a list with elements of the same type 'a and returns a list of the same type. 1.3 Functions as values *=*=*=*=*=*=*=*=*=*=*=*=* OCaml is a functional language: functions in the full mathematical sense are supported and can be passed around freely just as any other piece of data. For instance, here is a deriv function that takes any float function as argument and returns an approximation of its derivative function: << # let deriv f dx = fun x -> (f (x +. dx) -. f x) /. dx;; val deriv : (float -> float) -> float -> float -> float = >> << # let sin' = deriv sin 1e-6;; val sin' : float -> float = >> << # sin' pi;; - : float = -1.00000000013961143 >> Even function composition is definable: << # let compose f g = fun x -> f (g x);; val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b = >> << # let cos2 = compose square cos;; val cos2 : float -> float = >> Functions that take other functions as arguments are called “functionals”, or “higher-order functions”. Functionals are especially useful to provide iterators or similar generic operations over a data structure. For instance, the standard OCaml library provides a List.map functional that applies a given function to each element of a list, and returns the list of the results: << # List.map (fun n -> n * 2 + 1) [0;1;2;3;4];; - : int list = [1; 3; 5; 7; 9] >> This functional, along with a number of other list and array functionals, is predefined because it is often useful, but there is nothing magic with it: it can easily be defined as follows. << # let rec map f l = match l with [] -> [] | hd :: tl -> f hd :: map f tl;; val map : ('a -> 'b) -> 'a list -> 'b list = >> 1.4 Records and variants *=*=*=*=*=*=*=*=*=*=*=*=*= User-defined data structures include records and variants. Both are defined with the type declaration. Here, we declare a record type to represent rational numbers. << # type ratio = {num: int; denom: int};; type ratio = { num : int; denom : int; } >> << # let add_ratio r1 r2 = {num = r1.num * r2.denom + r2.num * r1.denom; denom = r1.denom * r2.denom};; val add_ratio : ratio -> ratio -> ratio = >> << # add_ratio {num=1; denom=3} {num=2; denom=5};; - : ratio = {num = 11; denom = 15} >> Record fields can also be accessed through pattern-matching: << # let integer_part r = match r with {num=num; denom=denom} -> num / denom;; val integer_part : ratio -> int = >> Since there is only one case in this pattern matching, it is safe to expand directly the argument r in a record pattern: << # let integer_part {num=num; denom=denom} = num / denom;; val integer_part : ratio -> int = >> Unneeded fields can be omitted: << # let get_denom {denom=denom} = denom;; val get_denom : ratio -> int = >> Optionally, missing fields can be made explicit by ending the list of fields with a trailing wildcard _:: << # let get_num {num=num; _ } = num;; val get_num : ratio -> int = >> When both sides of the = sign are the same, it is possible to avoid repeating the field name by eliding the =field part: << # let integer_part {num; denom} = num / denom;; val integer_part : ratio -> int = >> This short notation for fields also works when constructing records: << # let ratio num denom = {num; denom};; val ratio : int -> int -> ratio = >> At last, it is possible to update few fields of a record at once: << # let integer_product integer ratio = { ratio with num = integer * ratio.num };; val integer_product : int -> ratio -> ratio = >> With this functional update notation, the record on the left-hand side of with is copied except for the fields on the right-hand side which are updated. The declaration of a variant type lists all possible forms for values of that type. Each case is identified by a name, called a constructor, which serves both for constructing values of the variant type and inspecting them by pattern-matching. Constructor names are capitalized to distinguish them from variable names (which must start with a lowercase letter). For instance, here is a variant type for doing mixed arithmetic (integers and floats): << # type number = Int of int | Float of float | Error;; type number = Int of int | Float of float | Error >> This declaration expresses that a value of type number is either an integer, a floating-point number, or the constant Error representing the result of an invalid operation (e.g. a division by zero). Enumerated types are a special case of variant types, where all alternatives are constants: << # type sign = Positive | Negative;; type sign = Positive | Negative >> << # let sign_int n = if n >= 0 then Positive else Negative;; val sign_int : int -> sign = >> To define arithmetic operations for the number type, we use pattern-matching on the two numbers involved: << # let add_num n1 n2 = match (n1, n2) with (Int i1, Int i2) -> (* Check for overflow of integer addition *) if sign_int i1 = sign_int i2 && sign_int (i1 + i2) <> sign_int i1 then Float(float i1 +. float i2) else Int(i1 + i2) | (Int i1, Float f2) -> Float(float i1 +. f2) | (Float f1, Int i2) -> Float(f1 +. float i2) | (Float f1, Float f2) -> Float(f1 +. f2) | (Error, _) -> Error | (_, Error) -> Error;; val add_num : number -> number -> number = >> << # add_num (Int 123) (Float 3.14159);; - : number = Float 126.14159 >> Another interesting example of variant type is the built-in 'a option type which represents either a value of type 'a or an absence of value: << # type 'a option = Some of 'a | None;; type 'a option = Some of 'a | None >> This type is particularly useful when defining function that can fail in common situations, for instance << # let safe_square_root x = if x >= 0. then Some(sqrt x) else None;; val safe_square_root : float -> float option = >> The most common usage of variant types is to describe recursive data structures. Consider for example the type of binary trees: << # type 'a btree = Empty | Node of 'a * 'a btree * 'a btree;; type 'a btree = Empty | Node of 'a * 'a btree * 'a btree >> This definition reads as follows: a binary tree containing values of type 'a (an arbitrary type) is either empty, or is a node containing one value of type 'a and two subtrees also containing values of type 'a, that is, two 'a btree. Operations on binary trees are naturally expressed as recursive functions following the same structure as the type definition itself. For instance, here are functions performing lookup and insertion in ordered binary trees (elements increase from left to right): << # let rec member x btree = match btree with Empty -> false | Node(y, left, right) -> if x = y then true else if x < y then member x left else member x right;; val member : 'a -> 'a btree -> bool = >> << # let rec insert x btree = match btree with Empty -> Node(x, Empty, Empty) | Node(y, left, right) -> if x <= y then Node(y, insert x left, right) else Node(y, left, insert x right);; val insert : 'a -> 'a btree -> 'a btree = >> 1.4.1 Record and variant disambiguation ========================================= ( This subsection can be skipped on the first reading ) Astute readers may have wondered what happens when two or more record fields or constructors share the same name << # type first_record = { x:int; y:int; z:int } type middle_record = { x:int; z:int } type last_record = { x:int };; >> << # type first_variant = A | B | C type last_variant = A;; >> The answer is that when confronted with multiple options, OCaml tries to use locally available information to disambiguate between the various fields and constructors. First, if the type of the record or variant is known, OCaml can pick unambiguously the corresponding field or constructor. For instance: << # let look_at_x_then_z (r:first_record) = let x = r.x in x + r.z;; val look_at_x_then_z : first_record -> int = >> << # let permute (x:first_variant) = match x with | A -> (B:first_variant) | B -> A | C -> C;; val permute : first_variant -> first_variant = >> << # type wrapped = First of first_record let f (First r) = r, r.x;; type wrapped = First of first_record val f : wrapped -> first_record * int = >> In the first example, (r:first_record) is an explicit annotation telling OCaml that the type of r is first_record. With this annotation, Ocaml knows that r.x refers to the x field of the first record type. Similarly, the type annotation in the second example makes it clear to OCaml that the constructors A, B and C come from the first variant type. Contrarily, in the last example, OCaml has inferred by itself that the type of r can only be first_record and there are no needs for explicit type annotations. Those explicit type annotations can in fact be used anywhere. Most of the time they are unnecessary, but they are useful to guide disambiguation, to debug unexpected type errors, or combined with some of the more advanced features of OCaml described in later chapters. Secondly, for records, OCaml can also deduce the right record type by looking at the whole set of fields used in a expression or pattern: << # let project_and_rotate {x; y; _} = { x= - y; y = x; z = 0} ;; val project_and_rotate : first_record -> first_record = >> Since the fields x and y can only appear simultaneously in the first record type, OCaml infers that the type of project_and_rotate is first_record -> first_record. In last resort, if there is not enough information to disambiguate between different fields or constructors, Ocaml picks the last defined type amongst all locally valid choices: << # let look_at_xz {x; z} = x;; val look_at_xz : middle_record -> int = >> Here, OCaml has inferred that the possible choices for the type of {x;z} are first_record and middle_record, since the type last_record has no field z. Ocaml then picks the type middle_record as the last defined type between the two possibilities. Beware that this last resort disambiguation is local: once Ocaml has chosen a disambiguation, it sticks to this choice, even if it leads to an ulterior type error: << # let look_at_x_then_y r = let x = r.x in (* Ocaml deduces [r: last_record] *) x + r.y;; Error: This expression has type last_record There is no field y within type last_record >> << # let is_a_or_b x = match x with | A -> true (* OCaml infers [x: last_variant] *) | B -> true;; Error: This variant pattern is expected to have type last_variant There is no constructor B within type last_variant >> Moreover, being the last defined type is a quite unstable position that may change surreptitiously after adding or moving around a type definition, or after opening a module (see chapter 2). Consequently, adding explicit type annotations to guide disambiguation is more robust than relying on the last defined type disambiguation. 1.5 Imperative features *=*=*=*=*=*=*=*=*=*=*=*=* Though all examples so far were written in purely applicative style, OCaml is also equipped with full imperative features. This includes the usual while and for loops, as well as mutable data structures such as arrays. Arrays are either created by listing semicolon-separated element values between [| and |] brackets, or allocated and initialized with the Array.make function, then filled up later by assignments. For instance, the function below sums two vectors (represented as float arrays) componentwise. << # let add_vect v1 v2 = let len = min (Array.length v1) (Array.length v2) in let res = Array.make len 0.0 in for i = 0 to len - 1 do res.(i) <- v1.(i) +. v2.(i) done; res;; val add_vect : float array -> float array -> float array = >> << # add_vect [| 1.0; 2.0 |] [| 3.0; 4.0 |];; - : float array = [|4.; 6.|] >> Record fields can also be modified by assignment, provided they are declared mutable in the definition of the record type: << # type mutable_point = { mutable x: float; mutable y: float };; type mutable_point = { mutable x : float; mutable y : float; } >> << # let translate p dx dy = p.x <- p.x +. dx; p.y <- p.y +. dy;; val translate : mutable_point -> float -> float -> unit = >> << # let mypoint = { x = 0.0; y = 0.0 };; val mypoint : mutable_point = {x = 0.; y = 0.} >> << # translate mypoint 1.0 2.0;; - : unit = () >> << # mypoint;; - : mutable_point = {x = 1.; y = 2.} >> OCaml has no built-in notion of variable – identifiers whose current value can be changed by assignment. (The let binding is not an assignment, it introduces a new identifier with a new scope.) However, the standard library provides references, which are mutable indirection cells, with operators ! to fetch the current contents of the reference and := to assign the contents. Variables can then be emulated by let-binding a reference. For instance, here is an in-place insertion sort over arrays: << # let insertion_sort a = for i = 1 to Array.length a - 1 do let val_i = a.(i) in let j = ref i in while !j > 0 && val_i < a.(!j - 1) do a.(!j) <- a.(!j - 1); j := !j - 1 done; a.(!j) <- val_i done;; val insertion_sort : 'a array -> unit = >> References are also useful to write functions that maintain a current state between two calls to the function. For instance, the following pseudo-random number generator keeps the last returned number in a reference: << # let current_rand = ref 0;; val current_rand : int ref = {contents = 0} >> << # let random () = current_rand := !current_rand * 25713 + 1345; !current_rand;; val random : unit -> int = >> Again, there is nothing magical with references: they are implemented as a single-field mutable record, as follows. << # type 'a ref = { mutable contents: 'a };; type 'a ref = { mutable contents : 'a; } >> << # let ( ! ) r = r.contents;; val ( ! ) : 'a ref -> 'a = >> << # let ( := ) r newval = r.contents <- newval;; val ( := ) : 'a ref -> 'a -> unit = >> In some special cases, you may need to store a polymorphic function in a data structure, keeping its polymorphism. Doing this requires user-provided type annotations, since polymorphism is only introduced automatically for global definitions. However, you can explicitly give polymorphic types to record fields. << # type idref = { mutable id: 'a. 'a -> 'a };; type idref = { mutable id : 'a. 'a -> 'a; } >> << # let r = {id = fun x -> x};; val r : idref = {id = } >> << # let g s = (s.id 1, s.id true);; val g : idref -> int * bool = >> << # r.id <- (fun x -> print_string "called id\n"; x);; - : unit = () >> << # g r;; called id called id - : int * bool = (1, true) >> 1.6 Exceptions *=*=*=*=*=*=*=*= OCaml provides exceptions for signalling and handling exceptional conditions. Exceptions can also be used as a general-purpose non-local control structure, although this should not be overused since it can make the code harder to understand. Exceptions are declared with the exception construct, and signalled with the raise operator. For instance, the function below for taking the head of a list uses an exception to signal the case where an empty list is given. << # exception Empty_list;; exception Empty_list >> << # let head l = match l with [] -> raise Empty_list | hd :: tl -> hd;; val head : 'a list -> 'a = >> << # head [1; 2];; - : int = 1 >> << # head [];; Exception: Empty_list. >> Exceptions are used throughout the standard library to signal cases where the library functions cannot complete normally. For instance, the List.assoc function, which returns the data associated with a given key in a list of (key, data) pairs, raises the predefined exception Not_found when the key does not appear in the list: << # List.assoc 1 [(0, "zero"); (1, "one")];; - : string = "one" >> << # List.assoc 2 [(0, "zero"); (1, "one")];; Exception: Not_found. >> Exceptions can be trapped with the try...with construct: << # let name_of_binary_digit digit = try List.assoc digit [0, "zero"; 1, "one"] with Not_found -> "not a binary digit";; val name_of_binary_digit : int -> string = >> << # name_of_binary_digit 0;; - : string = "zero" >> << # name_of_binary_digit (-1);; - : string = "not a binary digit" >> The with part does pattern matching on the exception value with the same syntax and behavior as match. Thus, several exceptions can be caught by one try...with construct: << # let rec first_named_value values names = try List.assoc (head values) names with | Empty_list -> "no named value" | Not_found -> first_named_value (List.tl values) names;; val first_named_value : 'a list -> ('a * string) list -> string = >> << # first_named_value [0; 10] [1, "one"; 10, "ten"];; - : string = "ten" >> Also, finalization can be performed by trapping all exceptions, performing the finalization, then re-raising the exception: << # let temporarily_set_reference ref newval funct = let oldval = !ref in try ref := newval; let res = funct () in ref := oldval; res with x -> ref := oldval; raise x;; val temporarily_set_reference : 'a ref -> 'a -> (unit -> 'b) -> 'b = >> An alternative to try...with is to catch the exception while pattern matching: << # let assoc_may_map f x l = match List.assoc x l with | exception Not_found -> None | y -> f y;; val assoc_may_map : ('a -> 'b option) -> 'c -> ('c * 'a) list -> 'b option = >> Note that this construction is only useful if the exception is raised between match...with. Exception patterns can be combined with ordinary patterns at the toplevel, << # let flat_assoc_opt x l = match List.assoc x l with | None | exception Not_found -> None | Some _ as v -> v;; val flat_assoc_opt : 'a -> ('a * 'b option) list -> 'b option = >> but they cannot be nested inside other patterns. For instance, the pattern Some (exception A) is invalid. When exceptions are used as a control structure, it can be useful to make them as local as possible by using a locally defined exception. For instance, with << # let fixpoint f x = let exception Done in let x = ref x in try while true do let y = f !x in if !x = y then raise Done else x := y done with Done -> !x;; val fixpoint : ('a -> 'a) -> 'a -> 'a = >> the function f cannot raise a Done exception, which removes an entire class of misbehaving functions. 1.7 Lazy expressions *=*=*=*=*=*=*=*=*=*=*= OCaml allows us to defer some computation until later when we need the result of that computation. We use lazy (expr) to delay the evaluation of some expression expr. For example, we can defer the computation of 1+1 until we need the result of that expression, 2. Let us see how we initialize a lazy expression. << # let lazy_two = lazy (print_endline "lazy_two evaluation"; 1 + 1);; val lazy_two : int lazy_t = >> We added print_endline "lazy_two evaluation" to see when the lazy expression is being evaluated. The value of lazy_two is displayed as , which means the expression has not been evaluated yet, and its final value is unknown. Note that lazy_two has type int lazy_t. However, the type 'a lazy_t is an internal type name, so the type 'a Lazy.t should be preferred when possible. When we finally need the result of a lazy expression, we can call Lazy.force on that expression to force its evaluation. The function force comes from standard-library module Lazy. << # Lazy.force lazy_two;; lazy_two evaluation - : int = 2 >> Notice that our function call above prints “lazy_two evaluation” and then returns the plain value of the computation. Now if we look at the value of lazy_two, we see that it is not displayed as anymore but as lazy 2. << # lazy_two;; - : int lazy_t = lazy 2 >> This is because Lazy.force memoizes the result of the forced expression. In other words, every subsequent call of Lazy.force on that expression returns the result of the first computation without recomputing the lazy expression. Let us force lazy_two once again. << # Lazy.force lazy_two;; - : int = 2 >> The expression is not evaluated this time; notice that “lazy_two evaluation” is not printed. The result of the initial computation is simply returned. Lazy patterns provide another way to force a lazy expression. << # let lazy_l = lazy ([1; 2] @ [3; 4]);; val lazy_l : int list lazy_t = >> << # let lazy l = lazy_l;; val l : int list = [1; 2; 3; 4] >> We can also use lazy patterns in pattern matching. << # let maybe_eval lazy_guard lazy_expr = match lazy_guard, lazy_expr with | lazy false, _ -> "matches if (Lazy.force lazy_guard = false); lazy_expr not forced" | lazy true, lazy _ -> "matches if (Lazy.force lazy_guard = true); lazy_expr forced";; val maybe_eval : bool lazy_t -> 'a lazy_t -> string = >> The lazy expression lazy_expr is forced only if the lazy_guard value yields true once computed. Indeed, a simple wildcard pattern (not lazy) never forces the lazy expression’s evaluation. However, a pattern with keyword lazy, even if it is wildcard, always forces the evaluation of the deferred computation. 1.8 Symbolic processing of expressions *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= We finish this introduction with a more complete example representative of the use of OCaml for symbolic processing: formal manipulations of arithmetic expressions containing variables. The following variant type describes the expressions we shall manipulate: << # type expression = Const of float | Var of string | Sum of expression * expression (* e1 + e2 *) | Diff of expression * expression (* e1 - e2 *) | Prod of expression * expression (* e1 * e2 *) | Quot of expression * expression (* e1 / e2 *) ;; type expression = Const of float | Var of string | Sum of expression * expression | Diff of expression * expression | Prod of expression * expression | Quot of expression * expression >> We first define a function to evaluate an expression given an environment that maps variable names to their values. For simplicity, the environment is represented as an association list. << # exception Unbound_variable of string;; exception Unbound_variable of string >> << # let rec eval env exp = match exp with Const c -> c | Var v -> (try List.assoc v env with Not_found -> raise (Unbound_variable v)) | Sum(f, g) -> eval env f +. eval env g | Diff(f, g) -> eval env f -. eval env g | Prod(f, g) -> eval env f *. eval env g | Quot(f, g) -> eval env f /. eval env g;; val eval : (string * float) list -> expression -> float = >> << # eval [("x", 1.0); ("y", 3.14)] (Prod(Sum(Var "x", Const 2.0), Var "y"));; - : float = 9.42 >> Now for a real symbolic processing, we define the derivative of an expression with respect to a variable dv: << # let rec deriv exp dv = match exp with Const c -> Const 0.0 | Var v -> if v = dv then Const 1.0 else Const 0.0 | Sum(f, g) -> Sum(deriv f dv, deriv g dv) | Diff(f, g) -> Diff(deriv f dv, deriv g dv) | Prod(f, g) -> Sum(Prod(f, deriv g dv), Prod(deriv f dv, g)) | Quot(f, g) -> Quot(Diff(Prod(deriv f dv, g), Prod(f, deriv g dv)), Prod(g, g)) ;; val deriv : expression -> string -> expression = >> << # deriv (Quot(Const 1.0, Var "x")) "x";; - : expression = Quot (Diff (Prod (Const 0., Var "x"), Prod (Const 1., Const 1.)), Prod (Var "x", Var "x")) >> 1.9 Pretty-printing *=*=*=*=*=*=*=*=*=*=* As shown in the examples above, the internal representation (also called abstract syntax) of expressions quickly becomes hard to read and write as the expressions get larger. We need a printer and a parser to go back and forth between the abstract syntax and the concrete syntax, which in the case of expressions is the familiar algebraic notation (e.g. 2*x+1). For the printing function, we take into account the usual precedence rules (i.e. * binds tighter than +) to avoid printing unnecessary parentheses. To this end, we maintain the current operator precedence and print parentheses around an operator only if its precedence is less than the current precedence. << # let print_expr exp = (* Local function definitions *) let open_paren prec op_prec = if prec > op_prec then print_string "(" in let close_paren prec op_prec = if prec > op_prec then print_string ")" in let rec print prec exp = (* prec is the current precedence *) match exp with Const c -> print_float c | Var v -> print_string v | Sum(f, g) -> open_paren prec 0; print 0 f; print_string " + "; print 0 g; close_paren prec 0 | Diff(f, g) -> open_paren prec 0; print 0 f; print_string " - "; print 1 g; close_paren prec 0 | Prod(f, g) -> open_paren prec 2; print 2 f; print_string " * "; print 2 g; close_paren prec 2 | Quot(f, g) -> open_paren prec 2; print 2 f; print_string " / "; print 3 g; close_paren prec 2 in print 0 exp;; val print_expr : expression -> unit = >> << # let e = Sum(Prod(Const 2.0, Var "x"), Const 1.0);; val e : expression = Sum (Prod (Const 2., Var "x"), Const 1.) >> << # print_expr e; print_newline ();; 2. * x + 1. - : unit = () >> << # print_expr (deriv e "x"); print_newline ();; 2. * 1. + 0. * x + 0. - : unit = () >> 1.10 Printf formats *=*=*=*=*=*=*=*=*=*=* There is a printf function in the Printf module (see chapter 2) that allows you to make formatted output more concisely. It follows the behavior of the printf function from the C standard library. The printf function takes a format string that describes the desired output as a text interspersed with specifiers (for instance %d, %f). Next, the specifiers are substituted by the following arguments in their order of apparition in the format string: << # Printf.printf "%i + %i is an integer value, %F * %F is a float, %S\n" 3 2 4.5 1. "this is a string";; 3 + 2 is an integer value, 4.5 * 1. is a float, "this is a string" - : unit = () >> The OCaml type system checks that the type of the arguments and the specifiers are compatible. If you pass it an argument of a type that does not correspond to the format specifier, the compiler will display an error message: << # Printf.printf "Float value: %F" 42;; Error: This expression has type int but an expression was expected of type float Hint: Did you mean 42.? >> The fprintf function is like printf except that it takes an output channel as the first argument. The %a specifier can be useful to define custom printers (for custom types). For instance, we can create a printing template that converts an integer argument to signed decimal: << # let pp_int ppf n = Printf.fprintf ppf "%d" n;; val pp_int : out_channel -> int -> unit = >> << # Printf.printf "Outputting an integer using a custom printer: %a " pp_int 42;; Outputting an integer using a custom printer: 42 - : unit = () >> The advantage of those printers based on the %a specifier is that they can be composed together to create more complex printers step by step. We can define a combinator that can turn a printer for 'a type into a printer for 'a optional: << # let pp_option printer ppf = function | None -> Printf.fprintf ppf "None" | Some v -> Printf.fprintf ppf "Some(%a)" printer v;; val pp_option : (out_channel -> 'a -> unit) -> out_channel -> 'a option -> unit = >> << # Printf.fprintf stdout "The current setting is %a. \nThere is only %a\n" (pp_option pp_int) (Some 3) (pp_option pp_int) None ;; The current setting is Some(3). There is only None - : unit = () >> If the value of its argument its None, the printer returned by pp_option printer prints None otherwise it uses the provided printer to print Some . Here is how to rewrite the pretty-printer using fprintf: << # let pp_expr ppf expr = let open_paren prec op_prec output = if prec > op_prec then Printf.fprintf output "%s" "(" in let close_paren prec op_prec output = if prec > op_prec then Printf.fprintf output "%s" ")" in let rec print prec ppf expr = match expr with | Const c -> Printf.fprintf ppf "%F" c | Var v -> Printf.fprintf ppf "%s" v | Sum(f, g) -> open_paren prec 0 ppf; Printf.fprintf ppf "%a + %a" (print 0) f (print 0) g; close_paren prec 0 ppf | Diff(f, g) -> open_paren prec 0 ppf; Printf.fprintf ppf "%a - %a" (print 0) f (print 1) g; close_paren prec 0 ppf | Prod(f, g) -> open_paren prec 2 ppf; Printf.fprintf ppf "%a * %a" (print 2) f (print 2) g; close_paren prec 2 ppf | Quot(f, g) -> open_paren prec 2 ppf; Printf.fprintf ppf "%a / %a" (print 2) f (print 3) g; close_paren prec 2 ppf in print 0 ppf expr;; val pp_expr : out_channel -> expression -> unit = >> << # pp_expr stdout e; print_newline ();; 2. * x + 1. - : unit = () >> << # pp_expr stdout (deriv e "x"); print_newline ();; 2. * 1. + 0. * x + 0. - : unit = () >> Due to the way that format strings are built, storing a format string requires an explicit type annotation: << # let str : _ format = "%i is an integer value, %F is a float, %S\n";; >> << # Printf.printf str 3 4.5 "string value";; 3 is an integer value, 4.5 is a float, "string value" - : unit = () >> 1.11 Standalone OCaml programs *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= All examples given so far were executed under the interactive system. OCaml code can also be compiled separately and executed non-interactively using the batch compilers ocamlc and ocamlopt. The source code must be put in a file with extension .ml. It consists of a sequence of phrases, which will be evaluated at runtime in their order of appearance in the source file. Unlike in interactive mode, types and values are not printed automatically; the program must call printing functions explicitly to produce some output. The ;; used in the interactive examples is not required in source files created for use with OCaml compilers, but can be helpful to mark the end of a top-level expression unambiguously even when there are syntax errors. Here is a sample standalone program to print the greatest common divisor (gcd) of two numbers: <<(* File gcd.ml *) let rec gcd a b = if b = 0 then a else gcd b (a mod b);; let main () = let a = int_of_string Sys.argv.(1) in let b = int_of_string Sys.argv.(2) in Printf.printf "%d\n" (gcd a b); exit 0;; main ();; >> Sys.argv is an array of strings containing the command-line parameters. Sys.argv.(1) is thus the first command-line parameter. The program above is compiled and executed with the following shell commands: <<$ ocamlc -o gcd gcd.ml $ ./gcd 6 9 3 $ ./gcd 7 11 1 >> More complex standalone OCaml programs are typically composed of multiple source files, and can link with precompiled libraries. Chapters 13 and 16 explain how to use the batch compilers ocamlc and ocamlopt. Recompilation of multi-file OCaml projects can be automated using third-party build systems, such as dune (1). --------------------------------------- (1) https://github.com/ocaml/dune Chapter 2  The module system ******************************** This chapter introduces the module system of OCaml. 2.1 Structures *=*=*=*=*=*=*=*= A primary motivation for modules is to package together related definitions (such as the definitions of a data type and associated operations over that type) and enforce a consistent naming scheme for these definitions. This avoids running out of names or accidentally confusing names. Such a package is called a structure and is introduced by the struct...end construct, which contains an arbitrary sequence of definitions. The structure is usually given a name with the module binding. For instance, here is a structure packaging together a type of FIFO queues and their operations: << # module Fifo = struct type 'a queue = { front: 'a list; rear: 'a list } let make front rear = match front with | [] -> { front = List.rev rear; rear = [] } | _ -> { front; rear } let empty = { front = []; rear = [] } let is_empty = function { front = []; _ } -> true | _ -> false let add x q = make q.front (x :: q.rear) exception Empty let top = function | { front = []; _ } -> raise Empty | { front = x :: _; _ } -> x let pop = function | { front = []; _ } -> raise Empty | { front = _ :: f; rear = r } -> make f r end;; module Fifo : sig type 'a queue = { front : 'a list; rear : 'a list; } val make : 'a list -> 'a list -> 'a queue val empty : 'a queue val is_empty : 'a queue -> bool val add : 'a -> 'a queue -> 'a queue exception Empty val top : 'a queue -> 'a val pop : 'a queue -> 'a queue end >> Outside the structure, its components can be referred to using the “dot notation”, that is, identifiers qualified by a structure name. For instance, Fifo.add is the function add defined inside the structure Fifo and Fifo.queue is the type queue defined in Fifo. << # Fifo.add "hello" Fifo.empty;; - : string Fifo.queue = {Fifo.front = ["hello"]; rear = []} >> Another possibility is to open the module, which brings all identifiers defined inside the module into the scope of the current structure. << # open Fifo;; >> << # add "hello" empty;; - : string Fifo.queue = {front = ["hello"]; rear = []} >> Opening a module enables lighter access to its components, at the cost of making it harder to identify in which module an identifier has been defined. In particular, opened modules can shadow identifiers present in the current scope, potentially leading to confusing errors: << # let empty = [] open Fifo;; val empty : 'a list = [] >> << # let x = 1 :: empty ;; Error: This expression has type 'a Fifo.queue but an expression was expected of type int list >> A partial solution to this conundrum is to open modules locally, making the components of the module available only in the concerned expression. This can also make the code both easier to read (since the open statement is closer to where it is used) and easier to refactor (since the code fragment is more self-contained). Two constructions are available for this purpose: << # let open Fifo in add "hello" empty;; - : string Fifo.queue = {front = ["hello"]; rear = []} >> and << # Fifo.(add "hello" empty);; - : string Fifo.queue = {front = ["hello"]; rear = []} >> In the second form, when the body of a local open is itself delimited by parentheses, braces or bracket, the parentheses of the local open can be omitted. For instance, << # Fifo.[empty] = Fifo.([empty]);; - : bool = true >> << # Fifo.[|empty|] = Fifo.([|empty|]);; - : bool = true >> << # Fifo.{ contents = empty } = Fifo.({ contents = empty });; - : bool = true >> This second form also works for patterns: << # let at_most_one_element x = match x with | Fifo.{ front = ([] | [_]); rear = [] } -> true | _ -> false ;; val at_most_one_element : 'a Fifo.queue -> bool = >> It is also possible to copy the components of a module inside another module by using an include statement. This can be particularly useful to extend existing modules. As an illustration, we could add functions that return an optional value rather than an exception when the queue is empty. << # module FifoOpt = struct include Fifo let top_opt q = if is_empty q then None else Some(top q) let pop_opt q = if is_empty q then None else Some(pop q) end;; module FifoOpt : sig type 'a queue = 'a Fifo.queue = { front : 'a list; rear : 'a list; } val make : 'a list -> 'a list -> 'a queue val empty : 'a queue val is_empty : 'a queue -> bool val add : 'a -> 'a queue -> 'a queue exception Empty val top : 'a queue -> 'a val pop : 'a queue -> 'a queue val top_opt : 'a queue -> 'a option val pop_opt : 'a queue -> 'a queue option end >> 2.2 Signatures *=*=*=*=*=*=*=*= Signatures are interfaces for structures. A signature specifies which components of a structure are accessible from the outside, and with which type. It can be used to hide some components of a structure (e.g. local function definitions) or export some components with a restricted type. For instance, the signature below specifies the queue operations empty, add, top and pop, but not the auxiliary function make. Similarly, it makes the queue type abstract (by not providing its actual representation as a concrete type). This ensures that users of the Fifo module cannot violate data structure invariants that operations rely on, such as “if the front list is empty, the rear list must also be empty”. << # module type FIFO = sig type 'a queue (* now an abstract type *) val empty : 'a queue val add : 'a -> 'a queue -> 'a queue val top : 'a queue -> 'a val pop : 'a queue -> 'a queue exception Empty end;; module type FIFO = sig type 'a queue val empty : 'a queue val add : 'a -> 'a queue -> 'a queue val top : 'a queue -> 'a val pop : 'a queue -> 'a queue exception Empty end >> Restricting the Fifo structure to this signature results in another view of the Fifo structure where the make function is not accessible and the actual representation of queues is hidden: << # module AbstractQueue = (Fifo : FIFO);; module AbstractQueue : FIFO >> << # AbstractQueue.make [1] [2;3] ;; Error: Unbound value AbstractQueue.make >> << # AbstractQueue.add "hello" AbstractQueue.empty;; - : string AbstractQueue.queue = >> The restriction can also be performed during the definition of the structure, as in <> An alternate syntax is provided for the above: <> Like for modules, it is possible to include a signature to copy its components inside the current signature. For instance, we can extend the FIFO signature with the top_opt and pop_opt functions: << # module type FIFO_WITH_OPT = sig include FIFO val top_opt: 'a queue -> 'a option val pop_opt: 'a queue -> 'a queue option end;; module type FIFO_WITH_OPT = sig type 'a queue val empty : 'a queue val add : 'a -> 'a queue -> 'a queue val top : 'a queue -> 'a val pop : 'a queue -> 'a queue exception Empty val top_opt : 'a queue -> 'a option val pop_opt : 'a queue -> 'a queue option end >> 2.3 Functors *=*=*=*=*=*=*= Functors are “functions” from modules to modules. Functors let you create parameterized modules and then provide other modules as parameter(s) to get a specific implementation. For instance, a Set module implementing sets as sorted lists could be parameterized to work with any module that provides an element type and a comparison function compare (such as OrderedString): << # type comparison = Less | Equal | Greater;; type comparison = Less | Equal | Greater >> << # module type ORDERED_TYPE = sig type t val compare: t -> t -> comparison end;; module type ORDERED_TYPE = sig type t val compare : t -> t -> comparison end >> << # module Set = functor (Elt: ORDERED_TYPE) -> struct type element = Elt.t type set = element list let empty = [] let rec add x s = match s with [] -> [x] | hd::tl -> match Elt.compare x hd with Equal -> s (* x is already in s *) | Less -> x :: s (* x is smaller than all elements of s *) | Greater -> hd :: add x tl let rec member x s = match s with [] -> false | hd::tl -> match Elt.compare x hd with Equal -> true (* x belongs to s *) | Less -> false (* x is smaller than all elements of s *) | Greater -> member x tl end;; module Set : functor (Elt : ORDERED_TYPE) -> sig type element = Elt.t type set = element list val empty : 'a list val add : Elt.t -> Elt.t list -> Elt.t list val member : Elt.t -> Elt.t list -> bool end >> By applying the Set functor to a structure implementing an ordered type, we obtain set operations for this type: << # module OrderedString = struct type t = string let compare x y = if x = y then Equal else if x < y then Less else Grea ter end;; module OrderedString : sig type t = string val compare : 'a -> 'a -> comparison end >> << # module StringSet = Set(OrderedString);; module StringSet : sig type element = OrderedString.t type set = element list val empty : 'a list val add : OrderedString.t -> OrderedString.t list -> OrderedString.t list val member : OrderedString.t -> OrderedString.t list -> bool end >> << # StringSet.member "bar" (StringSet.add "foo" StringSet.empty);; - : bool = false >> 2.4 Functors and type abstraction *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* As in the Fifo example, it would be good style to hide the actual implementation of the type set, so that users of the structure will not rely on sets being lists, and we can switch later to another, more efficient representation of sets without breaking their code. This can be achieved by restricting Set by a suitable functor signature: << # module type SETFUNCTOR = functor (Elt: ORDERED_TYPE) -> sig type element = Elt.t (* concrete *) type set (* abstract *) val empty : set val add : element -> set -> set val member : element -> set -> bool end;; module type SETFUNCTOR = functor (Elt : ORDERED_TYPE) -> sig type element = Elt.t type set val empty : set val add : element -> set -> set val member : element -> set -> bool end >> << # module AbstractSet = (Set : SETFUNCTOR);; module AbstractSet : SETFUNCTOR >> << # module AbstractStringSet = AbstractSet(OrderedString);; module AbstractStringSet : sig type element = OrderedString.t type set = AbstractSet(OrderedString).set val empty : set val add : element -> set -> set val member : element -> set -> bool end >> << # AbstractStringSet.add "gee" AbstractStringSet.empty;; - : AbstractStringSet.set = >> In an attempt to write the type constraint above more elegantly, one may wish to name the signature of the structure returned by the functor, then use that signature in the constraint: << # module type SET = sig type element type set val empty : set val add : element -> set -> set val member : element -> set -> bool end;; module type SET = sig type element type set val empty : set val add : element -> set -> set val member : element -> set -> bool end >> << # module WrongSet = (Set : functor(Elt: ORDERED_TYPE) -> SET);; module WrongSet : functor (Elt : ORDERED_TYPE) -> SET >> << # module WrongStringSet = WrongSet(OrderedString);; module WrongStringSet : sig type element = WrongSet(OrderedString).element type set = WrongSet(OrderedString).set val empty : set val add : element -> set -> set val member : element -> set -> bool end >> << # WrongStringSet.add "gee" WrongStringSet.empty ;; Error: This expression has type string but an expression was expected of type WrongStringSet.element = WrongSet(OrderedString).element >> The problem here is that SET specifies the type element abstractly, so that the type equality between element in the result of the functor and t in its argument is forgotten. Consequently, WrongStringSet.element is not the same type as string, and the operations of WrongStringSet cannot be applied to strings. As demonstrated above, it is important that the type element in the signature SET be declared equal to Elt.t; unfortunately, this is impossible above since SET is defined in a context where Elt does not exist. To overcome this difficulty, OCaml provides a with type construct over signatures that allows enriching a signature with extra type equalities: << # module AbstractSet2 = (Set : functor(Elt: ORDERED_TYPE) -> (SET with type element = Elt.t));; module AbstractSet2 : functor (Elt : ORDERED_TYPE) -> sig type element = Elt.t type set val empty : set val add : element -> set -> set val member : element -> set -> bool end >> As in the case of simple structures, an alternate syntax is provided for defining functors and restricting their result: <> Abstracting a type component in a functor result is a powerful technique that provides a high degree of type safety, as we now illustrate. Consider an ordering over character strings that is different from the standard ordering implemented in the OrderedString structure. For instance, we compare strings without distinguishing upper and lower case. << # module NoCaseString = struct type t = string let compare s1 s2 = OrderedString.compare (String.lowercase_ascii s1) (String.lowercase_a scii s2) end;; module NoCaseString : sig type t = string val compare : string -> string -> comparison end >> << # module NoCaseStringSet = AbstractSet(NoCaseString);; module NoCaseStringSet : sig type element = NoCaseString.t type set = AbstractSet(NoCaseString).set val empty : set val add : element -> set -> set val member : element -> set -> bool end >> << # NoCaseStringSet.add "FOO" AbstractStringSet.empty ;; Error: This expression has type AbstractStringSet.set = AbstractSet(OrderedString).set but an expression was expected of type NoCaseStringSet.set = AbstractSet(NoCaseString).set >> Note that the two types AbstractStringSet.set and NoCaseStringSet.set are not compatible, and values of these two types do not match. This is the correct behavior: even though both set types contain elements of the same type (strings), they are built upon different orderings of that type, and different invariants need to be maintained by the operations (being strictly increasing for the standard ordering and for the case-insensitive ordering). Applying operations from AbstractStringSet to values of type NoCaseStringSet.set could give incorrect results, or build lists that violate the invariants of NoCaseStringSet. 2.5 Modules and separate compilation *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= All examples of modules so far have been given in the context of the interactive system. However, modules are most useful for large, batch-compiled programs. For these programs, it is a practical necessity to split the source into several files, called compilation units, that can be compiled separately, thus minimizing recompilation after changes. In OCaml, compilation units are special cases of structures and signatures, and the relationship between the units can be explained easily in terms of the module system. A compilation unit A comprises two files: - the implementation file A.ml, which contains a sequence of definitions, analogous to the inside of a struct...end construct; - the interface file A.mli, which contains a sequence of specifications, analogous to the inside of a sig...end construct. These two files together define a structure named A as if the following definition was entered at top-level: << module A: sig (* contents of file A.mli *) end = struct (* contents of file A.ml *) end;; >> The files that define the compilation units can be compiled separately using the ocamlc -c command (the -c option means “compile only, do not try to link”); this produces compiled interface files (with extension .cmi) and compiled object code files (with extension .cmo). When all units have been compiled, their .cmo files are linked together using the ocamlc command. For instance, the following commands compile and link a program composed of two compilation units Aux and Main: <<$ ocamlc -c Aux.mli # produces aux.cmi $ ocamlc -c Aux.ml # produces aux.cmo $ ocamlc -c Main.mli # produces main.cmi $ ocamlc -c Main.ml # produces main.cmo $ ocamlc -o theprogram Aux.cmo Main.cmo >> The program behaves exactly as if the following phrases were entered at top-level: << module Aux: sig (* contents of Aux.mli *) end = struct (* contents of Aux.ml *) end;; module Main: sig (* contents of Main.mli *) end = struct (* contents of Main.ml *) end;; >> In particular, Main can refer to Aux: the definitions and declarations contained in Main.ml and Main.mli can refer to definition in Aux.ml, using the Aux.ident notation, provided these definitions are exported in Aux.mli. The order in which the .cmo files are given to ocamlc during the linking phase determines the order in which the module definitions occur. Hence, in the example above, Aux appears first and Main can refer to it, but Aux cannot refer to Main. Note that only top-level structures can be mapped to separately-compiled files, but neither functors nor module types. However, all module-class objects can appear as components of a structure, so the solution is to put the functor or module type inside a structure, which can then be mapped to a file. Chapter 3  Objects in OCaml ******************************* (Chapter written by Jérôme Vouillon, Didier Rémy and Jacques Garrigue) This chapter gives an overview of the object-oriented features of OCaml. Note that the relationship between object, class and type in OCaml is different than in mainstream object-oriented languages such as Java and C++, so you shouldn’t assume that similar keywords mean the same thing. Object-oriented features are used much less frequently in OCaml than in those languages. OCaml has alternatives that are often more appropriate, such as modules and functors. Indeed, many OCaml programs do not use objects at all. 3.1 Classes and objects *=*=*=*=*=*=*=*=*=*=*=*=* The class point below defines one instance variable x and two methods get_x and move. The initial value of the instance variable is 0. The variable x is declared mutable, so the method move can change its value. << # class point = object val mutable x = 0 method get_x = x method move d = x <- x + d end;; class point : object val mutable x : int method get_x : int method move : int -> unit end >> We now create a new point p, instance of the point class. << # let p = new point;; val p : point = >> Note that the type of p is point. This is an abbreviation automatically defined by the class definition above. It stands for the object type unit>, listing the methods of class point along with their types. We now invoke some methods of p: << # p#get_x;; - : int = 0 >> << # p#move 3;; - : unit = () >> << # p#get_x;; - : int = 3 >> The evaluation of the body of a class only takes place at object creation time. Therefore, in the following example, the instance variable x is initialized to different values for two different objects. << # let x0 = ref 0;; val x0 : int ref = {contents = 0} >> << # class point = object val mutable x = incr x0; !x0 method get_x = x method move d = x <- x + d end;; class point : object val mutable x : int method get_x : int method move : int -> unit end >> << # new point#get_x;; - : int = 1 >> << # new point#get_x;; - : int = 2 >> The class point can also be abstracted over the initial values of the x coordinate. << # class point = fun x_init -> object val mutable x = x_init method get_x = x method move d = x <- x + d end;; class point : int -> object val mutable x : int method get_x : int method move : int -> unit end >> Like in function definitions, the definition above can be abbreviated as: << # class point x_init = object val mutable x = x_init method get_x = x method move d = x <- x + d end;; class point : int -> object val mutable x : int method get_x : int method move : int -> unit end >> An instance of the class point is now a function that expects an initial parameter to create a point object: << # new point;; - : int -> point = >> << # let p = new point 7;; val p : point = >> The parameter x_init is, of course, visible in the whole body of the definition, including methods. For instance, the method get_offset in the class below returns the position of the object relative to its initial position. << # class point x_init = object val mutable x = x_init method get_x = x method get_offset = x - x_init method move d = x <- x + d end;; class point : int -> object val mutable x : int method get_offset : int method get_x : int method move : int -> unit end >> Expressions can be evaluated and bound before defining the object body of the class. This is useful to enforce invariants. For instance, points can be automatically adjusted to the nearest point on a grid, as follows: << # class adjusted_point x_init = let origin = (x_init / 10) * 10 in object val mutable x = origin method get_x = x method get_offset = x - origin method move d = x <- x + d end;; class adjusted_point : int -> object val mutable x : int method get_offset : int method get_x : int method move : int -> unit end >> (One could also raise an exception if the x_init coordinate is not on the grid.) In fact, the same effect could be obtained here by calling the definition of class point with the value of the origin. << # class adjusted_point x_init = point ((x_init / 10) * 10);; class adjusted_point : int -> point >> An alternate solution would have been to define the adjustment in a special allocation function: << # let new_adjusted_point x_init = new point ((x_init / 10) * 10);; val new_adjusted_point : int -> point = >> However, the former pattern is generally more appropriate, since the code for adjustment is part of the definition of the class and will be inherited. This ability provides class constructors as can be found in other languages. Several constructors can be defined this way to build objects of the same class but with different initialization patterns; an alternative is to use initializers, as described below in section 3.4. 3.2 Immediate objects *=*=*=*=*=*=*=*=*=*=*=* There is another, more direct way to create an object: create it without going through a class. The syntax is exactly the same as for class expressions, but the result is a single object rather than a class. All the constructs described in the rest of this section also apply to immediate objects. << # let p = object val mutable x = 0 method get_x = x method move d = x <- x + d end;; val p : < get_x : int; move : int -> unit > = >> << # p#get_x;; - : int = 0 >> << # p#move 3;; - : unit = () >> << # p#get_x;; - : int = 3 >> Unlike classes, which cannot be defined inside an expression, immediate objects can appear anywhere, using variables from their environment. << # let minmax x y = if x < y then object method min = x method max = y end else object method min = y method max = x end;; val minmax : 'a -> 'a -> < max : 'a; min : 'a > = >> Immediate objects have two weaknesses compared to classes: their types are not abbreviated, and you cannot inherit from them. But these two weaknesses can be advantages in some situations, as we will see in sections 3.3 and 3.10. 3.3 Reference to self *=*=*=*=*=*=*=*=*=*=*=* A method or an initializer can invoke methods on self (that is, the current object). For that, self must be explicitly bound, here to the variable s (s could be any identifier, even though we will often choose the name self.) << # class printable_point x_init = object (s) val mutable x = x_init method get_x = x method move d = x <- x + d method print = print_int s#get_x end;; class printable_point : int -> object val mutable x : int method get_x : int method move : int -> unit method print : unit end >> << # let p = new printable_point 7;; val p : printable_point = >> << # p#print;; 7- : unit = () >> Dynamically, the variable s is bound at the invocation of a method. In particular, when the class printable_point is inherited, the variable s will be correctly bound to the object of the subclass. A common problem with self is that, as its type may be extended in subclasses, you cannot fix it in advance. Here is a simple example. << # let ints = ref [];; val ints : '_weak1 list ref = {contents = []} >> << # class my_int = object (self) method n = 1 method register = ints := self :: !ints end ;; Error: This expression has type < n : int; register : 'a; .. > but an expression was expected of type 'weak1 Self type cannot escape its class >> You can ignore the first two lines of the error message. What matters is the last one: putting self into an external reference would make it impossible to extend it through inheritance. We will see in section 3.12 a workaround to this problem. Note however that, since immediate objects are not extensible, the problem does not occur with them. << # let my_int = object (self) method n = 1 method register = ints := self :: !ints end;; val my_int : < n : int; register : unit > = >> 3.4 Initializers *=*=*=*=*=*=*=*=*= Let-bindings within class definitions are evaluated before the object is constructed. It is also possible to evaluate an expression immediately after the object has been built. Such code is written as an anonymous hidden method called an initializer. Therefore, it can access self and the instance variables. << # class printable_point x_init = let origin = (x_init / 10) * 10 in object (self) val mutable x = origin method get_x = x method move d = x <- x + d method print = print_int self#get_x initializer print_string "new point at "; self#print; print_newline () end;; class printable_point : int -> object val mutable x : int method get_x : int method move : int -> unit method print : unit end >> << # let p = new printable_point 17;; new point at 10 val p : printable_point = >> Initializers cannot be overridden. On the contrary, all initializers are evaluated sequentially. Initializers are particularly useful to enforce invariants. Another example can be seen in section 8.1. 3.5 Virtual methods *=*=*=*=*=*=*=*=*=*=* It is possible to declare a method without actually defining it, using the keyword virtual. This method will be provided later in subclasses. A class containing virtual methods must be flagged virtual, and cannot be instantiated (that is, no object of this class can be created). It still defines type abbreviations (treating virtual methods as other methods.) << # class virtual abstract_point x_init = object (self) method virtual get_x : int method get_offset = self#get_x - x_init method virtual move : int -> unit end;; class virtual abstract_point : int -> object method get_offset : int method virtual get_x : int method virtual move : int -> unit end >> << # class point x_init = object inherit abstract_point x_init val mutable x = x_init method get_x = x method move d = x <- x + d end;; class point : int -> object val mutable x : int method get_offset : int method get_x : int method move : int -> unit end >> Instance variables can also be declared as virtual, with the same effect as with methods. << # class virtual abstract_point2 = object val mutable virtual x : int method move d = x <- x + d end;; class virtual abstract_point2 : object val mutable virtual x : int method move : int -> unit end >> << # class point2 x_init = object inherit abstract_point2 val mutable x = x_init method get_offset = x - x_init end;; class point2 : int -> object val mutable x : int method get_offset : int method move : int -> unit end >> 3.6 Private methods *=*=*=*=*=*=*=*=*=*=* Private methods are methods that do not appear in object interfaces. They can only be invoked from other methods of the same object. << # class restricted_point x_init = object (self) val mutable x = x_init method get_x = x method private move d = x <- x + d method bump = self#move 1 end;; class restricted_point : int -> object val mutable x : int method bump : unit method get_x : int method private move : int -> unit end >> << # let p = new restricted_point 0;; val p : restricted_point = >> << # p#move 10 ;; Error: This expression has type restricted_point It has no method move >> << # p#bump;; - : unit = () >> Note that this is not the same thing as private and protected methods in Java or C++, which can be called from other objects of the same class. This is a direct consequence of the independence between types and classes in OCaml: two unrelated classes may produce objects of the same type, and there is no way at the type level to ensure that an object comes from a specific class. However a possible encoding of friend methods is given in section 3.17. Private methods are inherited (they are by default visible in subclasses), unless they are hidden by signature matching, as described below. Private methods can be made public in a subclass. << # class point_again x = object (self) inherit restricted_point x method virtual move : _ end;; class point_again : int -> object val mutable x : int method bump : unit method get_x : int method move : int -> unit end >> The annotation virtual here is only used to mention a method without providing its definition. Since we didn’t add the private annotation, this makes the method public, keeping the original definition. An alternative definition is << # class point_again x = object (self : < move : _; ..> ) inherit restricted_point x end;; class point_again : int -> object val mutable x : int method bump : unit method get_x : int method move : int -> unit end >> The constraint on self’s type is requiring a public move method, and this is sufficient to override private. One could think that a private method should remain private in a subclass. However, since the method is visible in a subclass, it is always possible to pick its code and define a method of the same name that runs that code, so yet another (heavier) solution would be: << # class point_again x = object inherit restricted_point x as super method move = super#move end;; class point_again : int -> object val mutable x : int method bump : unit method get_x : int method move : int -> unit end >> Of course, private methods can also be virtual. Then, the keywords must appear in this order: method private virtual. 3.7 Class interfaces *=*=*=*=*=*=*=*=*=*=*= Class interfaces are inferred from class definitions. They may also be defined directly and used to restrict the type of a class. Like class declarations, they also define a new type abbreviation. << # class type restricted_point_type = object method get_x : int method bump : unit end;; class type restricted_point_type = object method bump : unit method get_x : int end >> << # fun (x : restricted_point_type) -> x;; - : restricted_point_type -> restricted_point_type = >> In addition to program documentation, class interfaces can be used to constrain the type of a class. Both concrete instance variables and concrete private methods can be hidden by a class type constraint. Public methods and virtual members, however, cannot. << # class restricted_point' x = (restricted_point x : restricted_point_type);; class restricted_point' : int -> restricted_point_type >> Or, equivalently: << # class restricted_point' = (restricted_point : int -> restricted_point_type) ;; class restricted_point' : int -> restricted_point_type >> The interface of a class can also be specified in a module signature, and used to restrict the inferred signature of a module. << # module type POINT = sig class restricted_point' : int -> object method get_x : int method bump : unit end end;; module type POINT = sig class restricted_point' : int -> object method bump : unit method get_x : int end end >> << # module Point : POINT = struct class restricted_point' = restricted_point end;; module Point : POINT >> 3.8 Inheritance *=*=*=*=*=*=*=*=* We illustrate inheritance by defining a class of colored points that inherits from the class of points. This class has all instance variables and all methods of class point, plus a new instance variable c and a new method color. << # class colored_point x (c : string) = object inherit point x val c = c method color = c end;; class colored_point : int -> string -> object val c : string val mutable x : int method color : string method get_offset : int method get_x : int method move : int -> unit end >> << # let p' = new colored_point 5 "red";; val p' : colored_point = >> << # p'#get_x, p'#color;; - : int * string = (5, "red") >> A point and a colored point have incompatible types, since a point has no method color. However, the function get_x below is a generic function applying method get_x to any object p that has this method (and possibly some others, which are represented by an ellipsis in the type). Thus, it applies to both points and colored points. << # let get_succ_x p = p#get_x + 1;; val get_succ_x : < get_x : int; .. > -> int = >> << # get_succ_x p + get_succ_x p';; - : int = 8 >> Methods need not be declared previously, as shown by the example: << # let set_x p = p#set_x;; val set_x : < set_x : 'a; .. > -> 'a = >> << # let incr p = set_x p (get_succ_x p);; val incr : < get_x : int; set_x : int -> 'a; .. > -> 'a = >> 3.9 Multiple inheritance *=*=*=*=*=*=*=*=*=*=*=*=*= Multiple inheritance is allowed. Only the last definition of a method is kept: the redefinition in a subclass of a method that was visible in the parent class overrides the definition in the parent class. Previous definitions of a method can be reused by binding the related ancestor. Below, super is bound to the ancestor printable_point. The name super is a pseudo value identifier that can only be used to invoke a super-class method, as in super#print. << # class printable_colored_point y c = object (self) val c = c method color = c inherit printable_point y as super method! print = print_string "("; super#print; print_string ", "; print_string (self#color); print_string ")" end;; class printable_colored_point : int -> string -> object val c : string val mutable x : int method color : string method get_x : int method move : int -> unit method print : unit end >> << # let p' = new printable_colored_point 17 "red";; new point at (10, red) val p' : printable_colored_point = >> << # p'#print;; (10, red)- : unit = () >> A private method that has been hidden in the parent class is no longer visible, and is thus not overridden. Since initializers are treated as private methods, all initializers along the class hierarchy are evaluated, in the order they are introduced. Note that for clarity’s sake, the method print is explicitly marked as overriding another definition by annotating the method keyword with an exclamation mark !. If the method print were not overriding the print method of printable_point, the compiler would raise an error: << # object method! m = () end;; Error: The method m has no previous definition >> This explicit overriding annotation also works for val and inherit: << # class another_printable_colored_point y c c' = object (self) inherit printable_point y inherit! printable_colored_point y c val! c = c' end;; class another_printable_colored_point : int -> string -> string -> object val c : string val mutable x : int method color : string method get_x : int method move : int -> unit method print : unit end >> 3.10 Parameterized classes *=*=*=*=*=*=*=*=*=*=*=*=*=*= Reference cells can be implemented as objects. The naive definition fails to typecheck: << # class oref x_init = object val mutable x = x_init method get = x method set y = x <- y end;; Error: Some type variables are unbound in this type: class oref : 'a -> object val mutable x : 'a method get : 'a method set : 'a -> unit end The method get has type 'a where 'a is unbound >> The reason is that at least one of the methods has a polymorphic type (here, the type of the value stored in the reference cell), thus either the class should be parametric, or the method type should be constrained to a monomorphic type. A monomorphic instance of the class could be defined by: << # class oref (x_init:int) = object val mutable x = x_init method get = x method set y = x <- y end;; class oref : int -> object val mutable x : int method get : int method set : int -> unit end >> Note that since immediate objects do not define a class type, they have no such restriction. << # let new_oref x_init = object val mutable x = x_init method get = x method set y = x <- y end;; val new_oref : 'a -> < get : 'a; set : 'a -> unit > = >> On the other hand, a class for polymorphic references must explicitly list the type parameters in its declaration. Class type parameters are listed between [ and ]. The type parameters must also be bound somewhere in the class body by a type constraint. << # class ['a] oref x_init = object val mutable x = (x_init : 'a) method get = x method set y = x <- y end;; class ['a] oref : 'a -> object val mutable x : 'a method get : 'a method set : 'a -> unit end >> << # let r = new oref 1 in r#set 2; (r#get);; - : int = 2 >> The type parameter in the declaration may actually be constrained in the body of the class definition. In the class type, the actual value of the type parameter is displayed in the constraint clause. << # class ['a] oref_succ (x_init:'a) = object val mutable x = x_init + 1 method get = x method set y = x <- y end;; class ['a] oref_succ : 'a -> object constraint 'a = int val mutable x : int method get : int method set : int -> unit end >> Let us consider a more complex example: define a circle, whose center may be any kind of point. We put an additional type constraint in method move, since no free variables must remain unaccounted for by the class type parameters. << # class ['a] circle (c : 'a) = object val mutable center = c method center = center method set_center c = center <- c method move = (center#move : int -> unit) end;; class ['a] circle : 'a -> object constraint 'a = < move : int -> unit; .. > val mutable center : 'a method center : 'a method move : int -> unit method set_center : 'a -> unit end >> An alternate definition of circle, using a constraint clause in the class definition, is shown below. The type #point used below in the constraint clause is an abbreviation produced by the definition of class point. This abbreviation unifies with the type of any object belonging to a subclass of class point. It actually expands to < get_x : int; move : int -> unit; .. >. This leads to the following alternate definition of circle, which has slightly stronger constraints on its argument, as we now expect center to have a method get_x. << # class ['a] circle (c : 'a) = object constraint 'a = #point val mutable center = c method center = center method set_center c = center <- c method move = center#move end;; class ['a] circle : 'a -> object constraint 'a = #point val mutable center : 'a method center : 'a method move : int -> unit method set_center : 'a -> unit end >> The class colored_circle is a specialized version of class circle that requires the type of the center to unify with #colored_point, and adds a method color. Note that when specializing a parameterized class, the instance of type parameter must always be explicitly given. It is again written between [ and ]. << # class ['a] colored_circle c = object constraint 'a = #colored_point inherit ['a] circle c method color = center#color end;; class ['a] colored_circle : 'a -> object constraint 'a = #colored_point val mutable center : 'a method center : 'a method color : string method move : int -> unit method set_center : 'a -> unit end >> 3.11 Polymorphic methods *=*=*=*=*=*=*=*=*=*=*=*=*= While parameterized classes may be polymorphic in their contents, they are not enough to allow polymorphism of method use. A classical example is defining an iterator. << # List.fold_left;; - : ('acc -> 'a -> 'acc) -> 'acc -> 'a list -> 'acc = >> << # class ['a] intlist (l : int list) = object method empty = (l = []) method fold f (accu : 'a) = List.fold_left f accu l end;; class ['a] intlist : int list -> object method empty : bool method fold : ('a -> int -> 'a) -> 'a -> 'a end >> At first look, we seem to have a polymorphic iterator, however this does not work in practice. << # let l = new intlist [1; 2; 3];; val l : '_weak2 intlist = >> << # l#fold (fun x y -> x+y) 0;; - : int = 6 >> << # l;; - : int intlist = >> << # l#fold (fun s x -> s ^ Int.to_string x ^ " ") "" ;; Error: This expression has type int but an expression was expected of type string >> Our iterator works, as shows its first use for summation. However, since objects themselves are not polymorphic (only their constructors are), using the fold method fixes its type for this individual object. Our next attempt to use it as a string iterator fails. The problem here is that quantification was wrongly located: it is not the class we want to be polymorphic, but the fold method. This can be achieved by giving an explicitly polymorphic type in the method definition. << # class intlist (l : int list) = object method empty = (l = []) method fold : 'a. ('a -> int -> 'a) -> 'a -> 'a = fun f accu -> List.fold_left f accu l end;; class intlist : int list -> object method empty : bool method fold : ('a -> int -> 'a) -> 'a -> 'a end >> << # let l = new intlist [1; 2; 3];; val l : intlist = >> << # l#fold (fun x y -> x+y) 0;; - : int = 6 >> << # l#fold (fun s x -> s ^ Int.to_string x ^ " ") "";; - : string = "1 2 3 " >> As you can see in the class type shown by the compiler, while polymorphic method types must be fully explicit in class definitions (appearing immediately after the method name), quantified type variables can be left implicit in class descriptions. Why require types to be explicit? The problem is that (int -> int -> int) -> int -> int would also be a valid type for fold, and it happens to be incompatible with the polymorphic type we gave (automatic instantiation only works for toplevel types variables, not for inner quantifiers, where it becomes an undecidable problem.) So the compiler cannot choose between those two types, and must be helped. However, the type can be completely omitted in the class definition if it is already known, through inheritance or type constraints on self. Here is an example of method overriding. << # class intlist_rev l = object inherit intlist l method! fold f accu = List.fold_left f accu (List.rev l) end;; >> The following idiom separates description and definition. << # class type ['a] iterator = object method fold : ('b -> 'a -> 'b) -> 'b -> 'b end;; >> << # class intlist' l = object (self : int #iterator) method empty = (l = []) method fold f accu = List.fold_left f accu l end;; >> Note here the (self : int #iterator) idiom, which ensures that this object implements the interface iterator. Polymorphic methods are called in exactly the same way as normal methods, but you should be aware of some limitations of type inference. Namely, a polymorphic method can only be called if its type is known at the call site. Otherwise, the method will be assumed to be monomorphic, and given an incompatible type. << # let sum lst = lst#fold (fun x y -> x+y) 0;; val sum : < fold : (int -> int -> int) -> int -> 'a; .. > -> 'a = >> << # sum l ;; Error: This expression has type intlist but an expression was expected of type < fold : (int -> int -> int) -> int -> 'b; .. > The method fold has type 'a. ('a -> int -> 'a) -> 'a -> 'a, but the expected method type was (int -> int -> int) -> int -> 'b >> The workaround is easy: you should put a type constraint on the parameter. << # let sum (lst : _ #iterator) = lst#fold (fun x y -> x+y) 0;; val sum : int #iterator -> int = >> Of course the constraint may also be an explicit method type. Only occurrences of quantified variables are required. << # let sum lst = (lst : < fold : 'a. ('a -> _ -> 'a) -> 'a -> 'a; .. >)#fold (+) 0;; val sum : < fold : 'a. ('a -> int -> 'a) -> 'a -> 'a; .. > -> int = >> Another use of polymorphic methods is to allow some form of implicit subtyping in method arguments. We have already seen in section 3.8 how some functions may be polymorphic in the class of their argument. This can be extended to methods. << # class type point0 = object method get_x : int end;; class type point0 = object method get_x : int end >> << # class distance_point x = object inherit point x method distance : 'a. (#point0 as 'a) -> int = fun other -> abs (other#get_x - x) end;; class distance_point : int -> object val mutable x : int method distance : #point0 -> int method get_offset : int method get_x : int method move : int -> unit end >> << # let p = new distance_point 3 in (p#distance (new point 8), p#distance (new colored_point 1 "blue"));; - : int * int = (5, 2) >> Note here the special syntax (#point0 as 'a) we have to use to quantify the extensible part of #point0. As for the variable binder, it can be omitted in class specifications. If you want polymorphism inside object field it must be quantified independently. << # class multi_poly = object method m1 : 'a. (< n1 : 'b. 'b -> 'b; .. > as 'a) -> _ = fun o -> o#n1 true, o#n1 "hello" method m2 : 'a 'b. (< n2 : 'b -> bool; .. > as 'a) -> 'b -> _ = fun o x -> o#n2 x end;; class multi_poly : object method m1 : < n1 : 'b. 'b -> 'b; .. > -> bool * string method m2 : < n2 : 'b -> bool; .. > -> 'b -> bool end >> In method m1, o must be an object with at least a method n1, itself polymorphic. In method m2, the argument of n2 and x must have the same type, which is quantified at the same level as 'a. 3.12 Using coercions *=*=*=*=*=*=*=*=*=*=*= Subtyping is never implicit. There are, however, two ways to perform subtyping. The most general construction is fully explicit: both the domain and the codomain of the type coercion must be given. We have seen that points and colored points have incompatible types. For instance, they cannot be mixed in the same list. However, a colored point can be coerced to a point, hiding its color method: << # let colored_point_to_point cp = (cp : colored_point :> point);; val colored_point_to_point : colored_point -> point = >> << # let p = new point 3 and q = new colored_point 4 "blue";; val p : point = val q : colored_point = >> << # let l = [p; (colored_point_to_point q)];; val l : point list = [; ] >> An object of type t can be seen as an object of type t' only if t is a subtype of t'. For instance, a point cannot be seen as a colored point. << # (p : point :> colored_point);; Error: Type point = < get_offset : int; get_x : int; move : int -> unit > is not a subtype of colored_point = < color : string; get_offset : int; get_x : int; move : int -> unit > The first object type has no method color >> Indeed, narrowing coercions without runtime checks would be unsafe. Runtime type checks might raise exceptions, and they would require the presence of type information at runtime, which is not the case in the OCaml system. For these reasons, there is no such operation available in the language. Be aware that subtyping and inheritance are not related. Inheritance is a syntactic relation between classes while subtyping is a semantic relation between types. For instance, the class of colored points could have been defined directly, without inheriting from the class of points; the type of colored points would remain unchanged and thus still be a subtype of points. The domain of a coercion can often be omitted. For instance, one can define: << # let to_point cp = (cp :> point);; val to_point : #point -> point = >> In this case, the function colored_point_to_point is an instance of the function to_point. This is not always true, however. The fully explicit coercion is more precise and is sometimes unavoidable. Consider, for example, the following class: << # class c0 = object method m = {< >} method n = 0 end;; class c0 : object ('a) method m : 'a method n : int end >> The object type c0 is an abbreviation for as 'a. Consider now the type declaration: << # class type c1 = object method m : c1 end;; class type c1 = object method m : c1 end >> The object type c1 is an abbreviation for the type as 'a. The coercion from an object of type c0 to an object of type c1 is correct: << # fun (x:c0) -> (x : c0 :> c1);; - : c0 -> c1 = >> However, the domain of the coercion cannot always be omitted. In that case, the solution is to use the explicit form. Sometimes, a change in the class-type definition can also solve the problem << # class type c2 = object ('a) method m : 'a end;; class type c2 = object ('a) method m : 'a end >> << # fun (x:c0) -> (x :> c2);; - : c0 -> c2 = >> While class types c1 and c2 are different, both object types c1 and c2 expand to the same object type (same method names and types). Yet, when the domain of a coercion is left implicit and its co-domain is an abbreviation of a known class type, then the class type, rather than the object type, is used to derive the coercion function. This allows leaving the domain implicit in most cases when coercing from a subclass to its superclass. The type of a coercion can always be seen as below: << # let to_c1 x = (x :> c1);; val to_c1 : < m : #c1; .. > -> c1 = >> << # let to_c2 x = (x :> c2);; val to_c2 : #c2 -> c2 = >> Note the difference between these two coercions: in the case of to_c2, the type #c2 = < m : 'a; .. > as 'a is polymorphically recursive (according to the explicit recursion in the class type of c2); hence the success of applying this coercion to an object of class c0. On the other hand, in the first case, c1 was only expanded and unrolled twice to obtain < m : < m : c1; .. >; .. > (remember #c1 = < m : c1; .. >), without introducing recursion. You may also note that the type of to_c2 is #c2 -> c2 while the type of to_c1 is more general than #c1 -> c1. This is not always true, since there are class types for which some instances of #c are not subtypes of c, as explained in section 3.16. Yet, for parameterless classes the coercion (_ :> c) is always more general than (_ : #c :> c). A common problem may occur when one tries to define a coercion to a class c while defining class c. The problem is due to the type abbreviation not being completely defined yet, and so its subtypes are not clearly known. Then, a coercion (_ :> c) or (_ : #c :> c) is taken to be the identity function, as in << # fun x -> (x :> 'a);; - : 'a -> 'a = >> As a consequence, if the coercion is applied to self, as in the following example, the type of self is unified with the closed type c (a closed object type is an object type without ellipsis). This would constrain the type of self be closed and is thus rejected. Indeed, the type of self cannot be closed: this would prevent any further extension of the class. Therefore, a type error is generated when the unification of this type with another type would result in a closed object type. << # class c = object method m = 1 end and d = object (self) inherit c method n = 2 method as_c = (self :> c) end;; Error: This expression cannot be coerced to type c = < m : int >; it has type < as_c : c; m : int; n : int; .. > but is here used with type c Self type cannot escape its class >> However, the most common instance of this problem, coercing self to its current class, is detected as a special case by the type checker, and properly typed. << # class c = object (self) method m = (self :> c) end;; class c : object method m : c end >> This allows the following idiom, keeping a list of all objects belonging to a class or its subclasses: << # let all_c = ref [];; val all_c : '_weak3 list ref = {contents = []} >> << # class c (m : int) = object (self) method m = m initializer all_c := (self :> c) :: !all_c end;; class c : int -> object method m : int end >> This idiom can in turn be used to retrieve an object whose type has been weakened: << # let rec lookup_obj obj = function [] -> raise Not_found | obj' :: l -> if (obj :> < >) = (obj' :> < >) then obj' else lookup_obj obj l ;; val lookup_obj : < .. > -> (< .. > as 'a) list -> 'a = >> << # let lookup_c obj = lookup_obj obj !all_c;; val lookup_c : < .. > -> < m : int > = >> The type < m : int > we see here is just the expansion of c, due to the use of a reference; we have succeeded in getting back an object of type c. The previous coercion problem can often be avoided by first defining the abbreviation, using a class type: << # class type c' = object method m : int end;; class type c' = object method m : int end >> << # class c : c' = object method m = 1 end and d = object (self) inherit c method n = 2 method as_c = (self :> c') end;; class c : c' and d : object method as_c : c' method m : int method n : int end >> It is also possible to use a virtual class. Inheriting from this class simultaneously forces all methods of c to have the same type as the methods of c'. << # class virtual c' = object method virtual m : int end;; class virtual c' : object method virtual m : int end >> << # class c = object (self) inherit c' method m = 1 end;; class c : object method m : int end >> One could think of defining the type abbreviation directly: << # type c' = ;; >> However, the abbreviation #c' cannot be defined directly in a similar way. It can only be defined by a class or a class-type definition. This is because a #-abbreviation carries an implicit anonymous variable .. that cannot be explicitly named. The closer you get to it is: << # type 'a c'_class = 'a constraint 'a = < m : int; .. >;; >> with an extra type variable capturing the open object type. 3.13 Functional objects *=*=*=*=*=*=*=*=*=*=*=*=* It is possible to write a version of class point without assignments on the instance variables. The override construct {< ... >} returns a copy of “self” (that is, the current object), possibly changing the value of some instance variables. << # class functional_point y = object val x = y method get_x = x method move d = {< x = x + d >} method move_to x = {< x >} end;; class functional_point : int -> object ('a) val x : int method get_x : int method move : int -> 'a method move_to : int -> 'a end >> << # let p = new functional_point 7;; val p : functional_point = >> << # p#get_x;; - : int = 7 >> << # (p#move 3)#get_x;; - : int = 10 >> << # (p#move_to 15)#get_x;; - : int = 15 >> << # p#get_x;; - : int = 7 >> As with records, the form {< x >} is an elided version of {< x = x >} which avoids the repetition of the instance variable name. Note that the type abbreviation functional_point is recursive, which can be seen in the class type of functional_point: the type of self is 'a and 'a appears inside the type of the method move. The above definition of functional_point is not equivalent to the following: << # class bad_functional_point y = object val x = y method get_x = x method move d = new bad_functional_point (x+d) method move_to x = new bad_functional_point x end;; class bad_functional_point : int -> object val x : int method get_x : int method move : int -> bad_functional_point method move_to : int -> bad_functional_point end >> While objects of either class will behave the same, objects of their subclasses will be different. In a subclass of bad_functional_point, the method move will keep returning an object of the parent class. On the contrary, in a subclass of functional_point, the method move will return an object of the subclass. Functional update is often used in conjunction with binary methods as illustrated in section 8.2.1. 3.14 Cloning objects *=*=*=*=*=*=*=*=*=*=*= Objects can also be cloned, whether they are functional or imperative. The library function Oo.copy makes a shallow copy of an object. That is, it returns a new object that has the same methods and instance variables as its argument. The instance variables are copied but their contents are shared. Assigning a new value to an instance variable of the copy (using a method call) will not affect instance variables of the original, and conversely. A deeper assignment (for example if the instance variable is a reference cell) will of course affect both the original and the copy. The type of Oo.copy is the following: << # Oo.copy;; - : (< .. > as 'a) -> 'a = >> The keyword as in that type binds the type variable 'a to the object type < .. >. Therefore, Oo.copy takes an object with any methods (represented by the ellipsis), and returns an object of the same type. The type of Oo.copy is different from type < .. > -> < .. > as each ellipsis represents a different set of methods. Ellipsis actually behaves as a type variable. << # let p = new point 5;; val p : point = >> << # let q = Oo.copy p;; val q : point = >> << # q#move 7; (p#get_x, q#get_x);; - : int * int = (5, 12) >> In fact, Oo.copy p will behave as p#copy assuming that a public method copy with body {< >} has been defined in the class of p. Objects can be compared using the generic comparison functions = and <>. Two objects are equal if and only if they are physically equal. In particular, an object and its copy are not equal. << # let q = Oo.copy p;; val q : point = >> << # p = q, p = p;; - : bool * bool = (false, true) >> Other generic comparisons such as (<, <=, ...) can also be used on objects. The relation < defines an unspecified but strict ordering on objects. The ordering relationship between two objects is fixed permanently once the two objects have been created, and it is not affected by mutation of fields. Cloning and override have a non empty intersection. They are interchangeable when used within an object and without overriding any field: << # class copy = object method copy = {< >} end;; class copy : object ('a) method copy : 'a end >> << # class copy = object (self) method copy = Oo.copy self end;; class copy : object ('a) method copy : 'a end >> Only the override can be used to actually override fields, and only the Oo.copy primitive can be used externally. Cloning can also be used to provide facilities for saving and restoring the state of objects. << # class backup = object (self : 'mytype) val mutable copy = None method save = copy <- Some {< copy = None >} method restore = match copy with Some x -> x | None -> self end;; class backup : object ('a) val mutable copy : 'a option method restore : 'a method save : unit end >> The above definition will only backup one level. The backup facility can be added to any class by using multiple inheritance. << # class ['a] backup_ref x = object inherit ['a] oref x inherit backup end;; class ['a] backup_ref : 'a -> object ('b) val mutable copy : 'b option val mutable x : 'a method get : 'a method restore : 'b method save : unit method set : 'a -> unit end >> << # let rec get p n = if n = 0 then p # get else get (p # restore) (n-1);; val get : (< get : 'b; restore : 'a; .. > as 'a) -> int -> 'b = >> << # let p = new backup_ref 0 in p # save; p # set 1; p # save; p # set 2; [get p 0; get p 1; get p 2; get p 3; get p 4];; - : int list = [2; 1; 1; 1; 1] >> We can define a variant of backup that retains all copies. (We also add a method clear to manually erase all copies.) << # class backup = object (self : 'mytype) val mutable copy = None method save = copy <- Some {< >} method restore = match copy with Some x -> x | None -> self method clear = copy <- None end;; class backup : object ('a) val mutable copy : 'a option method clear : unit method restore : 'a method save : unit end >> << # class ['a] backup_ref x = object inherit ['a] oref x inherit backup end;; class ['a] backup_ref : 'a -> object ('b) val mutable copy : 'b option val mutable x : 'a method clear : unit method get : 'a method restore : 'b method save : unit method set : 'a -> unit end >> << # let p = new backup_ref 0 in p # save; p # set 1; p # save; p # set 2; [get p 0; get p 1; get p 2; get p 3; get p 4];; - : int list = [2; 1; 0; 0; 0] >> 3.15 Recursive classes *=*=*=*=*=*=*=*=*=*=*=*= Recursive classes can be used to define objects whose types are mutually recursive. << # class window = object val mutable top_widget = (None : widget option) method top_widget = top_widget end and widget (w : window) = object val window = w method window = window end;; class window : object val mutable top_widget : widget option method top_widget : widget option end and widget : window -> object val window : window method window : window end >> Although their types are mutually recursive, the classes widget and window are themselves independent. 3.16 Binary methods *=*=*=*=*=*=*=*=*=*=* A binary method is a method which takes an argument of the same type as self. The class comparable below is a template for classes with a binary method leq of type 'a -> bool where the type variable 'a is bound to the type of self. Therefore, #comparable expands to < leq : 'a -> bool; .. > as 'a. We see here that the binder as also allows writing recursive types. << # class virtual comparable = object (_ : 'a) method virtual leq : 'a -> bool end;; class virtual comparable : object ('a) method virtual leq : 'a -> bool end >> We then define a subclass money of comparable. The class money simply wraps floats as comparable objects. (1) We will extend money below with more operations. We have to use a type constraint on the class parameter x because the primitive <= is a polymorphic function in OCaml. The inherit clause ensures that the type of objects of this class is an instance of #comparable. << # class money (x : float) = object inherit comparable val repr = x method value = repr method leq p = repr <= p#value end;; class money : float -> object ('a) val repr : float method leq : 'a -> bool method value : float end >> Note that the type money is not a subtype of type comparable, as the self type appears in contravariant position in the type of method leq. Indeed, an object m of class money has a method leq that expects an argument of type money since it accesses its value method. Considering m of type comparable would allow a call to method leq on m with an argument that does not have a method value, which would be an error. Similarly, the type money2 below is not a subtype of type money. << # class money2 x = object inherit money x method times k = {< repr = k *. repr >} end;; class money2 : float -> object ('a) val repr : float method leq : 'a -> bool method times : float -> 'a method value : float end >> It is however possible to define functions that manipulate objects of type either money or money2: the function min will return the minimum of any two objects whose type unifies with #comparable. The type of min is not the same as #comparable -> #comparable -> #comparable, as the abbreviation #comparable hides a type variable (an ellipsis). Each occurrence of this abbreviation generates a new variable. << # let min (x : #comparable) y = if x#leq y then x else y;; val min : (#comparable as 'a) -> 'a -> 'a = >> This function can be applied to objects of type money or money2. << # (min (new money 1.3) (new money 3.1))#value;; - : float = 1.3 >> << # (min (new money2 5.0) (new money2 3.14))#value;; - : float = 3.14 >> More examples of binary methods can be found in sections 8.2.1 and 8.2.3. Note the use of override for method times. Writing new money2 (k *. repr) instead of {< repr = k *. repr >} would not behave well with inheritance: in a subclass money3 of money2 the times method would return an object of class money2 but not of class money3 as would be expected. The class money could naturally carry another binary method. Here is a direct definition: << # class money x = object (self : 'a) val repr = x method value = repr method print = print_float repr method times k = {< repr = k *. x >} method leq (p : 'a) = repr <= p#value method plus (p : 'a) = {< repr = x +. p#value >} end;; class money : float -> object ('a) val repr : float method leq : 'a -> bool method plus : 'a -> 'a method print : unit method times : float -> 'a method value : float end >> 3.17 Friends *=*=*=*=*=*=*= The above class money reveals a problem that often occurs with binary methods. In order to interact with other objects of the same class, the representation of money objects must be revealed, using a method such as value. If we remove all binary methods (here plus and leq), the representation can easily be hidden inside objects by removing the method value as well. However, this is not possible as soon as some binary method requires access to the representation of objects of the same class (other than self). << # class safe_money x = object (self : 'a) val repr = x method print = print_float repr method times k = {< repr = k *. x >} end;; class safe_money : float -> object ('a) val repr : float method print : unit method times : float -> 'a end >> Here, the representation of the object is known only to a particular object. To make it available to other objects of the same class, we are forced to make it available to the whole world. However we can easily restrict the visibility of the representation using the module system. << # module type MONEY = sig type t class c : float -> object ('a) val repr : t method value : t method print : unit method times : float -> 'a method leq : 'a -> bool method plus : 'a -> 'a end end;; >> << # module Euro : MONEY = struct type t = float class c x = object (self : 'a) val repr = x method value = repr method print = print_float repr method times k = {< repr = k *. x >} method leq (p : 'a) = repr <= p#value method plus (p : 'a) = {< repr = x +. p#value >} end end;; >> Another example of friend functions may be found in section 8.2.3. These examples occur when a group of objects (here objects of the same class) and functions should see each others internal representation, while their representation should be hidden from the outside. The solution is always to define all friends in the same module, give access to the representation and use a signature constraint to make the representation abstract outside the module. --------------------------------------- (1) floats are an approximation of decimal numbers, they are unsuitable for use in most monetary calculations as they may introduce errors. Chapter 4  Labeled arguments ******************************** (Chapter written by Jacques Garrigue) If you have a look at modules ending in Labels in the standard library, you will see that function types have annotations you did not have in the functions you defined yourself. << # ListLabels.map;; - : f:('a -> 'b) -> 'a list -> 'b list = >> << # StringLabels.sub;; - : string -> pos:int -> len:int -> string = >> Such annotations of the form name: are called labels. They are meant to document the code, allow more checking, and give more flexibility to function application. You can give such names to arguments in your programs, by prefixing them with a tilde ~. << # let f ~x ~y = x - y;; val f : x:int -> y:int -> int = >> << # let x = 3 and y = 2 in f ~x ~y;; - : int = 1 >> When you want to use distinct names for the variable and the label appearing in the type, you can use a naming label of the form ~name:. This also applies when the argument is not a variable. << # let f ~x:x1 ~y:y1 = x1 - y1;; val f : x:int -> y:int -> int = >> << # f ~x:3 ~y:2;; - : int = 1 >> Labels obey the same rules as other identifiers in OCaml, that is you cannot use a reserved keyword (like in or to) as a label. Formal parameters and arguments are matched according to their respective labels, the absence of label being interpreted as the empty label. This allows commuting arguments in applications. One can also partially apply a function on any argument, creating a new function of the remaining parameters. << # let f ~x ~y = x - y;; val f : x:int -> y:int -> int = >> << # f ~y:2 ~x:3;; - : int = 1 >> << # ListLabels.fold_left;; - : f:('acc -> 'a -> 'acc) -> init:'acc -> 'a list -> 'acc = >> << # ListLabels.fold_left [1;2;3] ~init:0 ~f:( + );; - : int = 6 >> << # ListLabels.fold_left ~init:0;; - : f:(int -> 'a -> int) -> 'a list -> int = >> If several arguments of a function bear the same label (or no label), they will not commute among themselves, and order matters. But they can still commute with other arguments. << # let hline ~x:x1 ~x:x2 ~y = (x1, x2, y);; val hline : x:'a -> x:'b -> y:'c -> 'a * 'b * 'c = >> << # hline ~x:3 ~y:2 ~x:5;; - : int * int * int = (3, 5, 2) >> 4.1 Optional arguments *=*=*=*=*=*=*=*=*=*=*=*= An interesting feature of labeled arguments is that they can be made optional. For optional parameters, the question mark ? replaces the tilde ~ of non-optional ones, and the label is also prefixed by ? in the function type. Default values may be given for such optional parameters. << # let bump ?(step = 1) x = x + step;; val bump : ?step:int -> int -> int = >> << # bump 2;; - : int = 3 >> << # bump ~step:3 2;; - : int = 5 >> A function taking some optional arguments must also take at least one non-optional argument. The criterion for deciding whether an optional argument has been omitted is the non-labeled application of an argument appearing after this optional argument in the function type. Note that if that argument is labeled, you will only be able to eliminate optional arguments by totally applying the function, omitting all optional arguments and omitting all labels for all remaining arguments. << # let test ?(x = 0) ?(y = 0) () ?(z = 0) () = (x, y, z);; val test : ?x:int -> ?y:int -> unit -> ?z:int -> unit -> int * int * int = >> << # test ();; - : ?z:int -> unit -> int * int * int = >> << # test ~x:2 () ~z:3 ();; - : int * int * int = (2, 0, 3) >> Optional parameters may also commute with non-optional or unlabeled ones, as long as they are applied simultaneously. By nature, optional arguments do not commute with unlabeled arguments applied independently. << # test ~y:2 ~x:3 () ();; - : int * int * int = (3, 2, 0) >> << # test () () ~z:1 ~y:2 ~x:3;; - : int * int * int = (3, 2, 1) >> << # (test () ()) ~z:1 ;; Error: This expression has type int * int * int This is not a function; it cannot be applied. >> Here (test () ()) is already (0,0,0) and cannot be further applied. Optional arguments are actually implemented as option types. If you do not give a default value, you have access to their internal representation, type 'a option = None | Some of 'a. You can then provide different behaviors when an argument is present or not. << # let bump ?step x = match step with | None -> x * 2 | Some y -> x + y ;; val bump : ?step:int -> int -> int = >> It may also be useful to relay an optional argument from a function call to another. This can be done by prefixing the applied argument with ?. This question mark disables the wrapping of optional argument in an option type. << # let test2 ?x ?y () = test ?x ?y () ();; val test2 : ?x:int -> ?y:int -> unit -> int * int * int = >> << # test2 ?x:None;; - : ?y:int -> unit -> int * int * int = >> 4.2 Labels and type inference *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* While they provide an increased comfort for writing function applications, labels and optional arguments have the pitfall that they cannot be inferred as completely as the rest of the language. You can see it in the following two examples. << # let h' g = g ~y:2 ~x:3;; val h' : (y:int -> x:int -> 'a) -> 'a = >> << # h' f ;; Error: This expression has type x:int -> y:int -> int but an expression was expected of type y:int -> x:int -> 'a >> << # let bump_it bump x = bump ~step:2 x;; val bump_it : (step:int -> 'a -> 'b) -> 'a -> 'b = >> << # bump_it bump 1 ;; Error: This expression has type ?step:int -> int -> int but an expression was expected of type step:int -> 'a -> 'b >> The first case is simple: g is passed ~y and then ~x, but f expects ~x and then ~y. This is correctly handled if we know the type of g to be x:int -> y:int -> int in advance, but otherwise this causes the above type clash. The simplest workaround is to apply formal parameters in a standard order. The second example is more subtle: while we intended the argument bump to be of type ?step:int -> int -> int, it is inferred as step:int -> int -> 'a. These two types being incompatible (internally normal and optional arguments are different), a type error occurs when applying bump_it to the real bump. We will not try here to explain in detail how type inference works. One must just understand that there is not enough information in the above program to deduce the correct type of g or bump. That is, there is no way to know whether an argument is optional or not, or which is the correct order, by looking only at how a function is applied. The strategy used by the compiler is to assume that there are no optional arguments, and that applications are done in the right order. The right way to solve this problem for optional parameters is to add a type annotation to the argument bump. << # let bump_it (bump : ?step:int -> int -> int) x = bump ~step:2 x;; val bump_it : (?step:int -> int -> int) -> int -> int = >> << # bump_it bump 1;; - : int = 3 >> In practice, such problems appear mostly when using objects whose methods have optional arguments, so writing the type of object arguments is often a good idea. Normally the compiler generates a type error if you attempt to pass to a function a parameter whose type is different from the expected one. However, in the specific case where the expected type is a non-labeled function type, and the argument is a function expecting optional parameters, the compiler will attempt to transform the argument to have it match the expected type, by passing None for all optional parameters. << # let twice f (x : int) = f(f x);; val twice : (int -> int) -> int -> int = >> << # twice bump 2;; - : int = 8 >> This transformation is coherent with the intended semantics, including side-effects. That is, if the application of optional parameters shall produce side-effects, these are delayed until the received function is really applied to an argument. 4.3 Suggestions for labeling *=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Like for names, choosing labels for functions is not an easy task. A good labeling is one which - makes programs more readable, - is easy to remember, - when possible, allows useful partial applications. We explain here the rules we applied when labeling OCaml libraries. To speak in an “object-oriented” way, one can consider that each function has a main argument, its object, and other arguments related with its action, the parameters. To permit the combination of functions through functionals in commuting label mode, the object will not be labeled. Its role is clear from the function itself. The parameters are labeled with names reminding of their nature or their role. The best labels combine nature and role. When this is not possible the role is to be preferred, since the nature will often be given by the type itself. Obscure abbreviations should be avoided. << ListLabels.map : f:('a -> 'b) -> 'a list -> 'b list UnixLabels.write : file_descr -> buf:bytes -> pos:int -> len:int -> unit >> When there are several objects of same nature and role, they are all left unlabeled. << ListLabels.iter2 : f:('a -> 'b -> unit) -> 'a list -> 'b list -> unit >> When there is no preferable object, all arguments are labeled. << BytesLabels.blit : src:bytes -> src_pos:int -> dst:bytes -> dst_pos:int -> len:int -> unit >> However, when there is only one argument, it is often left unlabeled. << BytesLabels.create : int -> bytes >> This principle also applies to functions of several arguments whose return type is a type variable, as long as the role of each argument is not ambiguous. Labeling such functions may lead to awkward error messages when one attempts to omit labels in an application, as we have seen with ListLabels.fold_left. Here are some of the label names you will find throughout the libraries. ------------------------------------------------------- |Label| Meaning | ------------------------------------------------------- | f: |a function to be applied | |pos: |a position in a string, array or byte sequence | |len: |a length | |buf: |a byte sequence or string used as buffer | |src: |the source of an operation | |dst: |the destination of an operation | |init:|the initial value for an iterator | |cmp: |a comparison function, e.g. Stdlib.compare | |mode:|an operation mode or a flag list | ------------------------------------------------------- All these are only suggestions, but keep in mind that the choice of labels is essential for readability. Bizarre choices will make the program harder to maintain. In the ideal, the right function name with right labels should be enough to understand the function’s meaning. Since one can get this information with OCamlBrowser or the ocaml toplevel, the documentation is only used when a more detailed specification is needed. Chapter 5  Polymorphic variants *********************************** (Chapter written by Jacques Garrigue) Variants as presented in section 1.4 are a powerful tool to build data structures and algorithms. However they sometimes lack flexibility when used in modular programming. This is due to the fact that every constructor is assigned to a unique type when defined and used. Even if the same name appears in the definition of multiple types, the constructor itself belongs to only one type. Therefore, one cannot decide that a given constructor belongs to multiple types, or consider a value of some type to belong to some other type with more constructors. With polymorphic variants, this original assumption is removed. That is, a variant tag does not belong to any type in particular, the type system will just check that it is an admissible value according to its use. You need not define a type before using a variant tag. A variant type will be inferred independently for each of its uses. 5.1 Basic use *=*=*=*=*=*=*=* In programs, polymorphic variants work like usual ones. You just have to prefix their names with a backquote character `. << # [`On; `Off];; - : [> `Off | `On ] list = [`On; `Off] >> << # `Number 1;; - : [> `Number of int ] = `Number 1 >> << # let f = function `On -> 1 | `Off -> 0 | `Number n -> n;; val f : [< `Number of int | `Off | `On ] -> int = >> << # List.map f [`On; `Off];; - : int list = [1; 0] >> [>`Off|`On] list means that to match this list, you should at least be able to match `Off and `On, without argument. [<`On|`Off|`Number of int] means that f may be applied to `Off, `On (both without argument), or `Number n where n is an integer. The > and < inside the variant types show that they may still be refined, either by defining more tags or by allowing less. As such, they contain an implicit type variable. Because each of the variant types appears only once in the whole type, their implicit type variables are not shown. The above variant types were polymorphic, allowing further refinement. When writing type annotations, one will most often describe fixed variant types, that is types that cannot be refined. This is also the case for type abbreviations. Such types do not contain < or >, but just an enumeration of the tags and their associated types, just like in a normal datatype definition. << # type 'a vlist = [`Nil | `Cons of 'a * 'a vlist];; type 'a vlist = [ `Cons of 'a * 'a vlist | `Nil ] >> << # let rec map f : 'a vlist -> 'b vlist = function | `Nil -> `Nil | `Cons(a, l) -> `Cons(f a, map f l) ;; val map : ('a -> 'b) -> 'a vlist -> 'b vlist = >> 5.2 Advanced use *=*=*=*=*=*=*=*=*= Type-checking polymorphic variants is a subtle thing, and some expressions may result in more complex type information. << # let f = function `A -> `C | `B -> `D | x -> x;; val f : ([> `A | `B | `C | `D ] as 'a) -> 'a = >> << # f `E;; - : [> `A | `B | `C | `D | `E ] = `E >> Here we are seeing two phenomena. First, since this matching is open (the last case catches any tag), we obtain the type [> `A | `B] rather than [< `A | `B] in a closed matching. Then, since x is returned as is, input and return types are identical. The notation as 'a denotes such type sharing. If we apply f to yet another tag `E, it gets added to the list. << # let f1 = function `A x -> x = 1 | `B -> true | `C -> false let f2 = function `A x -> x = "a" | `B -> true ;; val f1 : [< `A of int | `B | `C ] -> bool = val f2 : [< `A of string | `B ] -> bool = >> << # let f x = f1 x && f2 x;; val f : [< `A of string & int | `B ] -> bool = >> Here f1 and f2 both accept the variant tags `A and `B, but the argument of `A is int for f1 and string for f2. In f’s type `C, only accepted by f1, disappears, but both argument types appear for `A as int & string. This means that if we pass the variant tag `A to f, its argument should be both int and string. Since there is no such value, f cannot be applied to `A, and `B is the only accepted input. Even if a value has a fixed variant type, one can still give it a larger type through coercions. Coercions are normally written with both the source type and the destination type, but in simple cases the source type may be omitted. << # type 'a wlist = [`Nil | `Cons of 'a * 'a wlist | `Snoc of 'a wlist * 'a];; type 'a wlist = [ `Cons of 'a * 'a wlist | `Nil | `Snoc of 'a wlist * 'a ] >> << # let wlist_of_vlist l = (l : 'a vlist :> 'a wlist);; val wlist_of_vlist : 'a vlist -> 'a wlist = >> << # let open_vlist l = (l : 'a vlist :> [> 'a vlist]);; val open_vlist : 'a vlist -> [> 'a vlist ] = >> << # fun x -> (x :> [`A|`B|`C]);; - : [< `A | `B | `C ] -> [ `A | `B | `C ] = >> You may also selectively coerce values through pattern matching. << # let split_cases = function | `Nil | `Cons _ as x -> `A x | `Snoc _ as x -> `B x ;; val split_cases : [< `Cons of 'a | `Nil | `Snoc of 'b ] -> [> `A of [> `Cons of 'a | `Nil ] | `B of [> `Snoc of 'b ] ] = >> When an or-pattern composed of variant tags is wrapped inside an alias-pattern, the alias is given a type containing only the tags enumerated in the or-pattern. This allows for many useful idioms, like incremental definition of functions. << # let num x = `Num x let eval1 eval (`Num x) = x let rec eval x = eval1 eval x ;; val num : 'a -> [> `Num of 'a ] = val eval1 : 'a -> [< `Num of 'b ] -> 'b = val eval : [< `Num of 'a ] -> 'a = >> << # let plus x y = `Plus(x,y) let eval2 eval = function | `Plus(x,y) -> eval x + eval y | `Num _ as x -> eval1 eval x let rec eval x = eval2 eval x ;; val plus : 'a -> 'b -> [> `Plus of 'a * 'b ] = val eval2 : ('a -> int) -> [< `Num of int | `Plus of 'a * 'a ] -> int = val eval : ([< `Num of int | `Plus of 'a * 'a ] as 'a) -> int = >> To make this even more comfortable, you may use type definitions as abbreviations for or-patterns. That is, if you have defined type myvariant = [`Tag1 of int | `Tag2 of bool], then the pattern #myvariant is equivalent to writing (`Tag1(_ : int) | `Tag2(_ : bool)). Such abbreviations may be used alone, << # let f = function | #myvariant -> "myvariant" | `Tag3 -> "Tag3";; val f : [< `Tag1 of int | `Tag2 of bool | `Tag3 ] -> string = >> or combined with with aliases. << # let g1 = function `Tag1 _ -> "Tag1" | `Tag2 _ -> "Tag2";; val g1 : [< `Tag1 of 'a | `Tag2 of 'b ] -> string = >> << # let g = function | #myvariant as x -> g1 x | `Tag3 -> "Tag3";; val g : [< `Tag1 of int | `Tag2 of bool | `Tag3 ] -> string = >> 5.3 Weaknesses of polymorphic variants *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= After seeing the power of polymorphic variants, one may wonder why they were added to core language variants, rather than replacing them. The answer is twofold. The first aspect is that while being pretty efficient, the lack of static type information allows for less optimizations, and makes polymorphic variants slightly heavier than core language ones. However noticeable differences would only appear on huge data structures. More important is the fact that polymorphic variants, while being type-safe, result in a weaker type discipline. That is, core language variants do actually much more than ensuring type-safety, they also check that you use only declared constructors, that all constructors present in a data-structure are compatible, and they enforce typing constraints to their parameters. For this reason, you must be more careful about making types explicit when you use polymorphic variants. When you write a library, this is easy since you can describe exact types in interfaces, but for simple programs you are probably better off with core language variants. Beware also that some idioms make trivial errors very hard to find. For instance, the following code is probably wrong but the compiler has no way to see it. << # type abc = [`A | `B | `C] ;; type abc = [ `A | `B | `C ] >> << # let f = function | `As -> "A" | #abc -> "other" ;; val f : [< `A | `As | `B | `C ] -> string = >> << # let f : abc -> string = f ;; val f : abc -> string = >> You can avoid such risks by annotating the definition itself. << # let f : abc -> string = function | `As -> "A" | #abc -> "other" ;; Error: This pattern matches values of type [? `As ] but a pattern was expected which matches values of type abc The second variant type does not allow tag(s) `As >> Chapter 6  Polymorphism and its limitations *********************************************** This chapter covers more advanced questions related to the limitations of polymorphic functions and types. There are some situations in OCaml where the type inferred by the type checker may be less generic than expected. Such non-genericity can stem either from interactions between side-effects and typing or the difficulties of implicit polymorphic recursion and higher-rank polymorphism. This chapter details each of these situations and, if it is possible, how to recover genericity. 6.1 Weak polymorphism and mutation *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= 6.1.1 Weakly polymorphic types ================================ Maybe the most frequent examples of non-genericity derive from the interactions between polymorphic types and mutation. A simple example appears when typing the following expression << # let store = ref None ;; val store : '_weak1 option ref = {contents = None} >> Since the type of None is 'a option and the function ref has type 'b -> 'b ref, a natural deduction for the type of store would be 'a option ref. However, the inferred type, '_weak1 option ref, is different. Type variables whose names start with a _weak prefix like '_weak1 are weakly polymorphic type variables, sometimes shortened to “weak type variables”. A weak type variable is a placeholder for a single type that is currently unknown. Once the specific type t behind the placeholder type '_weak1 is known, all occurrences of '_weak1 will be replaced by t. For instance, we can define another option reference and store an int inside: << # let another_store = ref None ;; val another_store : '_weak2 option ref = {contents = None} >> << # another_store := Some 0; another_store ;; - : int option ref = {contents = Some 0} >> After storing an int inside another_store, the type of another_store has been updated from '_weak2 option ref to int option ref. This distinction between weakly and generic polymorphic type variable protects OCaml programs from unsoundness and runtime errors. To understand from where unsoundness might come, consider this simple function which swaps a value x with the value stored inside a store reference, if there is such value: << # let swap store x = match !store with | None -> store := Some x; x | Some y -> store := Some x; y;; val swap : 'a option ref -> 'a -> 'a = >> We can apply this function to our store << # let one = swap store 1 let one_again = swap store 2 let two = swap store 3;; val one : int = 1 val one_again : int = 1 val two : int = 2 >> After these three swaps the stored value is 3. Everything is fine up to now. We can then try to swap 3 with a more interesting value, for instance a function: << # let error = swap store (fun x -> x);; Error: This expression should not be a function, the expected type is int >> At this point, the type checker rightfully complains that it is not possible to swap an integer and a function, and that an int should always be traded for another int. Furthermore, the type checker prevents us from manually changing the type of the value stored by store: << # store := Some (fun x -> x);; Error: This expression should not be a function, the expected type is int >> Indeed, looking at the type of store, we see that the weak type '_weak1 has been replaced by the type int << # store;; - : int option ref = {contents = Some 3} >> Therefore, after placing an int in store, we cannot use it to store any value other than an int. More generally, weak types protect the program from undue mutation of values with a polymorphic type. Moreover, weak types cannot appear in the signature of toplevel modules: types must be known at compilation time. Otherwise, different compilation units could replace the weak type with different and incompatible types. For this reason, compiling the following small piece of code <> yields a compilation error <> To solve this error, it is enough to add an explicit type annotation to specify the type at declaration time: <> This is in any case a good practice for such global mutable variables. Otherwise, they will pick out the type of first use. If there is a mistake at this point, it can result in confusing type errors when later, correct uses are flagged as errors. 6.1.2 The value restriction ============================= Identifying the exact context in which polymorphic types should be replaced by weak types in a modular way is a difficult question. Indeed the type system must handle the possibility that functions may hide persistent mutable states. For instance, the following function uses an internal reference to implement a delayed identity function << # let make_fake_id () = let store = ref None in fun x -> swap store x ;; val make_fake_id : unit -> 'a -> 'a = >> << # let fake_id = make_fake_id();; val fake_id : '_weak3 -> '_weak3 = >> It would be unsound to apply this fake_id function to values with different types. The function fake_id is therefore rightfully assigned the type '_weak3 -> '_weak3 rather than 'a -> 'a. At the same time, it ought to be possible to use a local mutable state without impacting the type of a function. To circumvent these dual difficulties, the type checker considers that any value returned by a function might rely on persistent mutable states behind the scene and should be given a weak type. This restriction on the type of mutable values and the results of function application is called the value restriction. Note that this value restriction is conservative: there are situations where the value restriction is too cautious and gives a weak type to a value that could be safely generalized to a polymorphic type: << # let not_id = (fun x -> x) (fun x -> x);; val not_id : '_weak4 -> '_weak4 = >> Quite often, this happens when defining functions using higher order functions. To avoid this problem, a solution is to add an explicit argument to the function: << # let id_again = fun x -> (fun x -> x) (fun x -> x) x;; val id_again : 'a -> 'a = >> With this argument, id_again is seen as a function definition by the type checker and can therefore be generalized. This kind of manipulation is called eta-expansion in lambda calculus and is sometimes referred under this name. 6.1.3 The relaxed value restriction ===================================== There is another partial solution to the problem of unnecessary weak types, which is implemented directly within the type checker. Briefly, it is possible to prove that weak types that only appear as type parameters in covariant positions –also called positive positions– can be safely generalized to polymorphic types. For instance, the type 'a list is covariant in 'a: << # let f () = [];; val f : unit -> 'a list = >> << # let empty = f ();; val empty : 'a list = [] >> Note that the type inferred for empty is 'a list and not the '_weak5 list that should have occurred with the value restriction. The value restriction combined with this generalization for covariant type parameters is called the relaxed value restriction. 6.1.4 Variance and value restriction ====================================== Variance describes how type constructors behave with respect to subtyping. Consider for instance a pair of type x and xy with x a subtype of xy, denoted x :> xy: << # type x = [ `X ];; type x = [ `X ] >> << # type xy = [ `X | `Y ];; type xy = [ `X | `Y ] >> As x is a subtype of xy, we can convert a value of type x to a value of type xy: << # let x:x = `X;; val x : x = `X >> << # let x' = ( x :> xy);; val x' : xy = `X >> Similarly, if we have a value of type x list, we can convert it to a value of type xy list, since we could convert each element one by one: << # let l:x list = [`X; `X];; val l : x list = [`X; `X] >> << # let l' = ( l :> xy list);; val l' : xy list = [`X; `X] >> In other words, x :> xy implies that x list :> xy list, therefore the type constructor 'a list is covariant (it preserves subtyping) in its parameter 'a. Contrarily, if we have a function that can handle values of type xy << # let f: xy -> unit = function | `X -> () | `Y -> ();; val f : xy -> unit = >> it can also handle values of type x: << # let f' = (f :> x -> unit);; val f' : x -> unit = >> Note that we can rewrite the type of f and f' as << # type 'a proc = 'a -> unit let f' = (f: xy proc :> x proc);; type 'a proc = 'a -> unit val f' : x proc = >> In this case, we have x :> xy implies xy proc :> x proc. Notice that the second subtyping relation reverse the order of x and xy: the type constructor 'a proc is contravariant in its parameter 'a. More generally, the function type constructor 'a -> 'b is covariant in its return type 'b and contravariant in its argument type 'a. A type constructor can also be invariant in some of its type parameters, neither covariant nor contravariant. A typical example is a reference: << # let x: x ref = ref `X;; val x : x ref = {contents = `X} >> If we were able to coerce x to the type xy ref as a variable xy, we could use xy to store the value `Y inside the reference and then use the x value to read this content as a value of type x, which would break the type system. More generally, as soon as a type variable appears in a position describing mutable state it becomes invariant. As a corollary, covariant variables will never denote mutable locations and can be safely generalized. For a better description, interested readers can consult the original article by Jacques Garrigue on http://www.math.nagoya-u.ac.jp/~garrigue/papers/morepoly-long.pdf Together, the relaxed value restriction and type parameter covariance help to avoid eta-expansion in many situations. 6.1.5 Abstract data types =========================== Moreover, when the type definitions are exposed, the type checker is able to infer variance information on its own and one can benefit from the relaxed value restriction even unknowingly. However, this is not the case anymore when defining new abstract types. As an illustration, we can define a module type collection as: << # module type COLLECTION = sig type 'a t val empty: unit -> 'a t end module Implementation = struct type 'a t = 'a list let empty ()= [] end;; module type COLLECTION = sig type 'a t val empty : unit -> 'a t end module Implementation : sig type 'a t = 'a list val empty : unit -> 'a list end >> << # module List2: COLLECTION = Implementation;; module List2 : COLLECTION >> In this situation, when coercing the module List2 to the module type COLLECTION, the type checker forgets that 'a List2.t was covariant in 'a. Consequently, the relaxed value restriction does not apply anymore: << # List2.empty ();; - : '_weak5 List2.t = >> To keep the relaxed value restriction, we need to declare the abstract type 'a COLLECTION.t as covariant in 'a: << # module type COLLECTION = sig type +'a t val empty: unit -> 'a t end module List2: COLLECTION = Implementation;; module type COLLECTION = sig type +'a t val empty : unit -> 'a t end module List2 : COLLECTION >> We then recover polymorphism: << # List2.empty ();; - : 'a List2.t = >> 6.2 Polymorphic recursion *=*=*=*=*=*=*=*=*=*=*=*=*=* The second major class of non-genericity is directly related to the problem of type inference for polymorphic functions. In some circumstances, the type inferred by OCaml might be not general enough to allow the definition of some recursive functions, in particular for recursive functions acting on non-regular algebraic data types. With a regular polymorphic algebraic data type, the type parameters of the type constructor are constant within the definition of the type. For instance, we can look at arbitrarily nested list defined as: << # type 'a regular_nested = List of 'a list | Nested of 'a regular_nested li st let l = Nested[ List [1]; Nested [List[2;3]]; Nested[Nested[]] ];; type 'a regular_nested = List of 'a list | Nested of 'a regular_nested list val l : int regular_nested = Nested [List [1]; Nested [List [2; 3]]; Nested [Nested []]] >> Note that the type constructor regular_nested always appears as 'a regular_nested in the definition above, with the same parameter 'a. Equipped with this type, one can compute a maximal depth with a classic recursive function << # let rec maximal_depth = function | List _ -> 1 | Nested [] -> 0 | Nested (a::q) -> 1 + max (maximal_depth a) (maximal_depth (Nested q));; val maximal_depth : 'a regular_nested -> int = >> Non-regular recursive algebraic data types correspond to polymorphic algebraic data types whose parameter types vary between the left and right side of the type definition. For instance, it might be interesting to define a datatype that ensures that all lists are nested at the same depth: << # type 'a nested = List of 'a list | Nested of 'a list nested;; type 'a nested = List of 'a list | Nested of 'a list nested >> Intuitively, a value of type 'a nested is a list of list ...of list of elements a with k nested list. We can then adapt the maximal_depth function defined on regular_depth into a depth function that computes this k. As a first try, we may define << # let rec depth = function | List _ -> 1 | Nested n -> 1 + depth n;; Error: This expression has type 'a list nested but an expression was expected of type 'a nested The type variable 'a occurs inside 'a list >> The type error here comes from the fact that during the definition of depth, the type checker first assigns to depth the type 'a -> 'b . When typing the pattern matching, 'a -> 'b becomes 'a nested -> 'b, then 'a nested -> int once the List branch is typed. However, when typing the application depth n in the Nested branch, the type checker encounters a problem: depth n is applied to 'a list nested, it must therefore have the type 'a list nested -> 'b. Unifying this constraint with the previous one leads to the impossible constraint 'a list nested = 'a nested. In other words, within its definition, the recursive function depth is applied to values of type 'a t with different types 'a due to the non-regularity of the type constructor nested. This creates a problem because the type checker had introduced a new type variable 'a only at the definition of the function depth whereas, here, we need a different type variable for every application of the function depth. 6.2.1 Explicitly polymorphic annotations ========================================== The solution of this conundrum is to use an explicitly polymorphic type annotation for the type 'a: << # let rec depth: 'a. 'a nested -> int = function | List _ -> 1 | Nested n -> 1 + depth n;; val depth : 'a nested -> int = >> << # depth ( Nested(List [ [7]; [8] ]) );; - : int = 2 >> In the type of depth, 'a.'a nested -> int, the type variable 'a is universally quantified. In other words, 'a.'a nested -> int reads as “for all type 'a, depth maps 'a nested values to integers”. Whereas the standard type 'a nested -> int can be interpreted as “let be a type variable 'a, then depth maps 'a nested values to integers”. There are two major differences with these two type expressions. First, the explicit polymorphic annotation indicates to the type checker that it needs to introduce a new type variable every time the function depth is applied. This solves our problem with the definition of the function depth. Second, it also notifies the type checker that the type of the function should be polymorphic. Indeed, without explicit polymorphic type annotation, the following type annotation is perfectly valid << # let sum: 'a -> 'b -> 'c = fun x y -> x + y;; val sum : int -> int -> int = >> since 'a,'b and 'c denote type variables that may or may not be polymorphic. Whereas, it is an error to unify an explicitly polymorphic type with a non-polymorphic type: << # let sum: 'a 'b 'c. 'a -> 'b -> 'c = fun x y -> x + y;; Error: This definition has type int -> int -> int which is less general than 'a 'b 'c. 'a -> 'b -> 'c >> An important remark here is that it is not needed to explicit fully the type of depth: it is sufficient to add annotations only for the universally quantified type variables: << # let rec depth: 'a. 'a nested -> _ = function | List _ -> 1 | Nested n -> 1 + depth n;; val depth : 'a nested -> int = >> << # depth ( Nested(List [ [7]; [8] ]) );; - : int = 2 >> 6.2.2 More examples ===================== With explicit polymorphic annotations, it becomes possible to implement any recursive function that depends only on the structure of the nested lists and not on the type of the elements. For instance, a more complex example would be to compute the total number of elements of the nested lists: << # let len nested = let map_and_sum f = List.fold_left (fun acc x -> acc + f x) 0 in let rec len: 'a. ('a list -> int ) -> 'a nested -> int = fun nested_len n -> match n with | List l -> nested_len l | Nested n -> len (map_and_sum nested_len) n in len List.length nested;; val len : 'a nested -> int = >> << # len (Nested(Nested(List [ [ [1;2]; [3] ]; [ []; [4]; [5;6;7]]; [[]] ])));; - : int = 7 >> Similarly, it may be necessary to use more than one explicitly polymorphic type variables, like for computing the nested list of list lengths of the nested list: << # let shape n = let rec shape: 'a 'b. ('a nested -> int nested) -> ('b list list -> 'a list) -> 'b nested -> int nested = fun nest nested_shape -> function | List l -> raise (Invalid_argument "shape requires nested_list of depth greater than 1") | Nested (List l) -> nest @@ List (nested_shape l) | Nested n -> let nested_shape = List.map nested_shape in let nest x = nest (Nested x) in shape nest nested_shape n in shape (fun n -> n ) (fun l -> List.map List.length l ) n;; val shape : 'a nested -> int nested = >> << # shape (Nested(Nested(List [ [ [1;2]; [3] ]; [ []; [4]; [5;6;7]]; [[]] ]))); ; - : int nested = Nested (List [[2; 1]; [0; 1; 3]; [0]]) >> 6.3 Higher-rank polymorphic functions *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Explicit polymorphic annotations are however not sufficient to cover all the cases where the inferred type of a function is less general than expected. A similar problem arises when using polymorphic functions as arguments of higher-order functions. For instance, we may want to compute the average depth or length of two nested lists: << # let average_depth x y = (depth x + depth y) / 2;; val average_depth : 'a nested -> 'b nested -> int = >> << # let average_len x y = (len x + len y) / 2;; val average_len : 'a nested -> 'b nested -> int = >> << # let one = average_len (List [2]) (List [[]]);; val one : int = 1 >> It would be natural to factorize these two definitions as: << # let average f x y = (f x + f y) / 2;; val average : ('a -> int) -> 'a -> 'a -> int = >> However, the type of average len is less generic than the type of average_len, since it requires the type of the first and second argument to be the same: << # average_len (List [2]) (List [[]]);; - : int = 1 >> << # average len (List [2]) (List [[]]);; Error: This expression has type 'a list but an expression was expected of type int >> As previously with polymorphic recursion, the problem stems from the fact that type variables are introduced only at the start of the let definitions. When we compute both f x and f y, the type of x and y are unified together. To avoid this unification, we need to indicate to the type checker that f is polymorphic in its first argument. In some sense, we would want average to have type < int) -> 'a nested -> 'b nested -> int >> Note that this syntax is not valid within OCaml: average has an universally quantified type 'a inside the type of one of its argument whereas for polymorphic recursion the universally quantified type was introduced before the rest of the type. This position of the universally quantified type means that average is a second-rank polymorphic function. This kind of higher-rank functions is not directly supported by OCaml: type inference for second-rank polymorphic function and beyond is undecidable; therefore using this kind of higher-rank functions requires to handle manually these universally quantified types. In OCaml, there are two ways to introduce this kind of explicit universally quantified types: universally quantified record fields, << # type 'a nested_reduction = { f:'elt. 'elt nested -> 'a };; type 'a nested_reduction = { f : 'elt. 'elt nested -> 'a; } >> << # let boxed_len = { f = len };; val boxed_len : int nested_reduction = {f = } >> and universally quantified object methods: << # let obj_len = object method f:'a. 'a nested -> 'b = len end;; val obj_len : < f : 'a. 'a nested -> int > = >> To solve our problem, we can therefore use either the record solution: << # let average nsm x y = (nsm.f x + nsm.f y) / 2 ;; val average : int nested_reduction -> 'a nested -> 'b nested -> int = >> or the object one: << # let average (obj: _ > ) x y = (obj#f x + obj#f y) / 2 ;; val average : < f : 'a. 'a nested -> int > -> 'b nested -> 'c nested -> int = >> Chapter 7  Generalized algebraic datatypes ********************************************** Generalized algebraic datatypes, or GADTs, extend usual sum types in two ways: constraints on type parameters may change depending on the value constructor, and some type variables may be existentially quantified. Adding constraints is done by giving an explicit return type, where type parameters are instantiated: << type _ term = | Int : int -> int term | Add : (int -> int -> int) term | App : ('b -> 'a) term * 'b term -> 'a term >> This return type must use the same type constructor as the type being defined, and have the same number of parameters. Variables are made existential when they appear inside a constructor’s argument, but not in its return type. Since the use of a return type often eliminates the need to name type parameters in the left-hand side of a type definition, one can replace them with anonymous types _ in that case. The constraints associated to each constructor can be recovered through pattern-matching. Namely, if the type of the scrutinee of a pattern-matching contains a locally abstract type, this type can be refined according to the constructor used. These extra constraints are only valid inside the corresponding branch of the pattern-matching. If a constructor has some existential variables, fresh locally abstract types are generated, and they must not escape the scope of this branch. 7.1 Recursive functions *=*=*=*=*=*=*=*=*=*=*=*=* We write an eval function: << let rec eval : type a. a term -> a = function | Int n -> n (* a = int *) | Add -> (fun x y -> x+y) (* a = int -> int -> int *) | App(f,x) -> (eval f) (eval x) (* eval called at types (b->a) and b for fresh b *) >> And use it: << let two = eval (App (App (Add, Int 1), Int 1)) val two : int = 2 >> It is important to remark that the function eval is using the polymorphic syntax for locally abstract types. When defining a recursive function that manipulates a GADT, explicit polymorphic recursion should generally be used. For instance, the following definition fails with a type error: << let rec eval (type a) : a term -> a = function | Int n -> n | Add -> (fun x y -> x+y) | App(f,x) -> (eval f) (eval x) Error: This expression has type ($b -> a) term but an expression was expected of type 'a The type constructor $b would escape its scope Hint: $b is an existential type bound by the constructor App. >> In absence of an explicit polymorphic annotation, a monomorphic type is inferred for the recursive function. If a recursive call occurs inside the function definition at a type that involves an existential GADT type variable, this variable flows to the type of the recursive function, and thus escapes its scope. In the above example, this happens in the branch App(f,x) when eval is called with f as an argument. In this branch, the type of f is ($App_'b -> a) term. The prefix $ in $App_'b denotes an existential type named by the compiler (see 7.5). Since the type of eval is 'a term -> 'a, the call eval f makes the existential type $App_'b flow to the type variable 'a and escape its scope. This triggers the above error. 7.2 Type inference *=*=*=*=*=*=*=*=*=*= Type inference for GADTs is notoriously hard. This is due to the fact some types may become ambiguous when escaping from a branch. For instance, in the Int case above, n could have either type int or a, and they are not equivalent outside of that branch. As a first approximation, type inference will always work if a pattern-matching is annotated with types containing no free type variables (both on the scrutinee and the return type). This is the case in the above example, thanks to the type annotation containing only locally abstract types. In practice, type inference is a bit more clever than that: type annotations do not need to be immediately on the pattern-matching, and the types do not have to be always closed. As a result, it is usually enough to only annotate functions, as in the example above. Type annotations are propagated in two ways: for the scrutinee, they follow the flow of type inference, in a way similar to polymorphic methods; for the return type, they follow the structure of the program, they are split on functions, propagated to all branches of a pattern matching, and go through tuples, records, and sum types. Moreover, the notion of ambiguity used is stronger: a type is only seen as ambiguous if it was mixed with incompatible types (equated by constraints), without type annotations between them. For instance, the following program types correctly. << let rec sum : type a. a term -> _ = fun x -> let y = match x with | Int n -> n | Add -> 0 | App(f,x) -> sum f + sum x in y + 1 val sum : 'a term -> int = >> Here the return type int is never mixed with a, so it is seen as non-ambiguous, and can be inferred. When using such partial type annotations we strongly suggest specifying the -principal mode, to check that inference is principal. The exhaustiveness check is aware of GADT constraints, and can automatically infer that some cases cannot happen. For instance, the following pattern matching is correctly seen as exhaustive (the Add case cannot happen). << let get_int : int term -> int = function | Int n -> n | App(_,_) -> 0 >> 7.3 Refutation cases *=*=*=*=*=*=*=*=*=*=*= Usually, the exhaustiveness check only tries to check whether the cases omitted from the pattern matching are typable or not. However, you can force it to try harder by adding refutation cases, written as a full stop. In the presence of a refutation case, the exhaustiveness check will first compute the intersection of the pattern with the complement of the cases preceding it. It then checks whether the resulting patterns can really match any concrete values by trying to type-check them. Wild cards in the generated patterns are handled in a special way: if their type is a variant type with only GADT constructors, then the pattern is split into the different constructors, in order to check whether any of them is possible (this splitting is not done for arguments of these constructors, to avoid non-termination). We also split tuples and variant types with only one case, since they may contain GADTs inside. For instance, the following code is deemed exhaustive: << type _ t = | Int : int t | Bool : bool t let deep : (char t * int) option -> char = function | None -> 'c' | _ -> . >> Namely, the inferred remaining case is Some _, which is split into Some (Int, _) and Some (Bool, _), which are both untypable because deep expects a non-existing char t as the first element of the tuple. Note that the refutation case could be omitted here, because it is automatically added when there is only one case in the pattern matching. Another addition is that the redundancy check is now aware of GADTs: a case will be detected as redundant if it could be replaced by a refutation case using the same pattern. 7.4 Advanced examples *=*=*=*=*=*=*=*=*=*=*=* The term type we have defined above is an indexed type, where a type parameter reflects a property of the value contents. Another use of GADTs is singleton types, where a GADT value represents exactly one type. This value can be used as runtime representation for this type, and a function receiving it can have a polytypic behavior. Here is an example of a polymorphic function that takes the runtime representation of some type t and a value of the same type, then pretty-prints the value as a string: << type _ typ = | Int : int typ | String : string typ | Pair : 'a typ * 'b typ -> ('a * 'b) typ let rec to_string: type t. t typ -> t -> string = fun t x -> match t with | Int -> Int.to_string x | String -> Printf.sprintf "%S" x | Pair(t1,t2) -> let (x1, x2) = x in Printf.sprintf "(%s,%s)" (to_string t1 x1) (to_string t2 x2) >> Another frequent application of GADTs is equality witnesses. << type (_,_) eq = Eq : ('a,'a) eq let cast : type a b. (a,b) eq -> a -> b = fun Eq x -> x >> Here type eq has only one constructor, and by matching on it one adds a local constraint allowing the conversion between a and b. By building such equality witnesses, one can make equal types which are syntactically different. Here is an example using both singleton types and equality witnesses to implement dynamic types. << let rec eq_type : type a b. a typ -> b typ -> (a,b) eq option = fun a b -> match a, b with | Int, Int -> Some Eq | String, String -> Some Eq | Pair(a1,a2), Pair(b1,b2) -> begin match eq_type a1 b1, eq_type a2 b2 with | Some Eq, Some Eq -> Some Eq | _ -> None end | _ -> None type dyn = Dyn : 'a typ * 'a -> dyn let get_dyn : type a. a typ -> dyn -> a option = fun a (Dyn(b,x)) -> match eq_type a b with | None -> None | Some Eq -> Some x >> 7.5 Existential type names in error messages *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The typing of pattern matching in the presence of GADTs can generate many existential types. When necessary, error messages refer to these existential types using compiler-generated names. Currently, the compiler generates these names according to the following nomenclature: - First, types whose name starts with a $ are existentials. - $a denotes an existential type introduced for the type variable 'a of a GADT constructor: << type any = Any : 'name -> any let escape (Any x) = x Error: This expression has type $name but an expression was expected of ty pe 'a The type constructor $name would escape its scope Hint: $name is an existential type bound by the constructor Any. >> - $'a if the existential variable was unified with the type variable 'a during typing: << type ('arg,'result,'aux) fn = | Fun: ('a ->'b) -> ('a,'b,unit) fn | Mem1: ('a ->'b) * 'a * 'b -> ('a, 'b, 'a * 'b) fn let apply: ('arg,'result, _ ) fn -> 'arg -> 'result = fun f x -> match f with | Fun f -> f x | Mem1 (f,y,fy) -> if x = y then fy else f x Error: This pattern matches values of type ($'arg, 'result, $'arg * 'result) fn but a pattern was expected which matches values of type ($'arg, 'result, unit) fn The type constructor $'arg would escape its scope >> - $n (n a number) is an internally generated existential which could not be named using one of the previous schemes. As shown by the last item, the current behavior is imperfect and may be improved in future versions. 7.6 Explicit naming of existentials *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* As explained above, pattern-matching on a GADT constructor may introduce existential types. Syntax has been introduced which allows them to be named explicitly. For instance, the following code names the type of the argument of f and uses this name. << type _ closure = Closure : ('a -> 'b) * 'a -> 'b closure let eval = fun (Closure (type a) (f, x : (a -> _) * _)) -> f (x : a) >> All existential type variables of the constructor must by introduced by the (type ...) construct and bound by a type annotation on the outside of the constructor argument. 7.7 Equations on non-local abstract types *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* GADT pattern-matching may also add type equations to non-local abstract types. The behaviour is the same as with local abstract types. Reusing the above eq type, one can write: << module M : sig type t val x : t val e : (t,int) eq end = struct type t = int let x = 33 let e = Eq end let x : int = let Eq = M.e in M.x >> Of course, not all abstract types can be refined, as this would contradict the exhaustiveness check. Namely, builtin types (those defined by the compiler itself, such as int or array), and abstract types defined by the local module, are non-instantiable, and as such cause a type error rather than introduce an equation. Chapter 8  Advanced examples with classes and modules ********************************************************* (Chapter written by Didier Rémy) In this chapter, we show some larger examples using objects, classes and modules. We review many of the object features simultaneously on the example of a bank account. We show how modules taken from the standard library can be expressed as classes. Lastly, we describe a programming pattern known as virtual types through the example of window managers. 8.1 Extended example: bank accounts *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* In this section, we illustrate most aspects of Object and inheritance by refining, debugging, and specializing the following initial naive definition of a simple bank account. (We reuse the module Euro defined at the end of chapter 3.) << # let euro = new Euro.c;; val euro : float -> Euro.c = >> << # let zero = euro 0.;; val zero : Euro.c = >> << # let neg x = x#times (-1.);; val neg : < times : float -> 'a; .. > -> 'a = >> << # class account = object val mutable balance = zero method balance = balance method deposit x = balance <- balance # plus x method withdraw x = if x#leq balance then (balance <- balance # plus (neg x); x) else zer o end;; class account : object val mutable balance : Euro.c method balance : Euro.c method deposit : Euro.c -> unit method withdraw : Euro.c -> Euro.c end >> << # let c = new account in c # deposit (euro 100.); c # withdraw (euro 50.);; - : Euro.c = >> We now refine this definition with a method to compute interest. << # class account_with_interests = object (self) inherit account method private interest = self # deposit (self # balance # times 0.03) end;; class account_with_interests : object val mutable balance : Euro.c method balance : Euro.c method deposit : Euro.c -> unit method private interest : unit method withdraw : Euro.c -> Euro.c end >> We make the method interest private, since clearly it should not be called freely from the outside. Here, it is only made accessible to subclasses that will manage monthly or yearly updates of the account. We should soon fix a bug in the current definition: the deposit method can be used for withdrawing money by depositing negative amounts. We can fix this directly: << # class safe_account = object inherit account method deposit x = if zero#leq x then balance <- balance#plus x end;; class safe_account : object val mutable balance : Euro.c method balance : Euro.c method deposit : Euro.c -> unit method withdraw : Euro.c -> Euro.c end >> However, the bug might be fixed more safely by the following definition: << # class safe_account = object inherit account as unsafe method deposit x = if zero#leq x then unsafe # deposit x else raise (Invalid_argument "deposit") end;; class safe_account : object val mutable balance : Euro.c method balance : Euro.c method deposit : Euro.c -> unit method withdraw : Euro.c -> Euro.c end >> In particular, this does not require the knowledge of the implementation of the method deposit. To keep track of operations, we extend the class with a mutable field history and a private method trace to add an operation in the log. Then each method to be traced is redefined. << # type 'a operation = Deposit of 'a | Retrieval of 'a;; type 'a operation = Deposit of 'a | Retrieval of 'a >> << # class account_with_history = object (self) inherit safe_account as super val mutable history = [] method private trace x = history <- x :: history method deposit x = self#trace (Deposit x); super#deposit x method withdraw x = self#trace (Retrieval x); super#withdraw x method history = List.rev history end;; class account_with_history : object val mutable balance : Euro.c val mutable history : Euro.c operation list method balance : Euro.c method deposit : Euro.c -> unit method history : Euro.c operation list method private trace : Euro.c operation -> unit method withdraw : Euro.c -> Euro.c end >> One may wish to open an account and simultaneously deposit some initial amount. Although the initial implementation did not address this requirement, it can be achieved by using an initializer. << # class account_with_deposit x = object inherit account_with_history initializer balance <- x end;; class account_with_deposit : Euro.c -> object val mutable balance : Euro.c val mutable history : Euro.c operation list method balance : Euro.c method deposit : Euro.c -> unit method history : Euro.c operation list method private trace : Euro.c operation -> unit method withdraw : Euro.c -> Euro.c end >> A better alternative is: << # class account_with_deposit x = object (self) inherit account_with_history initializer self#deposit x end;; class account_with_deposit : Euro.c -> object val mutable balance : Euro.c val mutable history : Euro.c operation list method balance : Euro.c method deposit : Euro.c -> unit method history : Euro.c operation list method private trace : Euro.c operation -> unit method withdraw : Euro.c -> Euro.c end >> Indeed, the latter is safer since the call to deposit will automatically benefit from safety checks and from the trace. Let’s test it: << # let ccp = new account_with_deposit (euro 100.) in let _balance = ccp#withdraw (euro 50.) in ccp#history;; - : Euro.c operation list = [Deposit ; Retrieval ] >> Closing an account can be done with the following polymorphic function: << # let close c = c#withdraw c#balance;; val close : < balance : 'a; withdraw : 'a -> 'b; .. > -> 'b = >> Of course, this applies to all sorts of accounts. Finally, we gather several versions of the account into a module Account abstracted over some currency. << # let today () = (01,01,2000) (* an approximation *) module Account (M:MONEY) = struct type m = M.c let m = new M.c let zero = m 0. class bank = object (self) val mutable balance = zero method balance = balance val mutable history = [] method private trace x = history <- x::history method deposit x = self#trace (Deposit x); if zero#leq x then balance <- balance # plus x else raise (Invalid_argument "deposit") method withdraw x = if x#leq balance then (balance <- balance # plus (neg x); self#trace (Retrieval x); x ) else zero method history = List.rev history end class type client_view = object method deposit : m -> unit method history : m operation list method withdraw : m -> m method balance : m end class virtual check_client x = let y = if (m 100.)#leq x then x else raise (Failure "Insufficient initial deposit") in object (self) initializer self#deposit y method virtual deposit: m -> unit end module Client (B : sig class bank : client_view end) = struct class account x : client_view = object inherit B.bank inherit check_client x end let discount x = let c = new account x in if today() < (1998,10,30) then c # deposit (m 100.); c end end;; >> This shows the use of modules to group several class definitions that can in fact be thought of as a single unit. This unit would be provided by a bank for both internal and external uses. This is implemented as a functor that abstracts over the currency so that the same code can be used to provide accounts in different currencies. The class bank is the real implementation of the bank account (it could have been inlined). This is the one that will be used for further extensions, refinements, etc. Conversely, the client will only be given the client view. << # module Euro_account = Account(Euro);; >> << # module Client = Euro_account.Client (Euro_account);; >> << # new Client.account (new Euro.c 100.);; >> Hence, the clients do not have direct access to the balance, nor the history of their own accounts. Their only way to change their balance is to deposit or withdraw money. It is important to give the clients a class and not just the ability to create accounts (such as the promotional discount account), so that they can personalize their account. For instance, a client may refine the deposit and withdraw methods so as to do his own financial bookkeeping, automatically. On the other hand, the function discount is given as such, with no possibility for further personalization. It is important to provide the client’s view as a functor Client so that client accounts can still be built after a possible specialization of the bank. The functor Client may remain unchanged and be passed the new definition to initialize a client’s view of the extended account. << # module Investment_account (M : MONEY) = struct type m = M.c module A = Account(M) class bank = object inherit A.bank as super method deposit x = if (new M.c 1000.)#leq x then print_string "Would you like to invest?"; super#deposit x end module Client = A.Client end;; >> The functor Client may also be redefined when some new features of the account can be given to the client. << # module Internet_account (M : MONEY) = struct type m = M.c module A = Account(M) class bank = object inherit A.bank method mail s = print_string s end class type client_view = object method deposit : m -> unit method history : m operation list method withdraw : m -> m method balance : m method mail : string -> unit end module Client (B : sig class bank : client_view end) = struct class account x : client_view = object inherit B.bank inherit A.check_client x end end end;; >> 8.2 Simple modules as classes *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* One may wonder whether it is possible to treat primitive types such as integers and strings as objects. Although this is usually uninteresting for integers or strings, there may be some situations where this is desirable. The class money above is such an example. We show here how to do it for strings. 8.2.1 Strings =============== A naive definition of strings as objects could be: << # class ostring s = object method get n = String.get s n method print = print_string s method escaped = new ostring (String.escaped s) end;; class ostring : string -> object method escaped : ostring method get : int -> char method print : unit end >> However, the method escaped returns an object of the class ostring, and not an object of the current class. Hence, if the class is further extended, the method escaped will only return an object of the parent class. << # class sub_string s = object inherit ostring s method sub start len = new sub_string (String.sub s start len) end;; class sub_string : string -> object method escaped : ostring method get : int -> char method print : unit method sub : int -> int -> sub_string end >> As seen in section 3.16, the solution is to use functional update instead. We need to create an instance variable containing the representation s of the string. << # class better_string s = object val repr = s method get n = String.get repr n method print = print_string repr method escaped = {< repr = String.escaped repr >} method sub start len = {< repr = String.sub s start len >} end;; class better_string : string -> object ('a) val repr : string method escaped : 'a method get : int -> char method print : unit method sub : int -> int -> 'a end >> As shown in the inferred type, the methods escaped and sub now return objects of the same type as the one of the class. Another difficulty is the implementation of the method concat. In order to concatenate a string with another string of the same class, one must be able to access the instance variable externally. Thus, a method repr returning s must be defined. Here is the correct definition of strings: << # class ostring s = object (self : 'mytype) val repr = s method repr = repr method get n = String.get repr n method print = print_string repr method escaped = {< repr = String.escaped repr >} method sub start len = {< repr = String.sub s start len >} method concat (t : 'mytype) = {< repr = repr ^ t#repr >} end;; class ostring : string -> object ('a) val repr : string method concat : 'a -> 'a method escaped : 'a method get : int -> char method print : unit method repr : string method sub : int -> int -> 'a end >> Another constructor of the class string can be defined to return a new string of a given length: << # class cstring n = ostring (String.make n ' ');; class cstring : int -> ostring >> Here, exposing the representation of strings is probably harmless. We do could also hide the representation of strings as we hid the currency in the class money of section 3.17. Stacks ------ There is sometimes an alternative between using modules or classes for parametric data types. Indeed, there are situations when the two approaches are quite similar. For instance, a stack can be straightforwardly implemented as a class: << # exception Empty;; exception Empty >> << # class ['a] stack = object val mutable l = ([] : 'a list) method push x = l <- x::l method pop = match l with [] -> raise Empty | a::l' -> l <- l'; a method clear = l <- [] method length = List.length l end;; class ['a] stack : object val mutable l : 'a list method clear : unit method length : int method pop : 'a method push : 'a -> unit end >> However, writing a method for iterating over a stack is more problematic. A method fold would have type ('b -> 'a -> 'b) -> 'b -> 'b. Here 'a is the parameter of the stack. The parameter 'b is not related to the class 'a stack but to the argument that will be passed to the method fold. A naive approach is to make 'b an extra parameter of class stack: << # class ['a, 'b] stack2 = object inherit ['a] stack method fold f (x : 'b) = List.fold_left f x l end;; class ['a, 'b] stack2 : object val mutable l : 'a list method clear : unit method fold : ('b -> 'a -> 'b) -> 'b -> 'b method length : int method pop : 'a method push : 'a -> unit end >> However, the method fold of a given object can only be applied to functions that all have the same type: << # let s = new stack2;; val s : ('_weak1, '_weak2) stack2 = >> << # s#fold ( + ) 0;; - : int = 0 >> << # s;; - : (int, int) stack2 = >> A better solution is to use polymorphic methods, which were introduced in OCaml version 3.05. Polymorphic methods makes it possible to treat the type variable 'b in the type of fold as universally quantified, giving fold the polymorphic type Forall 'b. ('b -> 'a -> 'b) -> 'b -> 'b. An explicit type declaration on the method fold is required, since the type checker cannot infer the polymorphic type by itself. << # class ['a] stack3 = object inherit ['a] stack method fold : 'b. ('b -> 'a -> 'b) -> 'b -> 'b = fun f x -> List.fold_left f x l end;; class ['a] stack3 : object val mutable l : 'a list method clear : unit method fold : ('b -> 'a -> 'b) -> 'b -> 'b method length : int method pop : 'a method push : 'a -> unit end >> 8.2.2 Hashtbl =============== A simplified version of object-oriented hash tables should have the following class type. << # class type ['a, 'b] hash_table = object method find : 'a -> 'b method add : 'a -> 'b -> unit end;; class type ['a, 'b] hash_table = object method add : 'a -> 'b -> unit method find : 'a -> 'b end >> A simple implementation, which is quite reasonable for small hash tables is to use an association list: << # class ['a, 'b] small_hashtbl : ['a, 'b] hash_table = object val mutable table = [] method find key = List.assoc key table method add key value = table <- (key, value) :: table end;; class ['a, 'b] small_hashtbl : ['a, 'b] hash_table >> A better implementation, and one that scales up better, is to use a true hash table... whose elements are small hash tables! << # class ['a, 'b] hashtbl size : ['a, 'b] hash_table = object (self) val table = Array.init size (fun i -> new small_hashtbl) method private hash key = (Hashtbl.hash key) mod (Array.length table) method find key = table.(self#hash key) # find key method add key = table.(self#hash key) # add key end;; class ['a, 'b] hashtbl : int -> ['a, 'b] hash_table >> 8.2.3 Sets ============ Implementing sets leads to another difficulty. Indeed, the method union needs to be able to access the internal representation of another object of the same class. This is another instance of friend functions as seen in section 3.17. Indeed, this is the same mechanism used in the module Set in the absence of objects. In the object-oriented version of sets, we only need to add an additional method tag to return the representation of a set. Since sets are parametric in the type of elements, the method tag has a parametric type 'a tag, concrete within the module definition but abstract in its signature. From outside, it will then be guaranteed that two objects with a method tag of the same type will share the same representation. << # module type SET = sig type 'a tag class ['a] c : object ('b) method is_empty : bool method mem : 'a -> bool method add : 'a -> 'b method union : 'b -> 'b method iter : ('a -> unit) -> unit method tag : 'a tag end end;; >> << # module Set : SET = struct let rec merge l1 l2 = match l1 with [] -> l2 | h1 :: t1 -> match l2 with [] -> l1 | h2 :: t2 -> if h1 < h2 then h1 :: merge t1 l2 else if h1 > h2 then h2 :: merge l1 t2 else merge t1 l2 type 'a tag = 'a list class ['a] c = object (_ : 'b) val repr = ([] : 'a list) method is_empty = (repr = []) method mem x = List.exists (( = ) x) repr method add x = {< repr = merge [x] repr >} method union (s : 'b) = {< repr = merge repr s#tag >} method iter (f : 'a -> unit) = List.iter f repr method tag = repr end end;; >> 8.3 The subject/observer pattern *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The following example, known as the subject/observer pattern, is often presented in the literature as a difficult inheritance problem with inter-connected classes. The general pattern amounts to the definition a pair of two classes that recursively interact with one another. The class observer has a distinguished method notify that requires two arguments, a subject and an event to execute an action. << # class virtual ['subject, 'event] observer = object method virtual notify : 'subject -> 'event -> unit end;; class virtual ['subject, 'event] observer : object method virtual notify : 'subject -> 'event -> unit end >> The class subject remembers a list of observers in an instance variable, and has a distinguished method notify_observers to broadcast the message notify to all observers with a particular event e. << # class ['observer, 'event] subject = object (self) val mutable observers = ([]:'observer list) method add_observer obs = observers <- (obs :: observers) method notify_observers (e : 'event) = List.iter (fun x -> x#notify self e) observers end;; class ['a, 'event] subject : object ('b) constraint 'a = < notify : 'b -> 'event -> unit; .. > val mutable observers : 'a list method add_observer : 'a -> unit method notify_observers : 'event -> unit end >> The difficulty usually lies in defining instances of the pattern above by inheritance. This can be done in a natural and obvious manner in OCaml, as shown on the following example manipulating windows. << # type event = Raise | Resize | Move;; type event = Raise | Resize | Move >> << # let string_of_event = function Raise -> "Raise" | Resize -> "Resize" | Move -> "Move";; val string_of_event : event -> string = >> << # let count = ref 0;; val count : int ref = {contents = 0} >> << # class ['observer] window_subject = let id = count := succ !count; !count in object (self) inherit ['observer, event] subject val mutable position = 0 method identity = id method move x = position <- position + x; self#notify_observers Move method draw = Printf.printf "{Position = %d}\n" position; end;; class ['a] window_subject : object ('b) constraint 'a = < notify : 'b -> event -> unit; .. > val mutable observers : 'a list val mutable position : int method add_observer : 'a -> unit method draw : unit method identity : int method move : int -> unit method notify_observers : event -> unit end >> << # class ['subject] window_observer = object inherit ['subject, event] observer method notify s e = s#draw end;; class ['a] window_observer : object constraint 'a = < draw : unit; .. > method notify : 'a -> event -> unit end >> As can be expected, the type of window is recursive. << # let window = new window_subject;; val window : (< notify : 'a -> event -> unit; .. > as '_weak3) window_subject as 'a = >> However, the two classes of window_subject and window_observer are not mutually recursive. << # let window_observer = new window_observer;; val window_observer : (< draw : unit; .. > as '_weak4) window_observer = >> << # window#add_observer window_observer;; - : unit = () >> << # window#move 1;; {Position = 1} - : unit = () >> Classes window_observer and window_subject can still be extended by inheritance. For instance, one may enrich the subject with new behaviors and refine the behavior of the observer. << # class ['observer] richer_window_subject = object (self) inherit ['observer] window_subject val mutable size = 1 method resize x = size <- size + x; self#notify_observers Resize val mutable top = false method raise = top <- true; self#notify_observers Raise method draw = Printf.printf "{Position = %d; Size = %d}\n" position size; end;; class ['a] richer_window_subject : object ('b) constraint 'a = < notify : 'b -> event -> unit; .. > val mutable observers : 'a list val mutable position : int val mutable size : int val mutable top : bool method add_observer : 'a -> unit method draw : unit method identity : int method move : int -> unit method notify_observers : event -> unit method raise : unit method resize : int -> unit end >> << # class ['subject] richer_window_observer = object inherit ['subject] window_observer as super method notify s e = if e <> Raise then s#raise; super#notify s e end;; class ['a] richer_window_observer : object constraint 'a = < draw : unit; raise : unit; .. > method notify : 'a -> event -> unit end >> We can also create a different kind of observer: << # class ['subject] trace_observer = object inherit ['subject, event] observer method notify s e = Printf.printf "\n" s#identity (string_of_event e) end;; class ['a] trace_observer : object constraint 'a = < identity : int; .. > method notify : 'a -> event -> unit end >> and attach several observers to the same object: << # let window = new richer_window_subject;; val window : (< notify : 'a -> event -> unit; .. > as '_weak5) richer_window_subject as 'a = >> << # window#add_observer (new richer_window_observer);; - : unit = () >> << # window#add_observer (new trace_observer);; - : unit = () >> << # window#move 1; window#resize 2;; {Position = 1; Size = 1} {Position = 1; Size = 1} {Position = 1; Size = 3} {Position = 1; Size = 3} - : unit = () >> Chapter 9  Parallel programming *********************************** In this chapter, we shall look at the parallel programming facilities in OCaml. The OCaml standard library exposes low-level primitives for parallel programming. We recommend the users to utilise higher-level parallel programming libraries such as domainslib (1). This tutorial will first cover the high-level parallel programming using domainslib followed by low-level primitives exposed by the compiler. OCaml distinguishes concurrency and parallelism and provides distinct mechanisms for expressing them. Concurrency is overlapped execution of tasks (section 12.24.2) whereas parallelism is simultaneous execution of tasks. In particular, parallel tasks overlap in time but concurrent tasks may or may not overlap in time. Tasks may execute concurrently by yielding control to each other. While concurrency is a program structuring mechanism, parallelism is a mechanism to make your programs run faster. If you are interested in the concurrent programming mechanisms in OCaml, please refer to the section 12.24 on effect handlers and the chapter 34 on the threads library. 9.1 Domains *=*=*=*=*=*=* Domains are the units of parallelism in OCaml. The module Domain provides the primitives to create and manage domains. New domains can be spawned using the spawn function. << Domain.spawn (fun _ -> print_endline "I ran in parallel") I ran in parallel - : unit Domain.t = >> The spawn function executes the given computation in parallel with the calling domain. Domains are heavy-weight entities. Each domain maps 1:1 to an operating system thread. Each domain also has its own runtime state, which includes domain-local structures for allocating memory. Hence, they are relatively expensive to create and tear down. It is recommended that the programs do not spawn more domains than cores available. In this tutorial, we shall be implementing, running and measuring the performance of parallel programs. The results observed are dependent on the number of cores available on the target machine. This tutorial is being written on a 2.3 GHz Quad-Core Intel Core i7 MacBook Pro with 4 cores and 8 hardware threads. It is reasonable to expect roughly 4x performance on 4 domains for parallel programs with little coordination between the domains, and when the machine is not under load. Beyond 4 domains, the speedup is likely to be less than linear. We shall also use the command-line benchmarking tool hyperfine (2) for benchmarking our programs. 9.1.1 Joining domains ======================= We shall use the program to compute the nth Fibonacci number using recursion as a running example. The sequential program for computing the nth Fibonacci number is given below. << (* fib.ml *) let n = try int_of_string Sys.argv.(1) with _ -> 1 let rec fib n = if n < 2 then 1 else fib (n - 1) + fib (n - 2) let main () = let r = fib n in Printf.printf "fib(%d) = %d\n%!" n r let _ = main () >> The program can be compiled and benchmarked as follows. <<$ ocamlopt -o fib.exe fib.ml $ ./fib.exe 42 fib(42) = 433494437 $ hyperfine './fib.exe 42' # Benchmarking Benchmark 1: ./fib.exe 42 Time (mean ± sd): 1.193 s ± 0.006 s [User: 1.186 s, System: 0.003 s] Range (min … max): 1.181 s … 1.202 s 10 runs >> We see that it takes around 1.2 seconds to compute the 42nd Fibonacci number. Spawned domains can be joined using the join function to get their results. The join function waits for target domain to terminate. The following program computes the nth Fibonacci number twice in parallel. << (* fib_twice.ml *) let n = int_of_string Sys.argv.(1) let rec fib n = if n < 2 then 1 else fib (n - 1) + fib (n - 2) let main () = let d1 = Domain.spawn (fun _ -> fib n) in let d2 = Domain.spawn (fun _ -> fib n) in let r1 = Domain.join d1 in Printf.printf "fib(%d) = %d\n%!" n r1; let r2 = Domain.join d2 in Printf.printf "fib(%d) = %d\n%!" n r2 let _ = main () >> The program spawns two domains which compute the nth Fibonacci number. The spawn function returns a Domain.t value which can be joined to get the result of the parallel computation. The join function blocks until the computation runs to completion. <<$ ocamlopt -o fib_twice.exe fib_twice.ml $ ./fib_twice.exe 42 fib(42) = 433494437 fib(42) = 433494437 $ hyperfine './fib_twice.exe 42' Benchmark 1: ./fib_twice.exe 42 Time (mean ± sd): 1.249 s ± 0.025 s [User: 2.451 s, System: 0.012 s] Range (min … max): 1.221 s … 1.290 s 10 runs >> As one can see that computing the nth Fibonacci number twice almost took the same time as computing it once thanks to parallelism. 9.2 Domainslib: A library for nested-parallel programming *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Let us attempt to parallelise the Fibonacci function. The two recursive calls may be executed in parallel. However, naively parallelising the recursive calls by spawning domains for each one will not work as it spawns too many domains. << (* fib_par1.ml *) let n = try int_of_string Sys.argv.(1) with _ -> 1 let rec fib n = if n < 2 then 1 else begin let d1 = Domain.spawn (fun _ -> fib (n - 1)) in let d2 = Domain.spawn (fun _ -> fib (n - 2)) in Domain.join d1 + Domain.join d2 end let main () = let r = fib n in Printf.printf "fib(%d) = %d\n%!" n r let _ = main () fib(1) = 1 val n : int = 1 val fib : int -> int = val main : unit -> unit = >> <<$ ocamlopt -o fib_par1.exe fib_par1.ml $ ./fib_par1.exe 42 Fatal error: exception Failure("failed to allocate domain") >> OCaml has a limit of 128 domains that can be active at the same time. An attempt to spawn more domains will raise an exception. How then can we parallelise the Fibonacci function? 9.2.1 Parallelising Fibonacci using domainslib ================================================ The OCaml standard library provides only low-level primitives for concurrent and parallel programming, leaving high-level programming libraries to be developed and distributed outside the core compiler distribution. Domainslib (3) is such a library for nested-parallel programming, which is epitomised by the parallelism available in the recursive Fibonacci computation. Let us use domainslib to parallelise the recursive Fibonacci program. It is recommended that you install domainslib using the opam (4) package manager. This tutorial uses domainslib version 0.5.0. Domainslib provides an async/await mechanism for spawning parallel tasks and awaiting their results. On top of this mechanism, domainslib provides parallel iterators. At its core, domainslib has an efficient implementation of work-stealing queue in order to efficiently share tasks with other domains. A parallel implementation of the Fibonacci program is given below. <<(* fib_par2.ml *) let num_domains = int_of_string Sys.argv.(1) let n = int_of_string Sys.argv.(2) let rec fib n = if n < 2 then 1 else fib (n - 1) + fib (n - 2) module T = Domainslib.Task let rec fib_par pool n = if n > 20 then begin let a = T.async pool (fun _ -> fib_par pool (n-1)) in let b = T.async pool (fun _ -> fib_par pool (n-2)) in T.await pool a + T.await pool b end else fib n let main () = let pool = T.setup_pool ~num_domains:(num_domains - 1) () in let res = T.run pool (fun _ -> fib_par pool n) in T.teardown_pool pool; Printf.printf "fib(%d) = %d\n" n res let _ = main () >> The program takes the number of domains and the input to the Fibonacci function as the first and the second command-line arguments respectively. Let us start with the main function. First, we set up a pool of domains on which the nested parallel tasks will run. The domain invoking the run function will also participate in executing the tasks submitted to the pool. We invoke the parallel Fibonacci function fib_par in the run function. Finally, we tear down the pool and print the result. For sufficiently large inputs (n > 20), the fib_par function spawns the left and the right recursive calls asynchronously in the pool using the async function. The async function returns a promise for the result. The result of an asynchronous computation is obtained by awaiting the promise using the await function. The await function call blocks until the promise is resolved. For small inputs, the fib_par function simply calls the sequential Fibonacci function fib. It is important to switch to sequential mode for small problem sizes. If not, the cost of parallelisation will outweigh the work available. For simplicity, we use ocamlfind to compile this program. It is recommended that the users use dune (5) to build their programs that utilise libraries installed through opam (6). <<$ ocamlfind ocamlopt -package domainslib -linkpkg -o fib_par2.exe fib_par2.ml $ ./fib_par2.exe 1 42 fib(42) = 433494437 $ hyperfine './fib.exe 42' './fib_par2.exe 2 42' \ './fib_par2.exe 4 42' './fib_par2.exe 8 42' Benchmark 1: ./fib.exe 42 Time (mean ± sd): 1.217 s ± 0.018 s [User: 1.203 s, System: 0.004 s] Range (min … max): 1.202 s … 1.261 s 10 runs Benchmark 2: ./fib_par2.exe 2 42 Time (mean ± sd): 628.2 ms ± 2.9 ms [User: 1243.1 ms, System: 4.9 ms] Range (min … max): 625.7 ms … 634.5 ms 10 runs Benchmark 3: ./fib_par2.exe 4 42 Time (mean ± sd): 337.6 ms ± 23.4 ms [User: 1321.8 ms, System: 8.4 ms] Range (min … max): 318.5 ms … 377.6 ms 10 runs Benchmark 4: ./fib_par2.exe 8 42 Time (mean ± sd): 250.0 ms ± 9.4 ms [User: 1877.1 ms, System: 12.6 ms] Range (min … max): 242.5 ms … 277.3 ms 11 runs Summary './fib_par2.exe 8 42' ran 1.35 ± 0.11 times faster than './fib_par2.exe 4 42' 2.51 ± 0.10 times faster than './fib_par2.exe 2 42' 4.87 ± 0.20 times faster than './fib.exe 42' >> The results show that, with 8 domains, the parallel Fibonacci program runs 4.87 times faster than the sequential version. 9.2.2 Parallel iteration constructs ===================================== Many numerical algorithms use for-loops. The parallel-for primitive provides a straight-forward way to parallelise such code. Let us take the spectral-norm (7) benchmark from the computer language benchmarks game and parallelise it. The sequential version of the program is given below. << (* spectralnorm.ml *) let n = try int_of_string Sys.argv.(1) with _ -> 32 let eval_A i j = 1. /. float((i+j)*(i+j+1)/2+i+1) let eval_A_times_u u v = let n = Array.length v - 1 in for i = 0 to n do let vi = ref 0. in for j = 0 to n do vi := !vi +. eval_A i j *. u.(j) done; v.(i) <- !vi done let eval_At_times_u u v = let n = Array.length v - 1 in for i = 0 to n do let vi = ref 0. in for j = 0 to n do vi := !vi +. eval_A j i *. u.(j) done; v.(i) <- !vi done let eval_AtA_times_u u v = let w = Array.make (Array.length u) 0.0 in eval_A_times_u u w; eval_At_times_u w v let () = let u = Array.make n 1.0 and v = Array.make n 0.0 in for _i = 0 to 9 do eval_AtA_times_u u v; eval_AtA_times_u v u done; let vv = ref 0.0 and vBv = ref 0.0 in for i=0 to n-1 do vv := !vv +. v.(i) *. v.(i); vBv := !vBv +. u.(i) *. v.(i) done; Printf.printf "%0.9f\n" (sqrt(!vBv /. !vv)) >> Observe that the program has nested loops in eval_A_times_u and eval_At_times_u. Each iteration of the outer loop body reads from u but writes to disjoint memory locations in v. Hence, the iterations of the outer loop are not dependent on each other and can be executed in parallel. The parallel version of spectral norm is shown below. <<(* spectralnorm_par.ml *) let num_domains = try int_of_string Sys.argv.(1) with _ -> 1 let n = try int_of_string Sys.argv.(2) with _ -> 32 let eval_A i j = 1. /. float((i+j)*(i+j+1)/2+i+1) module T = Domainslib.Task let eval_A_times_u pool u v = let n = Array.length v - 1 in T.parallel_for pool ~start:0 ~finish:n ~body:(fun i -> let vi = ref 0. in for j = 0 to n do vi := !vi +. eval_A i j *. u.(j) done; v.(i) <- !vi ) let eval_At_times_u pool u v = let n = Array.length v - 1 in T.parallel_for pool ~start:0 ~finish:n ~body:(fun i -> let vi = ref 0. in for j = 0 to n do vi := !vi +. eval_A j i *. u.(j) done; v.(i) <- !vi ) let eval_AtA_times_u pool u v = let w = Array.make (Array.length u) 0.0 in eval_A_times_u pool u w; eval_At_times_u pool w v let () = let pool = T.setup_pool ~num_domains:(num_domains - 1) () in let u = Array.make n 1.0 and v = Array.make n 0.0 in T.run pool (fun _ -> for _i = 0 to 9 do eval_AtA_times_u pool u v; eval_AtA_times_u pool v u done); let vv = ref 0.0 and vBv = ref 0.0 in for i=0 to n-1 do vv := !vv +. v.(i) *. v.(i); vBv := !vBv +. u.(i) *. v.(i) done; T.teardown_pool pool; Printf.printf "%0.9f\n" (sqrt(!vBv /. !vv)) >> Observe that the parallel_for function is isomorphic to the for-loop in the sequential version. No other change is required except for the boiler plate code to set up and tear down the pools. <<$ ocamlopt -o spectralnorm.exe spectralnorm.ml $ ocamlfind ocamlopt -package domainslib -linkpkg -o spectralnorm_par.exe \ spectralnorm_par.ml $ hyperfine './spectralnorm.exe 4096' './spectralnorm_par.exe 2 4096' \ './spectralnorm_par.exe 4 4096' './spectralnorm_par.exe 8 4096' Benchmark 1: ./spectralnorm.exe 4096 Time (mean ± sd): 1.989 s ± 0.013 s [User: 1.972 s, System: 0.007 s] Range (min … max): 1.975 s … 2.018 s 10 runs Benchmark 2: ./spectralnorm_par.exe 2 4096 Time (mean ± sd): 1.083 s ± 0.015 s [User: 2.140 s, System: 0.009 s] Range (min … max): 1.064 s … 1.102 s 10 runs Benchmark 3: ./spectralnorm_par.exe 4 4096 Time (mean ± sd): 698.7 ms ± 10.3 ms [User: 2730.8 ms, System: 18.3 ms] Range (min … max): 680.9 ms … 721.7 ms 10 runs Benchmark 4: ./spectralnorm_par.exe 8 4096 Time (mean ± sd): 921.8 ms ± 52.1 ms [User: 6711.6 ms, System: 51.0 ms] Range (min … max): 838.6 ms … 989.2 ms 10 runs Summary './spectralnorm_par.exe 4 4096' ran 1.32 ± 0.08 times faster than './spectralnorm_par.exe 8 4096' 1.55 ± 0.03 times faster than './spectralnorm_par.exe 2 4096' 2.85 ± 0.05 times faster than './spectralnorm.exe 4096' >> On the author’s machine, the program scales reasonably well up to 4 domains but performs worse with 8 domains. Recall that the machine only has 4 physical cores. Debugging and fixing this performance issue is beyond the scope of this tutorial. 9.3 Parallel garbage collection *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* An important aspect of the scalability of parallel OCaml programs is the scalability of the garbage collector (GC). The OCaml GC is designed to have both low latency and good parallel scalability. OCaml has a generational garbage collector with a small minor heap and a large major heap. New objects (upto a certain size) are allocated in the minor heap. Each domain has its own domain-local minor heap arena into which new objects are allocated without synchronising with the other domains. When a domain exhausts its minor heap arena, it calls for a stop-the-world collection of the minor heaps. In the stop-the-world section, all the domains collect their minor heap arenas in parallel evacuating the survivors to the major heap. For the major heap, each domain maintains domain-local, size-segmented pools of memory into which large objects and survivors from the minor collection are allocated. Having domain-local pools avoids synchronisation for most major heap allocations. The major heap is collected by a concurrent mark-and-sweep algorithm that involves a few short stop-the-world pauses for each major cycle. Overall, the users should expect the garbage collector to scale well with increasing number of domains, with the latency remaining low. For more information on the design and evaluation of the garbage collector, please have a look at the ICFP 2020 paper on Retrofitting Parallelism onto OCaml (8). 9.4 Memory model: The easy bits *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Modern processors and compilers aggressively optimise programs. These optimisations accelerate without otherwise affecting sequential programs, but cause surprising behaviours to be visible in parallel programs. To benefit from these optimisations, OCaml adopts a relaxed memory model that precisely specifies which of these relaxed behaviours programs may observe. While these models are difficult to program against directly, the OCaml memory model provides recipes that retain the simplicity of sequential reasoning. Firstly, immutable values may be freely shared between multiple domains and may be accessed in parallel. For mutable data structures such as reference cells, arrays and mutable record fields, programmers should avoid data races. Reference cells, arrays and mutable record fields are said to be non-atomic data structures. A data race is said to occur when two domains concurrently access a non-atomic memory location without synchronisation and at least one of the accesses is a write. OCaml provides a number of ways to introduce synchronisation including atomic variables (section 9.7) and mutexes (section 9.5). Importantly, for data race free (DRF) programs, OCaml provides sequentially consistent (SC) semantics – the observed behaviour of such programs can be explained by the interleaving of operations from different domains. This property is known as DRF-SC guarantee. Moreover, in OCaml, DRF-SC guarantee is modular – if a part of a program is data race free, then the OCaml memory model ensures that those parts have sequential consistency despite other parts of the program having data races. Even for programs with data races, OCaml provides strong guarantees. While the user may observe non sequentially consistent behaviours, there are no crashes. For more details on the relaxed behaviours in the presence of data races, please have a look at the chapter on the hard bits of the memory model (chapter 10). 9.5 Blocking synchronisation *=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Domains may perform blocking synchronisation with the help of Mutex, Condition and Semaphore modules. These modules are the same as those used to synchronise threads created by the threads library (chapter 34). For clarity, in the rest of this chapter, we shall call the threads created by the threads library as systhreads. The following program implements a concurrent stack using mutex and condition variables. << module Blocking_stack : sig type 'a t val make : unit -> 'a t val push : 'a t -> 'a -> unit val pop : 'a t -> 'a end = struct type 'a t = { mutable contents: 'a list; mutex : Mutex.t; nonempty : Condition.t } let make () = { contents = []; mutex = Mutex.create (); nonempty = Condition.create () } let push r v = Mutex.lock r.mutex; r.contents <- v::r.contents; Condition.signal r.nonempty; Mutex.unlock r.mutex let pop r = Mutex.lock r.mutex; let rec loop () = match r.contents with | [] -> Condition.wait r.nonempty r.mutex; loop () | x::xs -> r.contents <- xs; x in let res = loop () in Mutex.unlock r.mutex; res end >> The concurrent stack is implemented using a record with three fields: a mutable field contents which stores the elements in the stack, a mutex to control access to the contents field, and a condition variable nonempty, which is used to signal blocked domains waiting for the stack to become non-empty. The push operation locks the mutex, updates the contents field with a new list whose head is the element being pushed and the tail is the old list. The condition variable nonempty is signalled while the lock is held in order to wake up any domains waiting on this condition. If there are waiting domains, one of the domains is woken up. If there are none, then the signal operation has no effect. The pop operation locks the mutex and checks whether the stack is empty. If so, the calling domain waits on the condition variable nonempty using the wait primitive. The wait call atomically suspends the execution of the current domain and unlocks the mutex. When this domain is woken up again (when the wait call returns), it holds the lock on mutex. The domain tries to read the contents of the stack again. If the pop operation sees that the stack is non-empty, it updates the contents to the tail of the old list, and returns the head. The use of mutex to control access to the shared resource contents introduces sufficient synchronisation between multiple domains using the stack. Hence, there are no data races when multiple domains use the stack in parallel. 9.5.1 Interaction with systhreads =================================== How do systhreads interact with domains? The systhreads created on a particular domain remain pinned to that domain. Only one systhread at a time is allowed to run OCaml code on a particular domain. However, systhreads belonging to a particular domain may run C library or system code in parallel. Systhreads belonging to different domains may execute in parallel. When using systhreads, the thread created for executing the computation given to Domain.spawn is also treated as a systhread. For example, the following program creates in total two domains (including the initial domain) with two systhreads each (including the initial systhread for each of the domains). <<(* dom_thr.ml *) let m = Mutex.create () let r = ref None (* protected by m *) let task () = let my_thr_id = Thread.(id (self ())) in let my_dom_id :> int = Domain.self () in Mutex.lock m; begin match !r with | None -> Printf.printf "Thread %d running on domain %d saw initial write\n%!" my_thr_id my_dom_id | Some their_thr_id -> Printf.printf "Thread %d running on domain %d saw the write by thread %d\n%!" my_thr_id my_dom_id their_thr_id; end; r := Some my_thr_id; Mutex.unlock m let task' () = let t = Thread.create task () in task (); Thread.join t let main () = let d = Domain.spawn task' in task' (); Domain.join d let _ = main () >> <<$ ocamlopt -I +threads unix.cmxa threads.cmxa -o dom_thr.exe dom_thr.ml $ ./dom_thr.exe Thread 1 running on domain 1 saw initial write Thread 0 running on domain 0 saw the write by thread 1 Thread 2 running on domain 1 saw the write by thread 0 Thread 3 running on domain 0 saw the write by thread 2 >> This program uses a shared reference cell protected by a mutex to communicate between the different systhreads running on two different domains. The systhread identifiers uniquely identify systhreads in the program. The initial domain gets the domain id and the thread id as 0. The newly spawned domain gets domain id as 1. 9.6 Interaction with C bindings *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* During parallel execution with multiple domains, C code running on a domain may run in parallel with any C code running in other domains even if neither of them has released the “domain lock”. Prior to OCaml 5.0, C bindings may have assumed that if the OCaml runtime lock is not released, then it would be safe to manipulate global C state (e.g. initialise a function-local static value). This is no longer true in the presence of parallel execution with multiple domains. 9.7 Atomics *=*=*=*=*=*=* Mutex, condition variables and semaphores are used to implement blocking synchronisation between domains. For non-blocking synchronisation, OCaml provides Atomic variables. As the name suggests, non-blocking synchronisation does not provide mechanisms for suspending and waking up domains. On the other hand, primitives used in non-blocking synchronisation are often compiled to atomic read-modify-write primitives that the hardware provides. As an example, the following program increments a non-atomic counter and an atomic counter in parallel. << (* incr.ml *) let twice_in_parallel f = let d1 = Domain.spawn f in let d2 = Domain.spawn f in Domain.join d1; Domain.join d2 let plain_ref n = let r = ref 0 in let f () = for _i=1 to n do incr r done in twice_in_parallel f; Printf.printf "Non-atomic ref count: %d\n" !r let atomic_ref n = let r = Atomic.make 0 in let f () = for _i=1 to n do Atomic.incr r done in twice_in_parallel f; Printf.printf "Atomic ref count: %d\n" (Atomic.get r) let main () = let n = try int_of_string Sys.argv.(1) with _ -> 1 in plain_ref n; atomic_ref n let _ = main () >> <<$ ocamlopt -o incr.exe incr.ml $ ./incr.exe 1_000_000 Non-atomic ref count: 1187193 Atomic ref count: 2000000 >> Observe that the result from using the non-atomic counter is lower than what one would naively expect. This is because the non-atomic incr function is equivalent to: << let incr r = let curr = !r in r := curr + 1 >> Observe that the load and the store are two separate operations, and the increment operation as a whole is not performed atomically. When two domains execute this code in parallel, both of them may read the same value of the counter curr and update it to curr + 1. Hence, instead of two increments, the effect will be that of a single increment. On the other hand, the atomic counter performs the load and the store atomically with the help of hardware support for atomicity. The atomic counter returns the expected result. The atomic variables can be used for low-level synchronisation between the domains. The following example uses an atomic variable to exchange a message between two domains. << let r = Atomic.make None let sender () = Atomic.set r (Some "Hello") let rec receiver () = match Atomic.get r with | None -> Domain.cpu_relax (); receiver () | Some m -> print_endline m let main () = let s = Domain.spawn sender in let d = Domain.spawn receiver in Domain.join s; Domain.join d let _ = main () Hello val r : string option Atomic.t = val sender : unit -> unit = val receiver : unit -> unit = val main : unit -> unit = >> While the sender and the receiver compete to access r, this is not a data race since r is an atomic reference. 9.7.1 Lock-free stack ======================= The Atomic module is used to implement non-blocking, lock-free data structures. The following program implements a lock-free stack. << module Lockfree_stack : sig type 'a t val make : unit -> 'a t val push : 'a t -> 'a -> unit val pop : 'a t -> 'a option end = struct type 'a t = 'a list Atomic.t let make () = Atomic.make [] let rec push r v = let s = Atomic.get r in if Atomic.compare_and_set r s (v::s) then () else (Domain.cpu_relax (); push r v) let rec pop r = let s = Atomic.get r in match s with | [] -> None | x::xs -> if Atomic.compare_and_set r s xs then Some x else (Domain.cpu_relax (); pop r) end >> The atomic stack is represented by an atomic reference that holds a list. The push and pop operations use the compare_and_set primitive to attempt to atomically update the atomic reference. The expression compare_and_set r seen v sets the value of r to v if and only if its current value is physically equal to seen. Importantly, the comparison and the update occur atomically. The expression evaluates to true if the comparison succeeded (and the update happened) and false otherwise. If the compare_and_set fails, then some other domain is also attempting to update the atomic reference at the same time. In this case, the push and pop operations call Domain.cpu_relax to back off for a short duration allowing competing domains to make progress before retrying the failed operation. This lock-free stack implementation is also known as Treiber stack. --------------------------------------- (1) https://github.com/ocaml-multicore/domainslib (2) https://github.com/sharkdp/hyperfine (3) https://github.com/ocaml-multicore/domainslib (4) https://opam.ocaml.org/ (5) https://github.com/ocaml/dune (6) https://opam.ocaml.org/ (7) https://benchmarksgame-team.pages.debian.net/benchmarksgame/description/sp ectralnorm.html#spectralnorm (8) https://arxiv.org/abs/2004.11663 Chapter 10  Memory model: The hard bits ******************************************* This chapter describes the details of OCaml relaxed memory model. The relaxed memory model describes what values an OCaml program is allowed to witness when reading a memory location. If you are interested in high-level parallel programming in OCaml, please have a look at the parallel programming chapter 9. This chapter is aimed at experts who would like to understand the details of the OCaml memory model from a practitioner’s perspective. For a formal definition of the OCaml memory model, its guarantees and the compilation to hardware memory models, please have a look at the PLDI 2018 paper on Bounding Data Races in Space and Time (1). The memory model presented in this chapter is an extension of the one presented in the PLDI 2018 paper. This chapter also covers some pragmatic aspects of the memory model that are not covered in the paper. 10.1 Why weakly consistent memory? *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The simplest memory model that we could give to our programs is sequential consistency. Under sequential consistency, the values observed by the program can be explained through some interleaving of the operations from different domains in the program. For example, consider the following program with two domains d1 and d2 executing in parallel: << let d1 a b = let r1 = !a * 2 in let r2 = !b in let r3 = !a * 2 in (r1, r2, r3) let d2 b = b := 0 let main () = let a = ref 1 in let b = ref 1 in let h = Domain.spawn (fun _ -> let r1, r2, r3 = d1 a b in Printf.printf "r1 = %d, r2 = %d, r3 = %d\n" r1 r2 r3) in d2 b; Domain.join h >> The reference cells a and b are initially 1. The user may observe r1 = 2, r2 = 0, r3 = 2 if the write to b in d2 occurred before the read of b in d1. Here, the observed behaviour can be explained in terms of interleaving of the operations from different domains. Let us now assume that a and b are aliases of each other. << let d1 a b = let r1 = !a * 2 in let r2 = !b in let r3 = !a * 2 in (r1, r2, r3) let d2 b = b := 0 let main () = let ab = ref 1 in let h = Domain.spawn (fun _ -> let r1, r2, r3 = d1 ab ab in assert (not (r1 = 2 && r2 = 0 && r3 = 2))) in d2 ab; Domain.join h >> In the above program, the variables ab, a and b refer to the same reference cell. One would expect that the assertion in the main function will never fail. The reasoning is that if r2 is 0, then the write in d2 occurred before the read of b in d1. Given that a and b are aliases, the second read of a in d1 should also return 0. 10.1.1 Compiler optimisations =============================== Surprisingly, this assertion may fail in OCaml due to compiler optimisations. The OCaml compiler observes the common sub-expression !a * 2 in d1 and optimises the program to: << let d1 a b = let r1 = !a * 2 in let r2 = !b in let r3 = r1 in (* CSE: !a * 2 ==> r1 *) (r1, r2, r3) let d2 b = b := 0 let main () = let ab = ref 1 in let h = Domain.spawn (fun _ -> let r1, r2, r3 = d1 ab ab in assert (not (r1 = 2 && r2 = 0 && r3 = 2))) in d2 ab; Domain.join h >> This optimisation is known as the common sub-expression elimination (CSE). Such optimisations are valid and necessary for good performance, and do not change the sequential meaning of the program. However, CSE breaks sequential reasoning. In the optimized program above, even if the write to b in d2 occurs between the first and the second reads in d1, the program will observe the value 2 for r3, causing the assertion to fail. The observed behaviour cannot be explained by interleaving of operations from different domains in the source program. Thus, CSE optimization is said to be invalid under sequential consistency. One way to explain the observed behaviour is as if the operations performed on a domain were reordered. For example, if the second and the third reads from d1 were reordered, << let d1 a b = let r1 = !a * 2 in let r3 = !a * 2 in let r2 = !b in (r1, r2, r3) >> then we can explain the observed behaviour (2,0,2) returned by d1. 10.1.2 Hardware optimisations =============================== The other source of reordering is by the hardware. Modern hardware architectures have complex cache hierarchies with multiple levels of cache. While cache coherence ensures that reads and writes to a single memory location respect sequential consistency, the guarantees on programs that operate on different memory locations are much weaker. Consider the following program: << let a = ref 0 and b = ref 0 let d1 () = a := 1; !b let d2 () = b := 1; !a let main () = let h = Domain.spawn d2 in let r1 = d1 () in let r2 = Domain.join h in assert (not (r1 = 0 && r2 = 0)) >> Under sequential consistency, we would never expect the assertion to fail. However, even on x86, which offers much stronger guarantees than ARM, the writes performed at a CPU core are not immediately published to all of the other cores. Since a and b are different memory locations, the reads of a and b may both witness the initial values, leading to the assertion failure. This behaviour can be explained if a load is allowed to be reordered before a preceding store to a different memory location. This reordering can happen due to the presence of in-core store-buffers on modern processors. Each core effectively has a FIFO buffer of pending writes to avoid the need to block while a write completes. The writes to a and b may be in the store-buffers of cores c1 and c2 running the domains d1 and d2, respectively. The reads of b and a running on the cores c1 and c2, respectively, will not see the writes if the writes have not propagated from the buffers to the main memory. 10.2 Data race freedom implies sequential consistency *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The aim of the OCaml relaxed memory model is to precisely describe which orders are preserved by the OCaml program. The compiler and the hardware are free to optimize the program as long as they respect the ordering guarantees of the memory model. While programming directly under the relaxed memory model is difficult, the memory model also describes the conditions under which a program will only exhibit sequentially consistent behaviours. This guarantee is known as data race freedom implies sequential consistency (DRF-SC). In this section, we shall describe this guarantee. In order to do this, we first need a number of definitions. 10.2.1 Memory locations ========================= OCaml classifies memory locations into atomic and non-atomic locations. Reference cells, array fields and mutable record fields are non-atomic memory locations. Immutable objects are non-atomic locations with an initialising write but no further updates. Atomic memory locations are those that are created using the Atomic module. 10.2.2 Happens-before relation ================================ Let us imagine that the OCaml programs are executed by an abstract machine that executes one action at a time, arbitrarily picking one of the available domains at each step. We classify actions into two: inter-domain and intra-domain. An inter-domain action is one which can be observed and be influenced by actions on other domains. There are several inter-domain actions: - Reads and writes of atomic and non-atomic locations. - Spawn and join of domains. - Operations on mutexes. On the other hand, intra-domain actions can neither be observed nor influence the execution of other domains. Examples include evaluating an arithmetic expression, calling a function, etc. The memory model specification ignores such intra-domain actions. In the sequel, we use the term action to indicate inter-domain actions. A totally ordered list of actions executed by the abstract machine is called an execution trace. There might be several possible execution traces for a given program due to non-determinism. For a given execution trace, we define an irreflexive, transitive happens-before relation that captures the causality between actions in the OCaml program. The happens-before relation is defined as the smallest transitive relation satisfying the following properties: - We define the order in which a domain executes its actions as the program order. If an action x precedes another action y in program order, then x precedes y in happens-before order. - If x is a write to an atomic location and y is a subsequent read or write to that memory location in the execution trace, then x precedes y in happens-before order. For atomic locations, compare_and_set, fetch_and_add, exchange, incr and decr are considered to perform both a read and a write. - If x is Domain.spawn f and y is the first action in the newly spawned domain executing f, then x precedes y in happens-before order. - If x is the last action in a domain d and y is Domain.join d, then x precedes y in happens-before order. - If x is an unlock operation on a mutex, and y is any subsequent operation on the mutex in the execution trace, then x precedes y in happens-before order. 10.2.3 Data race ================== In a given trace, two actions are said to be conflicting if they access the same non-atomic location, at least one is a write and neither is an initialising write to that location. We say that a program has a data race if there exists some execution trace of the program with two conflicting actions and there does not exist a happens-before relationship between the conflicting accesses. A program without data races is said to be correctly synchronised. 10.2.4 DRF-SC =============== DRF-SC guarantee: A program without data races will only exhibit sequentially consistent behaviours. DRF-SC is a strong guarantee for the programmers. Programmers can use sequential reasoning i.e., reasoning by executing one inter-domain action after the other, to identify whether their program has a data race. In particular, they do not need to reason about reorderings described in section 10.1 in order to determine whether their program has a data race. Once the determination that a particular program is data race free is made, they do not need to worry about reorderings in their code. 10.3 Reasoning with DRF-SC *=*=*=*=*=*=*=*=*=*=*=*=*=*= In this section, we will look at examples of using DRF-SC for program reasoning. In this section, we will use the functions with names dN to represent domains executing in parallel with other domains. That is, we assume that there is a main function that runs the dN functions in parallel as follows: <> Here is a simple example with a data race: << (* Has data race *) let r = ref 0 let d1 () = r := 1 let d2 () = !r >> r is a non-atomic reference. The two domains race to access the reference, and d1 is a write. Since there is no happens-before relationship between the conflicting accesses, there is a data race. Both of the programs that we had seen in the section 10.1 have data races. It is no surprise that they exhibit non sequentially consistent behaviours. Accessing disjoint array indices and fields of a record in parallel is not a data race. For example, << (* No data race *) let a = [| 0; 1 |] let d1 () = a.(0) <- 42 let d2 () = a.(1) <- 42 >> << (* No data race *) type t = { mutable a : int; mutable b : int } let r = {a = 0; b = 1} let d1 () = r.a <- 42 let d2 () = r.b <- 42 >> do not have data races. Races on atomic locations do not lead to a data race. << (* No data race *) let r = Atomic.make 0 let d1 () = Atomic.set r 1 let d2 () = Atomic.get r >> Message-passing --------------- Atomic variables may be used for implementing non-blocking communication between domains. << (* No data race *) let msg = ref 0 let flag = Atomic.make false let d1 () = msg := 42; (* a *) Atomic.set flag true (* b *) let d2 () = if Atomic.get flag (* c *) then !msg (* d *) else 0 >> Observe that the actions a and d write and read from the same non-atomic location msg, respectively, and hence are conflicting. We need to establish that a and d have a happens-before relationship in order to show that this program does not have a data race. The action a precedes b in program order, and hence, a happens-before b. Similarly, c happens-before d. If d2 observes the atomic variable flag to be true, then b precedes c in happens-before order. Since happens-before is transitive, the conflicting actions a and d are in happens-before order. If d2 observes the flag to be false, then the read of msg is not done. Hence, there is no conflicting access in this execution trace. Hence, the program does not have a data race. The following modified version of the message passing program does have a data race. << (* Has data race *) let msg = ref 0 let flag = Atomic.make false let d1 () = msg := 42; (* a *) Atomic.set flag true (* b *) let d2 () = ignore (Atomic.get flag); (* c *) !msg (* d *) >> The domain d2 now unconditionally reads the non-atomic reference msg. Consider the execution trace: <> In this trace, d and a are conflicting operations. But there is no happens-before relationship between them. Hence, this program has a data race. 10.4 Local data race freedom *=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The OCaml memory model offers strong guarantees even for programs with data races. It offers what is known as local data race freedom sequential consistency (LDRF-SC) guarantee. A formal definition of this property is beyond the scope of this manual chapter. Interested readers are encouraged to read the PLDI 2018 paper on Bounding Data Races in Space and Time (2). Informally, LDRF-SC says that the data race free parts of the program remain sequentially consistent. That is, even if the program has data races, those parts of the program that are disjoint from the parts with data races are amenable to sequential reasoning. Consider the following snippet: << let snippet () = let c = ref 0 in c := 42; let a = !c in (a, c) >> Observe that c is a newly allocated reference. Can the read of c return a value which is not 42? That is, can a ever be not 42? Surprisingly, in the C++ and Java memory models, the answer is yes. With the C++ memory model, if the program has a data race, even in unrelated parts, then the semantics is undefined. If this snippet were linked with a library that had a data race, then, under the C++ memory model, the read may return any value. Since data races on unrelated locations can affect program behaviour, we say that C++ memory model is not bounded in space. Unlike C++, Java memory model is bounded in space. But Java memory model is not bounded in time; data races in the future will affect the past behaviour. For example, consider the translation of this example to Java. We assume a prior definition of Class c {int x;} and a shared non-volatile variable C g. Now the snippet may be part of a larger program with parallel threads: <<(* Thread 1 *) C c = new C(); c.x = 42; a = c.x; g = c; (* Thread 2 *) g.x = 7; >> The read of c.x and the write of g in the first thread are done on separate memory locations. Hence, the Java memory model allows them to be reordered. As a result, the write in the second thread may occur before the read of c.x, and hence, c.x returns 7. The OCaml equivalent of the Java code above is: << let g = ref None let snippet () = let c = ref 0 in c := 42; let a = !c in (a, c) let d1 () = let (a,c) = snippet () in g := Some c; a let d2 () = match !g with | None -> () | Some c -> c := 7 >> Observe that there is a data race on both g and c. Consider only the first three instructions in snippet: <> The OCaml memory model is bounded both in space and time. The only memory location here is c. Reasoning only about this snippet, there is neither the data race in space (the race on g) nor in time (the future race on c). Hence, the snippet will have sequentially consistent behaviour, and the value returned by !c will be 42. The OCaml memory model guarantees that even for programs with data races, memory safety is preserved. While programs with data races may observe non-sequentially consistent behaviours, they will not crash. 10.5 An operational view of the memory model *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= In this section, we describe the semantics of the OCaml memory model. A formal definition of the operational view of the memory model is presented in section 3 of the PLDI 2018 paper on Bounding Data Races in Space and Time (3). This section presents an informal description of the memory model with the help of an example. Given an OCaml program, which may possibly contain data races, the operational semantics tells you the values that may be observed by the read of a memory location. For simplicity, we restrict the intra-thread actions to just the accesses to atomic and non-atomic locations, ignoring domain spawn and join operations, and the operations on mutexes. We describe the semantics of the OCaml memory model in a straightforward small-step operational manner. That is, the semantics is described by an abstract machine that executes one action at a time, arbitrarily picking one of the available domains at each step. This is similar to the abstract machine that we had used to describe the happens-before relationship in section 10.2.2. 10.5.1 Non-atomic locations ============================= In the semantics, we model non-atomic locations as finite maps from timestamps t to values v. We take timestamps to be rational numbers. The timestamps are totally ordered but dense; there is a timestamp between any two others. For example, < 1; t2 -> 2] b: [t3 -> 3; t4 -> 4; t5 -> 5] c: [t6 -> 5; t7 -> 6; t8 -> 7] >> represents three non-atomic locations a, b and c and their histories. The location a has two writes at timestamps t1 and t2 with values 1 and 2, respectively. When we write a: [t1 -> 1; t2 -> 2], we assume that t1 < t2. We assume that the locations are initialised with a history that has a single entry at timestamp 0 that maps to the initial value. 10.5.2 Domains ================ Each domain is equipped with a frontier, which is a map from non-atomic locations to timestamps. Intuitively, each domain’s frontier records, for each non-atomic location, the latest write known to the thread. More recent writes may have occurred, but are not guaranteed to be visible. For example, < t1; b -> t3; c -> t7] d2: [a -> t1; b -> t4; c -> t7] >> represents two domains d1 and d2 and their frontiers. 10.5.3 Non-atomic accesses ============================ Let us now define the semantics of non-atomic reads and writes. Suppose domain d1 performs the read of b. For non-atomic reads, the domains may read an arbitrary element of the history for that location, as long as it is not older than the timestamp in the domains’s frontier. In this case, since d1 frontier at b is at t3, the read may return the value 3, 4 or 5. A non-atomic read does not change the frontier of the current domain. Suppose domain d2 writes the value 10 to c (c := 10). We pick a new timestamp t9 for this write such that it is later than d2’s frontier at c. Note a subtlety here: this new timestamp might not be later than everything else in the history, but merely later than any other write known to the writing domain. Hence, t9 may be inserted in c’s history either (a) between t7 and t8 or (b) after t8. Let us pick the former option for our discussion. Since the new write appears after all the writes known by the domain d2 to the location c, d2’s frontier at c is also updated. The new state of the abstract machine is: <<(* Non-atomic locations *) a: [t1 -> 1; t2 -> 2] b: [t3 -> 3; t4 -> 4; t5 -> 5] c: [t6 -> 5; t7 -> 6; t9 -> 10; t8 -> 7] (* new write at t9 *) (* Domains *) d1: [a -> t1; b -> t3; c -> t7] d2: [a -> t1; b -> t4; c -> t9] (* frontier updated at c *) >> 10.5.4 Atomic accesses ======================== Atomic locations carry not only values but also synchronization information. We model atomic locations as a pair of the value held by that location and a frontier. The frontier models the synchronization information, which is merged with the frontiers of threads that operate on the location. In this way, non-atomic writes made by one thread can become known to another by communicating via an atomic location. For example, <<(* Atomic locations *) A: 10, [a -> t1; b -> t5; c -> t7] B: 5, [a -> t2; b -> t4; c -> t6] >> shows two atomic variables A and B with values 10 and 5, respectively, and frontiers of their own. We use upper-case variable names to indicate atomic locations. During atomic reads, the frontier of the location is merged into that of the domain performing the read. For example, suppose d1 reads B. The read returns 5, and d1’s frontier updated by merging it with B’s frontier, choosing the later timestamp for each location. The abstract machine state before the atomic read is: <<(* Non-atomic locations *) a: [t1 -> 1; t2 -> 2] b: [t3 -> 3; t4 -> 4; t5 -> 5] c: [t6 -> 5; t7 -> 6; t9 -> 10; t8 -> 7] (* Domains *) d1: [a -> t1; b -> t3; c -> t7] d2: [a -> t1; b -> t4; c -> t9] (* Atomic locations *) A: 10, [a -> t1; b -> t5; c -> t7] B: 5, [a -> t2; b -> t4; c -> t6] >> As a result of the atomic read, the abstract machine state is updated to: <<(* Non-atomic locations *) a: [t1 -> 1; t2 -> 2] b: [t3 -> 3; t4 -> 4; t5 -> 5] c: [t6 -> 5; t7 -> 6; t9 -> 10; t8 -> 7] (* Domains *) d1: [a -> t2; b -> t4; c -> t7] (* frontier updated at a and b *) d2: [a -> t1; b -> t4; c -> t9] (* Atomic locations *) A: 10, [a -> t1; b -> t5; c -> t7] B: 5, [a -> t2; b -> t4; c -> t6] >> During atomic writes, the value held by the atomic location is updated. The frontiers of both the writing domain and that of the location being written to are updated to the merge of the two frontiers. For example, if d2 writes 20 to A in the current machine state, the machine state is updated to: <<(* Non-atomic locations *) a: [t1 -> 1; t2 -> 2] b: [t3 -> 3; t4 -> 4; t5 -> 5] c: [t6 -> 5; t7 -> 6; t9 -> 10; t8 -> 7] (* Domains *) d1: [a -> t2; b -> t4; c -> t7] d2: [a -> t1; b -> t5; c -> t9] (* frontier updated at b *) (* Atomic locations *) A: 20, [a -> t1; b -> t5; c -> t9] (* value updated. frontier updated at c. *) B: 5, [a -> t2; b -> t4; c -> t6] >> 10.5.5 Reasoning with the semantics ===================================== Let us revisit an example from earlier (section 10.1). << let a = ref 0 and b = ref 0 let d1 () = a := 1; !b let d2 () = b := 1; !a let main () = let h = Domain.spawn d2 in let r1 = d1 () in let r2 = Domain.join h in assert (not (r1 = 0 && r2 = 0)) >> This program has a data race on a and b, and hence, the program may exhibit non sequentially consistent behaviour. Let us use the semantics to show that the program may exhibit r1 = 0 && r2 = 0. The initial state of the abstract machine is: <<(* Non-atomic locations *) a: [t0 -> 0] b: [t1 -> 0] (* Domains *) d1: [a -> t0; b -> t1] d2: [a -> t0; b -> t1] >> There are several possible schedules for executing this program. Let us consider the following schedule: <<1: a := 1 @ d1 2: b := 1 @ d2 3: !b @ d1 4: !a @ d2 >> After the first action a:=1 by d1, the machine state is: <<(* Non-atomic locations *) a: [t0 -> 0; t2 -> 1] (* new write at t2 *) b: [t1 -> 0] (* Domains *) d1: [a -> t2; b -> t1] (* frontier updated at a *) d2: [a -> t0; b -> t1] >> After the second action b:=1 by d2, the machine state is: <<(* Non-atomic locations *) a: [t0 -> 0; t2 -> 1] b: [t1 -> 0; t3 -> 1] (* new write at t3 *) (* Domains *) d1: [a -> t2; b -> t1] d2: [a -> t0; b -> t3] (* frontier updated at b *) >> Now, for the third action !b by d1, observe that d1’s frontier at b is at t1. Hence, the read may return either 0 or 1. Let us assume that it returns 0. The machine state is not updated by the non-atomic read. Similarly, for the fourth action !a by d2, d2’s frontier at a is at t0. Hence, this read may also return either 0 or 1. Let us assume that it returns 0. Hence, the assertion in the original program, assert (not (r1 = 0 && r2 = 0)), will fail for this particular execution. 10.6 Non-compliant operations *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* There are certain operations which are not memory model compliant. - Array.blit function on float arrays may cause tearing. When an unsynchronized blit operation runs concurrently with some overlapping write to the fields of the same float array, the field may end up with bits from either of the writes. - With flat-float arrays or records with only float fields on 32-bit architectures, getting or setting a field involves two separate memory accesses. In the presence of data races, the user may observe tearing. - The Bytes module Bytes permits mixed-mode accesses where reads and writes may be of different sizes. Unsynchronized mixed-mode accesses lead to tearing. --------------------------------------- (1) https://doi.org/10.1145/3192366.3192421 (2) https://doi.org/10.1145/3192366.3192421 (3) https://doi.org/10.1145/3192366.3192421 Part: II ******** The OCaml language ****************** Chapter 11  The OCaml language ********************************** Foreword ======== This document is intended as a reference manual for the OCaml language. It lists the language constructs, and gives their precise syntax and informal semantics. It is by no means a tutorial introduction to the language. A good working knowledge of OCaml is assumed. No attempt has been made at mathematical rigor: words are employed with their intuitive meaning, without further definition. As a consequence, the typing rules have been left out, by lack of the mathematical framework required to express them, while they are definitely part of a full formal definition of the language. Notations ========= The syntax of the language is given in BNF-like notation. Terminal symbols are set in typewriter font (like this). Non-terminal symbols are set in italic font (like that). Square brackets [...] denote optional components. Curly brackets {...} denotes zero, one or several repetitions of the enclosed components. Curly brackets with a trailing plus sign {...}^+ denote one or several repetitions of the enclosed components. Parentheses (...) denote grouping. 11.1 Lexical conventions *=*=*=*=*=*=*=*=*=*=*=*=*= Blanks ------ The following characters are considered as blanks: space, horizontal tabulation, carriage return, line feed and form feed. Blanks are ignored, but they separate adjacent identifiers, literals and keywords that would otherwise be confused as one single identifier, literal or keyword. Comments -------- Comments are introduced by the two characters (*, with no intervening blanks, and terminated by the characters *), with no intervening blanks. Comments are treated as blank characters. Comments do not occur inside string or character literals. Nested comments are handled correctly. << (* single line comment *) (* multiple line comment, commenting out part of a program, and containing a nested comment: let f = function | 'A'..'Z' -> "Uppercase" (* Add other cases later... *) *) >> Identifiers ----------- ident ::= (letter | _) { letter | 0...9 | _ | ' } capitalized-ident ::= (A...Z) { letter | 0...9 | _ | ' } lowercase-ident ::= (a...z | _) { letter | 0...9 | _ | ' } letter ::= A...Z | a...z Identifiers are sequences of letters, digits, _ (the underscore character), and ' (the single quote), starting with a letter or an underscore. Letters contain at least the 52 lowercase and uppercase letters from the ASCII set. The current implementation also recognizes as letters some characters from the ISO 8859-1 set (characters 192–214 and 216–222 as uppercase letters; characters 223–246 and 248–255 as lowercase letters). This feature is deprecated and should be avoided for future compatibility. All characters in an identifier are meaningful. The current implementation accepts identifiers up to 16000000 characters in length. In many places, OCaml makes a distinction between capitalized identifiers and identifiers that begin with a lowercase letter. The underscore character is considered a lowercase letter for this purpose. Integer literals ---------------- integer-literal ::= [-] (0...9) { 0...9 | _ } | [-] (0x | 0X) (0...9 | A...F | a...f) { 0...9 | A...F | a...f | _ } | [-] (0o | 0O) (0...7) { 0...7 | _ } | [-] (0b | 0B) (0...1) { 0...1 | _ } int32-literal ::= integer-literal l int64-literal ::= integer-literal L nativeint-literal ::= integer-literal n An integer literal is a sequence of one or more digits, optionally preceded by a minus sign. By default, integer literals are in decimal (radix 10). The following prefixes select a different radix: --------------------------------- |Prefix | Radix | --------------------------------- | 0x, 0X|hexadecimal (radix 16) | |0o, 0O |octal (radix 8) | |0b, 0B |binary (radix 2) | --------------------------------- (The initial 0 is the digit zero; the O for octal is the letter O.) An integer literal can be followed by one of the letters l, L or n to indicate that this integer has type int32, int64 or nativeint respectively, instead of the default type int for integer literals. The interpretation of integer literals that fall outside the range of representable integer values is undefined. For convenience and readability, underscore characters (_) are accepted (and ignored) within integer literals. << # let house_number = 37 let million = 1_000_000 let copyright = 0x00A9 let counter64bit = ref 0L;; val house_number : int = 37 val million : int = 1000000 val copyright : int = 169 val counter64bit : int64 ref = {contents = 0L} >> Floating-point literals ----------------------- float-literal ::= [-] (0...9) { 0...9 | _ } [. { 0...9 | _ }] [(e | E) [+ | -] (0...9) { 0...9 | _ }] | [-] (0x | 0X) (0...9 | A...F | a...f) { 0...9 | A...F | a...f | _ } [. { 0...9 | A...F | a...f | _ }] [(p | P) [+ | -] (0...9) { 0...9 | _ }] Floating-point decimal literals consist in an integer part, a fractional part and an exponent part. The integer part is a sequence of one or more digits, optionally preceded by a minus sign. The fractional part is a decimal point followed by zero, one or more digits. The exponent part is the character e or E followed by an optional + or - sign, followed by one or more digits. It is interpreted as a power of 10. The fractional part or the exponent part can be omitted but not both, to avoid ambiguity with integer literals. The interpretation of floating-point literals that fall outside the range of representable floating-point values is undefined. Floating-point hexadecimal literals are denoted with the 0x or 0X prefix. The syntax is similar to that of floating-point decimal literals, with the following differences. The integer part and the fractional part use hexadecimal digits. The exponent part starts with the character p or P. It is written in decimal and interpreted as a power of 2. For convenience and readability, underscore characters (_) are accepted (and ignored) within floating-point literals. << # let pi = 3.141_592_653_589_793_12 let small_negative = -1e-5 let machine_epsilon = 0x1p-52;; val pi : float = 3.14159265358979312 val small_negative : float = -1e-05 val machine_epsilon : float = 2.22044604925031308e-16 >> Character literals ------------------ char-literal ::= ' regular-char ' | ' escape-sequence ' escape-sequence ::= \ (\ | " | ' | n | t | b | r | space) | \ (0...9) (0...9) (0...9) | \x (0...9 | A...F | a...f) (0...9 | A...F | a...f) | \o (0...3) (0...7) (0...7) Character literals are delimited by ' (single quote) characters. The two single quotes enclose either one character different from ' and \, or one of the escape sequences below: ----------------------------------------------------------- |Sequence| Character denoted | ----------------------------------------------------------- | \\ |backslash (\) | |\" |double quote (") | |\' |single quote (') | |\n |linefeed (LF) | |\r |carriage return (CR) | |\t |horizontal tabulation (TAB) | |\b |backspace (BS) | |\space |space (SPC) | |\ddd |the character with ASCII code ddd in decimal | |\xhh |the character with ASCII code hh in hexadecimal | |\oooo |the character with ASCII code ooo in octal | ----------------------------------------------------------- << # let a = 'a' let single_quote = '\'' let copyright = '\xA9';; val a : char = 'a' val single_quote : char = '\'' val copyright : char = '\169' >> String literals --------------- string-literal ::= " { string-character } " | { quoted-string-id | { newline | any-char } | quoted-string-id } quoted-string-id ::= { a...z | _ } string-character ::= regular-string-char | escape-sequence + | \u{ { 0...9 | A...F | a...f } } | newline | \ newline { space | tab } String literals are delimited by " (double quote) characters. The two double quotes enclose a sequence of either characters different from " and \, or escape sequences from the table given above for character literals, or a Unicode character escape sequence. A Unicode character escape sequence is substituted by the UTF-8 encoding of the specified Unicode scalar value. The Unicode scalar value, an integer in the ranges 0x0000...0xD7FF or 0xE000...0x10FFFF, is defined using 1 to 6 hexadecimal digits; leading zeros are allowed. << # let greeting = "Hello, World!\n" let superscript_plus = "\u{207A}";; val greeting : string = "Hello, World!\n" val superscript_plus : string = "⁺" >> A newline sequence is a line feed optionally preceded by a carriage return. Since OCaml 5.2, a newline sequence occurring in a string literal is normalized into a single line feed character. To allow splitting long string literals across lines, the sequence \newline spaces-or-tabs (a backslash at the end of a line followed by any number of spaces and horizontal tabulations at the beginning of the next line) is ignored inside string literals. << # let longstr = "Call me Ishmael. Some years ago — never mind how long \ precisely — having little or no money in my purse, and \ nothing particular to interest me on shore, I thought I\ \ would sail about a little and see the watery part of t\ he world.";; val longstr : string = "Call me Ishmael. Some years ago — never mind how long precisely — having little or no money in my purse, and nothing particular to interest me on shore, I thought I would sail about a little and see the watery part of the world." >> Escaped newlines provide more convenient behavior than non-escaped newlines, as the indentation is not considered part of the string literal. << # let contains_unexpected_spaces = "This multiline literal contains three consecutive spaces." let no_unexpected_spaces = "This multiline literal \n\ uses a single space between all words.";; val contains_unexpected_spaces : string = "This multiline literal\n contains three consecutive spaces." val no_unexpected_spaces : string = "This multiline literal \nuses a single space between all words." >> Quoted string literals provide an alternative lexical syntax for string literals. They are useful to represent strings of arbitrary content without escaping. Quoted strings are delimited by a matching pair of { quoted-string-id | and | quoted-string-id } with the same quoted-string-id on both sides. Quoted strings do not interpret any character in a special way (1) but requires that the sequence | quoted-string-id } does not occur in the string itself. The identifier quoted-string-id is a (possibly empty) sequence of lowercase letters and underscores that can be freely chosen to avoid such issue. << # let quoted_greeting = {|"Hello, World!"|} let nested = {ext|hello {|world|}|ext};; val quoted_greeting : string = "\"Hello, World!\"" val nested : string = "hello {|world|}" >> The current implementation places practically no restrictions on the length of string literals. Naming labels ------------- To avoid ambiguities, naming labels in expressions cannot just be defined syntactically as the sequence of the three tokens ~, ident and :, and have to be defined at the lexical level. label-name ::= lowercase-ident label ::= ~ label-name : optlabel ::= ? label-name : Naming labels come in two flavours: label for normal arguments and optlabel for optional ones. They are simply distinguished by their first character, either ~ or ?. Despite label and optlabel being lexical entities in expressions, their expansions ~ label-name : and ? label-name : will be used in grammars, for the sake of readability. Note also that inside type expressions, this expansion can be taken literally, i.e. there are really 3 tokens, with optional blanks between them. Prefix and infix symbols ------------------------ infix-symbol ::= (core-operator-char | % | <) { operator-char } + | # { operator-char } prefix-symbol ::= ! { operator-char } + | (? | ~) { operator-char } operator-char ::= ~ | ! | ? | core-operator-char | % | < | : | . core-operator-char ::= $ | & | * | + | - | / | = | > | @ | ^ | | See also the following language extensions: extension operators, extended indexing operators, and binding operators. Sequences of “operator characters”, such as <=> or !!, are read as a single token from the infix-symbol or prefix-symbol class. These symbols are parsed as prefix and infix operators inside expressions, but otherwise behave like normal identifiers. Keywords -------- The identifiers below are reserved as keywords, and cannot be employed otherwise: << and as assert asr begin class constraint do done downto else end exception external false for fun function functor if in include inherit initializer land lazy let lor lsl lsr lxor match method mod module mutable new nonrec object of open or private rec sig struct then to true try type val virtual when while with >> The following character sequences are also keywords: << != # & && ' ( ) * + , - -. -> . .. .~ : :: := :> ; ;; < <- = > >] >} ? [ [< [> [| ] _ ` { {< | |] || } ~ >> Note that the following identifiers are keywords of the now unmaintained Camlp4 system and should be avoided for backwards compatibility reasons. << parser value $ $$ $: <: << >> ?? >> Ambiguities ----------- Lexical ambiguities are resolved according to the “longest match” rule: when a character sequence can be decomposed into two tokens in several different ways, the decomposition retained is the one with the longest first token. Line number directives ---------------------- + linenum-directive ::= # { 0...9 } " { string-character } " Preprocessors that generate OCaml source code can insert line number directives in their output so that error messages produced by the compiler contain line numbers and file names referring to the source file before preprocessing, instead of after preprocessing. A line number directive starts at the beginning of a line, is composed of a # (sharp sign), followed by a positive integer (the source line number), followed by a character string (the source file name). Line number directives are treated as blanks during lexical analysis. 11.2 Values *=*=*=*=*=*=* This section describes the kinds of values that are manipulated by OCaml programs. 11.2.1 Base values ==================== Integer numbers --------------- Integer values are integer numbers from −2^30 to 2^30−1, that is −1073741824 to 1073741823. The implementation may support a wider range of integer values: on 64-bit platforms, the current implementation supports integers ranging from −2^62 to 2^62−1. Floating-point numbers ---------------------- Floating-point values are numbers in floating-point representation. The current implementation uses double-precision floating-point numbers conforming to the IEEE 754 standard, with 53 bits of mantissa and an exponent ranging from −1022 to 1023. Characters ---------- Character values are represented as 8-bit integers between 0 and 255. Character codes between 0 and 127 are interpreted following the ASCII standard. The current implementation interprets character codes between 128 and 255 following the ISO 8859-1 standard. Character strings ----------------- String values are finite sequences of characters. The current implementation supports strings containing up to 2^24 − 5 characters (16777211 characters); on 64-bit platforms, the limit is 2^57 − 9. 11.2.2 Tuples =============== Tuples of values are written (v_1, ..., v_n), standing for the n-tuple of values v_1 to v_n. The current implementation supports tuple of up to 2^22 − 1 elements (4194303 elements). 11.2.3 Records ================ Record values are labeled tuples of values. The record value written { field_1 = v_1; ...; field_n = v_n } associates the value v_i to the record field field_i, for i = 1 ... n. The current implementation supports records with up to 2^22 − 1 fields (4194303 fields). 11.2.4 Arrays =============== Arrays are finite, variable-sized sequences of values of the same type. The current implementation supports arrays containing up to 2^22 − 1 elements (4194303 elements) unless the elements are floating-point numbers (2097151 elements in this case); on 64-bit platforms, the limit is 2^54 − 1 for all arrays. 11.2.5 Variant values ======================= Variant values are either a constant constructor, or a non-constant constructor applied to a number of values. The former case is written constr; the latter case is written constr (v_1, ... , v_n ), where the v_i are said to be the arguments of the non-constant constructor constr. The parentheses may be omitted if there is only one argument. The following constants are treated like built-in constant constructors: -------------------------------- |Constant| Constructor | -------------------------------- | false |the boolean false | |true |the boolean true | |() |the “unit” value | |[] |the empty list | -------------------------------- The current implementation limits each variant type to have at most 246 non-constant constructors and 2^30−1 constant constructors. 11.2.6 Polymorphic variants ============================= Polymorphic variants are an alternate form of variant values, not belonging explicitly to a predefined variant type, and following specific typing rules. They can be either constant, written `tag-name, or non-constant, written `tag-name(v). 11.2.7 Functions ================== Functional values are mappings from values to values. 11.2.8 Objects ================ Objects are composed of a hidden internal state which is a record of instance variables, and a set of methods for accessing and modifying these variables. The structure of an object is described by the toplevel class that created it. 11.3 Names *=*=*=*=*=*= Identifiers are used to give names to several classes of language objects and refer to these objects by name later: - value names (syntactic class value-name), - value constructors and exception constructors (class constr-name), - labels (label-name, defined in section 11.1), - polymorphic variant tags (tag-name), - type constructors (typeconstr-name), - record fields (field-name), - class names (class-name), - method names (method-name), - instance variable names (inst-var-name), - module names (module-name), - module type names (modtype-name). These eleven name spaces are distinguished both by the context and by the capitalization of the identifier: whether the first letter of the identifier is in lowercase (written lowercase-ident below) or in uppercase (written capitalized-ident). Underscore is considered a lowercase letter for this purpose. Naming objects -------------- value-name ::= lowercase-ident | ( operator-name ) operator-name ::= prefix-symbol | infix-op infix-op ::= infix-symbol | * | + | - | -. | = | != | < | > | or | || | & | && | := | mod | land | lor | lxor | lsl | lsr | asr constr-name ::= capitalized-ident tag-name ::= capitalized-ident typeconstr-name ::= lowercase-ident field-name ::= lowercase-ident module-name ::= capitalized-ident modtype-name ::= ident class-name ::= lowercase-ident inst-var-name ::= lowercase-ident method-name ::= lowercase-ident See also the following language extension: extended indexing operators. As shown above, prefix and infix symbols as well as some keywords can be used as value names, provided they are written between parentheses. The capitalization rules are summarized in the table below. ------------------------------------------------ | Name space |Case of first letter | ------------------------------------------------ | Values |lowercase | |Constructors |uppercase | |Labels |lowercase | |Polymorphic variant tags|uppercase | |Exceptions |uppercase | |Type constructors |lowercase | |Record fields |lowercase | |Classes |lowercase | |Instance variables |lowercase | |Methods |lowercase | |Modules |uppercase | |Module types |any | ------------------------------------------------ Note on polymorphic variant tags: the current implementation accepts lowercase variant tags in addition to capitalized variant tags, but we suggest you avoid lowercase variant tags for portability and compatibility with future OCaml versions. Referring to named objects -------------------------- value-path ::= [ module-path . ] value-name constr ::= [ module-path . ] constr-name typeconstr ::= [ extended-module-path . ] typeconstr-name field ::= [ module-path . ] field-name modtype-path ::= [ extended-module-path . ] modtype-name class-path ::= [ module-path . ] class-name classtype-path ::= [ extended-module-path . ] class-name module-path ::= module-name { . module-name } extended-module-path ::= extended-module-name { . extended-module-name } extended-module-name ::= module-name { ( extended-module-path ) } A named object can be referred to either by its name (following the usual static scoping rules for names) or by an access path prefix . name, where prefix designates a module and name is the name of an object defined in that module. The first component of the path, prefix, is either a simple module name or an access path name_1 . name_2 ..., in case the defining module is itself nested inside other modules. For referring to type constructors, module types, or class types, the prefix can also contain simple functor applications (as in the syntactic class extended-module-path above) in case the defining module is the result of a functor application. Label names, tag names, method names and instance variable names need not be qualified: the former three are global labels, while the latter are local to a class. 11.4 Type expressions *=*=*=*=*=*=*=*=*=*=*=* typexpr ::= ' ident | _ | ( typexpr ) | [[?]label-name:] typexpr -> typexpr + | typexpr { * typexpr } | typeconstr | typexpr typeconstr | ( typexpr { , typexpr } ) typeconstr | typexpr as ' ident | polymorphic-variant-type | < [..] > | < method-type { ; method-type } [; | ; ..] > | # classtype-path | typexpr # class-path | ( typexpr { , typexpr } ) # class-path poly-typexpr ::= typexpr + | { ' ident } . typexpr method-type ::= method-name : poly-typexpr See also the following language extensions: first-class modules, attributes and extension nodes. The table below shows the relative precedences and associativity of operators and non-closed type constructions. The constructions with higher precedences come first. ---------------------------------------------- | Operator |Associativity | ---------------------------------------------- | Type constructor application|– | |# |– | |* |– | |-> |right | |as |– | ---------------------------------------------- Type expressions denote types in definitions of data types as well as in type constraints over patterns and expressions. Type variables -------------- The type expression ' ident stands for the type variable named ident. The type expression _ stands for either an anonymous type variable or anonymous type parameters. In data type definitions, type variables are names for the data type parameters. In type constraints, they represent unspecified types that can be instantiated by any type to satisfy the type constraint. In general the scope of a named type variable is the whole top-level phrase where it appears, and it can only be generalized when leaving this scope. Anonymous variables have no such restriction. In the following cases, the scope of named type variables is restricted to the type expression where they appear: 1) for universal (explicitly polymorphic) type variables; 2) for type variables that only appear in public method specifications (as those variables will be made universal, as described in section 11.9.1); 3) for variables used as aliases, when the type they are aliased to would be invalid in the scope of the enclosing definition (i.e. when it contains free universal type variables, or locally defined types.) Parenthesized types ------------------- The type expression ( typexpr ) denotes the same type as typexpr. Function types -------------- The type expression typexpr_1 -> typexpr_2 denotes the type of functions mapping arguments of type typexpr_1 to results of type typexpr_2. label-name : typexpr_1 -> typexpr_2 denotes the same function type, but the argument is labeled label. ? label-name : typexpr_1 -> typexpr_2 denotes the type of functions mapping an optional labeled argument of type typexpr_1 to results of type typexpr_2. That is, the physical type of the function will be typexpr_1 option -> typexpr_2. Tuple types ----------- The type expression typexpr_1 * ... * typexpr_n denotes the type of tuples whose elements belong to types typexpr_1, ... typexpr_n respectively. Constructed types ----------------- Type constructors with no parameter, as in typeconstr, are type expressions. The type expression typexpr typeconstr, where typeconstr is a type constructor with one parameter, denotes the application of the unary type constructor typeconstr to the type typexpr. The type expression (typexpr_1,...,typexpr_n) typeconstr, where typeconstr is a type constructor with n parameters, denotes the application of the n-ary type constructor typeconstr to the types typexpr_1 through typexpr_n. In the type expression _ typeconstr , the anonymous type expression _ stands in for anonymous type parameters and is equivalent to (_, ...,_) with as many repetitions of _ as the arity of typeconstr. Aliased and recursive types --------------------------- The type expression typexpr as ' ident denotes the same type as typexpr, and also binds the type variable ident to type typexpr both in typexpr and in other types. In general the scope of an alias is the same as for a named type variable, and covers the whole enclosing definition. If the type variable ident actually occurs in typexpr, a recursive type is created. Recursive types for which there exists a recursive path that does not contain an object or polymorphic variant type constructor are rejected, except when the -rectypes mode is selected. If ' ident denotes an explicit polymorphic variable, and typexpr denotes either an object or polymorphic variant type, the row variable of typexpr is captured by ' ident, and quantified upon. Polymorphic variant types ------------------------- polymorphic-variant-type ::= [ tag-spec-first { | tag-spec } ] | [> [ tag-spec ] { | tag-spec } ] + | [< [|] tag-spec-full { | tag-spec-full } [ > { `tag-name } ] ] tag-spec-first ::= `tag-name [ of typexpr ] | [ typexpr ] | tag-spec tag-spec ::= `tag-name [ of typexpr ] | typexpr tag-spec-full ::= `tag-name [ of [&] typexpr { & typexpr } ] | typexpr Polymorphic variant types describe the values a polymorphic variant may take. The first case is an exact variant type: all possible tags are known, with their associated types, and they can all be present. Its structure is fully known. The second case is an open variant type, describing a polymorphic variant value: it gives the list of all tags the value could take, with their associated types. This type is still compatible with a variant type containing more tags. A special case is the unknown type, which does not define any tag, and is compatible with any variant type. The third case is a closed variant type. It gives information about all the possible tags and their associated types, and which tags are known to potentially appear in values. The exact variant type (first case) is just an abbreviation for a closed variant type where all possible tags are also potentially present. In all three cases, tags may be either specified directly in the `tag-name [of typexpr] form, or indirectly through a type expression, which must expand to an exact variant type, whose tag specifications are inserted in its place. Full specifications of variant tags are only used for non-exact closed types. They can be understood as a conjunctive type for the argument: it is intended to have all the types enumerated in the specification. Such conjunctive constraints may be unsatisfiable. In such a case the corresponding tag may not be used in a value of this type. This does not mean that the whole type is not valid: one can still use other available tags. Conjunctive constraints are mainly intended as output from the type checker. When they are used in source programs, unsolvable constraints may cause early failures. Object types ------------ An object type < [method-type { ; method-type }] > is a record of method types. Each method may have an explicit polymorphic type: { ' ident }^+ . typexpr. Explicit polymorphic variables have a local scope, and an explicit polymorphic type can only be unified to an equivalent one, where only the order and names of polymorphic variables may change. The type < { method-type ; } .. > is the type of an object whose method names and types are described by method-type_1, ..., method-type_n, and possibly some other methods represented by the ellipsis. This ellipsis actually is a special kind of type variable (called row variable in the literature) that stands for any number of extra method types. #-types ------- The type # classtype-path is a special kind of abbreviation. This abbreviation unifies with the type of any object belonging to a subclass of the class type classtype-path. It is handled in a special way as it usually hides a type variable (an ellipsis, representing the methods that may be added in a subclass). In particular, it vanishes when the ellipsis gets instantiated. Each type expression # classtype-path defines a new type variable, so type # classtype-path -> # classtype-path is usually not the same as type (# classtype-path as ' ident) -> ' ident. Variant and record types ------------------------ There are no type expressions describing (defined) variant types nor record types, since those are always named, i.e. defined before use and referred to by name. Type definitions are described in section 11.8.1. 11.5 Constants *=*=*=*=*=*=*=*= constant ::= integer-literal | int32-literal | int64-literal | nativeint-literal | float-literal | char-literal | string-literal | constr | false | true | () | begin end | [] | [||] | `tag-name See also the following language extension: extension literals. The syntactic class of constants comprises literals from the four base types (integers, floating-point numbers, characters, character strings), the integer variants, and constant constructors from both normal and polymorphic variants, as well as the special constants false, true, (), [], and [||], which behave like constant constructors, and begin end, which is equivalent to (). 11.6 Patterns *=*=*=*=*=*=*=* pattern ::= value-name | _ | constant | pattern as value-name | ( pattern ) | ( pattern : typexpr ) | pattern | pattern | constr pattern | `tag-name pattern | #typeconstr + | pattern { , pattern } | { field [: typexpr] [= pattern]{ ; field [: typexpr] [= pattern] } [; _ ] [ ; ] } | [ pattern { ; pattern } [ ; ] ] | pattern :: pattern | [| pattern { ; pattern } [ ; ] |] | char-literal .. char-literal | lazy pattern | exception pattern | module-path .( pattern ) | module-path .[ pattern ] | module-path .[| pattern |] | module-path .{ pattern } See also the following language extensions: first-class modules, attributes and extension nodes. The table below shows the relative precedences and associativity of operators and non-closed pattern constructions. The constructions with higher precedences come first. --------------------------------------------------------- | Operator |Associativity | --------------------------------------------------------- | .. |– | |lazy (see section 11.6) |– | |Constructor application, Tag application|right | |:: |right | |, |– | || |left | |as |– | --------------------------------------------------------- Patterns are templates that allow selecting data structures of a given shape, and binding identifiers to components of the data structure. This selection operation is called pattern matching; its outcome is either “this value does not match this pattern”, or “this value matches this pattern, resulting in the following bindings of names to values”. Variable patterns ----------------- A pattern that consists in a value name matches any value, binding the name to the value. The pattern _ also matches any value, but does not bind any name. << # let is_empty = function | [] -> true | _ :: _ -> false;; val is_empty : 'a list -> bool = >> Patterns are linear: a variable cannot be bound several times by a given pattern. In particular, there is no way to test for equality between two parts of a data structure using only a pattern: << # let pair_equal = function | x, x -> true | x, y -> false;; Error: Variable x is bound several times in this matching >> However, we can use a when guard for this purpose: << # let pair_equal = function | x, y when x = y -> true | _ -> false;; val pair_equal : 'a * 'a -> bool = >> Constant patterns ----------------- A pattern consisting in a constant matches the values that are equal to this constant. << # let bool_of_string = function | "true" -> true | "false" -> false | _ -> raise (Invalid_argument "bool_of_string");; val bool_of_string : string -> bool = >> Alias patterns -------------- The pattern pattern_1 as value-name matches the same values as pattern_1. If the matching against pattern_1 is successful, the name value-name is bound to the matched value, in addition to the bindings performed by the matching against pattern_1. << # let sort_pair ((x, y) as p) = if x <= y then p else (y, x);; val sort_pair : 'a * 'a -> 'a * 'a = >> Parenthesized patterns ---------------------- The pattern ( pattern_1 ) matches the same values as pattern_1. A type constraint can appear in a parenthesized pattern, as in ( pattern_1 : typexpr ). This constraint forces the type of pattern_1 to be compatible with typexpr. << # let int_triple_is_ordered ((a, b, c) : int * int * int) = a <= b && b <= c;; val int_triple_is_ordered : int * int * int -> bool = >> “Or” patterns ----------------- The pattern pattern_1 | pattern_2 represents the logical “or” of the two patterns pattern_1 and pattern_2. A value matches pattern_1 | pattern_2 if it matches pattern_1 or pattern_2. The two sub-patterns pattern_1 and pattern_2 must bind exactly the same identifiers to values having the same types. Matching is performed from left to right. More precisely, in case some value v matches pattern_1 | pattern_2, the bindings performed are those of pattern_1 when v matches pattern_1. Otherwise, value v matches pattern_2 whose bindings are performed. << # type shape = Square of float | Rect of (float * float) | Circle of float let is_rectangular = function | Square _ | Rect _ -> true | Circle _ -> false;; type shape = Square of float | Rect of (float * float) | Circle of float val is_rectangular : shape -> bool = >> Variant patterns ---------------- The pattern constr ( pattern_1 , ... , pattern_n ) matches all variants whose constructor is equal to constr, and whose arguments match pattern_1 ... pattern_n. It is a type error if n is not the number of arguments expected by the constructor. The pattern constr _ matches all variants whose constructor is constr. << # type 'a tree = Lf | Br of 'a tree * 'a * 'a tree let rec total = function | Br (l, x, r) -> total l + x + total r | Lf -> 0;; type 'a tree = Lf | Br of 'a tree * 'a * 'a tree val total : int tree -> int = >> The pattern pattern_1 :: pattern_2 matches non-empty lists whose heads match pattern_1, and whose tails match pattern_2. The pattern [ pattern_1 ; ... ; pattern_n ] matches lists of length n whose elements match pattern_1 ...pattern_n, respectively. This pattern behaves like pattern_1 :: ... :: pattern_n :: []. << # let rec destutter = function | [] -> [] | [a] -> [a] | a :: b :: t -> if a = b then destutter (b :: t) else a :: destutter (b :: t);; val destutter : 'a list -> 'a list = >> Polymorphic variant patterns ---------------------------- The pattern `tag-name pattern_1 matches all polymorphic variants whose tag is equal to tag-name, and whose argument matches pattern_1. << # let rec split = function | [] -> ([], []) | h :: t -> let ss, gs = split t in match h with | `Sheep _ as s -> (s :: ss, gs) | `Goat _ as g -> (ss, g :: gs);; val split : [< `Goat of 'a | `Sheep of 'b ] list -> [> `Sheep of 'b ] list * [> `Goat of 'a ] list = >> Polymorphic variant abbreviation patterns ----------------------------------------- If the type [('a,'b,...)] typeconstr = [ `tag-name_1 typexpr_1 | ... | `tag-name_n typexpr_n] is defined, then the pattern #typeconstr is a shorthand for the following or-pattern: ( `tag-name_1(_ : typexpr_1) | ... | `tag-name_n(_ : typexpr_n)). It matches all values of type [< typeconstr ]. << # type 'a rectangle = [`Square of 'a | `Rectangle of 'a * 'a] type 'a shape = [`Circle of 'a | 'a rectangle] let try_rectangle = function | #rectangle as r -> Some r | `Circle _ -> None;; type 'a rectangle = [ `Rectangle of 'a * 'a | `Square of 'a ] type 'a shape = [ `Circle of 'a | `Rectangle of 'a * 'a | `Square of 'a ] val try_rectangle : [< `Circle of 'a | `Rectangle of 'b * 'b | `Square of 'b ] -> [> `Rectangle of 'b * 'b | `Square of 'b ] option = >> Tuple patterns -------------- The pattern pattern_1 , ... , pattern_n matches n-tuples whose components match the patterns pattern_1 through pattern_n. That is, the pattern matches the tuple values (v_1, ..., v_n) such that pattern_i matches v_i for i = 1,... , n. << # let vector (x0, y0) (x1, y1) = (x1 -. x0, y1 -. y0);; val vector : float * float -> float * float -> float * float = >> Record patterns --------------- The pattern { field_1 [= pattern_1] ; ... ; field_n [= pattern_n] } matches records that define at least the fields field_1 through field_n, and such that the value associated to field_i matches the pattern pattern_i, for i = 1,... , n. A single identifier field_k stands for field_k = field_k , and a single qualified identifier module-path . field_k stands for module-path . field_k = field_k . The record value can define more fields than field_1 ...field_n; the values associated to these extra fields are not taken into account for matching. Optionally, a record pattern can be terminated by ; _ to convey the fact that not all fields of the record type are listed in the record pattern and that it is intentional. Optional type constraints can be added field by field with { field_1 : typexpr_1 = pattern_1 ;... ;field_n : typexpr_n = pattern_n } to force the type of field_k to be compatible with typexpr_k. << # let bytes_allocated {Gc.minor_words = minor; Gc.major_words = major; Gc.promoted_words = prom; _} = (Sys.word_size / 4) * int_of_float (minor +. major -. prom);; val bytes_allocated : Gc.stat -> int = >> Array patterns -------------- The pattern [| pattern_1 ; ... ; pattern_n |] matches arrays of length n such that the i-th array element matches the pattern pattern_i, for i = 1,... , n. << # let matrix3_is_symmetric = function | [|[|_; b; c|]; [|d; _; f|]; [|g; h; _|]|] -> b = d && c = g && f = h | _ -> failwith "matrix3_is_symmetric: not a 3x3 matrix";; val matrix3_is_symmetric : 'a array array -> bool = >> Range patterns -------------- The pattern ' c ' .. ' d ' is a shorthand for the pattern ' c ' | ' c_1 ' | ' c_2 ' | ... | ' c_n ' | ' d ' where c_1, c_2, ..., c_n are the characters that occur between c and d in the ASCII character set. For instance, the pattern '0'..'9' matches all characters that are digits. << # type char_class = Uppercase | Lowercase | Digit | Other let classify_char = function | 'A'..'Z' -> Uppercase | 'a'..'z' -> Lowercase | '0'..'9' -> Digit | _ -> Other;; type char_class = Uppercase | Lowercase | Digit | Other val classify_char : char -> char_class = >> Lazy patterns ------------- (Introduced in Objective Caml 3.11) The pattern lazy pattern matches a value v of type Lazy.t, provided pattern matches the result of forcing v with Lazy.force. A successful match of a pattern containing lazy sub-patterns forces the corresponding parts of the value being matched, even those that imply no test such as lazy value-name or lazy _. Matching a value with a pattern-matching where some patterns contain lazy sub-patterns may imply forcing parts of the value, even when the pattern selected in the end has no lazy sub-pattern. << # let force_opt = function | Some (lazy n) -> n | None -> 0;; val force_opt : int lazy_t option -> int = >> For more information, see the description of module Lazy in the standard library (module Lazy). Exception patterns ------------------ (Introduced in OCaml 4.02) A new form of exception pattern, exception pattern , is allowed only as a toplevel pattern or inside a toplevel or-pattern under a match...with pattern-matching (other occurrences are rejected by the type-checker). Cases with such a toplevel pattern are called “exception cases”, as opposed to regular “value cases”. Exception cases are applied when the evaluation of the matched expression raises an exception. The exception value is then matched against all the exception cases and re-raised if none of them accept the exception (as with a try...with block). Since the bodies of all exception and value cases are outside the scope of the exception handler, they are all considered to be in tail-position: if the match...with block itself is in tail position in the current function, any function call in tail position in one of the case bodies results in an actual tail call. A pattern match must contain at least one value case. It is an error if all cases are exceptions, because there would be no code to handle the return of a value. << # let find_opt p l = match List.find p l with | exception Not_found -> None | x -> Some x;; val find_opt : ('a -> bool) -> 'a list -> 'a option = >> Local opens for patterns ------------------------ (Introduced in OCaml 4.04) For patterns, local opens are limited to the module-path.(pattern) construction. This construction locally opens the module referred to by the module path module-path in the scope of the pattern pattern. When the body of a local open pattern is delimited by [ ], [| |], or { }, the parentheses can be omitted. For example, module-path.[pattern] is equivalent to module-path.([pattern]), and module-path.[| pattern |] is equivalent to module-path.([| pattern |]). << # let bytes_allocated Gc.{minor_words; major_words; promoted_words; _} = (Sys.word_size / 4) * int_of_float (minor_words +. major_words -. promoted_words);; val bytes_allocated : Gc.stat -> int = >> 11.7 Expressions *=*=*=*=*=*=*=*=*= expr ::= value-path | constant | ( expr ) | begin expr end | ( expr : typexpr ) + | expr { , expr } | constr expr | `tag-name expr | expr :: expr | [ expr { ; expr } [;] ] | [| expr { ; expr } [;] |] | { field [: typexpr] [= expr]{ ; field [: typexpr] [= expr] } [;] } | { expr with field [: typexpr] [= expr]{ ; field [: typexpr] [= expr] } [;] } + | expr { argument } | prefix-symbol expr | - expr | -. expr | expr infix-op expr | expr . field | expr . field <- expr | expr .( expr ) | expr .( expr ) <- expr | expr .[ expr ] | expr .[ expr ] <- expr | if expr then expr [ else expr ] | while expr do expr done | for value-name = expr ( to | downto ) expr do expr done | expr ; expr | match expr with pattern-matching | function pattern-matching + | fun { parameter } [ : typexpr ] -> expr | try expr with pattern-matching | let [rec] let-binding { and let-binding } in expr | let exception constr-decl in expr | let module module-name { ( module-name : module-type ) } [ : module-type ] = module-expr in expr | ( expr :> typexpr ) | ( expr : typexpr :> typexpr ) | assert expr | lazy expr | local-open | object-expr argument ::= expr | ~ label-name | ~ label-name : expr | ? label-name | ? label-name : expr pattern-matching ::= [ | ] pattern [when expr] -> expr { | pattern [when expr] -> expr } let-binding ::= pattern = expr | value-name { parameter } [: typexpr] [:> typexpr] = expr | value-name : poly-typexpr = expr parameter ::= pattern | ~ label-name | ~ ( label-name [: typexpr] ) | ~ label-name : pattern | ? label-name | ? ( label-name [: typexpr] [= expr] ) | ? label-name : pattern | ? label-name : ( pattern [: typexpr] [= expr] ) local-open ::= | let open module-path in expr | module-path .( expr ) | module-path .[ expr ] | module-path .[| expr |] | module-path .{ expr } | module-path .{< expr >} object-expr ::= | new class-path | object class-body end | expr # method-name | inst-var-name | inst-var-name <- expr | {< [ inst-var-name [= expr] { ; inst-var-name [= expr] } [;] ] >} See also the following language extensions: first-class modules, overriding in open statements, syntax for Bigarray access, attributes, extension nodes and extended indexing operators. 11.7.1 Precedence and associativity ===================================== The table below shows the relative precedences and associativity of operators and non-closed constructions. The constructions with higher precedence come first. For infix and prefix symbols, we write “*...” to mean “any symbol starting with *”. ------------------------------------------------------------------------------- -------------- | Construction or operator |Associativity | ------------------------------------------------------------------------------- -------------- | prefix-symbol |– | |. .( .[ .{ (see section 12.11) |– | |#... |left | |function application, constructor application, tag application, assert, lazy|left | |- -. (prefix) |– | |**... lsl lsr asr |right | |*... /... %... mod land lor lxor |left | | +... -... |left | |:: |right | |@... ^... |right | |=... <... >... |... &... $... != |left | |& && |right | |or || |right | |, |– | |<- := |right | |if |– | |; |right | |let match fun function try |– | ------------------------------------------------------------------------------- -------------- It is simple to test or refresh one’s understanding: << # 3 + 3 mod 2, 3 + (3 mod 2), (3 + 3) mod 2;; - : int * int * int = (4, 4, 0) >> 11.7.2 Basic expressions ========================== Constants --------- An expression consisting in a constant evaluates to this constant. For example, 3.14 or [||]. Value paths ----------- An expression consisting in an access path evaluates to the value bound to this path in the current evaluation environment. The path can be either a value name or an access path to a value component of a module. << # Float.ArrayLabels.to_list;; - : Float.ArrayLabels.t -> float list = >> Parenthesized expressions ------------------------- The expressions ( expr ) and begin expr end have the same value as expr. The two constructs are semantically equivalent, but it is good style to use begin ... end inside control structures: << if ... then begin ... ; ... end else begin ... ; ... end >> and ( ... ) for the other grouping situations. << # let x = 1 + 2 * 3 let y = (1 + 2) * 3;; val x : int = 7 val y : int = 9 >> << # let f a b = if a = b then print_endline "Equal" else begin print_string "Not Equal: "; print_int a; print_string " and "; print_int b; print_newline () end;; val f : int -> int -> unit = >> Parenthesized expressions can contain a type constraint, as in ( expr : typexpr ). This constraint forces the type of expr to be compatible with typexpr. Parenthesized expressions can also contain coercions ( expr [: typexpr] :> typexpr) (see subsection 11.7.7 below). Function application -------------------- Function application is denoted by juxtaposition of (possibly labeled) expressions. The expression expr argument_1 ... argument_n evaluates the expression expr and those appearing in argument_1 to argument_n. The expression expr must evaluate to a functional value f, which is then applied to the values of argument_1, ..., argument_n. The order in which the expressions expr, argument_1, ..., argument_n are evaluated is not specified. << # List.fold_left ( + ) 0 [1; 2; 3; 4; 5];; - : int = 15 >> Arguments and parameters are matched according to their respective labels. Argument order is irrelevant, except among arguments with the same label, or no label. << # ListLabels.fold_left ~f:( @ ) ~init:[] [[1; 2; 3]; [4; 5; 6]; [7; 8; 9]];; - : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9] >> If a parameter is specified as optional (label prefixed by ?) in the type of expr, the corresponding argument will be automatically wrapped with the constructor Some, except if the argument itself is also prefixed by ?, in which case it is passed as is. << # let fullname ?title first second = match title with | Some t -> t ^ " " ^ first ^ " " ^ second | None -> first ^ " " ^ second let name = fullname ~title:"Mrs" "Jane" "Fisher" let address ?title first second town = fullname ?title first second ^ "\n" ^ town;; val fullname : ?title:string -> string -> string -> string = val name : string = "Mrs Jane Fisher" val address : ?title:string -> string -> string -> string -> string = >> If a non-labeled argument is passed, and its corresponding parameter is preceded by one or several optional parameters, then these parameters are defaulted, i.e. the value None will be passed for them. All other missing parameters (without corresponding argument), both optional and non-optional, will be kept, and the result of the function will still be a function of these missing parameters to the body of f. << # let fullname ?title first second = match title with | Some t -> t ^ " " ^ first ^ " " ^ second | None -> first ^ " " ^ second let name = fullname "Jane" "Fisher";; val fullname : ?title:string -> string -> string -> string = val name : string = "Jane Fisher" >> In all cases but exact match of order and labels, without optional parameters, the function type should be known at the application point. This can be ensured by adding a type constraint. Principality of the derivation can be checked in the -principal mode. As a special case, OCaml supports labels-omitted full applications: if the function has a known arity, all the arguments are unlabeled, and their number matches the number of non-optional parameters, then labels are ignored and non-optional parameters are matched in their definition order. Optional arguments are defaulted. This omission of labels is discouraged and results in a warning, see 13.5.1. Function definition ------------------- Two syntactic forms are provided to define functions. The first form is introduced by the keyword function: function pattern -> expr 1 1 | ... | pattern -> expr n n This expression evaluates to a functional value with one argument. When this function is applied to a value v, this value is matched against each pattern pattern_1 to pattern_n. If one of these matchings succeeds, that is, if the value v matches the pattern pattern_i for some i, then the expression expr_i associated to the selected pattern is evaluated, and its value becomes the value of the function application. The evaluation of expr_i takes place in an environment enriched by the bindings performed during the matching. If several patterns match the argument v, the one that occurs first in the function definition is selected. If none of the patterns matches the argument, the exception Match_failure is raised. << # (function (0, 0) -> "both zero" | (0, _) -> "first only zero" | (_, 0) -> "second only zero" | (_, _) -> "neither zero") (7, 0);; - : string = "second only zero" >> The other form of function definition is introduced by the keyword fun: fun parameter_1 ... parameter_n -> expr This expression is equivalent to: fun parameter_1 -> ... fun parameter_n -> expr << # let f = (fun a -> fun b -> fun c -> a + b + c) let g = (fun a b c -> a + b + c);; val f : int -> int -> int -> int = val g : int -> int -> int -> int = >> An optional type constraint typexpr can be added before -> to enforce the type of the result to be compatible with the constraint typexpr: fun parameter_1 ... parameter_n : typexpr -> expr is equivalent to fun parameter_1 -> ... fun parameter_n -> (expr : typexpr ) Beware of the small syntactic difference between a type constraint on the last parameter fun parameter_1 ... (parameter_n:typexpr)-> expr and one on the result fun parameter_1 ... parameter_n: typexpr -> expr << # let eq = fun (a : int) (b : int) -> a = b let eq2 = fun a b : bool -> a = b let eq3 = fun (a : int) (b : int) : bool -> a = b;; val eq : int -> int -> bool = val eq2 : 'a -> 'a -> bool = val eq3 : int -> int -> bool = >> The parameter patterns ~lab and ~(lab [: typ]) are shorthands for respectively ~lab:lab and ~lab:(lab [: typ]), and similarly for their optional counterparts. << # let bool_map ~cmp:(cmp : int -> int -> bool) l = List.map cmp l let bool_map' ~(cmp : int -> int -> bool) l = List.map cmp l;; val bool_map : cmp:(int -> int -> bool) -> int list -> (int -> bool) list = val bool_map' : cmp:(int -> int -> bool) -> int list -> (int -> bool) list = >> A function of the form fun ? lab :( pattern = expr_0 ) -> expr is equivalent to fun ? lab : ident -> let pattern = match ident with Some ident -> ident | None -> expr_0 in expr where ident is a fresh variable, except that it is unspecified when expr_0 is evaluated. << # let open_file_for_input ?binary filename = match binary with | Some true -> open_in_bin filename | Some false | None -> open_in filename let open_file_for_input' ?(binary=false) filename = if binary then open_in_bin filename else open_in filename;; val open_file_for_input : ?binary:bool -> string -> in_channel = val open_file_for_input' : ?binary:bool -> string -> in_channel = >> After these two transformations, expressions are of the form fun [label_1] pattern_1 -> ... fun [label_n] pattern_n -> expr If we ignore labels, which will only be meaningful at function application, this is equivalent to function pattern_1 -> ... function pattern_n -> expr That is, the fun expression above evaluates to a curried function with n arguments: after applying this function n times to the values v_1 ... v_n, the values will be matched in parallel against the patterns pattern_1 ... pattern_n. If the matching succeeds, the function returns the value of expr in an environment enriched by the bindings performed during the matchings. If the matching fails, the exception Match_failure is raised. Guards in pattern-matchings --------------------------- The cases of a pattern matching (in the function, match and try constructs) can include guard expressions, which are arbitrary boolean expressions that must evaluate to true for the match case to be selected. Guards occur just before the -> token and are introduced by the when keyword: function pattern   [when   cond ] -> expr 1 1 1 | ... | pattern   [when   cond ] -> expr n n n Matching proceeds as described before, except that if the value matches some pattern pattern_i which has a guard cond_i, then the expression cond_i is evaluated (in an environment enriched by the bindings performed during matching). If cond_i evaluates to true, then expr_i is evaluated and its value returned as the result of the matching, as usual. But if cond_i evaluates to false, the matching is resumed against the patterns following pattern_i. << # let rec repeat f = function | 0 -> () | n when n > 0 -> f (); repeat f (n - 1) | _ -> raise (Invalid_argument "repeat");; val repeat : (unit -> 'a) -> int -> unit = >> Local definitions ----------------- The let and let rec constructs bind value names locally. The construct let pattern_1 = expr_1 and ... and pattern_n = expr_n in expr evaluates expr_1 ... expr_n in some unspecified order and matches their values against the patterns pattern_1 ... pattern_n. If the matchings succeed, expr is evaluated in the environment enriched by the bindings performed during matching, and the value of expr is returned as the value of the whole let expression. If one of the matchings fails, the exception Match_failure is raised. << # let v = let x = 1 in [x; x; x] let v' = let a, b = (1, 2) in a + b let v'' = let a = 1 and b = 2 in a + b;; val v : int list = [1; 1; 1] val v' : int = 3 val v'' : int = 3 >> An alternate syntax is provided to bind variables to functional values: instead of writing let ident = fun parameter_1 ... parameter_m -> expr in a let expression, one may instead write let ident parameter_1 ... parameter_m = expr << # let f = fun x -> fun y -> fun z -> x + y + z let f' = fun x y z -> x + y + z let f'' x y z = x + y + z;; val f : int -> int -> int -> int = val f' : int -> int -> int -> int = val f'' : int -> int -> int -> int = >> Recursive definitions of names are introduced by let rec: let rec pattern_1 = expr_1 and ... and pattern_n = expr_n in expr The only difference with the let construct described above is that the bindings of names to values performed by the pattern-matching are considered already performed when the expressions expr_1 to expr_n are evaluated. That is, the expressions expr_1 to expr_n can reference identifiers that are bound by one of the patterns pattern_1, ..., pattern_n, and expect them to have the same value as in expr, the body of the let rec construct. << # let rec even = function 0 -> true | n -> odd (n - 1) and odd = function 0 -> false | n -> even (n - 1) in even 1000;; - : bool = true >> The recursive definition is guaranteed to behave as described above if the expressions expr_1 to expr_n are function definitions (fun ... or function ...), and the patterns pattern_1 ... pattern_n are just value names, as in: let rec name_1 = fun ... and ... and name_n = fun ... in expr This defines name_1 ... name_n as mutually recursive functions local to expr. The behavior of other forms of let rec definitions is implementation-dependent. The current implementation also supports a certain class of recursive definitions of non-functional values, as explained in section 12.1. Local exceptions ---------------- (Introduced in OCaml 4.04) It is possible to define local exceptions in expressions: let exception constr-decl in expr . << # let map_empty_on_negative f l = let exception Negative in let aux x = if x < 0 then raise Negative else f x in try List.map aux l with Negative -> [];; val map_empty_on_negative : (int -> 'a) -> int list -> 'a list = >> The syntactic scope of the exception constructor is the inner expression, but nothing prevents exception values created with this constructor from escaping this scope. Two executions of the definition above result in two incompatible exception constructors (as for any exception definition). For instance: << # let gen () = let exception A in A let () = assert(gen () = gen ());; Exception: Assert_failure ("expr.etex", 3, 9). >> Explicit polymorphic type annotations ------------------------------------- (Introduced in OCaml 3.12) Polymorphic type annotations in let-definitions behave in a way similar to polymorphic methods: let pattern_1 : typ_1 ... typ_n . typexpr = expr These annotations explicitly require the defined value to be polymorphic, and allow one to use this polymorphism in recursive occurrences (when using let rec). Note however that this is a normal polymorphic type, unifiable with any instance of itself. 11.7.3 Control structures =========================== Sequence -------- The expression expr_1 ; expr_2 evaluates expr_1 first, then expr_2, and returns the value of expr_2. << # let print_pair (a, b) = print_string "("; print_string (string_of_int a); print_string ","; print_string (string_of_int b); print_endline ")";; val print_pair : int * int -> unit = >> Conditional ----------- The expression if expr_1 then expr_2 else expr_3 evaluates to the value of expr_2 if expr_1 evaluates to the boolean true, and to the value of expr_3 if expr_1 evaluates to the boolean false. << # let rec factorial x = if x <= 1 then 1 else x * factorial (x - 1);; val factorial : int -> int = >> The else expr_3 part can be omitted, in which case it defaults to else (). << # let debug = ref false let log msg = if !debug then prerr_endline msg;; val debug : bool ref = {contents = false} val log : string -> unit = >> Case expression --------------- The expression match expr with pattern -> expr 1 1 | ... | pattern -> expr n n matches the value of expr against the patterns pattern_1 to pattern_n. If the matching against pattern_i succeeds, the associated expression expr_i is evaluated, and its value becomes the value of the whole match expression. The evaluation of expr_i takes place in an environment enriched by the bindings performed during matching. If several patterns match the value of expr, the one that occurs first in the match expression is selected. << # let rec sum l = match l with | [] -> 0 | h :: t -> h + sum t;; val sum : int list -> int = >> If none of the patterns match the value of expr, the exception Match_failure is raised. << # let unoption o = match o with | Some x -> x ;; Warning 8 [partial-match]: this pattern-matching is not exhaustive. Here is an example of a case that is not matched: None val unoption : 'a option -> 'a = >> << # let l = List.map unoption [Some 1; Some 10; None; Some 2];; Exception: Match_failure ("expr.etex", 2, 2). >> Boolean operators ----------------- The expression expr_1 && expr_2 evaluates to true if both expr_1 and expr_2 evaluate to true; otherwise, it evaluates to false. The first component, expr_1, is evaluated first. The second component, expr_2, is not evaluated if the first component evaluates to false. Hence, the expression expr_1 && expr_2 behaves exactly as if expr_1 then expr_2 else false. The expression expr_1 || expr_2 evaluates to true if one of the expressions expr_1 and expr_2 evaluates to true; otherwise, it evaluates to false. The first component, expr_1, is evaluated first. The second component, expr_2, is not evaluated if the first component evaluates to true. Hence, the expression expr_1 || expr_2 behaves exactly as if expr_1 then true else expr_2. The boolean operators & and or are deprecated synonyms for (respectively) && and ||. << # let xor a b = (a || b) && not (a && b);; val xor : bool -> bool -> bool = >> Loops ----- The expression while expr_1 do expr_2 done repeatedly evaluates expr_2 while expr_1 evaluates to true. The loop condition expr_1 is evaluated and tested at the beginning of each iteration. The whole while ... done expression evaluates to the unit value (). << # let chars_of_string s = let i = ref 0 in let chars = ref [] in while !i < String.length s do chars := s.[!i] :: !chars; i := !i + 1 done; List.rev !chars;; val chars_of_string : string -> char list = >> As a special case, while true do expr done is given a polymorphic type, allowing it to be used in place of any expression (for example as a branch of any pattern-matching). The expression for name = expr_1 to expr_2 do expr_3 done first evaluates the expressions expr_1 and expr_2 (the boundaries) into integer values n and p. Then, the loop body expr_3 is repeatedly evaluated in an environment where name is successively bound to the values n, n+1, ..., p−1, p. The loop body is never evaluated if n > p. << # let chars_of_string s = let l = ref [] in for p = 0 to String.length s - 1 do l := s.[p] :: !l done; List.rev !l;; val chars_of_string : string -> char list = >> The expression for name = expr_1 downto expr_2 do expr_3 done evaluates similarly, except that name is successively bound to the values n, n−1, ..., p+1, p. The loop body is never evaluated if n < p. << # let chars_of_string s = let l = ref [] in for p = String.length s - 1 downto 0 do l := s.[p] :: !l done; !l;; val chars_of_string : string -> char list = >> In both cases, the whole for expression evaluates to the unit value (). Exception handling ------------------ The expression try expr with pattern -> expr 1 1 | ... | pattern -> expr n n evaluates the expression expr and returns its value if the evaluation of expr does not raise any exception. If the evaluation of expr raises an exception, the exception value is matched against the patterns pattern_1 to pattern_n. If the matching against pattern_i succeeds, the associated expression expr_i is evaluated, and its value becomes the value of the whole try expression. The evaluation of expr_i takes place in an environment enriched by the bindings performed during matching. If several patterns match the value of expr, the one that occurs first in the try expression is selected. If none of the patterns matches the value of expr, the exception value is raised again, thereby transparently “passing through” the try construct. << # let find_opt p l = try Some (List.find p l) with Not_found -> None;; val find_opt : ('a -> bool) -> 'a list -> 'a option = >> 11.7.4 Operations on data structures ====================================== Products -------- The expression expr_1 , ... , expr_n evaluates to the n-tuple of the values of expressions expr_1 to expr_n. The evaluation order of the subexpressions is not specified. << # (1 + 2 * 3, (1 + 2) * 3, 1 + (2 * 3));; - : int * int * int = (7, 9, 7) >> Variants -------- The expression constr expr evaluates to the unary variant value whose constructor is constr, and whose argument is the value of expr. Similarly, the expression constr ( expr_1 , ... , expr_n ) evaluates to the n-ary variant value whose constructor is constr and whose arguments are the values of expr_1, ..., expr_n. The expression constr (expr_1, ..., expr_n) evaluates to the variant value whose constructor is constr, and whose arguments are the values of expr_1 ... expr_n. << # type t = Var of string | Not of t | And of t * t | Or of t * t let test = And (Var "x", Not (Or (Var "y", Var "z")));; type t = Var of string | Not of t | And of t * t | Or of t * t val test : t = And (Var "x", Not (Or (Var "y", Var "z"))) >> For lists, some syntactic sugar is provided. The expression expr_1 :: expr_2 stands for the constructor ( :: ) applied to the arguments ( expr_1 , expr_2 ), and therefore evaluates to the list whose head is the value of expr_1 and whose tail is the value of expr_2. The expression [ expr_1 ; ... ; expr_n ] is equivalent to expr_1 :: ... :: expr_n :: [], and therefore evaluates to the list whose elements are the values of expr_1 to expr_n. << # 0 :: [1; 2; 3] = 0 :: 1 :: 2 :: 3 :: [];; - : bool = true >> Polymorphic variants -------------------- The expression `tag-name expr evaluates to the polymorphic variant value whose tag is tag-name, and whose argument is the value of expr. << # let with_counter x = `V (x, ref 0);; val with_counter : 'a -> [> `V of 'a * int ref ] = >> Records ------- The expression { field_1 [= expr_1] ; ... ; field_n [= expr_n ]} evaluates to the record value { field_1 = v_1; ...; field_n = v_n } where v_i is the value of expr_i for i = 1,... , n. A single identifier field_k stands for field_k = field_k, and a qualified identifier module-path . field_k stands for module-path . field_k = field_k. The fields field_1 to field_n must all belong to the same record type; each field of this record type must appear exactly once in the record expression, though they can appear in any order. The order in which expr_1 to expr_n are evaluated is not specified. Optional type constraints can be added after each field { field_1 : typexpr_1 = expr_1 ;... ; field_n : typexpr_n = expr_n } to force the type of field_k to be compatible with typexpr_k. << # type t = {house_no : int; street : string; town : string; postcode : string } let address x = Printf.sprintf "The occupier\n%i %s\n%s\n%s" x.house_no x.street x.town x.postcode;; type t = { house_no : int; street : string; town : string; postcode : string; } val address : t -> string = >> The expression { expr with field_1 [= expr_1] ; ... ; field_n [= expr_n] } builds a fresh record with fields field_1 ... field_n equal to expr_1 ... expr_n, and all other fields having the same value as in the record expr. In other terms, it returns a shallow copy of the record expr, except for the fields field_1 ... field_n, which are initialized to expr_1 ... expr_n. As previously, single identifier field_k stands for field_k = field_k, a qualified identifier module-path . field_k stands for module-path . field_k = field_k and it is possible to add an optional type constraint on each field being updated with { expr with field_1 : typexpr_1 = expr_1 ; ... ; field_n : typexpr_n = expr_n }. << # type t = {house_no : int; street : string; town : string; postcode : string } let uppercase_town address = {address with town = String.uppercase_ascii address.town};; type t = { house_no : int; street : string; town : string; postcode : string; } val uppercase_town : t -> t = >> The expression expr_1 . field evaluates expr_1 to a record value, and returns the value associated to field in this record value. The expression expr_1 . field <- expr_2 evaluates expr_1 to a record value, which is then modified in-place by replacing the value associated to field in this record by the value of expr_2. This operation is permitted only if field has been declared mutable in the definition of the record type. The whole expression expr_1 . field <- expr_2 evaluates to the unit value (). << # type t = {mutable upper : int; mutable lower : int; mutable other : int} let stats = {upper = 0; lower = 0; other = 0} let collect = String.iter (function | 'A'..'Z' -> stats.upper <- stats.upper + 1 | 'a'..'z' -> stats.lower <- stats.lower + 1 | _ -> stats.other <- stats.other + 1);; type t = { mutable upper : int; mutable lower : int; mutable other : int; } val stats : t = {upper = 0; lower = 0; other = 0} val collect : string -> unit = >> Arrays ------ The expression [| expr_1 ; ... ; expr_n |] evaluates to a n-element array, whose elements are initialized with the values of expr_1 to expr_n respectively. The order in which these expressions are evaluated is unspecified. The expression expr_1 .( expr_2 ) returns the value of element number expr_2 in the array denoted by expr_1. The first element has number 0; the last element has number n−1, where n is the size of the array. The exception Invalid_argument is raised if the access is out of bounds. The expression expr_1 .( expr_2 ) <- expr_3 modifies in-place the array denoted by expr_1, replacing element number expr_2 by the value of expr_3. The exception Invalid_argument is raised if the access is out of bounds. The value of the whole expression is (). << # let scale arr n = for x = 0 to Array.length arr - 1 do arr.(x) <- arr.(x) * n done let x = [|1; 10; 100|] let _ = scale x 2;; val scale : int array -> int -> unit = val x : int array = [|2; 20; 200|] >> Strings ------- The expression expr_1 .[ expr_2 ] returns the value of character number expr_2 in the string denoted by expr_1. The first character has number 0; the last character has number n−1, where n is the length of the string. The exception Invalid_argument is raised if the access is out of bounds. << # let iter f s = for x = 0 to String.length s - 1 do f s.[x] done;; val iter : (char -> 'a) -> string -> unit = >> The expression expr_1 .[ expr_2 ] <- expr_3 modifies in-place the string denoted by expr_1, replacing character number expr_2 by the value of expr_3. The exception Invalid_argument is raised if the access is out of bounds. The value of the whole expression is (). Note: this possibility is offered only for backward compatibility with older versions of OCaml and will be removed in a future version. New code should use byte sequences and the Bytes.set function. 11.7.5 Operators ================== Symbols from the class infix-symbol, as well as the keywords *, +, -, -., =, !=, <, >, or, ||, &, &&, :=, mod, land, lor, lxor, lsl, lsr, and asr can appear in infix position (between two expressions). Symbols from the class prefix-symbol, as well as the keywords - and -. can appear in prefix position (in front of an expression). << # (( * ), ( := ), ( || ));; - : (int -> int -> int) * ('a ref -> 'a -> unit) * (bool -> bool -> bool) = (, , ) >> Infix and prefix symbols do not have a fixed meaning: they are simply interpreted as applications of functions bound to the names corresponding to the symbols. The expression prefix-symbol expr is interpreted as the application ( prefix-symbol ) expr. Similarly, the expression expr_1 infix-symbol expr_2 is interpreted as the application ( infix-symbol ) expr_1 expr_2. The table below lists the symbols defined in the initial environment and their initial meaning. (See the description of the core library module Stdlib in chapter 28 for more details). Their meaning may be changed at any time using let ( infix-op ) name_1 name_2 = ... << # let ( + ), ( - ), ( * ), ( / ) = Int64.(add, sub, mul, div);; val ( + ) : int64 -> int64 -> int64 = val ( - ) : int64 -> int64 -> int64 = val ( * ) : int64 -> int64 -> int64 = val ( / ) : int64 -> int64 -> int64 = >> Note: the operators &&, ||, and ~- are handled specially and it is not advisable to change their meaning. The keywords - and -. can appear both as infix and prefix operators. When they appear as prefix operators, they are interpreted respectively as the functions (~-) and (~-.). ---------------------------------------------------------- | Operator | Initial meaning | ---------------------------------------------------------- | + |Integer addition. | |- (infix) |Integer subtraction. | |~- - (prefix) |Integer negation. | |* |Integer multiplication. | |/ |Integer division. Raise | | |Division_by_zero if second argument is| | |zero. | |mod |Integer modulus. Raise | | |Division_by_zero if second argument is| | |zero. | |land |Bitwise logical “and” on integers.| | | | |lor |Bitwise logical “or” on integers. | |lxor |Bitwise logical “exclusive or” on | | |integers. | |lsl |Bitwise logical shift left on | | |integers. | |lsr |Bitwise logical shift right on | | |integers. | |asr |Bitwise arithmetic shift right on | | |integers. | |+. |Floating-point addition. | |-. (infix) |Floating-point subtraction. | |~-. -. (prefix)|Floating-point negation. | |*. |Floating-point multiplication. | |/. |Floating-point division. | |** |Floating-point exponentiation. | |@ |List concatenation. | |^ |String concatenation. | |! |Dereferencing (return the current | | |contents of a reference). | |:= |Reference assignment (update the | | |reference given as first argument with| | |the value of the second argument). | |= |Structural equality test. | |<> |Structural inequality test. | |== |Physical equality test. | |!= |Physical inequality test. | |< |Test “less than”. | |<= |Test “less than or equal”. | |> |Test “greater than”. | |>= |Test “greater than or equal”. | |&& & |Boolean conjunction. | ||| or |Boolean disjunction. | ---------------------------------------------------------- 11.7.6 Objects ================ Object creation --------------- When class-path evaluates to a class body, new class-path evaluates to a new object containing the instance variables and methods of this class. << # class of_list (lst : int list) = object val mutable l = lst method next = match l with | [] -> raise (Failure "empty list"); | h::t -> l <- t; h end let a = new of_list [1; 1; 2; 3; 5; 8; 13] let b = new of_list;; class of_list : int list -> object val mutable l : int list method next : int end val a : of_list = val b : int list -> of_list = >> When class-path evaluates to a class function, new class-path evaluates to a function expecting the same number of arguments and returning a new object of this class. Immediate object creation ------------------------- Creating directly an object through the object class-body end construct is operationally equivalent to defining locally a class class-name = object class-body end —see sections 11.9.2 and following for the syntax of class-body— and immediately creating a single object from it by new class-name. << # let o = object val secret = 99 val password = "unlock" method get guess = if guess <> password then None else Some secret end;; val o : < get : string -> int option > = >> The typing of immediate objects is slightly different from explicitly defining a class in two respects. First, the inferred object type may contain free type variables. Second, since the class body of an immediate object will never be extended, its self type can be unified with a closed object type. Method invocation ----------------- The expression expr # method-name invokes the method method-name of the object denoted by expr. << # class of_list (lst : int list) = object val mutable l = lst method next = match l with | [] -> raise (Failure "empty list"); | h::t -> l <- t; h end let a = new of_list [1; 1; 2; 3; 5; 8; 13] let third = ignore a#next; ignore a#next; a#next;; class of_list : int list -> object val mutable l : int list method next : int end val a : of_list = val third : int = 2 >> If method-name is a polymorphic method, its type should be known at the invocation site. This is true for instance if expr is the name of a fresh object (let ident = new class-path ... ) or if there is a type constraint. Principality of the derivation can be checked in the -principal mode. Accessing and modifying instance variables ------------------------------------------ The instance variables of a class are visible only in the body of the methods defined in the same class or a class that inherits from the class defining the instance variables. The expression inst-var-name evaluates to the value of the given instance variable. The expression inst-var-name <- expr assigns the value of expr to the instance variable inst-var-name, which must be mutable. The whole expression inst-var-name <- expr evaluates to (). << # class of_list (lst : int list) = object val mutable l = lst method next = match l with (* access instance variable *) | [] -> raise (Failure "empty list"); | h::t -> l <- t; h (* modify instance variable *) end;; class of_list : int list -> object val mutable l : int list method next : int end >> Object duplication ------------------ An object can be duplicated using the library function Oo.copy (see module Oo). Inside a method, the expression {< [inst-var-name [= expr] { ; inst-var-name [= expr] }] >} returns a copy of self with the given instance variables replaced by the values of the associated expressions. A single instance variable name id stands for id = id. Other instance variables have the same value in the returned object as in self. << # let o = object val secret = 99 val password = "unlock" method get guess = if guess <> password then None else Some secret method with_new_secret s = {< secret = s >} end;; val o : < get : string -> int option; with_new_secret : int -> 'a > as 'a = >> 11.7.7 Coercions ================== Expressions whose type contains object or polymorphic variant types can be explicitly coerced (weakened) to a supertype. The expression (expr :> typexpr) coerces the expression expr to type typexpr. The expression (expr : typexpr_1 :> typexpr_2) coerces the expression expr from type typexpr_1 to type typexpr_2. The former operator will sometimes fail to coerce an expression expr from a type typ_1 to a type typ_2 even if type typ_1 is a subtype of type typ_2: in the current implementation it only expands two levels of type abbreviations containing objects and/or polymorphic variants, keeping only recursion when it is explicit in the class type (for objects). As an exception to the above algorithm, if both the inferred type of expr and typ are ground (i.e. do not contain type variables), the former operator behaves as the latter one, taking the inferred type of expr as typ_1. In case of failure with the former operator, the latter one should be used. It is only possible to coerce an expression expr from type typ_1 to type typ_2, if the type of expr is an instance of typ_1 (like for a type annotation), and typ_1 is a subtype of typ_2. The type of the coerced expression is an instance of typ_2. If the types contain variables, they may be instantiated by the subtyping algorithm, but this is only done after determining whether typ_1 is a potential subtype of typ_2. This means that typing may fail during this latter unification step, even if some instance of typ_1 is a subtype of some instance of typ_2. In the following paragraphs we describe the subtyping relation used. Object types ------------ A fixed object type admits as subtype any object type that includes all its methods. The types of the methods shall be subtypes of those in the supertype. Namely, < met_1 : typ_1 ; ... ; met_n : typ_n > is a supertype of < met_1 : typ′_1 ; ... ; met_n : typ′_n ; met_n+1 : typ′_n+1 ; ... ; met_n+m : typ′_n+m [; ..] > which may contain an ellipsis .. if every typ_i is a supertype of the corresponding typ′_i. A monomorphic method type can be a supertype of a polymorphic method type. Namely, if typ is an instance of typ′, then 'a_1 ... 'a_n . typ′ is a subtype of typ. Inside a class definition, newly defined types are not available for subtyping, as the type abbreviations are not yet completely defined. There is an exception for coercing self to the (exact) type of its class: this is allowed if the type of self does not appear in a contravariant position in the class type, i.e. if there are no binary methods. Polymorphic variant types ------------------------- A polymorphic variant type typ is a subtype of another polymorphic variant type typ′ if the upper bound of typ (i.e. the maximum set of constructors that may appear in an instance of typ) is included in the lower bound of typ′, and the types of arguments for the constructors of typ are subtypes of those in typ′. Namely, [[<] `C_1 of typ_1 | ... | `C_n of typ_n ] which may be a shrinkable type, is a subtype of [[>] `C_1 of typ′_1 | ... | `C_n of typ′_n | `C_n+1 of typ′_n+1 | ... | `C_n+m of typ′_n+m ] which may be an extensible type, if every typ_i is a subtype of typ′_i. Variance -------- Other types do not introduce new subtyping, but they may propagate the subtyping of their arguments. For instance, typ_1 * typ_2 is a subtype of typ′_1 * typ′_2 when typ_1 and typ_2 are respectively subtypes of typ′_1 and typ′_2. For function types, the relation is more subtle: typ_1 -> typ_2 is a subtype of typ′_1 -> typ′_2 if typ_1 is a supertype of typ′_1 and typ_2 is a subtype of typ′_2. For this reason, function types are covariant in their second argument (like tuples), but contravariant in their first argument. Mutable types, like array or ref are neither covariant nor contravariant, they are nonvariant, that is they do not propagate subtyping. For user-defined types, the variance is automatically inferred: a parameter is covariant if it has only covariant occurrences, contravariant if it has only contravariant occurrences, variance-free if it has no occurrences, and nonvariant otherwise. A variance-free parameter may change freely through subtyping, it does not have to be a subtype or a supertype. For abstract and private types, the variance must be given explicitly (see section 11.8.1), otherwise the default is nonvariant. This is also the case for constrained arguments in type definitions. 11.7.8 Other ============== Assertion checking ------------------ OCaml supports the assert construct to check debugging assertions. The expression assert expr evaluates the expression expr and returns () if expr evaluates to true. If it evaluates to false the exception Assert_failure is raised with the source file name and the location of expr as arguments. Assertion checking can be turned off with the -noassert compiler option. In this case, expr is not evaluated at all. << # let f a b c = assert (a <= b && b <= c); (b -. a) /. (c -. b);; val f : float -> float -> float -> float = >> As a special case, assert false is reduced to raise (Assert_failure ...), which gives it a polymorphic type. This means that it can be used in place of any expression (for example as a branch of any pattern-matching). It also means that the assert false “assertions” cannot be turned off by the -noassert option. << # let min_known_nonempty = function | [] -> assert false | l -> List.hd (List.sort compare l);; val min_known_nonempty : 'a list -> 'a = >> Lazy expressions ---------------- The expression lazy expr returns a value v of type Lazy.t that encapsulates the computation of expr. The argument expr is not evaluated at this point in the program. Instead, its evaluation will be performed the first time the function Lazy.force is applied to the value v, returning the actual value of expr. Subsequent applications of Lazy.force to v do not evaluate expr again. Applications of Lazy.force may be implicit through pattern matching (see 11.6). << # let lazy_greeter = lazy (print_string "Hello, World!\n");; val lazy_greeter : unit lazy_t = >> << # Lazy.force lazy_greeter;; Hello, World! - : unit = () >> Local modules ------------- The expression let module module-name = module-expr in expr locally binds the module expression module-expr to the identifier module-name during the evaluation of the expression expr. It then returns the value of expr. For example: << # let remove_duplicates comparison_fun string_list = let module StringSet = Set.Make(struct type t = string let compare = comparison_fun end) in StringSet.elements (List.fold_right StringSet.add string_list StringSet.empty);; val remove_duplicates : (string -> string -> int) -> string list -> string list = >> Local opens ----------- The expressions let open module-path in expr and module-path.(expr) are strictly equivalent. These constructions locally open the module referred to by the module path module-path in the respective scope of the expression expr. << # let map_3d_matrix f m = let open Array in map (map (map f)) m let map_3d_matrix' f = Array.(map (map (map f)));; val map_3d_matrix : ('a -> 'b) -> 'a array array array -> 'b array array array = val map_3d_matrix' : ('a -> 'b) -> 'a array array array -> 'b array array array = >> When the body of a local open expression is delimited by [ ], [| |], or { }, the parentheses can be omitted. For expression, parentheses can also be omitted for {< >}. For example, module-path.[expr] is equivalent to module-path.([expr]), and module-path.[| expr |] is equivalent to module-path.([| expr |]). << # let vector = Random.[|int 255; int 255; int 255; int 255|];; val vector : int array = [|220; 90; 247; 144|] >> 11.8 Type and exception definitions *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* 11.8.1 Type definitions ========================= Type definitions bind type constructors to data types: either variant types, record types, type abbreviations, or abstract data types. They also bind the value constructors and record fields associated with the definition. type-definition ::= type [nonrec] typedef { and typedef } typedef ::= [type-params] typeconstr-name type-information type-information ::= [type-equation] [type-representation] { type-constraint } type-equation ::= = typexpr type-representation ::= = [|] constr-decl { | constr-decl } | = record-decl | = | type-params ::= type-param | ( type-param { , type-param } ) type-param ::= [ext-variance] ' ident ext-variance ::= variance [injectivity] | injectivity [variance] variance ::= + | - injectivity ::= ! record-decl ::= { field-decl { ; field-decl } [;] } constr-decl ::= (constr-name | [] | (::)) [ of constr-args ] constr-args ::= typexpr { * typexpr } field-decl ::= [mutable] field-name : poly-typexpr type-constraint ::= constraint typexpr = typexpr See also the following language extensions: private types, generalized algebraic datatypes, attributes, extension nodes, extensible variant types and inline records. Type definitions are introduced by the type keyword, and consist in one or several simple definitions, possibly mutually recursive, separated by the and keyword. Each simple definition defines one type constructor. A simple definition consists in a lowercase identifier, possibly preceded by one or several type parameters, and followed by an optional type equation, then an optional type representation, and then a constraint clause. The identifier is the name of the type constructor being defined. <> In the right-hand side of type definitions, references to one of the type constructor name being defined are considered as recursive, unless type is followed by nonrec. The nonrec keyword was introduced in OCaml 4.02.2. The optional type parameters are either one type variable ' ident, for type constructors with one parameter, or a list of type variables ('ident_1,...,'ident_n), for type constructors with several parameters. Each type parameter may be prefixed by a variance constraint + (resp. -) indicating that the parameter is covariant (resp. contravariant), and an injectivity annotation ! indicating that the parameter can be deduced from the whole type. These type parameters can appear in the type expressions of the right-hand side of the definition, optionally restricted by a variance constraint ; i.e. a covariant parameter may only appear on the right side of a functional arrow (more precisely, follow the left branch of an even number of arrows), and a contravariant parameter only the left side (left branch of an odd number of arrows). If the type has a representation or an equation, and the parameter is free (i.e. not bound via a type constraint to a constructed type), its variance constraint is checked but subtyping etc. will use the inferred variance of the parameter, which may be less restrictive; otherwise (i.e. for abstract types or non-free parameters), the variance must be given explicitly, and the parameter is invariant if no variance is given. The optional type equation = typexpr makes the defined type equivalent to the type expression typexpr: one can be substituted for the other during typing. If no type equation is given, a new type is generated: the defined type is incompatible with any other type. The optional type representation describes the data structure representing the defined type, by giving the list of associated constructors (if it is a variant type) or associated fields (if it is a record type). If no type representation is given, nothing is assumed on the structure of the type besides what is stated in the optional type equation. The type representation = [|] constr-decl { | constr-decl } describes a variant type. The constructor declarations constr-decl_1, ..., constr-decl_n describe the constructors associated to this variant type. The constructor declaration constr-name of typexpr_1 * ... * typexpr_n declares the name constr-name as a non-constant constructor, whose arguments have types typexpr_1 ...typexpr_n. The constructor declaration constr-name declares the name constr-name as a constant constructor. Constructor names must be capitalized. The type representation = { field-decl { ; field-decl } [;] } describes a record type. The field declarations field-decl_1, ..., field-decl_n describe the fields associated to this record type. The field declaration field-name : poly-typexpr declares field-name as a field whose argument has type poly-typexpr. The field declaration mutable field-name : poly-typexpr behaves similarly; in addition, it allows physical modification of this field. Immutable fields are covariant, mutable fields are non-variant. Both mutable and immutable fields may have explicitly polymorphic types. The polymorphism of the contents is statically checked whenever a record value is created or modified. Extracted values may have their types instantiated. The two components of a type definition, the optional equation and the optional representation, can be combined independently, giving rise to four typical situations: Abstract type: no equation, no representation. When appearing in a module signature, this definition specifies nothing on the type constructor, besides its number of parameters: its representation is hidden and it is assumed incompatible with any other type. Type abbreviation: an equation, no representation. This defines the type constructor as an abbreviation for the type expression on the right of the = sign. New variant type or record type: no equation, a representation. This generates a new type constructor and defines associated constructors or fields, through which values of that type can be directly built or inspected. Re-exported variant type or record type: an equation, a representation. In this case, the type constructor is defined as an abbreviation for the type expression given in the equation, but in addition the constructors or fields given in the representation remain attached to the defined type constructor. The type expression in the equation part must agree with the representation: it must be of the same kind (record or variant) and have exactly the same constructors or fields, in the same order, with the same arguments. Moreover, the new type constructor must have the same arity and the same type constraints as the original type constructor. The type variables appearing as type parameters can optionally be prefixed by + or - to indicate that the type constructor is covariant or contravariant with respect to this parameter. This variance information is used to decide subtyping relations when checking the validity of :> coercions (see section 11.7.7). For instance, type +'a t declares t as an abstract type that is covariant in its parameter; this means that if the type tau is a subtype of the type sigma, then tau t is a subtype of sigma t. Similarly, type -'a t declares that the abstract type t is contravariant in its parameter: if tau is a subtype of sigma, then sigma t is a subtype of tau t. If no + or - variance annotation is given, the type constructor is assumed non-variant in the corresponding parameter. For instance, the abstract type declaration type 'a t means that tau t is neither a subtype nor a supertype of sigma t if tau is subtype of sigma. The variance indicated by the + and - annotations on parameters is enforced only for abstract and private types, or when there are type constraints. Otherwise, for abbreviations, variant and record types without type constraints, the variance properties of the type constructor are inferred from its definition, and the variance annotations are only checked for conformance with the definition. Injectivity annotations are only necessary for abstract types and private row types, since they can otherwise be deduced from the type declaration: all parameters are injective for record and variant type declarations (including extensible types); for type abbreviations a parameter is injective if it has an injective occurrence in its defining equation (be it private or not). For constrained type parameters in type abbreviations, they are injective if either they appear at an injective position in the body, or if all their type variables are injective; in particular, if a constrained type parameter contains a variable that doesn’t appear in the body, it cannot be injective. The construct constraint ' ident = typexpr allows the specification of type parameters. Any actual type argument corresponding to the type parameter ident has to be an instance of typexpr (more precisely, ident and typexpr are unified). Type variables of typexpr can appear in the type equation and the type declaration. 11.8.2 Exception definitions ============================== exception-definition ::= exception constr-decl | exception constr-name = constr Exception definitions add new constructors to the built-in variant type exn of exception values. The constructors are declared as for a definition of a variant type. << # exception E of int * string;; exception E of int * string >> The form exception constr-decl generates a new exception, distinct from all other exceptions in the system. The form exception constr-name = constr gives an alternate name to an existing exception. << # exception E of int * string exception F = E let eq = E (1, "one") = F (1, "one");; exception E of int * string exception F of int * string val eq : bool = true >> 11.9 Classes *=*=*=*=*=*=*= Classes are defined using a small language, similar to the module language. 11.9.1 Class types ==================== Class types are the class-level equivalent of type expressions: they specify the general shape and type properties of classes. class-type ::= [[?]label-name:] typexpr -> class-type | class-body-type class-body-type ::= object [( typexpr )] { class-field-spec } end | [[ typexpr { , typexpr } ]] classtype-path | let open module-path in class-body-type class-field-spec ::= inherit class-body-type | val [mutable] [virtual] inst-var-name : typexpr | val virtual mutable inst-var-name : typexpr | method [private] [virtual] method-name : poly-typexpr | method virtual private method-name : poly-typexpr | constraint typexpr = typexpr See also the following language extensions: attributes and extension nodes. Simple class expressions ------------------------ The expression classtype-path is equivalent to the class type bound to the name classtype-path. Similarly, the expression [ typexpr_1 , ... typexpr_n ] classtype-path is equivalent to the parametric class type bound to the name classtype-path, in which type parameters have been instantiated to respectively typexpr_1, ...typexpr_n. Class function type ------------------- The class type expression typexpr -> class-type is the type of class functions (functions from values to classes) that take as argument a value of type typexpr and return as result a class of type class-type. Class body type --------------- The class type expression object [( typexpr )] { class-field-spec } end is the type of a class body. It specifies its instance variables and methods. In this type, typexpr is matched against the self type, therefore providing a name for the self type. A class body will match a class body type if it provides definitions for all the components specified in the class body type, and these definitions meet the type requirements given in the class body type. Furthermore, all methods either virtual or public present in the class body must also be present in the class body type (on the other hand, some instance variables and concrete private methods may be omitted). A virtual method will match a concrete method, which makes it possible to forget its implementation. An immutable instance variable will match a mutable instance variable. Local opens ----------- Local opens are supported in class types since OCaml 4.06. Inheritance ----------- The inheritance construct inherit class-body-type provides for inclusion of methods and instance variables from other class types. The instance variable and method types from class-body-type are added into the current class type. Instance variable specification ------------------------------- A specification of an instance variable is written val [mutable] [virtual] inst-var-name : typexpr, where inst-var-name is the name of the instance variable and typexpr its expected type. The flag mutable indicates whether this instance variable can be physically modified. The flag virtual indicates that this instance variable is not initialized. It can be initialized later through inheritance. An instance variable specification will hide any previous specification of an instance variable of the same name. Method specification -------------------- The specification of a method is written method [private] method-name : poly-typexpr, where method-name is the name of the method and poly-typexpr its expected type, possibly polymorphic. The flag private indicates that the method cannot be accessed from outside the object. The polymorphism may be left implicit in public method specifications: any type variable which is not bound to a class parameter and does not appear elsewhere inside the class specification will be assumed to be universal, and made polymorphic in the resulting method type. Writing an explicit polymorphic type will disable this behaviour. If several specifications are present for the same method, they must have compatible types. Any non-private specification of a method forces it to be public. Virtual method specification ---------------------------- A virtual method specification is written method [private] virtual method-name : poly-typexpr, where method-name is the name of the method and poly-typexpr its expected type. Constraints on type parameters ------------------------------ The construct constraint typexpr_1 = typexpr_2 forces the two type expressions to be equal. This is typically used to specify type parameters: in this way, they can be bound to specific type expressions. 11.9.2 Class expressions ========================== Class expressions are the class-level equivalent of value expressions: they evaluate to classes, thus providing implementations for the specifications expressed in class types. class-expr ::= class-path | [ typexpr { , typexpr } ] class-path | ( class-expr ) | ( class-expr : class-type ) + | class-expr { argument } + | fun { parameter } -> class-expr | let [rec] let-binding { and let-binding } in class-expr | object class-body end | let open module-path in class-expr class-field ::= inherit class-expr [as lowercase-ident] | inherit! class-expr [as lowercase-ident] | val [mutable] inst-var-name [: typexpr] = expr | val! [mutable] inst-var-name [: typexpr] = expr | val [mutable] virtual inst-var-name : typexpr | val virtual mutable inst-var-name : typexpr | method [private] method-name { parameter } [: typexpr] = expr | method! [private] method-name { parameter } [: typexpr] = expr | method [private] method-name : poly-typexpr = expr | method! [private] method-name : poly-typexpr = expr | method [private] virtual method-name : poly-typexpr | method virtual private method-name : poly-typexpr | constraint typexpr = typexpr | initializer expr See also the following language extensions: locally abstract types, attributes and extension nodes. Simple class expressions ------------------------ The expression class-path evaluates to the class bound to the name class-path. Similarly, the expression [ typexpr_1 , ... typexpr_n ] class-path evaluates to the parametric class bound to the name class-path, in which type parameters have been instantiated respectively to typexpr_1, ...typexpr_n. The expression ( class-expr ) evaluates to the same module as class-expr. The expression ( class-expr : class-type ) checks that class-type matches the type of class-expr (that is, that the implementation class-expr meets the type specification class-type). The whole expression evaluates to the same class as class-expr, except that all components not specified in class-type are hidden and can no longer be accessed. Class application ----------------- Class application is denoted by juxtaposition of (possibly labeled) expressions. It denotes the class whose constructor is the first expression applied to the given arguments. The arguments are evaluated as for expression application, but the constructor itself will only be evaluated when objects are created. In particular, side-effects caused by the application of the constructor will only occur at object creation time. Class function -------------- The expression fun [[?]label-name:]pattern -> class-expr evaluates to a function from values to classes. When this function is applied to a value v, this value is matched against the pattern pattern and the result is the result of the evaluation of class-expr in the extended environment. Conversion from functions with default values to functions with patterns only works identically for class functions as for normal functions. The expression fun parameter_1 ... parameter_n -> class-expr is a short form for fun parameter_1 -> ... fun parameter_n -> expr Local definitions ----------------- The let and let rec constructs bind value names locally, as for the core language expressions. If a local definition occurs at the very beginning of a class definition, it will be evaluated when the class is created (just as if the definition was outside of the class). Otherwise, it will be evaluated when the object constructor is called. Local opens ----------- Local opens are supported in class expressions since OCaml 4.06. Class body ---------- class-body ::= [( pattern [: typexpr] )] { class-field } The expression object class-body end denotes a class body. This is the prototype for an object : it lists the instance variables and methods of an object of this class. A class body is a class value: it is not evaluated at once. Rather, its components are evaluated each time an object is created. In a class body, the pattern ( pattern [: typexpr] ) is matched against self, therefore providing a binding for self and self type. Self can only be used in method and initializers. Self type cannot be a closed object type, so that the class remains extensible. Since OCaml 4.01, it is an error if the same method or instance variable name is defined several times in the same class body. Inheritance ----------- The inheritance construct inherit class-expr allows reusing methods and instance variables from other classes. The class expression class-expr must evaluate to a class body. The instance variables, methods and initializers from this class body are added into the current class. The addition of a method will override any previously defined method of the same name. An ancestor can be bound by appending as lowercase-ident to the inheritance construct. lowercase-ident is not a true variable and can only be used to select a method, i.e. in an expression lowercase-ident # method-name. This gives access to the method method-name as it was defined in the parent class even if it is redefined in the current class. The scope of this ancestor binding is limited to the current class. The ancestor method may be called from a subclass but only indirectly. Instance variable definition ---------------------------- The definition val [mutable] inst-var-name = expr adds an instance variable inst-var-name whose initial value is the value of expression expr. The flag mutable allows physical modification of this variable by methods. An instance variable can only be used in the methods and initializers that follow its definition. Since version 3.10, redefinitions of a visible instance variable with the same name do not create a new variable, but are merged, using the last value for initialization. They must have identical types and mutability. However, if an instance variable is hidden by omitting it from an interface, it will be kept distinct from other instance variables with the same name. Virtual instance variable definition ------------------------------------ A variable specification is written val [mutable] virtual inst-var-name : typexpr. It specifies whether the variable is modifiable, and gives its type. Virtual instance variables were added in version 3.10. Method definition ----------------- A method definition is written method method-name = expr. The definition of a method overrides any previous definition of this method. The method will be public (that is, not private) if any of the definition states so. A private method, method private method-name = expr, is a method that can only be invoked on self (from other methods of the same object, defined in this class or one of its subclasses). This invocation is performed using the expression value-name # method-name, where value-name is directly bound to self at the beginning of the class definition. Private methods do not appear in object types. A method may have both public and private definitions, but as soon as there is a public one, all subsequent definitions will be made public. Methods may have an explicitly polymorphic type, allowing them to be used polymorphically in programs (even for the same object). The explicit declaration may be done in one of three ways: (1) by giving an explicit polymorphic type in the method definition, immediately after the method name, i.e. method [private] method-name : { ' ident }^+ . typexpr = expr; (2) by a forward declaration of the explicit polymorphic type through a virtual method definition; (3) by importing such a declaration through inheritance and/or constraining the type of self. Some special expressions are available in method bodies for manipulating instance variables and duplicating self: expr ::= ... | inst-var-name <- expr | {< [ inst-var-name = expr { ; inst-var-name = expr } [;] ] >} The expression inst-var-name <- expr modifies in-place the current object by replacing the value associated to inst-var-name by the value of expr. Of course, this instance variable must have been declared mutable. The expression {< inst-var-name_1 = expr_1 ; ... ; inst-var-name_n = expr_n >} evaluates to a copy of the current object in which the values of instance variables inst-var-name_1, ..., inst-var-name_n have been replaced by the values of the corresponding expressions expr_1, ..., expr_n. Virtual method definition ------------------------- A method specification is written method [private] virtual method-name : poly-typexpr. It specifies whether the method is public or private, and gives its type. If the method is intended to be polymorphic, the type must be explicitly polymorphic. Explicit overriding ------------------- Since Ocaml 3.12, the keywords inherit!, val! and method! have the same semantics as inherit, val and method, but they additionally require the definition they introduce to be overriding. Namely, method! requires method-name to be already defined in this class, val! requires inst-var-name to be already defined in this class, and inherit! requires class-expr to override some definitions. If no such overriding occurs, an error is signaled. As a side-effect, these 3 keywords avoid the warnings 7 (method override) and 13 (instance variable override). Note that warning 7 is disabled by default. Constraints on type parameters ------------------------------ The construct constraint typexpr_1 = typexpr_2 forces the two type expressions to be equals. This is typically used to specify type parameters: in that way they can be bound to specific type expressions. Initializers ------------ A class initializer initializer expr specifies an expression that will be evaluated whenever an object is created from the class, once all its instance variables have been initialized. 11.9.3 Class definitions ========================== class-definition ::= class class-binding { and class-binding } class-binding ::= [virtual] [[ type-parameters ]] class-name { parameter } [: class-type] = class-expr type-parameters ::= ' ident { , ' ident } A class definition class class-binding { and class-binding } is recursive. Each class-binding defines a class-name that can be used in the whole expression except for inheritance. It can also be used for inheritance, but only in the definitions that follow its own. A class binding binds the class name class-name to the value of expression class-expr. It also binds the class type class-name to the type of the class, and defines two type abbreviations : class-name and # class-name. The first one is the type of objects of this class, while the second is more general as it unifies with the type of any object belonging to a subclass (see section 11.4). Virtual class ------------- A class must be flagged virtual if one of its methods is virtual (that is, appears in the class type, but is not actually defined). Objects cannot be created from a virtual class. Type parameters --------------- The class type parameters correspond to the ones of the class type and of the two type abbreviations defined by the class binding. They must be bound to actual types in the class definition using type constraints. So that the abbreviations are well-formed, type variables of the inferred type of the class must either be type parameters or be bound in the constraint clause. 11.9.4 Class specifications ============================= class-specification ::= class class-spec { and class-spec } class-spec ::= [virtual] [[ type-parameters ]] class-name : class-type This is the counterpart in signatures of class definitions. A class specification matches a class definition if they have the same type parameters and their types match. 11.9.5 Class type definitions =============================== classtype-definition ::= class type classtype-def { and classtype-def } classtype-def ::= [virtual] [[ type-parameters ]] class-name = class-body-type A class type definition class class-name = class-body-type defines an abbreviation class-name for the class body type class-body-type. As for class definitions, two type abbreviations class-name and # class-name are also defined. The definition can be parameterized by some type parameters. If any method in the class type body is virtual, the definition must be flagged virtual. Two class type definitions match if they have the same type parameters and they expand to matching types. 11.10 Module types (module specifications) *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Module types are the module-level equivalent of type expressions: they specify the general shape and type properties of modules. module-type ::= modtype-path | sig { specification [;;] } end | functor ( module-name : module-type ) -> module-type | module-type -> module-type | module-type with mod-constraint { and mod-constraint } | ( module-type ) mod-constraint ::= type [type-params] typeconstr type-equation { type-constraint } | module module-path = extended-module-path specification ::= val value-name : typexpr | external value-name : typexpr = external-declaration | type-definition | exception constr-decl | class-specification | classtype-definition | module module-name : module-type | module module-name { ( module-name : module-type ) } : module-type | module type modtype-name | module type modtype-name = module-type | open module-path | include module-type See also the following language extensions: recovering the type of a module, substitution inside a signature, type-level module aliases, attributes, extension nodes, generative functors, and module type substitutions. 11.10.1 Simple module types ============================= The expression modtype-path is equivalent to the module type bound to the name modtype-path. The expression ( module-type ) denotes the same type as module-type. 11.10.2 Signatures ==================== Signatures are type specifications for structures. Signatures sig ... end are collections of type specifications for value names, type names, exceptions, module names and module type names. A structure will match a signature if the structure provides definitions (implementations) for all the names specified in the signature (and possibly more), and these definitions meet the type requirements given in the signature. An optional ;; is allowed after each specification in a signature. It serves as a syntactic separator with no semantic meaning. Value specifications -------------------- A specification of a value component in a signature is written val value-name : typexpr, where value-name is the name of the value and typexpr its expected type. The form external value-name : typexpr = external-declaration is similar, except that it requires in addition the name to be implemented as the external function specified in external-declaration (see chapter 22). Type specifications ------------------- A specification of one or several type components in a signature is written type typedef { and typedef } and consists of a sequence of mutually recursive definitions of type names. Each type definition in the signature specifies an optional type equation = typexpr and an optional type representation = constr-decl ... or = { field-decl ... }. The implementation of the type name in a matching structure must be compatible with the type expression specified in the equation (if given), and have the specified representation (if given). Conversely, users of that signature will be able to rely on the type equation or type representation, if given. More precisely, we have the following four situations: Abstract type: no equation, no representation. Names that are defined as abstract types in a signature can be implemented in a matching structure by any kind of type definition (provided it has the same number of type parameters). The exact implementation of the type will be hidden to the users of the structure. In particular, if the type is implemented as a variant type or record type, the associated constructors and fields will not be accessible to the users; if the type is implemented as an abbreviation, the type equality between the type name and the right-hand side of the abbreviation will be hidden from the users of the structure. Users of the structure consider that type as incompatible with any other type: a fresh type has been generated. Type abbreviation: an equation = typexpr, no representation. The type name must be implemented by a type compatible with typexpr. All users of the structure know that the type name is compatible with typexpr. New variant type or record type: no equation, a representation. The type name must be implemented by a variant type or record type with exactly the constructors or fields specified. All users of the structure have access to the constructors or fields, and can use them to create or inspect values of that type. However, users of the structure consider that type as incompatible with any other type: a fresh type has been generated. Re-exported variant type or record type: an equation, a representation. This case combines the previous two: the representation of the type is made visible to all users, and no fresh type is generated. Exception specification ----------------------- The specification exception constr-decl in a signature requires the matching structure to provide an exception with the name and arguments specified in the definition, and makes the exception available to all users of the structure. Class specifications -------------------- A specification of one or several classes in a signature is written class class-spec { and class-spec } and consists of a sequence of mutually recursive definitions of class names. Class specifications are described more precisely in section 11.9.4. Class type specifications ------------------------- A specification of one or several class types in a signature is written class type classtype-def { and classtype-def } and consists of a sequence of mutually recursive definitions of class type names. Class type specifications are described more precisely in section 11.9.5. Module specifications --------------------- A specification of a module component in a signature is written module module-name : module-type, where module-name is the name of the module component and module-type its expected type. Modules can be nested arbitrarily; in particular, functors can appear as components of structures and functor types as components of signatures. For specifying a module component that is a functor, one may write module module-name ( name_1 : module-type_1 ) ... ( name_n : module-type_n ) : module-type instead of module module-name : functor ( name_1 : module-type_1 ) -> ... -> module-type Module type specifications -------------------------- A module type component of a signature can be specified either as a manifest module type or as an abstract module type. An abstract module type specification module type modtype-name allows the name modtype-name to be implemented by any module type in a matching signature, but hides the implementation of the module type to all users of the signature. A manifest module type specification module type modtype-name = module-type requires the name modtype-name to be implemented by the module type module-type in a matching signature, but makes the equality between modtype-name and module-type apparent to all users of the signature. Opening a module path --------------------- The expression open module-path in a signature does not specify any components. It simply affects the parsing of the following items of the signature, allowing components of the module denoted by module-path to be referred to by their simple names name instead of path accesses module-path . name. The scope of the open stops at the end of the signature expression. Including a signature --------------------- The expression include module-type in a signature performs textual inclusion of the components of the signature denoted by module-type. It behaves as if the components of the included signature were copied at the location of the include. The module-type argument must refer to a module type that is a signature, not a functor type. 11.10.3 Functor types ======================= The module type expression functor ( module-name : module-type_1 ) -> module-type_2 is the type of functors (functions from modules to modules) that take as argument a module of type module-type_1 and return as result a module of type module-type_2. The module type module-type_2 can use the name module-name to refer to type components of the actual argument of the functor. If the type module-type_2 does not depend on type components of module-name, the module type expression can be simplified with the alternative short syntax module-type_1 -> module-type_2 . No restrictions are placed on the type of the functor argument; in particular, a functor may take another functor as argument (“higher-order” functor). When the result module type is itself a functor, functor ( name_1 : module-type_1 ) -> ... -> functor ( name_n : module-type_n ) -> module-type one may use the abbreviated form functor ( name_1 : module-type_1 ) ... ( name_n : module-type_n ) -> module-type 11.10.4 The with operator =========================== Assuming module-type denotes a signature, the expression module-type with mod-constraint { and mod-constraint } denotes the same signature where type equations have been added to some of the type specifications, as described by the constraints following the with keyword. The constraint type [type-parameters] typeconstr = typexpr adds the type equation = typexpr to the specification of the type component named typeconstr of the constrained signature. The constraint module module-path = extended-module-path adds type equations to all type components of the sub-structure denoted by module-path, making them equivalent to the corresponding type components of the structure denoted by extended-module-path. For instance, if the module type name S is bound to the signature << sig type t module M: (sig type u end) end >> then S with type t=int denotes the signature << sig type t=int module M: (sig type u end) end >> and S with module M = N denotes the signature << sig type t module M: (sig type u=N.u end) end >> A functor taking two arguments of type S that share their t component is written << functor (A: S) (B: S with type t = A.t) ... >> Constraints are added left to right. After each constraint has been applied, the resulting signature must be a subtype of the signature before the constraint was applied. Thus, the with operator can only add information on the type components of a signature, but never remove information. 11.11 Module expressions (module implementations) *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Module expressions are the module-level equivalent of value expressions: they evaluate to modules, thus providing implementations for the specifications expressed in module types. module-expr ::= module-path | struct [ module-items ] end | functor ( module-name : module-type ) -> module-expr | module-expr ( module-expr ) | ( module-expr ) | ( module-expr : module-type ) module-items ::= { ;; } ( definition | expr ) { { ;; } ( definition | ;; expr) } { ;; } definition ::= let [rec] let-binding { and let-binding } | external value-name : typexpr = external-declaration | type-definition | exception-definition | class-definition | classtype-definition | module module-name { ( module-name : module-type ) } [ : module-type ] = module-expr | module type modtype-name = module-type | open module-path | include module-expr See also the following language extensions: recursive modules, first-class modules, overriding in open statements, attributes, extension nodes and generative functors. 11.11.1 Simple module expressions =================================== The expression module-path evaluates to the module bound to the name module-path. The expression ( module-expr ) evaluates to the same module as module-expr. The expression ( module-expr : module-type ) checks that the type of module-expr is a subtype of module-type, that is, that all components specified in module-type are implemented in module-expr, and their implementation meets the requirements given in module-type. In other terms, it checks that the implementation module-expr meets the type specification module-type. The whole expression evaluates to the same module as module-expr, except that all components not specified in module-type are hidden and can no longer be accessed. 11.11.2 Structures ==================== Structures struct ... end are collections of definitions for value names, type names, exceptions, module names and module type names. The definitions are evaluated in the order in which they appear in the structure. The scopes of the bindings performed by the definitions extend to the end of the structure. As a consequence, a definition may refer to names bound by earlier definitions in the same structure. For compatibility with toplevel phrases (chapter 14), optional ;; are allowed after and before each definition in a structure. These ;; have no semantic meanings. Similarly, an expr preceded by ;; is allowed as a component of a structure. It is equivalent to let _ = expr, i.e. expr is evaluated for its side-effects but is not bound to any identifier. If expr is the first component of a structure, the preceding ;; can be omitted. Value definitions ----------------- A value definition let [rec] let-binding { and let-binding } bind value names in the same way as a let ... in ... expression (see section 11.7.2). The value names appearing in the left-hand sides of the bindings are bound to the corresponding values in the right-hand sides. A value definition external value-name : typexpr = external-declaration implements value-name as the external function specified in external-declaration (see chapter 22). Type definitions ---------------- A definition of one or several type components is written type typedef { and typedef } and consists of a sequence of mutually recursive definitions of type names. Exception definitions --------------------- Exceptions are defined with the syntax exception constr-decl or exception constr-name = constr. Class definitions ----------------- A definition of one or several classes is written class class-binding { and class-binding } and consists of a sequence of mutually recursive definitions of class names. Class definitions are described more precisely in section 11.9.3. Class type definitions ---------------------- A definition of one or several classes is written class type classtype-def { and classtype-def } and consists of a sequence of mutually recursive definitions of class type names. Class type definitions are described more precisely in section 11.9.5. Module definitions ------------------ The basic form for defining a module component is module module-name = module-expr, which evaluates module-expr and binds the result to the name module-name. One can write module module-name : module-type = module-expr instead of module module-name = ( module-expr : module-type ). Another derived form is module module-name ( name_1 : module-type_1 ) ... ( name_n : module-type_n ) = module-expr which is equivalent to module module-name = functor ( name_1 : module-type_1 ) -> ... -> module-expr Module type definitions ----------------------- A definition for a module type is written module type modtype-name = module-type. It binds the name modtype-name to the module type denoted by the expression module-type. Opening a module path --------------------- The expression open module-path in a structure does not define any components nor perform any bindings. It simply affects the parsing of the following items of the structure, allowing components of the module denoted by module-path to be referred to by their simple names name instead of path accesses module-path . name. The scope of the open stops at the end of the structure expression. Including the components of another structure --------------------------------------------- The expression include module-expr in a structure re-exports in the current structure all definitions of the structure denoted by module-expr. For instance, if you define a module S as below << module S = struct type t = int let x = 2 end >> defining the module B as << module B = struct include S let y = (x + 1 : t) end >> is equivalent to defining it as << module B = struct type t = S.t let x = S.x let y = (x + 1 : t) end >> The difference between open and include is that open simply provides short names for the components of the opened structure, without defining any components of the current structure, while include also adds definitions for the components of the included structure. 11.11.3 Functors ================== Functor definition ------------------ The expression functor ( module-name : module-type ) -> module-expr evaluates to a functor that takes as argument modules of the type module-type_1, binds module-name to these modules, evaluates module-expr in the extended environment, and returns the resulting modules as results. No restrictions are placed on the type of the functor argument; in particular, a functor may take another functor as argument (“higher-order” functor). When the result module expression is itself a functor, functor ( name_1 : module-type_1 ) -> ... -> functor ( name_n : module-type_n ) -> module-expr one may use the abbreviated form functor ( name_1 : module-type_1 ) ... ( name_n : module-type_n ) -> module-expr Functor application ------------------- The expression module-expr_1 ( module-expr_2 ) evaluates module-expr_1 to a functor and module-expr_2 to a module, and applies the former to the latter. The type of module-expr_2 must match the type expected for the arguments of the functor module-expr_1. 11.12 Compilation units *=*=*=*=*=*=*=*=*=*=*=*=* unit-interface ::= { specification [;;] } unit-implementation ::= [ module-items ] Compilation units bridge the module system and the separate compilation system. A compilation unit is composed of two parts: an interface and an implementation. The interface contains a sequence of specifications, just as the inside of a sig ... end signature expression. The implementation contains a sequence of definitions and expressions, just as the inside of a struct ... end module expression. A compilation unit also has a name unit-name, derived from the names of the files containing the interface and the implementation (see chapter 13 for more details). A compilation unit behaves roughly as the module definition module unit-name : sig unit-interface end = struct unit-implementation end A compilation unit can refer to other compilation units by their names, as if they were regular modules. For instance, if U is a compilation unit that defines a type t, other compilation units can refer to that type under the name U.t; they can also refer to U as a whole structure. Except for names of other compilation units, a unit interface or unit implementation must not have any other free variables. In other terms, the type-checking and compilation of an interface or implementation proceeds in the initial environment name_1 : sig specification_1 end ... name_n : sig specification_n end where name_1 ... name_n are the names of the other compilation units available in the search path (see chapter 13 for more details) and specification_1 ... specification_n are their respective interfaces. --------------------------------------- (1) Except for the normalization of newline sequences into a single line feed mentioned earlier. Chapter 12  Language extensions *********************************** This chapter describes language extensions and convenience features that are implemented in OCaml, but not described in chapter 11. 12.1 Recursive definitions of values *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= (Introduced in Objective Caml 1.00) As mentioned in section 11.7.2, the let rec binding construct, in addition to the definition of recursive functions, also supports a certain class of recursive definitions of non-functional values, such as let rec name_1 = 1 :: name_2 and name_2 = 2 :: name_1 in expr which binds name_1 to the cyclic list 1::2::1::2::..., and name_2 to the cyclic list 2::1::2::1::...Informally, the class of accepted definitions consists of those definitions where the defined names occur only inside function bodies or as argument to a data constructor. More precisely, consider the expression: let rec name_1 = expr_1 and ... and name_n = expr_n in expr It will be accepted if each one of expr_1 ... expr_n is statically constructive with respect to name_1 ... name_n, is not immediately linked to any of name_1 ... name_n, and is not an array constructor whose arguments have abstract type. An expression e is said to be statically constructive with respect to the variables name_1 ... name_n if at least one of the following conditions is true: - e has no free occurrence of any of name_1 ... name_n - e is a variable - e has the form fun ... -> ... - e has the form function ... -> ... - e has the form lazy ( ... ) - e has one of the following forms, where each one of expr_1 ... expr_m is statically constructive with respect to name_1 ... name_n, and expr_0 is statically constructive with respect to name_1 ... name_n, xname_1 ... xname_m: - let [rec] xname_1 = expr_1 and ... and xname_m = expr_m in expr_0 - let module ... in expr_1 - constr (expr_1, ... , expr_m) - `tag-name (expr_1, ... , expr_m) - [| expr_1; ... ; expr_m |] - { field_1 = expr_1; ... ; field_m = expr_m } - { expr_1 with field_2 = expr_2; ... ; field_m = expr_m } where expr_1 is not immediately linked to name_1 ... name_n - ( expr_1, ... , expr_m ) - expr_1; ... ; expr_m An expression e is said to be immediately linked to the variable name in the following cases: - e is name - e has the form expr_1; ... ; expr_m where expr_m is immediately linked to name - e has the form let [rec] xname_1 = expr_1 and ... and xname_m = expr_m in expr_0 where expr_0 is immediately linked to name or to one of the xname_i such that expr_i is immediately linked to name. 12.2 Recursive modules *=*=*=*=*=*=*=*=*=*=*=*= (Introduced in Objective Caml 3.07) definition ::= ... | module rec module-name : module-type = module-expr { and module-name : module-type = module-expr } specification ::= ... | module rec module-name : module-type { and module-name: module-type } Recursive module definitions, introduced by the module rec ...and ... construction, generalize regular module definitions module module-name = module-expr and module specifications module module-name : module-type by allowing the defining module-expr and the module-type to refer recursively to the module identifiers being defined. A typical example of a recursive module definition is: << module rec A : sig type t = Leaf of string | Node of ASet.t val compare: t -> t -> int end = struct type t = Leaf of string | Node of ASet.t let compare t1 t2 = match (t1, t2) with | (Leaf s1, Leaf s2) -> Stdlib.compare s1 s2 | (Leaf _, Node _) -> 1 | (Node _, Leaf _) -> -1 | (Node n1, Node n2) -> ASet.compare n1 n2 end and ASet : Set.S with type elt = A.t = Set.Make(A) >> It can be given the following specification: << module rec A : sig type t = Leaf of string | Node of ASet.t val compare: t -> t -> int end and ASet : Set.S with type elt = A.t >> This is an experimental extension of OCaml: the class of recursive definitions accepted, as well as its dynamic semantics are not final and subject to change in future releases. Currently, the compiler requires that all dependency cycles between the recursively-defined module identifiers go through at least one “safe” module. A module is “safe” if all value definitions that it contains have function types typexpr_1 -> typexpr_2. Evaluation of a recursive module definition proceeds by building initial values for the safe modules involved, binding all (functional) values to fun _ -> raise Undefined_recursive_module. The defining module expressions are then evaluated, and the initial values for the safe modules are replaced by the values thus computed. If a function component of a safe module is applied during this computation (which corresponds to an ill-founded recursive definition), the Undefined_recursive_module exception is raised at runtime: << module rec M: sig val f: unit -> int end = struct let f () = N.x end and N:sig val x: int end = struct let x = M.f () end Exception: Undefined_recursive_module ("extensions/recursivemodules.etex", 1, 43). >> If there are no safe modules along a dependency cycle, an error is raised << module rec M: sig val x: int end = struct let x = N.y end and N:sig val x: int val y:int end = struct let x = M.x let y = 0 end Error: Cannot safely evaluate the definition of the following cycle of recursively-defined modules: M -> N -> M. There are no safe modules in this cycle (see manual section 12.2). Module M defines an unsafe value, x . Module N defines an unsafe value, x . >> Note that, in the specification case, the module-types must be parenthesized if they use the with mod-constraint construct. 12.3 Private types *=*=*=*=*=*=*=*=*=*= Private type declarations in module signatures, of the form type t = private ..., enable libraries to reveal some, but not all aspects of the implementation of a type to clients of the library. In this respect, they strike a middle ground between abstract type declarations, where no information is revealed on the type implementation, and data type definitions and type abbreviations, where all aspects of the type implementation are publicized. Private type declarations come in three flavors: for variant and record types (section 12.3.1), for type abbreviations (section 12.3.2), and for row types (section 12.3.3). 12.3.1 Private variant and record types ========================================= (Introduced in Objective Caml 3.07) type-representation ::= ... | = private [ | ] constr-decl { | constr-decl } | = private record-decl Values of a variant or record type declared private can be de-structured normally in pattern-matching or via the expr . field notation for record accesses. However, values of these types cannot be constructed directly by constructor application or record construction. Moreover, assignment on a mutable field of a private record type is not allowed. The typical use of private types is in the export signature of a module, to ensure that construction of values of the private type always go through the functions provided by the module, while still allowing pattern-matching outside the defining module. For example: << module M : sig type t = private A | B of int val a : t val b : int -> t end = struct type t = A | B of int let a = A let b n = assert (n > 0); B n end >> Here, the private declaration ensures that in any value of type M.t, the argument to the B constructor is always a positive integer. With respect to the variance of their parameters, private types are handled like abstract types. That is, if a private type has parameters, their variance is the one explicitly given by prefixing the parameter by a ‘+’ or a ‘-’, it is invariant otherwise. 12.3.2 Private type abbreviations =================================== (Introduced in Objective Caml 3.11) type-equation ::= ... | = private typexpr Unlike a regular type abbreviation, a private type abbreviation declares a type that is distinct from its implementation type typexpr. However, coercions from the type to typexpr are permitted. Moreover, the compiler “knows” the implementation type and can take advantage of this knowledge to perform type-directed optimizations. The following example uses a private type abbreviation to define a module of nonnegative integers: << module N : sig type t = private int val of_int: int -> t val to_int: t -> int end = struct type t = int let of_int n = assert (n >= 0); n let to_int n = n end >> The type N.t is incompatible with int, ensuring that nonnegative integers and regular integers are not confused. However, if x has type N.t, the coercion (x :> int) is legal and returns the underlying integer, just like N.to_int x. Deep coercions are also supported: if l has type N.t list, the coercion (l :> int list) returns the list of underlying integers, like List.map N.to_int l but without copying the list l. Note that the coercion ( expr :> typexpr ) is actually an abbreviated form, and will only work in presence of private abbreviations if neither the type of expr nor typexpr contain any type variables. If they do, you must use the full form ( expr : typexpr_1 :> typexpr_2 ) where typexpr_1 is the expected type of expr. Concretely, this would be (x : N.t :> int) and (l : N.t list :> int list) for the above examples. 12.3.3 Private row types ========================== (Introduced in Objective Caml 3.09) type-equation ::= ... | = private typexpr Private row types are type abbreviations where part of the structure of the type is left abstract. Concretely typexpr in the above should denote either an object type or a polymorphic variant type, with some possibility of refinement left. If the private declaration is used in an interface, the corresponding implementation may either provide a ground instance, or a refined private type. << module M : sig type c = private < x : int; .. > val o : c end = struct class c = object method x = 3 method y = 2 end let o = new c end >> This declaration does more than hiding the y method, it also makes the type c incompatible with any other closed object type, meaning that only o will be of type c. In that respect it behaves similarly to private record types. But private row types are more flexible with respect to incremental refinement. This feature can be used in combination with functors. << module F(X : sig type c = private < x : int; .. > end) = struct let get_x (o : X.c) = o#x end module G(X : sig type c = private < x : int; y : int; .. > end) = struct include F(X) let get_y (o : X.c) = o#y end >> A polymorphic variant type [t], for example << type t = [ `A of int | `B of bool ] >> can be refined in two ways. A definition [u] may add new field to [t], and the declaration << type u = private [> t] >> will keep those new fields abstract. Construction of values of type [u] is possible using the known variants of [t], but any pattern-matching will require a default case to handle the potential extra fields. Dually, a declaration [u] may restrict the fields of [t] through abstraction: the declaration << type v = private [< t > `A] >> corresponds to private variant types. One cannot create a value of the private type [v], except using the constructors that are explicitly listed as present, (`A n) in this example; yet, when pattern-matching on a [v], one should assume that any of the constructors of [t] could be present. Similarly to abstract types, the variance of type parameters is not inferred, and must be given explicitly. 12.4 Locally abstract types *=*=*=*=*=*=*=*=*=*=*=*=*=*=* (Introduced in OCaml 3.12, short syntax added in 4.03) parameter ::= ... + | ( type { typeconstr-name } ) The expression fun ( type typeconstr-name ) -> expr introduces a type constructor named typeconstr-name which is considered abstract in the scope of the sub-expression, but then replaced by a fresh type variable. Note that contrary to what the syntax could suggest, the expression fun ( type typeconstr-name ) -> expr itself does not suspend the evaluation of expr as a regular abstraction would. The syntax has been chosen to fit nicely in the context of function declarations, where it is generally used. It is possible to freely mix regular function parameters with pseudo type parameters, as in: << let f = fun (type t) (foo : t list) -> ... >> and even use the alternative syntax for declaring functions: << let f (type t) (foo : t list) = ... >> If several locally abstract types need to be introduced, it is possible to use the syntax fun ( type typeconstr-name_1 ... typeconstr-name_n ) -> expr as syntactic sugar for fun ( type typeconstr-name_1 ) -> ... -> fun ( type typeconstr-name_n ) -> expr. For instance, << let f = fun (type t u v) -> fun (foo : (t * u * v) list) -> ... let f' (type t u v) (foo : (t * u * v) list) = ... >> This construction is useful because the type constructors it introduces can be used in places where a type variable is not allowed. For instance, one can use it to define an exception in a local module within a polymorphic function. << let f (type t) () = let module M = struct exception E of t end in (fun x -> M.E x), (function M.E x -> Some x | _ -> None) >> Here is another example: << let sort_uniq (type s) (cmp : s -> s -> int) = let module S = Set.Make(struct type t = s let compare = cmp end) in fun l -> S.elements (List.fold_right S.add l S.empty) >> It is also extremely useful for first-class modules (see section 12.5) and generalized algebraic datatypes (GADTs: see section 12.10). Polymorphic syntax (Introduced in OCaml 4.00) let-binding ::= ... + | value-name : type { typeconstr-name } . typexpr = expr class-field ::= ... + | method [private] method-name : type { typeconstr-name } . typexpr = expr + | method! [private] method-name : type { typeconstr-name } . typexpr = expr The (type typeconstr-name) syntax construction by itself does not make polymorphic the type variable it introduces, but it can be combined with explicit polymorphic annotations where needed. The above rule is provided as syntactic sugar to make this easier: << let rec f : type t1 t2. t1 * t2 list -> t1 = ... >> is automatically expanded into << let rec f : 't1 't2. 't1 * 't2 list -> 't1 = fun (type t1) (type t2) -> ( ... : t1 * t2 list -> t1) >> This syntax can be very useful when defining recursive functions involving GADTs, see the section 12.10 for a more detailed explanation. The same feature is provided for method definitions. 12.5 First-class modules *=*=*=*=*=*=*=*=*=*=*=*=*= (Introduced in OCaml 3.12; pattern syntax and package type inference introduced in 4.00; structural comparison of package types introduced in 4.02.; fewer parens required starting from 4.05) typexpr ::= ... | (module package-type) module-expr ::= ... | (val expr [: package-type]) expr ::= ... | (module module-expr [: package-type]) pattern ::= ... | (module module-name [: package-type]) package-type ::= modtype-path | modtype-path with package-constraint { and package-constraint } package-constraint ::= type typeconstr = typexpr Modules are typically thought of as static components. This extension makes it possible to pack a module as a first-class value, which can later be dynamically unpacked into a module. The expression ( module module-expr : package-type ) converts the module (structure or functor) denoted by module expression module-expr to a value of the core language that encapsulates this module. The type of this core language value is ( module package-type ). The package-type annotation can be omitted if it can be inferred from the context. Conversely, the module expression ( val expr : package-type ) evaluates the core language expression expr to a value, which must have type module package-type, and extracts the module that was encapsulated in this value. Again package-type can be omitted if the type of expr is known. If the module expression is already parenthesized, like the arguments of functors are, no additional parens are needed: Map.Make(val key). The pattern ( module module-name : package-type ) matches a package with type package-type and binds it to module-name. It is not allowed in toplevel let bindings. Again package-type can be omitted if it can be inferred from the enclosing pattern. The package-type syntactic class appearing in the ( module package-type ) type expression and in the annotated forms represents a subset of module types. This subset consists of named module types with optional constraints of a limited form: only non-parametrized types can be specified. For type-checking purposes (and starting from OCaml 4.02), package types are compared using the structural comparison of module types. In general, the module expression ( val expr : package-type ) cannot be used in the body of a functor, because this could cause unsoundness in conjunction with applicative functors. Since OCaml 4.02, this is relaxed in two ways: if package-type does not contain nominal type declarations (i.e. types that are created with a proper identity), then this expression can be used anywhere, and even if it contains such types it can be used inside the body of a generative functor, described in section 12.15. It can also be used anywhere in the context of a local module binding let module module-name = ( val expr_1 : package-type ) in expr_2. Basic example A typical use of first-class modules is to select at run-time among several implementations of a signature. Each implementation is a structure that we can encapsulate as a first-class module, then store in a data structure such as a hash table: << type picture = ... module type DEVICE = sig val draw : picture -> unit ... end let devices : (string, (module DEVICE)) Hashtbl.t = Hashtbl.create 17 module SVG = struct ... end let _ = Hashtbl.add devices "SVG" (module SVG : DEVICE) module PDF = struct ... end let _ = Hashtbl.add devices "PDF" (module PDF : DEVICE) >> We can then select one implementation based on command-line arguments, for instance: << let parse_cmdline () = ... module Device = (val (let device_name = parse_cmdline () in try Hashtbl.find devices device_name with Not_found -> Printf.eprintf "Unknown device %s\n" device_name; exit 2) : DEVICE) >> Alternatively, the selection can be performed within a function: << let draw_using_device device_name picture = let module Device = (val (Hashtbl.find devices device_name) : DEVICE) in Device.draw picture >> Advanced examples With first-class modules, it is possible to parametrize some code over the implementation of a module without using a functor. << let sort (type s) (module Set : Set.S with type elt = s) l = Set.elements (List.fold_right Set.add l Set.empty) val sort : (module Set.S with type elt = 's) -> 's list -> 's list = >> To use this function, one can wrap the Set.Make functor: << let make_set (type s) cmp = let module S = Set.Make(struct type t = s let compare = cmp end) in (module S : Set.S with type elt = s) val make_set : ('s -> 's -> int) -> (module Set.S with type elt = 's) = >> 12.6 Recovering the type of a module *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= (Introduced in OCaml 3.12) module-type ::= ... | module type of module-expr The construction module type of module-expr expands to the module type (signature or functor type) inferred for the module expression module-expr. To make this module type reusable in many situations, it is intentionally not strengthened: abstract types and datatypes are not explicitly related with the types of the original module. For the same reason, module aliases in the inferred type are expanded. A typical use, in conjunction with the signature-level include construct, is to extend the signature of an existing structure. In that case, one wants to keep the types equal to types in the original module. This can done using the following idiom. << module type MYHASH = sig include module type of struct include Hashtbl end val replace: ('a, 'b) t -> 'a -> 'b -> unit end >> The signature MYHASH then contains all the fields of the signature of the module Hashtbl (with strengthened type definitions), plus the new field replace. An implementation of this signature can be obtained easily by using the include construct again, but this time at the structure level: << module MyHash : MYHASH = struct include Hashtbl let replace t k v = remove t k; add t k v end >> Another application where the absence of strengthening comes handy, is to provide an alternative implementation for an existing module. << module MySet : module type of Set = struct ... end >> This idiom guarantees that Myset is compatible with Set, but allows it to represent sets internally in a different way. 12.7 Substituting inside a signature *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= 12.7.1 Destructive substitutions ================================== (Introduced in OCaml 3.12, generalized in 4.06) mod-constraint ::= ... | type [type-params] typeconstr-name := typexpr | module module-path := extended-module-path A “destructive” substitution (with ... := ...) behaves essentially like normal signature constraints (with ... = ...), but it additionally removes the redefined type or module from the signature. Prior to OCaml 4.06, there were a number of restrictions: one could only remove types and modules at the outermost level (not inside submodules), and in the case of with type the definition had to be another type constructor with the same type parameters. A natural application of destructive substitution is merging two signatures sharing a type name. << module type Printable = sig type t val print : Format.formatter -> t -> unit end module type Comparable = sig type t val compare : t -> t -> int end module type PrintableComparable = sig include Printable include Comparable with type t := t end >> One can also use this to completely remove a field: << module type S = Comparable with type t := int module type S = sig val compare : int -> int -> int end >> or to rename one: << module type S = sig type u include Comparable with type t := u end module type S = sig type u val compare : u -> u -> int end >> Note that you can also remove manifest types, by substituting with the same type. << module type ComparableInt = Comparable with type t = int ;; module type ComparableInt = sig type t = int val compare : t -> t -> int end >> << module type CompareInt = ComparableInt with type t := int module type CompareInt = sig val compare : int -> int -> int end >> 12.7.2 Local substitution declarations ======================================== (Introduced in OCaml 4.08, module type substitution introduced in 4.13) specification ::= ... | type type-subst { and type-subst } | module module-name := extended-module-path | module type module-name := module-type type-subst ::= [type-params] typeconstr-name := typexpr { type-constraint } Local substitutions behave like destructive substitutions (with ... := ...) but instead of being applied to a whole signature after the fact, they are introduced during the specification of the signature, and will apply to all the items that follow. This provides a convenient way to introduce local names for types and modules when defining a signature: << module type S = sig type t module Sub : sig type outer := t type t val to_outer : t -> outer end end module type S = sig type t module Sub : sig type t val to_outer : t -> t/2 end end >> Note that, unlike type declarations, type substitution declarations are not recursive, so substitutions like the following are rejected: << # module type S = sig type 'a poly_list := [ `Cons of 'a * 'a poly_list | `Nil ] end ;; Error: Unbound type constructor poly_list >> Local substitutions can also be used to give a local name to a type or a module type introduced by a functor application: << # module type F = sig type set := Set.Make(Int).t module type Type = sig type t end module Nest : Type -> sig module type T = Type end module type T := Nest(Int).T val set: set val m : (module T) end;; module type F = sig module type Type = sig type t end module Nest : Type -> sig module type T = Type end val set : Set.Make(Int).t val m : (module Nest(Int).T) end >> Local module type substitutions are subject to the same limitations as module type substitutions, see section 12.7.3. 12.7.3 Module type substitutions ================================== (Introduced in OCaml 4.13) mod-constraint ::= ... | module type modtype-path = module-type | module type modtype-path := module-type Module type substitution essentially behaves like type substitutions. They are useful to refine an abstract module type in a signature into a concrete module type, << # module type ENDO = sig module type T module F: T -> T end module Endo(X: sig module type T end): ENDO with module type T = X.T = struct module type T = X.T module F(X:T) = X end;; module type ENDO = sig module type T module F : T -> T end module Endo : functor (X : sig module type T end) -> sig module type T = X.T module F : T -> T end >> It is also possible to substitute a concrete module type with an equivalent module types. << module type A = sig type x module type R = sig type a = A of x type b end end module type S = sig type a = A of int type b end module type B = A with type x = int and module type R = S >> However, such substitutions are never necessary. Destructive module type substitution removes the module type substitution from the signature << # module type ENDO' = ENDO with module type T := ENDO;; module type ENDO' = sig module F : ENDO -> ENDO end >> Limitations ----------- If the right hand side of a module type substitution or a local module type substitution is not a modtype-path, then the destructive substitution is only valid if the left-hand side of the substitution is never used as the type of a first-class module in the original module type. << module type T = sig module type S val x: (module S) end module type Error = T with module type S := sig end Error: This with constraint S := sig end makes a packed module ill-formed. (see manual section 12.7.3) >> << module type T = sig module type S := sig end val x: (module S) end Error: The module type S is not a valid type for a packed module: it is defined as a local substitution (temporary name) for an anonymous module type. (see manual section 12.7.3) >> 12.8 Type-level module aliases *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= (Introduced in OCaml 4.02) specification ::= ... | module module-name = module-path The above specification, inside a signature, only matches a module definition equal to module-path. Conversely, a type-level module alias can be matched by itself, or by any supertype of the type of the module it references. There are several restrictions on module-path: 1. it should be of the form M_0.M_1...M_n (i.e. without functor applications); 2. inside the body of a functor, M_0 should not be one of the functor parameters; 3. inside a recursive module definition, M_0 should not be one of the recursively defined modules. Such specifications are also inferred. Namely, when P is a path satisfying the above constraints, << module N = P >> has type << module N = P >> Type-level module aliases are used when checking module path equalities. That is, in a context where module name N is known to be an alias for P, not only these two module paths check as equal, but F(N) and F(P) are also recognized as equal. In the default compilation mode, this is the only difference with the previous approach of module aliases having just the same module type as the module they reference. When the compiler flag -no-alias-deps is enabled, type-level module aliases are also exploited to avoid introducing dependencies between compilation units. Namely, a module alias referring to a module inside another compilation unit does not introduce a link-time dependency on that compilation unit, as long as it is not dereferenced; it still introduces a compile-time dependency if the interface needs to be read, i.e. if the module is a submodule of the compilation unit, or if some type components are referred to. Additionally, accessing a module alias introduces a link-time dependency on the compilation unit containing the module referenced by the alias, rather than the compilation unit containing the alias. Note that these differences in link-time behavior may be incompatible with the previous behavior, as some compilation units might not be extracted from libraries, and their side-effects ignored. These weakened dependencies make possible to use module aliases in place of the -pack mechanism. Suppose that you have a library Mylib composed of modules A and B. Using -pack, one would issue the command line <> and as a result obtain a Mylib compilation unit, containing physically A and B as submodules, and with no dependencies on their respective compilation units. Here is a concrete example of a possible alternative approach: 1. Rename the files containing A and B to Mylib__A and Mylib__B. 2. Create a packing interface Mylib.ml, containing the following lines. <> 3. Compile Mylib.ml using -no-alias-deps, and the other files using -no-alias-deps and -open Mylib (the last one is equivalent to adding the line open! Mylib at the top of each file). <> 4. Finally, create a library containing all the compilation units, and export all the compiled interfaces. <> This approach lets you access A and B directly inside the library, and as Mylib.A and Mylib.B from outside. It also has the advantage that Mylib is no longer monolithic: if you use Mylib.A, only Mylib__A will be linked in, not Mylib__B. Note the use of double underscores in Mylib__A and Mylib__B. These were chosen on purpose; the compiler uses the following heuristic when printing paths: given a path Lib__fooBar, if Lib.FooBar exists and is an alias for Lib__fooBar, then the compiler will always display Lib.FooBar instead of Lib__fooBar. This way the long Mylib__ names stay hidden and all the user sees is the nicer dot names. This is how the OCaml standard library is compiled. 12.9 Overriding in open statements *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= (Introduced in OCaml 4.01) definition ::= ... | open! module-path specification ::= ... | open! module-path expr ::= ... | let open! module-path in expr class-body-type ::= ... | let open! module-path in class-body-type class-expr ::= ... | let open! module-path in class-expr Since OCaml 4.01, open statements shadowing an existing identifier (which is later used) trigger the warning 44. Adding a ! character after the open keyword indicates that such a shadowing is intentional and should not trigger the warning. This is also available (since OCaml 4.06) for local opens in class expressions and class type expressions. 12.10 Generalized algebraic datatypes *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Generalized algebraic datatypes, or GADTs, extend usual sum types in two ways: constraints on type parameters may change depending on the value constructor, and some type variables may be existentially quantified. They are described in chapter 7. (Introduced in OCaml 4.00) constr-decl ::= ... | constr-name : [ constr-args -> ] typexpr type-param ::= ... | [variance] _ Refutation cases. (Introduced in OCaml 4.03) matching-case ::= pattern [when expr] -> expr | pattern -> . Explicit naming of existentials. (Introduced in OCaml 4.13.0) pattern ::= ... + | constr ( type { typeconstr-name } ) ( pattern ) 12.11 Syntax for Bigarray access *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= (Introduced in Objective Caml 3.00) expr ::= ... | expr .{ expr { , expr } } | expr .{ expr { , expr } } <- expr This extension provides syntactic sugar for getting and setting elements in the arrays provided by the Bigarray module. The short expressions are translated into calls to functions of the Bigarray module as described in the following table. ------------------------------------------------------------------------------- ------------------------ | expression | translation | ------------------------------------------------------------------------------- ------------------------ | expr_0.{expr_1} |Bigarray.Array1.get expr_0 expr_1 | |expr_0.{expr_1} <-expr |Bigarray.Array1.set expr_0 expr_1 expr | |expr_0.{expr_1, expr_2} |Bigarray.Array2.get expr_0 expr_1 expr_2 | |expr_0.{expr_1, expr_2} <-expr |Bigarray.Array2.set expr_0 expr_1 expr_2 expr | |expr_0.{expr_1, expr_2, expr_3} |Bigarray.Array3.get expr_0 expr_1 expr_2 expr_3 | |expr_0.{expr_1, expr_2, expr_3} <-expr|Bigarray.Array3.set expr_0 expr_1 expr_2 expr_3 expr | |expr_0.{expr_1, ..., expr_n} |Bigarray.Genarray.get expr_0 [| expr_1, ... , expr_n |] | |expr_0.{expr_1, ..., expr_n} <-expr |Bigarray.Genarray.set expr_0 [| expr_1, ... , expr_n |] expr | ------------------------------------------------------------------------------- ------------------------ The last two entries are valid for any n > 3. 12.12 Attributes *=*=*=*=*=*=*=*=*= (Introduced in OCaml 4.02, infix notations for constructs other than expressions added in 4.03) Attributes are “decorations” of the syntax tree which are mostly ignored by the type-checker but can be used by external tools. An attribute is made of an identifier and a payload, which can be a structure, a type expression (prefixed with :), a signature (prefixed with :) or a pattern (prefixed with ?) optionally followed by a when clause: attr-id ::= lowercase-ident | capitalized-ident | attr-id . attr-id attr-payload ::= [ module-items ] | : typexpr | : [ specification ] | ? pattern [when expr] The first form of attributes is attached with a postfix notation on “algebraic” categories: attribute ::= [@ attr-id attr-payload ] expr ::= ... | expr attribute typexpr ::= ... | typexpr attribute pattern ::= ... | pattern attribute module-expr ::= ... | module-expr attribute module-type ::= ... | module-type attribute class-expr ::= ... | class-expr attribute class-type ::= ... | class-type attribute This form of attributes can also be inserted after the `tag-name in polymorphic variant type expressions (tag-spec-first, tag-spec, tag-spec-full) or after the method-name in method-type. The same syntactic form is also used to attach attributes to labels and constructors in type declarations: field-decl ::= [mutable] field-name : poly-typexpr { attribute } constr-decl ::= (constr-name | ()) [ of constr-args ] { attribute } Note: when a label declaration is followed by a semi-colon, attributes can also be put after the semi-colon (in which case they are merged to those specified before). The second form of attributes are attached to “blocks” such as type declarations, class fields, etc: item-attribute ::= [@@ attr-id attr-payload ] typedef ::= ... | typedef item-attribute exception-definition ::= exception constr-decl | exception constr-name = constr module-items ::= [;;] ( definition | expr { item-attribute } ) { [;;] definition | ;; expr { item-attribute } } [;;] class-binding ::= ... | class-binding item-attribute class-spec ::= ... | class-spec item-attribute classtype-def ::= ... | classtype-def item-attribute definition ::= let [rec] let-binding { and let-binding } | external value-name : typexpr = external-declaration { item-attribute } | type-definition | exception-definition { item-attribute } | class-definition | classtype-definition | module module-name { ( module-name : module-type ) } [ : module-type ] = module-expr { item-attribute } | module type modtype-name = module-type { item-attribute } | open module-path { item-attribute } | include module-expr { item-attribute } | module rec module-name : module-type = module-expr { item-attribute } { and module-name : module-type = module-expr { item-attribute } } specification ::= val value-name : typexpr { item-attribute } | external value-name : typexpr = external-declaration { item-attribute } | type-definition | exception constr-decl { item-attribute } | class-specification | classtype-definition | module module-name : module-type { item-attribute } | module module-name { ( module-name : module-type ) } : module-type { item-attribute } | module type modtype-name { item-attribute } | module type modtype-name = module-type { item-attribute } | open module-path { item-attribute } | include module-type { item-attribute } class-field-spec ::= ... | class-field-spec item-attribute class-field ::= ... | class-field item-attribute A third form of attributes appears as stand-alone structure or signature items in the module or class sub-languages. They are not attached to any specific node in the syntax tree: floating-attribute ::= [@@@ attr-id attr-payload ] definition ::= ... | floating-attribute specification ::= ... | floating-attribute class-field-spec ::= ... | floating-attribute class-field ::= ... | floating-attribute (Note: contrary to what the grammar above describes, item-attributes cannot be attached to these floating attributes in class-field-spec and class-field.) It is also possible to specify attributes using an infix syntax. For instance: <> For let, the attributes are applied to each bindings: <> 12.12.1 Built-in attributes ============================= Some attributes are understood by the compiler: - “ocaml.warning” or “warning”, with a string literal payload. This can be used as floating attributes in a signature/structure/object/object type. The string is parsed and has the same effect as the -w command-line option, in the scope between the attribute and the end of the current signature/structure/object/object type. The attribute can also be attached to any kind of syntactic item which support attributes (such as an expression, or a type expression) in which case its scope is limited to that item. Note that it is not well-defined which scope is used for a specific warning. This is implementation dependent and can change between versions. Some warnings are even completely outside the control of “ocaml.warning” (for instance, warnings 1, 2, 14, 29 and 50). - “ocaml.warnerror” or “warnerror”, with a string literal payload. Same as “ocaml.warning”, for the -warn-error command-line option. - “ocaml.alert” or “alert”: see section 12.21. - “ocaml.deprecated” or “deprecated”: alias for the “deprecated” alert, see section 12.21. - “ocaml.deprecated_mutable” or “deprecated_mutable”. Can be applied to a mutable record label. If the label is later used to modify the field (with “expr.l <- expr”), the “deprecated” alert will be triggered. If the payload of the attribute is a string literal, the alert message includes this text. - “ocaml.ppwarning” or “ppwarning”, in any context, with a string literal payload. The text is reported as warning (22) by the compiler (currently, the warning location is the location of the string payload). This is mostly useful for preprocessors which need to communicate warnings to the user. This could also be used to mark explicitly some code location for further inspection. - “ocaml.warn_on_literal_pattern” or “warn_on_literal_pattern” annotate constructors in type definition. A warning (52) is then emitted when this constructor is pattern matched with a constant literal as argument. This attribute denotes constructors whose argument is purely informative and may change in the future. Therefore, pattern matching on this argument with a constant literal is unreliable. For instance, all built-in exception constructors are marked as “warn_on_literal_pattern”. Note that, due to an implementation limitation, this warning (52) is only triggered for single argument constructor. - “ocaml.tailcall” or “tailcall” can be applied to function application in order to check that the call is tailcall optimized. If it it not the case, a warning (51) is emitted. - “ocaml.inline” or “inline” take either “never”, “always” or nothing as payload on a function or functor definition. If no payload is provided, the default value is “always”. This payload controls when applications of the annotated functions should be inlined. - “ocaml.inlined” or “inlined” can be applied to any function or functor application to check that the call is inlined by the compiler. If the call is not inlined, a warning (55) is emitted. - “ocaml.noalloc”, “ocaml.unboxed”and “ocaml.untagged” or “noalloc”, “unboxed” and “untagged” can be used on external definitions to obtain finer control over the C-to-OCaml interface. See 22.11 for more details. - “ocaml.immediate” or “immediate” applied on an abstract type mark the type as having a non-pointer implementation (e.g. “int”, “bool”, “char” or enumerated types). Mutation of these immediate types does not activate the garbage collector’s write barrier, which can significantly boost performance in programs relying heavily on mutable state. - “ocaml.immediate64” or “immediate64” applied on an abstract type mark the type as having a non-pointer implementation on 64 bit platforms. No assumption is made on other platforms. In order to produce a type with the “immediate64“ attribute, one must use “Sys.Immediate64.Make“ functor. - ocaml.unboxed or unboxed can be used on a type definition if the type is a single-field record or a concrete type with a single constructor that has a single argument. It tells the compiler to optimize the representation of the type by removing the block that represents the record or the constructor (i.e. a value of this type is physically equal to its argument). In the case of GADTs, an additional restriction applies: the argument must not be an existential variable, represented by an existential type variable, or an abstract type constructor applied to an existential type variable. - ocaml.boxed or boxed can be used on type definitions to mean the opposite of ocaml.unboxed: keep the unoptimized representation of the type. When there is no annotation, the default is currently boxed but it may change in the future. - ocaml.local or local take either never, always, maybe or nothing as payload on a function definition. If no payload is provided, the default is always. The attribute controls an optimization which consists in compiling a function into a static continuation. Contrary to inlining, this optimization does not duplicate the function’s body. This is possible when all references to the function are full applications, all sharing the same continuation (for instance, the returned value of several branches of a pattern matching). never disables the optimization, always asserts that the optimization applies (otherwise a warning 55 is emitted) and maybe lets the optimization apply when possible (this is the default behavior when the attribute is not specified). The optimization is implicitly disabled when using the bytecode compiler in debug mode (-g), and for functions marked with an ocaml.inline always or ocaml.unrolled attribute which supersede ocaml.local. - ocaml.poll or poll with an error payload on a function definition emits an error whenever the compiler inserts a runtime polling point in the body of the annotated function. << module X = struct [@@@warning "+9"] (* locally enable warning 9 in this structure *) ... end [@@deprecated "Please use module 'Y' instead."] let x = begin[@warning "+9"] [...] end type t = A | B [@@deprecated "Please use type 's' instead."] >> << let fires_warning_22 x = assert (x >= 0) [@ppwarning "TODO: remove this later"] Warning 22 [preprocessor]: TODO: remove this later >> << let rec is_a_tail_call = function | [] -> () | _ :: q -> (is_a_tail_call[@tailcall]) q let rec not_a_tail_call = function | [] -> [] | x :: q -> x :: (not_a_tail_call[@tailcall]) q Warning 51 [wrong-tailcall-expectation]: expected tailcall >> << let f x = x [@@inline] let () = (f[@inlined]) () >> << type fragile = | Int of int [@warn_on_literal_pattern] | String of string [@warn_on_literal_pattern] >> << let fragile_match_1 = function | Int 0 -> () | _ -> () Warning 52 [fragile-literal-pattern]: Code should not depend on the actual va lues of this constructor's arguments. They are only for information and may change in future versions. (see manual section 13.5.3) val fragile_match_1 : fragile -> unit = >> << let fragile_match_2 = function | String "constant" -> () | _ -> () Warning 52 [fragile-literal-pattern]: Code should not depend on the actual va lues of this constructor's arguments. They are only for information and may change in future versions. (see manual section 13.5.3) val fragile_match_2 : fragile -> unit = >> << module Immediate: sig type t [@@immediate] val x: t ref end = struct type t = A | B let x = ref A end >> << module Int_or_int64 : sig type t [@@immediate64] val zero : t val one : t val add : t -> t -> t end = struct include Sys.Immediate64.Make(Int)(Int64) module type S = sig val zero : t val one : t val add : t -> t -> t end let impl : (module S) = match repr with | Immediate -> (module Int : S) | Non_immediate -> (module Int64 : S) include (val impl : S) end >> 12.13 Extension nodes *=*=*=*=*=*=*=*=*=*=*=* (Introduced in OCaml 4.02, infix notations for constructs other than expressions added in 4.03, infix notation (e1 ;%ext e2) added in 4.04. ) Extension nodes are generic placeholders in the syntax tree. They are rejected by the type-checker and are intended to be “expanded” by external tools such as -ppx rewriters. Extension nodes share the same notion of identifier and payload as attributes 12.12. The first form of extension node is used for “algebraic” categories: extension ::= [% attr-id attr-payload ] expr ::= ... | extension typexpr ::= ... | extension pattern ::= ... | extension module-expr ::= ... | extension module-type ::= ... | extension class-expr ::= ... | extension class-type ::= ... | extension A second form of extension node can be used in structures and signatures, both in the module and object languages: item-extension ::= [%% attr-id attr-payload ] definition ::= ... | item-extension specification ::= ... | item-extension class-field-spec ::= ... | item-extension class-field ::= ... | item-extension An infix form is available for extension nodes when the payload is of the same kind (expression with expression, pattern with pattern ...). Examples: <> When this form is used together with the infix syntax for attributes, the attributes are considered to apply to the payload: < x + 1 === [%foo (fun x -> x + 1)[@bar ] ]; >> An additional shorthand let%foo x in ... is available for convenience when extension nodes are used to implement binding operators (See 12.23.4). Furthermore, quoted strings {|...|} can be combined with extension nodes to embed foreign syntax fragments. Those fragments can be interpreted by a preprocessor and turned into OCaml code without requiring escaping quotes. A syntax shortcut is available for them: <<{%%foo|...|} === [%%foo{|...|}] let x = {%foo|...|} === let x = [%foo{|...|}] let y = {%foo bar|...|bar} === let y = [%foo{bar|...|bar}] >> For instance, you can use {%sql|...|} to represent arbitrary SQL statements – assuming you have a ppx-rewriter that recognizes the %sql extension. Note that the word-delimited form, for example {sql|...|sql}, should not be used for signaling that an extension is in use. Indeed, the user cannot see from the code whether this string literal has different semantics than they expect. Moreover, giving semantics to a specific delimiter limits the freedom to change the delimiter to avoid escaping issues. 12.13.1 Built-in extension nodes ================================== (Introduced in OCaml 4.03) Some extension nodes are understood by the compiler itself: - “ocaml.extension_constructor” or “extension_constructor” take as payload a constructor from an extensible variant type (see 12.14) and return its extension constructor slot. << type t = .. type t += X of int | Y of string let x = [%extension_constructor X] let y = [%extension_constructor Y] >> << # x <> y;; - : bool = true >> 12.14 Extensible variant types *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= (Introduced in OCaml 4.02) type-representation ::= ... | = .. specification ::= ... | type [type-params] typeconstr type-extension-spec definition ::= ... | type [type-params] typeconstr type-extension-def type-extension-spec ::= += [private] [|] constr-decl { | constr-decl } type-extension-def ::= += [private] [|] constr-def { | constr-def } constr-def ::= constr-decl | constr-name = constr Extensible variant types are variant types which can be extended with new variant constructors. Extensible variant types are defined using ... New variant constructors are added using +=. << module Expr = struct type attr = .. type attr += Str of string type attr += | Int of int | Float of float end >> Pattern matching on an extensible variant type requires a default case to handle unknown variant constructors: << let to_string = function | Expr.Str s -> s | Expr.Int i -> Int.to_string i | Expr.Float f -> string_of_float f | _ -> "?" >> A preexisting example of an extensible variant type is the built-in exn type used for exceptions. Indeed, exception constructors can be declared using the type extension syntax: << type exn += Exc of int >> Extensible variant constructors can be rebound to a different name. This allows exporting variants from another module. << # let not_in_scope = Str "Foo";; Error: Unbound constructor Str >> << type Expr.attr += Str = Expr.Str >> << # let now_works = Str "foo";; val now_works : Expr.attr = Expr.Str "foo" >> Extensible variant constructors can be declared private. As with regular variants, this prevents them from being constructed directly by constructor application while still allowing them to be de-structured in pattern-matching. << module B : sig type Expr.attr += private Bool of int val bool : bool -> Expr.attr end = struct type Expr.attr += Bool of int let bool p = if p then Bool 1 else Bool 0 end >> << # let inspection_works = function | B.Bool p -> (p = 1) | _ -> true;; val inspection_works : Expr.attr -> bool = >> << # let construction_is_forbidden = B.Bool 1;; Error: Cannot use private constructor Bool to create values of type Expr.attr >> 12.14.1 Private extensible variant types ========================================== (Introduced in OCaml 4.06) type-representation ::= ... | = private .. Extensible variant types can be declared private. This prevents new constructors from being declared directly, but allows extension constructors to be referred to in interfaces. << module Msg : sig type t = private .. module MkConstr (X : sig type t end) : sig type t += C of X.t end end = struct type t = .. module MkConstr (X : sig type t end) = struct type t += C of X.t end end >> 12.15 Generative functors *=*=*=*=*=*=*=*=*=*=*=*=*=* (Introduced in OCaml 4.02) module-expr ::= ... | functor () -> module-expr | module-expr () definition ::= ... | module module-name { ( module-name : module-type ) | () } [ : module-type ] = module-expr module-type ::= ... | [functor] () -> module-type specification ::= ... | module module-name { ( module-name : module-type ) | () } : module-type A generative functor takes a unit () argument. In order to use it, one must necessarily apply it to this unit argument, ensuring that all type components in the result of the functor behave in a generative way, i.e. they are different from types obtained by other applications of the same functor. This is equivalent to taking an argument of signature sig end, and always applying to struct end, but not to some defined module (in the latter case, applying twice to the same module would return identical types). As a side-effect of this generativity, one is allowed to unpack first-class modules in the body of generative functors. 12.16 Extension-only syntax *=*=*=*=*=*=*=*=*=*=*=*=*=*=* (Introduced in OCaml 4.02.2, extended in 4.03) Some syntactic constructions are accepted during parsing and rejected during type checking. These syntactic constructions can therefore not be used directly in vanilla OCaml. However, -ppx rewriters and other external tools can exploit this parser leniency to extend the language with these new syntactic constructions by rewriting them to vanilla constructions. 12.16.1 Extension operators ============================= (Introduced in OCaml 4.02.2, extended to unary operators in OCaml 4.12.0) infix-symbol ::= ... | # { operator-char } # { operator-char | # } prefix-symbol ::= ... | (? | ~ | !) { operator-char } # { operator-char | # } There are two classes of operators available for extensions: infix operators with a name starting with a # character and containing more than one # character, and unary operators with a name (starting with a ?, ~, or ! character) containing at least one # character. For instance: << # let infix x y = x##y;; Error: ## is not a valid value identifier. >> << # let prefix x = !#x;; Error: !# is not a valid value identifier. >> Note that both ## and !# must be eliminated by a ppx rewriter to make this example valid. 12.16.2 Extension literals ============================ (Introduced in OCaml 4.03) float-literal ::= ... | [-] (0...9) { 0...9 | _ } [. { 0...9 | _ }] [(e | E) [+ | -] (0...9) { 0...9 | _ }] [g...z | G...Z] | [-] (0x | 0X) (0...9 | A...F | a...f) { 0...9 | A...F | a...f | _ } [. { 0...9 | A...F | a...f | _ }] [(p | P) [+ | -] (0...9) { 0...9 | _ }] [g...z | G...Z] int-literal ::= ... | [-] (0...9) { 0...9 | _ }[g...z | G...Z] | [-] (0x | 0X) (0...9 | A...F | a...f) { 0...9 | A...F | a...f | _ } [g...z | G...Z] | [-] (0o | 0O) (0...7) { 0...7 | _ } [g...z | G...Z] | [-] (0b | 0B) (0...1) { 0...1 | _ } [g...z | G...Z] Int and float literals followed by an one-letter identifier in the range [g..z|G..Z] are extension-only literals. 12.17 Inline records *=*=*=*=*=*=*=*=*=*=*= (Introduced in OCaml 4.03) constr-args ::= ... | record-decl The arguments of sum-type constructors can now be defined using the same syntax as records. Mutable and polymorphic fields are allowed. GADT syntax is supported. Attributes can be specified on individual fields. Syntactically, building or matching constructors with such an inline record argument is similar to working with a unary constructor whose unique argument is a declared record type. A pattern can bind the inline record as a pseudo-value, but the record cannot escape the scope of the binding and can only be used with the dot-notation to extract or modify fields or to build new constructor values. << type t = | Point of {width: int; mutable x: float; mutable y: float} | Other let v = Point {width = 10; x = 0.; y = 0.} let scale l = function | Point p -> Point {p with x = l *. p.x; y = l *. p.y} | Other -> Other let print = function | Point {x; y; _} -> Printf.printf "%f/%f" x y | Other -> () let reset = function | Point p -> p.x <- 0.; p.y <- 0. | Other -> () >> << let invalid = function | Point p -> p Error: This form is not allowed as the type of the inlined record could escap e. >> 12.18 Documentation comments *=*=*=*=*=*=*=*=*=*=*=*=*=*=*= (Introduced in OCaml 4.03) Comments which start with ** are treated specially by the compiler. They are automatically converted during parsing into attributes (see 12.12) to allow tools to process them as documentation. Such comments can take three forms: floating comments, item comments and label comments. Any comment starting with ** which does not match one of these forms will cause the compiler to emit warning 50. Comments which start with ** are also used by the ocamldoc documentation generator (see 19). The three comment forms recognised by the compiler are a subset of the forms accepted by ocamldoc (see 19.2). 12.18.1 Floating comments =========================== Comments surrounded by blank lines that appear within structures, signatures, classes or class types are converted into floating-attributes. For example: << type t = T (** Now some definitions for [t] *) let mkT = T >> will be converted to: << type t = T [@@@ocaml.text " Now some definitions for [t] "] let mkT = T >> 12.18.2 Item comments ======================= Comments which appear immediately before or immediately after a structure item, signature item, class item or class type item are converted into item-attributes. Immediately before or immediately after means that there must be no blank lines, ;;, or other documentation comments between them. For example: << type t = T (** A description of [t] *) >> or << (** A description of [t] *) type t = T >> will be converted to: << type t = T [@@ocaml.doc " A description of [t] "] >> Note that, if a comment appears immediately next to multiple items, as in: << type t = T (** An ambiguous comment *) type s = S >> then it will be attached to both items: << type t = T [@@ocaml.doc " An ambiguous comment "] type s = S [@@ocaml.doc " An ambiguous comment "] >> and the compiler will emit warning 50. 12.18.3 Label comments ======================== Comments which appear immediately after a labelled argument, record field, variant constructor, object method or polymorphic variant constructor are are converted into attributes. Immediately after means that there must be no blank lines or other documentation comments between them. For example: << type t1 = lbl:int (** Labelled argument *) -> unit type t2 = { fld: int; (** Record field *) fld2: float; } type t3 = | Cstr of string (** Variant constructor *) | Cstr2 of string type t4 = < meth: int * int; (** Object method *) > type t5 = [ `PCstr (** Polymorphic variant constructor *) ] >> will be converted to: << type t1 = lbl:(int [@ocaml.doc " Labelled argument "]) -> unit type t2 = { fld: int [@ocaml.doc " Record field "]; fld2: float; } type t3 = | Cstr of string [@ocaml.doc " Variant constructor "] | Cstr2 of string type t4 = < meth : int * int [@ocaml.doc " Object method "] > type t5 = [ `PCstr [@ocaml.doc " Polymorphic variant constructor "] ] >> Note that label comments take precedence over item comments, so: << type t = T of string (** Attaches to T not t *) >> will be converted to: << type t = T of string [@ocaml.doc " Attaches to T not t "] >> whilst: << type t = T of string (** Attaches to T not t *) (** Attaches to t *) >> will be converted to: << type t = T of string [@ocaml.doc " Attaches to T not t "] [@@ocaml.doc " Attaches to t "] >> In the absence of meaningful comment on the last constructor of a type, an empty comment (**) can be used instead: << type t = T of string (**) (** Attaches to t *) >> will be converted directly to << type t = T of string [@@ocaml.doc " Attaches to t "] >> 12.19 Extended indexing operators *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* (Introduced in 4.06) dot-ext ::= | dot-operator-char { operator-char } dot-operator-char ::= ! | ? | core-operator-char | % | : expr ::= ... | expr . [module-path .] dot-ext ( ( expr ) | [ expr ] | { expr } ) [ <- expr ] operator-name ::= ... | . dot-ext (() | [] | {}) [<-] This extension provides syntactic sugar for getting and setting elements for user-defined indexed types. For instance, we can define python-like dictionaries with << module Dict = struct include Hashtbl let ( .%{} ) tabl index = find tabl index let ( .%{}<- ) tabl index value = add tabl index value end let dict = let dict = Dict.create 10 in let () = dict.Dict.%{"one"} <- 1; let open Dict in dict.%{"two"} <- 2 in dict >> << # dict.Dict.%{"one"};; - : int = 1 >> << # let open Dict in dict.%{"two"};; - : int = 2 >> 12.19.1 Multi-index notation ============================== expr ::= ... + | expr . [module-path .] dot-ext ( expr { ; expr } ) [ <- expr ] + | expr . [module-path .] dot-ext [ expr { ; expr } ] [ <- expr ] + | expr . [module-path .] dot-ext { expr { ; expr } } [ <- expr ] operator-name ::= ... | . dot-ext ((;..) | [;..] | {;..}) [<-] Multi-index are also supported through a second variant of indexing operators << let (.%[;..]) = Bigarray.Genarray.get let (.%{;..}) = Bigarray.Genarray.get let (.%(;..)) = Bigarray.Genarray.get >> which is called when an index literals contain a semicolon separated list of expressions with two and more elements: << let sum x y = x.%[1;2;3] + y.%[1;2] (* is equivalent to *) let sum x y = (.%[;..]) x [|1;2;3|] + (.%[;..]) y [|1;2|] >> In particular this multi-index notation makes it possible to uniformly handle indexing Genarray and other implementations of multidimensional arrays. << module A = Bigarray.Genarray let (.%{;..}) = A.get let (.%{;..}<- ) = A.set let (.%{ }) a k = A.get a [|k|] let (.%{ }<-) a k x = A.set a [|k|] x let syntax_compare vec mat t3 t4 = vec.%{0} = A.get vec [|0|] && mat.%{0;0} = A.get mat [|0;0|] && t3.%{0;0;0} = A.get t3 [|0;0;0|] && t4.%{0;0;0;0} = t4.{0,0,0,0} >> Beware that the differentiation between the multi-index and single index operators is purely syntactic: multi-index operators are restricted to index expressions that contain one or more semicolons ;. For instance, << let pair vec mat = vec.%{0}, mat.%{0;0} >> is equivalent to << let pair vec mat = (.%{ }) vec 0, (.%{;..}) mat [|0;0|] >> Notice that in the vec case, we are calling the single index operator, (.%{}), and not the multi-index variant, (.{;..}). For this reason, it is expected that most users of multi-index operators will need to define conjointly a single index variant << let (.%{;..}) = A.get let (.%{ }) a k = A.get a [|k|] >> to handle both cases uniformly. 12.20 Empty variant types *=*=*=*=*=*=*=*=*=*=*=*=*=* (Introduced in 4.07.0) type-representation ::= ... | = | This extension allows user to define empty variants. Empty variant type can be eliminated by refutation case of pattern matching. << type t = | let f (x: t) = match x with _ -> . >> 12.21 Alerts *=*=*=*=*=*=*= (Introduced in 4.08) Since OCaml 4.08, it is possible to mark components (such as value or type declarations) in signatures with “alerts” that will be reported when those components are referenced. This generalizes the notion of “deprecated” components which were previously reported as warning 3. Those alerts can be used for instance to report usage of unsafe features, or of features which are only available on some platforms, etc. Alert categories are identified by a symbolic identifier (a lowercase identifier, following the usual lexical rules) and an optional message. The identifier is used to control which alerts are enabled, and which ones are turned into fatal errors. The message is reported to the user when the alert is triggered (i.e. when the marked component is referenced). The ocaml.alert or alert attribute serves two purposes: (i) to mark component with an alert to be triggered when the component is referenced, and (ii) to control which alert names are enabled. In the first form, the attribute takes an identifier possibly followed by a message. Here is an example of a value declaration marked with an alert: < bool [@@alert unix "This function is only available under Unix."] end >> Here unix is the identifier for the alert. If this alert category is enabled, any reference to U.fork will produce a message at compile time, which can be turned or not into a fatal error. And here is another example as a floating attribute on top of an “.mli” file (i.e. before any other non-attribute item) or on top of an “.ml” file without a corresponding interface file, so that any reference to that unit will trigger the alert: <<[@@@alert unsafe "This module is unsafe!"] >> Controlling which alerts are enabled and whether they are turned into fatal errors is done either through the compiler’s command-line option -alert or locally in the code through the alert or ocaml.alert attribute taking a single string payload . In both cases, the syntax for is a concatenation of items of the form: - +id enables alert id. - -id disables alert id. - ++id turns alert id into a fatal error. - –id turns alert id into non-fatal mode. - @id equivalent to ++id+id (enables id and turns it into a fatal-error) As a special case, if id is all, it stands for all alerts. Here are some examples: << (* Disable all alerts, reenables just unix (as a soft alert) and window (as a fatal-error), for the rest of the current structure *) [@@@alert "-all--all+unix@window"] ... let x = (* Locally disable the window alert *) begin[@alert "-window"] ... end >> Before OCaml 4.08, there was support for a single kind of deprecation alert. It is now known as the deprecated alert, but legacy attributes to trigger it and the legacy ways to control it as warning 3 are still supported. For instance, passing -w +3 on the command-line is equivalent to -alert +deprecated, and: <> is equivalent to: <> 12.22 Generalized open statements *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* (Introduced in 4.08) definition ::= ... | open module-expr | open! module-expr specification ::= ... | open extended-module-path | open! extended-module-path expr ::= ... | let open module-expr in expr | let open! module-expr in expr This extension makes it possible to open any module expression in module structures and expressions. A similar mechanism is also available inside module types, but only for extended module paths (e.g. F(X).G(Y)). For instance, a module can be constrained when opened with << module M = struct let x = 0 let hidden = 1 end open (M:sig val x: int end) let y = hidden Error: Unbound value hidden >> Another possibility is to immediately open the result of a functor application << let sort (type x) (x:x list) = let open Set.Make(struct type t = x let compare=compare end) in elements (of_list x) val sort : 'x list -> 'x list = >> Going further, this construction can introduce local components inside a structure, << module M = struct let x = 0 open! struct let x = 0 let y = 1 end let w = x + y end module M : sig val x : int val w : int end >> One important restriction is that types introduced by open struct ... end cannot appear in the signature of the enclosing structure, unless they are defined equal to some non-local type. So: << module M = struct open struct type 'a t = 'a option = None | Some of 'a end let x : int t = Some 1 end module M : sig val x : int option end >> is OK, but: << module M = struct open struct type t = A end let x = A end Error: The type t introduced by this open appears in the signature. The value x has no valid type if t is hidden. >> is not because x cannot be given any type other than t, which only exists locally. Although the above would be OK if x too was local: << module M: sig end = struct open struct type t = A end ... open struct let x = A end ... end module M : sig end >> Inside signatures, extended opens are limited to extended module paths, << module type S = sig module F: sig end -> sig type t end module X: sig end open F(X) val f: t end module type S = sig module F : sig end -> sig type t end module X : sig end val f : F(X).t end >> and not << open struct type t = int end >> In those situations, local substitutions(see 12.7.2) can be used instead. Beware that this extension is not available inside class definitions: <> 12.23 Binding operators *=*=*=*=*=*=*=*=*=*=*=*=* (Introduced in 4.08.0) let-operator ::= | let (core-operator-char | <) { dot-operator-char } and-operator ::= | and (core-operator-char | <) { dot-operator-char } operator-name ::= ... | let-operator | and-operator letop-binding ::= pattern = expr | value-name expr ::= ... | let-operator letop-binding { and-operator letop-binding } in expr Binding operators offer syntactic sugar to expose library functions under (a variant of) the familiar syntax of standard keywords. Currently supported “binding operators” are let and and, where is an operator symbol, for example and+$. Binding operators were introduced to offer convenient syntax for working with monads and applicative functors; for those, we propose conventions using operators * and + respectively. They may be used for other purposes, but one should keep in mind that each new unfamiliar notation introduced makes programs harder to understand for non-experts. We expect that new conventions will be developed over time on other families of operator. 12.23.1 Examples ================== Users can define let operators: << let ( let* ) o f = match o with | None -> None | Some x -> f x let return x = Some x val ( let* ) : 'a option -> ('a -> 'b option) -> 'b option = val return : 'a -> 'a option = >> and then apply them using this convenient syntax: << let find_and_sum tbl k1 k2 = let* x1 = Hashtbl.find_opt tbl k1 in let* x2 = Hashtbl.find_opt tbl k2 in return (x1 + x2) val find_and_sum : ('a, int) Hashtbl.t -> 'a -> 'a -> int option = >> which is equivalent to this expanded form: << let find_and_sum tbl k1 k2 = ( let* ) (Hashtbl.find_opt tbl k1) (fun x1 -> ( let* ) (Hashtbl.find_opt tbl k2) (fun x2 -> return (x1 + x2))) val find_and_sum : ('a, int) Hashtbl.t -> 'a -> 'a -> int option = >> Users can also define and operators: << module ZipSeq = struct type 'a t = 'a Seq.t open Seq let rec return x = fun () -> Cons(x, return x) let rec prod a b = fun () -> match a (), b () with | Nil, _ | _, Nil -> Nil | Cons(x, a), Cons(y, b) -> Cons((x, y), prod a b) let ( let+ ) f s = map s f let ( and+ ) a b = prod a b end module ZipSeq : sig type 'a t = 'a Seq.t val return : 'a -> 'a Seq.t val prod : 'a Seq.t -> 'b Seq.t -> ('a * 'b) Seq.t val ( let+ ) : 'a Seq.t -> ('a -> 'b) -> 'b Seq.t val ( and+ ) : 'a Seq.t -> 'b Seq.t -> ('a * 'b) Seq.t end >> to support the syntax: << open ZipSeq let sum3 z1 z2 z3 = let+ x1 = z1 and+ x2 = z2 and+ x3 = z3 in x1 + x2 + x3 val sum3 : int Seq.t -> int Seq.t -> int Seq.t -> int Seq.t = >> which is equivalent to this expanded form: << open ZipSeq let sum3 z1 z2 z3 = ( let+ ) (( and+ ) (( and+ ) z1 z2) z3) (fun ((x1, x2), x3) -> x1 + x2 + x3) val sum3 : int Seq.t -> int Seq.t -> int Seq.t -> int Seq.t = >> 12.23.2 Conventions ===================== An applicative functor should provide a module implementing the following interface: << module type Applicative_syntax = sig type 'a t val ( let+ ) : 'a t -> ('a -> 'b) -> 'b t val ( and+ ): 'a t -> 'b t -> ('a * 'b) t end >> where (let+) is bound to the map operation and (and+) is bound to the monoidal product operation. A monad should provide a module implementing the following interface: << module type Monad_syntax = sig include Applicative_syntax val ( let* ) : 'a t -> ('a -> 'b t) -> 'b t val ( and* ): 'a t -> 'b t -> ('a * 'b) t end >> where (let*) is bound to the bind operation, and (and*) is also bound to the monoidal product operation. 12.23.3 General desugaring rules ================================== The form < x1 = e1 and x2 = e2 and x3 = e3 in e >> desugars into <<( let ) (( and ) (( and ) e1 e2) e3) (fun ((x1, x2), x3) -> e) >> This of course works for any number of nested and-operators. One can express the general rule by repeating the following simplification steps: - The first and-operator in let x1 = e1 and x2 = e2 and... in e can be desugared into a function application let (x1, x2) = ( and ) e1 e2 and... in e. - Once all and-operators have been simplified away, the let-operator in let x1 = e1 in e can be desugared into an application ( let ) e1 (fun x1 -> e). Note that the grammar allows mixing different operator symbols in the same binding (, , may be distinct), but we strongly recommend APIs where let-operators and and-operators working together use the same symbol. 12.23.4 Short notation for variable bindings (let-punning) ============================================================ (Introduced in 4.13.0) When the expression being bound is a variable, it can be convenient to use the shorthand notation let+ x in ..., which expands to let+ x = x in .... This notation, also known as let-punning, allows the sum3 function above can be written more concisely as: << open ZipSeq let sum3 z1 z2 z3 = let+ z1 and+ z2 and+ z3 in z1 + z2 + z3 val sum3 : int Seq.t -> int Seq.t -> int Seq.t -> int Seq.t = >> This notation is also supported for extension nodes, expanding let%foo x in ... to let%foo x = x in .... However, to avoid confusion, this notation is not supported for plain let bindings. 12.24 Effect handlers *=*=*=*=*=*=*=*=*=*=*=* (Introduced in 5.0) Note: Effect handlers in OCaml 5.0 should be considered experimental. Effect handlers are exposed in the standard library’s Effect module as a thin wrapper around their implementation in the runtime. They are not supported as a language feature with new syntax. You can rely on them to build non-local control-flow abstractions such as user-level threading that do not expose the effect handler primitives to the user. Expect breaking changes in the future. Effect handlers are a mechanism for modular programming with user-defined effects. Effect handlers allow the programmers to describe computations that perform effectful operations, whose meaning is described by handlers that enclose the computations. Effect handlers are a generalization of exception handlers and enable non-local control-flow mechanisms such as resumable exceptions, lightweight threads, coroutines, generators and asynchronous I/O to be composably expressed. In this tutorial, we shall see how some of these mechanisms can be built using effect handlers. 12.24.1 Basics ================ To understand the basics, let us define an effect (that is, an operation) that takes an integer argument and returns an integer result. We name this effect Xchg. << open Effect open Effect.Deep type _ Effect.t += Xchg: int -> int t let comp1 () = perform (Xchg 0) + perform (Xchg 1) >> We declare the exchange effect Xchg by extending the pre-defined extensible variant type Effect.t with a new constructor Xchg: int -> int t. The declaration may be intuitively read as “the Xchg effect takes an integer parameter, and when this effect is performed, it returns an integer”. The computation comp1 performs the effect twice using the perform primitive and returns their sum. We can handle the Xchg effect by implementing a handler that always returns the successor of the offered value: << try_with comp1 () { effc = fun (type a) (eff: a t) -> match eff with | Xchg n -> Some (fun (k: (a, _) continuation) -> continue k (n+1)) | _ -> None } - : int = 3 >> try_with runs the computation comp1 () under an effect handler that handles the Xchg effect. As mentioned earlier, effect handlers are a generalization of exception handlers. Similar to exception handlers, when the computation performs the Xchg effect, the control jumps to the corresponding handler. However, unlike exception handlers, the handler is also provided with the delimited continuation k, which represents the suspended computation between the point of perform and this handler. The handler uses the continue primitive to resume the suspended computation with the successor of the offered value. In this example, the computation comp1 performs Xchg 0 and Xchg 1 and receives the values 1 and 2 from the handler respectively. Hence, the whole expression evaluates to 3. It is useful to note that we must use a locally abstract type (type a) in the effect handler. The type Effect.t is a GADT, and the effect declarations may have different type parameters for different effects. The type parameter a in the type a Effect.t represents the type of the value returned when performing the effect. From the fact that eff has type a Effect.t and from the fact that Xchg n has type int Effect.t, the type-checker deduces that a must be int, which is why we are allowed to pass the integer value n+1 as an argument to continue k. Another point to note is that the catch-all case “| _ -> None” is necessary when handling effects. This case may be intuitively read as “forward the unhandled effects to the outer handler”. In this example, we use the deep version of the effect handlers here as opposed to the shallow version. A deep handler monitors a computation until the computation terminates (either normally or via an exception), and handles all of the effects performed (in sequence) by the computation. In contrast, a shallow handler monitors a computation until either the computation terminates or the computation performs one effect, and it handles this single effect only. In situations where they are applicable, deep handlers are usually preferred. An example that utilises shallow handlers is discussed later in 12.24.6. Limitations ----------- OCaml’s effects are synchronous: It is not possible to perform an effect asynchronously from a signal handler, a finaliser, a memprof callback, or a GC alarm, and catch it from the main part of the code. Instead, this would result in an Effect.Unhandled exception (12.24.5). Similarly, effects are incompatible with the use of callbacks from C to OCaml (section 22.7). It is not possible for an effect to cross a call to caml_callback, this would instead result in an Effect.Unhandled exception. In particular, care must be taken when mixing libraries that use callbacks from C to OCaml and libraries that use effects. 12.24.2 Concurrency ===================== The expressive power of effect handlers comes from the delimited continuation. While the previous example immediately resumed the computation, the computation may be resumed later, running some other computation in the interim. Let us extend the previous example and implement message-passing concurrency between two concurrent computations using the Xchg effect. We call these concurrent computations tasks. A task either is in a suspended state or is completed. We represent the task status as follows: << type 'a status = Complete of 'a | Suspended of {msg: int; cont: (int, 'a status) continuation} >> A task either is complete, with a result of type 'a, or is suspended with the message msg to send and the continuation cont. The type (int,'a status) continuation says that the suspended computation expects an int value to resume and returns a 'a status value when resumed. Next, we define a step function that executes one step of computation until it completes or suspends: << let step (f : unit -> 'a) () : 'a status = match_with f () { retc = (fun v -> Complete v); exnc = raise; effc = fun (type a) (eff: a t) -> match eff with | Xchg msg -> Some (fun (cont: (a, _) continuation) -> Suspended {msg; cont}) | _ -> None } >> The argument to the step function, f, is a computation that can perform an Xchg effect and returns a result of type 'a. The step function itself returns a 'a status value. In the step function, we use the match_with primitive. Like try_with, match_with primitive installs an effect handler. However, unlike try_with, where only the effect case effc is provided, match_with expects the handlers for the value (retc) and exceptional (exnc) return cases. In fact, try_with can be defined using match_with as follows: let try_with f v {effc} = match_with f v {retc = Fun.id; exnc = raise; effc}. In the step function, - Case retc: If the computation returns with a value v, we return Complete v. - Case exnc: If the computation raises an exception, then the handler raises the same exception. - Case effc: If the computation performs the effect Xchg msg with the continuation cont, then we return Suspended{msg;cont}. Thus, in this case, the continuation cont is not immediately invoked by the handler; instead, it is stored in a data structure for later use. Since the step function handles the Xchg effect, step f is a computation that does not perform the Xchg effect. It may however perform other effects. Moreover, since we are using deep handlers, the continuation cont stored in the status does not perform the Xchg effect. We can now write a simple scheduler that runs a pair of tasks to completion: << let rec run_both a b = match a (), b () with | Complete va, Complete vb -> (va, vb) | Suspended {msg = m1; cont = k1}, Suspended {msg = m2; cont = k2} -> run_both (fun () -> continue k1 m2) (fun () -> continue k2 m1) | _ -> failwith "Improper synchronization" >> Both of the tasks may run to completion, or both may offer to exchange a message. In the latter case, each computation receives the value offered by the other computation. The situation where one computation offers an exchange while the other computation terminates is regarded as a programmer error, and causes the handler to raise an exception We can now define a second computation that also exchanges two messages: << let comp2 () = perform (Xchg 21) * perform (Xchg 21) >> Finally, we can run the two computations together: << run_both (step comp1) (step comp2) - : int * int = (42, 0) >> The computation comp1 offers the values 0 and 1 and in exchange receives the values 21 and 21, which it adds, producing 42. The computation comp2 offers the values 21 and 21 and in exchange receives the values 0 and 1, which it multiplies, producing 0. The communication between the two computations is programmed entirely inside run_both. Indeed, the definitions of comp1 and comp2, alone, do not assign any meaning to the Xchg effect. 12.24.3 User-level threads ============================ Let us extend the previous example for an arbitrary number of tasks. Many languages such as GHC Haskell and Go provide user-level threads as a primitive feature implemented in the runtime system. With effect handlers, user-level threads and their schedulers can be implemented in OCaml itself. Typically, user-level threading systems provide a fork primitive to spawn off a new concurrent task and a yield primitive to yield control to some other task. Correspondingly, we shall declare two effects as follows: << type _ Effect.t += Fork : (unit -> unit) -> unit t | Yield : unit t >> The Fork effect takes a thunk (a suspended computation, represented as a function of type unit -> unit) and returns a unit to the performer. The Yield effect is unparameterized and returns a unit when performed. Let us consider that a task performing an Xchg effect may match with any other task also offering to exchange a value. We shall also define helper functions that simply perform these effects: << let fork f = perform (Fork f) let yield () = perform Yield let xchg v = perform (Xchg v) >> A top-level run function defines the scheduler: << (* A concurrent round-robin scheduler *) let run (main : unit -> unit) : unit = let exchanger = ref None in (* waiting exchanger *) let run_q = Queue.create () in (* scheduler queue *) let enqueue k v = let task () = continue k v in Queue.push task run_q in let dequeue () = if Queue.is_empty run_q then () (* done *) else begin let task = Queue.pop run_q in task () end in let rec spawn (f : unit -> unit) : unit = match_with f () { retc = dequeue; exnc = (fun e -> print_endline (Printexc.to_string e); dequeue ()); effc = fun (type a) (eff : a t) -> match eff with | Yield -> Some (fun (k : (a, unit) continuation) -> enqueue k (); dequeue ()) | Fork f -> Some (fun (k : (a, unit) continuation) -> enqueue k (); spawn f) | Xchg n -> Some (fun (k : (int, unit) continuation) -> begin match !exchanger with | Some (n', k') -> exchanger := None; enqueue k' n; continue k n' | None -> exchanger := Some (n, k); dequeue () end) | _ -> None } in spawn main >> We use a mutable queue run_q to hold the scheduler queue. The FIFO queue enables round-robin scheduling of tasks in the scheduler. enqueue inserts tasks into the queue, and dequeue extracts tasks from the queue and runs them. The reference cell exchanger holds a (suspended) task offering to exchange a value. At any time, there is either zero or one suspended task that is offering an exchange. The heavy lifting is done by the spawn function. The spawn function runs the given computation f in an effect handler. If f returns with a value (case retc), we dequeue and run the next task from the scheduler queue. If the computation f raises an exception (case exnc), we print the exception and run the next task from the scheduler. The computation f may also perform effects. If f performs the Yield effect, the current task is suspended (inserted into the queue of ready tasks), and the next task from the scheduler queue is run. If the effect is Fork f, then the current task is suspended, and the new task f is executed immediately via a tail call to spawn f. Note that this choice to run the new task first is arbitrary. We could very well have chosen instead to insert the task for f into the ready queue and resumed k immediately. If the effect is Xchg, then we first check whether there is a task waiting to exchange. If so, we enqueue the waiting task with the current value being offered and immediately resume the current task with the value being offered. If not, we make the current task the waiting exchanger, and run the next task from the scheduler queue. Note that this scheduler code is not perfect – it can leak resources. We shall explain and fix this in the next section 12.24.3. Now we can write a concurrent program that utilises the newly defined operations: << open Printf let _ = run (fun _ -> fork (fun _ -> printf "[t1] Sending 0\n"; let v = xchg 0 in printf "[t1] received %d\n" v); fork (fun _ -> printf "[t2] Sending 1\n"; let v = xchg 1 in printf "[t2] received %d\n" v)) [t1] Sending 0 [t2] Sending 1 [t2] received 0 [t1] received 1 >> Observe that the messages from the two tasks are interleaved. Notice also that the snippet above makes no reference to the effect handlers and is in direct style (no monadic operations). This example illustrates that, with effect handlers, the user code in a concurrent program can remain in simple direct style, and the use of effect handlers can be fully contained within the concurrency library implementation. Resuming with an exception -------------------------- In addition to resuming a continuation with a value, effect handlers also permit resuming by raising an effect at the point of perform. This is done with the help of the discontinue primitive. The discontinue primitive helps ensure that resources are always eventually deallocated, even in the presence of effects. For example, consider the dequeue operation in the previous example reproduced below: << ... let dequeue () = if Queue.is_empty run_q then () (* done *) else (Queue.pop run_q) () >> If the scheduler queue is empty, dequeue considers that the scheduler is done and returns to the caller. However, there may still be a task waiting to exchange a value (stored in the reference cell exchanger), which remains blocked forever! If the blocked task holds onto resources, these resources are leaked. For example, consider the following task: << let leaky_task () = fork (fun _ -> let oc = open_out "secret.txt" in Fun.protect ~finally:(fun _ -> close_out oc) (fun _ -> output_value oc (xchg 0))) >> The task writes the received message to the file secret.txt. It uses Fun.protect to ensure that the output channel oc is closed on both normal and exceptional return cases. Unfortunately, this is not sufficient. If the exchange effect xchg 0 cannot be matched with an exchange effect performed by some other thread, then this task remains blocked forever. Thus, the output channel oc is never closed. To avoid this problem, one must adhere to a simple discipline: every continuation must be eventually either continued or discontinued. Here, we use discontinue to ensure that the blocked task does not remain blocked forever. By discontinuing this task, we force it to terminate (with an exception): << exception Improper_synchronization let dequeue () = if Queue.is_empty run_q then begin match !exchanger with | None -> () (* done *) | Some (n, k) -> exchanger := None; discontinue k Improper_synchronization end else (Queue.pop run_q) () >> When the scheduler queue is empty and there is a blocked exchanger thread, the dequeue function discontinues the blocked thread with an Improper_synchronization exception. This exception is raised at the blocked xchg function call, which causes the finally block to be run and closes the output channel oc. From the point of view of the user, it seems as though the function call xchg 0 raises the exception Improper_synchronization. 12.24.4 Control inversion =========================== When it comes to performing traversals on a data structure, there are two fundamental ways depending on whether the producer or the consumer has the control over the traversal. For example, in List.iter f l, the producer List.iter has the control and pushes the element to the consumer f who processes them. On the other hand, the Seq module provides a mechanism similar to delayed lists where the consumer controls the traversal. For example, Seq.forever Random.bool returns an infinite sequence of random bits where every bit is produced (on demand) when queried by the consumer. Naturally, producers such as List.iter are easier to write in the former style. The latter style is ergonomically better for the consumer since it is preferable and more natural to be in control. To have the best of both worlds, we would like to write a producer in the former style and automatically convert it to the latter style. The conversion can be written once and for all as a library function, thanks to effect handlers. Let us name this function invert. We will first look at how to use the invert function before looking at its implementation details. The type of this function is given below: << val invert : iter:(('a -> unit) -> unit) -> 'a Seq.t >> The invert function takes an iter function (a producer that pushes elements to the consumer) and returns a sequence (where the consumer has the control). For example, << let lst_iter = Fun.flip List.iter [1;2;3] val lst_iter : (int -> unit) -> unit = >> is an iter function with type (int -> unit) -> unit. The expression lst_iter f pushes the elements 1, 2 and 3 to the consumer f. For example, << lst_iter (fun i -> Printf.printf "%d\n" i) 1 2 3 - : unit = () >> The expression invert lst_iter returns a sequence that allows the consumer to traverse the list on demand. For example, << let s = invert ~iter:lst_iter let next = Seq.to_dispenser s;; val s : int Seq.t = val next : unit -> int option = >> << next();; - : int option = Some 1 >> << next();; - : int option = Some 2 >> << next();; - : int option = Some 3 >> << next();; - : int option = None >> We can use the same invert function on any iter function. For example, << let s = invert ~iter:(Fun.flip String.iter "OCaml") let next = Seq.to_dispenser s;; val s : char Seq.t = val next : unit -> char option = >> << next();; - : char option = Some 'O' >> << next();; - : char option = Some 'C' >> << next();; - : char option = Some 'a' >> << next();; - : char option = Some 'm' >> << next();; - : char option = Some 'l' >> << next();; - : char option = None >> Implementing control inversion ------------------------------ The implementation of the invert function is given below: << let invert (type a) ~(iter : (a -> unit) -> unit) : a Seq.t = let module M = struct type _ Effect.t += Yield : a -> unit t end in let yield v = perform (M.Yield v) in fun () -> match_with iter yield { retc = (fun _ -> Seq.Nil); exnc = raise; effc = fun (type b) (eff : b Effect.t) -> match eff with | M.Yield v -> Some (fun (k: (b,_) continuation) -> Seq.Cons (v, continue k)) | _ -> None } >> The invert function declares an effect Yield that takes the element to be yielded as a parameter. The yield function performs the Yield effect. The lambda abstraction fun () -> ... delays all action until the first element of the sequence is demanded. Once this happens, the computation iter yield is executed under an effect handler. Every time the iter function pushes an element to the yield function, the computation is interrupted by the Yield effect. The Yield effect is handled by returning the value Seq.Cons(v,continue k) to the consumer. The consumer gets the element v as well as the suspended computation, which in the consumer’s eyes is just the tail of sequence. When the consumer demands the next element from the sequence (by applying it to ()), the continuation k is resumed. This allows the computation iter yield to make progress, until it either yields another element or terminates normally. In the latter case, the value Seq.Nil is returned, indicating to the consumer that the iteration is over. It is important to note that the sequence returned by the invert function is ephemeral (as defined by the Seq module) i.e., the sequence must be used at most once. Additionally, the sequence must be fully consumed (i.e., used at least once) so as to ensure that the captured continuation is used linearly. 12.24.5 Semantics =================== In this section, we shall see the semantics of effect handlers with the help of examples. Nesting handlers ---------------- Like exception handlers, effect handlers can be nested. << type _ Effect.t += E : int t | F : string t let foo () = perform F let bar () = try_with foo () { effc = fun (type a) (eff: a t) -> match eff with | E -> Some (fun (k: (a,_) continuation) -> failwith "impossible") | _ -> None } let baz () = try_with bar () { effc = fun (type a) (eff: a t) -> match eff with | F -> Some (fun (k: (a,_) continuation) -> continue k "Hello, world!") | _ -> None } >> In this example, the computation foo performs F, the inner handler handles only E and the outer handler handles F. The call to baz returns Hello, world!. << baz () - : string = "Hello, world!" >> Fibers ------ It is useful to know a little bit about the implementation of effect handlers to appreciate the design choices and their performance characteristics. Effect handlers are implemented with the help of runtime-managed, dynamically growing segments of stack called fibers. The program stack in OCaml is a linked list of such fibers. A new fiber is allocated for evaluating the computation enclosed by an effect handler. The fiber is freed when the computation returns to the caller either normally by returning a value or by raising an exception. At the point of perform in foo in the previous example, the program stack looks like this: << +-----+ +-----+ +-----+ | | | | | | | baz |<--| bar |<--| foo | | | | | | | | | | | | | +-----+ +-----+ +-----+ <- stack_pointer >> The two links correspond to the two effect handlers in the program. When the effect F is handled in baz, the program state looks as follows: << +-----+ +-----+ +-----+ | | | | | | +-+ | baz | | bar |<--| foo |<--|k| | | | | | | +-+ +-----+ <- stack_pointer +-----+ +-----+ >> The delimited continuation k is an object on the heap that refers to the segment of the stack that corresponds to the suspended computation. Capturing a continuation does not involve copying stack frames. When the continuation is resumed, the stack is restored to the previous state by linking together the segment pointed to by k to the current stack. Since neither continuation capture nor resumption requires copying stack frames, suspending the execution using perform and resuming it using either continue or discontinue are fast. Unhandled effects ----------------- Unlike languages such as Eff and Koka, effect handlers in OCaml do not provide effect safety; the compiler does not statically ensure that all the effects performed by the program are handled. If effects do not have a matching handler, then an Effect.Unhandled exception is raised at the point of the corresponding perform. For example, in the previous example, bar does not handle the effect F. Hence, we will get an Effect.Unhandled F exception when we run bar. << try bar () with Effect.Unhandled F -> "Saw Effect.Unhandled exception" - : string = "Saw Effect.Unhandled exception" >> Linear continuations -------------------- As discussed earlier 12.24.3, the delimited continuations in OCaml must be used linearly – every captured continuation must be resumed either with a continue or discontinue exactly once. Attempting to use a continuation more than once raises a Continuation_already_resumed exception. For example: << try_with perform (Xchg 0) { effc = fun (type a) (eff : a t) -> match eff with | Xchg n -> Some (fun (k: (a, _) continuation) -> continue k 21 + continue k 21) | _ -> None } Exception: Stdlib.Effect.Continuation_already_resumed. >> The primary motivation for adding effect handlers to OCaml is to enable concurrent programming. One-shot continuations are sufficient for almost all concurrent programming needs. They are also much cheaper to implement compared to multi-shot continuations since they do not require stack frames to be copied. Moreover, OCaml programs may also manipulate linear resources such as sockets and file descriptors. The linearity discipline is easily broken if the continuations are allowed to resume more than once. It would be quite hard to debug such linearity violations on resources due to the lack of static checks for linearity and the non-local nature of control flow. Hence, OCaml does not support multi-shot continuations. While the “at most once resumption” property of continuations is ensured with a dynamic check, there is no check to ensure that the continuations are resumed “at least once”. It is left to the user to ensure that the captured continuations are resumed at least once. Not resuming continuations will leak the memory allocated for the fibers as well as any resources that the suspended computation may hold. One may install a finaliser on the captured continuation to ensure that the resources are freed: << exception Unwind Gc.finalise (fun k -> try ignore (discontinue k Unwind) with _ -> ()) k >> In this case, if k becomes unreachable, then the finaliser ensures that the continuation stack is unwound by discontinuing with an Unwind exception, allowing the computation to free up resources. However, the runtime cost of finalisers is much more than the cost of capturing a continuation. Hence, it is recommended that the user take care of resuming the continuation exactly once rather than relying on the finaliser. 12.24.6 Shallow handlers ========================== The examples that we have seen so far have used deep handlers. A deep handler handles all the effects performed (in sequence) by the computation. Whenever a continuation is captured in a deep handler, the captured continuation also includes the handler. This means that, when the continuation is resumed, the effect handler is automatically re-installed, and will handle the effect(s) that the computation may perform in the future. OCaml also provides shallow handlers. Compared to deep handlers, a shallow handler handles only the first effect performed by the computation. The continuation captured in a shallow handler does not include the handler. This means that, when the continuation is resumed, the handler is no longer present. For this reason, when the continuation is resumed, the user is expected to provide a new effect handler (possibly a different one) to handle the next effect that the computation may perform. Shallow handlers make it easier to express certain kinds of programs. Let us implement a shallow handler that enforces a particular sequence of effects (a protocol) on a computation. For this example, let us consider that the computation may perform the following effects: << type _ Effect.t += Send : int -> unit Effect.t | Recv : int Effect.t >> Let us assume that we want to enforce a protocol that only permits an alternating sequence of Send and Recv effects that conform to the regular expression (Send;Recv)*;Send?. Hence, the sequence of effects [] (the empty sequence), [Send], [Send;Recv], [Send;Recv;Send], etc., are allowed, but not [Recv], [Send;Send], [Send;Recv;Recv], etc. The key observation here is that the set of effects handled evolves over time. We can enforce this protocol quite naturally using shallow handlers as shown below: << open Effect.Shallow let run (comp: unit -> unit) : unit = let rec loop_send : type a. (a,unit) continuation -> a -> unit = fun k v -> continue_with k v { retc = Fun.id; exnc = raise; effc = fun (type b) (eff : b Effect.t) -> match eff with | Send n -> Some (fun (k: (b,_) continuation) -> loop_recv n k ()) | Recv -> failwith "protocol violation" | _ -> None } and loop_recv : type a. int -> (a,unit) continuation -> a -> unit = fun n k v -> continue_with k v { retc = Fun.id; exnc = raise; effc = fun (type b) (eff : b Effect.t) -> match eff with | Recv -> Some (fun (k: (b,_) continuation) -> loop_send k n) | Send v -> failwith "protocol violation" | _ -> None } in loop_send (fiber comp) () >> The run function executes the computation comp ensuring that it can only perform an alternating sequence of Send and Recv effects. The shallow handler uses a different set of primitives compared to the deep handler. The primitive fiber (on the last line) takes an 'a -> 'b function and returns a ('a,'b) Effect.Shallow.continuation. The expression continue_with k v h resumes the continuation k with value v under the handler h. The mutually recursive functions loop_send and loop_recv resume the given continuation k with value v under different handlers. The loop_send function handles the Send effect and tail calls the loop_recv function. If the computation performs the Recv effect, then loop_send aborts the computation by raising an exception. Similarly, the loop_recv function handles the Recv effect and tail calls the loop_send function. If the computation performs the Send effect, then loop_recv aborts the computation. Given that the continuation captured in the shallow handler do not include the handler, there is only ever one handler installed in the dynamic scope of the computation comp. The computation is initially executed by the loop_send function (see last line in the code above) which ensures that the first effect that the computation is allowed to perform is the Send effect. Note that the computation is free to perform effects other than Send and Recv, which may be handled by an outer handler. We can see that the run function will permit a computation that follows the protocol: << run (fun () -> printf "Send 42\n"; perform (Send 42); printf "Recv: %d\n" (perform Recv); printf "Send 43\n"; perform (Send 43); printf "Recv: %d\n" (perform Recv)) Send 42 Recv: 42 Send 43 Recv: 43 - : unit = () >> and aborts those that do not: << run (fun () -> Printf.printf "Send 0\n"; perform (Send 0); Printf.printf "Send 1\n"; perform (Send 1) (* protocol violation *)) Send 0 Send 1 Exception: Failure "protocol violation". >> We may implement the same example using deep handlers using reference cells (easy, but unsatisfying) or without them (harder). We leave this as an exercise to the reader. Part: III ********* The OCaml tools *************** Chapter 13  Batch compilation (ocamlc) ****************************************** This chapter describes the OCaml batch compiler ocamlc, which compiles OCaml source files to bytecode object files and links these object files to produce standalone bytecode executable files. These executable files are then run by the bytecode interpreter ocamlrun. 13.1 Overview of the compiler *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The ocamlc command has a command-line interface similar to the one of most C compilers. It accepts several types of arguments and processes them sequentially, after all options have been processed: - Arguments ending in .mli are taken to be source files for compilation unit interfaces. Interfaces specify the names exported by compilation units: they declare value names with their types, define public data types, declare abstract data types, and so on. From the file x.mli, the ocamlc compiler produces a compiled interface in the file x.cmi. - Arguments ending in .ml are taken to be source files for compilation unit implementations. Implementations provide definitions for the names exported by the unit, and also contain expressions to be evaluated for their side-effects. From the file x.ml, the ocamlc compiler produces compiled object bytecode in the file x.cmo. If the interface file x.mli exists, the implementation x.ml is checked against the corresponding compiled interface x.cmi, which is assumed to exist. If no interface x.mli is provided, the compilation of x.ml produces a compiled interface file x.cmi in addition to the compiled object code file x.cmo. The file x.cmi produced corresponds to an interface that exports everything that is defined in the implementation x.ml. - Arguments ending in .cmo are taken to be compiled object bytecode. These files are linked together, along with the object files obtained by compiling .ml arguments (if any), and the OCaml standard library, to produce a standalone executable program. The order in which .cmo and .ml arguments are presented on the command line is relevant: compilation units are initialized in that order at run-time, and it is a link-time error to use a component of a unit before having initialized it. Hence, a given x.cmo file must come before all .cmo files that refer to the unit x. - Arguments ending in .cma are taken to be libraries of object bytecode. A library of object bytecode packs in a single file a set of object bytecode files (.cmo files). Libraries are built with ocamlc -a (see the description of the -a option below). The object files contained in the library are linked as regular .cmo files (see above), in the order specified when the .cma file was built. The only difference is that if an object file contained in a library is not referenced anywhere in the program, then it is not linked in. - Arguments ending in .c are passed to the C compiler, which generates a .o object file (.obj under Windows). This object file is linked with the program if the -custom flag is set (see the description of -custom below). - Arguments ending in .o or .a (.obj or .lib under Windows) are assumed to be C object files and libraries. They are passed to the C linker when linking in -custom mode (see the description of -custom below). - Arguments ending in .so (.dll under Windows) are assumed to be C shared libraries (DLLs). During linking, they are searched for external C functions referenced from the OCaml code, and their names are written in the generated bytecode executable. The run-time system ocamlrun then loads them dynamically at program start-up time. The output of the linking phase is a file containing compiled bytecode that can be executed by the OCaml bytecode interpreter: the command named ocamlrun. If a.out is the name of the file produced by the linking phase, the command << ocamlrun a.out arg_1 arg_2 ... arg_n >> executes the compiled code contained in a.out, passing it as arguments the character strings arg_1 to arg_n. (See chapter 15 for more details.) On most systems, the file produced by the linking phase can be run directly, as in: << ./a.out arg_1 arg_2 ... arg_n >> The produced file has the executable bit set, and it manages to launch the bytecode interpreter by itself. The compiler is able to emit some information on its internal stages. It can output .cmt files for the implementation of the compilation unit and .cmti for signatures if the option -bin-annot is passed to it (see the description of -bin-annot below). Each such file contains a typed abstract syntax tree (AST), that is produced during the type checking procedure. This tree contains all available information about the location and the specific type of each term in the source file. The AST is partial if type checking was unsuccessful. These .cmt and .cmti files are typically useful for code inspection tools. 13.2 Options *=*=*=*=*=*=*= The following command-line options are recognized by ocamlc. The options -pack, -a, -c, -output-obj and -output-complete-obj are mutually exclusive. -a Build a library(.cma file) with the object files ( .cmo files) given on the command line, instead of linking them into an executable file. The name of the library must be set with the -o option. If -custom, -cclib or -ccopt options are passed on the command line, these options are stored in the resulting .cmalibrary. Then, linking with this library automatically adds back the -custom, -cclib and -ccopt options as if they had been provided on the command line, unless the -noautolink option is given. -absname Force error messages to show absolute paths for file names. -no-absname Do not try to show absolute filenames in error messages. -annot Deprecated since OCaml 4.11. Please use -bin-annot instead. -args filename Read additional newline-terminated command line arguments from filename. -args0 filename Read additional null character terminated command line arguments from filename. -bin-annot Dump detailed information about the compilation (types, bindings, tail-calls, etc) in binary format. The information for file src.ml (resp. src.mli) is put into file src.cmt (resp. src.cmti). In case of a type error, dump all the information inferred by the type-checker before the error. The *.cmt and *.cmti files produced by -bin-annot contain more information and are much more compact than the files produced by -annot. -c Compile only. Suppress the linking phase of the compilation. Source code files are turned into compiled files, but no executable file is produced. This option is useful to compile modules separately. -cc ccomp Use ccomp as the C linker when linking in “custom runtime” mode (see the -custom option) and as the C compiler for compiling .c source files. When linking object files produced by a C++ compiler (such as g++ or clang++), it is recommended to use -cc c++. -cclib -llibname Pass the -llibname option to the C linker when linking in “custom runtime” mode (see the -custom option). This causes the given C library to be linked with the program. -ccopt option Pass the given option to the C compiler and linker. When linking in “custom runtime” mode, for instance -ccopt -Ldir causes the C linker to search for C libraries in directory dir. (See the -custom option.) -cmi-file filename Use the given interface file to type-check the ML source file to compile. When this option is not specified, the compiler looks for a .mli file with the same base name than the implementation it is compiling and in the same directory. If such a file is found, the compiler looks for a corresponding .cmi file in the included directories and reports an error if it fails to find one. -color mode Enable or disable colors in compiler messages (especially warnings and errors). The following modes are supported: auto use heuristics to enable colors only if the output supports them (an ANSI-compatible tty terminal); always enable colors unconditionally; never disable color output. The environment variable OCAML_COLOR is considered if -color is not provided. Its values are auto/always/never as above. If -color is not provided, OCAML_COLOR is not set and the environment variable NO_COLOR is set, then color output is disabled. Otherwise, the default setting is ’auto’, and the current heuristic checks that the TERM environment variable exists and is not empty or dumb, and that ’isatty(stderr)’ holds. -error-style mode Control the way error messages and warnings are printed. The following modes are supported: short only print the error and its location; contextual like short, but also display the source code snippet corresponding to the location of the error. The default setting is contextual. The environment variable OCAML_ERROR_STYLE is considered if -error-style is not provided. Its values are short/contextual as above. -compat-32 Check that the generated bytecode executable can run on 32-bit platforms and signal an error if it cannot. This is useful when compiling bytecode on a 64-bit machine. -config Print the version number of ocamlc and a detailed summary of its configuration, then exit. -config-var var Print the value of a specific configuration variable from the -config output, then exit. If the variable does not exist, the exit code is non-zero. This option is only available since OCaml 4.08, so script authors should have a fallback for older versions. -custom Link in “custom runtime” mode. In the default linking mode, the linker produces bytecode that is intended to be executed with the shared runtime system, ocamlrun. In the custom runtime mode, the linker produces an output file that contains both the runtime system and the bytecode for the program. The resulting file is larger, but it can be executed directly, even if the ocamlrun command is not installed. Moreover, the “custom runtime” mode enables static linking of OCaml code with user-defined C functions, as described in chapter 22.  Unix: Never use the strip command on executables produced by ocamlc -custom, this would remove the bytecode part of the executable.  Unix: Security warning: never set the “setuid” or “setgid” bits on executables produced by ocamlc -custom, this would make them vulnerable to attacks. -depend ocamldep-args Compute dependencies, as the ocamldep command would do. The remaining arguments are interpreted as if they were given to the ocamldep command. -dllib -llibname Arrange for the C shared library dlllibname.so (dlllibname.dll under Windows) to be loaded dynamically by the run-time system ocamlrun at program start-up time. -dllpath dir Adds the directory dir to the run-time search path for shared C libraries. At link-time, shared libraries are searched in the standard search path (the one corresponding to the -I option). The -dllpath option simply stores dir in the produced executable file, where ocamlrun can find it and use it as described in section 15.3. -for-pack module-path Generate an object file (.cmo) that can later be included as a sub-module (with the given access path) of a compilation unit constructed with -pack. For instance, ocamlc -for-pack P -c A.ml will generate a..cmo that can later be used with ocamlc -pack -o P.cmo a.cmo. Note: you can still pack a module that was compiled without -for-pack but in this case exceptions will be printed with the wrong names. -g Add debugging information while compiling and linking. This option is required in order to be able to debug the program with ocamldebug (see chapter 20), and to produce stack backtraces when the program terminates on an uncaught exception (see section 15.2). -no-g Do not record debugging information (default). -i Cause the compiler to print all defined names (with their inferred types or their definitions) when compiling an implementation (.ml file). No compiled files (.cmo and .cmi files) are produced. This can be useful to check the types inferred by the compiler. Also, since the output follows the syntax of interfaces, it can help in writing an explicit interface (.mli file) for a file: just redirect the standard output of the compiler to a .mli file, and edit that file to remove all declarations of unexported names. -I directory Add the given directory to the list of directories searched for compiled interface files (.cmi), compiled object code files .cmo, libraries (.cma) and C libraries specified with -cclib -lxxx. By default, the current directory is searched first, then the standard library directory. Directories added with -I are searched after the current directory, in the order in which they were given on the command line, but before the standard library directory. See also option -nostdlib. If the given directory starts with +, it is taken relative to the standard library directory. For instance, -I +unix adds the subdirectory unix of the standard library to the search path. -H directory Behaves identically to -I, except that (a) programs may not directly refer to modules added to the search path this way, and (b) these directories are searched after any -I directories. This makes it possible to provide the compiler with compiled interface and object code files for the current program’s transitive dependencies (the dependencies of its dependencies) without allowing them to silently become direct dependencies. -impl filename Compile the file filename as an implementation file, even if its extension is not .ml. -intf filename Compile the file filename as an interface file, even if its extension is not .mli. -intf-suffix string Recognize file names ending with string as interface files (instead of the default .mli). -labels Labels are not ignored in types, labels may be used in applications, and labelled parameters can be given in any order. This is the default. -linkall Force all modules contained in libraries to be linked in. If this flag is not given, unreferenced modules are not linked in. When building a library (option -a), setting the -linkall option forces all subsequent links of programs involving that library to link all the modules contained in the library. When compiling a module (option -c), setting the -linkall option ensures that this module will always be linked if it is put in a library and this library is linked. -make-runtime Build a custom runtime system (in the file specified by option -o) incorporating the C object files and libraries given on the command line. This custom runtime system can be used later to execute bytecode executables produced with the ocamlc -use-runtime runtime-name option. See section 22.1.6 for more information. -match-context-rows Set the number of rows of context used for optimization during pattern matching compilation. The default value is 32. Lower values cause faster compilation, but less optimized code. This advanced option is meant for use in the event that a pattern-match-heavy program leads to significant increases in compilation time. -no-alias-deps Do not record dependencies for module aliases. See section 12.8 for more information. -no-app-funct Deactivates the applicative behaviour of functors. With this option, each functor application generates new types in its result and applying the same functor twice to the same argument yields two incompatible structures. -noassert Do not compile assertion checks. Note that the special form assert false is always compiled because it is typed specially. This flag has no effect when linking already-compiled files. -noautolink When linking .cmalibraries, ignore -custom, -cclib and -ccopt options potentially contained in the libraries (if these options were given when building the libraries). This can be useful if a library contains incorrect specifications of C libraries or C options; in this case, during linking, set -noautolink and pass the correct C libraries and options on the command line. -nolabels Ignore non-optional labels in types. Labels cannot be used in applications, and parameter order becomes strict. -nostdlib Do not include the standard library directory in the list of directories searched for compiled interface files (.cmi), compiled object code files (.cmo), libraries (.cma), and C libraries specified with -cclib -lxxx. See also option -I. -o output-file Specify the name of the output file to produce. For executable files, the default output name is a.out under Unix and camlprog.exe under Windows. If the -a option is given, specify the name of the library produced. If the -pack option is given, specify the name of the packed object file produced. If the -output-obj or -output-complete-obj options are given, specify the name of the produced object file. If the -c option is given, specify the name of the object file produced for the next source file that appears on the command line. -opaque When the native compiler compiles an implementation, by default it produces a .cmx file containing information for cross-module optimization. It also expects .cmx files to be present for the dependencies of the currently compiled source, and uses them for optimization. Since OCaml 4.03, the compiler will emit a warning if it is unable to locate the .cmx file of one of those dependencies. The -opaque option, available since 4.04, disables cross-module optimization information for the currently compiled unit. When compiling .mli interface, using -opaque marks the compiled .cmi interface so that subsequent compilations of modules that depend on it will not rely on the corresponding .cmx file, nor warn if it is absent. When the native compiler compiles a .ml implementation, using -opaque generates a .cmx that does not contain any cross-module optimization information. Using this option may degrade the quality of generated code, but it reduces compilation time, both on clean and incremental builds. Indeed, with the native compiler, when the implementation of a compilation unit changes, all the units that depend on it may need to be recompiled – because the cross-module information may have changed. If the compilation unit whose implementation changed was compiled with -opaque, no such recompilation needs to occur. This option can thus be used, for example, to get faster edit-compile-test feedback loops. -open Module Opens the given module before processing the interface or implementation files. If several -open options are given, they are processed in order, just as if the statements open! Module1;; ... open! ModuleN;; were added at the top of each file. -output-obj Cause the linker to produce a C object file instead of a bytecode executable file. This is useful to wrap OCaml code as a C library, callable from any C program. See chapter 22, section 22.7.5. The name of the output object file must be set with the -o option. This option can also be used to produce a C source file (.c extension) or a compiled shared/dynamic library (.so extension, .dll under Windows). -output-complete-exe Build a self-contained executable by linking a C object file containing the bytecode program, the OCaml runtime system and any other static C code given to ocamlc. The resulting effect is similar to -custom, except that the bytecode is embedded in the C code so it is no longer accessible to tools such as ocamldebug. On the other hand, the resulting binary is resistant to strip. -output-complete-obj Same as -output-obj options except the object file produced includes the runtime and autolink libraries. -pack Build a bytecode object file (.cmo file) and its associated compiled interface (.cmi) that combines the object files given on the command line, making them appear as sub-modules of the output .cmo file. The name of the output .cmo file must be given with the -o option. For instance, << ocamlc -pack -o p.cmo a.cmo b.cmo c.cmo >> generates compiled files p.cmo and p.cmi describing a compilation unit having three sub-modules A, B and C, corresponding to the contents of the object files a.cmo, b.cmo and c.cmo. These contents can be referenced as P.A, P.B and P.C in the remainder of the program. -pp command Cause the compiler to call the given command as a preprocessor for each source file. The output of command is redirected to an intermediate file, which is compiled. If there are no compilation errors, the intermediate file is deleted afterwards. -ppx command After parsing, pipe the abstract syntax tree through the preprocessor command. The module Ast_mapper, described in section 30.1, implements the external interface of a preprocessor. -principal Check information path during type-checking, to make sure that all types are derived in a principal way. When using labelled arguments and/or polymorphic methods, this flag is required to ensure future versions of the compiler will be able to infer types correctly, even if internal algorithms change. All programs accepted in -principal mode are also accepted in the default mode with equivalent types, but different binary signatures, and this may slow down type checking; yet it is a good idea to use it once before publishing source code. -rectypes Allow arbitrary recursive types during type-checking. By default, only recursive types where the recursion goes through an object type are supported. Note that once you have created an interface using this flag, you must use it again for all dependencies. -runtime-variant suffix Add the suffix string to the name of the runtime library used by the program. Currently, only one such suffix is supported: d, and only if the OCaml compiler was configured with option -with-debug-runtime. This suffix gives the debug version of the runtime, which is useful for debugging pointer problems in low-level code such as C stubs. -safe-string Enforce the separation between types string and bytes, thereby making strings read-only. This is the default, and enforced since OCaml 5.0. -safer-matching Do not use type information to optimize pattern-matching. This allows to detect match failures even if a pattern-matching was wrongly assumed to be exhaustive. This only impacts GADT and polymorphic variant compilation. -short-paths When a type is visible under several module-paths, use the shortest one when printing the type’s name in inferred interfaces and error and warning messages. Identifier names starting with an underscore _ or containing double underscores __ incur a penalty of +10 when computing their length. -stop-after pass Stop compilation after the given compilation pass. The currently supported passes are: parsing, typing. -strict-sequence Force the left-hand part of each sequence to have type unit. -strict-formats Reject invalid formats that were accepted in legacy format implementations. You should use this flag to detect and fix such invalid formats, as they will be rejected by future OCaml versions. -unboxed-types When a type is unboxable (i.e. a record with a single argument or a concrete datatype with a single constructor of one argument) it will be unboxed unless annotated with [@@ocaml.boxed]. -no-unboxed-types When a type is unboxable it will be boxed unless annotated with [@@ocaml.unboxed]. This is the default. -unsafe Turn bound checking off for array and string accesses (the v.(i) and s.[i] constructs). Programs compiled with -unsafe are therefore slightly faster, but unsafe: anything can happen if the program accesses an array or string outside of its bounds. Additionally, turn off the check for zero divisor in integer division and modulus operations. With -unsafe, an integer division (or modulus) by zero can halt the program or continue with an unspecified result instead of raising a Division_by_zero exception. -unsafe-string Identify the types string and bytes, thereby making strings writable. This is intended for compatibility with old source code and should not be used with new software. This option raises an error unconditionally since OCaml 5.0. -use-runtime runtime-name Generate a bytecode executable file that can be executed on the custom runtime system runtime-name, built earlier with ocamlc -make-runtime runtime-name. See section 22.1.6 for more information. -v Print the version number of the compiler and the location of the standard library directory, then exit. -verbose Print all external commands before they are executed, in particular invocations of the C compiler and linker in -custom mode. Useful to debug C library problems. -version or -vnum Print the version number of the compiler in short form (e.g. 3.11.0), then exit. -w warning-list Enable, disable, or mark as fatal the warnings specified by the argument warning-list. Each warning can be enabled or disabled, and each warning can be fatal or non-fatal. If a warning is disabled, it isn’t displayed and doesn’t affect compilation in any way (even if it is fatal). If a warning is enabled, it is displayed normally by the compiler whenever the source code triggers it. If it is enabled and fatal, the compiler will also stop with an error after displaying it. The warning-list argument is a sequence of warning specifiers, with no separators between them. A warning specifier is one of the following: +num Enable warning number num. -num Disable warning number num. @num Enable and mark as fatal warning number num. +num1..num2 Enable warnings in the given range. -num1..num2 Disable warnings in the given range. @num1..num2 Enable and mark as fatal warnings in the given range. +letter Enable the set of warnings corresponding to letter. The letter may be uppercase or lowercase. -letter Disable the set of warnings corresponding to letter. The letter may be uppercase or lowercase. @letter Enable and mark as fatal the set of warnings corresponding to letter. The letter may be uppercase or lowercase. uppercase-letter Enable the set of warnings corresponding to uppercase-letter. lowercase-letter Disable the set of warnings corresponding to lowercase-letter. Alternatively, warning-list can specify a single warning using its mnemonic name (see below), as follows: +name Enable warning name. -name Disable warning name. @name Enable and mark as fatal warning name. Warning numbers, letters and names which are not currently defined are ignored. The warnings are as follows (the name following each number specifies the mnemonic for that warning). 1 comment-start Suspicious-looking start-of-comment mark. 2 comment-not-end Suspicious-looking end-of-comment mark. 3 Deprecated synonym for the ’deprecated’ alert. 4 fragile-match Fragile pattern matching: matching that will remain complete even if additional constructors are added to one of the variant types matched. 5 ignored-partial-application Partially applied function: expression whose result has function type and is ignored. 6 labels-omitted Label omitted in function application. 7 method-override Method overridden. 8 partial-match Partial match: missing cases in pattern-matching. 9 missing-record-field-pattern Missing fields in a record pattern. 10 non-unit-statement Expression on the left-hand side of a sequence that doesn’t have type unit (and that is not a function, see warning number 5). 11 redundant-case Redundant case in a pattern matching (unused match case). 12 redundant-subpat Redundant sub-pattern in a pattern-matching. 13 instance-variable-override Instance variable overridden. 14 illegal-backslash Illegal backslash escape in a string constant. 15 implicit-public-methods Private method made public implicitly. 16 unerasable-optional-argument Unerasable optional argument. 17 undeclared-virtual-method Undeclared virtual method. 18 not-principal Non-principal type. 19 non-principal-labels Type without principality. 20 ignored-extra-argument Unused function argument. 21 nonreturning-statement Non-returning statement. 22 preprocessor Preprocessor warning. 23 useless-record-with Useless record with clause. 24 bad-module-name Bad module name: the source file name is not a valid OCaml module name. 25 Ignored: now part of warning 8. 26 unused-var Suspicious unused variable: unused variable that is bound with let or as, and doesn’t start with an underscore (_) character. 27 unused-var-strict Innocuous unused variable: unused variable that is not bound with let nor as, and doesn’t start with an underscore (_) character. 28 wildcard-arg-to-constant-constr Wildcard pattern given as argument to a constant constructor. 29 eol-in-string Unescaped end-of-line in a string constant (non-portable code). 30 duplicate-definitions Two labels or constructors of the same name are defined in two mutually recursive types. 31 module-linked-twice A module is linked twice in the same executable. I gnored: now a hard error (since 5.1). 32 unused-value-declaration Unused value declaration. (since 4.00) 33 unused-open Unused open statement. (since 4.00) 34 unused-type-declaration Unused type declaration. (since 4.00) 35 unused-for-index Unused for-loop index. (since 4.00) 36 unused-ancestor Unused ancestor variable. (since 4.00) 37 unused-constructor Unused constructor. (since 4.00) 38 unused-extension Unused extension constructor. (since 4.00) 39 unused-rec-flag Unused rec flag. (since 4.00) 40 name-out-of-scope Constructor or label name used out of scope. (since 4.01) 41 ambiguous-name Ambiguous constructor or label name. (since 4.01) 42 disambiguated-name Disambiguated constructor or label name (compatibility warning). (since 4.01) 43 nonoptional-label Nonoptional label applied as optional. (since 4.01) 44 open-shadow-identifier Open statement shadows an already defined identifier. (since 4.01) 45 open-shadow-label-constructor Open statement shadows an already defined label or constructor. (since 4.01) 46 bad-env-variable Error in environment variable. (since 4.01) 47 attribute-payload Illegal attribute payload. (since 4.02) 48 eliminated-optional-arguments Implicit elimination of optional arguments. (since 4.02) 49 no-cmi-file Absent cmi file when looking up module alias. (since 4.02) 50 unexpected-docstring Unexpected documentation comment. (since 4.03) 51 wrong-tailcall-expectation Function call annotated with an incorrect @tailcall attribute. (since 4.03) 52 fragile-literal-pattern (see 13.5.3) Fragile constant pattern. (since 4.03) 53 misplaced-attribute Attribute cannot appear in this context. (since 4.03) 54 duplicated-attribute Attribute used more than once on an expression. (since 4.03) 55 inlining-impossible Inlining impossible. (since 4.03) 56 unreachable-case Unreachable case in a pattern-matching (based on type information). (since 4.03) 57 ambiguous-var-in-pattern-guard (see 13.5.4) Ambiguous or-pattern variables under guard. (since 4.03) 58 no-cmx-file Missing cmx file. (since 4.03) 59 flambda-assignment-to-non-mutable-value Assignment to non-mutable value. (since 4.03) 60 unused-module Unused module declaration. (since 4.04) 61 unboxable-type-in-prim-decl Unboxable type in primitive declaration. (since 4.04) 62 constraint-on-gadt Type constraint on GADT type declaration. (since 4.06) 63 erroneous-printed-signature Erroneous printed signature. (since 4.08) 64 unsafe-array-syntax-without-parsing -unsafe used with a preprocessor returning a syntax tree. (since 4.08) 65 redefining-unit Type declaration defining a new ’()’ constructor. (since 4.08) 66 unused-open-bang Unused open! statement. (since 4.08) 67 unused-functor-parameter Unused functor parameter. (since 4.10) 68 match-on-mutable-state-prevent-uncurry Pattern-matching depending on mutable state prevents the remaining arguments from being uncurried. (since 4.12) 69 unused-field Unused record field. (since 4.13) 70 missing-mli Missing interface file. (since 4.13) 71 unused-tmc-attribute Unused @tail_mod_cons attribute. (since 4.14) 72 tmc-breaks-tailcall A tail call is turned into a non-tail call by the @tail_mod_cons transformation. (since 4.14) 73 generative-application-expects-unit A generative functor is applied to an empty structure (struct end) rather than to (). (since 5.1) A all warnings C warnings 1, 2. D Alias for warning 3. E Alias for warning 4. F Alias for warning 5. K warnings 32, 33, 34, 35, 36, 37, 38, 39. L Alias for warning 6. M Alias for warning 7. P Alias for warning 8. R Alias for warning 9. S Alias for warning 10. U warnings 11, 12. V Alias for warning 13. X warnings 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30. Y Alias for warning 26. Z Alias for warning 27. The default setting is -w +a-4-6-7-9-27-29-32..42-44-45-48-50-60. It is displayed by ocamlc -help. Note that warnings 5 and 10 are not always triggered, depending on the internals of the type checker. -warn-error warning-list Mark as fatal the warnings specified in the argument warning-list. The compiler will stop with an error when one of these warnings is emitted. The warning-list has the same meaning as for the -w option: a + sign (or an uppercase letter) marks the corresponding warnings as fatal, a - sign (or a lowercase letter) turns them back into non-fatal warnings, and a @ sign both enables and marks as fatal the corresponding warnings. Note: it is not recommended to use warning sets (i.e. letters) as arguments to -warn-error in production code, because this can break your build when future versions of OCaml add some new warnings. The default setting is -warn-error -a (no warning is fatal). -warn-help Show the description of all available warning numbers. -where Print the location of the standard library, then exit. -with-runtime Include the runtime system in the generated program. This is the default. -without-runtime The compiler does not include the runtime system (nor a reference to it) in the generated program; it must be supplied separately. - file Process file as a file name, even if it starts with a dash (-) character. -help or –help Display a short usage summary and exit. contextual-cli-control Contextual control of command-line options The compiler command line can be modified “from the outside” with the following mechanisms. These are experimental and subject to change. They should be used only for experimental and development work, not in released packages. OCAMLPARAM (environment variable) A set of arguments that will be inserted before or after the arguments from the command line. Arguments are specified in a comma-separated list of name=value pairs. A _ is used to specify the position of the command line arguments, i.e. a=x,_,b=y means that a=x should be executed before parsing the arguments, and b=y after. Finally, an alternative separator can be specified as the first character of the string, within the set :|; ,. ocaml_compiler_internal_params (file in the stdlib directory) A mapping of file names to lists of arguments that will be added to the command line (and OCAMLPARAM) arguments. 13.3 Modules and the file system *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This short section is intended to clarify the relationship between the names of the modules corresponding to compilation units and the names of the files that contain their compiled interface and compiled implementation. The compiler always derives the module name by taking the capitalized base name of the source file (.ml or .mli file). That is, it strips the leading directory name, if any, as well as the .ml or .mli suffix; then, it set the first letter to uppercase, in order to comply with the requirement that module names must be capitalized. For instance, compiling the file mylib/misc.ml provides an implementation for the module named Misc. Other compilation units may refer to components defined in mylib/misc.ml under the names Misc.name; they can also do open Misc, then use unqualified names name. The .cmi and .cmo files produced by the compiler have the same base name as the source file. Hence, the compiled files always have their base name equal (modulo capitalization of the first letter) to the name of the module they describe (for .cmi files) or implement (for .cmo files). When the compiler encounters a reference to a free module identifier Mod, it looks in the search path for a file named Mod.cmi or mod.cmi and loads the compiled interface contained in that file. As a consequence, renaming .cmi files is not advised: the name of a .cmi file must always correspond to the name of the compilation unit it implements. It is admissible to move them to another directory, if their base name is preserved, and the correct -I options are given to the compiler. The compiler will flag an error if it loads a .cmi file that has been renamed. Compiled bytecode files (.cmo files), on the other hand, can be freely renamed once created. That’s because the linker never attempts to find by itself the .cmo file that implements a module with a given name: it relies instead on the user providing the list of .cmo files by hand. 13.4 Common errors *=*=*=*=*=*=*=*=*=*= This section describes and explains the most frequently encountered error messages. Cannot find file filename The named file could not be found in the current directory, nor in the directories of the search path. The filename is either a compiled interface file (.cmi file), or a compiled bytecode file (.cmo file). If filename has the format mod.cmi, this means you are trying to compile a file that references identifiers from module mod, but you have not yet compiled an interface for module mod. Fix: compile mod.mli or mod.ml first, to create the compiled interface mod.cmi. If filename has the format mod.cmo, this means you are trying to link a bytecode object file that does not exist yet. Fix: compile mod.ml first. If your program spans several directories, this error can also appear because you haven’t specified the directories to look into. Fix: add the correct -I options to the command line. Corrupted compiled interface filename The compiler produces this error when it tries to read a compiled interface file (.cmi file) that has the wrong structure. This means something went wrong when this .cmi file was written: the disk was full, the compiler was interrupted in the middle of the file creation, and so on. This error can also appear if a .cmi file is modified after its creation by the compiler. Fix: remove the corrupted .cmi file, and rebuild it. This expression has type t_1, but is used with type t_2 This is by far the most common type error in programs. Type t_1 is the type inferred for the expression (the part of the program that is displayed in the error message), by looking at the expression itself. Type t_2 is the type expected by the context of the expression; it is deduced by looking at how the value of this expression is used in the rest of the program. If the two types t_1 and t_2 are not compatible, then the error above is produced. In some cases, it is hard to understand why the two types t_1 and t_2 are incompatible. For instance, the compiler can report that “expression of type foo cannot be used with type foo”, and it really seems that the two types foo are compatible. This is not always true. Two type constructors can have the same name, but actually represent different types. This can happen if a type constructor is redefined. Example: << type foo = A | B let f = function A -> 0 | B -> 1 type foo = C | D f C >> This result in the error message “expression C of type foo cannot be used with type foo”. The type of this expression, t, contains type variables that cannot be generalized Type variables ('a, 'b, ...) in a type t can be in either of two states: generalized (which means that the type t is valid for all possible instantiations of the variables) and not generalized (which means that the type t is valid only for one instantiation of the variables). In a let binding let name = expr, the type-checker normally generalizes as many type variables as possible in the type of expr. However, this leads to unsoundness (a well-typed program can crash) in conjunction with polymorphic mutable data structures. To avoid this, generalization is performed at let bindings only if the bound expression expr belongs to the class of “syntactic values”, which includes constants, identifiers, functions, tuples of syntactic values, etc. In all other cases (for instance, expr is a function application), a polymorphic mutable could have been created and generalization is therefore turned off for all variables occurring in contravariant or non-variant branches of the type. For instance, if the type of a non-value is 'a list the variable is generalizable (list is a covariant type constructor), but not in 'a list -> 'a list (the left branch of -> is contravariant) or 'a ref (ref is non-variant). Non-generalized type variables in a type cause no difficulties inside a given structure or compilation unit (the contents of a .ml file, or an interactive session), but they cannot be allowed inside signatures nor in compiled interfaces (.cmi file), because they could be used inconsistently later. Therefore, the compiler flags an error when a structure or compilation unit defines a value name whose type contains non-generalized type variables. There are two ways to fix this error: - Add a type constraint or a .mli file to give a monomorphic type (without type variables) to name. For instance, instead of writing << let sort_int_list = List.sort Stdlib.compare (* inferred type 'a list -> 'a list, with 'a not generalized *) >> write << let sort_int_list = (List.sort Stdlib.compare : int list -> int list);; >> - If you really need name to have a polymorphic type, turn its defining expression into a function by adding an extra parameter. For instance, instead of writing << let map_length = List.map Array.length (* inferred type 'a array list -> int list, with 'a not generalized *) >> write << let map_length lv = List.map Array.length lv >> Reference to undefined global mod This error appears when trying to link an incomplete or incorrectly ordered set of files. Either you have forgotten to provide an implementation for the compilation unit named mod on the command line (typically, the file named mod.cmo, or a library containing that file). Fix: add the missing .ml or .cmo file to the command line. Or, you have provided an implementation for the module named mod, but it comes too late on the command line: the implementation of mod must come before all bytecode object files that reference mod. Fix: change the order of .ml and .cmo files on the command line. Of course, you will always encounter this error if you have mutually recursive functions across modules. That is, function Mod1.f calls function Mod2.g, and function Mod2.g calls function Mod1.f. In this case, no matter what permutations you perform on the command line, the program will be rejected at link-time. Fixes: - Put f and g in the same module. - Parameterize one function by the other. That is, instead of having <> define <> and link mod1.cmo before mod2.cmo. - Use a reference to hold one of the two functions, as in : < failwith "forward_g") : ) let f x = ... !forward_g ... mod2.ml: let g y = ... Mod1.f ... let _ = Mod1.forward_g := g >> The external function f is not available This error appears when trying to link code that calls external functions written in C. As explained in chapter 22, such code must be linked with C libraries that implement the required f C function. If the C libraries in question are not shared libraries (DLLs), the code must be linked in “custom runtime” mode. Fix: add the required C libraries to the command line, and possibly the -custom option. 13.5 Warning reference *=*=*=*=*=*=*=*=*=*=*=*= This section describes and explains in detail some warnings: 13.5.1 Warning 6: Label omitted in function application ========================================================= OCaml supports labels-omitted full applications: if the function has a known arity, all the arguments are unlabeled, and their number matches the number of non-optional parameters, then labels are ignored and non-optional parameters are matched in their definition order. Optional arguments are defaulted. < let test = f 2 3 > ^ > Warning 6 [labels-omitted]: labels x, y were omitted in the application of this function. >> This support for labels-omitted application was introduced when labels were added to OCaml, to ease the progressive introduction of labels in a codebase. However, it has the downside of weakening the labeling discipline: if you use labels to prevent callers from mistakenly reordering two parameters of the same type, labels-omitted make this mistake possible again. Warning 6 warns when labels-omitted applications are used, to discourage their use. When labels were introduced, this warning was not enabled by default, so users would use labels-omitted applications, often without noticing. Over time, it has become idiomatic to enable this warning to avoid argument-order mistakes. The warning is now on by default, since OCaml 4.13. Labels-omitted applications are not recommended anymore, but users wishing to preserve this transitory style can disable the warning explicitly. 13.5.2 Warning 9: missing fields in a record pattern ====================================================== When pattern matching on records, it can be useful to match only few fields of a record. Eliding fields can be done either implicitly or explicitly by ending the record pattern with ; _. However, implicit field elision is at odd with pattern matching exhaustiveness checks. Enabling warning 9 prioritizes exhaustiveness checks over the convenience of implicit field elision and will warn on implicit field elision in record patterns. In particular, this warning can help to spot exhaustive record pattern that may need to be updated after the addition of new fields to a record type. <> 13.5.3 Warning 52: fragile constant pattern ============================================= Some constructors, such as the exception constructors Failure and Invalid_argument, take as parameter a string value holding a text message intended for the user. These text messages are usually not stable over time: call sites building these constructors may refine the message in a future version to make it more explicit, etc. Therefore, it is dangerous to match over the precise value of the message. For example, until OCaml 4.02, Array.iter2 would raise the exception << Invalid_argument "arrays must have the same length" >> Since 4.03 it raises the more helpful message << Invalid_argument "Array.iter2: arrays must have the same length" >> but this means that any code of the form << try ... with Invalid_argument "arrays must have the same length" -> ... >> is now broken and may suffer from uncaught exceptions. Warning 52 is there to prevent users from writing such fragile code in the first place. It does not occur on every matching on a literal string, but only in the case in which library authors expressed their intent to possibly change the constructor parameter value in the future, by using the attribute ocaml.warn_on_literal_pattern (see the manual section on builtin attributes in 12.12.1): << type t = | Foo of string [@ocaml.warn_on_literal_pattern] | Bar of string let no_warning = function | Bar "specific value" -> 0 | _ -> 1 let warning = function | Foo "specific value" -> 0 | _ -> 1 Warning 52 [fragile-literal-pattern]: Code should not depend on the actual va lues of this constructor's arguments. They are only for information and may change in future versions. (see manual section 13.5.3) >> In particular, all built-in exceptions with a string argument have this attribute set: Invalid_argument, Failure, Sys_error will all raise this warning if you match for a specific string argument. Additionally, built-in exceptions with a structured argument that includes a string also have the attribute set: Assert_failure and Match_failure will raise the warning for a pattern that uses a literal string to match the first element of their tuple argument. If your code raises this warning, you should not change the way you test for the specific string to avoid the warning (for example using a string equality inside the right-hand-side instead of a literal pattern), as your code would remain fragile. You should instead enlarge the scope of the pattern by matching on all possible values. << let warning = function | Foo _ -> 0 | _ -> 1 >> This may require some care: if the scrutinee may return several different cases of the same pattern, or raise distinct instances of the same exception, you may need to modify your code to separate those several cases. For example, < (0, true) | Failure "bool_of_string" -> (-1, false) >> should be rewritten into more atomic tests. For example, using the exception patterns documented in Section 11.6, one can write: < (0, true) | count -> begin match bool_of_string choice_str with | exception (Failure _) -> (-1, false) | choice -> (count, choice) end >> The only case where that transformation is not possible is if a given function call may raise distinct exceptions with the same constructor but different string values. In this case, you will have to check for specific string values. This is dangerous API design and it should be discouraged: it’s better to define more precise exception constructors than store useful information in strings. 13.5.4 Warning 57: Ambiguous or-pattern variables under guard =============================================================== The semantics of or-patterns in OCaml is specified with a left-to-right bias: a value v matches the pattern p | q if it matches p or q, but if it matches both, the environment captured by the match is the environment captured by p, never the one captured by q. While this property is generally intuitive, there is at least one specific case where a different semantics might be expected. Consider a pattern followed by a when-guard: | p when g -> e, for example: << | ((Const x, _) | (_, Const x)) when is_neutral x -> branch >> The semantics is clear: match the scrutinee against the pattern, if it matches, test the guard, and if the guard passes, take the branch. In particular, consider the input (Const a, Const b), where a fails the test is_neutral a, while b passes the test is_neutral b. With the left-to-right semantics, the clause above is not taken by its input: matching (Const a, Const b) against the or-pattern succeeds in the left branch, it returns the environment x -> a, and then the guard is_neutral a is tested and fails, the branch is not taken. However, another semantics may be considered more natural here: any pair that has one side passing the test will take the branch. With this semantics the previous code fragment would be equivalent to << | (Const x, _) when is_neutral x -> branch | (_, Const x) when is_neutral x -> branch >> This is not the semantics adopted by OCaml. Warning 57 is dedicated to these confusing cases where the specified left-to-right semantics is not equivalent to a non-deterministic semantics (any branch can be taken) relatively to a specific guard. More precisely, it warns when guard uses “ambiguous” variables, that are bound to different parts of the scrutinees by different sides of a or-pattern. Chapter 14  The toplevel system or REPL (ocaml) *************************************************** This chapter describes ocaml, the toplevel system for OCaml, that permits interactive use of the OCaml system through a read-eval-print loop (REPL). In this mode, the system repeatedly reads OCaml phrases from the input, then typechecks, compile and evaluate them, then prints the inferred type and result value, if any. End-of-file on standard input terminates ocaml. Input to the toplevel can span several lines. It begins after the # (sharp) prompt printed by the system and is terminated by ;; (a double-semicolon) followed by optional white space and comments and an end of line. The toplevel input consists in one or several toplevel phrases, with the following syntax: toplevel-input ::= { definition } ;; | expr ;; | # ident [ directive-argument ] ;; directive-argument ::= string-literal | integer-literal | value-path | true | false A phrase can consist of a sequence of definitions, like those found in implementations of compilation units or in struct ... end module expressions. The definitions can bind value names, type names, exceptions, module names, or module type names. The toplevel system performs the bindings, then prints the types and values (if any) for the names thus defined. A phrase may also consist in a value expression (section 11.7). It is simply evaluated without performing any bindings, and its value is printed. Finally, a phrase can also consist in a toplevel directive, starting with # (the sharp sign). These directives control the behavior of the toplevel; they are listed below in section 14.2.  Unix: The toplevel system is started by the command ocaml, as follows: << ocaml options objects # interactive mode ocaml options objects scriptfile # script mode >> options are described below. objects are filenames ending in .cmo or .cma; they are loaded into the interpreter immediately after options are set. scriptfile is any file name not ending in .cmo or .cma. If no scriptfile is given on the command line, the toplevel system enters interactive mode: phrases are read on standard input, results are printed on standard output, errors on standard error. End-of-file on standard input terminates ocaml (see also the #quit directive in section 14.2). On start-up (before the first phrase is read), the contents of initialization file are read as a sequence of OCaml phrases and executed as per the #use directive described in section 14.2. The evaluation outcode for each phrase are not displayed. The initialization file is the first found of: 1. .ocamlinit in the current directory; 2. XDG_CONFIG_HOME/ocaml/init.ml, if XDG_CONFIG_HOME is an absolute path; 3. otherwise, on Unix, HOME/ocaml/init.ml or, on Windows, ocaml\init.ml under LocalAppData (e.g. C:\Users\Bactrian\AppData\Local\ocaml\init.ml); 4. ocaml/init.ml under any of the absolute paths in XDG_CONFIG_DIRS. Paths in XDG_CONFIG_DIRS are colon-delimited on Unix, and semicolon-delimited on Windows; 5. if XDG_CONFIG_DIRS contained no absolute paths, /usr/xdg/ocaml/init.ml on Unix or, ocaml\init.ml under any of LocalAppData (e.g. C:\Users\Bactrian\AppData\Local), RoamingAppData (e.g. C:\Users\Bactrian\AppData\Roaming), or ProgramData (e.g. C:\ProgramData) on Windows; 6. HOME/.ocamlinit, if HOME is non-empty; The toplevel system does not perform line editing, but it can easily be used in conjunction with an external line editor such as ledit, or rlwrap. An improved toplevel, utop, is also available. Another option is to use ocaml under Gnu Emacs, which gives the full editing power of Emacs (command run-caml from library inf-caml). At any point, the parsing, compilation or evaluation of the current phrase can be interrupted by pressing ctrl-C (or, more precisely, by sending the INTR signal to the ocaml process). The toplevel then immediately returns to the # prompt. If scriptfile is given on the command-line to ocaml, the toplevel system enters script mode: the contents of the file are read as a sequence of OCaml phrases and executed, as per the #use directive (section 14.2). The outcome of the evaluation is not printed. On reaching the end of file, the ocaml command exits immediately. No commands are read from standard input. Sys.argv is transformed, ignoring all OCaml parameters, and starting with the script file name in Sys.argv.(0). In script mode, the first line of the script is ignored if it starts with #!. Thus, it should be possible to make the script itself executable and put as first line #!/usr/local/bin/ocaml, thus calling the toplevel system automatically when the script is run. However, ocaml itself is a #! script on most installations of OCaml, and Unix kernels usually do not handle nested #! scripts. A better solution is to put the following as the first line of the script: << #!/usr/local/bin/ocamlrun /usr/local/bin/ocaml >> 14.1 Options *=*=*=*=*=*=*= The following command-line options are recognized by the ocaml command. -absname Force error messages to show absolute paths for file names. -no-absname Do not try to show absolute filenames in error messages. -args filename Read additional newline-terminated command line arguments from filename. It is not possible to pass a scriptfile via file to the toplevel. -args0 filename Read additional null character terminated command line arguments from filename. It is not possible to pass a scriptfile via file to the toplevel. -I directory Add the given directory to the list of directories searched for source and compiled files. By default, the current directory is searched first, then the standard library directory. Directories added with -I are searched after the current directory, in the order in which they were given on the command line, but before the standard library directory. See also option -nostdlib. If the given directory starts with +, it is taken relative to the standard library directory. For instance, -I +unix adds the subdirectory unix of the standard library to the search path. Directories can also be added to the list once the toplevel is running with the #directory directive (section 14.2). -init file Load the given file instead of the default initialization file. The default initialization file is the first found of: 1. .ocamlinit in the current directory; 2. XDG_CONFIG_HOME/ocaml/init.ml, if XDG_CONFIG_HOME is an absolute path; 3. otherwise, on Unix, HOME/ocaml/init.ml or, on Windows, ocaml\init.ml under LocalAppData (e.g. C:\Users\Bactrian\AppData\Local\ocaml\init.ml); 4. ocaml/init.ml under any of the absolute paths in XDG_CONFIG_DIRS. Paths in XDG_CONFIG_DIRS are colon-delimited on Unix, and semicolon-delimited on Windows; 5. if XDG_CONFIG_DIRS contained no absolute paths, /usr/xdg/ocaml/init.ml on Unix or, ocaml\init.ml under any of LocalAppData (e.g. C:\Users\Bactrian\AppData\Local), RoamingAppData (e.g. C:\Users\Bactrian\AppData\Roaming), or ProgramData (e.g. C:\ProgramData) on Windows; 6. HOME/.ocamlinit, if HOME is non-empty; -labels Labels are not ignored in types, labels may be used in applications, and labelled parameters can be given in any order. This is the default. -no-app-funct Deactivates the applicative behaviour of functors. With this option, each functor application generates new types in its result and applying the same functor twice to the same argument yields two incompatible structures. -noassert Do not compile assertion checks. Note that the special form assert false is always compiled because it is typed specially. -nolabels Ignore non-optional labels in types. Labels cannot be used in applications, and parameter order becomes strict. -noprompt Do not display any prompt when waiting for input. -nopromptcont Do not display the secondary prompt when waiting for continuation lines in multi-line inputs. This should be used e.g. when running ocaml in an emacs window. -nostdlib Do not include the standard library directory in the list of directories searched for source and compiled files. -ppx command After parsing, pipe the abstract syntax tree through the preprocessor command. The module Ast_mapper, described in section 30.1, implements the external interface of a preprocessor. -principal Check information path during type-checking, to make sure that all types are derived in a principal way. When using labelled arguments and/or polymorphic methods, this flag is required to ensure future versions of the compiler will be able to infer types correctly, even if internal algorithms change. All programs accepted in -principal mode are also accepted in the default mode with equivalent types, but different binary signatures, and this may slow down type checking; yet it is a good idea to use it once before publishing source code. -rectypes Allow arbitrary recursive types during type-checking. By default, only recursive types where the recursion goes through an object type are supported. -safe-string Enforce the separation between types string and bytes, thereby making strings read-only. This is the default, and enforced since OCaml 5.0. -safer-matching Do not use type information to optimize pattern-matching. This allows to detect match failures even if a pattern-matching was wrongly assumed to be exhaustive. This only impacts GADT and polymorphic variant compilation. -short-paths When a type is visible under several module-paths, use the shortest one when printing the type’s name in inferred interfaces and error and warning messages. Identifier names starting with an underscore _ or containing double underscores __ incur a penalty of +10 when computing their length. -stdin Read the standard input as a script file rather than starting an interactive session. -strict-sequence Force the left-hand part of each sequence to have type unit. -strict-formats Reject invalid formats that were accepted in legacy format implementations. You should use this flag to detect and fix such invalid formats, as they will be rejected by future OCaml versions. -unsafe Turn bound checking off for array and string accesses (the v.(i) and s.[i] constructs). Programs compiled with -unsafe are therefore faster, but unsafe: anything can happen if the program accesses an array or string outside of its bounds. -unsafe-string Identify the types string and bytes, thereby making strings writable. This is intended for compatibility with old source code and should not be used with new software. This option raises an error unconditionally since OCaml 5.0. -v Print the version number of the compiler and the location of the standard library directory, then exit. -verbose Print all external commands before they are executed, Useful to debug C library problems. -version Print version string and exit. -vnum Print short version number and exit. -no-version Do not print the version banner at startup. -w warning-list Enable, disable, or mark as fatal the warnings specified by the argument warning-list. Each warning can be enabled or disabled, and each warning can be fatal or non-fatal. If a warning is disabled, it isn’t displayed and doesn’t affect compilation in any way (even if it is fatal). If a warning is enabled, it is displayed normally by the compiler whenever the source code triggers it. If it is enabled and fatal, the compiler will also stop with an error after displaying it. The warning-list argument is a sequence of warning specifiers, with no separators between them. A warning specifier is one of the following: +num Enable warning number num. -num Disable warning number num. @num Enable and mark as fatal warning number num. +num1..num2 Enable warnings in the given range. -num1..num2 Disable warnings in the given range. @num1..num2 Enable and mark as fatal warnings in the given range. +letter Enable the set of warnings corresponding to letter. The letter may be uppercase or lowercase. -letter Disable the set of warnings corresponding to letter. The letter may be uppercase or lowercase. @letter Enable and mark as fatal the set of warnings corresponding to letter. The letter may be uppercase or lowercase. uppercase-letter Enable the set of warnings corresponding to uppercase-letter. lowercase-letter Disable the set of warnings corresponding to lowercase-letter. Alternatively, warning-list can specify a single warning using its mnemonic name (see below), as follows: +name Enable warning name. -name Disable warning name. @name Enable and mark as fatal warning name. Warning numbers, letters and names which are not currently defined are ignored. The warnings are as follows (the name following each number specifies the mnemonic for that warning). 1 comment-start Suspicious-looking start-of-comment mark. 2 comment-not-end Suspicious-looking end-of-comment mark. 3 Deprecated synonym for the ’deprecated’ alert. 4 fragile-match Fragile pattern matching: matching that will remain complete even if additional constructors are added to one of the variant types matched. 5 ignored-partial-application Partially applied function: expression whose result has function type and is ignored. 6 labels-omitted Label omitted in function application. 7 method-override Method overridden. 8 partial-match Partial match: missing cases in pattern-matching. 9 missing-record-field-pattern Missing fields in a record pattern. 10 non-unit-statement Expression on the left-hand side of a sequence that doesn’t have type unit (and that is not a function, see warning number 5). 11 redundant-case Redundant case in a pattern matching (unused match case). 12 redundant-subpat Redundant sub-pattern in a pattern-matching. 13 instance-variable-override Instance variable overridden. 14 illegal-backslash Illegal backslash escape in a string constant. 15 implicit-public-methods Private method made public implicitly. 16 unerasable-optional-argument Unerasable optional argument. 17 undeclared-virtual-method Undeclared virtual method. 18 not-principal Non-principal type. 19 non-principal-labels Type without principality. 20 ignored-extra-argument Unused function argument. 21 nonreturning-statement Non-returning statement. 22 preprocessor Preprocessor warning. 23 useless-record-with Useless record with clause. 24 bad-module-name Bad module name: the source file name is not a valid OCaml module name. 25 Ignored: now part of warning 8. 26 unused-var Suspicious unused variable: unused variable that is bound with let or as, and doesn’t start with an underscore (_) character. 27 unused-var-strict Innocuous unused variable: unused variable that is not bound with let nor as, and doesn’t start with an underscore (_) character. 28 wildcard-arg-to-constant-constr Wildcard pattern given as argument to a constant constructor. 29 eol-in-string Unescaped end-of-line in a string constant (non-portable code). 30 duplicate-definitions Two labels or constructors of the same name are defined in two mutually recursive types. 31 module-linked-twice A module is linked twice in the same executable. I gnored: now a hard error (since 5.1). 32 unused-value-declaration Unused value declaration. (since 4.00) 33 unused-open Unused open statement. (since 4.00) 34 unused-type-declaration Unused type declaration. (since 4.00) 35 unused-for-index Unused for-loop index. (since 4.00) 36 unused-ancestor Unused ancestor variable. (since 4.00) 37 unused-constructor Unused constructor. (since 4.00) 38 unused-extension Unused extension constructor. (since 4.00) 39 unused-rec-flag Unused rec flag. (since 4.00) 40 name-out-of-scope Constructor or label name used out of scope. (since 4.01) 41 ambiguous-name Ambiguous constructor or label name. (since 4.01) 42 disambiguated-name Disambiguated constructor or label name (compatibility warning). (since 4.01) 43 nonoptional-label Nonoptional label applied as optional. (since 4.01) 44 open-shadow-identifier Open statement shadows an already defined identifier. (since 4.01) 45 open-shadow-label-constructor Open statement shadows an already defined label or constructor. (since 4.01) 46 bad-env-variable Error in environment variable. (since 4.01) 47 attribute-payload Illegal attribute payload. (since 4.02) 48 eliminated-optional-arguments Implicit elimination of optional arguments. (since 4.02) 49 no-cmi-file Absent cmi file when looking up module alias. (since 4.02) 50 unexpected-docstring Unexpected documentation comment. (since 4.03) 51 wrong-tailcall-expectation Function call annotated with an incorrect @tailcall attribute. (since 4.03) 52 fragile-literal-pattern (see 13.5.3) Fragile constant pattern. (since 4.03) 53 misplaced-attribute Attribute cannot appear in this context. (since 4.03) 54 duplicated-attribute Attribute used more than once on an expression. (since 4.03) 55 inlining-impossible Inlining impossible. (since 4.03) 56 unreachable-case Unreachable case in a pattern-matching (based on type information). (since 4.03) 57 ambiguous-var-in-pattern-guard (see 13.5.4) Ambiguous or-pattern variables under guard. (since 4.03) 58 no-cmx-file Missing cmx file. (since 4.03) 59 flambda-assignment-to-non-mutable-value Assignment to non-mutable value. (since 4.03) 60 unused-module Unused module declaration. (since 4.04) 61 unboxable-type-in-prim-decl Unboxable type in primitive declaration. (since 4.04) 62 constraint-on-gadt Type constraint on GADT type declaration. (since 4.06) 63 erroneous-printed-signature Erroneous printed signature. (since 4.08) 64 unsafe-array-syntax-without-parsing -unsafe used with a preprocessor returning a syntax tree. (since 4.08) 65 redefining-unit Type declaration defining a new ’()’ constructor. (since 4.08) 66 unused-open-bang Unused open! statement. (since 4.08) 67 unused-functor-parameter Unused functor parameter. (since 4.10) 68 match-on-mutable-state-prevent-uncurry Pattern-matching depending on mutable state prevents the remaining arguments from being uncurried. (since 4.12) 69 unused-field Unused record field. (since 4.13) 70 missing-mli Missing interface file. (since 4.13) 71 unused-tmc-attribute Unused @tail_mod_cons attribute. (since 4.14) 72 tmc-breaks-tailcall A tail call is turned into a non-tail call by the @tail_mod_cons transformation. (since 4.14) 73 generative-application-expects-unit A generative functor is applied to an empty structure (struct end) rather than to (). (since 5.1) A all warnings C warnings 1, 2. D Alias for warning 3. E Alias for warning 4. F Alias for warning 5. K warnings 32, 33, 34, 35, 36, 37, 38, 39. L Alias for warning 6. M Alias for warning 7. P Alias for warning 8. R Alias for warning 9. S Alias for warning 10. U warnings 11, 12. V Alias for warning 13. X warnings 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30. Y Alias for warning 26. Z Alias for warning 27. The default setting is -w +a-4-6-7-9-27-29-32..42-44-45-48-50-60. It is displayed by -help. Note that warnings 5 and 10 are not always triggered, depending on the internals of the type checker. -warn-error warning-list Mark as fatal the warnings specified in the argument warning-list. The compiler will stop with an error when one of these warnings is emitted. The warning-list has the same meaning as for the -w option: a + sign (or an uppercase letter) marks the corresponding warnings as fatal, a - sign (or a lowercase letter) turns them back into non-fatal warnings, and a @ sign both enables and marks as fatal the corresponding warnings. Note: it is not recommended to use warning sets (i.e. letters) as arguments to -warn-error in production code, because this can break your build when future versions of OCaml add some new warnings. The default setting is -warn-error -a (no warning is fatal). -warn-help Show the description of all available warning numbers. - file Use file as a script file name, even when it starts with a hyphen (-). -help or –help Display a short usage summary and exit.  Unix: The following environment variables are also consulted: OCAMLTOP_INCLUDE_PATH Additional directories to search for compiled object code files (.cmi, .cmo and .cma). The specified directories are considered from left to right, after the include directories specified on the command line via -I have been searched. Available since OCaml 4.08. OCAMLTOP_UTF_8 When printing string values, non-ascii bytes ( > \0x7E ) are printed as decimal escape sequence if OCAMLTOP_UTF_8 is set to false. Otherwise, they are printed unescaped. TERM When printing error messages, the toplevel system attempts to underline visually the location of the error. It consults the TERM variable to determines the type of output terminal and look up its capabilities in the terminal database. XDG_CONFIG_HOME, HOME, XDG_CONFIG_DIRS Initialization file lookup procedure (see above). 14.2 Toplevel directives *=*=*=*=*=*=*=*=*=*=*=*=*= The following directives control the toplevel behavior, load files in memory, and trace program execution. Note: all directives start with a # (sharp) symbol. This # must be typed before the directive, and must not be confused with the # prompt displayed by the interactive loop. For instance, typing #quit;; will exit the toplevel loop, but typing quit;; will result in an “unbound value quit” error. General #help;; Prints a list of all available directives, with corresponding argument type if appropriate. #quit;; Exit the toplevel loop and terminate the ocaml command. Loading codes #cd "dir-name";; Change the current working directory. #directory "dir-name";; Add the given directory to the list of directories searched for source and compiled files. #remove_directory "dir-name";; Remove the given directory from the list of directories searched for source and compiled files. Do nothing if the list does not contain the given directory. #load "file-name";; Load in memory a bytecode object file (.cmo file) or library file (.cma file) produced by the batch compiler ocamlc. #load_rec "file-name";; Load in memory a bytecode object file (.cmo file) or library file (.cma file) produced by the batch compiler ocamlc. When loading an object file that depends on other modules which have not been loaded yet, the .cmo files for these modules are searched and loaded as well, recursively. The loading order is not specified. #use "file-name";; Read, compile and execute source phrases from the given file. This is textual inclusion: phrases are processed just as if they were typed on standard input. The reading of the file stops at the first error encountered. #use_output "command";; Execute a command and evaluate its output as if it had been captured to a file and passed to #use. #mod_use "file-name";; Similar to #use but also wrap the code into a top-level module of the same name as capitalized file name without extensions, following semantics of the compiler. For directives that take file names as arguments, if the given file name specifies no directory, the file is searched in the following directories: 1. In script mode, the directory containing the script currently executing; in interactive mode, the current working directory. 2. Directories added with the #directory directive. 3. Directories given on the command line with -I options. 4. The standard library directory. Environment queries #show_class class-path;; #show_class_type class-path;; #show_exception ident;; #show_module module-path;; #show_module_type modtype-path;; #show_type typeconstr;; #show_val value-path;; Print the signature of the corresponding component. #show ident;; Print the signatures of components with name ident in all the above categories. Pretty-printing #install_printer printer-name;; This directive registers the function named printer-name (a value path) as a printer for values whose types match the argument type of the function. That is, the toplevel loop will call printer-name when it has such a value to print. The printing function printer-name should have type Format.formatter -> t -> unit, where t is the type for the values to be printed, and should output its textual representation for the value of type t on the given formatter, using the functions provided by the Format library. For backward compatibility, printer-name can also have type t -> unit and should then output on the standard formatter, but this usage is deprecated. #print_depth n;; Limit the printing of values to a maximal depth of n. The parts of values whose depth exceeds n are printed as ... (ellipsis). #print_length n;; Limit the number of value nodes printed to at most n. Remaining parts of values are printed as ... (ellipsis). #remove_printer printer-name;; Remove the named function from the table of toplevel printers. Tracing #trace function-name;; After executing this directive, all calls to the function named function-name will be “traced”. That is, the argument and the result are displayed for each call, as well as the exceptions escaping out of the function, raised either by the function itself or by another function it calls. If the function is curried, each argument is printed as it is passed to the function. #untrace function-name;; Stop tracing the given function. #untrace_all;; Stop tracing all functions traced so far. Compiler options #debug bool;; Turn on/off the insertion of debugging events. Default is true. #labels bool;; Ignore labels in function types if argument is false, or switch back to default behaviour (commuting style) if argument is true. #ppx "file-name";; After parsing, pipe the abstract syntax tree through the preprocessor command. #principal bool;; If the argument is true, check information paths during type-checking, to make sure that all types are derived in a principal way. If the argument is false, do not check information paths. #rectypes;; Allow arbitrary recursive types during type-checking. Note: once enabled, this option cannot be disabled because that would lead to unsoundness of the type system. #warn_error "warning-list";; Treat as errors the warnings enabled by the argument and as normal warnings the warnings disabled by the argument. #warnings "warning-list";; Enable or disable warnings according to the argument. 14.3 The toplevel and the module system *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Toplevel phrases can refer to identifiers defined in compilation units with the same mechanisms as for separately compiled units: either by using qualified names (Modulename.localname), or by using the open construct and unqualified names (see section 11.3). However, before referencing another compilation unit, an implementation of that unit must be present in memory. At start-up, the toplevel system contains implementations for all the modules in the the standard library. Implementations for user modules can be entered with the #load directive described above. Referencing a unit for which no implementation has been provided results in the error Reference to undefined global `...'. Note that entering open Mod merely accesses the compiled interface (.cmi file) for Mod, but does not load the implementation of Mod, and does not cause any error if no implementation of Mod has been loaded. The error “reference to undefined global Mod” will occur only when executing a value or module definition that refers to Mod. 14.4 Common errors *=*=*=*=*=*=*=*=*=*= This section describes and explains the most frequently encountered error messages. Cannot find file filename The named file could not be found in the current directory, nor in the directories of the search path. If filename has the format mod.cmi, this means you have referenced the compilation unit mod, but its compiled interface could not be found. Fix: compile mod.mli or mod.ml first, to create the compiled interface mod.cmi. If filename has the format mod.cmo, this means you are trying to load with #load a bytecode object file that does not exist yet. Fix: compile mod.ml first. If your program spans several directories, this error can also appear because you haven’t specified the directories to look into. Fix: use the #directory directive to add the correct directories to the search path. This expression has type t_1, but is used with type t_2 See section 13.4. Reference to undefined global mod You have neglected to load in memory an implementation for a module with #load. See section 14.3 above. 14.5 Building custom toplevel systems: ocamlmktop *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The ocamlmktop command builds OCaml toplevels that contain user code preloaded at start-up. The ocamlmktop command takes as argument a set of .cmo and .cma files, and links them with the object files that implement the OCaml toplevel. The typical use is: << ocamlmktop -o mytoplevel foo.cmo bar.cmo gee.cmo >> This creates the bytecode file mytoplevel, containing the OCaml toplevel system, plus the code from the three .cmo files. This toplevel is directly executable and is started by: << ./mytoplevel >> This enters a regular toplevel loop, except that the code from foo.cmo, bar.cmo and gee.cmo is already loaded in memory, just as if you had typed: << #load "foo.cmo";; #load "bar.cmo";; #load "gee.cmo";; >> on entrance to the toplevel. The modules Foo, Bar and Gee are not opened, though; you still have to do << open Foo;; >> yourself, if this is what you wish. 14.5.1 Options ================ The following command-line options are recognized by ocamlmktop. -cclib libname Pass the -llibname option to the C linker when linking in “custom runtime” mode. See the corresponding option for ocamlc, in chapter 13. -ccopt option Pass the given option to the C compiler and linker, when linking in “custom runtime” mode. See the corresponding option for ocamlc, in chapter 13. -custom Link in “custom runtime” mode. See the corresponding option for ocamlc, in chapter 13. -I directory Add the given directory to the list of directories searched for compiled object code files (.cmo and .cma). -o exec-file Specify the name of the toplevel file produced by the linker. The default is a.out. 14.6 The native toplevel: ocamlnat (experimental) *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This section describes a tool that is not yet officially supported but may be found useful. OCaml code executing in the traditional toplevel system uses the bytecode interpreter. When increased performance is required, or for testing programs that will only execute correctly when compiled to native code, the native toplevel may be used instead. For the majority of installations the native toplevel will not have been installed along with the rest of the OCaml toolchain. In such circumstances it will be necessary to build the OCaml distribution from source. From the built source tree of the distribution you may use make natruntop to build and execute a native toplevel. (Alternatively make ocamlnat can be used, which just performs the build step.) If the make install command is run after having built the native toplevel then the ocamlnat program (either from the source or the installation directory) may be invoked directly rather than using make natruntop. Chapter 15  The runtime system (ocamlrun) ********************************************* The ocamlrun command executes bytecode files produced by the linking phase of the ocamlc command. 15.1 Overview *=*=*=*=*=*=*=* The ocamlrun command comprises three main parts: the bytecode interpreter, that actually executes bytecode files; the memory allocator and garbage collector; and a set of C functions that implement primitive operations such as input/output. The usage for ocamlrun is: << ocamlrun options bytecode-executable arg_1 ... arg_n >> The first non-option argument is taken to be the name of the file containing the executable bytecode. (That file is searched in the executable path as well as in the current directory.) The remaining arguments are passed to the OCaml program, in the string array Sys.argv. Element 0 of this array is the name of the bytecode executable file; elements 1 to n are the remaining arguments arg_1 to arg_n. As mentioned in chapter 13, the bytecode executable files produced by the ocamlc command are self-executable, and manage to launch the ocamlrun command on themselves automatically. That is, assuming a.out is a bytecode executable file, << a.out arg_1 ... arg_n >> works exactly as << ocamlrun a.out arg_1 ... arg_n >> Notice that it is not possible to pass options to ocamlrun when invoking a.out directly.  Windows: Under several versions of Windows, bytecode executable files are self-executable only if their name ends in .exe. It is recommended to always give .exe names to bytecode executables, e.g. compile with ocamlc -o myprog.exe ... rather than ocamlc -o myprog .... 15.2 Options *=*=*=*=*=*=*= The following command-line options are recognized by ocamlrun. -b When the program aborts due to an uncaught exception, print a detailed “back trace” of the execution, showing where the exception was raised and which function calls were outstanding at this point. The back trace is printed only if the bytecode executable contains debugging information, i.e. was compiled and linked with the -g option to ocamlc set. This is equivalent to setting the b flag in the OCAMLRUNPARAM environment variable (see below). -config Print the version number of ocamlrun and a detailed summary of its configuration, then exit. -I dir Search the directory dir for dynamically-loaded libraries, in addition to the standard search path (see section 15.3). -m Print the magic number of the bytecode executable given as argument and exit. -M Print the magic number expected for bytecode executables by this version of the runtime and exit. -p Print the names of the primitives known to this version of ocamlrun and exit. -t Increments the trace level for the debug runtime (ignored otherwise). -v Direct the memory manager to print some progress messages on standard error. This is equivalent to setting v=61 in the OCAMLRUNPARAM environment variable (see below). -version Print version string and exit. -vnum Print short version number and exit. The following environment variables are also consulted: CAML_LD_LIBRARY_PATH Additional directories to search for dynamically-loaded libraries (see section 15.3). OCAMLLIB The directory containing the OCaml standard library. (If OCAMLLIB is not set, CAMLLIB will be used instead.) Used to locate the ld.conf configuration file for dynamic loading (see section 15.3). If not set, default to the library directory specified when compiling OCaml. OCAMLRUNPARAM Set the runtime system options and garbage collection parameters. (If OCAMLRUNPARAM is not set, CAMLRUNPARAM will be used instead.) This variable must be a sequence of parameter specifications separated by commas. For convenience, commas at the beginning of the variable are ignored, and multiple runs of commas are interpreted as a single one. A parameter specification is an option letter followed by an = sign, a decimal number (or an hexadecimal number prefixed by 0x), and an optional multiplier. The options are documented below; the options a, i, l, m, M, n, o, O, s, v, w correspond to the fields of the control record documented in section 29.24. b (backtrace) Trigger the printing of a stack backtrace when an uncaught exception aborts the program. An optional argument can be provided: b=0 turns backtrace printing off; b=1 is equivalent to b and turns backtrace printing on; b=2 turns backtrace printing on and forces the runtime system to load debugging information at program startup time instead of at backtrace printing time. b=2 can be used if the runtime is unable to load debugging information at backtrace printing time, for example if there are no file descriptors available. c (cleanup_on_exit) Shut the runtime down gracefully on exit (see caml_shutdown in section 22.7.5). The option also enables pooling (as in caml_startup_pooled). This mode can be used to detect leaks with a third-party memory debugger. e (runtime_events_log_wsize) Size of the per-domain runtime events ring buffers in log powers of two words. Defaults to 16, giving 64k word or 512kb buffers on 64-bit systems. l (stack_limit) The limit (in words) of the stack size. This is relevant to both the byte-code runtime and the native code runtime: OCaml always uses its own stack and not the operating system’s stack. m (custom_minor_ratio) Bound on floating garbage for out-of-heap memory held by custom values in the minor heap. A minor GC is triggered when this much memory is held by custom values located in the minor heap. Expressed as a percentage of minor heap size. Default: 100. Note: this only applies to values allocated with caml_alloc_custom_mem. M (custom_major_ratio) Target ratio of floating garbage to major heap size for out-of-heap memory held by custom values (e.g. bigarrays) located in the major heap. The GC speed is adjusted to try to use this much memory for dead values that are not yet collected. Expressed as a percentage of major heap size. Default: 44. Note: this only applies to values allocated with caml_alloc_custom_mem. n (custom_minor_max_size) Maximum amount of out-of-heap memory for each custom value allocated in the minor heap. When a custom value is allocated on the minor heap and holds more than this many bytes, only this value is counted against custom_minor_ratio and the rest is directly counted against custom_major_ratio. Default: 8192 bytes. Note: this only applies to values allocated with caml_alloc_custom_mem. The multiplier is k, M, or G, for multiplication by 2^10, 2^20, and 2^30 respectively. o (space_overhead) The major GC speed setting. See the Gc module documentation for details. p (parser trace) Turn on debugging support for ocamlyacc-generated parsers. When this option is on, the pushdown automaton that executes the parsers prints a trace of its actions. This option takes no argument. R (randomize) Turn on randomization of all hash tables by default (see section 29.25). This option takes no argument. s (minor_heap_size) Size of the minor heap. (in words) t Set the trace level for the debug runtime (ignored by the standard runtime). v (verbose) What GC messages to print to stderr. This is a sum of values selected from the following: 1 (= 0x001) Start and end of major GC cycle. 2 (= 0x002) Minor collection and major GC slice. 4 (= 0x004) Growing and shrinking of the heap. 8 (= 0x008) Resizing of stacks and memory manager tables. 16 (= 0x010) Heap compaction. 32 (= 0x020) Change of GC parameters. 64 (= 0x040) Computation of major GC slice size. 128 (= 0x080) Calling of finalization functions 256 (= 0x100) Startup messages (loading the bytecode executable file, resolving shared libraries). 512 (= 0x200) Computation of compaction-triggering condition. 1024 (= 0x400) Output GC statistics at program exit. 2048 (= 0x800) GC debugging messages. 4096 (= 0x1000) Address space reservation changes. V (verify_heap) runs an integrity check on the heap just after the completion of a major GC cycle W Print runtime warnings to stderr (such as Channel opened on file dies without being closed, unflushed data, etc.) If the option letter is not recognized, the whole parameter is ignored; if the equal sign or the number is missing, the value is taken as 1; if the multiplier is not recognized, it is ignored. For example, on a 32-bit machine, under bash the command << export OCAMLRUNPARAM='b,s=256k,v=0x015' >> tells a subsequent ocamlrun to print backtraces for uncaught exceptions, set its initial minor heap size to 1 megabyte and print a message at the start of each major GC cycle, when the heap size changes, and when compaction is triggered. CAMLRUNPARAM If OCAMLRUNPARAM is not found in the environment, then CAMLRUNPARAM will be used instead. If CAMLRUNPARAM is also not found, then the default values will be used. PATH List of directories searched to find the bytecode executable file. 15.3 Dynamic loading of shared libraries *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= On platforms that support dynamic loading, ocamlrun can link dynamically with C shared libraries (DLLs) providing additional C primitives beyond those provided by the standard runtime system. The names for these libraries are provided at link time as described in section 22.1.4), and recorded in the bytecode executable file; ocamlrun, then, locates these libraries and resolves references to their primitives when the bytecode executable program starts. The ocamlrun command searches shared libraries in the following directories, in the order indicated: 1. Directories specified on the ocamlrun command line with the -I option. 2. Directories specified in the CAML_LD_LIBRARY_PATH environment variable. 3. Directories specified at link-time via the -dllpath option to ocamlc. (These directories are recorded in the bytecode executable file.) 4. Directories specified in the file ld.conf. This file resides in the OCaml standard library directory, and lists directory names (one per line) to be searched. Typically, it contains only one line naming the stublibs subdirectory of the OCaml standard library directory. Users can add there the names of other directories containing frequently-used shared libraries; however, for consistency of installation, we recommend that shared libraries are installed directly in the system stublibs directory, rather than adding lines to the ld.conf file. 5. Default directories searched by the system dynamic loader. Under Unix, these generally include /lib and /usr/lib, plus the directories listed in the file /etc/ld.so.conf and the environment variable LD_LIBRARY_PATH. Under Windows, these include the Windows system directories, plus the directories listed in the PATH environment variable. 15.4 Common errors *=*=*=*=*=*=*=*=*=*= This section describes and explains the most frequently encountered error messages. filename: no such file or directory If filename is the name of a self-executable bytecode file, this means that either that file does not exist, or that it failed to run the ocamlrun bytecode interpreter on itself. The second possibility indicates that OCaml has not been properly installed on your system. Cannot exec ocamlrun (When launching a self-executable bytecode file.) The ocamlrun could not be found in the executable path. Check that OCaml has been properly installed on your system. Cannot find the bytecode file The file that ocamlrun is trying to execute (e.g. the file given as first non-option argument to ocamlrun) either does not exist, or is not a valid executable bytecode file. Truncated bytecode file The file that ocamlrun is trying to execute is not a valid executable bytecode file. Probably it has been truncated or mangled since created. Erase and rebuild it. Uncaught exception The program being executed contains a “stray” exception. That is, it raises an exception at some point, and this exception is never caught. This causes immediate termination of the program. The name of the exception is printed, along with its string, byte sequence, and integer arguments (arguments of more complex types are not correctly printed). To locate the context of the uncaught exception, compile the program with the -g option and either run it again under the ocamldebug debugger (see chapter 20), or run it with ocamlrun -b or with the OCAMLRUNPARAM environment variable set to b=1. Out of memory The program being executed requires more memory than available. Either the program builds excessively large data structures; or the program contains too many nested function calls, and the stack overflows. In some cases, your program is perfectly correct, it just requires more memory than your machine provides. In other cases, the “out of memory” message reveals an error in your program: non-terminating recursive function, allocation of an excessively large array, string or byte sequence, attempts to build an infinite list or other data structure, ... To help you diagnose this error, run your program with the -v option to ocamlrun, or with the OCAMLRUNPARAM environment variable set to v=63. If it displays lots of “Growing stack...” messages, this is probably a looping recursive function. If it displays lots of “Growing heap...” messages, with the heap size growing slowly, this is probably an attempt to construct a data structure with too many (infinitely many?) cells. If it displays few “Growing heap...” messages, but with a huge increment in the heap size, this is probably an attempt to build an excessively large array, string or byte sequence. Chapter 16  Native-code compilation (ocamlopt) ************************************************** This chapter describes the OCaml high-performance native-code compiler ocamlopt, which compiles OCaml source files to native code object files and links these object files to produce standalone executables. The native-code compiler is only available on certain platforms. It produces code that runs faster than the bytecode produced by ocamlc, at the cost of increased compilation time and executable code size. Compatibility with the bytecode compiler is extremely high: the same source code should run identically when compiled with ocamlc and ocamlopt. It is not possible to mix native-code object files produced by ocamlopt with bytecode object files produced by ocamlc: a program must be compiled entirely with ocamlopt or entirely with ocamlc. Native-code object files produced by ocamlopt cannot be loaded in the toplevel system ocaml. 16.1 Overview of the compiler *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The ocamlopt command has a command-line interface very close to that of ocamlc. It accepts the same types of arguments, and processes them sequentially, after all options have been processed: - Arguments ending in .mli are taken to be source files for compilation unit interfaces. Interfaces specify the names exported by compilation units: they declare value names with their types, define public data types, declare abstract data types, and so on. From the file x.mli, the ocamlopt compiler produces a compiled interface in the file x.cmi. The interface produced is identical to that produced by the bytecode compiler ocamlc. - Arguments ending in .ml are taken to be source files for compilation unit implementations. Implementations provide definitions for the names exported by the unit, and also contain expressions to be evaluated for their side-effects. From the file x.ml, the ocamlopt compiler produces two files: x.o, containing native object code, and x.cmx, containing extra information for linking and optimization of the clients of the unit. The compiled implementation should always be referred to under the name x.cmx (when given a .o or .obj file, ocamlopt assumes that it contains code compiled from C, not from OCaml). The implementation is checked against the interface file x.mli (if it exists) as described in the manual for ocamlc (chapter 13). - Arguments ending in .cmx are taken to be compiled object code. These files are linked together, along with the object files obtained by compiling .ml arguments (if any), and the OCaml standard library, to produce a native-code executable program. The order in which .cmx and .ml arguments are presented on the command line is relevant: compilation units are initialized in that order at run-time, and it is a link-time error to use a component of a unit before having initialized it. Hence, a given x.cmx file must come before all .cmx files that refer to the unit x. - Arguments ending in .cmxa are taken to be libraries of object code. Such a library packs in two files (lib.cmxa and lib.a/.lib) a set of object files (.cmx and .o/.obj files). Libraries are build with ocamlopt -a (see the description of the -a option below). The object files contained in the library are linked as regular .cmx files (see above), in the order specified when the library was built. The only difference is that if an object file contained in a library is not referenced anywhere in the program, then it is not linked in. - Arguments ending in .c are passed to the C compiler, which generates a .o/.obj object file. This object file is linked with the program. - Arguments ending in .o, .a or .so (.obj, .lib and .dll under Windows) are assumed to be C object files and libraries. They are linked with the program. The output of the linking phase is a regular Unix or Windows executable file. It does not need ocamlrun to run. The compiler is able to emit some information on its internal stages: - .cmt files for the implementation of the compilation unit and .cmti for signatures if the option -bin-annot is passed to it (see the description of -bin-annot below). Each such file contains a typed abstract syntax tree (AST), that is produced during the type checking procedure. This tree contains all available information about the location and the specific type of each term in the source file. The AST is partial if type checking was unsuccessful. These .cmt and .cmti files are typically useful for code inspection tools. - .cmir-linear files for the implementation of the compilation unit if the option -save-ir-after scheduling is passed to it. Each such file contains a low-level intermediate representation, produced by the instruction scheduling pass. An external tool can perform low-level optimisations, such as code layout, by transforming a .cmir-linear file. To continue compilation, the compiler can be invoked with (a possibly modified) .cmir-linear file as an argument, instead of the corresponding source file. 16.2 Options *=*=*=*=*=*=*= The following command-line options are recognized by ocamlopt. The options -pack, -a, -shared, -c, -output-obj and -output-complete-obj are mutually exclusive. -a Build a library(.cmxa and .a/.lib files) with the object files (.cmx and .o/.obj files) given on the command line, instead of linking them into an executable file. The name of the library must be set with the -o option. If -cclib or -ccopt options are passed on the command line, these options are stored in the resulting .cmxalibrary. Then, linking with this library automatically adds back the -cclib and -ccopt options as if they had been provided on the command line, unless the -noautolink option is given. -absname Force error messages to show absolute paths for file names. -no-absname Do not try to show absolute filenames in error messages. -annot Deprecated since OCaml 4.11. Please use -bin-annot instead. -args filename Read additional newline-terminated command line arguments from filename. -args0 filename Read additional null character terminated command line arguments from filename. -bin-annot Dump detailed information about the compilation (types, bindings, tail-calls, etc) in binary format. The information for file src.ml (resp. src.mli) is put into file src.cmt (resp. src.cmti). In case of a type error, dump all the information inferred by the type-checker before the error. The *.cmt and *.cmti files produced by -bin-annot contain more information and are much more compact than the files produced by -annot. -c Compile only. Suppress the linking phase of the compilation. Source code files are turned into compiled files, but no executable file is produced. This option is useful to compile modules separately. -cc ccomp Use ccomp as the C linker called to build the final executable and as the C compiler for compiling .c source files. When linking object files produced by a C++ compiler (such as g++ or clang++), it is recommended to use -cc c++. -cclib -llibname Pass the -llibname option to the linker . This causes the given C library to be linked with the program. -ccopt option Pass the given option to the C compiler and linker. For instance, -ccopt -Ldir causes the C linker to search for C libraries in directory dir. -cmi-file filename Use the given interface file to type-check the ML source file to compile. When this option is not specified, the compiler looks for a .mli file with the same base name than the implementation it is compiling and in the same directory. If such a file is found, the compiler looks for a corresponding .cmi file in the included directories and reports an error if it fails to find one. -color mode Enable or disable colors in compiler messages (especially warnings and errors). The following modes are supported: auto use heuristics to enable colors only if the output supports them (an ANSI-compatible tty terminal); always enable colors unconditionally; never disable color output. The environment variable OCAML_COLOR is considered if -color is not provided. Its values are auto/always/never as above. If -color is not provided, OCAML_COLOR is not set and the environment variable NO_COLOR is set, then color output is disabled. Otherwise, the default setting is ’auto’, and the current heuristic checks that the TERM environment variable exists and is not empty or dumb, and that ’isatty(stderr)’ holds. -error-style mode Control the way error messages and warnings are printed. The following modes are supported: short only print the error and its location; contextual like short, but also display the source code snippet corresponding to the location of the error. The default setting is contextual. The environment variable OCAML_ERROR_STYLE is considered if -error-style is not provided. Its values are short/contextual as above. -compact Optimize the produced code for space rather than for time. This results in slightly smaller but slightly slower programs. The default is to optimize for speed. -config Print the version number of ocamlopt and a detailed summary of its configuration, then exit. -config-var var Print the value of a specific configuration variable from the -config output, then exit. If the variable does not exist, the exit code is non-zero. This option is only available since OCaml 4.08, so script authors should have a fallback for older versions. -depend ocamldep-args Compute dependencies, as the ocamldep command would do. The remaining arguments are interpreted as if they were given to the ocamldep command. -for-pack module-path Generate an object file (.cmx and .o/.obj files) that can later be included as a sub-module (with the given access path) of a compilation unit constructed with -pack. For instance, ocamlopt -for-pack P -c A.ml will generate a..cmx and a.o files that can later be used with ocamlopt -pack -o P.cmx a.cmx. Note: you can still pack a module that was compiled without -for-pack but in this case exceptions will be printed with the wrong names. -g Add debugging information while compiling and linking. This option is required in order to produce stack backtraces when the program terminates on an uncaught exception (see section 15.2). -no-g Do not record debugging information (default). -i Cause the compiler to print all defined names (with their inferred types or their definitions) when compiling an implementation (.ml file). No compiled files (.cmo and .cmi files) are produced. This can be useful to check the types inferred by the compiler. Also, since the output follows the syntax of interfaces, it can help in writing an explicit interface (.mli file) for a file: just redirect the standard output of the compiler to a .mli file, and edit that file to remove all declarations of unexported names. -I directory Add the given directory to the list of directories searched for compiled interface files (.cmi), compiled object code files (.cmx), and libraries (.cmxa). By default, the current directory is searched first, then the standard library directory. Directories added with -I are searched after the current directory, in the order in which they were given on the command line, but before the standard library directory. See also option -nostdlib. If the given directory starts with +, it is taken relative to the standard library directory. For instance, -I +unix adds the subdirectory unix of the standard library to the search path. -H directory Behaves identically to -I, except that (a) programs may not directly refer to modules added to the search path this way, and (b) these directories are searched after any -I directories. This makes it possible to provide the compiler with compiled interface and object code files for the current program’s transitive dependencies (the dependencies of its dependencies) without allowing them to silently become direct dependencies. -impl filename Compile the file filename as an implementation file, even if its extension is not .ml. -inline n Set aggressiveness of inlining to n, where n is a positive integer. Specifying -inline 0 prevents all functions from being inlined, except those whose body is smaller than the call site. Thus, inlining causes no expansion in code size. The default aggressiveness, -inline 1, allows slightly larger functions to be inlined, resulting in a slight expansion in code size. Higher values for the -inline option cause larger and larger functions to become candidate for inlining, but can result in a serious increase in code size. -intf filename Compile the file filename as an interface file, even if its extension is not .mli. -intf-suffix string Recognize file names ending with string as interface files (instead of the default .mli). -labels Labels are not ignored in types, labels may be used in applications, and labelled parameters can be given in any order. This is the default. -linkall Force all modules contained in libraries to be linked in. If this flag is not given, unreferenced modules are not linked in. When building a library (option -a), setting the -linkall option forces all subsequent links of programs involving that library to link all the modules contained in the library. When compiling a module (option -c), setting the -linkall option ensures that this module will always be linked if it is put in a library and this library is linked. -linscan Use linear scan register allocation. Compiling with this allocator is faster than with the usual graph coloring allocator, sometimes quite drastically so for long functions and modules. On the other hand, the generated code can be a bit slower. -match-context-rows Set the number of rows of context used for optimization during pattern matching compilation. The default value is 32. Lower values cause faster compilation, but less optimized code. This advanced option is meant for use in the event that a pattern-match-heavy program leads to significant increases in compilation time. -no-alias-deps Do not record dependencies for module aliases. See section 12.8 for more information. -no-app-funct Deactivates the applicative behaviour of functors. With this option, each functor application generates new types in its result and applying the same functor twice to the same argument yields two incompatible structures. -no-float-const-prop Deactivates the constant propagation for floating-point operations. This option should be given if the program changes the float rounding mode during its execution. -noassert Do not compile assertion checks. Note that the special form assert false is always compiled because it is typed specially. This flag has no effect when linking already-compiled files. -noautolink When linking .cmxalibraries, ignore -cclib and -ccopt options potentially contained in the libraries (if these options were given when building the libraries). This can be useful if a library contains incorrect specifications of C libraries or C options; in this case, during linking, set -noautolink and pass the correct C libraries and options on the command line. -nodynlink Allow the compiler to use some optimizations that are valid only for code that is statically linked to produce a non-relocatable executable. The generated code cannot be linked to produce a shared library nor a position-independent executable (PIE). Many operating systems produce PIEs by default, causing errors when linking code compiled with -nodynlink. Either do not use -nodynlink or pass the option -ccopt -no-pie at link-time. -nolabels Ignore non-optional labels in types. Labels cannot be used in applications, and parameter order becomes strict. -nostdlib Do not automatically add the standard library directory to the list of directories searched for compiled interface files (.cmi), compiled object code files (.cmx), and libraries (.cmxa). See also option -I. -o output-file Specify the name of the output file to produce. For executable files, the default output name is a.out under Unix and camlprog.exe under Windows. If the -a option is given, specify the name of the library produced. If the -pack option is given, specify the name of the packed object file produced. If the -output-obj or -output-complete-obj options are given, specify the name of the produced object file. If the -shared option is given, specify the name of plugin file produced. -opaque When the native compiler compiles an implementation, by default it produces a .cmx file containing information for cross-module optimization. It also expects .cmx files to be present for the dependencies of the currently compiled source, and uses them for optimization. Since OCaml 4.03, the compiler will emit a warning if it is unable to locate the .cmx file of one of those dependencies. The -opaque option, available since 4.04, disables cross-module optimization information for the currently compiled unit. When compiling .mli interface, using -opaque marks the compiled .cmi interface so that subsequent compilations of modules that depend on it will not rely on the corresponding .cmx file, nor warn if it is absent. When the native compiler compiles a .ml implementation, using -opaque generates a .cmx that does not contain any cross-module optimization information. Using this option may degrade the quality of generated code, but it reduces compilation time, both on clean and incremental builds. Indeed, with the native compiler, when the implementation of a compilation unit changes, all the units that depend on it may need to be recompiled – because the cross-module information may have changed. If the compilation unit whose implementation changed was compiled with -opaque, no such recompilation needs to occur. This option can thus be used, for example, to get faster edit-compile-test feedback loops. -open Module Opens the given module before processing the interface or implementation files. If several -open options are given, they are processed in order, just as if the statements open! Module1;; ... open! ModuleN;; were added at the top of each file. -output-obj Cause the linker to produce a C object file instead of an executable file. This is useful to wrap OCaml code as a C library, callable from any C program. See chapter 22, section 22.7.5. The name of the output object file must be set with the -o option. This option can also be used to produce a compiled shared/dynamic library (.so extension, .dll under Windows). -output-complete-obj Same as -output-obj options except the object file produced includes the runtime and autolink libraries. -pack Build an object file (.cmx and .o/.obj files) and its associated compiled interface (.cmi) that combines the .cmx object files given on the command line, making them appear as sub-modules of the output .cmx file. The name of the output .cmx file must be given with the -o option. For instance, << ocamlopt -pack -o P.cmx A.cmx B.cmx C.cmx >> generates compiled files P.cmx, P.o and P.cmi describing a compilation unit having three sub-modules A, B and C, corresponding to the contents of the object files A.cmx, B.cmx and C.cmx. These contents can be referenced as P.A, P.B and P.C in the remainder of the program. The .cmx object files being combined must have been compiled with the appropriate -for-pack option. In the example above, A.cmx, B.cmx and C.cmx must have been compiled with ocamlopt -for-pack P. Multiple levels of packing can be achieved by combining -pack with -for-pack. Consider the following example: << ocamlopt -for-pack P.Q -c A.ml ocamlopt -pack -o Q.cmx -for-pack P A.cmx ocamlopt -for-pack P -c B.ml ocamlopt -pack -o P.cmx Q.cmx B.cmx >> The resulting P.cmx object file has sub-modules P.Q, P.Q.A and P.B. -pp command Cause the compiler to call the given command as a preprocessor for each source file. The output of command is redirected to an intermediate file, which is compiled. If there are no compilation errors, the intermediate file is deleted afterwards. -ppx command After parsing, pipe the abstract syntax tree through the preprocessor command. The module Ast_mapper, described in section 30.1, implements the external interface of a preprocessor. -principal Check information path during type-checking, to make sure that all types are derived in a principal way. When using labelled arguments and/or polymorphic methods, this flag is required to ensure future versions of the compiler will be able to infer types correctly, even if internal algorithms change. All programs accepted in -principal mode are also accepted in the default mode with equivalent types, but different binary signatures, and this may slow down type checking; yet it is a good idea to use it once before publishing source code. -rectypes Allow arbitrary recursive types during type-checking. By default, only recursive types where the recursion goes through an object type are supported. Note that once you have created an interface using this flag, you must use it again for all dependencies. -runtime-variant suffix Add the suffix string to the name of the runtime library used by the program. Currently, only one such suffix is supported: d, and only if the OCaml compiler was configured with option -with-debug-runtime. This suffix gives the debug version of the runtime, which is useful for debugging pointer problems in low-level code such as C stubs. -S Keep the assembly code produced during the compilation. The assembly code for the source file x.ml is saved in the file x.s. -safe-string Enforce the separation between types string and bytes, thereby making strings read-only. This is the default, and enforced since OCaml 5.0. -safer-matching Do not use type information to optimize pattern-matching. This allows to detect match failures even if a pattern-matching was wrongly assumed to be exhaustive. This only impacts GADT and polymorphic variant compilation. -save-ir-after pass Save intermediate representation after the given compilation pass to a file. The currently supported passes and the corresponding file extensions are: scheduling (.cmir-linear). This experimental feature enables external tools to inspect and manipulate compiler’s intermediate representation of the program using compiler-libs library (see section 30). -shared Build a plugin (usually .cmxs) that can be dynamically loaded with the Dynlink module. The name of the plugin must be set with the -o option. A plugin can include a number of OCaml modules and libraries, and extra native objects (.o, .obj, .a, .lib files). Building native plugins is only supported for some operating system. Under some systems (currently, only Linux AMD 64), all the OCaml code linked in a plugin must have been compiled without the -nodynlink flag. Some constraints might also apply to the way the extra native objects have been compiled (under Linux AMD 64, they must contain only position-independent code). -short-paths When a type is visible under several module-paths, use the shortest one when printing the type’s name in inferred interfaces and error and warning messages. Identifier names starting with an underscore _ or containing double underscores __ incur a penalty of +10 when computing their length. -stop-after pass Stop compilation after the given compilation pass. The currently supported passes are: parsing, typing, scheduling, emit. -strict-sequence Force the left-hand part of each sequence to have type unit. -strict-formats Reject invalid formats that were accepted in legacy format implementations. You should use this flag to detect and fix such invalid formats, as they will be rejected by future OCaml versions. -unboxed-types When a type is unboxable (i.e. a record with a single argument or a concrete datatype with a single constructor of one argument) it will be unboxed unless annotated with [@@ocaml.boxed]. -no-unboxed-types When a type is unboxable it will be boxed unless annotated with [@@ocaml.unboxed]. This is the default. -unsafe Turn bound checking off for array and string accesses (the v.(i) and s.[i] constructs). Programs compiled with -unsafe are therefore faster, but unsafe: anything can happen if the program accesses an array or string outside of its bounds. Additionally, turn off the check for zero divisor in integer division and modulus operations. With -unsafe, an integer division (or modulus) by zero can halt the program or continue with an unspecified result instead of raising a Division_by_zero exception. -unsafe-string Identify the types string and bytes, thereby making strings writable. This is intended for compatibility with old source code and should not be used with new software. This option raises an error unconditionally since OCaml 5.0. -v Print the version number of the compiler and the location of the standard library directory, then exit. -verbose Print all external commands before they are executed, in particular invocations of the assembler, C compiler, and linker. Useful to debug C library problems. -version or -vnum Print the version number of the compiler in short form (e.g. 3.11.0), then exit. -w warning-list Enable, disable, or mark as fatal the warnings specified by the argument warning-list. Each warning can be enabled or disabled, and each warning can be fatal or non-fatal. If a warning is disabled, it isn’t displayed and doesn’t affect compilation in any way (even if it is fatal). If a warning is enabled, it is displayed normally by the compiler whenever the source code triggers it. If it is enabled and fatal, the compiler will also stop with an error after displaying it. The warning-list argument is a sequence of warning specifiers, with no separators between them. A warning specifier is one of the following: +num Enable warning number num. -num Disable warning number num. @num Enable and mark as fatal warning number num. +num1..num2 Enable warnings in the given range. -num1..num2 Disable warnings in the given range. @num1..num2 Enable and mark as fatal warnings in the given range. +letter Enable the set of warnings corresponding to letter. The letter may be uppercase or lowercase. -letter Disable the set of warnings corresponding to letter. The letter may be uppercase or lowercase. @letter Enable and mark as fatal the set of warnings corresponding to letter. The letter may be uppercase or lowercase. uppercase-letter Enable the set of warnings corresponding to uppercase-letter. lowercase-letter Disable the set of warnings corresponding to lowercase-letter. Alternatively, warning-list can specify a single warning using its mnemonic name (see below), as follows: +name Enable warning name. -name Disable warning name. @name Enable and mark as fatal warning name. Warning numbers, letters and names which are not currently defined are ignored. The warnings are as follows (the name following each number specifies the mnemonic for that warning). 1 comment-start Suspicious-looking start-of-comment mark. 2 comment-not-end Suspicious-looking end-of-comment mark. 3 Deprecated synonym for the ’deprecated’ alert. 4 fragile-match Fragile pattern matching: matching that will remain complete even if additional constructors are added to one of the variant types matched. 5 ignored-partial-application Partially applied function: expression whose result has function type and is ignored. 6 labels-omitted Label omitted in function application. 7 method-override Method overridden. 8 partial-match Partial match: missing cases in pattern-matching. 9 missing-record-field-pattern Missing fields in a record pattern. 10 non-unit-statement Expression on the left-hand side of a sequence that doesn’t have type unit (and that is not a function, see warning number 5). 11 redundant-case Redundant case in a pattern matching (unused match case). 12 redundant-subpat Redundant sub-pattern in a pattern-matching. 13 instance-variable-override Instance variable overridden. 14 illegal-backslash Illegal backslash escape in a string constant. 15 implicit-public-methods Private method made public implicitly. 16 unerasable-optional-argument Unerasable optional argument. 17 undeclared-virtual-method Undeclared virtual method. 18 not-principal Non-principal type. 19 non-principal-labels Type without principality. 20 ignored-extra-argument Unused function argument. 21 nonreturning-statement Non-returning statement. 22 preprocessor Preprocessor warning. 23 useless-record-with Useless record with clause. 24 bad-module-name Bad module name: the source file name is not a valid OCaml module name. 25 Ignored: now part of warning 8. 26 unused-var Suspicious unused variable: unused variable that is bound with let or as, and doesn’t start with an underscore (_) character. 27 unused-var-strict Innocuous unused variable: unused variable that is not bound with let nor as, and doesn’t start with an underscore (_) character. 28 wildcard-arg-to-constant-constr Wildcard pattern given as argument to a constant constructor. 29 eol-in-string Unescaped end-of-line in a string constant (non-portable code). 30 duplicate-definitions Two labels or constructors of the same name are defined in two mutually recursive types. 31 module-linked-twice A module is linked twice in the same executable. I gnored: now a hard error (since 5.1). 32 unused-value-declaration Unused value declaration. (since 4.00) 33 unused-open Unused open statement. (since 4.00) 34 unused-type-declaration Unused type declaration. (since 4.00) 35 unused-for-index Unused for-loop index. (since 4.00) 36 unused-ancestor Unused ancestor variable. (since 4.00) 37 unused-constructor Unused constructor. (since 4.00) 38 unused-extension Unused extension constructor. (since 4.00) 39 unused-rec-flag Unused rec flag. (since 4.00) 40 name-out-of-scope Constructor or label name used out of scope. (since 4.01) 41 ambiguous-name Ambiguous constructor or label name. (since 4.01) 42 disambiguated-name Disambiguated constructor or label name (compatibility warning). (since 4.01) 43 nonoptional-label Nonoptional label applied as optional. (since 4.01) 44 open-shadow-identifier Open statement shadows an already defined identifier. (since 4.01) 45 open-shadow-label-constructor Open statement shadows an already defined label or constructor. (since 4.01) 46 bad-env-variable Error in environment variable. (since 4.01) 47 attribute-payload Illegal attribute payload. (since 4.02) 48 eliminated-optional-arguments Implicit elimination of optional arguments. (since 4.02) 49 no-cmi-file Absent cmi file when looking up module alias. (since 4.02) 50 unexpected-docstring Unexpected documentation comment. (since 4.03) 51 wrong-tailcall-expectation Function call annotated with an incorrect @tailcall attribute. (since 4.03) 52 fragile-literal-pattern (see 13.5.3) Fragile constant pattern. (since 4.03) 53 misplaced-attribute Attribute cannot appear in this context. (since 4.03) 54 duplicated-attribute Attribute used more than once on an expression. (since 4.03) 55 inlining-impossible Inlining impossible. (since 4.03) 56 unreachable-case Unreachable case in a pattern-matching (based on type information). (since 4.03) 57 ambiguous-var-in-pattern-guard (see 13.5.4) Ambiguous or-pattern variables under guard. (since 4.03) 58 no-cmx-file Missing cmx file. (since 4.03) 59 flambda-assignment-to-non-mutable-value Assignment to non-mutable value. (since 4.03) 60 unused-module Unused module declaration. (since 4.04) 61 unboxable-type-in-prim-decl Unboxable type in primitive declaration. (since 4.04) 62 constraint-on-gadt Type constraint on GADT type declaration. (since 4.06) 63 erroneous-printed-signature Erroneous printed signature. (since 4.08) 64 unsafe-array-syntax-without-parsing -unsafe used with a preprocessor returning a syntax tree. (since 4.08) 65 redefining-unit Type declaration defining a new ’()’ constructor. (since 4.08) 66 unused-open-bang Unused open! statement. (since 4.08) 67 unused-functor-parameter Unused functor parameter. (since 4.10) 68 match-on-mutable-state-prevent-uncurry Pattern-matching depending on mutable state prevents the remaining arguments from being uncurried. (since 4.12) 69 unused-field Unused record field. (since 4.13) 70 missing-mli Missing interface file. (since 4.13) 71 unused-tmc-attribute Unused @tail_mod_cons attribute. (since 4.14) 72 tmc-breaks-tailcall A tail call is turned into a non-tail call by the @tail_mod_cons transformation. (since 4.14) 73 generative-application-expects-unit A generative functor is applied to an empty structure (struct end) rather than to (). (since 5.1) A all warnings C warnings 1, 2. D Alias for warning 3. E Alias for warning 4. F Alias for warning 5. K warnings 32, 33, 34, 35, 36, 37, 38, 39. L Alias for warning 6. M Alias for warning 7. P Alias for warning 8. R Alias for warning 9. S Alias for warning 10. U warnings 11, 12. V Alias for warning 13. X warnings 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30. Y Alias for warning 26. Z Alias for warning 27. The default setting is -w +a-4-6-7-9-27-29-32..42-44-45-48-50-60. It is displayed by ocamlopt -help. Note that warnings 5 and 10 are not always triggered, depending on the internals of the type checker. -warn-error warning-list Mark as fatal the warnings specified in the argument warning-list. The compiler will stop with an error when one of these warnings is emitted. The warning-list has the same meaning as for the -w option: a + sign (or an uppercase letter) marks the corresponding warnings as fatal, a - sign (or a lowercase letter) turns them back into non-fatal warnings, and a @ sign both enables and marks as fatal the corresponding warnings. Note: it is not recommended to use warning sets (i.e. letters) as arguments to -warn-error in production code, because this can break your build when future versions of OCaml add some new warnings. The default setting is -warn-error -a (no warning is fatal). -warn-help Show the description of all available warning numbers. -where Print the location of the standard library, then exit. -with-runtime Include the runtime system in the generated program. This is the default. -without-runtime The compiler does not include the runtime system (nor a reference to it) in the generated program; it must be supplied separately. - file Process file as a file name, even if it starts with a dash (-) character. -help or –help Display a short usage summary and exit. Options for the 64-bit x86 architecture The 64-bit code generator for Intel/AMD x86 processors (amd64 architecture) supports the following additional options: -fPIC Generate position-independent machine code. This is the default. -fno-PIC Generate position-dependent machine code. Contextual control of command-line options The compiler command line can be modified “from the outside” with the following mechanisms. These are experimental and subject to change. They should be used only for experimental and development work, not in released packages. OCAMLPARAM (environment variable) A set of arguments that will be inserted before or after the arguments from the command line. Arguments are specified in a comma-separated list of name=value pairs. A _ is used to specify the position of the command line arguments, i.e. a=x,_,b=y means that a=x should be executed before parsing the arguments, and b=y after. Finally, an alternative separator can be specified as the first character of the string, within the set :|; ,. ocaml_compiler_internal_params (file in the stdlib directory) A mapping of file names to lists of arguments that will be added to the command line (and OCAMLPARAM) arguments. 16.3 Common errors *=*=*=*=*=*=*=*=*=*= The error messages are almost identical to those of ocamlc. See section 13.4. 16.4 Running executables produced by ocamlopt *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Executables generated by ocamlopt are native, stand-alone executable files that can be invoked directly. They do not depend on the ocamlrun bytecode runtime system nor on dynamically-loaded C/OCaml stub libraries. During execution of an ocamlopt-generated executable, the following environment variables are also consulted: OCAMLRUNPARAM Same usage as in ocamlrun (see section 15.2), except that option l is ignored (the operating system’s stack size limit is used instead). CAMLRUNPARAM If OCAMLRUNPARAM is not found in the environment, then CAMLRUNPARAM will be used instead. If CAMLRUNPARAM is not found, then the default values will be used. 16.5 Compatibility with the bytecode compiler *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This section lists the known incompatibilities between the bytecode compiler and the native-code compiler. Except on those points, the two compilers should generate code that behave identically. - Signals are detected only when the program performs an allocation in the heap. That is, if a signal is delivered while in a piece of code that does not allocate, its handler will not be called until the next heap allocation. - On ARM and PowerPC processors (32 and 64 bits), fused multiply-add (FMA) instructions can be generated for a floating-point multiplication followed by a floating-point addition or subtraction, as in x *. y +. z. The FMA instruction avoids rounding the intermediate result x *. y, which is generally beneficial, but produces floating-point results that differ slightly from those produced by the bytecode interpreter. - The native-code compiler performs a number of optimizations that the bytecode compiler does not perform, especially when the Flambda optimizer is active. In particular, the native-code compiler identifies and eliminates “dead code”, i.e. computations that do not contribute to the results of the program. For example, << let _ = ignore M.f >> contains a reference to compilation unit M when compiled to bytecode. This reference forces M to be linked and its initialization code to be executed. The native-code compiler eliminates the reference to M, hence the compilation unit M may not be linked and executed. A workaround is to compile M with the -linkall flag so that it will always be linked and executed, even if not referenced. See also the Sys.opaque_identity function from the Sys standard library module. - Before 4.10, stack overflows, typically caused by excessively deep recursion, are not always turned into a Stack_overflow exception like with the bytecode compiler. The runtime system makes a best effort to trap stack overflows and raise the Stack_overflow exception, but sometimes it fails and a “segmentation fault” or another system fault occurs instead. Chapter 17  Lexer and parser generators (ocamllex, ocamlyacc) ***************************************************************** This chapter describes two program generators: ocamllex, that produces a lexical analyzer from a set of regular expressions with associated semantic actions, and ocamlyacc, that produces a parser from a grammar with associated semantic actions. These program generators are very close to the well-known lex and yacc commands that can be found in most C programming environments. This chapter assumes a working knowledge of lex and yacc: while it describes the input syntax for ocamllex and ocamlyacc and the main differences with lex and yacc, it does not explain the basics of writing a lexer or parser description in lex and yacc. Readers unfamiliar with lex and yacc are referred to “Compilers: principles, techniques, and tools” by Aho, Lam, Sethi and Ullman (Pearson, 2006), or “Lex & Yacc”, by Levine, Mason and Brown (O’Reilly, 1992). 17.1 Overview of ocamllex *=*=*=*=*=*=*=*=*=*=*=*=*=* The ocamllex command produces a lexical analyzer from a set of regular expressions with attached semantic actions, in the style of lex. Assuming the input file is lexer.mll, executing << ocamllex lexer.mll >> produces OCaml code for a lexical analyzer in file lexer.ml. This file defines one lexing function per entry point in the lexer definition. These functions have the same names as the entry points. Lexing functions take as argument a lexer buffer, and return the semantic attribute of the corresponding entry point. Lexer buffers are an abstract data type implemented in the standard library module Lexing. The functions Lexing.from_channel, Lexing.from_string and Lexing.from_function create lexer buffers that read from an input channel, a character string, or any reading function, respectively. (See the description of module Lexing in chapter 29.) When used in conjunction with a parser generated by ocamlyacc, the semantic actions compute a value belonging to the type token defined by the generated parsing module. (See the description of ocamlyacc below.) 17.1.1 Options ================ The following command-line options are recognized by ocamllex. -ml Output code that does not use OCaml’s built-in automata interpreter. Instead, the automaton is encoded by OCaml functions. This option improves performance when using the native compiler, but decreases it when using the bytecode compiler. -o output-file Specify the name of the output file produced by ocamllex. The default is the input file name with its extension replaced by .ml. -q Quiet mode. ocamllex normally outputs informational messages to standard output. They are suppressed if option -q is used. -v or -version Print version string and exit. -vnum Print short version number and exit. -help or –help Display a short usage summary and exit. 17.2 Syntax of lexer definitions *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The format of lexer definitions is as follows: << { header } let ident = regexp ... [refill { refill-handler }] rule entrypoint [arg_1... arg_n] = parse regexp { action } | ... | regexp { action } and entrypoint [arg_1... arg_n] = parse ... and ... { trailer } >> Comments are delimited by (* and *), as in OCaml. The parse keyword, can be replaced by the shortest keyword, with the semantic consequences explained below. Refill handlers are a recent (optional) feature introduced in 4.02, documented below in subsection 17.2.7. 17.2.1 Header and trailer =========================== The header and trailer sections are arbitrary OCaml text enclosed in curly braces. Either or both can be omitted. If present, the header text is copied as is at the beginning of the output file and the trailer text at the end. Typically, the header section contains the open directives required by the actions, and possibly some auxiliary functions used in the actions. 17.2.2 Naming regular expressions =================================== Between the header and the entry points, one can give names to frequently-occurring regular expressions. This is written let ident = regexp. In regular expressions that follow this declaration, the identifier ident can be used as shorthand for regexp. 17.2.3 Entry points ===================== The names of the entry points must be valid identifiers for OCaml values (starting with a lowercase letter). Similarly, the arguments arg_1... arg_n must be valid identifiers for OCaml. Each entry point becomes an OCaml function that takes n+1 arguments, the extra implicit last argument being of type Lexing.lexbuf. Characters are read from the Lexing.lexbuf argument and matched against the regular expressions provided in the rule, until a prefix of the input matches one of the rule. The corresponding action is then evaluated and returned as the result of the function. If several regular expressions match a prefix of the input, the “longest match” rule applies: the regular expression that matches the longest prefix of the input is selected. In case of tie, the regular expression that occurs earlier in the rule is selected. However, if lexer rules are introduced with the shortest keyword in place of the parse keyword, then the “shortest match” rule applies: the shortest prefix of the input is selected. In case of tie, the regular expression that occurs earlier in the rule is still selected. This feature is not intended for use in ordinary lexical analyzers, it may facilitate the use of ocamllex as a simple text processing tool. 17.2.4 Regular expressions ============================ The regular expressions are in the style of lex, with a more OCaml-like syntax. regexp ::= ... ' regular-char | escape-sequence ' A character constant, with the same syntax as OCaml character constants. Match the denoted character. _ (underscore) Match any character. eof Match the end of the lexer input. Note: On some systems, with interactive input, an end-of-file may be followed by more characters. However, ocamllex will not correctly handle regular expressions that contain eof followed by something else. " { string-character } " A string constant, with the same syntax as OCaml string constants. Match the corresponding sequence of characters. [ character-set ] Match any single character belonging to the given character set. Valid character sets are: single character constants ' c '; ranges of characters ' c_1 ' - ' c_2 ' (all characters between c_1 and c_2, inclusive); and the union of two or more character sets, denoted by concatenation. [ ^ character-set ] Match any single character not belonging to the given character set. regexp_1 # regexp_2 (difference of character sets) Regular expressions regexp_1 and regexp_2 must be character sets defined with [... ] (or a single character expression or underscore _). Match the difference of the two specified character sets. regexp * (repetition) Match the concatenation of zero or more strings that match regexp. regexp + (strict repetition) Match the concatenation of one or more strings that match regexp. regexp ? (option) Match the empty string, or a string matching regexp. regexp_1 | regexp_2 (alternative) Match any string that matches regexp_1 or regexp_2. If both regexp_1 and regexp_2 are character sets, this constructions produces another character set, obtained by taking the union of regexp_1 and regexp_2. regexp_1 regexp_2 (concatenation) Match the concatenation of two strings, the first matching regexp_1, the second matching regexp_2. ( regexp ) Match the same strings as regexp. ident Reference the regular expression bound to ident by an earlier let ident = regexp definition. regexp as ident Bind the substring matched by regexp to identifier ident. Concerning the precedences of operators, # has the highest precedence, followed by *, + and ?, then concatenation, then | (alternation), then as. 17.2.5 Actions ================ The actions are arbitrary OCaml expressions. They are evaluated in a context where the identifiers defined by using the as construct are bound to subparts of the matched string. Additionally, lexbuf is bound to the current lexer buffer. Some typical uses for lexbuf, in conjunction with the operations on lexer buffers provided by the Lexing standard library module, are listed below. Lexing.lexeme lexbuf Return the matched string. Lexing.lexeme_char lexbuf n Return the n^th character in the matched string. The first character corresponds to n = 0. Lexing.lexeme_start lexbuf Return the absolute position in the input text of the beginning of the matched string (i.e. the offset of the first character of the matched string). The first character read from the input text has offset 0. Lexing.lexeme_end lexbuf Return the absolute position in the input text of the end of the matched string (i.e. the offset of the first character after the matched string). The first character read from the input text has offset 0. entrypoint [exp_1... exp_n] lexbuf (Where entrypoint is the name of another entry point in the same lexer definition.) Recursively call the lexer on the given entry point. Notice that lexbuf is the last argument. Useful for lexing nested comments, for example. 17.2.6 Variables in regular expressions ========================================= The as construct is similar to “groups” as provided by numerous regular expression packages. The type of these variables can be string, char, string option or char option. We first consider the case of linear patterns, that is the case when all as bound variables are distinct. In regexp as ident, the type of ident normally is string (or string option) except when regexp is a character constant, an underscore, a string constant of length one, a character set specification, or an alternation of those. Then, the type of ident is char (or char option). Option types are introduced when overall rule matching does not imply matching of the bound sub-pattern. This is in particular the case of ( regexp as ident ) ? and of regexp_1 | ( regexp_2 as ident ). There is no linearity restriction over as bound variables. When a variable is bound more than once, the previous rules are to be extended as follows: - A variable is a char variable when all its occurrences bind char occurrences in the previous sense. - A variable is an option variable when the overall expression can be matched without binding this variable. For instance, in ('a' as x) | ( 'a' (_ as x) ) the variable x is of type char, whereas in ("ab" as x) | ( 'a' (_ as x) ? ) the variable x is of type string option. In some cases, a successful match may not yield a unique set of bindings. For instance the matching of aba by the regular expression (('a'|"ab") as x) (("ba"|'a') as y) may result in binding either x to "ab" and y to "a", or x to "a" and y to "ba". The automata produced ocamllex on such ambiguous regular expressions will select one of the possible resulting sets of bindings. The selected set of bindings is purposely left unspecified. 17.2.7 Refill handlers ======================== By default, when ocamllex reaches the end of its lexing buffer, it will silently call the refill_buff function of lexbuf structure and continue lexing. It is sometimes useful to be able to take control of refilling action; typically, if you use a library for asynchronous computation, you may want to wrap the refilling action in a delaying function to avoid blocking synchronous operations. Since OCaml 4.02, it is possible to specify a refill-handler, a function that will be called when refill happens. It is passed the continuation of the lexing, on which it has total control. The OCaml expression used as refill action should have a type that is an instance of << (Lexing.lexbuf -> 'a) -> Lexing.lexbuf -> 'a >> where the first argument is the continuation which captures the processing ocamllex would usually perform (refilling the buffer, then calling the lexing function again), and the result type that instantiates [’a] should unify with the result type of all lexing rules. As an example, consider the following lexer that is parametrized over an arbitrary monad: <<{ type token = EOL | INT of int | PLUS module Make (M : sig type 'a t val return: 'a -> 'a t val bind: 'a t -> ('a -> 'b t) -> 'b t val fail : string -> 'a t (* Set up lexbuf *) val on_refill : Lexing.lexbuf -> unit t end) = struct let refill_handler k lexbuf = M.bind (M.on_refill lexbuf) (fun () -> k lexbuf) } refill {refill_handler} rule token = parse | [' ' '\t'] { token lexbuf } | '\n' { M.return EOL } | ['0'-'9']+ as i { M.return (INT (int_of_string i)) } | '+' { M.return PLUS } | _ { M.fail "unexpected character" } { end } >> 17.2.8 Reserved identifiers ============================= All identifiers starting with __ocaml_lex are reserved for use by ocamllex; do not use any such identifier in your programs. 17.3 Overview of ocamlyacc *=*=*=*=*=*=*=*=*=*=*=*=*=*= The ocamlyacc command produces a parser from a context-free grammar specification with attached semantic actions, in the style of yacc. Assuming the input file is grammar.mly, executing << ocamlyacc options grammar.mly >> produces OCaml code for a parser in the file grammar.ml, and its interface in file grammar.mli. The generated module defines one parsing function per entry point in the grammar. These functions have the same names as the entry points. Parsing functions take as arguments a lexical analyzer (a function from lexer buffers to tokens) and a lexer buffer, and return the semantic attribute of the corresponding entry point. Lexical analyzer functions are usually generated from a lexer specification by the ocamllex program. Lexer buffers are an abstract data type implemented in the standard library module Lexing. Tokens are values from the concrete type token, defined in the interface file grammar.mli produced by ocamlyacc. 17.4 Syntax of grammar definitions *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Grammar definitions have the following format: << %{ header %} declarations %% rules %% trailer >> Comments are delimited by (* and *), as in OCaml. Additionally, comments can be delimited by /* and */, as in C, in the “declarations” and “rules” sections. C-style comments do not nest, but OCaml-style comments do. 17.4.1 Header and trailer =========================== The header and the trailer sections are OCaml code that is copied as is into file grammar.ml. Both sections are optional. The header goes at the beginning of the output file; it usually contains open directives and auxiliary functions required by the semantic actions of the rules. The trailer goes at the end of the output file. 17.4.2 Declarations ===================== Declarations are given one per line. They all start with a % sign. %token constr ... constr Declare the given symbols constr ... constr as tokens (terminal symbols). These symbols are added as constant constructors for the token concrete type. %token < typexpr > constr ... constr Declare the given symbols constr ... constr as tokens with an attached attribute of the given type. These symbols are added as constructors with arguments of the given type for the token concrete type. The typexpr part is an arbitrary OCaml type expression, except that all type constructor names must be fully qualified (e.g. Modname.typename) for all types except standard built-in types, even if the proper open directives (e.g. open Modname) were given in the header section. That’s because the header is copied only to the .ml output file, but not to the .mli output file, while the typexpr part of a %token declaration is copied to both. %start symbol ... symbol Declare the given symbols as entry points for the grammar. For each entry point, a parsing function with the same name is defined in the output module. Non-terminals that are not declared as entry points have no such parsing function. Start symbols must be given a type with the %type directive below. %type < typexpr > symbol ... symbol Specify the type of the semantic attributes for the given symbols. This is mandatory for start symbols only. Other nonterminal symbols need not be given types by hand: these types will be inferred when running the output files through the OCaml compiler (unless the -s option is in effect). The typexpr part is an arbitrary OCaml type expression, except that all type constructor names must be fully qualified, as explained above for %token. %left symbol ... symbol %right symbol ... symbol %nonassoc symbol ... symbol Associate precedences and associativities to the given symbols. All symbols on the same line are given the same precedence. They have higher precedence than symbols declared before in a %left, %right or %nonassoc line. They have lower precedence than symbols declared after in a %left, %right or %nonassoc line. The symbols are declared to associate to the left (%left), to the right (%right), or to be non-associative (%nonassoc). The symbols are usually tokens. They can also be dummy nonterminals, for use with the %prec directive inside the rules. The precedence declarations are used in the following way to resolve reduce/reduce and shift/reduce conflicts: - Tokens and rules have precedences. By default, the precedence of a rule is the precedence of its rightmost terminal. You can override this default by using the %prec directive in the rule. - A reduce/reduce conflict is resolved in favor of the first rule (in the order given by the source file), and ocamlyacc outputs a warning. - A shift/reduce conflict is resolved by comparing the precedence of the rule to be reduced with the precedence of the token to be shifted. If the precedence of the rule is higher, then the rule will be reduced; if the precedence of the token is higher, then the token will be shifted. - A shift/reduce conflict between a rule and a token with the same precedence will be resolved using the associativity: if the token is left-associative, then the parser will reduce; if the token is right-associative, then the parser will shift. If the token is non-associative, then the parser will declare a syntax error. - When a shift/reduce conflict cannot be resolved using the above method, then ocamlyacc will output a warning and the parser will always shift. 17.4.3 Rules ============== The syntax for rules is as usual: << nonterminal : symbol ... symbol { semantic-action } | ... | symbol ... symbol { semantic-action } ; >> Rules can also contain the %prec symbol directive in the right-hand side part, to override the default precedence and associativity of the rule with the precedence and associativity of the given symbol. Semantic actions are arbitrary OCaml expressions, that are evaluated to produce the semantic attribute attached to the defined nonterminal. The semantic actions can access the semantic attributes of the symbols in the right-hand side of the rule with the $ notation: $1 is the attribute for the first (leftmost) symbol, $2 is the attribute for the second symbol, etc. The rules may contain the special symbol error to indicate resynchronization points, as in yacc. Actions occurring in the middle of rules are not supported. Nonterminal symbols are like regular OCaml symbols, except that they cannot end with ' (single quote). 17.4.4 Error handling ======================= Error recovery is supported as follows: when the parser reaches an error state (no grammar rules can apply), it calls a function named parse_error with the string "syntax error" as argument. The default parse_error function does nothing and returns, thus initiating error recovery (see below). The user can define a customized parse_error function in the header section of the grammar file. The parser also enters error recovery mode if one of the grammar actions raises the Parsing.Parse_error exception. In error recovery mode, the parser discards states from the stack until it reaches a place where the error token can be shifted. It then discards tokens from the input until it finds three successive tokens that can be accepted, and starts processing with the first of these. If no state can be uncovered where the error token can be shifted, then the parser aborts by raising the Parsing.Parse_error exception. Refer to documentation on yacc for more details and guidance in how to use error recovery. 17.5 Options *=*=*=*=*=*=*= The ocamlyacc command recognizes the following options: -bprefix Name the output files prefix.ml, prefix.mli, prefix.output, instead of the default naming convention. -q This option has no effect. -v Generate a description of the parsing tables and a report on conflicts resulting from ambiguities in the grammar. The description is put in file grammar.output. -version Print version string and exit. -vnum Print short version number and exit. - Read the grammar specification from standard input. The default output file names are stdin.ml and stdin.mli. – file Process file as the grammar specification, even if its name starts with a dash (-) character. This option must be the last on the command line. At run-time, the ocamlyacc-generated parser can be debugged by setting the p option in the OCAMLRUNPARAM environment variable (see section 15.2). This causes the pushdown automaton executing the parser to print a trace of its action (tokens shifted, rules reduced, etc). The trace mentions rule numbers and state numbers that can be interpreted by looking at the file grammar.output generated by ocamlyacc -v. 17.6 A complete example *=*=*=*=*=*=*=*=*=*=*=*=* The all-time favorite: a desk calculator. This program reads arithmetic expressions on standard input, one per line, and prints their values. Here is the grammar definition: << /* File parser.mly */ %token INT %token PLUS MINUS TIMES DIV %token LPAREN RPAREN %token EOL %left PLUS MINUS /* lowest precedence */ %left TIMES DIV /* medium precedence */ %nonassoc UMINUS /* highest precedence */ %start main /* the entry point */ %type main %% main: expr EOL { $1 } ; expr: INT { $1 } | LPAREN expr RPAREN { $2 } | expr PLUS expr { $1 + $3 } | expr MINUS expr { $1 - $3 } | expr TIMES expr { $1 * $3 } | expr DIV expr { $1 / $3 } | MINUS expr %prec UMINUS { - $2 } ; >> Here is the definition for the corresponding lexer: << (* File lexer.mll *) { open Parser (* The type token is defined in parser.mli *) exception Eof } rule token = parse [' ' '\t'] { token lexbuf } (* skip blanks *) | ['\n' ] { EOL } | ['0'-'9']+ as lxm { INT(int_of_string lxm) } | '+' { PLUS } | '-' { MINUS } | '*' { TIMES } | '/' { DIV } | '(' { LPAREN } | ')' { RPAREN } | eof { raise Eof } >> Here is the main program, that combines the parser with the lexer: << (* File calc.ml *) let _ = try let lexbuf = Lexing.from_channel stdin in while true do let result = Parser.main Lexer.token lexbuf in print_int result; print_newline(); flush stdout done with Lexer.Eof -> exit 0 >> To compile everything, execute: << ocamllex lexer.mll # generates lexer.ml ocamlyacc parser.mly # generates parser.ml and parser.mli ocamlc -c parser.mli ocamlc -c lexer.ml ocamlc -c parser.ml ocamlc -c calc.ml ocamlc -o calc lexer.cmo parser.cmo calc.cmo >> 17.7 Common errors *=*=*=*=*=*=*=*=*=*= ocamllex: transition table overflow, automaton is too big The deterministic automata generated by ocamllex are limited to at most 32767 transitions. The message above indicates that your lexer definition is too complex and overflows this limit. This is commonly caused by lexer definitions that have separate rules for each of the alphabetic keywords of the language, as in the following example. <> To keep the generated automata small, rewrite those definitions with only one general “identifier” rule, followed by a hashtable lookup to separate keywords from identifiers: <<{ let keyword_table = Hashtbl.create 53 let _ = List.iter (fun (kwd, tok) -> Hashtbl.add keyword_table kwd tok) [ "keyword1", KWD1; "keyword2", KWD2; ... "keyword100", KWD100 ] } rule token = parse ['A'-'Z' 'a'-'z'] ['A'-'Z' 'a'-'z' '0'-'9' '_'] * as id { try Hashtbl.find keyword_table id with Not_found -> IDENT id } >> ocamllex: Position memory overflow, too many bindings The deterministic automata generated by ocamllex maintain a table of positions inside the scanned lexer buffer. The size of this table is limited to at most 255 cells. This error should not show up in normal situations. ocamlyacc: concurrency safety Parsers generated by ocamlyacc are not thread-safe. Those parsers rely on an internal work state which is shared by all ocamlyacc generated parsers. The menhir (1) parser generator is a better option if you want thread-safe parsers. --------------------------------------- (1) https://cambium.inria.fr/~fpottier/menhir/ Chapter 18  Dependency generator (ocamldep) *********************************************** The ocamldep command scans a set of OCaml source files (.ml and .mli files) for references to external compilation units, and outputs dependency lines in a format suitable for the make utility. This ensures that make will compile the source files in the correct order, and recompile those files that need to when a source file is modified. The typical usage is: << ocamldep options *.mli *.ml > .depend >> where *.mli *.ml expands to all source files in the current directory and .depend is the file that should contain the dependencies. (See below for a typical Makefile.) Dependencies are generated both for compiling with the bytecode compiler ocamlc and with the native-code compiler ocamlopt. 18.1 Options *=*=*=*=*=*=*= The following command-line options are recognized by ocamldep. -absname Show absolute filenames in error messages. -all Generate dependencies on all required files, rather than assuming implicit dependencies. -allow-approx Allow falling back on a lexer-based approximation when parsing fails. -args filename Read additional newline-terminated command line arguments from filename. -args0 filename Read additional null character terminated command line arguments from filename. -as-map For the following files, do not include delayed dependencies for module aliases. This option assumes that they are compiled using options -no-alias-deps -w -49, and that those files or their interface are passed with the -map option when computing dependencies for other files. Note also that for dependencies to be correct in the implementation of a map file, its interface should not coerce any of the aliases it contains. -debug-map Dump the delayed dependency map for each map file. -I directory Add the given directory to the list of directories searched for source files. If a source file foo.ml mentions an external compilation unit Bar, a dependency on that unit’s interface bar.cmi is generated only if the source for bar is found in the current directory or in one of the directories specified with -I. Otherwise, Bar is assumed to be a module from the standard library, and no dependencies are generated. For programs that span multiple directories, it is recommended to pass ocamldep the same -I options that are passed to the compiler. -H directory Behaves identically to -I, except that the -H directories are searched last. This flag is included to make it easier to invoke ocamldep with the same options as the compiler, where -H is used for transitive dependencies that the program should not directly mention. -nocwd Do not add current working directory to the list of include directories. -impl file Process file as a .ml file. -intf file Process file as a .mli file. -map file Read and propagate the delayed dependencies for module aliases in file, so that the following files will depend on the exported aliased modules if they use them. See the example below. -ml-synonym .ext Consider the given extension (with leading dot) to be a synonym for .ml. -mli-synonym .ext Consider the given extension (with leading dot) to be a synonym for .mli. -modules Output raw dependencies of the form << filename: Module1 Module2 ... ModuleN >> where Module1, ..., ModuleN are the names of the compilation units referenced within the file filename, but these names are not resolved to source file names. Such raw dependencies cannot be used by make, but can be post-processed by other tools such as Omake. -native Generate dependencies for a pure native-code program (no bytecode version). When an implementation file (.ml file) has no explicit interface file (.mli file), ocamldep generates dependencies on the bytecode compiled file (.cmo file) to reflect interface changes. This can cause unnecessary bytecode recompilations for programs that are compiled to native-code only. The flag -native causes dependencies on native compiled files (.cmx) to be generated instead of on .cmo files. (This flag makes no difference if all source files have explicit .mli interface files.) -one-line Output one line per file, regardless of the length. -open module Assume that module module is opened before parsing each of the following files. -pp command Cause ocamldep to call the given command as a preprocessor for each source file. -ppx command Pipe abstract syntax trees through preprocessor command. -shared Generate dependencies for native plugin files (.cmxs) in addition to native compiled files (.cmx). -slash Under Windows, use a forward slash (/) as the path separator instead of the usual backward slash (\). Under Unix, this option does nothing. -sort Sort files according to their dependencies. -version Print version string and exit. -vnum Print short version number and exit. -help or –help Display a short usage summary and exit. 18.2 A typical Makefile *=*=*=*=*=*=*=*=*=*=*=*=* Here is a template Makefile for a OCaml program. < .depend include .depend >> If you use module aliases to give shorter names to modules, you need to change the above definitions. Assuming that your map file is called mylib.mli, here are minimal modifications. < .depend >> Note that in this case you should not compute dependencies for mylib.mli together with the other files, hence the need to pass explicitly the list of files to process. If mylib.mli itself has dependencies, you should compute them using -as-map. Chapter 19  The documentation generator (ocamldoc) ****************************************************** This chapter describes OCamldoc, a tool that generates documentation from special comments embedded in source files. The comments used by OCamldoc are of the form (**...*) and follow the format described in section 19.2. OCamldoc can produce documentation in various formats: HTML, LaTeX, TeXinfo, Unix man pages, and dot dependency graphs. Moreover, users can add their own custom generators, as explained in section 19.3. In this chapter, we use the word element to refer to any of the following parts of an OCaml source file: a type declaration, a value, a module, an exception, a module type, a type constructor, a record field, a class, a class type, a class method, a class value or a class inheritance clause. 19.1 Usage *=*=*=*=*=*= 19.1.1 Invocation =================== OCamldoc is invoked via the command ocamldoc, as follows: << ocamldoc options sourcefiles >> Options for choosing the output format -------------------------------------- The following options determine the format for the generated documentation. -html Generate documentation in HTML default format. The generated HTML pages are stored in the current directory, or in the directory specified with the -d option. You can customize the style of the generated pages by editing the generated style.css file, or by providing your own style sheet using option -css-style. The file style.css is not generated if it already exists or if -css-style is used. -latex Generate documentation in LaTeX default format. The generated LaTeX document is saved in file ocamldoc.out, or in the file specified with the -o option. The document uses the style file ocamldoc.sty. This file is generated when using the -latex option, if it does not already exist. You can change this file to customize the style of your LaTeX documentation. -texi Generate documentation in TeXinfo default format. The generated LaTeX document is saved in file ocamldoc.out, or in the file specified with the -o option. -man Generate documentation as a set of Unix man pages. The generated pages are stored in the current directory, or in the directory specified with the -d option. -dot Generate a dependency graph for the toplevel modules, in a format suitable for displaying and processing by dot. The dot tool is available from https://graphviz.org/. The textual representation of the graph is written to the file ocamldoc.out, or to the file specified with the -o option. Use dot ocamldoc.out to display it. -g file.cm[o,a,xs] Dynamically load the given file, which defines a custom documentation generator. See section 19.4.1. This option is supported by the ocamldoc command (to load .cmo and .cma files) and by its native-code version ocamldoc.opt (to load .cmxs files). If the given file is a simple one and does not exist in the current directory, then ocamldoc looks for it in the custom generators default directory, and in the directories specified with optional -i options. -customdir Display the custom generators default directory. -i directory Add the given directory to the path where to look for custom generators. General options --------------- -d dir Generate files in directory dir, rather than the current directory. -dump file Dump collected information into file. This information can be read with the -load option in a subsequent invocation of ocamldoc. -hide modules Hide the given complete module names in the generated documentation. modules is a list of complete module names separated by ’,’, without blanks. For instance: Stdlib,M2.M3. -inv-merge-ml-mli Reverse the precedence of implementations and interfaces when merging. All elements in implementation files are kept, and the -m option indicates which parts of the comments in interface files are merged with the comments in implementation files. -keep-code Always keep the source code for values, methods and instance variables, when available. -load file Load information from file, which has been produced by ocamldoc -dump. Several -load options can be given. -m flags Specify merge options between interfaces and implementations. (see section 19.1.2 for details). flags can be one or several of the following characters: d merge description a merge @author v merge @version l merge @see s merge @since b merge @before o merge @deprecated p merge @param e merge @raise r merge @return A merge everything -no-custom-tags Do not allow custom @-tags (see section 19.2.5). -no-stop Keep elements placed after/between the (**/**) special comment(s) (see section 19.2). -o file Output the generated documentation to file instead of ocamldoc.out. This option is meaningful only in conjunction with the -latex, -texi, or -dot options. -pp command Pipe sources through preprocessor command. -impl filename Process the file filename as an implementation file, even if its extension is not .ml. -intf filename Process the file filename as an interface file, even if its extension is not .mli. -text filename Process the file filename as a text file, even if its extension is not .txt. -sort Sort the list of top-level modules before generating the documentation. -stars Remove blank characters until the first asterisk (’*’) in each line of comments. -t title Use title as the title for the generated documentation. -intro file Use content of file as ocamldoc text to use as introduction (HTML, LaTeX and TeXinfo only). For HTML, the file is used to create the whole index.html file. -v Verbose mode. Display progress information. -version Print version string and exit. -vnum Print short version number and exit. -warn-error Treat Ocamldoc warnings as errors. -hide-warnings Do not print OCamldoc warnings. -help or –help Display a short usage summary and exit. Type-checking options --------------------- OCamldoc calls the OCaml type-checker to obtain type information. The following options impact the type-checking phase. They have the same meaning as for the ocamlc and ocamlopt commands. -I directory Add directory to the list of directories search for compiled interface files (.cmi files). -H directory Like -I, but the -H directories are searched last and the program may not directly refer to the modules added to the search path this way. -nolabels Ignore non-optional labels in types. -rectypes Allow arbitrary recursive types. (See the -rectypes option to ocamlc.) Options for generating HTML pages --------------------------------- The following options apply in conjunction with the -html option: -all-params Display the complete list of parameters for functions and methods. -charset charset Add information about character encoding being charset (default is iso-8859-1). -colorize-code Colorize the OCaml code enclosed in [ ] and {[ ]}, using colors to emphasize keywords, etc. If the code fragments are not syntactically correct, no color is added. -css-style filename Use filename as the Cascading Style Sheet file. -index-only Generate only index files. -short-functors Use a short form to display functors: << module M : functor (A:Module) -> functor (B:Module2) -> sig .. end >> is displayed as: << module M (A:Module) (B:Module2) : sig .. end >> Options for generating LaTeX files ---------------------------------- The following options apply in conjunction with the -latex option: -latex-value-prefix prefix Give a prefix to use for the labels of the values in the generated LaTeX document. The default prefix is the empty string. You can also use the options -latex-type-prefix, -latex-exception-prefix, -latex-module-prefix, -latex-module-type-prefix, -latex-class-prefix, -latex-class-type-prefix, -latex-attribute-prefix and -latex-method-prefix. These options are useful when you have, for example, a type and a value with the same name. If you do not specify prefixes, LaTeX will complain about multiply defined labels. -latextitle n,style Associate style number n to the given LaTeX sectioning command style, e.g. section or subsection. (LaTeX only.) This is useful when including the generated document in another LaTeX document, at a given sectioning level. The default association is 1 for section, 2 for subsection, 3 for subsubsection, 4 for paragraph and 5 for subparagraph. -noheader Suppress header in generated documentation. -notoc Do not generate a table of contents. -notrailer Suppress trailer in generated documentation. -sepfiles Generate one .tex file per toplevel module, instead of the global ocamldoc.out file. Options for generating TeXinfo files ------------------------------------ The following options apply in conjunction with the -texi option: -esc8 Escape accented characters in Info files. -info-entry Specify Info directory entry. -info-section Specify section of Info directory. -noheader Suppress header in generated documentation. -noindex Do not build index for Info files. -notrailer Suppress trailer in generated documentation. Options for generating dot graphs --------------------------------- The following options apply in conjunction with the -dot option: -dot-colors colors Specify the colors to use in the generated dot code. When generating module dependencies, ocamldoc uses different colors for modules, depending on the directories in which they reside. When generating types dependencies, ocamldoc uses different colors for types, depending on the modules in which they are defined. colors is a list of color names separated by ’,’, as in Red,Blue,Green. The available colors are the ones supported by the dot tool. -dot-include-all Include all modules in the dot output, not only modules given on the command line or loaded with the -load option. -dot-reduce Perform a transitive reduction of the dependency graph before outputting the dot code. This can be useful if there are a lot of transitive dependencies that clutter the graph. -dot-types Output dot code describing the type dependency graph instead of the module dependency graph. Options for generating man files -------------------------------- The following options apply in conjunction with the -man option: -man-mini Generate man pages only for modules, module types, classes and class types, instead of pages for all elements. -man-suffix suffix Set the suffix used for generated man filenames. Default is ’3o’, as in List.3o. -man-section section Set the section number used for generated man filenames. Default is ’3’. 19.1.2 Merging of module information ====================================== Information on a module can be extracted either from the .mli or .ml file, or both, depending on the files given on the command line. When both .mli and .ml files are given for the same module, information extracted from these files is merged according to the following rules: - Only elements (values, types, classes, ...) declared in the .mli file are kept. In other terms, definitions from the .ml file that are not exported in the .mli file are not documented. - Descriptions of elements and descriptions in @-tags are handled as follows. If a description for the same element or in the same @-tag of the same element is present in both files, then the description of the .ml file is concatenated to the one in the .mli file, if the corresponding -m flag is given on the command line. If a description is present in the .ml file and not in the .mli file, the .ml description is kept. In either case, all the information given in the .mli file is kept. 19.1.3 Coding rules ===================== The following rules must be respected in order to avoid name clashes resulting in cross-reference errors: - In a module, there must not be two modules, two module types or a module and a module type with the same name. In the default HTML generator, modules ab and AB will be printed to the same file on case insensitive file systems. - In a module, there must not be two classes, two class types or a class and a class type with the same name. - In a module, there must not be two values, two types, or two exceptions with the same name. - Values defined in tuple, as in let (x,y,z) = (1,2,3) are not kept by OCamldoc. - Avoid the following construction: << open Foo (* which has a module Bar with a value x *) module Foo = struct module Bar = struct let x = 1 end end let dummy = Bar.x >> In this case, OCamldoc will associate Bar.x to the x of module Foo defined just above, instead of to the Bar.x defined in the opened module Foo. 19.2 Syntax of documentation comments *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Comments containing documentation material are called special comments and are written between (** and *). Special comments must start exactly with (**. Comments beginning with ( and more than two * are ignored. 19.2.1 Placement of documentation comments ============================================ OCamldoc can associate comments to some elements of the language encountered in the source files. The association is made according to the locations of comments with respect to the language elements. The locations of comments in .mli and .ml files are different. Comments in .mli files ---------------------- A special comment is associated to an element if it is placed before or after the element. A special comment before an element is associated to this element if : - There is no blank line or another special comment between the special comment and the element. However, a regular comment can occur between the special comment and the element. - The special comment is not already associated to the previous element. - The special comment is not the first one of a toplevel module. A special comment after an element is associated to this element if there is no blank line or comment between the special comment and the element. There are two exceptions: for constructors and record fields in type definitions, the associated comment can only be placed after the constructor or field definition, without blank lines or other comments between them. The special comment for a constructor with another constructor following must be placed before the ’|’ character separating the two constructors. The following sample interface file foo.mli illustrates the placement rules for comments in .mli files. << (** The first special comment of the file is the comment associated with the whole module.*) (** Special comments can be placed between elements and are kept by the OCamldoc tool, but are not associated to any element. @-tags in these comments are ignored.*) (*******************************************************************) (** Comments like the one above, with more than two asterisks, are ignored. *) (** The comment for function f. *) val f : int -> int -> int (** The continuation of the comment for function f. *) (** Comment for exception My_exception, even with a simple comment between the special comment and the exception.*) (* Hello, I'm a simple comment :-) *) exception My_exception of (int -> int) * int (** Comment for type weather *) type weather = | Rain of int (** The comment for constructor Rain *) | Sun (** The comment for constructor Sun *) (** Comment for type weather2 *) type weather2 = | Rain of int (** The comment for constructor Rain *) | Sun (** The comment for constructor Sun *) (** I can continue the comment for type weather2 here because there is already a comment associated to the last constructor.*) (** The comment for type my_record *) type my_record = { foo : int ; (** Comment for field foo *) bar : string ; (** Comment for field bar *) } (** Continuation of comment for type my_record *) (** Comment for foo *) val foo : string (** This comment is associated to foo and not to bar. *) val bar : string (** This comment is associated to bar. *) (** The comment for class my_class *) class my_class : object (** A comment to describe inheritance from cl *) inherit cl (** The comment for attribute tutu *) val mutable tutu : string (** The comment for attribute toto. *) val toto : int (** This comment is not attached to titi since there is a blank line before titi, but is kept as a comment in the class. *) val titi : string (** Comment for method toto *) method toto : string (** Comment for method m *) method m : float -> int end (** The comment for the class type my_class_type *) class type my_class_type = object (** The comment for variable x. *) val mutable x : int (** The comment for method m. *) method m : int -> int end (** The comment for module Foo *) module Foo : sig (** The comment for x *) val x : int (** A special comment that is kept but not associated to any element *) end (** The comment for module type my_module_type. *) module type my_module_type = sig (** The comment for value x. *) val x : int (** The comment for module M. *) module M : sig (** The comment for value y. *) val y : int (* ... *) end end >> Comments in .ml files --------------------- A special comment is associated to an element if it is placed before the element and there is no blank line between the comment and the element. Meanwhile, there can be a simple comment between the special comment and the element. There are two exceptions, for constructors and record fields in type definitions, whose associated comment must be placed after the constructor or field definition, without blank line between them. The special comment for a constructor with another constructor following must be placed before the ’|’ character separating the two constructors. The following example of file toto.ml shows where to place comments in a .ml file. << (** The first special comment of the file is the comment associated to the whole module. *) (** The comment for function f *) let f x y = x + y (** This comment is not attached to any element since there is another special comment just before the next element. *) (** Comment for exception My_exception, even with a simple comment between the special comment and the exception.*) (* A simple comment. *) exception My_exception of (int -> int) * int (** Comment for type weather *) type weather = | Rain of int (** The comment for constructor Rain *) | Sun (** The comment for constructor Sun *) (** The comment for type my_record *) type my_record = { foo : int ; (** Comment for field foo *) bar : string ; (** Comment for field bar *) } (** The comment for class my_class *) class my_class = object (** A comment to describe inheritance from cl *) inherit cl (** The comment for the instance variable tutu *) val mutable tutu = "tutu" (** The comment for toto *) val toto = 1 val titi = "titi" (** Comment for method toto *) method toto = tutu ^ "!" (** Comment for method m *) method m (f : float) = 1 end (** The comment for class type my_class_type *) class type my_class_type = object (** The comment for the instance variable x. *) val mutable x : int (** The comment for method m. *) method m : int -> int end (** The comment for module Foo *) module Foo = struct (** The comment for x *) let x = 0 (** A special comment in the class, but not associated to any element. *) end (** The comment for module type my_module_type. *) module type my_module_type = sig (* Comment for value x. *) val x : int (* ... *) end >> 19.2.2 The Stop special comment ================================= The special comment (**/**) tells OCamldoc to discard elements placed after this comment, up to the end of the current class, class type, module or module type, or up to the next stop comment. For instance: << class type foo = object (** comment for method m *) method m : string (**/**) (** This method won't appear in the documentation *) method bar : int end (** This value appears in the documentation, since the Stop special comment in the class does not affect the parent module of the class.*) val foo : string (**/**) (** The value bar does not appear in the documentation.*) val bar : string (**/**) (** The type t appears since in the documentation since the previous stop comment toggled off the "no documentation mode". *) type t = string >> The -no-stop option to ocamldoc causes the Stop special comments to be ignored. 19.2.3 Syntax of documentation comments ========================================= The inside of documentation comments (**...*) consists of free-form text with optional formatting annotations, followed by optional tags giving more specific information about parameters, version, authors, ... The tags are distinguished by a leading @ character. Thus, a documentation comment has the following shape: <<(** The comment begins with a description, which is text formatted according to the rules described in the next section. The description continues until the first non-escaped '@' character. @author Mr Smith @param x description for parameter x *) >> Some elements support only a subset of all @-tags. Tags that are not relevant to the documented element are simply ignored. For instance, all tags are ignored when documenting type constructors, record fields, and class inheritance clauses. Similarly, a @param tag on a class instance variable is ignored. At last, (**) is the empty documentation comment. 19.2.4 Text formatting ======================== Here is the BNF grammar for the simple markup language used to format text descriptions. + text ::= {text-element} + inline-text ::= {inline-text-element} text-element ::= | inline-text-element | blank-line force a new line. inline-text-element ::= | { { 0 ... 9 }^+ inline-text } format text as a section header; the integer following { indicates the sectioning level. | { { 0 ... 9 }^+ : label inline-text } same, but also associate the name label to the current point. This point can be referenced by its fully-qualified label in a {! command, just like any other element. | {b inline-text } set text in bold. | {i inline-text } set text in italic. | {e inline-text } emphasize text. | {C inline-text } center text. | {L inline-text } left align text. | {R inline-text } right align text. | {ul list } build a list. | {ol list } build an enumerated list. | {{: string } inline-text } put a link to the given address (given as string) on the given text. | [ string ] set the given string in source code style. | {[ string ]} set the given string in preformatted source code style. | {v string v} set the given string in verbatim style. | {% string %} target-specific content (LaTeX code by default, see details in 19.2.4.4) | {! string } insert a cross-reference to an element (see section 19.2.4.2 for the syntax of cross-references). | {{! string } inline-text } insert a cross-reference with the given text. | {!modules: string string ... } insert an index table for the given module names. Used in HTML only. | {!indexlist} insert a table of links to the various indexes (types, values, modules, ...). Used in HTML only. | {^ inline-text } set text in superscript. | {_ inline-text } set text in subscript. | escaped-string typeset the given string as is; special characters (’{’, ’}’, ’[’, ’]’ and ’@’) must be escaped by a ’\’ 19.2.4.1 List formatting -------------------------- list ::= + | { {- inline-text } } + | { {li inline-text } } A shortcut syntax exists for lists and enumerated lists: <<(** Here is a {b list} - item 1 - item 2 - item 3 The list is ended by the blank line.*) >> is equivalent to: <<(** Here is a {b list} {ul {- item 1} {- item 2} {- item 3}} The list is ended by the blank line.*) >> The same shortcut is available for enumerated lists, using ’+’ instead of ’-’. Note that only one list can be defined by this shortcut in nested lists. 19.2.4.2 Cross-reference formatting ------------------------------------- Cross-references are fully qualified element names, as in the example {!Foo.Bar.t}. This is an ambiguous reference as it may designate a type name, a value name, a class name, etc. It is possible to make explicit the intended syntactic class, using {!type:Foo.Bar.t} to designate a type, and {!val:Foo.Bar.t} a value of the same name. The list of possible syntactic class is as follows: tag syntactic class --------------------------------- module: module modtype: module type class: class classtype: class type val: value type: type exception: exception attribute: attribute method: class method section: ocamldoc section const: variant constructor recfield: record field In the case of variant constructors or record fields, the constructor or field name should be preceded by the name of the corresponding type to avoid the ambiguity of several types having the same constructor names. For example, the constructor Node of the type tree will be referenced as {!tree.Node} or {!const:tree.Node}, or possibly {!Mod1.Mod2.tree.Node} from outside the module. 19.2.4.3 First sentence ------------------------- In the description of a value, type, exception, module, module type, class or class type, the first sentence is sometimes used in indexes, or when just a part of the description is needed. The first sentence is composed of the first characters of the description, until - the first dot followed by a blank, or - the first blank line outside of the following text formatting : {ul list } , {ol list } , [ string ] , {[ string ]} , {v string v} , {% string %} , {! string } , {^ text } , {_ text } . 19.2.4.4 Target-specific formatting ------------------------------------- The content inside {%foo: ... %} is target-specific and will be interpreted only by the backend foo, and ignored by other backends. The backends of the distribution are latex, html, texi and man. If no target is specified (syntax {% ... %}), latex is chosen by default. Custom generators may support their own target prefix. 19.2.4.5 Recognized HTML tags ------------------------------- The HTML tags .., .., ..,
    ..
,
    ..
,
  • ..
    • ,
    ..
    and .. can be used instead of, respectively, {b ..} , [..] , {i ..} , {ul ..} , {ol ..} , {li ..} , {C ..} and {[0-9] ..}. 19.2.5 Documentation tags (@-tags) ==================================== Predefined tags --------------- The following table gives the list of predefined @-tags, with their syntax and meaning. ------------------------------------------------- | @author string|The author of the element. One | | |author per @author tag. There | | |may be several @author tags for| | |the same element. | ------------------------------------------------- | @deprecated |The text should describe when | |text |the element was deprecated, | | |what to use as a replacement, | | |and possibly the reason for | | |deprecation. | ------------------------------------------------- | @param id |Associate the given description| |text |(text) to the given parameter | | |name id. This tag is used for | | |functions, methods, classes and| | |functors. | ------------------------------------------------- | @raise Exc |Explain that the element may | |text |raise the exception Exc. | ------------------------------------------------- | @return text |Describe the return value and | | |its possible values. This tag | | |is used for functions and | | |methods. | ------------------------------------------------- | @see < URL > |Add a reference to the URL with| |text |the given text as comment. | ------------------------------------------------- | @see |Add a reference to the given | |'filename' text|file name (written between | | |single quotes), with the given | | |text as comment. | ------------------------------------------------- | @see |Add a reference to the given | |"document-name"|document name (written between | |text |double quotes), with the given | | |text as comment. | ------------------------------------------------- | @since string|Indicate when the element was | | |introduced. | ------------------------------------------------- | @before |Associate the given description| |version text |(text) to the given version in | | |order to document compatibility| | |issues. | ------------------------------------------------- | @version |The version number for the | |string |element. | ------------------------------------------------- Custom tags ----------- You can use custom tags in the documentation comments, but they will have no effect if the generator used does not handle them. To use a custom tag, for example foo, just put @foo with some text in your comment, as in: <<(** My comment to show you a custom tag. @foo this is the text argument to the [foo] custom tag. *) >> To handle custom tags, you need to define a custom generator, as explained in section 19.3.2. 19.3 Custom generators *=*=*=*=*=*=*=*=*=*=*=*= OCamldoc operates in two steps: 1. analysis of the source files; 2. generation of documentation, through a documentation generator, which is an object of class Odoc_args.class_generator. Users can provide their own documentation generator to be used during step 2 instead of the default generators. All the information retrieved during the analysis step is available through the Odoc_info module, which gives access to all the types and functions representing the elements found in the given modules, with their associated description. The files you can use to define custom generators are installed in the ocamldoc sub-directory of the OCaml standard library. 19.3.1 The generator modules ============================== The type of a generator module depends on the kind of generated documentation. Here is the list of generator module types, with the name of the generator class in the module : - for HTML : Odoc_html.Html_generator (class html), - for LaTeX : Odoc_latex.Latex_generator (class latex), - for TeXinfo : Odoc_texi.Texi_generator (class texi), - for man pages : Odoc_man.Man_generator (class man), - for graphviz (dot) : Odoc_dot.Dot_generator (class dot), - for other kinds : Odoc_gen.Base (class generator). That is, to define a new generator, one must implement a module with the expected signature, and with the given generator class, providing the generate method as entry point to make the generator generates documentation for a given list of modules : << method generate : Odoc_info.Module.t_module list -> unit >> This method will be called with the list of analysed and possibly merged Odoc_info.t_module structures. It is recommended to inherit from the current generator of the same kind as the one you want to define. Doing so, it is possible to load various custom generators to combine improvements brought by each one. This is done using first class modules (see chapter 12.5). The easiest way to define a custom generator is the following this example, here extending the current HTML generator. We don’t have to know if this is the original HTML generator defined in ocamldoc or if it has been extended already by a previously loaded custom generator : <> To know which methods to override and/or which methods are available, have a look at the different base implementations, depending on the kind of generator you are extending : - for HTML : odoc_html.ml (1), - for LaTeX : odoc_latex.ml (2), - for TeXinfo : odoc_texi.ml (3), - for man pages : odoc_man.ml (4), - for graphviz (dot) : odoc_dot.ml (5). 19.3.2 Handling custom tags ============================= Making a custom generator handle custom tags (see 19.2.5) is very simple. For HTML -------- Here is how to develop a HTML generator handling your custom tags. The class Odoc_html.Generator.html inherits from the class Odoc_html.info, containing a field tag_functions which is a list pairs composed of a custom tag (e.g. "foo") and a function taking a text and returning HTML code (of type string). To handle a new tag bar, extend the current HTML generator and complete the tag_functions field: <> Another method of the class Odoc_html.info will look for the function associated to a custom tag and apply it to the text given to the tag. If no function is associated to a custom tag, then the method prints a warning message on stderr. For other generators -------------------- You can act the same way for other kinds of generators. 19.4 Adding command line options *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The command line analysis is performed after loading the module containing the documentation generator, thus allowing command line options to be added to the list of existing ones. Adding an option can be done with the function << Odoc_args.add_option : string * Arg.spec * string -> unit >> Note: Existing command line options can be redefined using this function. 19.4.1 Compilation and usage ============================== Defining a custom generator class in one file --------------------------------------------- Let custom.ml be the file defining a new generator class. Compilation of custom.ml can be performed by the following command : << ocamlc -I +ocamldoc -c custom.ml >> The file custom.cmo is created and can be used this way : << ocamldoc -g custom.cmo other-options source-files >> Options selecting a built-in generator to ocamldoc, such as -html, have no effect if a custom generator of the same kind is provided using -g. If the kinds do not match, the selected built-in generator is used and the custom one is ignored. Defining a custom generator class in several files -------------------------------------------------- It is possible to define a generator class in several modules, which are defined in several files file_1.ml[i], file_2.ml[i], ..., file_n.ml[i]. A .cma library file must be created, including all these files. The following commands create the custom.cma file from files file_1.ml[i], ..., file_n.ml[i] : << ocamlc -I +ocamldoc -c file_1.ml[i] ocamlc -I +ocamldoc -c file_2.ml[i] ... ocamlc -I +ocamldoc -c file_n.ml[i] ocamlc -o custom.cma -a file_1.cmo file_2.cmo ... file_n.cmo >> Then, the following command uses custom.cma as custom generator: << ocamldoc -g custom.cma other-options source-files >> --------------------------------------- (1) https://github.com/ocaml/ocaml/blob/5.2/ocamldoc/odoc_html.ml (2) https://github.com/ocaml/ocaml/blob/5.2/ocamldoc/odoc_latex.ml (3) https://github.com/ocaml/ocaml/blob/5.2/ocamldoc/odoc_texi.ml (4) https://github.com/ocaml/ocaml/blob/5.2/ocamldoc/odoc_man.ml (5) https://github.com/ocaml/ocaml/blob/5.2/ocamldoc/odoc_dot.ml Chapter 20  The debugger (ocamldebug) ***************************************** This chapter describes the OCaml source-level replay debugger ocamldebug.  Unix: The debugger is available on Unix systems that provide BSD sockets.  Windows: The debugger is available under the Cygwin port of OCaml, but not under the native Win32 ports. 20.1 Compiling for debugging *=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Before the debugger can be used, the program must be compiled and linked with the -g option: all .cmo and .cma files that are part of the program should have been created with ocamlc -g, and they must be linked together with ocamlc -g. Compiling with -g entails no penalty on the running time of programs: object files and bytecode executable files are bigger and take longer to produce, but the executable files run at exactly the same speed as if they had been compiled without -g. 20.2 Invocation *=*=*=*=*=*=*=*=* 20.2.1 Starting the debugger ============================== The OCaml debugger is invoked by running the program ocamldebug with the name of the bytecode executable file as first argument: << ocamldebug [options] program [arguments] >> The arguments following program are optional, and are passed as command-line arguments to the program being debugged. (See also the set arguments command.) The following command-line options are recognized: -c count Set the maximum number of simultaneously live checkpoints to count. -cd dir Run the debugger program from the working directory dir, instead of the current directory. (See also the cd command.) -emacs Tell the debugger it is executed under Emacs. (See section 20.10 for information on how to run the debugger under Emacs.) -I directory Add directory to the list of directories searched for source files and compiled files. (See also the directory command.) -s socket Use socket for communicating with the debugged program. See the description of the command set socket (section 20.8.8) for the format of socket. -version Print version string and exit. -vnum Print short version number and exit. -help or –help Display a short usage summary and exit. 20.2.2 Initialization file ============================ On start-up, the debugger will read commands from an initialization file before giving control to the user. The default file is .ocamldebug in the current directory if it exists, otherwise .ocamldebug in the user’s home directory. 20.2.3 Exiting the debugger ============================= The command quit exits the debugger. You can also exit the debugger by typing an end-of-file character (usually ctrl-D). Typing an interrupt character (usually ctrl-C) will not exit the debugger, but will terminate the action of any debugger command that is in progress and return to the debugger command level. 20.3 Commands *=*=*=*=*=*=*=* A debugger command is a single line of input. It starts with a command name, which is followed by arguments depending on this name. Examples: << run goto 1000 set arguments arg1 arg2 >> A command name can be truncated as long as there is no ambiguity. For instance, go 1000 is understood as goto 1000, since there are no other commands whose name starts with go. For the most frequently used commands, ambiguous abbreviations are allowed. For instance, r stands for run even though there are others commands starting with r. You can test the validity of an abbreviation using the help command. If the previous command has been successful, a blank line (typing just RET) will repeat it. 20.3.1 Getting help ===================== The OCaml debugger has a simple on-line help system, which gives a brief description of each command and variable. help Print the list of commands. help command Give help about the command command. help set variable, help show variable Give help about the variable variable. The list of all debugger variables can be obtained with help set. help info topic Give help about topic. Use help info to get a list of known topics. 20.3.2 Accessing the debugger state ===================================== set variable value Set the debugger variable variable to the value value. show variable Print the value of the debugger variable variable. info subject Give information about the given subject. For instance, info breakpoints will print the list of all breakpoints. 20.4 Executing a program *=*=*=*=*=*=*=*=*=*=*=*=*= 20.4.1 Events =============== Events are “interesting” locations in the source code, corresponding to the beginning or end of evaluation of “interesting” sub-expressions. Events are the unit of single-stepping (stepping goes to the next or previous event encountered in the program execution). Also, breakpoints can only be set at events. Thus, events play the role of line numbers in debuggers for conventional languages. During program execution, a counter is incremented at each event encountered. The value of this counter is referred as the current time. Thanks to reverse execution, it is possible to jump back and forth to any time of the execution. Here is where the debugger events (written §§) are located in the source code: - Following a function application: << (f arg)§§ >> - On entrance to a function: << fun x y z -> §§ ... >> - On each case of a pattern-matching definition (function, match...with construct, try...with construct): << function pat1 -> §§ expr1 | ... | patN -> §§ exprN >> - Between subexpressions of a sequence: << expr1; §§ expr2; §§ ...; §§ exprN >> - In the two branches of a conditional expression: << if cond then §§ expr1 else §§ expr2 >> - At the beginning of each iteration of a loop: << while cond do §§ body done for i = a to b do §§ body done >> Exceptions: A function application followed by a function return is replaced by the compiler by a jump (tail-call optimization). In this case, no event is put after the function application. 20.4.2 Starting the debugged program ====================================== The debugger starts executing the debugged program only when needed. This allows setting breakpoints or assigning debugger variables before execution starts. There are several ways to start execution: run Run the program until a breakpoint is hit, or the program terminates. goto 0 Load the program and stop on the first event. goto time Load the program and execute it until the given time. Useful when you already know approximately at what time the problem appears. Also useful to set breakpoints on function values that have not been computed at time 0 (see section 20.5). The execution of a program is affected by certain information it receives when the debugger starts it, such as the command-line arguments to the program and its working directory. The debugger provides commands to specify this information (set arguments and cd). These commands must be used before program execution starts. If you try to change the arguments or the working directory after starting your program, the debugger will kill the program (after asking for confirmation). 20.4.3 Running the program ============================ The following commands execute the program forward or backward, starting at the current time. The execution will stop either when specified by the command or when a breakpoint is encountered. run Execute the program forward from current time. Stops at next breakpoint or when the program terminates. reverse Execute the program backward from current time. Mostly useful to go to the last breakpoint encountered before the current time. step [count] Run the program and stop at the next event. With an argument, do it count times. If count is 0, run until the program terminates or a breakpoint is hit. backstep [count] Run the program backward and stop at the previous event. With an argument, do it count times. next [count] Run the program and stop at the next event, skipping over function calls. With an argument, do it count times. previous [count] Run the program backward and stop at the previous event, skipping over function calls. With an argument, do it count times. finish Run the program until the current function returns. start Run the program backward and stop at the first event before the current function invocation. 20.4.4 Time travel ==================== You can jump directly to a given time, without stopping on breakpoints, using the goto command. As you move through the program, the debugger maintains an history of the successive times you stop at. The last command can be used to revisit these times: each last command moves one step back through the history. That is useful mainly to undo commands such as step and next. goto time Jump to the given time. last [count] Go back to the latest time recorded in the execution history. With an argument, do it count times. set history size Set the size of the execution history. 20.4.5 Killing the program ============================ kill Kill the program being executed. This command is mainly useful if you wish to recompile the program without leaving the debugger. 20.5 Breakpoints *=*=*=*=*=*=*=*=*= A breakpoint causes the program to stop whenever a certain point in the program is reached. It can be set in several ways using the break command. Breakpoints are assigned numbers when set, for further reference. The most comfortable way to set breakpoints is through the Emacs interface (see section 20.10). break Set a breakpoint at the current position in the program execution. The current position must be on an event (i.e., neither at the beginning, nor at the end of the program). break function Set a breakpoint at the beginning of function. This works only when the functional value of the identifier function has been computed and assigned to the identifier. Hence this command cannot be used at the very beginning of the program execution, when all identifiers are still undefined; use goto time to advance execution until the functional value is available. break @ [module] line Set a breakpoint in module module (or in the current module if module is not given), at the first event of line line. break @ [module] line column Set a breakpoint in module module (or in the current module if module is not given), at the event closest to line line, column column. break @ [module] # character Set a breakpoint in module module at the event closest to character number character. break frag:pc, break pc Set a breakpoint at code address frag:pc. The integer frag is the identifier of a code fragment, a set of modules that have been loaded at once, either initially or with the Dynlink module. The integer pc is the instruction counter within this code fragment. If frag is omitted, it defaults to 0, which is the code fragment of the program loaded initially. delete [breakpoint-numbers] Delete the specified breakpoints. Without argument, all breakpoints are deleted (after asking for confirmation). info breakpoints Print the list of all breakpoints. 20.6 The call stack *=*=*=*=*=*=*=*=*=*=* Each time the program performs a function application, it saves the location of the application (the return address) in a block of data called a stack frame. The frame also contains the local variables of the caller function. All the frames are allocated in a region of memory called the call stack. The command backtrace (or bt) displays parts of the call stack. At any time, one of the stack frames is “selected” by the debugger; several debugger commands refer implicitly to the selected frame. In particular, whenever you ask the debugger for the value of a local variable, the value is found in the selected frame. The commands frame, up and down select whichever frame you are interested in. When the program stops, the debugger automatically selects the currently executing frame and describes it briefly as the frame command does. frame Describe the currently selected stack frame. frame frame-number Select a stack frame by number and describe it. The frame currently executing when the program stopped has number 0; its caller has number 1; and so on up the call stack. backtrace [count], bt [count] Print the call stack. This is useful to see which sequence of function calls led to the currently executing frame. With a positive argument, print only the innermost count frames. With a negative argument, print only the outermost -count frames. up [count] Select and display the stack frame just “above” the selected frame, that is, the frame that called the selected frame. An argument says how many frames to go up. down [count] Select and display the stack frame just “below” the selected frame, that is, the frame that was called by the selected frame. An argument says how many frames to go down. 20.7 Examining variable values *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The debugger can print the current value of simple expressions. The expressions can involve program variables: all the identifiers that are in scope at the selected program point can be accessed. Expressions that can be printed are a subset of OCaml expressions, as described by the following grammar: simple-expr ::= lowercase-ident | { capitalized-ident . } lowercase-ident | * | $ integer | simple-expr . lowercase-ident | simple-expr .( integer ) | simple-expr .[ integer ] | ! simple-expr | ( simple-expr ) The first two cases refer to a value identifier, either unqualified or qualified by the path to the structure that define it. * refers to the result just computed (typically, the value of a function application), and is valid only if the selected event is an “after” event (typically, a function application). $ integer refer to a previously printed value. The remaining four forms select part of an expression: respectively, a record field, an array element, a string element, and the current contents of a reference. print variables Print the values of the given variables. print can be abbreviated as p. display variables Same as print, but limit the depth of printing to 1. Useful to browse large data structures without printing them in full. display can be abbreviated as d. When printing a complex expression, a name of the form $integer is automatically assigned to its value. Such names are also assigned to parts of the value that cannot be printed because the maximal printing depth is exceeded. Named values can be printed later on with the commands p $integer or d $integer. Named values are valid only as long as the program is stopped. They are forgotten as soon as the program resumes execution. set print_depth d Limit the printing of values to a maximal depth of d. set print_length l Limit the printing of values to at most l nodes printed. 20.8 Controlling the debugger *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* 20.8.1 Setting the program name and arguments =============================================== set program file Set the program name to file. set arguments arguments Give arguments as command-line arguments for the program. A shell is used to pass the arguments to the debugged program. You can therefore use wildcards, shell variables, and file redirections inside the arguments. To debug programs that read from standard input, it is recommended to redirect their input from a file (using set arguments < input-file), otherwise input to the program and input to the debugger are not properly separated, and inputs are not properly replayed when running the program backwards. 20.8.2 How programs are loaded ================================ The loadingmode variable controls how the program is executed. set loadingmode direct The program is run directly by the debugger. This is the default mode. set loadingmode runtime The debugger execute the OCaml runtime ocamlrun on the program. Rarely useful; moreover it prevents the debugging of programs compiled in “custom runtime” mode. set loadingmode manual The user starts manually the program, when asked by the debugger. Allows remote debugging (see section 20.8.8). 20.8.3 Search path for files ============================== The debugger searches for source files and compiled interface files in a list of directories, the search path. The search path initially contains the current directory . and the standard library directory. The directory command adds directories to the path. Whenever the search path is modified, the debugger will clear any information it may have cached about the files. directory directorynames Add the given directories to the search path. These directories are added at the front, and will therefore be searched first. directory directorynames for modulename Same as directory directorynames, but the given directories will be searched only when looking for the source file of a module that has been packed into modulename. directory Reset the search path. This requires confirmation. 20.8.4 Working directory ========================== Each time a program is started in the debugger, it inherits its working directory from the current working directory of the debugger. This working directory is initially whatever it inherited from its parent process (typically the shell), but you can specify a new working directory in the debugger with the cd command or the -cd command-line option. cd directory Set the working directory for ocamldebug to directory. pwd Print the working directory for ocamldebug. 20.8.5 Turning reverse execution on and off ============================================= In some cases, you may want to turn reverse execution off. This speeds up the program execution, and is also sometimes useful for interactive programs. Normally, the debugger takes checkpoints of the program state from time to time. That is, it makes a copy of the current state of the program (using the Unix system call fork). If the variable checkpoints is set to off, the debugger will not take any checkpoints. set checkpoints on/off Select whether the debugger makes checkpoints or not. 20.8.6 Behavior of the debugger with respect to fork ====================================================== When the program issues a call to fork, the debugger can either follow the child or the parent. By default, the debugger follows the parent process. The variable follow_fork_mode controls this behavior: set follow_fork_mode child/parent Select whether to follow the child or the parent in case of a call to fork. 20.8.7 Stopping execution when new code is loaded =================================================== The debugger is compatible with the Dynlink module. However, when an external module is not yet loaded, it is impossible to set a breakpoint in its code. In order to facilitate setting breakpoints in dynamically loaded code, the debugger stops the program each time new modules are loaded. This behavior can be disabled using the break_on_load variable: set break_on_load on/off Select whether to stop after loading new code. 20.8.8 Communication between the debugger and the program =========================================================== The debugger communicate with the program being debugged through a Unix socket. You may need to change the socket name, for example if you need to run the debugger on a machine and your program on another. set socket socket Use socket for communication with the program. socket can be either a file name, or an Internet port specification host:port, where host is a host name or an Internet address in dot notation, and port is a port number on the host. On the debugged program side, the socket name is passed through the CAML_DEBUG_SOCKET environment variable. 20.8.9 Fine-tuning the debugger ================================= Several variables enables to fine-tune the debugger. Reasonable defaults are provided, and you should normally not have to change them. set processcount count Set the maximum number of checkpoints to count. More checkpoints facilitate going far back in time, but use more memory and create more Unix processes. As checkpointing is quite expensive, it must not be done too often. On the other hand, backward execution is faster when checkpoints are taken more often. In particular, backward single-stepping is more responsive when many checkpoints have been taken just before the current time. To fine-tune the checkpointing strategy, the debugger does not take checkpoints at the same frequency for long displacements (e.g. run) and small ones (e.g. step). The two variables bigstep and smallstep contain the number of events between two checkpoints in each case. set bigstep count Set the number of events between two checkpoints for long displacements. set smallstep count Set the number of events between two checkpoints for small displacements. The following commands display information on checkpoints and events: info checkpoints Print a list of checkpoints. info events [module] Print the list of events in the given module (the current module, by default). 20.8.10 User-defined printers =============================== Just as in the toplevel system (section 14.2), the user can register functions for printing values of certain types. For technical reasons, the debugger cannot call printing functions that reside in the program being debugged. The code for the printing functions must therefore be loaded explicitly in the debugger. load_printer "file-name" Load in the debugger the indicated .cmo or .cma object file. The file is loaded in an environment consisting only of the OCaml standard library plus the definitions provided by object files previously loaded using load_printer. If this file depends on other object files not yet loaded, the debugger automatically loads them if it is able to find them in the search path. The loaded file does not have direct access to the modules of the program being debugged. install_printer printer-name Register the function named printer-name (a value path) as a printer for objects whose types match the argument type of the function. That is, the debugger will call printer-name when it has such an object to print. The printing function printer-name must use the Format library module to produce its output, otherwise its output will not be correctly located in the values printed by the toplevel loop. The value path printer-name must refer to one of the functions defined by the object files loaded using load_printer. It cannot reference the functions of the program being debugged. remove_printer printer-name Remove the named function from the table of value printers. 20.9 Miscellaneous commands *=*=*=*=*=*=*=*=*=*=*=*=*=*=* list [module] [beginning] [end] List the source of module module, from line number beginning to line number end. By default, 20 lines of the current module are displayed, starting 10 lines before the current position. source filename Read debugger commands from the script filename. 20.10 Running the debugger under Emacs *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The most user-friendly way to use the debugger is to run it under Emacs with the OCaml mode available through MELPA and also at https://github.com/ocaml/caml-mode. The OCaml debugger is started under Emacs by the command M-x camldebug, with argument the name of the executable file progname to debug. Communication with the debugger takes place in an Emacs buffer named *camldebug-progname*. The editing and history facilities of Shell mode are available for interacting with the debugger. In addition, Emacs displays the source files containing the current event (the current position in the program execution) and highlights the location of the event. This display is updated synchronously with the debugger action. The following bindings for the most common debugger commands are available in the *camldebug-progname* buffer: C-c C-s (command step): execute the program one step forward. C-c C-k (command backstep): execute the program one step backward. C-c C-n (command next): execute the program one step forward, skipping over function calls. Middle mouse button (command display): display named value. $n under mouse cursor (support incremental browsing of large data structures). C-c C-p (command print): print value of identifier at point. C-c C-d (command display): display value of identifier at point. C-c C-r (command run): execute the program forward to next breakpoint. C-c C-v (command reverse): execute the program backward to latest breakpoint. C-c C-l (command last): go back one step in the command history. C-c C-t (command backtrace): display backtrace of function calls. C-c C-f (command finish): run forward till the current function returns. C-c < (command up): select the stack frame below the current frame. C-c > (command down): select the stack frame above the current frame. In all buffers in OCaml editing mode, the following debugger commands are also available: C-x C-a C-b (command break): set a breakpoint at event closest to point C-x C-a C-p (command print): print value of identifier at point C-x C-a C-d (command display): display value of identifier at point Chapter 21  Profiling (ocamlprof) ************************************* This chapter describes how the execution of OCaml programs can be profiled, by recording how many times functions are called, branches of conditionals are taken, ... 21.1 Compiling for profiling *=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Before profiling an execution, the program must be compiled in profiling mode, using the ocamlcp front-end to the ocamlc compiler (see chapter 13) or the ocamloptp front-end to the ocamlopt compiler (see chapter 16). When compiling modules separately, ocamlcp or ocamloptp must be used when compiling the modules (production of .cmo or .cmx files), and can also be used (though this is not strictly necessary) when linking them together. Note If a module (.ml file) doesn’t have a corresponding interface (.mli file), then compiling it with ocamlcp will produce object files (.cmi and .cmo) that are not compatible with the ones produced by ocamlc, which may lead to problems (if the .cmi or .cmo is still around) when switching between profiling and non-profiling compilations. To avoid this problem, you should always have a .mli file for each .ml file. The same problem exists with ocamloptp. Note To make sure your programs can be compiled in profiling mode, avoid using any identifier that begins with __ocaml_prof. The amount of profiling information can be controlled through the -P option to ocamlcp or ocamloptp, followed by one or several letters indicating which parts of the program should be profiled: a all options f function calls : a count point is set at the beginning of each function body i if ...then ...else ... : count points are set in both then branch and else branch l while, for loops: a count point is set at the beginning of the loop body m match branches: a count point is set at the beginning of the body of each branch t try ...with ... branches: a count point is set at the beginning of the body of each branch For instance, compiling with ocamlcp -P film profiles function calls, if...then...else..., loops and pattern matching. Calling ocamlcp or ocamloptp without the -P option defaults to -P fm, meaning that only function calls and pattern matching are profiled. Note For compatibility with previous releases, ocamlcp also accepts the -p option, with the same arguments and behaviour as -P. The ocamlcp and ocamloptp commands also accept all the options of the corresponding ocamlc or ocamlopt compiler, except the -pp (preprocessing) option. 21.2 Profiling an execution *=*=*=*=*=*=*=*=*=*=*=*=*=*=* Running an executable that has been compiled with ocamlcp or ocamloptp records the execution counts for the specified parts of the program and saves them in a file called ocamlprof.dump in the current directory. If the environment variable OCAMLPROF_DUMP is set when the program exits, its value is used as the file name instead of ocamlprof.dump. The dump file is written only if the program terminates normally (by calling exit or by falling through). It is not written if the program terminates with an uncaught exception. If a compatible dump file already exists in the current directory, then the profiling information is accumulated in this dump file. This allows, for instance, the profiling of several executions of a program on different inputs. Note that dump files produced by byte-code executables (compiled with ocamlcp) are compatible with the dump files produced by native executables (compiled with ocamloptp). 21.3 Printing profiling information *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The ocamlprof command produces a source listing of the program modules where execution counts have been inserted as comments. For instance, << ocamlprof foo.ml >> prints the source code for the foo module, with comments indicating how many times the functions in this module have been called. Naturally, this information is accurate only if the source file has not been modified after it was compiled. The following options are recognized by ocamlprof: -args filename Read additional newline-terminated command line arguments from filename. -args0 filename Read additional null character terminated command line arguments from filename. -f dumpfile Specifies an alternate dump file of profiling information to be read. -F string Specifies an additional string to be output with profiling information. By default, ocamlprof will annotate programs with comments of the form (* n *) where n is the counter value for a profiling point. With option -F s, the annotation will be (* sn *). -impl filename Process the file filename as an implementation file, even if its extension is not .ml. -intf filename Process the file filename as an interface file, even if its extension is not .mli. -version Print version string and exit. -vnum Print short version number and exit. -help or –help Display a short usage summary and exit. 21.4 Time profiling *=*=*=*=*=*=*=*=*=*=* Profiling with ocamlprof only records execution counts, not the actual time spent within each function. There is currently no way to perform time profiling on bytecode programs generated by ocamlc. For time profiling of native code, users are recommended to use standard tools such as perf (on Linux), Instruments (on macOS) and DTrace. Profiling with gprof is no longer supported. Chapter 22  Interfacing C with OCaml **************************************** This chapter describes how user-defined primitives, written in C, can be linked with OCaml code and called from OCaml functions, and how these C functions can call back to OCaml code. 22.1 Overview and compilation information *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* 22.1.1 Declaring primitives ============================= definition ::= ... | external value-name : typexpr = external-declaration external-declaration ::= string-literal [ string-literal [ string-literal ] ] User primitives are declared in an implementation file or struct...end module expression using the external keyword: << external name : type = C-function-name >> This defines the value name name as a function with type type that executes by calling the given C function. For instance, here is how the seek_in primitive is declared in the standard library module Stdlib: << external seek_in : in_channel -> int -> unit = "caml_ml_seek_in" >> Primitives with several arguments are always curried. The C function does not necessarily have the same name as the ML function. External functions thus defined can be specified in interface files or sig...end signatures either as regular values << val name : type >> thus hiding their implementation as C functions, or explicitly as “manifest” external functions << external name : type = C-function-name >> The latter is slightly more efficient, as it allows clients of the module to call directly the C function instead of going through the corresponding OCaml function. On the other hand, it should not be used in library modules if they have side-effects at toplevel, as this direct call interferes with the linker’s algorithm for removing unused modules from libraries at link-time. The arity (number of arguments) of a primitive is automatically determined from its OCaml type in the external declaration, by counting the number of function arrows in the type. For instance, seek_in above has arity 2, and the caml_ml_seek_in C function is called with two arguments. Similarly, << external seek_in_pair: in_channel * int -> unit = "caml_ml_seek_in_pair" >> has arity 1, and the caml_ml_seek_in_pair C function receives one argument (which is a pair of OCaml values). Type abbreviations are not expanded when determining the arity of a primitive. For instance, << type int_endo = int -> int external f : int_endo -> int_endo = "f" external g : (int -> int) -> (int -> int) = "f" >> f has arity 1, but g has arity 2. This allows a primitive to return a functional value (as in the f example above): just remember to name the functional return type in a type abbreviation. The language accepts external declarations with one or two flag strings in addition to the C function’s name. These flags are reserved for the implementation of the standard library. 22.1.2 Implementing primitives ================================ User primitives with arity n <= 5 are implemented by C functions that take n arguments of type value, and return a result of type value. The type value is the type of the representations for OCaml values. It encodes objects of several base types (integers, floating-point numbers, strings, ...) as well as OCaml data structures. The type value and the associated conversion functions and macros are described in detail below. For instance, here is the declaration for the C function implementing the In_channel.input primitive, which takes 4 arguments: <> When the primitive function is applied in an OCaml program, the C function is called with the values of the expressions to which the primitive is applied as arguments. The value returned by the function is passed back to the OCaml program as the result of the function application. User primitives with arity greater than 5 should be implemented by two C functions. The first function, to be used in conjunction with the bytecode compiler ocamlc, receives two arguments: a pointer to an array of OCaml values (the values for the arguments), and an integer which is the number of arguments provided. The other function, to be used in conjunction with the native-code compiler ocamlopt, takes its arguments directly. For instance, here are the two C functions for the 7-argument primitive Nat.add_nat: <> The names of the two C functions must be given in the primitive declaration, as follows: << external name : type = bytecode-C-function-name native-code-C-function-name >> For instance, in the case of add_nat, the declaration is: << external add_nat: nat -> int -> int -> nat -> int -> int -> int -> int = "add_nat_bytecode" "add_nat_native" >> Implementing a user primitive is actually two separate tasks: on the one hand, decoding the arguments to extract C values from the given OCaml values, and encoding the return value as an OCaml value; on the other hand, actually computing the result from the arguments. Except for very simple primitives, it is often preferable to have two distinct C functions to implement these two tasks. The first function actually implements the primitive, taking native C values as arguments and returning a native C value. The second function, often called the “stub code”, is a simple wrapper around the first function that converts its arguments from OCaml values to C values, calls the first function, and converts the returned C value to an OCaml value. For instance, here is the stub code for the Int64.float_of_bits primitive: <> (Here, caml_copy_double and Int64_val are conversion functions and macros for the type value, that will be described later. The CAMLprim macro expands to the required compiler directives to ensure that the function is exported and accessible from OCaml.) The hard work is performed by the function caml_int64_float_of_bits_unboxed, which is declared as: <> To write C code that operates on OCaml values, the following include files are provided: --------------------------------------------------------- | Include file | Provides | --------------------------------------------------------- | caml/mlvalues.h|definition of the value type, and | | |conversion macros | |caml/alloc.h |allocation functions (to create | | |structured OCaml objects) | |caml/memory.h |miscellaneous memory-related functions| | |and macros (for GC interface, in-place| | |modification of structures, etc). | |caml/fail.h |functions for raising exceptions (see | | |section 22.4.5) | |caml/callback.h |callback from C to OCaml (see | | |section 22.7). | |caml/custom.h |operations on custom blocks (see | | |section 22.9). | |caml/intext.h |operations for writing user-defined | | |serialization and deserialization | | |functions for custom blocks (see | | |section 22.9). | |caml/threads.h |operations for interfacing in the | | |presence of multiple threads (see | | |section 22.12). | --------------------------------------------------------- These files reside in the caml/ subdirectory of the OCaml standard library directory, which is returned by the command ocamlc -where (usually /usr/local/lib/ocaml or /usr/lib/ocaml). 22.1.3 Statically linking C code with OCaml code ================================================== The OCaml runtime system comprises three main parts: the bytecode interpreter, the memory manager, and a set of C functions that implement the primitive operations. Some bytecode instructions are provided to call these C functions, designated by their offset in a table of functions (the table of primitives). In the default mode, the OCaml linker produces bytecode for the standard runtime system, with a standard set of primitives. References to primitives that are not in this standard set result in the “unavailable C primitive” error. (Unless dynamic loading of C libraries is supported – see section 22.1.4 below.) In the “custom runtime” mode, the OCaml linker scans the object files and determines the set of required primitives. Then, it builds a suitable runtime system, by calling the native code linker with: - the table of the required primitives; - a library that provides the bytecode interpreter, the memory manager, and the standard primitives; - libraries and object code files (.o files) mentioned on the command line for the OCaml linker, that provide implementations for the user’s primitives. This builds a runtime system with the required primitives. The OCaml linker generates bytecode for this custom runtime system. The bytecode is appended to the end of the custom runtime system, so that it will be automatically executed when the output file (custom runtime + bytecode) is launched. To link in “custom runtime” mode, execute the ocamlc command with: - the -custom option; - the names of the desired OCaml object files (.cmo and .cma files) ; - the names of the C object files and libraries (.o and .a files) that implement the required primitives. Under Unix and Windows, a library named libname.a (respectively, .lib) residing in one of the standard library directories can also be specified as -cclib -lname. If you are using the native-code compiler ocamlopt, the -custom flag is not needed, as the final linking phase of ocamlopt always builds a standalone executable. To build a mixed OCaml/C executable, execute the ocamlopt command with: - the names of the desired OCaml native object files (.cmx and .cmxa files); - the names of the C object files and libraries (.o, .a, .so or .dll files) that implement the required primitives. Starting with Objective Caml 3.00, it is possible to record the -custom option as well as the names of C libraries in an OCaml library file .cma or .cmxa. For instance, consider an OCaml library mylib.cma, built from the OCaml object files a.cmo and b.cmo, which reference C code in libmylib.a. If the library is built as follows: << ocamlc -a -o mylib.cma -custom a.cmo b.cmo -cclib -lmylib >> users of the library can simply link with mylib.cma: << ocamlc -o myprog mylib.cma ... >> and the system will automatically add the -custom and -cclib -lmylib options, achieving the same effect as << ocamlc -o myprog -custom a.cmo b.cmo ... -cclib -lmylib >> The alternative is of course to build the library without extra options: << ocamlc -a -o mylib.cma a.cmo b.cmo >> and then ask users to provide the -custom and -cclib -lmylib options themselves at link-time: << ocamlc -o myprog -custom mylib.cma ... -cclib -lmylib >> The former alternative is more convenient for the final users of the library, however. 22.1.4 Dynamically linking C code with OCaml code =================================================== Starting with Objective Caml 3.03, an alternative to static linking of C code using the -custom code is provided. In this mode, the OCaml linker generates a pure bytecode executable (no embedded custom runtime system) that simply records the names of dynamically-loaded libraries containing the C code. The standard OCaml runtime system ocamlrun then loads dynamically these libraries, and resolves references to the required primitives, before executing the bytecode. This facility is currently available on all platforms supported by OCaml except Cygwin 64 bits. To dynamically link C code with OCaml code, the C code must first be compiled into a shared library (under Unix) or DLL (under Windows). This involves 1- compiling the C files with appropriate C compiler flags for producing position-independent code (when required by the operating system), and 2- building a shared library from the resulting object files. The resulting shared library or DLL file must be installed in a place where ocamlrun can find it later at program start-up time (see section 15.3). Finally (step 3), execute the ocamlc command with - the names of the desired OCaml object files (.cmo and .cma files) ; - the names of the C shared libraries (.so or .dll files) that implement the required primitives. Under Unix and Windows, a library named dllname.so (respectively, .dll) residing in one of the standard library directories can also be specified as -dllib -lname. Do not set the -custom flag, otherwise you’re back to static linking as described in section 22.1.3. The ocamlmklib tool (see section 22.14) automates steps 2 and 3. As in the case of static linking, it is possible (and recommended) to record the names of C libraries in an OCaml .cma library archive. Consider again an OCaml library mylib.cma, built from the OCaml object files a.cmo and b.cmo, which reference C code in dllmylib.so. If the library is built as follows: << ocamlc -a -o mylib.cma a.cmo b.cmo -dllib -lmylib >> users of the library can simply link with mylib.cma: << ocamlc -o myprog mylib.cma ... >> and the system will automatically add the -dllib -lmylib option, achieving the same effect as << ocamlc -o myprog a.cmo b.cmo ... -dllib -lmylib >> Using this mechanism, users of the library mylib.cma do not need to know that it references C code, nor whether this C code must be statically linked (using -custom) or dynamically linked. 22.1.5 Choosing between static linking and dynamic linking ============================================================ After having described two different ways of linking C code with OCaml code, we now review the pros and cons of each, to help developers of mixed OCaml/C libraries decide. The main advantage of dynamic linking is that it preserves the platform-independence of bytecode executables. That is, the bytecode executable contains no machine code, and can therefore be compiled on platform A and executed on other platforms B, C, ..., as long as the required shared libraries are available on all these platforms. In contrast, executables generated by ocamlc -custom run only on the platform on which they were created, because they embark a custom-tailored runtime system specific to that platform. In addition, dynamic linking results in smaller executables. Another advantage of dynamic linking is that the final users of the library do not need to have a C compiler, C linker, and C runtime libraries installed on their machines. This is no big deal under Unix and Cygwin, but many Windows users are reluctant to install Microsoft Visual C just to be able to do ocamlc -custom. There are two drawbacks to dynamic linking. The first is that the resulting executable is not stand-alone: it requires the shared libraries, as well as ocamlrun, to be installed on the machine executing the code. If you wish to distribute a stand-alone executable, it is better to link it statically, using ocamlc -custom -ccopt -static or ocamlopt -ccopt -static. Dynamic linking also raises the “DLL hell” problem: some care must be taken to ensure that the right versions of the shared libraries are found at start-up time. The second drawback of dynamic linking is that it complicates the construction of the library. The C compiler and linker flags to compile to position-independent code and build a shared library vary wildly between different Unix systems. Also, dynamic linking is not supported on all Unix systems, requiring a fall-back case to static linking in the Makefile for the library. The ocamlmklib command (see section 22.14) tries to hide some of these system dependencies. In conclusion: dynamic linking is highly recommended under the native Windows port, because there are no portability problems and it is much more convenient for the end users. Under Unix, dynamic linking should be considered for mature, frequently used libraries because it enhances platform-independence of bytecode executables. For new or rarely-used libraries, static linking is much simpler to set up in a portable way. 22.1.6 Building standalone custom runtime systems =================================================== It is sometimes inconvenient to build a custom runtime system each time OCaml code is linked with C libraries, like ocamlc -custom does. For one thing, the building of the runtime system is slow on some systems (that have bad linkers or slow remote file systems); for another thing, the platform-independence of bytecode files is lost, forcing to perform one ocamlc -custom link per platform of interest. An alternative to ocamlc -custom is to build separately a custom runtime system integrating the desired C libraries, then generate “pure” bytecode executables (not containing their own runtime system) that can run on this custom runtime. This is achieved by the -make-runtime and -use-runtime flags to ocamlc. For example, to build a custom runtime system integrating the C parts of the “Unix” and “Threads” libraries, do: << ocamlc -make-runtime -o /home/me/ocamlunixrun unix.cma threads.cma >> To generate a bytecode executable that runs on this runtime system, do: << ocamlc -use-runtime /home/me/ocamlunixrun -o myprog \ unix.cma threads.cma your .cmo and .cma files >> The bytecode executable myprog can then be launched as usual: myprog args or /home/me/ocamlunixrun myprog args. Notice that the bytecode libraries unix.cma and threads.cma must be given twice: when building the runtime system (so that ocamlc knows which C primitives are required) and also when building the bytecode executable (so that the bytecode from unix.cma and threads.cma is actually linked in). 22.2 The value type *=*=*=*=*=*=*=*=*=*=* All OCaml objects are represented by the C type value, defined in the include file caml/mlvalues.h, along with macros to manipulate values of that type. An object of type value is either: - an unboxed integer; - or a pointer to a block inside the heap, allocated through one of the caml_alloc_* functions described in section 22.4.4. 22.2.1 Integer values ======================= Integer values encode 63-bit signed integers (31-bit on 32-bit architectures). They are unboxed (unallocated). 22.2.2 Blocks =============== Blocks in the heap are garbage-collected, and therefore have strict structure constraints. Each block includes a header containing the size of the block (in words), and the tag of the block. The tag governs how the contents of the blocks are structured. A tag lower than No_scan_tag indicates a structured block, containing well-formed values, which is recursively traversed by the garbage collector. A tag greater than or equal to No_scan_tag indicates a raw block, whose contents are not scanned by the garbage collector. For the benefit of ad-hoc polymorphic primitives such as equality and structured input-output, structured and raw blocks are further classified according to their tags as follows: ------------------------------------------------------- | Tag | Contents of the block | ------------------------------------------------------- | 0 to No_scan_tag−1|A structured block (an array of| | |OCaml objects). Each field is a| | |value. | |Closure_tag |A closure representing a | | |functional value. The first | | |word is a pointer to a piece of| | |code, the remaining words are | | |value containing the | | |environment. | |String_tag |A character string or a byte | | |sequence. | |Double_tag |A double-precision | | |floating-point number. | |Double_array_tag |An array or record of | | |double-precision floating-point| | |numbers. | |Abstract_tag |A block representing an | | |abstract datatype. | |Custom_tag |A block representing an | | |abstract datatype with | | |user-defined finalization, | | |comparison, hashing, | | |serialization and | | |deserialization functions | | |attached. | ------------------------------------------------------- 22.2.3 Pointers outside the heap ================================== In earlier versions of OCaml, it was possible to use word-aligned pointers to addresses outside the heap as OCaml values, just by casting the pointer to type value. This usage is no longer supported since OCaml 5.0. A correct way to manipulate pointers to out-of-heap blocks from OCaml is to store those pointers in OCaml blocks with tag Abstract_tag or Custom_tag, then use the blocks as the OCaml values. Here is an example of encapsulation of out-of-heap pointers of C type ty * inside Abstract_tag blocks. Section 22.6 gives a more complete example using Custom_tag blocks. <> Alternatively, out-of-heap pointers can be treated as “native” integers, that is, boxed 32-bit integers on a 32-bit platform and boxed 64-bit integers on a 64-bit platform. <> For pointers that are at least 2-aligned (the low bit is guaranteed to be zero), we have yet another valid representation as an OCaml tagged integer. <> 22.3 Representation of OCaml data types *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This section describes how OCaml data types are encoded in the value type. 22.3.1 Atomic types ===================== -------------------------------------------------- |OCaml type| Encoding | -------------------------------------------------- | int |Unboxed integer values. | |char |Unboxed integer values (ASCII code). | |float |Blocks with tag Double_tag. | |bytes |Blocks with tag String_tag. | |string |Blocks with tag String_tag. | |int32 |Blocks with tag Custom_tag. | |int64 |Blocks with tag Custom_tag. | |nativeint |Blocks with tag Custom_tag. | -------------------------------------------------- 22.3.2 Tuples and records =========================== Tuples are represented by pointers to blocks, with tag 0. Records are also represented by zero-tagged blocks. The ordering of labels in the record type declaration determines the layout of the record fields: the value associated to the label declared first is stored in field 0 of the block, the value associated to the second label goes in field 1, and so on. As an optimization, records whose fields all have static type float are represented as arrays of floating-point numbers, with tag Double_array_tag. (See the section below on arrays.) As another optimization, unboxable record types are represented specially; unboxable record types are the immutable record types that have only one field. An unboxable type will be represented in one of two ways: boxed or unboxed. Boxed record types are represented as described above (by a block with tag 0 or Double_array_tag). An unboxed record type is represented directly by the value of its field (i.e. there is no block to represent the record itself). The representation is chosen according to the following, in decreasing order of priority: - An attribute ([@@boxed] or [@@unboxed]) on the type declaration. - A compiler option (-unboxed-types or -no-unboxed-types). - The default representation. In the present version of OCaml, the default is the boxed representation. 22.3.3 Arrays =============== Arrays of integers and pointers are represented like tuples and records, that is, as pointers to blocks tagged 0. They are accessed with the Field macro for reading and the caml_modify function for writing. Values of type floatarray (as manipulated by the Float.Array module), as well as records whose declaration contains only float fields, use an efficient unboxed representation: blocks with tag Double_array_tag whose content consist of raw double values, which are not themselves valid OCaml values. They should be accessed using the Double_flat_field and Store_double_flat_field macros. Finally, arrays of type float array may use either the boxed or the unboxed representation depending on the how the compiler is configured. They currently use the unboxed representation by default, but can be made to use the boxed representation by passing the –disable-flat-float-array flag to the ‘configure‘ script. They should be accessed using the Double_array_field and Store_double_array_field macros, which will work correctly under both modes. 22.3.4 Concrete data types ============================ Constructed terms are represented either by unboxed integers (for constant constructors) or by blocks whose tag encode the constructor (for non-constant constructors). The constant constructors and the non-constant constructors for a given concrete type are numbered separately, starting from 0, in the order in which they appear in the concrete type declaration. A constant constructor is represented by the unboxed integer equal to its constructor number. A non-constant constructor declared with n arguments is represented by a block of size n, tagged with the constructor number; the n fields contain its arguments. Example: -------------------------------------------- |Constructed term| Representation | -------------------------------------------- | () |Val_int(0) | |false |Val_int(0) | |true |Val_int(1) | |[] |Val_int(0) | |h::t |Block with size = 2 and | | |tag = 0; first field | | |contains h, second field | | |t. | -------------------------------------------- As a convenience, caml/mlvalues.h defines the macros Val_unit, Val_false, Val_true and Val_emptylist to refer to (), false, true and []. The following example illustrates the assignment of integers and block tags to constructors: < integer "Val_int(0)" *) | B of string (* First non-constant constructor -> block with tag 0 *) | C (* Second constant constructor -> integer "Val_int(1)" *) | D of bool (* Second non-constant constructor -> block with tag 1 *) | E of t * t (* Third non-constant constructor -> block with tag 2 *) >> As an optimization, unboxable concrete data types are represented specially; a concrete data type is unboxable if it has exactly one constructor and this constructor has exactly one argument. Unboxable concrete data types are represented in the same ways as unboxable record types: see the description in section 22.3.2. 22.3.5 Objects ================ Objects are represented as blocks with tag Object_tag. The first field of the block refers to the object’s class and associated method suite, in a format that cannot easily be exploited from C. The second field contains a unique object ID, used for comparisons. The remaining fields of the object contain the values of the instance variables of the object. It is unsafe to access directly instance variables, as the type system provides no guarantee about the instance variables contained by an object. One may extract a public method from an object using the C function caml_get_public_method (declared in .) Since public method tags are hashed in the same way as variant tags, and methods are functions taking self as first argument, if you want to do the method call foo#bar from the C side, you should call: << callback(caml_get_public_method(foo, hash_variant("bar")), foo); >> 22.3.6 Polymorphic variants ============================= Like constructed terms, polymorphic variant values are represented either as integers (for polymorphic variants without argument), or as blocks (for polymorphic variants with an argument). Unlike constructed terms, variant constructors are not numbered starting from 0, but identified by a hash value (an OCaml integer), as computed by the C function hash_variant (declared in ): the hash value for a variant constructor named, say, VConstr is hash_variant("VConstr"). The variant value `VConstr is represented by hash_variant("VConstr"). The variant value `VConstr(v) is represented by a block of size 2 and tag 0, with field number 0 containing hash_variant("VConstr") and field number 1 containing v. Unlike constructed values, polymorphic variant values taking several arguments are not flattened. That is, `VConstr(v, w) is represented by a block of size 2, whose field number 1 contains the representation of the pair (v, w), rather than a block of size 3 containing v and w in fields 1 and 2. 22.4 Operations on values *=*=*=*=*=*=*=*=*=*=*=*=*=* 22.4.1 Kind tests =================== - Is_long(v) is true if value v is an immediate integer, false otherwise - Is_block(v) is true if value v is a pointer to a block, and false if it is an immediate integer. - Is_none(v) is true if value v is None. - Is_some(v) is true if value v (assumed to be of option type) corresponds to the Some constructor. 22.4.2 Operations on integers =============================== - Val_long(l) returns the value encoding the long int l. - Long_val(v) returns the long int encoded in value v. - Val_int(i) returns the value encoding the int i. - Int_val(v) returns the int encoded in value v. - Val_bool(x) returns the OCaml boolean representing the truth value of the C integer x. - Bool_val(v) returns 0 if v is the OCaml boolean false, 1 if v is true. - Val_true, Val_false represent the OCaml booleans true and false. - Val_emptylist, Val_emptylist represents the empty list. - Val_none represents the OCaml value None. 22.4.3 Accessing blocks ========================= - Wosize_val(v) returns the size of the block v, in words, excluding the header. - Tag_val(v) returns the tag of the block v. - Field(v, n) returns the value contained in the n^th field of the structured block v. Fields are numbered from 0 to Wosize_val(v)−1. - Store_field(b, n, v) stores the value v in the field number n of value b, which must be a structured block. - Code_val(v) returns the code part of the closure v. - caml_string_length(v) returns the length (number of bytes) of the string or byte sequence v. - Byte(v, n) returns the n^th byte of the string or byte sequence v, with type char. Bytes are numbered from 0 to string_length(v)−1. - Byte_u(v, n) returns the n^th byte of the string or byte sequence v, with type unsigned char. Bytes are numbered from 0 to string_length(v)−1. - String_val(v) returns a pointer to the first byte of the string v, with type const char *. This pointer is a valid C string: there is a null byte after the last byte in the string. However, OCaml strings can contain embedded null bytes, which will confuse the usual C functions over strings. - Bytes_val(v) returns a pointer to the first byte of the byte sequence v, with type unsigned char *. - Double_val(v) returns the floating-point number contained in value v, with type double. - Double_array_field(v, n) returns the n^th element of a float array v. - Store_double_array_field(v, n, d) stores the double precision floating-point number d in the n^th element of a float array v. - Double_flat_field(v, n) returns the n^th element of a floatarray or a record of floats v (an unboxed block tagged Double_array_tag). - Store_double_flat_field(v, n, d) stores the double precision floating-point number d in the n^th element of a floatarray or a record of floats v. - Data_custom_val(v) returns a pointer to the data part of the custom block v. This pointer has type void * and must be cast to the type of the data contained in the custom block. - Int32_val(v) returns the 32-bit integer contained in the int32 v. - Int64_val(v) returns the 64-bit integer contained in the int64 v. - Nativeint_val(v) returns the long integer contained in the nativeint v. - caml_field_unboxed(v) returns the value of the field of a value v of any unboxed type (record or concrete data type). - caml_field_boxed(v) returns the value of the field of a value v of any boxed type (record or concrete data type). - caml_field_unboxable(v) calls either caml_field_unboxed or caml_field_boxed according to the default representation of unboxable types in the current version of OCaml. - Some_val(v) returns the argument \var{x} of a value v of the form Some(x). The expressions Field(v, n), Byte(v, n) and Byte_u(v, n) are valid l-values. Hence, they can be assigned to, resulting in an in-place modification of value v. Assigning directly to Field(v, n) must be done with care to avoid confusing the garbage collector (see below). 22.4.4 Allocating blocks ========================== Simple interface ---------------- - Atom(t) returns an “atom” (zero-sized block) with tag t. Zero-sized blocks are preallocated outside of the heap. It is incorrect to try and allocate a zero-sized block using the functions below. For instance, Atom(0) represents the empty array. - caml_alloc(n, t) returns a fresh block of size n with tag t. If t is less than No_scan_tag, then the fields of the block are initialized with a valid value in order to satisfy the GC constraints. - caml_alloc_tuple(n) returns a fresh block of size n words, with tag 0. - caml_alloc_string(n) returns a byte sequence (or string) value of length n bytes. The sequence initially contains uninitialized bytes. - caml_alloc_initialized_string(n, p) returns a byte sequence (or string) value of length n bytes. The value is initialized from the n bytes starting at address p. - caml_copy_string(s) returns a string or byte sequence value containing a copy of the null-terminated C string s (a char *). - caml_copy_double(d) returns a floating-point value initialized with the double d. - caml_copy_int32(i), caml_copy_int64(i) and caml_copy_nativeint(i) return a value of OCaml type int32, int64 and nativeint, respectively, initialized with the integer i. - caml_alloc_array(f, a) allocates an array of values, calling function f over each element of the input array a to transform it into a value. The array a is an array of pointers terminated by the null pointer. The function f receives each pointer as argument, and returns a value. The zero-tagged block returned by alloc_array(f, a) is filled with the values returned by the successive calls to f. (This function must not be used to build an array of floating-point numbers.) - caml_copy_string_array(p) allocates an array of strings or byte sequences, copied from the pointer to a string array p (a char **). p must be NULL-terminated. - caml_alloc_float_array(n) allocates an array of floating point numbers of size n. The array initially contains uninitialized values. - caml_alloc_unboxed(v) returns the value (of any unboxed type) whose field is the value v. - caml_alloc_boxed(v) allocates and returns a value (of any boxed type) whose field is the value v. - caml_alloc_unboxable(v) calls either caml_alloc_unboxed or caml_alloc_boxed according to the default representation of unboxable types in the current version of OCaml. - caml_alloc_some(v) allocates a block representing Some(v). Low-level interface ------------------- The following functions are slightly more efficient than caml_alloc, but also much more difficult to use. From the standpoint of the allocation functions, blocks are divided according to their size as zero-sized blocks, small blocks (with size less than or equal to Max_young_wosize), and large blocks (with size greater than Max_young_wosize). The constant Max_young_wosize is declared in the include file mlvalues.h. It is guaranteed to be at least 64 (words), so that any block with constant size less than or equal to 64 can be assumed to be small. For blocks whose size is computed at run-time, the size must be compared against Max_young_wosize to determine the correct allocation procedure. - caml_alloc_small(n, t) returns a fresh small block of size n <= Max_young_wosize words, with tag t. If this block is a structured block (i.e. if t < No_scan_tag), then the fields of the block (initially containing garbage) must be initialized with legal values (using direct assignment to the fields of the block) before the next allocation. - caml_alloc_shr(n, t) returns a fresh block of size n, with tag t. The size of the block can be greater than Max_young_wosize. (It can also be smaller, but in this case it is more efficient to call caml_alloc_small instead of caml_alloc_shr.) If this block is a structured block (i.e. if t < No_scan_tag), then the fields of the block (initially containing garbage) must be initialized with legal values (using the caml_initialize function described below) before the next allocation. 22.4.5 Raising exceptions =========================== Two functions are provided to raise two standard exceptions: - caml_failwith(s), where s is a null-terminated C string (with type char *), raises exception Failure with argument s. - caml_invalid_argument(s), where s is a null-terminated C string (with type char *), raises exception Invalid_argument with argument s. Raising arbitrary exceptions from C is more delicate: the exception identifier is dynamically allocated by the OCaml program, and therefore must be communicated to the C function using the registration facility described below in section 22.7.3. Once the exception identifier is recovered in C, the following functions actually raise the exception: - caml_raise_constant(id) raises the exception id with no argument; - caml_raise_with_arg(id, v) raises the exception id with the OCaml value v as argument; - caml_raise_with_args(id, n, v) raises the exception id with the OCaml values v[0], ..., v[n-1] as arguments; - caml_raise_with_string(id, s), where s is a null-terminated C string, raises the exception id with a copy of the C string s as argument. 22.5 Living in harmony with the garbage collector *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Unused blocks in the heap are automatically reclaimed by the garbage collector. This requires some cooperation from C code that manipulates heap-allocated blocks. 22.5.1 Simple interface ========================= All the macros described in this section are declared in the memory.h header file. Rule 1  A function that has parameters or local variables of type value must begin with a call to one of the CAMLparam macros and return with CAMLreturn, CAMLreturn0, or CAMLreturnT. There are six CAMLparam macros: CAMLparam0 to CAMLparam5, which take zero to five arguments respectively. If your function has no more than 5 parameters of type value, use the corresponding macros with these parameters as arguments. If your function has more than 5 parameters of type value, use CAMLparam5 with five of these parameters, and use one or more calls to the CAMLxparam macros for the remaining parameters (CAMLxparam1 to CAMLxparam5). The macros CAMLreturn, CAMLreturn0, and CAMLreturnT are used to replace the C keyword return; any function using a CAMLparam macro on entry should use CAMLreturn on all exit points. C functions exported as OCaml externals must return a value, and they should use CAMLreturn (x) instead of return x. Some helper functions may manipulate OCaml values yet return void or another datatype. void-returning procedures should explicitly use CAMLreturn0, and not have any implicit return. Helper functions returning C data of some type t should use CAMLreturnT (t, x) instead of return x. Note: Some C compilers give bogus warnings about unused variables caml__dummy_xxx at each use of CAMLparam and CAMLlocal. You should ignore them. Examples: <> Note: If your function is a primitive with more than 5 arguments for use with the byte-code runtime, its arguments are not values and must not be declared (they have types value * and int). Warning: CAMLreturn0 should only be used for internal procedures that return void. CAMLreturn(Val_unit) should be used for functions that return an OCaml unit value. Primitives (C functions that can be called from OCaml) should never return void. Rule 2  Local variables of type value must be declared with one of the CAMLlocal macros. Arrays of values are declared with CAMLlocalN. These macros must be used at the beginning of the function, not in a nested block. The macros CAMLlocal1 to CAMLlocal5 declare and initialize one to five local variables of type value. The variable names are given as arguments to the macros. CAMLlocalN(x, n) declares and initializes a local variable of type value [n]. You can use several calls to these macros if you have more than 5 local variables. Example: <> Warning: CAMLlocal (and CAMLxparam) can only be called after CAMLparam. If a function declares local values but takes no value argument, it should start with CAMLparam0 (). <> Rule 3  Assignments to the fields of structured blocks must be done with the Store_field macro (for normal blocks), Store_double_array_field macro (for float array values) or Store_double_flat_field (for floatarray values and records of floating-point numbers). Other assignments must not use Store_field, Store_double_array_field nor Store_double_flat_field. Store_field (b, n, v) stores the value v in the field number n of value b, which must be a block (i.e. Is_block(b) must be true). Example: <> Warning: The first argument of Store_field and Store_double_field must be a variable declared by CAMLparam* or a parameter declared by CAMLlocal* to ensure that a garbage collection triggered by the evaluation of the other arguments will not invalidate the first argument after it is computed. Use with CAMLlocalN: Arrays of values declared using CAMLlocalN must not be written to using Store_field. Use the normal C array syntax instead. Rule 4  Global variables containing values must be registered with the garbage collector using the caml_register_global_root function, save that global variables and locations that will only ever contain OCaml integers (and never pointers) do not have to be registered. The same is true for any memory location outside the OCaml heap that contains a value and is not guaranteed to be reachable—for as long as it contains such value—from either another registered global variable or location, local variable declared with CAMLlocal or function parameter declared with CAMLparam. Registration of a global variable v is achieved by calling caml_register_global_root(&v) just before or just after a valid value is stored in v for the first time; likewise, registration of an arbitrary location p is achieved by calling caml_register_global_root(p). You must not call any of the OCaml runtime functions or macros between registering and storing the value. Neither must you store anything in the variable v (likewise, the location p) that is not a valid value. The registration causes the contents of the variable or memory location to be updated by the garbage collector whenever the value in such variable or location is moved within the OCaml heap. In the presence of threads care must be taken to ensure appropriate synchronisation with the OCaml runtime to avoid a race condition against the garbage collector when reading or writing the value. (See section 22.12.2.) A registered global variable v can be un-registered by calling caml_remove_global_root(&v). If the contents of the global variable v are seldom modified after registration, better performance can be achieved by calling caml_register_generational_global_root(&v) to register v (after its initialization with a valid value, but before any allocation or call to the GC functions), and caml_remove_generational_global_root(&v) to un-register it. In this case, you must not modify the value of v directly, but you must use caml_modify_generational_global_root(&v,x) to set it to x. The garbage collector takes advantage of the guarantee that v is not modified between calls to caml_modify_generational_global_root to scan it less often. This improves performance if the modifications of v happen less often than minor collections. Note: The CAML macros use identifiers (local variables, type identifiers, structure tags) that start with caml__. Do not use any identifier starting with caml__ in your programs. 22.5.2 Low-level interface ============================ We now give the GC rules corresponding to the low-level allocation functions caml_alloc_small and caml_alloc_shr. You can ignore those rules if you stick to the simplified allocation function caml_alloc. Rule 5  After a structured block (a block with tag less than No_scan_tag) is allocated with the low-level functions, all fields of this block must be filled with well-formed values before the next allocation operation. If the block has been allocated with caml_alloc_small, filling is performed by direct assignment to the fields of the block: << Field(v, n) = v_n; >> If the block has been allocated with caml_alloc_shr, filling is performed through the caml_initialize function: << caml_initialize(&Field(v, n), v_n); >> The next allocation can trigger a garbage collection. The garbage collector assumes that all structured blocks contain well-formed values. Newly created blocks contain random data, which generally do not represent well-formed values. If you really need to allocate before the fields can receive their final value, first initialize with a constant value (e.g. Val_unit), then allocate, then modify the fields with the correct value (see rule 6). Rule 6  Direct assignment to a field of a block, as in << Field(v, n) = w; >> is safe only if v is a block newly allocated by caml_alloc_small; that is, if no allocation took place between the allocation of v and the assignment to the field. In all other cases, never assign directly. If the block has just been allocated by caml_alloc_shr, use caml_initialize to assign a value to a field for the first time: << caml_initialize(&Field(v, n), w); >> Otherwise, you are updating a field that previously contained a well-formed value; then, call the caml_modify function: << caml_modify(&Field(v, n), w); >> To illustrate the rules above, here is a C function that builds and returns a list containing the two integers given as parameters. First, we write it using the simplified allocation functions: <> Here, the registering of result is not strictly needed, because no allocation takes place after it gets its value, but it’s easier and safer to simply register all the local variables that have type value. Here is the same function written using the low-level allocation functions. We notice that the cons cells are small blocks and can be allocated with caml_alloc_small, and filled by direct assignments on their fields. <> In the two examples above, the list is built bottom-up. Here is an alternate way, that proceeds top-down. It is less efficient, but illustrates the use of caml_modify. <> It would be incorrect to perform Field(r, 1) = tail directly, because the allocation of tail has taken place since r was allocated. 22.5.3 Pending actions and asynchronous exceptions ==================================================== Since 4.10, allocation functions are guaranteed not to run any OCaml code, including finalisers, signal handlers and other threads running on the same domain. Instead, their execution is delayed to a later safe point. The function caml_process_pending_actions from executes any pending signal handlers and finalisers, Memprof callbacks, preemptive systhread switching, and requested minor and major garbage collections. In particular, it can raise asynchronous exceptions and cause mutations on the OCaml heap from the same domain. It is recommended to call it regularly at safe points inside long-running non-blocking C code. The variant caml_process_pending_actions_exn is provided, that returns the exception instead of raising it directly into OCaml code. Its result must be tested using Is_exception_result, and followed by Extract_exception if appropriate. It is typically used for clean up before re-raising: << CAMLlocal1(exn); ... exn = caml_process_pending_actions_exn(); if(Is_exception_result(exn)) { exn = Extract_exception(exn); ...cleanup... caml_raise(exn); } >> Correct use of exceptional return, in particular in the presence of garbage collection, is further detailed in Section 22.7.1. 22.6 A complete example *=*=*=*=*=*=*=*=*=*=*=*=* This section outlines how the functions from the Unix curses library can be made available to OCaml programs. First of all, here is the interface curses.ml that declares the curses primitives and data types: <<(* File curses.ml -- declaration of primitives and data types *) type window (* The type "window" remains abstract *) external initscr: unit -> window = "caml_curses_initscr" external endwin: unit -> unit = "caml_curses_endwin" external refresh: unit -> unit = "caml_curses_refresh" external wrefresh : window -> unit = "caml_curses_wrefresh" external newwin: int -> int -> int -> int -> window = "caml_curses_newwin" external addch: char -> unit = "caml_curses_addch" external mvwaddch: window -> int -> int -> char -> unit = "caml_curses_mvwaddch" external addstr: string -> unit = "caml_curses_addstr" external mvwaddstr: window -> int -> int -> string -> unit = "caml_curses_mvwaddstr" (* lots more omitted *) >> To compile this interface: << ocamlc -c curses.ml >> To implement these functions, we just have to provide the stub code; the core functions are already implemented in the curses library. The stub code file, curses_stubs.c, looks like this: < #include #include #include #include /* Encapsulation of opaque window handles (of type WINDOW *) as OCaml custom blocks. */ static struct custom_operations curses_window_ops = { "fr.inria.caml.curses_windows", custom_finalize_default, custom_compare_default, custom_hash_default, custom_serialize_default, custom_deserialize_default, custom_compare_ext_default, custom_fixed_length_default }; /* Accessing the WINDOW * part of an OCaml custom block */ #define Window_val(v) (*((WINDOW **) Data_custom_val(v))) /* Allocating an OCaml custom block to hold the given WINDOW * */ static value alloc_window(WINDOW * w) { value v = caml_alloc_custom(&curses_window_ops, sizeof(WINDOW *), 0, 1); Window_val(v) = w; return v; } CAMLprim value caml_curses_initscr(value unit) { CAMLparam1 (unit); CAMLreturn (alloc_window(initscr())); } CAMLprim value caml_curses_endwin(value unit) { CAMLparam1 (unit); endwin(); CAMLreturn (Val_unit); } CAMLprim value caml_curses_refresh(value unit) { CAMLparam1 (unit); refresh(); CAMLreturn (Val_unit); } CAMLprim value caml_curses_wrefresh(value win) { CAMLparam1 (win); wrefresh(Window_val(win)); CAMLreturn (Val_unit); } CAMLprim value caml_curses_newwin(value nlines, value ncols, value x0, value y0) { CAMLparam4 (nlines, ncols, x0, y0); CAMLreturn (alloc_window(newwin(Int_val(nlines), Int_val(ncols), Int_val(x0), Int_val(y0)))); } CAMLprim value caml_curses_addch(value c) { CAMLparam1 (c); addch(Int_val(c)); /* Characters are encoded like integers */ CAMLreturn (Val_unit); } CAMLprim value caml_curses_mvwaddch(value win, value x, value y, value c) { CAMLparam4 (win, x, y, c); mvwaddch(Window_val(win), Int_val(x), Int_val(y), Int_val(c)); CAMLreturn (Val_unit); } CAMLprim value caml_curses_addstr(value s) { CAMLparam1 (s); addstr(String_val(s)); CAMLreturn (Val_unit); } CAMLprim value caml_curses_mvwaddstr(value win, value x, value y, value s) { CAMLparam4 (win, x, y, s); mvwaddstr(Window_val(win), Int_val(x), Int_val(y), String_val(s)); CAMLreturn (Val_unit); } /* This goes on for pages. */ >> The file curses_stubs.c can be compiled with: << cc -c -I`ocamlc -where` curses_stubs.c >> or, even simpler, << ocamlc -c curses_stubs.c >> (When passed a .c file, the ocamlc command simply calls the C compiler on that file, with the right -I option.) Now, here is a sample OCaml program prog.ml that uses the curses module: <<(* File prog.ml -- main program using curses *) open Curses;; let main_window = initscr () in let small_window = newwin 10 5 20 10 in mvwaddstr main_window 10 2 "Hello"; mvwaddstr small_window 4 3 "world"; refresh(); Unix.sleep 5; endwin() >> To compile and link this program, run: << ocamlc -custom -o prog unix.cma curses.cmo prog.ml curses_stubs.o -cclib -lcurses >> (On some machines, you may need to put -cclib -lcurses -cclib -ltermcap or -cclib -ltermcap instead of -cclib -lcurses.) 22.7 Advanced topic: callbacks from C to OCaml *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= So far, we have described how to call C functions from OCaml. In this section, we show how C functions can call OCaml functions, either as callbacks (OCaml calls C which calls OCaml), or with the main program written in C. 22.7.1 Applying OCaml closures from C ======================================= C functions can apply OCaml function values (closures) to OCaml values. The following functions are provided to perform the applications: - caml_callback(f, a) applies the functional value f to the value a and returns the value returned by f. - caml_callback2(f, a, b) applies the functional value f (which is assumed to be a curried OCaml function with two arguments) to a and b. - caml_callback3(f, a, b, c) applies the functional value f (a curried OCaml function with three arguments) to a, b and c. - caml_callbackN(f, n, args) applies the functional value f to the n arguments contained in the C array of values args. If the function f does not return, but raises an exception that escapes the scope of the application, then this exception is propagated to the next enclosing OCaml code, skipping over the C code. That is, if an OCaml function f calls a C function g that calls back an OCaml function h that raises a stray exception, then the execution of g is interrupted and the exception is propagated back into f. If the C code wishes to catch exceptions escaping the OCaml function, it can use the functions caml_callback_exn, caml_callback2_exn, caml_callback3_exn, caml_callbackN_exn. These functions take the same arguments as their non-_exn counterparts, but catch escaping exceptions and return them to the C code. The return value v of the caml_callback*_exn functions must be tested with the macro Is_exception_result(v). If the macro returns “false”, no exception occurred, and v is the value returned by the OCaml function. If Is_exception_result(v) returns “true”, an exception escaped, and its value (the exception descriptor) can be recovered using Extract_exception(v). Warning: If the OCaml function returned with an exception, Extract_exception should be applied to the exception result prior to calling a function that may trigger garbage collection. Otherwise, if v is reachable during garbage collection, the runtime can crash since v does not contain a valid value. Example: << CAMLprim value call_caml_f_ex(value closure, value arg) { CAMLparam2(closure, arg); CAMLlocal2(res, tmp); res = caml_callback_exn(closure, arg); if(Is_exception_result(res)) { res = Extract_exception(res); tmp = caml_alloc(3, 0); /* Safe to allocate: res contains valid value. */ ... } CAMLreturn (res); } >> 22.7.2 Obtaining or registering OCaml closures for use in C functions ======================================================================= There are two ways to obtain OCaml function values (closures) to be passed to the callback functions described above. One way is to pass the OCaml function as an argument to a primitive function. For example, if the OCaml code contains the declaration << external apply : ('a -> 'b) -> 'a -> 'b = "caml_apply" >> the corresponding C stub can be written as follows: << CAMLprim value caml_apply(value vf, value vx) { CAMLparam2(vf, vx); CAMLlocal1(vy); vy = caml_callback(vf, vx); CAMLreturn(vy); } >> Another possibility is to use the registration mechanism provided by OCaml. This registration mechanism enables OCaml code to register OCaml functions under some global name, and C code to retrieve the corresponding closure by this global name. On the OCaml side, registration is performed by evaluating Callback.register n v. Here, n is the global name (an arbitrary string) and v the OCaml value. For instance: << let f x = print_string "f is applied to "; print_int x; print_newline() let _ = Callback.register "test function" f >> On the C side, a pointer to the value registered under name n is obtained by calling caml_named_value(n). The returned pointer must then be dereferenced to recover the actual OCaml value. If no value is registered under the name n, the null pointer is returned. For example, here is a C wrapper that calls the OCaml function f above: << void call_caml_f(int arg) { caml_callback(*caml_named_value("test function"), Val_int(arg)); } >> The pointer returned by caml_named_value is constant and can safely be cached in a C variable to avoid repeated name lookups. The value pointed to cannot be changed from C. However, it might change during garbage collection, so must always be recomputed at the point of use. Here is a more efficient variant of call_caml_f above that calls caml_named_value only once: << void call_caml_f(int arg) { static const value * closure_f = NULL; if (closure_f == NULL) { /* First time around, look up by name */ closure_f = caml_named_value("test function"); } caml_callback(*closure_f, Val_int(arg)); } >> 22.7.3 Registering OCaml exceptions for use in C functions ============================================================ The registration mechanism described above can also be used to communicate exception identifiers from OCaml to C. The OCaml code registers the exception by evaluating Callback.register_exception n exn, where n is an arbitrary name and exn is an exception value of the exception to register. For example: << exception Error of string let _ = Callback.register_exception "test exception" (Error "any string") >> The C code can then recover the exception identifier using caml_named_value and pass it as first argument to the functions raise_constant, raise_with_arg, and raise_with_string (described in section 22.4.5) to actually raise the exception. For example, here is a C function that raises the Error exception with the given argument: << void raise_error(char * msg) { caml_raise_with_string(*caml_named_value("test exception"), msg); } >> 22.7.4 Main program in C ========================== In normal operation, a mixed OCaml/C program starts by executing the OCaml initialization code, which then may proceed to call C functions. We say that the main program is the OCaml code. In some applications, it is desirable that the C code plays the role of the main program, calling OCaml functions when needed. This can be achieved as follows: - The C part of the program must provide a main function, which will override the default main function provided by the OCaml runtime system. Execution will start in the user-defined main function just like for a regular C program. - At some point, the C code must call caml_main(argv) to initialize the OCaml code. The argv argument is a C array of strings (type char **), terminated with a NULL pointer, which represents the command-line arguments, as passed as second argument to main. The OCaml array Sys.argv will be initialized from this parameter. For the bytecode compiler, argv[0] and argv[1] are also consulted to find the file containing the bytecode. - The call to caml_main initializes the OCaml runtime system, loads the bytecode (in the case of the bytecode compiler), and executes the initialization code of the OCaml program. Typically, this initialization code registers callback functions using Callback.register. Once the OCaml initialization code is complete, control returns to the C code that called caml_main. - The C code can then invoke OCaml functions using the callback mechanism (see section 22.7.1). 22.7.5 Embedding the OCaml code in the C code =============================================== The bytecode compiler in custom runtime mode (ocamlc -custom) normally appends the bytecode to the executable file containing the custom runtime. This has two consequences. First, the final linking step must be performed by ocamlc. Second, the OCaml runtime library must be able to find the name of the executable file from the command-line arguments. When using caml_main(argv) as in section 22.7.4, this means that argv[0] or argv[1] must contain the executable file name. An alternative is to embed the bytecode in the C code. The -output-obj and -output-complete-obj options to ocamlc are provided for this purpose. They cause the ocamlc compiler to output a C object file (.o file, .obj under Windows) containing the bytecode for the OCaml part of the program, as well as a caml_startup function. The C object file produced by ocamlc -output-complete-obj also contains the runtime and autolink libraries. The C object file produced by ocamlc -output-obj or ocamlc -output-complete-obj can then be linked with C code using the standard C compiler, or stored in a C library. The caml_startup function must be called from the main C program in order to initialize the OCaml runtime and execute the OCaml initialization code. Just like caml_main, it takes one argv parameter containing the command-line parameters. Unlike caml_main, this argv parameter is used only to initialize Sys.argv, but not for finding the name of the executable file. The caml_startup function calls the uncaught exception handler (or enters the debugger, if running under ocamldebug) if an exception escapes from a top-level module initialiser. Such exceptions may be caught in the C code by instead using the caml_startup_exn function and testing the result using Is_exception_result (followed by Extract_exception if appropriate). The -output-obj and -output-complete-obj options can also be used to obtain the C source file. More interestingly, these options can also produce directly a shared library (.so file, .dll under Windows) that contains the OCaml code, the OCaml runtime system and any other static C code given to ocamlc (.o, .a, respectively, .obj, .lib). This use of -output-obj and -output-complete-obj is very similar to a normal linking step, but instead of producing a main program that automatically runs the OCaml code, it produces a shared library that can run the OCaml code on demand. The three possible behaviors of -output-obj and -output-complete-obj (to produce a C source code .c, a C object file .o, a shared library .so), are selected according to the extension of the resulting file (given with -o). The native-code compiler ocamlopt also supports the -output-obj and -output-complete-obj options, causing it to output a C object file or a shared library containing the native code for all OCaml modules on the command-line, as well as the OCaml startup code. Initialization is performed by calling caml_startup (or caml_startup_exn) as in the case of the bytecode compiler. The file produced by ocamlopt -output-complete-obj also contains the runtime and autolink libraries. For the final linking phase, in addition to the object file produced by -output-obj, you will have to provide the OCaml runtime library (libcamlrun.a for bytecode, libasmrun.a for native-code), as well as all C libraries that are required by the OCaml libraries used. For instance, assume the OCaml part of your program uses the Unix library. With ocamlc, you should do: << ocamlc -output-obj -o camlcode.o unix.cma other .cmo and .cma files cc -o myprog C objects and libraries \ camlcode.o -L‘ocamlc -where‘ -lunix -lcamlrun >> With ocamlopt, you should do: << ocamlopt -output-obj -o camlcode.o unix.cmxa other .cmx and .cmxa files cc -o myprog C objects and libraries \ camlcode.o -L‘ocamlc -where‘ -lunix -lasmrun >> For the final linking phase, in addition to the object file produced by -output-complete-obj, you will have only to provide the C libraries required by the OCaml runtime. For instance, assume the OCaml part of your program uses the Unix library. With ocamlc, you should do: << ocamlc -output-complete-obj -o camlcode.o unix.cma other .cmo and .cma files cc -o myprog C objects and libraries \ camlcode.o C libraries required by the runtime, eg -lm -ldl -lcurses -lpthread >> With ocamlopt, you should do: << ocamlopt -output-complete-obj -o camlcode.o unix.cmxa other .cmx and .cmxa files cc -o myprog C objects and libraries \ camlcode.o C libraries required by the runtime, eg -lm -ldl >> Warning: On some ports, special options are required on the final linking phase that links together the object file produced by the -output-obj and -output-complete-obj options and the remainder of the program. Those options are shown in the configuration file Makefile.config generated during compilation of OCaml, as the variable OC_LDFLAGS. - Windows with the MSVC compiler: the object file produced by OCaml have been compiled with the /MD flag, and therefore all other object files linked with it should also be compiled with /MD. - other systems: you may have to add one or both of -lm and -ldl, depending on your OS and C compiler. Stack backtraces. When OCaml bytecode produced by ocamlc -g is embedded in a C program, no debugging information is included, and therefore it is impossible to print stack backtraces on uncaught exceptions. This is not the case when native code produced by ocamlopt -g is embedded in a C program: stack backtrace information is available, but the backtrace mechanism needs to be turned on programmatically. This can be achieved from the OCaml side by calling Printexc.record_backtrace true in the initialization of one of the OCaml modules. This can also be achieved from the C side by calling caml_record_backtraces(1); in the OCaml-C glue code. (caml_record_backtraces is declared in backtrace.h) Unloading the runtime. In case the shared library produced with -output-obj is to be loaded and unloaded repeatedly by a single process, care must be taken to unload the OCaml runtime explicitly, in order to avoid various system resource leaks. Since 4.05, caml_shutdown function can be used to shut the runtime down gracefully, which equals the following: - Running the functions that were registered with Stdlib.at_exit. - Triggering finalization of allocated custom blocks (see section 22.9). For example, Stdlib.in_channel and Stdlib.out_channel are represented by custom blocks that enclose file descriptors, which are to be released. - Unloading the dependent shared libraries that were loaded by the runtime, including dynlink plugins. - Freeing the memory blocks that were allocated by the runtime with malloc. Inside C primitives, it is advised to use caml_stat_* functions from memory.h for managing static (that is, non-moving) blocks of heap memory, as all the blocks allocated with these functions are automatically freed by caml_shutdown. For ensuring compatibility with legacy C stubs that have used caml_stat_* incorrectly, this behaviour is only enabled if the runtime is started with a specialized caml_startup_pooled function. As a shared library may have several clients simultaneously, it is made for convenience that caml_startup (and caml_startup_pooled) may be called multiple times, given that each such call is paired with a corresponding call to caml_shutdown (in a nested fashion). The runtime will be unloaded once there are no outstanding calls to caml_startup. Once a runtime is unloaded, it cannot be started up again without reloading the shared library and reinitializing its static data. Therefore, at the moment, the facility is only useful for building reloadable shared libraries. Unix signal handling. Depending on the target platform and operating system, the native-code runtime system may install signal handlers for one or several of the SIGSEGV, SIGTRAP and SIGFPE signals when caml_startup is called, and reset these signals to their default behaviors when caml_shutdown is called. The main program written in C should not try to handle these signals itself. 22.8 Advanced example with callbacks *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This section illustrates the callback facilities described in section 22.7. We are going to package some OCaml functions in such a way that they can be linked with C code and called from C just like any C functions. The OCaml functions are defined in the following mod.ml OCaml source: <<(* File mod.ml -- some "useful" OCaml functions *) let rec fib n = if n < 2 then 1 else fib(n-1) + fib(n-2) let format_result n = Printf.sprintf "Result is: %d\n" n (* Export those two functions to C *) let _ = Callback.register "fib" fib let _ = Callback.register "format_result" format_result >> Here is the C stub code for calling these functions from C: < #include #include #include int fib(int n) { static const value * fib_closure = NULL; if (fib_closure == NULL) fib_closure = caml_named_value("fib"); return Int_val(caml_callback(*fib_closure, Val_int(n))); } char * format_result(int n) { static const value * format_result_closure = NULL; if (format_result_closure == NULL) format_result_closure = caml_named_value("format_result"); return strdup(String_val(caml_callback(*format_result_closure, Val_int(n)))); /* We copy the C string returned by String_val to the C heap so that it remains valid after garbage collection. */ } >> We now compile the OCaml code to a C object file and put it in a C library along with the stub code in modwrap.c and the OCaml runtime system: << ocamlc -custom -output-obj -o modcaml.o mod.ml ocamlc -c modwrap.c cp `ocamlc -where`/libcamlrun.a mod.a && chmod +w mod.a ar r mod.a modcaml.o modwrap.o >> (One can also use ocamlopt -output-obj instead of ocamlc -custom -output-obj. In this case, replace libcamlrun.a (the bytecode runtime library) by libasmrun.a (the native-code runtime library).) Now, we can use the two functions fib and format_result in any C program, just like regular C functions. Just remember to call caml_startup (or caml_startup_exn) once before. < #include extern int fib(int n); extern char * format_result(int n); int main(int argc, char ** argv) { int result; /* Initialize OCaml code */ caml_startup(argv); /* Do some computation */ result = fib(10); printf("fib(10) = %s\n", format_result(result)); return 0; } >> To build the whole program, just invoke the C compiler as follows: << cc -o prog -I `ocamlc -where` main.c mod.a -lcurses >> (On some machines, you may need to put -ltermcap or -lcurses -ltermcap instead of -lcurses.) 22.9 Advanced topic: custom blocks *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Blocks with tag Custom_tag contain both arbitrary user data and a pointer to a C struct, with type struct custom_operations, that associates user-provided finalization, comparison, hashing, serialization and deserialization functions to this block. 22.9.1 The struct custom_operations ===================================== The struct custom_operations is defined in and contains the following fields: - char *identifier A zero-terminated character string serving as an identifier for serialization and deserialization operations. - void (*finalize)(value v) The finalize field contains a pointer to a C function that is called when the block becomes unreachable and is about to be reclaimed. The block is passed as first argument to the function. The finalize field can also be custom_finalize_default to indicate that no finalization function is associated with the block. - int (*compare)(value v1, value v2) The compare field contains a pointer to a C function that is called whenever two custom blocks are compared using OCaml’s generic comparison operators (=, <>, <=, >=, <, > and compare). The C function should return 0 if the data contained in the two blocks are structurally equal, a negative integer if the data from the first block is less than the data from the second block, and a positive integer if the data from the first block is greater than the data from the second block. The compare field can be set to custom_compare_default; this default comparison function simply raises Failure. - int (*compare_ext)(value v1, value v2) (Since 3.12.1) The compare_ext field contains a pointer to a C function that is called whenever one custom block and one unboxed integer are compared using OCaml’s generic comparison operators (=, <>, <=, >=, <, > and compare). As in the case of the compare field, the C function should return 0 if the two arguments are structurally equal, a negative integer if the first argument compares less than the second argument, and a positive integer if the first argument compares greater than the second argument. The compare_ext field can be set to custom_compare_ext_default; this default comparison function simply raises Failure. - intnat (*hash)(value v) The hash field contains a pointer to a C function that is called whenever OCaml’s generic hash operator (see module Hashtbl) is applied to a custom block. The C function can return an arbitrary integer representing the hash value of the data contained in the given custom block. The hash value must be compatible with the compare function, in the sense that two structurally equal data (that is, two custom blocks for which compare returns 0) must have the same hash value. The hash field can be set to custom_hash_default, in which case the custom block is ignored during hash computation. - void (*serialize)(value v, uintnat * bsize_32, uintnat * bsize_64) The serialize field contains a pointer to a C function that is called whenever the custom block needs to be serialized (marshaled) using the OCaml functions output_value or Marshal.to_.... For a custom block, those functions first write the identifier of the block (as given by the identifier field) to the output stream, then call the user-provided serialize function. That function is responsible for writing the data contained in the custom block, using the serialize_... functions defined in and listed in section 22.9.4. The user-provided serialize function must then store in its bsize_32 and bsize_64 parameters the sizes in bytes of the data part of the custom block on a 32-bit architecture and on a 64-bit architecture, respectively. The serialize field can be set to custom_serialize_default, in which case the Failure exception is raised when attempting to serialize the custom block. - uintnat (*deserialize)(void * dst) The deserialize field contains a pointer to a C function that is called whenever a custom block with identifier identifier needs to be deserialized (un-marshaled) using the OCaml functions input_value or Marshal.from_.... This user-provided function is responsible for reading back the data written by the serialize operation, using the deserialize_... functions defined in and listed in section 22.9.4. It must then rebuild the data part of the custom block and store it at the pointer given as the dst argument. Finally, it returns the size in bytes of the data part of the custom block. This size must be identical to the wsize_32 result of the serialize operation if the architecture is 32 bits, or wsize_64 if the architecture is 64 bits. The deserialize field can be set to custom_deserialize_default to indicate that deserialization is not supported. In this case, do not register the struct custom_operations with the deserializer using register_custom_operations (see below). - const struct custom_fixed_length* fixed_length (Since 4.08.0) Normally, space in the serialized output is reserved to write the bsize_32 and bsize_64 fields returned by serialize. However, for very short custom blocks, this space can be larger than the data itself! As a space optimisation, if serialize always returns the same values for bsize_32 and bsize_64, then these values may be specified in the fixed_length structure, and do not consume space in the serialized output. Note: the finalize, compare, hash, serialize, and deserialize functions attached to custom blocks descriptors are only allowed limited interactions with the OCaml runtime. Within these functions, do not call any of the OCaml allocation functions, and do not perform any callback into OCaml code. Do not use CAMLparam to register the parameters to these functions, and do not use CAMLreturn to return the result. Do not raise exceptions (to signal an error during deserialization, use caml_deserialize_error). Do not remove global roots. When in doubt, err on the side of caution. Within serialize and deserialize functions, use of the corresponding functions from section 22.9.4 is allowed (and even recommended). 22.9.2 Allocating custom blocks ================================= Custom blocks must be allocated via caml_alloc_custom or caml_alloc_custom_mem: caml_alloc_custom(ops, size, used, max) returns a fresh custom block, with room for size bytes of user data, and whose associated operations are given by ops (a pointer to a struct custom_operations, usually statically allocated as a C global variable). The two parameters used and max are used to control the speed of garbage collection when the finalized object contains pointers to out-of-heap resources. Generally speaking, the OCaml incremental major collector adjusts its speed relative to the allocation rate of the program. The faster the program allocates, the harder the GC works in order to reclaim quickly unreachable blocks and avoid having large amount of “floating garbage” (unreferenced objects that the GC has not yet collected). Normally, the allocation rate is measured by counting the in-heap size of allocated blocks. However, it often happens that finalized objects contain pointers to out-of-heap memory blocks and other resources (such as file descriptors, X Windows bitmaps, etc.). For those blocks, the in-heap size of blocks is not a good measure of the quantity of resources allocated by the program. The two arguments used and max give the GC an idea of how much out-of-heap resources are consumed by the finalized block being allocated: you give the amount of resources allocated to this object as parameter used, and the maximum amount that you want to see in floating garbage as parameter max. The units are arbitrary: the GC cares only about the ratio used / max. For instance, if you are allocating a finalized block holding an X Windows bitmap of w by h pixels, and you’d rather not have more than 1 mega-pixels of unreclaimed bitmaps, specify used = w * h and max = 1000000. Another way to describe the effect of the used and max parameters is in terms of full GC cycles. If you allocate many custom blocks with used / max = 1 / N, the GC will then do one full cycle (examining every object in the heap and calling finalization functions on those that are unreachable) every N allocations. For instance, if used = 1 and max = 1000, the GC will do one full cycle at least every 1000 allocations of custom blocks. If your finalized blocks contain no pointers to out-of-heap resources, or if the previous discussion made little sense to you, just take used = 0 and max = 1. But if you later find that the finalization functions are not called “often enough”, consider increasing the used / max ratio. caml_alloc_custom_mem(ops, size, used) Use this function when your custom block holds only out-of-heap memory (memory allocated with malloc or caml_stat_alloc) and no other resources. used should be the number of bytes of out-of-heap memory that are held by your custom block. This function works like caml_alloc_custom except that the max parameter is under the control of the user (via the custom_major_ratio, custom_minor_ratio, and custom_minor_max_size parameters) and proportional to the heap sizes. It has been available since OCaml 4.08.0. 22.9.3 Accessing custom blocks ================================ The data part of a custom block v can be accessed via the pointer Data_custom_val(v). This pointer has type void * and should be cast to the actual type of the data stored in the custom block. The contents of custom blocks are not scanned by the garbage collector, and must therefore not contain any pointer inside the OCaml heap. In other terms, never store an OCaml value in a custom block, and do not use Field, Store_field nor caml_modify to access the data part of a custom block. Conversely, any C data structure (not containing heap pointers) can be stored in a custom block. 22.9.4 Writing custom serialization and deserialization functions =================================================================== The following functions, defined in , are provided to write and read back the contents of custom blocks in a portable way. Those functions handle endianness conversions when e.g. data is written on a little-endian machine and read back on a big-endian machine. ---------------------------------------------------------- | Function | Action | ---------------------------------------------------------- | caml_serialize_int_1 |Write a 1-byte integer | |caml_serialize_int_2 |Write a 2-byte integer | |caml_serialize_int_4 |Write a 4-byte integer | |caml_serialize_int_8 |Write a 8-byte integer | |caml_serialize_float_4 |Write a 4-byte float | |caml_serialize_float_8 |Write a 8-byte float | |caml_serialize_block_1 |Write an array of 1-byte | | |quantities | |caml_serialize_block_2 |Write an array of 2-byte | | |quantities | |caml_serialize_block_4 |Write an array of 4-byte | | |quantities | |caml_serialize_block_8 |Write an array of 8-byte | | |quantities | |caml_deserialize_uint_1 |Read an unsigned 1-byte integer| | | | |caml_deserialize_sint_1 |Read a signed 1-byte integer | |caml_deserialize_uint_2 |Read an unsigned 2-byte integer| | | | |caml_deserialize_sint_2 |Read a signed 2-byte integer | |caml_deserialize_uint_4 |Read an unsigned 4-byte integer| | | | |caml_deserialize_sint_4 |Read a signed 4-byte integer | |caml_deserialize_uint_8 |Read an unsigned 8-byte integer| | | | |caml_deserialize_sint_8 |Read a signed 8-byte integer | |caml_deserialize_float_4|Read a 4-byte float | |caml_deserialize_float_8|Read an 8-byte float | |caml_deserialize_block_1|Read an array of 1-byte | | |quantities | |caml_deserialize_block_2|Read an array of 2-byte | | |quantities | |caml_deserialize_block_4|Read an array of 4-byte | | |quantities | |caml_deserialize_block_8|Read an array of 8-byte | | |quantities | |caml_deserialize_error |Signal an error during | | |deserialization; input_value or| | |Marshal.from_... raise a | | |Failure exception after | | |cleaning up their internal data| | |structures | ---------------------------------------------------------- Serialization functions are attached to the custom blocks to which they apply. Obviously, deserialization functions cannot be attached this way, since the custom block does not exist yet when deserialization begins! Thus, the struct custom_operations that contain deserialization functions must be registered with the deserializer in advance, using the register_custom_operations function declared in . Deserialization proceeds by reading the identifier off the input stream, allocating a custom block of the size specified in the input stream, searching the registered struct custom_operation blocks for one with the same identifier, and calling its deserialize function to fill the data part of the custom block. 22.9.5 Choosing identifiers ============================= Identifiers in struct custom_operations must be chosen carefully, since they must identify uniquely the data structure for serialization and deserialization operations. In particular, consider including a version number in the identifier; this way, the format of the data can be changed later, yet backward-compatible deserialisation functions can be provided. Identifiers starting with _ (an underscore character) are reserved for the OCaml runtime system; do not use them for your custom data. We recommend to use a URL (http://mymachine.mydomain.com/mylibrary/version-number) or a Java-style package name (com.mydomain.mymachine.mylibrary.version-number) as identifiers, to minimize the risk of identifier collision. 22.9.6 Finalized blocks ========================= Custom blocks generalize the finalized blocks that were present in OCaml prior to version 3.00. For backwards compatibility, the format of custom blocks is compatible with that of finalized blocks, and the caml_alloc_final function is still available to allocate a custom block with a given finalization function, but default comparison, hashing and serialization functions. (In particular, the finalization function must not access the OCaml runtime.) caml_alloc_final(n, f, used, max) returns a fresh custom block of size n+1 words, with finalization function f. The first word is reserved for storing the custom operations; the other n words are available for your data. The two parameters used and max are used to control the speed of garbage collection, as described for caml_alloc_custom. 22.10 Advanced topic: Bigarrays and the OCaml-C interface *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This section explains how C stub code that interfaces C or Fortran code with OCaml code can use Bigarrays. 22.10.1 Include file ====================== The include file must be included in the C stub file. It declares the functions, constants and macros discussed below. 22.10.2 Accessing an OCaml bigarray from C or Fortran ======================================================= If v is a OCaml value representing a Bigarray, the expression Caml_ba_data_val(v) returns a pointer to the data part of the array. This pointer is of type void * and can be cast to the appropriate C type for the array (e.g. double [], char [][10], etc). Various characteristics of the OCaml Bigarray can be consulted from C as follows: ------------------------------------------------------------------------- | C expression | Returns | ------------------------------------------------------------------------- | Caml_ba_array_val(v)->num_dims |number of dimensions | |Caml_ba_array_val(v)->dim[i] |i-th dimension | |Caml_ba_array_val(v)->flags & CAML_BA_KIND_MASK|kind of array elements | ------------------------------------------------------------------------- The kind of array elements is one of the following constants: -------------------------------------------------------------- | Constant | Element kind | -------------------------------------------------------------- | CAML_BA_FLOAT16 |16-bit half-precision floats | |CAML_BA_FLOAT32 |32-bit single-precision floats | |CAML_BA_FLOAT64 |64-bit double-precision floats | |CAML_BA_SINT8 |8-bit signed integers | |CAML_BA_UINT8 |8-bit unsigned integers | |CAML_BA_SINT16 |16-bit signed integers | |CAML_BA_UINT16 |16-bit unsigned integers | |CAML_BA_INT32 |32-bit signed integers | |CAML_BA_INT64 |64-bit signed integers | |CAML_BA_CAML_INT |31- or 63-bit signed integers | |CAML_BA_NATIVE_INT|32- or 64-bit (platform-native) integers | |CAML_BA_COMPLEX32 |32-bit single-precision complex numbers | |CAML_BA_COMPLEX64 |64-bit double-precision complex numbers | |CAML_BA_CHAR |8-bit characters | -------------------------------------------------------------- Warning: Caml_ba_array_val(v) must always be dereferenced immediately and not stored anywhere, including local variables. It resolves to a derived pointer: it is not a valid OCaml value but points to a memory region managed by the GC. For this reason this value must not be stored in any memory location that could be live cross a GC. The following example shows the passing of a two-dimensional Bigarray to a C function and a Fortran function. << extern void my_c_function(double * data, int dimx, int dimy); extern void my_fortran_function_(double * data, int * dimx, int * dimy); CAMLprim value caml_stub(value bigarray) { int dimx = Caml_ba_array_val(bigarray)->dim[0]; int dimy = Caml_ba_array_val(bigarray)->dim[1]; /* C passes scalar parameters by value */ my_c_function(Caml_ba_data_val(bigarray), dimx, dimy); /* Fortran passes all parameters by reference */ my_fortran_function_(Caml_ba_data_val(bigarray), &dimx, &dimy); return Val_unit; } >> 22.10.3 Wrapping a C or Fortran array as an OCaml Bigarray ============================================================ A pointer p to an already-allocated C or Fortran array can be wrapped and returned to OCaml as a Bigarray using the caml_ba_alloc or caml_ba_alloc_dims functions. - caml_ba_alloc(kind | layout, numdims, p, dims) Return an OCaml Bigarray wrapping the data pointed to by p. kind is the kind of array elements (one of the CAML_BA_ kind constants above). layout is CAML_BA_C_LAYOUT for an array with C layout and CAML_BA_FORTRAN_LAYOUT for an array with Fortran layout. numdims is the number of dimensions in the array. dims is an array of numdims long integers, giving the sizes of the array in each dimension. - caml_ba_alloc_dims(kind | layout, numdims, p, (long) dim_1, (long) dim_2, ..., (long) dim_numdims) Same as caml_ba_alloc, but the sizes of the array in each dimension are listed as extra arguments in the function call, rather than being passed as an array. The following example illustrates how statically-allocated C and Fortran arrays can be made available to OCaml. << extern long my_c_array[100][200]; extern float my_fortran_array_[300][400]; CAMLprim value caml_get_c_array(value unit) { long dims[2]; dims[0] = 100; dims[1] = 200; return caml_ba_alloc(CAML_BA_NATIVE_INT | CAML_BA_C_LAYOUT, 2, my_c_array, dims); } CAMLprim value caml_get_fortran_array(value unit) { return caml_ba_alloc_dims(CAML_BA_FLOAT32 | CAML_BA_FORTRAN_LAYOUT, 2, my_fortran_array_, 300L, 400L); } >> 22.11 Advanced topic: cheaper C call *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This section describe how to make calling C functions cheaper. Note: This only applies to the native compiler. So whenever you use any of these methods, you have to provide an alternative byte-code stub that ignores all the special annotations. 22.11.1 Passing unboxed values ================================ We said earlier that all OCaml objects are represented by the C type value, and one has to use macros such as Int_val to decode data from the value type. It is however possible to tell the OCaml native-code compiler to do this for us and pass arguments unboxed to the C function. Similarly it is possible to tell OCaml to expect the result unboxed and box it for us. The motivation is that, by letting ‘ocamlopt‘ deal with boxing, it can often decide to suppress it entirely. For instance let’s consider this example: < float -> float = "foo" let f a b = let len = Array.length a in assert (Array.length b = len); let res = Array.make len 0. in for i = 0 to len - 1 do res.(i) <- foo a.(i) b.(i) done >> Float arrays are unboxed in OCaml, however the C function foo expect its arguments as boxed floats and returns a boxed float. Hence the OCaml compiler has no choice but to box a.(i) and b.(i) and unbox the result of foo. This results in the allocation of 3 * len temporary float values. Now if we annotate the arguments and result with [@unboxed], the native-code compiler will be able to avoid all these allocations: < (float [@unboxed]) -> (float [@unboxed]) = "foo_byte" "foo" >> In this case the C functions must look like: <> For convenience, when all arguments and the result are annotated with [@unboxed], it is possible to put the attribute only once on the declaration itself. So we can also write instead: < float -> float = "foo_byte" "foo" [@@unboxed] >> The following table summarize what OCaml types can be unboxed, and what C types should be used in correspondence: --------------------- |OCaml type|C type | --------------------- | float |double | |int32 |int32_t | |int64 |int64_t | |nativeint |intnat | --------------------- Similarly, it is possible to pass untagged OCaml integers between OCaml and C. This is done by annotating the arguments and/or result with [@untagged]: < (int [@untagged]) = "f_byte" "f" >> The corresponding C type must be intnat. Note: Do not use the C int type in correspondence with (int [@untagged]). This is because they often differ in size. It is possible to annotate with [@untagged] any immediate type, i.e. types that are represented like int. This includes bool, char, any variant type with only constant constructors. Note: this does not include Unix.file_descr which is not represented as an interger on all platforms. 22.11.2 Direct C call ======================= In order to be able to run the garbage collector in the middle of a C function, the OCaml native-code compiler generates some bookkeeping code around C calls. Technically it wraps every C call with the C function caml_c_call which is part of the OCaml runtime. For small functions that are called repeatedly, this indirection can have a big impact on performances. However this is not needed if we know that the C function doesn’t allocate, doesn’t raise exceptions, and doesn’t release the domain lock (see section 22.12.2). We can instruct the OCaml native-code compiler of this fact by annotating the external declaration with the attribute [@@noalloc]: < int -> int = "foo" [@@noalloc] >> In this case calling bar from OCaml is as cheap as calling any other OCaml function, except for the fact that the OCaml compiler can’t inline C functions... 22.11.3 Example: calling C library functions without indirection ================================================================== Using these attributes, it is possible to call C library functions with no indirection. For instance many math functions are defined this way in the OCaml standard library: < float = "caml_sqrt_float" "sqrt" [@@unboxed] [@@noalloc] (** Square root. *) external exp : float -> float = "caml_exp_float" "exp" [@@unboxed] [@@noalloc] (** Exponential. *) external log : float -> float = "caml_log_float" "log" [@@unboxed] [@@noalloc] (** Natural logarithm. *) >> 22.12 Advanced topic: multithreading *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Using multiple threads (shared-memory concurrency) in a mixed OCaml/C application requires special precautions, which are described in this section. 22.12.1 Registering threads created from C ============================================ Callbacks from C to OCaml are possible only if the calling thread is known to the OCaml run-time system. Threads created from OCaml (through the Thread.create function of the system threads library) are automatically known to the run-time system. If the application creates additional threads from C and wishes to callback into OCaml code from these threads, it must first register them with the run-time system. The following functions are declared in the include file . - caml_c_thread_register() registers the calling thread with the OCaml run-time system. Returns 1 on success, 0 on error. Registering an already-registered thread does nothing and returns 0. - caml_c_thread_unregister() must be called before the thread terminates, to unregister it from the OCaml run-time system. Returns 1 on success, 0 on error. If the calling thread was not previously registered, does nothing and returns 0. 22.12.2 Parallel execution of long-running C code with systhreads =================================================================== Domains are the unit of parallelism for OCaml programs. When using the systhreads library, multiple threads might be attached to the same domain. However, at any time, at most one of those thread can be executing OCaml code or C code that uses the OCaml run-time system by domain. Technically, this is enforced by a “domain lock” that any thread must hold while executing such code within a domain. When OCaml calls the C code implementing a primitive, the domain lock is held, therefore the C code has full access to the facilities of the run-time system. However, no other thread in the same domain can execute OCaml code concurrently with the C code of the primitive. See also chapter 9.6 for the behaviour with multiple domains. If a C primitive runs for a long time or performs potentially blocking input-output operations, it can explicitly release the domain lock, enabling other OCaml threads in the same domain to run concurrently with its operations. The C code must re-acquire the domain lock before returning to OCaml. This is achieved with the following functions, declared in the include file . - caml_release_runtime_system() The calling thread releases the domain lock and other OCaml resources, enabling other threads to run OCaml code in parallel with the execution of the calling thread. - caml_acquire_runtime_system() The calling thread re-acquires the domain lock and other OCaml resources. It may block until no other thread in the same domain uses the OCaml run-time system. These functions poll for pending signals by calling asynchronous callbacks (section 22.5.3) before releasing and after acquiring the lock. They can therefore execute arbitrary OCaml code including raising an asynchronous exception. After caml_release_runtime_system() was called and until caml_acquire_runtime_system() is called, the C code must not access any OCaml data, nor call any function of the run-time system, nor call back into OCaml code. Consequently, arguments provided by OCaml to the C primitive must be copied into C data structures before calling caml_release_runtime_system(), and results to be returned to OCaml must be encoded as OCaml values after caml_acquire_runtime_system() returns. Example: the following C primitive invokes gethostbyname to find the IP address of a host name. The gethostbyname function can block for a long time, so we choose to release the OCaml run-time system while it is running. <> The macro Caml_state evaluates to the domain state variable, and checks in debug mode that the domain lock is held. Such a check is also placed in normal mode at key entry points of the C API; this is why calling some of the runtime functions and macros without correctly owning the domain lock can result in a fatal error: no domain lock held. The variant Caml_state_opt does not perform any check but evaluates to NULL when the domain lock is not held. This lets you determine whether a thread belonging to a domain currently holds its domain lock, for various purposes. Callbacks from C to OCaml must be performed while holding the domain lock to the OCaml run-time system. This is naturally the case if the callback is performed by a C primitive that did not release the run-time system. If the C primitive released the run-time system previously, or the callback is performed from other C code that was not invoked from OCaml (e.g. an event loop in a GUI application), the run-time system must be acquired before the callback and released after: << caml_acquire_runtime_system(); /* Resolve OCaml function vfun to be invoked */ /* Build OCaml argument varg to the callback */ vres = callback(vfun, varg); /* Copy relevant parts of result vres to C data structures */ caml_release_runtime_system(); >> Note: the acquire and release functions described above were introduced in OCaml 3.12. Older code uses the following historical names, declared in : - caml_enter_blocking_section as an alias for caml_release_runtime_system - caml_leave_blocking_section as an alias for caml_acquire_runtime_system Intuition: a “blocking section” is a piece of C code that does not use the OCaml run-time system, typically a blocking input/output operation. 22.13 Advanced topic: interfacing with Windows Unicode APIs *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This section contains some general guidelines for writing C stubs that use Windows Unicode APIs. The OCaml system under Windows can be configured at build time in one of two modes: - legacy mode: All path names, environment variables, command line arguments, etc. on the OCaml side are assumed to be encoded using the current 8-bit code page of the system. - Unicode mode: All path names, environment variables, command line arguments, etc. on the OCaml side are assumed to be encoded using UTF-8. In what follows, we say that a string has the OCaml encoding if it is encoded in UTF-8 when in Unicode mode, in the current code page in legacy mode, or is an arbitrary string under Unix. A string has the platform encoding if it is encoded in UTF-16 under Windows or is an arbitrary string under Unix. From the point of view of the writer of C stubs, the challenges of interacting with Windows Unicode APIs are twofold: - The Windows API uses the UTF-16 encoding to support Unicode. The runtime system performs the necessary conversions so that the OCaml programmer only needs to deal with the OCaml encoding. C stubs that call Windows Unicode APIs need to use specific runtime functions to perform the necessary conversions in a compatible way. - When writing stubs that need to be compiled under both Windows and Unix, the stubs need to be written in a way that allow the necessary conversions under Windows but that also work under Unix, where typically nothing particular needs to be done to support Unicode. The native C character type under Windows is WCHAR, two bytes wide, while under Unix it is char, one byte wide. A type char_os is defined in that stands for the concrete C character type of each platform. Strings in the platform encoding are of type char_os *. The following functions are exposed to help write compatible C stubs. To use them, you need to include both and . - char_os* caml_stat_strdup_to_os(const char *) copies the argument while translating from OCaml encoding to the platform encoding. This function is typically used to convert the char * underlying an OCaml string before passing it to an operating system API that takes a Unicode argument. Under Unix, it is equivalent to caml_stat_strdup. Note: For maximum backwards compatibility in Unicode mode, if the argument is not a valid UTF-8 string, this function will fall back to assuming that it is encoded in the current code page. - char* caml_stat_strdup_of_os(const char_os *) copies the argument while translating from the platform encoding to the OCaml encoding. It is the inverse of caml_stat_strdup_to_os. This function is typically used to convert a string obtained from the operating system before passing it on to OCaml code. Under Unix, it is equivalent to caml_stat_strdup. - value caml_copy_string_of_os(char_os *) allocates an OCaml string with contents equal to the argument string converted to the OCaml encoding. This function is essentially equivalent to caml_stat_strdup_of_os followed by caml_copy_string, except that it avoids the allocation of the intermediate string returned by caml_stat_strdup_of_os. Under Unix, it is equivalent to caml_copy_string. Note: The strings returned by caml_stat_strdup_to_os and caml_stat_strdup_of_os are allocated using caml_stat_alloc, so they need to be deallocated using caml_stat_free when they are no longer needed. Example We want to bind the function getenv in a way that works both under Unix and Windows. Under Unix this function has the prototype: << char *getenv(const char *); >> While the Unicode version under Windows has the prototype: << WCHAR *_wgetenv(const WCHAR *); >> In terms of char_os, both functions take an argument of type char_os * and return a result of the same type. We begin by choosing the right implementation of the function to bind: <<#ifdef _WIN32 #define getenv_os _wgetenv #else #define getenv_os getenv #endif >> The rest of the binding is the same for both platforms: <<#include #include #include #include #include #include CAMLprim value stub_getenv(value var_name) { CAMLparam1(var_name); CAMLlocal1(var_value); char_os *var_name_os, *var_value_os; var_name_os = caml_stat_strdup_to_os(String_val(var_name)); var_value_os = getenv_os(var_name_os); caml_stat_free(var_name_os); if (var_value_os == NULL) caml_raise_not_found(); var_value = caml_copy_string_of_os(var_value_os); CAMLreturn(var_value); } >> 22.14 Building mixed C/OCaml libraries: ocamlmklib *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The ocamlmklib command facilitates the construction of libraries containing both OCaml code and C code, and usable both in static linking and dynamic linking modes. This command is available under Windows since Objective Caml 3.11 and under other operating systems since Objective Caml 3.03. The ocamlmklib command takes three kinds of arguments: - OCaml source files and object files (.cmo, .cmx, .ml) comprising the OCaml part of the library; - C object files (.o, .a, respectively, .obj, .lib) comprising the C part of the library; - Support libraries for the C part (-llib). It generates the following outputs: - An OCaml bytecode library .cma incorporating the .cmo and .ml OCaml files given as arguments, and automatically referencing the C library generated with the C object files. - An OCaml native-code library .cmxa incorporating the .cmx and .ml OCaml files given as arguments, and automatically referencing the C library generated with the C object files. - If dynamic linking is supported on the target platform, a .so (respectively, .dll) shared library built from the C object files given as arguments, and automatically referencing the support libraries. - A C static library .a(respectively, .lib) built from the C object files. In addition, the following options are recognized: -cclib, -ccopt, -I, -linkall These options are passed as is to ocamlc or ocamlopt. See the documentation of these commands. -rpath, -R, -Wl,-rpath, -Wl,-R These options are passed as is to the C compiler. Refer to the documentation of the C compiler. -custom Force the construction of a statically linked library only, even if dynamic linking is supported. -failsafe Fall back to building a statically linked library if a problem occurs while building the shared library (e.g. some of the support libraries are not available as shared libraries). -Ldir Add dir to the search path for support libraries (-llib). -ocamlc cmd Use cmd instead of ocamlc to call the bytecode compiler. -ocamlopt cmd Use cmd instead of ocamlopt to call the native-code compiler. -o output Set the name of the generated OCaml library. ocamlmklib will generate output.cma and/or output.cmxa. If not specified, defaults to a. -oc outputc Set the name of the generated C library. ocamlmklib will generate liboutputc.so (if shared libraries are supported) and liboutputc.a. If not specified, defaults to the output name given with -o. Example Consider an OCaml interface to the standard libz C library for reading and writing compressed files. Assume this library resides in /usr/local/zlib. This interface is composed of an OCaml part zip.cmo/zip.cmx and a C part zipstubs.o containing the stub code around the libz entry points. The following command builds the OCaml libraries zip.cma and zip.cmxa, as well as the companion C libraries dllzip.so and libzip.a: <> If shared libraries are supported, this performs the following commands: <> Note: This example is on a Unix system. The exact command lines may be different on other systems. If shared libraries are not supported, the following commands are performed instead: <> Instead of building simultaneously the bytecode library, the native-code library and the C libraries, ocamlmklib can be called three times to build each separately. Thus, <> builds the bytecode library zip.cma, and <> builds the native-code library zip.cmxa, and <> builds the C libraries dllzip.so and libzip.a. Notice that the support libraries (-lz) and the corresponding options (-L/usr/local/zlib) must be given on all three invocations of ocamlmklib, because they are needed at different times depending on whether shared libraries are supported. 22.15 Cautionary words: the internal runtime API *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Not all header available in the caml/ directory were described in previous sections. All those unmentioned headers are part of the internal runtime API, for which there is no stability guarantee. If you really need access to this internal runtime API, this section provides some guidelines that may help you to write code that might not break on every new version of OCaml. Note Programmers which come to rely on the internal API for a use-case which they find realistic and useful are encouraged to open a request for improvement on the bug tracker. 22.15.1 Internal variables and CAML_INTERNALS =============================================== Since OCaml 4.04, it is possible to get access to every part of the internal runtime API by defining the CAML_INTERNALS macro before loading caml header files. If this macro is not defined, parts of the internal runtime API are hidden. If you are using internal C variables, do not redefine them by hand. You should import those variables by including the corresponding header files. The representation of those variables has already changed once in OCaml 4.10, and is still under evolution. If your code relies on such internal and brittle properties, it will be broken at some point in time. For instance, rather than redefining caml_young_limit: <> which breaks in OCaml >= 4.10, you should include the minor_gc header: <<#include >> 22.15.2 OCaml version macros ============================== Finally, if including the right headers is not enough, or if you need to support version older than OCaml 4.04, the header file caml/version.h should help you to define your own compatibility layer. This file provides few macros defining the current OCaml version. In particular, the OCAML_VERSION macro describes the current version, its format is MmmPP. For example, if you need some specific handling for versions older than 4.10.0, you could write <<#include #if OCAML_VERSION >= 41000 ... #else ... #endif >> Chapter 23  Optimisation with Flambda ***************************************** 23.1 Overview *=*=*=*=*=*=*=* Flambda is the term used to describe a series of optimisation passes provided by the native code compilers as of OCaml 4.03. Flambda aims to make it easier to write idiomatic OCaml code without incurring performance penalties. To use the Flambda optimisers it is necessary to pass the -flambda option to the OCaml configure script. (There is no support for a single compiler that can operate in both Flambda and non-Flambda modes.) Code compiled with Flambda cannot be linked into the same program as code compiled without Flambda. Attempting to do this will result in a compiler error. Whether or not a particular ocamlopt uses Flambda may be determined by invoking it with the -config option and looking for any line starting with “flambda:”. If such a line is present and says “true”, then Flambda is supported, otherwise it is not. Flambda provides full optimisation across different compilation units, so long as the .cmx files for the dependencies of the unit currently being compiled are available. (A compilation unit corresponds to a single .ml source file.) However it does not yet act entirely as a whole-program compiler: for example, elimination of dead code across a complete set of compilation units is not supported. Optimisation with Flambda is not currently supported when generating bytecode. Flambda should not in general affect the semantics of existing programs. Two exceptions to this rule are: possible elimination of pure code that is being benchmarked (see section 23.14) and changes in behaviour of code using unsafe operations (see section 23.15). Flambda does not yet optimise array or string bounds checks. Neither does it take hints for optimisation from any assertions written by the user in the code. Consult the Glossary at the end of this chapter for definitions of technical terms used below. 23.2 Command-line flags *=*=*=*=*=*=*=*=*=*=*=*=* The Flambda optimisers provide a variety of command-line flags that may be used to control their behaviour. Detailed descriptions of each flag are given in the referenced sections. Those sections also describe any arguments which the particular flags take. Commonly-used options: -O2 Perform more optimisation than usual. Compilation times may be lengthened. (This flag is an abbreviation for a certain set of parameters described in section 23.5.) -O3 Perform even more optimisation than usual, possibly including unrolling of recursive functions. Compilation times may be significantly lengthened. -Oclassic Make inlining decisions at the point of definition of a function rather than at the call site(s). This mirrors the behaviour of OCaml compilers not using Flambda. Compared to compilation using the new Flambda inlining heuristics (for example at -O2) it produces smaller .cmx files, shorter compilation times and code that probably runs rather slower. When using -Oclassic, only the following options described in this section are relevant: -inlining-report and -inline. If any other of the options described in this section are used, the behaviour is undefined and may cause an error in future versions of the compiler. -inlining-report Emit .inlining files (one per round of optimisation) showing all of the inliner’s decisions. Less commonly-used options: -remove-unused-arguments Remove unused function arguments even when the argument is not specialised. This may have a small performance penalty. See section 23.10.3. -unbox-closures Pass free variables via specialised arguments rather than closures (an optimisation for reducing allocation). See section 23.9.3. This may have a small performance penalty. Advanced options, only needed for detailed tuning: -inline The behaviour depends on whether -Oclassic is used. - When not in -Oclassic mode, -inline limits the total size of functions considered for inlining during any speculative inlining search. (See section 23.3.6.) Note that this parameter does not control the assessment as to whether any particular function may be inlined. Raising it to excessive amounts will not necessarily cause more functions to be inlined. - When in -Oclassic mode, -inline behaves as in previous versions of the compiler: it is the maximum size of function to be considered for inlining. See section 23.3.1. -inline-toplevel The equivalent of -inline but used when speculative inlining starts at toplevel. See section 23.3.6. Not used in -Oclassic mode. -inline-branch-factor Controls how the inliner assesses whether a code path is likely to be hot or cold. See section 23.3.5. -inline-alloc-cost, -inline-branch-cost, -inline-call-cost Controls how the inliner assesses the runtime performance penalties associated with various operations. See section 23.3.5. -inline-indirect-cost, -inline-prim-cost Likewise. -inline-lifting-benefit Controls inlining of functors at toplevel. See section 23.3.5. -inline-max-depth The maximum depth of any speculative inlining search. See section 23.3.6. -inline-max-unroll The maximum depth of any unrolling of recursive functions during any speculative inlining search. See section 23.3.6. -no-unbox-free-vars-of-closures Do not unbox closure variables. See section 23.9.1. -no-unbox-specialised-args Do not unbox arguments to which functions have been specialised. See section 23.9.2. -rounds How many rounds of optimisation to perform. See section 23.2.1. -unbox-closures-factor Scaling factor for benefit calculation when using -unbox-closures. See section 23.9.3. Notes - The set of command line flags relating to optimisation should typically be specified to be the same across an entire project. Flambda does not currently record the requested flags in the .cmx files. As such, inlining of functions from previously-compiled units will subject their code to the optimisation parameters of the unit currently being compiled, rather than those specified when they were previously compiled. It is hoped to rectify this deficiency in the future. - Flambda-specific flags do not affect linking with the exception of affecting the optimisation of code in the startup file (containing generated functions such as currying helpers). Typically such optimisation will not be significant, so eliding such flags at link time might be reasonable. - Flambda-specific flags are silently accepted even when the -flambda option was not provided to the configure script. (There is no means provided to change this behaviour.) This is intended to make it more straightforward to run benchmarks with and without the Flambda optimisers in effect. - Some of the Flambda flags may be subject to change in future releases. 23.2.1 Specification of optimisation parameters by round ========================================================== Flambda operates in rounds: one round consists of a certain sequence of transformations that may then be repeated in order to achieve more satisfactory results. The number of rounds can be set manually using the -rounds parameter (although this is not necessary when using predefined optimisation levels such as with -O2 and -O3). For high optimisation the number of rounds might be set at 3 or 4. Command-line flags that may apply per round, for example those with -cost in the name, accept arguments of the form: n | round=n[,...] - If the first form is used, with a single integer specified, the value will apply to all rounds. - If the second form is used, zero-based round integers specify values which are to be used only for those rounds. The flags -Oclassic, -O2 and -O3 are applied before all other flags, meaning that certain parameters may be overridden without having to specify every parameter usually invoked by the given optimisation level. 23.3 Inlining *=*=*=*=*=*=*=* Inlining refers to the copying of the code of a function to a place where the function is called. The code of the function will be surrounded by bindings of its parameters to the corresponding arguments. The aims of inlining are: - to reduce the runtime overhead caused by function calls (including setting up for such calls and returning afterwards); - to reduce instruction cache misses by expressing frequently-taken paths through the program using fewer machine instructions; and - to reduce the amount of allocation (especially of closures). These goals are often reached not just by inlining itself but also by other optimisations that the compiler is able to perform as a result of inlining. When a recursive call to a function (within the definition of that function or another in the same mutually-recursive group) is inlined, the procedure is also known as unrolling. This is somewhat akin to loop peeling. For example, given the following code: <> unrolling once at the call site fact 4 produces (with the body of fact unchanged): <> This simplifies to: <> Flambda provides significantly enhanced inlining capabilities relative to previous versions of the compiler. Aside: when inlining is performed --------------------------------- Inlining is performed together with all of the other Flambda optimisation passes, that is to say, after closure conversion. This has three particular advantages over a potentially more straightforward implementation prior to closure conversion: - It permits higher-order inlining, for example when a non-inlinable function always returns the same function yet with different environments of definition. Not all such cases are supported yet, but it is intended that such support will be improved in future. - It is easier to integrate with cross-module optimisation, since imported information about other modules is already in the correct intermediate language. - It becomes more straightforward to optimise closure allocations since the layout of closures does not have to be estimated in any way: it is known. Similarly, it becomes more straightforward to control which variables end up in which closures, helping to avoid closure bloat. 23.3.1 Classic inlining heuristic =================================== In -Oclassic mode the behaviour of the Flambda inliner mimics previous versions of the compiler. (Code may still be subject to further optimisations not performed by previous versions of the compiler: functors may be inlined, constants are lifted and unused code is eliminated all as described elsewhere in this chapter. See sections 23.3.3, 23.8.1 and 23.10. At the definition site of a function, the body of the function is measured. It will then be marked as eligible for inlining (and hence inlined at every direct call site) if: - the measured size (in unspecified units) is smaller than that of a function call plus the argument of the -inline command-line flag; and - the function is not recursive. Non-Flambda versions of the compiler cannot inline functions that contain a definition of another function. However -Oclassic does permit this. Further, non-Flambda versions also cannot inline functions that are only themselves exposed as a result of a previous pass of inlining, but again this is permitted by -Oclassic. For example: <> All of this contrasts with the normal Flambda mode, that is to say without -Oclassic, where: - the inlining decision is made at the call site; and - recursive functions can be handled, by specialisation (see below). The Flambda mode is described in the next section. 23.3.2 Overview of “Flambda” inlining heuristics ====================================================== The Flambda inlining heuristics, used whenever the compiler is configured for Flambda and -Oclassic was not specified, make inlining decisions at call sites. This helps in situations where the context is important. For example: <> In this case, we would like to inline f into g, because a conditional jump can be eliminated and the code size should reduce. If the inlining decision has been made after the declaration of f without seeing the use, its size would have probably made it ineligible for inlining; but at the call site, its final size can be known. Further, this function should probably not be inlined systematically: if b is unknown, or indeed false, there is little benefit to trade off against a large increase in code size. In the existing non-Flambda inliner this isn’t a great problem because chains of inlining were cut off fairly quickly. However it has led to excessive use of overly-large inlining parameters such as -inline 10000. In more detail, at each call site the following procedure is followed: - Determine whether it is clear that inlining would be beneficial without, for the moment, doing any inlining within the function itself. (The exact assessment of benefit is described below.) If so, the function is inlined. - If inlining the function is not clearly beneficial, then inlining will be performed speculatively inside the function itself. The search for speculative inlining possibilities is controlled by two parameters: the inlining threshold and the inlining depth. (These are described in more detail below.) - If such speculation shows that performing some inlining inside the function would be beneficial, then such inlining is performed and the resulting function inlined at the original call site. - Otherwise, nothing happens. Inlining within recursive functions of calls to other functions in the same mutually-recursive group is kept in check by an unrolling depth, described below. This ensures that functions are not unrolled to excess. (Unrolling is only enabled if -O3 optimisation level is selected and/or the -inline-max-unroll flag is passed with an argument greater than zero.) 23.3.3 Handling of specific language constructs ================================================= Functors -------- There is nothing particular about functors that inhibits inlining compared to normal functions. To the inliner, these both look the same, except that functors are marked as such. Applications of functors at toplevel are biased in favour of inlining. (This bias may be adjusted: see the documentation for -inline-lifting-benefit below.) Applications of functors not at toplevel, for example in a local module inside some other expression, are treated by the inliner identically to normal function calls. First-class modules ------------------- The inliner will be able to consider inlining a call to a function in a first class module if it knows which particular function is going to be called. The presence of the first-class module record that wraps the set of functions in the module does not per se inhibit inlining. Objects ------- Method calls to objects are not at present inlined by Flambda. 23.3.4 Inlining reports ========================= If the -inlining-report option is provided to the compiler then a file will be emitted corresponding to each round of optimisation. For the OCaml source file basename.ml the files are named basename.round.inlining.org, with round a zero-based integer. Inside the files, which are formatted as “org mode”, will be found English prose describing the decisions that the inliner took. 23.3.5 Assessment of inlining benefit ======================================= Inlining typically results in an increase in code size, which if left unchecked, may not only lead to grossly large executables and excessive compilation times but also a decrease in performance due to worse locality. As such, the Flambda inliner trades off the change in code size against the expected runtime performance benefit, with the benefit being computed based on the number of operations that the compiler observes may be removed as a result of inlining. For example given the following code: <> it would be observed that inlining of f would remove: - one direct call; - one conditional branch. Formally, an estimate of runtime performance benefit is computed by first summing the cost of the operations that are known to be removed as a result of the inlining and subsequent simplification of the inlined body. The individual costs for the various kinds of operations may be adjusted using the various -inline-...-cost flags as follows. Costs are specified as integers. All of these flags accept a single argument describing such integers using the conventions detailed in section 23.2.1. -inline-alloc-cost The cost of an allocation. -inline-branch-cost The cost of a branch. -inline-call-cost The cost of a direct function call. -inline-indirect-cost The cost of an indirect function call. -inline-prim-cost The cost of a primitive. Primitives encompass operations including arithmetic and memory access. (Default values are described in section 23.5 below.) The initial benefit value is then scaled by a factor that attempts to compensate for the fact that the current point in the code, if under some number of conditional branches, may be cold. (Flambda does not currently compute hot and cold paths.) The factor—the estimated probability that the inliner really is on a hot path—is calculated as 1/(1 + f)^d, where f is set by -inline-branch-factor and d is the nesting depth of branches at the current point. As the inliner descends into more deeply-nested branches, the benefit of inlining thus lessens. The resulting benefit value is known as the estimated benefit. The change in code size is also estimated: morally speaking it should be the change in machine code size, but since that is not available to the inliner, an approximation is used. If the estimated benefit exceeds the increase in code size then the inlined version of the function will be kept. Otherwise the function will not be inlined. Applications of functors at toplevel will be given an additional benefit (which may be controlled by the -inline-lifting-benefit flag) to bias inlining in such situations towards keeping the inlined version. 23.3.6 Control of speculation =============================== As described above, there are three parameters that restrict the search for inlining opportunities during speculation: - the inlining threshold; - the inlining depth; - the unrolling depth. These parameters are ultimately bounded by the arguments provided to the corresponding command-line flags (or their default values): - -inline (or, if the call site that triggered speculation is at toplevel, -inline-toplevel); - -inline-max-depth; - -inline-max-unroll. Note in particular that -inline does not have the meaning that it has in the previous compiler or in -Oclassic mode. In both of those situations -inline was effectively some kind of basic assessment of inlining benefit. However in Flambda inlining mode it corresponds to a constraint on the search; the assessment of benefit is independent, as described above. When speculation starts the inlining threshold starts at the value set by -inline (or -inline-toplevel if appropriate, see above). Upon making a speculative inlining decision the threshold is reduced by the code size of the function being inlined. If the threshold becomes exhausted, at or below zero, no further speculation will be performed. The inlining depth starts at zero and is increased by one every time the inliner descends into another function. It is then decreased by one every time the inliner leaves such function. If the depth exceeds the value set by -inline-max-depth then speculation stops. This parameter is intended as a general backstop for situations where the inlining threshold does not control the search sufficiently. The unrolling depth applies to calls within the same mutually-recursive group of functions. Each time an inlining of such a call is performed the depth is incremented by one when examining the resulting body. If the depth reaches the limit set by -inline-max-unroll then speculation stops. 23.4 Specialisation *=*=*=*=*=*=*=*=*=*=* The inliner may discover a call site to a recursive function where something is known about the arguments: for example, they may be equal to some other variables currently in scope. In this situation it may be beneficial to specialise the function to those arguments. This is done by copying the declaration of the function (and any others involved in any same mutually-recursive declaration) and noting the extra information about the arguments. The arguments augmented by this information are known as specialised arguments. In order to try to ensure that specialisation is not performed uselessly, arguments are only specialised if it can be shown that they are invariant: in other words, during the execution of the recursive function(s) themselves, the arguments never change. Unless overridden by an attribute (see below), specialisation of a function will not be attempted if: - the compiler is in -Oclassic mode; - the function is not obviously recursive; - the function is not closed. The compiler can prove invariance of function arguments across multiple functions within a recursive group (although this has some limitations, as shown by the example below). It should be noted that the unboxing of closures pass (see below) can introduce specialised arguments on non-recursive functions. (No other place in the compiler currently does this.) Example: the well-known List.iter function This function might be written like so: < () | h :: t -> f h; iter f t >> and used like this: <> The argument f to iter is invariant so the function may be specialised: < () | h :: t -> f h; iter' f t in iter' print_int (List.rev xs) >> The compiler notes down that for the function iter’, the argument f is specialised to the constant closure print_int. This means that the body of iter’ may be simplified: < () | h :: t -> print_int h; (* this is now a direct call *) iter' f t in iter' print_int (List.rev xs) >> The call to print_int can indeed be inlined: < () | h :: t -> print_endline (Int.to_string h); iter' f t in iter' print_int (List.rev xs) >> The unused specialised argument f may now be removed, leaving: < () | h :: t -> print_endline (Int.to_string h); iter' t in iter' (List.rev xs) >> Aside on invariant parameters. The compiler cannot currently detect invariance in cases such as the following. < () | 0 :: t -> iter_swap g f l | h :: t -> f h; iter_swap f g t >> 23.4.1 Assessment of specialisation benefit ============================================= The benefit of specialisation is assessed in a similar way as for inlining. Specialised argument information may mean that the body of the function being specialised can be simplified: the removed operations are accumulated into a benefit. This, together with the size of the duplicated (specialised) function declaration, is then assessed against the size of the call to the original function. 23.5 Default settings of parameters *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The default settings (when not using -Oclassic) are for one round of optimisation using the following parameters. ---------------------------------- | Parameter |Setting | ---------------------------------- | -inline |10 | |-inline-branch-factor |0.1 | |-inline-alloc-cost |7 | |-inline-branch-cost |5 | |-inline-call-cost |5 | |-inline-indirect-cost |4 | |-inline-prim-cost |3 | |-inline-lifting-benefit|1300 | |-inline-toplevel |160 | |-inline-max-depth |1 | |-inline-max-unroll |0 | |-unbox-closures-factor |10 | ---------------------------------- 23.5.1 Settings at -O2 optimisation level =========================================== When -O2 is specified two rounds of optimisation are performed. The first round uses the default parameters (see above). The second uses the following parameters. --------------------------------------------- | Parameter | Setting | --------------------------------------------- | -inline |25 | |-inline-branch-factor |Same as default | |-inline-alloc-cost |Double the default | |-inline-branch-cost |Double the default | |-inline-call-cost |Double the default | |-inline-indirect-cost |Double the default | |-inline-prim-cost |Double the default | |-inline-lifting-benefit|Same as default | |-inline-toplevel |400 | |-inline-max-depth |2 | |-inline-max-unroll |Same as default | |-unbox-closures-factor |Same as default | --------------------------------------------- 23.5.2 Settings at -O3 optimisation level =========================================== When -O3 is specified three rounds of optimisation are performed. The first two rounds are as for -O2. The third round uses the following parameters. --------------------------------------------- | Parameter | Setting | --------------------------------------------- | -inline |50 | |-inline-branch-factor |Same as default | |-inline-alloc-cost |Triple the default | |-inline-branch-cost |Triple the default | |-inline-call-cost |Triple the default | |-inline-indirect-cost |Triple the default | |-inline-prim-cost |Triple the default | |-inline-lifting-benefit|Same as default | |-inline-toplevel |800 | |-inline-max-depth |3 | |-inline-max-unroll |1 | |-unbox-closures-factor |Same as default | --------------------------------------------- 23.6 Manual control of inlining and specialisation *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Should the inliner prove recalcitrant and refuse to inline a particular function, or if the observed inlining decisions are not to the programmer’s satisfaction for some other reason, inlining behaviour can be dictated by the programmer directly in the source code. One example where this might be appropriate is when the programmer, but not the compiler, knows that a particular function call is on a cold code path. It might be desirable to prevent inlining of the function so that the code size along the hot path is kept smaller, so as to increase locality. The inliner is directed using attributes. For non-recursive functions (and one-step unrolling of recursive functions, although @unroll is more clear for this purpose) the following are supported: @@inline always or @@inline never Attached to a declaration of a function or functor, these direct the inliner to either always or never inline, irrespective of the size/benefit calculation. (If the function is recursive then the body is substituted and no special action is taken for the recursive call site(s).) @@inline with no argument is equivalent to @@inline always. @inlined always or @inlined never Attached to a function application, these direct the inliner likewise. These attributes at call sites override any other attribute that may be present on the corresponding declaration. @inlined with no argument is equivalent to @inlined always. @@inlined hint is equivalent to @@inline always except that it will not trigger warning 55 if the function application cannot be inlined. For recursive functions the relevant attributes are: @@specialise always or @@specialise never Attached to a declaration of a function or functor, this directs the inliner to either always or never specialise the function so long as it has appropriate contextual knowledge, irrespective of the size/benefit calculation. @@specialise with no argument is equivalent to @@specialise always. @specialised always or @specialised never Attached to a function application, this directs the inliner likewise. This attribute at a call site overrides any other attribute that may be present on the corresponding declaration. (Note that the function will still only be specialised if there exist one or more invariant parameters whose values are known.) @specialised with no argument is equivalent to @specialised always. @unrolled n This attribute is attached to a function application and always takes an integer argument. Each time the inliner sees the attribute it behaves as follows: - If n is zero or less, nothing happens. - Otherwise the function being called is substituted at the call site with its body having been rewritten such that any recursive calls to that function or any others in the same mutually-recursive group are annotated with the attribute unrolled(n − 1). Inlining may continue on that body. As such, n behaves as the “maximum depth of unrolling”. A compiler warning will be emitted if it was found impossible to obey an annotation from an @inlined or @specialised attribute. Example showing correct placement of attributes <> 23.7 Simplification *=*=*=*=*=*=*=*=*=*=* Simplification, which is run in conjunction with inlining, propagates information (known as approximations) about which variables hold what values at runtime. Certain relationships between variables and symbols are also tracked: for example, some variable may be known to always hold the same value as some other variable; or perhaps some variable may be known to always hold the value pointed to by some symbol. The propagation can help to eliminate allocations in cases such as: <> The projections from p may be replaced by uses of the variables x and y, potentially meaning that p becomes unused. The propagation performed by the simplification pass is also important for discovering which functions flow to indirect call sites. This can enable the transformation of such call sites into direct call sites, which makes them eligible for an inlining transformation. Note that no information is propagated about the contents of strings, even in safe-string mode, because it cannot yet be guaranteed that they are immutable throughout a given program. 23.8 Other code motion transformations *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= 23.8.1 Lifting of constants ============================= Expressions found to be constant will be lifted to symbol bindings—that is to say, they will be statically allocated in the object file—when they evaluate to boxed values. Such constants may be straightforward numeric constants, such as the floating-point number 42.0, or more complicated values such as constant closures. Lifting of constants to toplevel reduces allocation at runtime. The compiler aims to share constants lifted to toplevel such that there are no duplicate definitions. However if .cmx files are hidden from the compiler then maximal sharing may not be possible. Notes about float arrays The following language semantics apply specifically to constant float arrays. (By “constant float array” is meant an array consisting entirely of floating point numbers that are known at compile time. A common case is a literal such as [| 42.0; 43.0; |]. - Constant float arrays at the toplevel are mutable and never shared. (That is to say, for each such definition there is a distinct symbol in the data section of the object file pointing at the array.) - Constant float arrays not at toplevel are mutable and are created each time the expression is evaluated. This can be thought of as an operation that takes an immutable array (which in the source code has no associated name; let us call it the initialising array) and duplicates it into a fresh mutable array. - If the array is of size four or less, the expression will create a fresh block and write the values into it one by one. There is no reference to the initialising array as a whole. - Otherwise, the initialising array is lifted out and subject to the normal constant sharing procedure; creation of the array consists of bulk copying the initialising array into a fresh value on the OCaml heap. 23.8.2 Lifting of toplevel let bindings ========================================= Toplevel let-expressions may be lifted to symbol bindings to ensure that the corresponding bound variables are not captured by closures. If the defining expression of a given binding is found to be constant, it is bound as such (the technical term is a let-symbol binding). Otherwise, the symbol is bound to a (statically-allocated) preallocated block containing one field. At runtime, the defining expression will be evaluated and the first field of the block filled with the resulting value. This initialise-symbol binding causes one extra indirection but ensures, by virtue of the symbol’s address being known at compile time, that uses of the value are not captured by closures. It should be noted that the blocks corresponding to initialise-symbol bindings are kept alive forever, by virtue of them occurring in a static table of GC roots within the object file. This extended lifetime of expressions may on occasion be surprising. If it is desired to create some non-constant value (for example when writing GC tests) that does not have this extended lifetime, then it may be created and used inside a function, with the application point of that function (perhaps at toplevel)—or indeed the function declaration itself—marked as to never be inlined. This technique prevents lifting of the definition of the value in question (assuming of course that it is not constant). 23.9 Unboxing transformations *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The transformations in this section relate to the splitting apart of boxed (that is to say, non-immediate) values. They are largely intended to reduce allocation, which tends to result in a runtime performance profile with lower variance and smaller tails. 23.9.1 Unboxing of closure variables ====================================== This transformation is enabled unless -no-unbox-free-vars-of-closures is provided. Variables that appear in closure environments may themselves be boxed values. As such, they may be split into further closure variables, each of which corresponds to some projection from the original closure variable(s). This transformation is called unboxing of closure variables or unboxing of free variables of closures. It is only applied when there is reasonable certainty that there are no uses of the boxed free variable itself within the corresponding function bodies. Example: In the following code, the compiler observes that the closure returned from the function f contains a variable pair (free in the body of f) that may be split into two separate variables. < fst pair + snd pair + y >> After some simplification one obtains: < pair_0 + pair_1 + y >> and then: < x0 + x1 + y >> The allocation of the pair has been eliminated. This transformation does not operate if it would cause the closure to contain more than twice as many closure variables as it did beforehand. 23.9.2 Unboxing of specialised arguments ========================================== This transformation is enabled unless -no-unbox-specialised-args is provided. It may become the case during compilation that one or more invariant arguments to a function become specialised to a particular value. When such values are themselves boxed the corresponding specialised arguments may be split into more specialised arguments corresponding to the projections out of the boxed value that occur within the function body. This transformation is called unboxing of specialised arguments. It is only applied when there is reasonable certainty that the boxed argument itself is unused within the function. If the function in question is involved in a recursive group then unboxing of specialised arguments may be immediately replicated across the group based on the dataflow between invariant arguments. Example: Having been given the following code, the compiler will inline loop into f, and then observe inv being invariant and always the pair formed by adding 42 and 43 to the argument x of the function f. < fst inv + snd inv | x::xs -> x + loop2 xs inv and loop2 ys inv = match ys with | [] -> 4 | y::ys -> y - loop inv ys let f x = Printf.printf "%d\n" (loop (x + 42, x + 43) [1; 2; 3]) >> Since the functions have sufficiently few arguments, more specialised arguments will be added. After some simplification one obtains: < inv_0 + inv_1 | x::xs -> x + loop2' xs inv_0 inv_1 and loop2' ys inv_0 inv_1 = match ys with | [] -> 4 | y::ys -> y - loop' ys inv_0 inv_1 in Printf.printf "%d\n" (loop' [1; 2; 3] (x + 42) (x + 43)) >> The allocation of the pair within f has been removed. (Since the two closures for loop’ and loop2’ are constant they will also be lifted to toplevel with no runtime allocation penalty. This would also happen without having run the transformation to unbox specialise arguments.) The transformation to unbox specialised arguments never introduces extra allocation. The transformation will not unbox arguments if it would result in the original function having sufficiently many arguments so as to inhibit tail-call optimisation. The transformation is implemented by creating a wrapper function that accepts the original arguments. Meanwhile, the original function is renamed and extra arguments are added corresponding to the unboxed specialised arguments; this new function is called from the wrapper. The wrapper will then be inlined at direct call sites. Indeed, all call sites will be direct unless -unbox-closures is being used, since they will have been generated by the compiler when originally specialising the function. (In the case of -unbox-closures other functions may appear with specialised arguments; in this case there may be indirect calls and these will incur a small penalty owing to having to bounce through the wrapper. The technique of direct call surrogates used for -unbox-closures is not used by the transformation to unbox specialised arguments.) 23.9.3 Unboxing of closures ============================= This transformation is not enabled by default. It may be enabled using the -unbox-closures flag. The transformation replaces closure variables by specialised arguments. The aim is to cause more closures to become closed. It is particularly applicable, as a means of reducing allocation, where the function concerned cannot be inlined or specialised. For example, some non-recursive function might be too large to inline; or some recursive function might offer no opportunities for specialisation perhaps because its only argument is one of type unit. At present there may be a small penalty in terms of actual runtime performance when this transformation is enabled, although more stable performance may be obtained due to reduced allocation. It is recommended that developers experiment to determine whether the option is beneficial for their code. (It is expected that in the future it will be possible for the performance degradation to be removed.) Simple example: In the following code (which might typically occur when g is too large to inline) the value of x would usually be communicated to the application of the + function via the closure of g. <> Unboxing of the closure causes the value for x inside g to be passed as an argument to g rather than through its closure. This means that the closure of g becomes constant and may be lifted to toplevel, eliminating the runtime allocation. The transformation is implemented by adding a new wrapper function in the manner of that used when unboxing specialised arguments. The closure variables are still free in the wrapper, but the intention is that when the wrapper is inlined at direct call sites, the relevant values are passed directly to the main function via the new specialised arguments. Adding such a wrapper will penalise indirect calls to the function (which might exist in arbitrary places; remember that this transformation is not for example applied only on functions the compiler has produced as a result of specialisation) since such calls will bounce through the wrapper. To mitigate this, if a function is small enough when weighed up against the number of free variables being removed, it will be duplicated by the transformation to obtain two versions: the original (used for indirect calls, since we can do no better) and the wrapper/rewritten function pair as described in the previous paragraph. The wrapper/rewritten function pair will only be used at direct call sites of the function. (The wrapper in this case is known as a direct call surrogate, since it takes the place of another function—the unchanged version used for indirect calls—at direct call sites.) The -unbox-closures-factor command line flag, which takes an integer, may be used to adjust the point at which a function is deemed large enough to be ineligible for duplication. The benefit of duplication is scaled by the integer before being evaluated against the size. Harder example: In the following code, there are two closure variables that would typically cause closure allocations. One is called fv and occurs inside the function baz; the other is called z and occurs inside the function bar. In this toy (yet sophisticated) example we again use an attribute to simulate the typical situation where the first argument of baz is too large to inline. < [] | z::zs -> let rec baz f = function | [] -> [] | a::l -> let r = fv + ((f [@inlined never]) a) in r :: baz f l in (map2 (fun y -> z + y) [z; 2; 3; 4]) @ bar zs fv in Printf.printf "%d" (List.length (bar [1; 2; 3; 4] c)) >> The code resulting from applying -O3 -unbox-closures to this code passes the free variables via function arguments in order to eliminate all closure allocation in this example (aside from any that might be performed inside printf). 23.10 Removal of unused code and values *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* 23.10.1 Removal of redundant let expressions ============================================== The simplification pass removes unused let bindings so long as their corresponding defining expressions have “no effects”. See the section “Treatment of effects” below for the precise definition of this term. 23.10.2 Removal of redundant program constructs ================================================= This transformation is analogous to the removal of let-expressions whose defining expressions have no effects. It operates instead on symbol bindings, removing those that have no effects. 23.10.3 Removal of unused arguments ===================================== This transformation is only enabled by default for specialised arguments. It may be enabled for all arguments using the -remove-unused-arguments flag. The pass analyses functions to determine which arguments are unused. Removal is effected by creating a wrapper function, which will be inlined at every direct call site, that accepts the original arguments and then discards the unused ones before calling the original function. As a consequence, this transformation may be detrimental if the original function is usually indirectly called, since such calls will now bounce through the wrapper. (The technique of direct call surrogates used to reduce this penalty during unboxing of closure variables (see above) does not yet apply to the pass that removes unused arguments.) 23.10.4 Removal of unused closure variables ============================================= This transformation performs an analysis across the whole compilation unit to determine whether there exist closure variables that are never used. Such closure variables are then eliminated. (Note that this has to be a whole-unit analysis because a projection of a closure variable from some particular closure may have propagated to an arbitrary location within the code due to inlining.) 23.11 Other code transformations *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= 23.11.1 Transformation of non-escaping references into mutable variables ========================================================================== Flambda performs a simple analysis analogous to that performed elsewhere in the compiler that can transform refs into mutable variables that may then be held in registers (or on the stack as appropriate) rather than being allocated on the OCaml heap. This only happens so long as the reference concerned can be shown to not escape from its defining scope. 23.11.2 Substitution of closure variables for specialised arguments ===================================================================== This transformation discovers closure variables that are known to be equal to specialised arguments. Such closure variables are replaced by the specialised arguments; the closure variables may then be removed by the “removal of unused closure variables” pass (see below). 23.12 Treatment of effects *=*=*=*=*=*=*=*=*=*=*=*=*=*= The Flambda optimisers classify expressions in order to determine whether an expression: - does not need to be evaluated at all; and/or - may be duplicated. This is done by forming judgements on the effects and the coeffects that might be performed were the expression to be executed. Effects talk about how the expression might affect the world; coeffects talk about how the world might affect the expression. Effects are classified as follows: No effects: The expression does not change the observable state of the world. For example, it must not write to any mutable storage, call arbitrary external functions or change control flow (e.g. by raising an exception). Note that allocation is not classed as having “no effects” (see below). - It is assumed in the compiler that expressions with no effects, whose results are not used, may be eliminated. (This typically happens where the expression in question is the defining expression of a let; in such cases the let-expression will be eliminated.) It is further assumed that such expressions with no effects may be duplicated (and thus possibly executed more than once). - Exceptions arising from allocation points, for example “out of memory” or exceptions propagated from finalizers or signal handlers, are treated as “effects out of the ether” and thus ignored for our determination here of effectfulness. The same goes for floating point operations that may cause hardware traps on some platforms. Only generative effects: The expression does not change the observable state of the world save for possibly affecting the state of the garbage collector by performing an allocation. Expressions that only have generative effects and whose results are unused may be eliminated by the compiler. However, unlike expressions with “no effects”, such expressions will never be eligible for duplication. Arbitrary effects: All other expressions. There is a single classification for coeffects: No coeffects: The expression does not observe the effects (in the sense described above) of other expressions. For example, it must not read from any mutable storage or call arbitrary external functions. It is assumed in the compiler that, subject to data dependencies, expressions with neither effects nor coeffects may be reordered with respect to other expressions. 23.13 Compilation of statically-allocated modules *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Compilation of modules that are able to be statically allocated (for example, the module corresponding to an entire compilation unit, as opposed to a first class module dependent on values computed at runtime) initially follows the strategy used for bytecode. A sequence of let-bindings, which may be interspersed with arbitrary effects, surrounds a record creation that becomes the module block. The Flambda-specific transformation follows: these bindings are lifted to toplevel symbols, as described above. 23.14 Inhibition of optimisation *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Especially when writing benchmarking suites that run non-side-effecting algorithms in loops, it may be found that the optimiser entirely elides the code being benchmarked. This behaviour can be prevented by using the Sys.opaque_identity function (which indeed behaves as a normal OCaml function and does not possess any “magic” semantics). The documentation of the Sys module should be consulted for further details. 23.15 Use of unsafe operations *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= The behaviour of the Flambda simplification pass means that certain unsafe operations, which may without Flambda or when using previous versions of the compiler be safe, must not be used. This specifically refers to functions found in the Obj module. In particular, it is forbidden to change any value (for example using Obj.set_field or Obj.set_tag) that is not mutable. (Values returned from C stubs are always treated as mutable.) The compiler will emit warning 59 if it detects such a write—but it cannot warn in all cases. Here is an example of code that will trigger the warning: <> The reason this is unsafe is because the simplification pass believes that fst a holds the value 42; and indeed it must, unless type soundness has been broken via unsafe operations. If it must be the case that code has to be written that triggers warning 59, but the code is known to actually be correct (for some definition of correct), then Sys.opaque_identity may be used to wrap the value before unsafe operations are performed upon it. Great care must be taken when doing this to ensure that the opacity is added at the correct place. It must be emphasised that this use of Sys.opaque_identity is only for exceptional cases. It should not be used in normal code or to try to guide the optimiser. As an example, this code will return the integer 1: <> However the following code will still return 42: <> High levels of inlining performed by Flambda may expose bugs in code thought previously to be correct. Take care, for example, not to add type annotations that claim some mutable value is always immediate if it might be possible for an unsafe operation to update it to a boxed value. 23.16 Glossary *=*=*=*=*=*=*=*= The following terminology is used in this chapter of the manual. Call site See direct call site and indirect call site below. Closed function A function whose body has no free variables except its parameters and any to which are bound other functions within the same (possibly mutually-recursive) declaration. Closure The runtime representation of a function. This includes pointers to the code of the function together with the values of any variables that are used in the body of the function but actually defined outside of the function, in the enclosing scope. The values of such variables, collectively known as the environment, are required because the function may be invoked from a place where the original bindings of such variables are no longer in scope. A group of possibly mutually-recursive functions defined using let rec all share a single closure. (Note to developers: in the Flambda source code a closure always corresponds to a single function; a set of closures refers to a group of such.) Closure variable A member of the environment held within the closure of a given function. Constant Some entity (typically an expression) the value of which is known by the compiler at compile time. Constantness may be explicit from the source code or inferred by the Flambda optimisers. Constant closure A closure that is statically allocated in an object file. It is almost always the case that the environment portion of such a closure is empty. Defining expression The expression e in let x = e in e’. Direct call site A place in a program’s code where a function is called and it is known at compile time which function it will always be. Indirect call site A place in a program’s code where a function is called but is not known to be a direct call site. Program A collection of symbol bindings forming the definition of a single compilation unit (i.e. .cmx file). Specialised argument An argument to a function that is known to always hold a particular value at runtime. These are introduced by the inliner when specialising recursive functions; and the unbox-closures pass. (See section 23.4.) Symbol A name referencing a particular place in an object file or executable image. At that particular place will be some constant value. Symbols may be examined using operating system-specific tools (for example objdump on Linux). Symbol binding Analogous to a let-expression but working at the level of symbols defined in the object file. The address of a symbol is fixed, but it may be bound to both constant and non-constant expressions. Toplevel An expression in the current program which is not enclosed within any function declaration. Variable A named entity to which some OCaml value is bound by a let expression, pattern-matching construction, or similar. Chapter 24  Fuzzing with afl-fuzz ************************************* 24.1 Overview *=*=*=*=*=*=*=* American fuzzy lop (“afl-fuzz”) is a fuzzer, a tool for testing software by providing randomly-generated inputs, searching for those inputs which cause the program to crash. Unlike most fuzzers, afl-fuzz observes the internal behaviour of the program being tested, and adjusts the test cases it generates to trigger unexplored execution paths. As a result, test cases generated by afl-fuzz cover more of the possible behaviours of the tested program than other fuzzers. This requires that programs to be tested are instrumented to communicate with afl-fuzz. The native-code compiler “ocamlopt” can generate such instrumentation, allowing afl-fuzz to be used against programs written in OCaml. For more information on afl-fuzz, see the website at http://lcamtuf.coredump.cx/afl/ 24.2 Generating instrumentation *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The instrumentation that afl-fuzz requires is not generated by default, and must be explicitly enabled, by passing the -afl-instrument option to ocamlopt. To fuzz a large system without modifying build tools, OCaml’s configure script also accepts the afl-instrument option. If OCaml is configured with afl-instrument, then all programs compiled by ocamlopt will be instrumented. 24.2.1 Advanced options ========================= In rare cases, it is useful to control the amount of instrumentation generated. By passing the -afl-inst-ratio N argument to ocamlopt with N less than 100, instrumentation can be generated for only N% of branches. (See the afl-fuzz documentation on the parameter AFL_INST_RATIO for the precise effect of this). 24.3 Example *=*=*=*=*=*=*= As an example, we fuzz-test the following program, readline.ml: < failwith "uh oh" | _ -> () >> There is a single input (the string “secret code”) which causes this program to crash, but finding it by blind random search is infeasible. Instead, we compile with afl-fuzz instrumentation enabled: <> Next, we run the program under afl-fuzz: < input/testcase mkdir output afl-fuzz -m none -i input -o output ./readline >> By inspecting instrumentation output, the fuzzer finds the crashing input quickly. Note: To fuzz-test an OCaml program with afl-fuzz, passing the option -m none is required to disable afl-fuzz’s default 50MB virtual memory limit. Chapter 25  Runtime tracing with runtime events *************************************************** This chapter describes the runtime events tracing system which enables continuous extraction of performance information from the OCaml runtime with very low overhead. The system and interfaces are low-level and tightly coupled to the runtime implementation, it is intended for end-users to rely on tooling to consume and visualise data of interest. Data emitted includes: - Event times of garbage collector and runtime phases - Minor and major heap sizings and utilization - Allocation and promotion rates between heaps Additional events can be declared and consumed, providing higher-level monitoring capabilities to OCaml libraries. They are referred to as custom events. 25.1 Overview *=*=*=*=*=*=*=* There are three main classes of events emitted by the runtime events system: Spans Events spanning over a duration in time. For example, the runtime events tracing system emits a span event that starts when a minor collection begins in the OCaml garbage collector and ends when the collection is completed. Spans can contain other spans, e.g other span events may be emitted that begin after a minor collection has begun and end before it does. Lifecycle events Events that occur at a moment in time. For example, when a domain terminates, a corresponding lifecycle event is emitted. Counters Events that include a measurement of some quantity of interest. For example, the number of words promoted from the minor to the major heap during the last minor garbage collection is emitted as a counter event. The runtime events tracing system is designed to be used in different contexts: Self monitoring OCaml programs and libraries can install their own callbacks to listen for runtime events and react to them programmatically, for example, to export events to disk or over the network. External monitoring An external process can consume the runtime events of an OCaml program whose runtime tracing system has been enabled by setting the corresponding environment variable. The runtime events tracing system logs events to a ring buffer. Consequently, old events are being overwritten by new events. Consumers can either continuously consume events or choose to only do so in response to some circumstance, e.g if a particular query or operation takes longer than expected to complete. 25.2 Architecture *=*=*=*=*=*=*=*=*=* The runtime tracing system conceptually consists of two parts: 1) the event sources which emit events and 2) the events transport that ingests and transports these events. 25.2.1 Event sources ====================== Event sources are event-emitting points. There are a number of such sources in the OCaml runtime system. These are further split into two sets: 1) event sources that are always available and 2) event sources that are only available in the instrumented runtime. Event sources in the instrumented runtime are primarily of interest to developers of the OCaml runtime and garbage collector and, at present, only consist of major heap allocation size counter events. The full set of events emitted by event sources and their documentation can be found in section ??. 25.2.2 Events transport ========================= The events transport part of the system ingests events emitted by the event sources and makes them available to consumers. Ring buffers ------------ Events are transported using a data structure known as a ring buffer. This data structure consists of two pointers into a linear backing array, the tail pointer points to a location where new events can be written and the head pointer points to the oldest event in the buffer that can be read. When insufficient space is available in the backing array to write new events, the head pointer is advanced and the oldest events are overwritten by new ones. The ring buffer implementation used in runtime events can be written by at most one producer at a time but can be read simultaneously by multiple consumers without coordination from the producer. There is a unique ring buffer for every running domain and, on domain termination, ring buffers may be re-used for newly spawned domains. Ring buffers are only allocated (including for the main domain) when runtime events are enabled. The ring buffers themselves are stored in a memory-mapped file with the processes identifier as the name and the extension .events, this enables them to be read from outside the main OCaml process. See librefRuntime_eventsRuntime_events for more information. Consumption APIs ---------------- The runtime event tracing system provides both OCaml and C APIs which are cursor-based and polling-driven. The high-level process for consuming events is as follows: 1. A cursor is created via Runtime_events.create_cursor for either the current process or an external process (specified by a path and PID). 2. Runtime_events.Callbacks.create is called to register a callback function to receive the events. 3. The cursor is polled via Runtime_events.read_poll using the callbacks created in the previous step. For each matching event in the ring buffers, the provided callback functions are called. In addition to the emitted events, callbacks are given the emitter domain’s ID and the emission timestamp. 25.3 Usage *=*=*=*=*=*= 25.3.1 With OCaml APIs ======================== We start with a simple example that prints the name, begin and end times of events emitted by the runtime event tracing system: <> The next step is to compile and link the program with the runtime_events library. This can be done as follows: << ocamlopt -I +runtime_events -I +unix unix.cmxa runtime_events.cmxa example.ml -o example >> When using the dune build system, this example can be built as follows: <<(executable (name example) (modules example) (libraries unix runtime_events)) >> Running the compiled binary of the example gives an output similar to: <> This is an example of self-monitoring, where a program explicitly starts listening to runtime events and monitors itself. For external monitoring, a program does not need to be aware of the existence of runtime events. Runtime events can be controlled via the environment variable OCAML_RUNTIME_EVENTS_START which, when set, will cause the runtime tracing system to be started at program initialization. We could remove Runtime_events.start (); from the previous example and, instead, call the program as below to produce the same result: <> Environment variables --------------------- Environment variables can be used to control different aspects of the runtime event tracing system. The following environment variables are available: - OCAML_RUNTIME_EVENTS_START if set will cause the runtime events system to be started as part of the OCaml runtime initialization. - OCAML_RUNTIME_EVENTS_DIR sets the directory where the .events files containing the runtime event tracing system’s ring buffers will be located. If not present the program’s working directory will be used. - OCAML_RUNTIME_EVENTS_PRESERVE if set will make the OCaml runtime preserve the runtime events ring buffer files past the termination of the OCaml program. This can be useful for monitoring very short running programs. If not set, the .events files of the OCaml program will be deleted at program termination. The size of the runtime events ring buffers can be configured via OCAMLRUNPARAM, see section 15.2 for more information. Building with the instrumented runtime -------------------------------------- Some events are only emitted by the instrumented runtime. To receive them, the OCaml program needs to be compiled and linked against the instrumented runtime. For our example program from earlier, this is achieved as follows: <> And for dune: <<(executable (name example) (modules example) (flags "-runtime-variant=i") (libraries unix runtime_events)) >> 25.3.2 With tooling ===================== Programmatic access to events is intended primarily for writers of observability libraries and tooling for end-users. The flexible API enables use of the performance data from runtime events for logging and monitoring purposes. In this section we cover several utilities in the runtime_events_tools package which provide simple ways of extracting and summarising data from runtime events. The trace utility in particular produces similar data to the previous ’eventlog’ instrumentation system available in OCaml 4.12 to 4.14. First, install runtime_events_tools in an OCaml 5.0+ opam switch: <> This should install the olly tool in your path. You can now generate runtime traces for programs compiled with OCaml 5.0+ using the trace subcommand: <> Runtime tracing data will be generated in the json Trace Event Format to trace.json. This can then be loaded into the Chrome tracing viewer or into Perfetto to visualize the collected trace. Measuring GC latency -------------------- The olly utility also includes a latency subcommand which consumes runtime events data and on program completion emits a parseable histogram summary of pause durations. It can be run as follows: <> This should produce an output similar to the following: <> 25.4 Custom events *=*=*=*=*=*=*=*=*=*= 25.4.1 Overview ================= The runtime events system supports defining custom events. Identified by a globally unique name, they are emitted with payloads of built-in (unit, int, span) and user-defined types. To understand the manipulation of custom events, it is useful to know how they are transported and stored: their representation consists of a name string (in fact, an index into an array of all custom names) and an arbitrary byte sequence. Custom event types can be registered by providing encoding and decoding functions to and from a byte sequence, via the function Runtime_events.Type.register. Defining a new custom event (whether its payload is of a built-in type or a custom type) is done via another registration function, Runtime_events.User.register. This function records the association between the custom event’s name, its type, and a tag. The tag is then used when emitting or consuming custom events; it acts as a shorthand for the event name. Once an event is registered, values for that event are emitted using Runtime_events.User.write. To summarize, for a user to emit and consume custom events using a custom type they need to: 1. register the custom type 2. extend the Runtime_events.User.tag variant with a new constructor 3. register the new custom event, binding together the custom event name, the new tag, and the new custom type 4. emit instances of the event using Runtime_events.User.write 5. indicate a callback which should receive all events of the custom type using Runtime_events.Callbacks.add_user_event to register it inside a Runtime_events.Callbacks.t object to be used when polling (see section 25.3.1 above). 6. (Optional, if there are distinct events registered with the same custom type:) In that callback, pattern-match on the event tag in order to discriminate between different event tags of the same custom type. Note that if the emitter and the consumer are different programs, both must perform steps 1 to 3 to register custom events and custom event types (if any). Note that the tag values need not be the same in both programs; the only values that should match are the names. Unregistered events for user-defined types are currently ignored. As a fallback, unregistered, custom events of a built-in type are available, but are all tagged UNK (unknown). There are thus three cases for the consumer when an event is received: - event is registered: payload and tag are available. - event is not registered and has a built-in event type (unit, int, span): only the payload is available. - event is not registered and has a custom event type: event is dropped. Note that event consumers bind callbacks to event types, so they can work as generic listeners interpreting payloads coming from events that were not registered. Because this only works for events of built-in types, it can be useful to emit events in pairs: an event of a custom type with an event of a built-in type, enabling the design of a specialized consumer while staying compatible with generic tracing tools. 25.4.2 Tracing custom events: an example ========================================== The following program uses the Runtime_events.User and Runtime_events.Type modules to declare two custom events providing span and int values. The tag extensible variant is extended with CustomSpan and CustomInt. <> On the consumer side, one can use the provided event tag and type to match on the relevant events. For the sake of completeness, we assume that the consumer is a different program, and repeat the definition of the new tag constructors, as well as the registering of the custom events. < Printf.printf "> count begin\n" | CustomSpan, End -> Printf.printf "< count end\n" | _ -> () let int_event_handler domain_id ts event value = (* we're only interested in our CustomInt event *) match Runtime_events.User.tag event with | CustomInt -> Printf.printf "| count %d\n" value | _ -> () let () = let open Runtime_events in let cursor = create_cursor None in let callbacks = Callbacks.create () |> Callbacks.add_user_event Type.span span_event_handler |> Callbacks.add_user_event Type.int int_event_handler in for _ = 0 to 100 do ignore(read_poll cursor callbacks None) done >> Giving the following output: <<> count begin | count 1 | count 2 | count 3 | count 4 | count 5 < count end > count begin | count 1 | count 2 [...] >> Chapter 26  The “Tail Modulo Constructor” program transformation ************************************************************************ (Introduced in OCaml 4.14) Note: this feature is considered experimental, and its interface may evolve, with user feedback, in the next few releases of the language. Consider this natural implementation of the List.map function: << let rec map f l = match l with | [] -> [] | x :: xs -> let y = f x in y :: map f xs >> A well-known limitation of this implementation is that the recursive call, map f xs, is not in tail position. The runtime needs to remember to continue with y :: r after the call returns a value r, therefore this function consumes some amount of call-stack space on each recursive call. The stack usage of map f li is proportional to the length of li. This is a correctness issue for large lists on systems configured with limited stack space – the dreaded Stack_overflow exception. << # let with_stack_limit stack_limit f = let old_gc_settings = Gc.get () in Gc.set { old_gc_settings with stack_limit }; Fun.protect ~finally:(fun () -> Gc.set old_gc_settings) f ;; val with_stack_limit : int -> (unit -> 'a) -> 'a = >> << # with_stack_limit 20_000 (fun () -> List.length (map Fun.id (List.init 1_000_000 Fun.id)) );; Stack overflow during evaluation (looping recursion?). >> In this implementation of map, the recursive call happens in a position that is not a tail position in the program, but within a datatype constructor application that is itself in tail position. We say that those positions, that are composed of tail positions and constructor applications, are tail modulo constructor (TMC) positions – we sometimes write tail modulo cons for brevity. It is possible to rewrite programs such that tail modulo cons positions become tail positions; after this transformation, the implementation of map above becomes tail-recursive, in the sense that it only consumes a constant amount of stack space. The OCaml compiler implements this transformation on demand, using the [@tail_mod_cons] or [@ocaml.tail_mod_cons] attribute on the function to transform. << let[@tail_mod_cons] rec map f l = match l with | [] -> [] | x :: xs -> let y = f x in y :: map f xs >> << # List.length (map Fun.id (List.init 1_000_000 Fun.id));; - : int = 1000000 >> This transformation only improves calls in tail-modulo-cons position, it does not improve recursive calls that do not fit in this fragment: << (* does *not* work: addition is not a data constructor *) let[@tail_mod_cons] rec length l = match l with | [] -> 0 | _ :: xs -> 1 + length xs Warning 71 [unused-tmc-attribute]: This function is marked @tail_mod_cons but is never applied in TMC position. >> It is of course possible to use the [@tail_mod_cons] transformation on functions that contain some recursive calls in tail-modulo-cons position, and some calls in other, arbitrary positions. Only the tail calls and tail-modulo-cons calls will happen in constant stack space. General design This feature is provided as an explicit program transformation, not an implicit optimization. It is annotation-driven: the user is expected to express their intent by adding annotations in the program using attributes, and will be asked to do so in any ambiguous situation. We expect it to be used mostly by advanced OCaml users needing to get some guarantees on the stack-consumption behavior of their programs. Our recommendation is to use the [@tailcall] annotation on all callsites that should not consume any stack space. [@tail_mod_cons] extends the set of functions on which calls can be annotated to be tail calls, helping establish stack-consumption guarantees in more cases. Performance A standard approach to get a tail-recursive version of List.map is to use an accumulator to collect output elements, and reverse it at the end of the traversal. << let rec map f l = map_aux f [] l and map_aux f acc l = match l with | [] -> List.rev acc | x :: xs -> let y = f x in map_aux f (y :: acc) xs >> This version is tail-recursive, but it is measurably slower than the simple, non-tail-recursive version. In contrast, the tail-mod-cons transformation provides an implementation that has comparable performance to the original version, even on small inputs. Evaluation order Beware that the tail-modulo-cons transformation has an effect on evaluation order: the constructor argument that is transformed into tail-position will always be evaluated last. Consider the following example: << type 'a two_headed_list = | Nil | Consnoc of 'a * 'a two_headed_list * 'a let[@tail_mod_cons] rec map f = function | Nil -> Nil | Consnoc (front, body, rear) -> Consnoc (f front, map f body, f rear) >> Due to the [@tail_mod_cons] transformation, the calls to f front and f rear will be evaluated before map f body. In particular, this is likely to be different from the evaluation order of the unannotated version. (The evaluation order of constructor arguments is unspecified in OCaml, but many implementations typically use left-to-right or right-to-left.) This effect on evaluation order is one of the reasons why the tail-modulo-cons transformation has to be explicitly requested by the user, instead of being applied as an automatic optimization. Why tail-modulo-cons? Other program transformations, in particular a transformation to continuation-passing style (CPS), can make all functions tail-recursive, instead of targeting only a small fragment. Some reasons to provide builtin support for the less-general tail-mod-cons are as follows: - The tail-mod-cons transformation preserves the performance of the original, non-tail-recursive version, while a continuation-passing-style transformation incurs a measurable constant-factor overhead. - The tail-mod-cons transformation cannot be expressed as a source-to-source transformation of OCaml programs, as it relies on mutable state in type-unsafe ways. In contrast, continuation-passing-style versions can be written by hand, possibly using a convenient monadic notation. Note: OCaml call stack size In OCaml 4.x and earlier, bytecode programs respect the stack_limit runtime parameter configuration (as set using Gc.set in the example above), or the l setting of the OCAMLRUNPARAM variable. Native programs ignore these settings and only respect the operating system native stack limit, as set by ulimit on Unix systems. Most operating systems run with a relatively low stack size limit by default, so stack overflow on non-tail-recursive functions are a common programming bug. Starting from OCaml 5.0, native code does not use the native system stack for OCaml function calls anymore, so it is not affected by the operating system native stack size; both native and bytecode programs respect the OCaml runtime’s own limit. The runtime limit is set to a much higher default than most operating system native stacks, with a limit of at least 512MiB, so stack overflow should be much less common in practice. There is still a stack limit by default, as it remains useful to quickly catch bugs with looping non-tail-recursive functions. Without a stack limit, one has to wait for the whole memory to be consumed by the stack for the program to crash, which can take a long time and make the system unresponsive. This means that the tail modulo constructor transformation is less important on OCaml 5: it does improve performance noticeably in some cases, but it is not necessary for basic correctness for most use-cases. 26.1 Disambiguation *=*=*=*=*=*=*=*=*=*=* It may happen that several arguments of a constructor are recursive calls to a tail-modulo-cons function. The transformation can only turn one of these calls into a tail call. The compiler will not make an implicit choice, but ask the user to provide an explicit disambiguation. Consider this type of syntactic expressions (assuming some pre-existing type var of expression variables): << type var (* some pre-existing type of variables *) type exp = | Var of var | Let of binding * exp and binding = var * exp >> Consider a map function on variables. The direct definition has two recursive calls inside arguments of the Let constructor, so it gets rejected as ambiguous. << let[@tail_mod_cons] rec map_vars f exp = match exp with | Var v -> Var (f v) | Let ((v, def), body) -> Let ((f v, map_vars f def), map_vars f body) Error: [@tail_mod_cons]: this constructor application may be TMC-transformed in several different ways. Please disambiguate by adding an explicit [@tailcall] attribute to the call that should be made tail-recursive, or a [@tailcall false] attribute on calls that should not be transformed. This call could be annotated. This call could be annotated. >> To disambiguate, the user should add a [@tailcall] attribute to the recursive call that should be transformed to tail position: << let[@tail_mod_cons] rec map_vars f exp = match exp with | Var v -> Var (f v) | Let ((v, def), body) -> Let ((f v, map_vars f def), (map_vars[@tailcall]) f body) >> Be aware that the resulting function is not tail-recursive, the recursive call on def will consume stack space. However, expression trees tend to be right-leaning (lots of Let in sequence, rather than nested inside each other), so putting the call on body in tail position is an interesting improvement over the naive definition: it gives bounded stack space consumption if we assume a bound on the nesting depth of Let constructs. One would also get an error when using conflicting annotations, asking for two of the constructor arguments to be put in tail position: << let[@tail_mod_cons] rec map_vars f exp = match exp with | Var v -> Var (f v) | Let ((v, def), body) -> Let ((f v, (map_vars[@tailcall]) f def), (map_vars[@tailcall]) f body) Error: [@tail_mod_cons]: this constructor application may be TMC-transformed in several different ways. Only one of the arguments may become a TMC call, but several arguments contain calls that are explicitly marked as tail-recursive. Please fix the conflict by reviewing and fixing the conflicting annotations. This call is explicitly annotated. This call is explicitly annotated. >> 26.2 Danger: getting out of tail-mod-cons *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Due to the nature of the tail-mod-cons transformation (see Section 26.3 for a presentation of transformation): - Calls from a tail-mod-cons function to another tail-mod-cons function declared in the same recursive-binding group are transformed into tail calls, as soon as they occur in tail position or tail-modulo-cons position in the source function. - Calls from a function not annotated tail-mod-cons to a tail-mod-cons function or, conversely, from a tail-mod-cons function to a non-tail-mod-cons function are transformed into non-tail calls, even if they syntactically appear in tail position in the source program. The fact that calls in tail position in the source program may become non-tail calls if they go from a tail-mod-cons to a non-tail-mod-cons function is surprising, and the transformation will warn about them. For example: << let[@tail_mod_cons] rec flatten = function | [] -> [] | xs :: xss -> let rec append_flatten xs xss = match xs with | [] -> flatten xss | x :: xs -> x :: append_flatten xs xss in append_flatten xs xss Warning 71 [unused-tmc-attribute]: This function is marked @tail_mod_cons but is never applied in TMC position. Warning 72 [tmc-breaks-tailcall]: This call is in tail-modulo-cons position in a TMC function, but the function called is not itself specialized for TMC, so the call will not be transformed into a tail call. Please either mark the called function with the [@tail_mod_cons] attribute, or mark this call with the [@tailcall false] attribute to make its non-tailness explicit. >> Here the append_flatten helper is not annotated with [@tail_mod_cons], so the calls append_flatten xs xss and flatten xss will not be tail calls. The correct fix here is to annotate append_flatten to be tail-mod-cons. << let[@tail_mod_cons] rec flatten = function | [] -> [] | xs :: xss -> let[@tail_mod_cons] rec append_flatten xs xss = match xs with | [] -> flatten xss | x :: xs -> x :: append_flatten xs xss in append_flatten xs xss >> The same warning occurs when append_flatten is a non-tail-mod-cons function of the same recursive group; using the tail-mod-cons transformation is a property of individual functions, not whole recursive groups. << let[@tail_mod_cons] rec flatten = function | [] -> [] | xs :: xss -> append_flatten xs xss and append_flatten xs xss = match xs with | [] -> flatten xss | x :: xs -> x :: append_flatten xs xss Warning 71 [unused-tmc-attribute]: This function is marked @tail_mod_cons but is never applied in TMC position. Warning 72 [tmc-breaks-tailcall]: This call is in tail-modulo-cons position in a TMC function, but the function called is not itself specialized for TMC, so the call will not be transformed into a tail call. Please either mark the called function with the [@tail_mod_cons] attribute, or mark this call with the [@tailcall false] attribute to make its non-tailness explicit. >> Again, the fix is to specialize append_flatten as well: << let[@tail_mod_cons] rec flatten = function | [] -> [] | xs :: xss -> append_flatten xs xss and[@tail_mod_cons] append_flatten xs xss = match xs with | [] -> flatten xss | x :: xs -> x :: append_flatten xs xss >> Non-recursive functions can also be annotated [@tail_mod_cons]; this is typically useful for local bindings to recursive functions. Incorrect version: << let[@tail_mod_cons] rec map_vars f exp = let self exp = map_vars f exp in match exp with | Var v -> Var (f v) | Let ((v, def), body) -> Let ((f v, self def), (self[@tailcall]) body) Warning 51 [wrong-tailcall-expectation]: expected tailcall Warning 51 [wrong-tailcall-expectation]: expected tailcall Warning 71 [unused-tmc-attribute]: This function is marked @tail_mod_cons but is never applied in TMC position. >> Recommended fix: << let[@tail_mod_cons] rec map_vars f exp = let[@tail_mod_cons] self exp = map_vars f exp in match exp with | Var v -> Var (f v) | Let ((v, def), body) -> Let ((f v, self def), (self[@tailcall]) body) >> In other cases, there is either no benefit in making the called function tail-mod-cons, or it is not possible: for example, it is a function parameter (the transformation only works with direct calls to known functions). For example, consider a substitution function on binary trees: << type 'a tree = Leaf of 'a | Node of 'a tree * 'a tree let[@tail_mod_cons] rec bind (f : 'a -> 'a tree) (t : 'a tree) : 'a tree = match t with | Leaf v -> f v | Node (left, right) -> Node (bind f left, (bind[@tailcall]) f right) Warning 72 [tmc-breaks-tailcall]: This call is in tail-modulo-cons position in a TMC function, but the function called is not itself specialized for TMC, so the call will not be transformed into a tail call. Please either mark the called function with the [@tail_mod_cons] attribute, or mark this call with the [@tailcall false] attribute to make its non-tailness explicit. >> Here f is a function parameter, not a direct call, and the current implementation is strictly first-order, it does not support tail-mod-cons arguments. In this case, the user should indicate that they realize this call to f v is not, in fact, in tail position, by using (f[@tailcall false]) v. << type 'a tree = Leaf of 'a | Node of 'a tree * 'a tree let[@tail_mod_cons] rec bind (f : 'a -> 'a tree) (t : 'a tree) : 'a tree = match t with | Leaf v -> (f[@tailcall false]) v | Node (left, right) -> Node (bind f left, (bind[@tailcall]) f right) >> 26.3 Details on the transformation *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= To use this advanced feature, it helps to be aware that the function transformation produces a specialized function in destination-passing-style. Recall our map example: << let rec map f l = match l with | [] -> [] | x :: xs -> let y = f x in y :: map f xs >> Below is a description of the transformed program in pseudo-OCaml notation: some operations are not expressible in OCaml source code. (The transformation in fact happens on the Lambda intermediate representation of the OCaml compiler.) < [] | x :: xs -> let y = f x in let dst = y ::{mutable} Hole in map_dps f xs dst 1; dst and map_dps f l dst idx = match l with | [] -> dst.idx <- [] | x :: xs -> let y = f x in let dst' = y ::{mutable} Hole in dst.idx <- dst'; map_dps f xs dst' 1 >> The source version of map gets transformed into two functions, a direct-style version that is also called map, and a destination-passing-style version (DPS) called map_dps. The destination-passing-style version does not return a result directly, instead it writes it into a memory location specified by two additional function parameters, dst (a memory block) and i (a position within the memory block). The source call y :: map f xs gets transformed into the creation of a mutable block y ::{mutable} Hole, whose second parameter is an un-initialized hole. The block is then passed to map_dps as a destination parameter (with offset 1). Notice that map does not call itself recursively, it calls map_dps. Then, map_dps calls itself recursively, in a tail-recursive way. The call from map to map_dps is not a tail call (this is something that we could improve in the future); but this call happens only once when invoking map f l, with all list elements after the first one processed in constant stack by map_dps. This explains the “getting out of tail-mod-cons” subtleties. Consider our previous example involving mutual recursion between flatten and append_flatten. < [] | xs :: xss -> append_flatten xs xss >> The call to append_flatten, which syntactically appears in tail position, gets transformed differently depending on whether the function has a destination-passing-style version available, that is, whether it is itself annotated [@tail_mod_cons]: <<(* if append_flatten_dps exists *) and flatten_dps l dst i = match l with | [] -> dst.i <- [] | xs :: xss -> append_flatten_dps xs xss dst i (* if append_flatten_dps does not exist *) and rec flatten_dps l dst i = match l with | [] -> dst.i <- [] | xs :: xss -> dst.i <- append_flatten xs xss >> If append_flatten does not have a destination-passing-style version, the call gets transformed to a non-tail call. 26.4 Current limitations *=*=*=*=*=*=*=*=*=*=*=*=*= Purely syntactic criterion Just like tail calls in general, the notion of tail-modulo-constructor position is purely syntactic; some simple refactoring will move calls out of tail-modulo-constructor position. << (* works as expected *) let[@tail_mod_cons] rec map f li = match li with | [] -> [] | x :: xs -> let y = f x in y :: (* this call is in TMC position *) map f xs >> << (* not optimizable anymore *) let[@tail_mod_cons] rec map f li = match li with | [] -> [] | x :: xs -> let y = f x in let ys = (* this call is not in TMC position anymore *) map f xs in y :: ys Warning 71 [unused-tmc-attribute]: This function is marked @tail_mod_cons but is never applied in TMC position. >> Local, first-order transformation When a function gets transformed with tail-mod-cons, two definitions are generated, one providing a direct-style interface and one providing the destination-passing-style version. However, not all calls to this function in tail-modulo-cons position will use the destination-passing-style version and become tail calls: - The transformation is local: only tail-mod-cons calls to foo within the same compilation unit as foo become tail calls. - The transformation is first-order: only direct calls to known tail-mod-cons functions become tail calls when in tail-mod-cons position, never calls to function parameters. Consider the call Option.map foo x for example: even if foo is called in tail-mod-cons position within the definition of Option.map, that call will never become a tail call. (This would be the case even if the call to Option.map was inside the Option module.) In general this limitation is not a problem for recursive functions: the first call from an outside module or a higher-order function will consume stack space, but further recursive calls in tail-mod-cons position will get optimized. For example, if List.map is defined as a tail-mod-cons function, calls from outside the List module will not become tail calls when in tail positions, but the recursive calls within the definition of List.map are in tail-modulo-cons positions and do become tail calls: processing the first element of the list will consume stack space, but all further elements are handled in constant space. These limitations may be an issue in more complex situations where mutual recursion happens between functions, with some functions not annotated tail-mod-cons, or defined across different modules, or called indirectly, for example through function parameters. Non-exact calls to tupled functions OCaml performs an implicit optimization for “tupled” functions, which take a single parameter that is a tuple: let f (x, y, z) = .... Direct calls to these functions with a tuple literal argument (like f (a, b, c)) will call the “tupled” function by passing the parameters directly, instead of building a tuple of them. Other calls, either indirect calls or calls passing a more complex tuple value (like let t = (a, b, c) in f t) are compiled as “inexact” calls that go through a wrapper. The [@tail_mod_cons] transformation supports tupled functions, but will only optimize “exact” calls in tail position; direct calls to something other than a tuple literal will not become tail calls. The user can manually unpack a tuple to force a call to be “exact”: let (x, y, z) = t in f (x, y, z). If there is any doubt as to whether a call can be tail-mod-cons-optimized or not, one can use the [@tailcall] attribute on the called function, which will warn if the transformation is not possible. << let rec map (f, l) = match l with | [] -> [] | x :: xs -> let y = f x in let args = (f, xs) in (* this inexact call cannot be tail-optimized, so a warning will be raised *) y :: (map[@tailcall]) args Warning 51 [wrong-tailcall-expectation]: expected tailcall >> Chapter 27  Runtime detection of data races with ThreadSanitizer ******************************************************************** 27.1 Overview and usage *=*=*=*=*=*=*=*=*=*=*=*=* OCaml, since version 5.0, allows shared-memory parallelism and thus mutation of data shared between multiple threads. This creates the possibility of data races, i.e., unordered accesses to the same memory location with at least one of them being a write. In OCaml, data races are easy to introduce, and the behaviour of programs with data races can be unintuitive — the observed behaviours cannot be explained by simply interleaving operations from different concurrent threads. More information about data races and their consequences can be found in section 9.4 and Chapter 10. To help detect data races, OCaml supports ThreadSantizer (TSan), a dynamic data race detector that has been successfully used in languages such as C/C++, Swift, etc. TSan support for OCaml is available since OCaml 5.2. To use TSan, you must configure the compiler with –enable-tsan. You can also install an opam switch with the TSan feature enabled as follows: < ocaml-option-tsan >> TSan support for OCaml is currently available for the x86_64 architecture, on FreeBSD, Linux and macOS, for the arm64 architecture on Linux and macOS, and for the POWER, riscv and s390x architectures on Linux. Building OCaml with TSan support requires GCC or Clang. Minimal supported versions are GCC 11 and Clang 14. Note that TSan data race reports with GCC 11 are known to result in poor stack trace reporting (no line numbers), which is fixed in GCC 12. A TSan-enabled compiler differs from a regular compiler in the following way: all programs compiled by ocamlopt are instrumented with calls to the TSan runtime, and TSan will detect data races encountered during execution. For instance, consider the following program: << let a = ref 0 and b = ref 0 let d1 () = a := 1; !b let d2 () = b := 1; !a let () = let h = Domain.spawn d2 in let r1 = d1 () in let r2 = Domain.join h in assert (not (r1 = 0 && r2 = 0)) >> This program has data races. The memory locations a and b are read and written concurrently by multiple domains d1 and d2. a and b are “non-atomic” locations according to the memory model (see Chapter 10), and there is no synchronization between accesses to them. Hence, there are two data races here corresponding to the two memory locations a and b. When you compile and run this program with ocamlopt, you may observe data race reports on the standard error, such as: <<================== WARNING: ThreadSanitizer: data race (pid=3808831) Write of size 8 at 0x8febe0 by thread T1 (mutexes: write M90): #0 camlSimple_race.d2_274 simple_race.ml:8 (simple_race.exe+0x420a72) #1 camlDomain.body_706 stdlib/domain.ml:211 (simple_race.exe+0x440f2f) #2 caml_start_program (simple_race.exe+0x47cf37) #3 caml_callback_exn runtime/callback.c:197 (simple_race.exe+0x445f7b) #4 domain_thread_func runtime/domain.c:1167 (simple_race.exe+0x44a113) Previous read of size 8 at 0x8febe0 by main thread (mutexes: write M86): #0 camlSimple_race.d1_271 simple_race.ml:5 (simple_race.exe+0x420a22) #1 camlSimple_race.entry simple_race.ml:13 (simple_race.exe+0x420d16) #2 caml_program (simple_race.exe+0x41ffb9) #3 caml_start_program (simple_race.exe+0x47cf37) [...] WARNING: ThreadSanitizer: data race (pid=3808831) Read of size 8 at 0x8febf0 by thread T1 (mutexes: write M90): #0 camlSimple_race.d2_274 simple_race.ml:9 (simple_race.exe+0x420a92) #1 camlDomain.body_706 stdlib/domain.ml:211 (simple_race.exe+0x440f2f) #2 caml_start_program (simple_race.exe+0x47cf37) #3 caml_callback_exn runtime/callback.c:197 (simple_race.exe+0x445f7b) #4 domain_thread_func runtime/domain.c:1167 (simple_race.exe+0x44a113) Previous write of size 8 at 0x8febf0 by main thread (mutexes: write M86): #0 camlSimple_race.d1_271 simple_race.ml:4 (simple_race.exe+0x420a01) #1 camlSimple_race.entry simple_race.ml:13 (simple_race.exe+0x420d16) #2 caml_program (simple_race.exe+0x41ffb9) #3 caml_start_program (simple_race.exe+0x47cf37) [...] ================== ThreadSanitizer: reported 2 warnings >> For each detected data race, TSan reports the location of the conflicting accesses, their nature (read, write, atomic read, etc.), and the associated stack trace. If you run the above program several times, the output may vary: sometimes TSan will report two data races, sometimes one, and sometimes none. This is due to the combination of two factors: - First, TSan reports only the data races encountered during execution, i.e., conflicting, unordered memory accesses that are effectively performed. - In addition, in this program, depending on executions, there may be no such memory accesses: if d1 returns before d2 has finished spawning, then all memory accesses originating from d1 may happen-before the ones originating from d2, since spawning a domain involves inter-thread synchronization. In that case, the accesses are considered to be ordered and no data race is reported. This example illustrates the fact that data races can sometimes be hidden by unrelated synchronizing operations. 27.2 Performance implications *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* TSan instrumentation imposes a non-negligible cost at runtime. Empirically, this cost has been observed to cause a slowdown which can range from 2x to 7x. One of the main factors of high slowdowns is frequent access to mutable data. In contrast, the initialising writes to and reads from immutable memory locations are not instrumented. TSan also allocates very large amounts of virtual memory, although it uses only a fraction of it. The memory consumption is increased by a factor between 4 and 7. 27.3 False negatives and false positives *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= As illustrated by the previous example, TSan will only report the data races encountered during execution. Another important caveat is that TSan remembers only a finite number of memory accesses per memory location. At the time of writing, this number is 4. Data races involving a forgotten access will not be detected. Lastly, the documentation of TSan (1) states that there is a tiny probability to miss a race if two threads access the same location at the same time. TSan may overlook data races only in these three specific cases. For data races between two memory accesses made from OCaml code, TSan does not produce false positives; that is, TSan will not emit spurious reports. When mixing OCaml and C code, through the use of C primitives, the very notion of false positive becomes less clear, as it involves two memory models – OCaml and C11. However, TSan should behave mostly as one would expect: non-atomic reads and writes in C will race with non-atomic reads and writes in OCaml, and C atomics will not race with OCaml atomics. There is one theoretical possibility of false positive: if a value is initialized from C without using caml_initialize (which is allowed under the condition that the GC does not run between the allocation and the write, see Chapter 22) and a conflicting access is made later by another thread. This does not constitute a data race, but TSan may report it as such. 27.4 Runtime options *=*=*=*=*=*=*=*=*=*=*= TSan supports a number of configuration options at runtime using the TSAN_OPTIONS environment variable. TSAN_OPTIONS should contain one or more options separated by spaces. See the documentation of TSan flags (2) and the documentation of flags common to all sanitizers (3) for more information. Notably, TSAN_OPTIONS allows suppressing some data races from TSan reports. Suppressing data race reports is useful for intentional races or libraries that cannot be fixed. For example, to suppress reports originating from functions in the OCaml module My_module, one can run <> with suppr.txt a file containing: <> (Note that this depends on the format of OCaml symbols in the executable. Some builders, like Dune, might result in different formats. You should adapt this example to the symbols effectively present in your stack traces.) The TSAN_OPTIONS variable also allows for increasing the “history size”, e.g.: <> TSan’s history records events such as function entry and exit, and is used to reconstruct stack traces. Increasing the history size can sometimes be necessary to obtain the second stack trace, but it also increases memory consumption. This setting does not change the number of memory accesses remembered per memory location. 27.5 Guidelines for linking *=*=*=*=*=*=*=*=*=*=*=*=*=*=* As a general rule, OCaml programs instrumented with TSan should only be linked with OCaml or C objects also instrumented with TSan. Doing otherwise may result in crashes. The only exception to this rule are C libraries that do not call into the OCaml runtime system in any way, i.e., do not allocate, raise exceptions, call back into OCaml code, etc. Examples include the libc or system libraries. Data races in non-instrumented libraries will not be reported. C code interacting with OCaml should always be built through the ocamlopt command, which will pass the required instrumentation flags to the C compiler. The CAMLno_tsan qualifier can be used to prevent functions from being instrumented: <> Races from non-instrumented functions will not be reported. CAMLno_tsan should only be used by experts. It can be used to reduce the performance overhead in certain corner cases, or to suppress some known alarms. For the latter, using a suppressions file with TSAN_OPTIONS should be preferred when possible, as it allows for finer-grained control, and qualifying a function f with CAMLno_tsan results in missing entries in TSan’s stack traces when a data race happens in a transitive callee of f. There is no way to disable instrumentation in OCaml code. 27.6 Changes in the delivery of signals *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* TSan intercepts all signals and passes them down to the instrumented program. This overlay from TSan is not always transparent for the program. Synchronous signals such as SIGSEV, SIGILL, SIGBUS, etc. will be passed down immediately, whereas asynchronous signals such as SIGINT will be delayed until the next call to the TSan runtime (e.g. until the next access to mutable data). This limitation of TSan can have surprising effects: for instance, pure, recursive functions that do not allocate cannot be interrupted until they terminate. --------------------------------------- (1) https://github.com/google/sanitizers/wiki/ThreadSanitizerAlgorithm (2) https://github.com/google/sanitizers/wiki/ThreadSanitizerFlags (3) https://github.com/google/sanitizers/wiki/SanitizerCommonFlags Part: IV ******** The OCaml library ***************** Chapter 28  The core library ******************************** This chapter describes the OCaml core library, which is composed of declarations for built-in types and exceptions, plus the module Stdlib that provides basic operations on these built-in types. The Stdlib module is special in two ways: - It is automatically linked with the user’s object code files by the ocamlc command (chapter 13). - It is automatically “opened” when a compilation starts, or when the toplevel system is launched. Hence, it is possible to use unqualified identifiers to refer to the functions provided by the Stdlib module, without adding a open Stdlib directive. 28.1 Built-in types and predefined exceptions *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The following built-in types and predefined exceptions are always defined in the compilation environment, but are not part of any module. As a consequence, they can only be referred by their short names. Built-in types ============== << type int >> The type of integer numbers. << type char >> The type of characters. << type bytes >> The type of (writable) byte sequences. << type string >> The type of (read-only) character strings. << type float >> The type of floating-point numbers. << type bool = false | true >> The type of booleans (truth values). << type unit = () >> The type of the unit value. << type exn >> The type of exception values. << type 'a array >> The type of arrays whose elements have type 'a. << type 'a list = [] | :: of 'a * 'a list >> The type of lists whose elements have type 'a. <> The type of optional values of type 'a. <> The type of signed 32-bit integers. Literals for 32-bit integers are suffixed by l. See the Int32 module. <> The type of signed 64-bit integers. Literals for 64-bit integers are suffixed by L. See the Int64 module. <> The type of signed, platform-native integers (32 bits on 32-bit processors, 64 bits on 64-bit processors). Literals for native integers are suffixed by n. See the Nativeint module. <> The type of format strings. 'a is the type of the parameters of the format, 'f is the result type for the printf-style functions, 'b is the type of the first argument given to %a and %t printing functions (see module Printf), 'c is the result type of these functions, and also the type of the argument transmitted to the first argument of kprintf-style functions, 'd is the result type for the scanf-style functions (see module Scanf), and 'e is the type of the receiver function for the scanf-style functions. <> This type is used to implement the Lazy module. It should not be used directly. Predefined exceptions ===================== <> Exception raised when none of the cases of a pattern-matching apply. The arguments are the location of the match keyword in the source code (file name, line number, column number). <> Exception raised when an assertion fails. The arguments are the location of the assert keyword in the source code (file name, line number, column number). <> Exception raised by library functions to signal that the given arguments do not make sense. The string gives some information to the programmer. As a general rule, this exception should not be caught, it denotes a programming error and the code should be modified not to trigger it. <> Exception raised by library functions to signal that they are undefined on the given arguments. The string is meant to give some information to the programmer; you must not pattern match on the string literal because it may change in future versions (use Failure _ instead). <> Exception raised by search functions when the desired object could not be found. <> Exception raised by the garbage collector when there is insufficient memory to complete the computation. (Not reliable for allocations on the minor heap.) <> Exception raised by the bytecode interpreter when the evaluation stack reaches its maximal size. This often indicates infinite or excessively deep recursion in the user’s program. Before 4.10, it was not fully implemented by the native-code compiler. <> Exception raised by the input/output functions to report an operating system error. The string is meant to give some information to the programmer; you must not pattern match on the string literal because it may change in future versions (use Sys_error _ instead). <> Exception raised by input functions to signal that the end of file has been reached. <> Exception raised by integer division and remainder operations when their second argument is zero. <> A special case of Sys_error raised when no I/O is possible on a non-blocking I/O channel. <> Exception raised when an ill-founded recursive module definition is evaluated. (See section 12.2.) The arguments are the location of the definition in the source code (file name, line number, column number). 28.2 Module Stdlib : The OCaml Standard library. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This module is automatically opened at the beginning of each compilation. All components of this module can therefore be referred by their short name, without prefixing them by Stdlib. In particular, it provides the basic operations over the built-in types (numbers, booleans, byte sequences, strings, exceptions, references, lists, arrays, input-output channels, ...) and the standard library modules[28.2]. Exceptions ========== << val raise : exn -> 'a >> Raise the given exception value << val raise_notrace : exn -> 'a >> A faster version raise which does not record the backtrace. Since: 4.02 << val invalid_arg : string -> 'a >> Raise exception Invalid_argument with the given string. << val failwith : string -> 'a >> Raise exception Failure with the given string. << exception Exit >> The Exit exception is not raised by any library function. It is provided for use in your programs. << exception Match_failure of (string * int * int) >> Exception raised when none of the cases of a pattern-matching apply. The arguments are the location of the match keyword in the source code (file name, line number, column number). << exception Assert_failure of (string * int * int) >> Exception raised when an assertion fails. The arguments are the location of the assert keyword in the source code (file name, line number, column number). << exception Invalid_argument of string >> Exception raised by library functions to signal that the given arguments do not make sense. The string gives some information to the programmer. As a general rule, this exception should not be caught, it denotes a programming error and the code should be modified not to trigger it. << exception Failure of string >> Exception raised by library functions to signal that they are undefined on the given arguments. The string is meant to give some information to the programmer; you must not pattern match on the string literal because it may change in future versions (use Failure _ instead). << exception Not_found >> Exception raised by search functions when the desired object could not be found. << exception Out_of_memory >> Exception raised by the garbage collector when there is insufficient memory to complete the computation. (Not reliable for allocations on the minor heap.) << exception Stack_overflow >> Exception raised by the bytecode interpreter when the evaluation stack reaches its maximal size. This often indicates infinite or excessively deep recursion in the user’s program. Before 4.10, it was not fully implemented by the native-code compiler. << exception Sys_error of string >> Exception raised by the input/output functions to report an operating system error. The string is meant to give some information to the programmer; you must not pattern match on the string literal because it may change in future versions (use Sys_error _ instead). << exception End_of_file >> Exception raised by input functions to signal that the end of file has been reached. << exception Division_by_zero >> Exception raised by integer division and remainder operations when their second argument is zero. << exception Sys_blocked_io >> A special case of Sys_error raised when no I/O is possible on a non-blocking I/O channel. << exception Undefined_recursive_module of (string * int * int) >> Exception raised when an ill-founded recursive module definition is evaluated. The arguments are the location of the definition in the source code (file name, line number, column number). Comparisons =========== << val (=) : 'a -> 'a -> bool >> e1 = e2 tests for structural equality of e1 and e2. Mutable structures (e.g. references and arrays) are equal if and only if their current contents are structurally equal, even if the two mutable objects are not the same physical object. Equality between functional values raises Invalid_argument. Equality between cyclic data structures may not terminate. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (<>) : 'a -> 'a -> bool >> Negation of (=)[28.2]. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (<) : 'a -> 'a -> bool >> See (>=)[28.2]. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (>) : 'a -> 'a -> bool >> See (>=)[28.2]. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (<=) : 'a -> 'a -> bool >> See (>=)[28.2]. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (>=) : 'a -> 'a -> bool >> Structural ordering functions. These functions coincide with the usual orderings over integers, characters, strings, byte sequences and floating-point numbers, and extend them to a total ordering over all types. The ordering is compatible with ( = ). As in the case of ( = ), mutable structures are compared by contents. Comparison between functional values raises Invalid_argument. Comparison between cyclic structures may not terminate. Left-associative operator, see Ocaml_operators[29.61] for more information. << val compare : 'a -> 'a -> int >> compare x y returns 0 if x is equal to y, a negative integer if x is less than y, and a positive integer if x is greater than y. The ordering implemented by compare is compatible with the comparison predicates =, < and > defined above, with one difference on the treatment of the float value nan[28.2]. Namely, the comparison predicates treat nan as different from any other float value, including itself; while compare treats nan as equal to itself and less than any other float value. This treatment of nan ensures that compare defines a total ordering relation. compare applied to functional values may raise Invalid_argument. compare applied to cyclic structures may not terminate. The compare function can be used as the comparison function required by the Set.Make[29.50] and Map.Make[29.34] functors, as well as the List.sort[29.32] and Array.sort[29.2] functions. << val min : 'a -> 'a -> 'a >> Return the smaller of the two arguments. The result is unspecified if one of the arguments contains the float value nan. << val max : 'a -> 'a -> 'a >> Return the greater of the two arguments. The result is unspecified if one of the arguments contains the float value nan. << val (==) : 'a -> 'a -> bool >> e1 == e2 tests for physical equality of e1 and e2. On mutable types such as references, arrays, byte sequences, records with mutable fields and objects with mutable instance variables, e1 == e2 is true if and only if physical modification of e1 also affects e2. On non-mutable types, the behavior of ( == ) is implementation-dependent; however, it is guaranteed that e1 == e2 implies compare e1 e2 = 0. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (!=) : 'a -> 'a -> bool >> Negation of (==)[28.2]. Left-associative operator, see Ocaml_operators[29.61] for more information. Boolean operations ================== << val not : bool -> bool >> The boolean negation. << val (&&) : bool -> bool -> bool >> The boolean ’and’. Evaluation is sequential, left-to-right: in e1 && e2, e1 is evaluated first, and if it returns false, e2 is not evaluated at all. Right-associative operator, see Ocaml_operators[29.61] for more information. << val (||) : bool -> bool -> bool >> The boolean ’or’. Evaluation is sequential, left-to-right: in e1 || e2, e1 is evaluated first, and if it returns true, e2 is not evaluated at all. Right-associative operator, see Ocaml_operators[29.61] for more information. Debugging ========= << val __LOC__ : string >> __LOC__ returns the location at which this expression appears in the file currently being parsed by the compiler, with the standard error format of OCaml: "File %S, line %d, characters %d-%d". Since: 4.02 << val __FILE__ : string >> __FILE__ returns the name of the file currently being parsed by the compiler. Since: 4.02 << val __LINE__ : int >> __LINE__ returns the line number at which this expression appears in the file currently being parsed by the compiler. Since: 4.02 << val __MODULE__ : string >> __MODULE__ returns the module name of the file being parsed by the compiler. Since: 4.02 << val __POS__ : string * int * int * int >> __POS__ returns a tuple (file,lnum,cnum,enum), corresponding to the location at which this expression appears in the file currently being parsed by the compiler. file is the current filename, lnum the line number, cnum the character position in the line and enum the last character position in the line. Since: 4.02 << val __FUNCTION__ : string >> __FUNCTION__ returns the name of the current function or method, including any enclosing modules or classes. Since: 4.12 << val __LOC_OF__ : 'a -> string * 'a >> __LOC_OF__ expr returns a pair (loc, expr) where loc is the location of expr in the file currently being parsed by the compiler, with the standard error format of OCaml: "File %S, line %d, characters %d-%d". Since: 4.02 << val __LINE_OF__ : 'a -> int * 'a >> __LINE_OF__ expr returns a pair (line, expr), where line is the line number at which the expression expr appears in the file currently being parsed by the compiler. Since: 4.02 << val __POS_OF__ : 'a -> (string * int * int * int) * 'a >> __POS_OF__ expr returns a pair (loc,expr), where loc is a tuple (file,lnum,cnum,enum) corresponding to the location at which the expression expr appears in the file currently being parsed by the compiler. file is the current filename, lnum the line number, cnum the character position in the line and enum the last character position in the line. Since: 4.02 Composition operators ===================== << val (|>) : 'a -> ('a -> 'b) -> 'b >> Reverse-application operator: x |> f |> g is exactly equivalent to g (f (x)). Left-associative operator, see Ocaml_operators[29.61] for more information. Since: 4.01 << val (@@) : ('a -> 'b) -> 'a -> 'b >> Application operator: g @@ f @@ x is exactly equivalent to g (f (x)). Right-associative operator, see Ocaml_operators[29.61] for more information. Since: 4.01 Integer arithmetic ================== Integers are Sys.int_size bits wide. All operations are taken modulo 2^Sys.int_size. They do not fail on overflow. << val (~-) : int -> int >> Unary negation. You can also write - e instead of ~- e. Unary operator, see Ocaml_operators[29.61] for more information. << val (~+) : int -> int >> Unary addition. You can also write + e instead of ~+ e. Unary operator, see Ocaml_operators[29.61] for more information. Since: 3.12 << val succ : int -> int >> succ x is x + 1. << val pred : int -> int >> pred x is x - 1. << val (+) : int -> int -> int >> Integer addition. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (-) : int -> int -> int >> Integer subtraction. Left-associative operator, , see Ocaml_operators[29.61] for more information. << val ( * ) : int -> int -> int >> Integer multiplication. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (/) : int -> int -> int >> Integer division. Integer division rounds the real quotient of its arguments towards zero. More precisely, if x >= 0 and y > 0, x / y is the greatest integer less than or equal to the real quotient of x by y. Moreover, (- x) / y = x / (- y) = - (x / y). Left-associative operator, see Ocaml_operators[29.61] for more information. Raises Division_by_zero if the second argument is 0. << val (mod) : int -> int -> int >> Integer remainder. If y is not zero, the result of x mod y satisfies the following properties: x = (x / y) * y + x mod y and abs(x mod y) <= abs(y) - 1. If y = 0, x mod y raises Division_by_zero. Note that x mod y is negative only if x < 0. Left-associative operator, see Ocaml_operators[29.61] for more information. Raises Division_by_zero if y is zero. << val abs : int -> int >> abs x is the absolute value of x. On min_int this is min_int itself and thus remains negative. << val max_int : int >> The greatest representable integer. << val min_int : int >> The smallest representable integer. Bitwise operations ------------------ << val (land) : int -> int -> int >> Bitwise logical and. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (lor) : int -> int -> int >> Bitwise logical or. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (lxor) : int -> int -> int >> Bitwise logical exclusive or. Left-associative operator, see Ocaml_operators[29.61] for more information. << val lnot : int -> int >> Bitwise logical negation. << val (lsl) : int -> int -> int >> n lsl m shifts n to the left by m bits. The result is unspecified if m < 0 or m > Sys.int_size. Right-associative operator, see Ocaml_operators[29.61] for more information. << val (lsr) : int -> int -> int >> n lsr m shifts n to the right by m bits. This is a logical shift: zeroes are inserted regardless of the sign of n. The result is unspecified if m < 0 or m > Sys.int_size. Right-associative operator, see Ocaml_operators[29.61] for more information. << val (asr) : int -> int -> int >> n asr m shifts n to the right by m bits. This is an arithmetic shift: the sign bit of n is replicated. The result is unspecified if m < 0 or m > Sys.int_size. Right-associative operator, see Ocaml_operators[29.61] for more information. Floating-point arithmetic ========================= OCaml’s floating-point numbers follow the IEEE 754 standard, using double precision (64 bits) numbers. Floating-point operations never raise an exception on overflow, underflow, division by zero, etc. Instead, special IEEE numbers are returned as appropriate, such as infinity for 1.0 /. 0.0, neg_infinity for -1.0 /. 0.0, and nan (’not a number’) for 0.0 /. 0.0. These special numbers then propagate through floating-point computations as expected: for instance, 1.0 /. infinity is 0.0, basic arithmetic operations (+., -., *., /.) with nan as an argument return nan, ... << val (~-.) : float -> float >> Unary negation. You can also write -. e instead of ~-. e. Unary operator, see Ocaml_operators[29.61] for more information. << val (~+.) : float -> float >> Unary addition. You can also write +. e instead of ~+. e. Unary operator, see Ocaml_operators[29.61] for more information. Since: 3.12 << val (+.) : float -> float -> float >> Floating-point addition. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (-.) : float -> float -> float >> Floating-point subtraction. Left-associative operator, see Ocaml_operators[29.61] for more information. << val ( *. ) : float -> float -> float >> Floating-point multiplication. Left-associative operator, see Ocaml_operators[29.61] for more information. << val (/.) : float -> float -> float >> Floating-point division. Left-associative operator, see Ocaml_operators[29.61] for more information. << val ( ** ) : float -> float -> float >> Exponentiation. Right-associative operator, see Ocaml_operators[29.61] for more information. << val sqrt : float -> float >> Square root. << val exp : float -> float >> Exponential. << val log : float -> float >> Natural logarithm. << val log10 : float -> float >> Base 10 logarithm. << val expm1 : float -> float >> expm1 x computes exp x -. 1.0, giving numerically-accurate results even if x is close to 0.0. Since: 3.12 << val log1p : float -> float >> log1p x computes log(1.0 +. x) (natural logarithm), giving numerically-accurate results even if x is close to 0.0. Since: 3.12 << val cos : float -> float >> Cosine. Argument is in radians. << val sin : float -> float >> Sine. Argument is in radians. << val tan : float -> float >> Tangent. Argument is in radians. << val acos : float -> float >> Arc cosine. The argument must fall within the range [-1.0, 1.0]. Result is in radians and is between 0.0 and pi. << val asin : float -> float >> Arc sine. The argument must fall within the range [-1.0, 1.0]. Result is in radians and is between -pi/2 and pi/2. << val atan : float -> float >> Arc tangent. Result is in radians and is between -pi/2 and pi/2. << val atan2 : float -> float -> float >> atan2 y x returns the arc tangent of y /. x. The signs of x and y are used to determine the quadrant of the result. Result is in radians and is between -pi and pi. << val hypot : float -> float -> float >> hypot x y returns sqrt(x *. x + y *. y), that is, the length of the hypotenuse of a right-angled triangle with sides of length x and y, or, equivalently, the distance of the point (x,y) to origin. If one of x or y is infinite, returns infinity even if the other is nan. Since: 4.00 << val cosh : float -> float >> Hyperbolic cosine. Argument is in radians. << val sinh : float -> float >> Hyperbolic sine. Argument is in radians. << val tanh : float -> float >> Hyperbolic tangent. Argument is in radians. << val acosh : float -> float >> Hyperbolic arc cosine. The argument must fall within the range [1.0, inf]. Result is in radians and is between 0.0 and inf. Since: 4.13 << val asinh : float -> float >> Hyperbolic arc sine. The argument and result range over the entire real line. Result is in radians. Since: 4.13 << val atanh : float -> float >> Hyperbolic arc tangent. The argument must fall within the range [-1.0, 1.0]. Result is in radians and ranges over the entire real line. Since: 4.13 << val ceil : float -> float >> Round above to an integer value. ceil f returns the least integer value greater than or equal to f. The result is returned as a float. << val floor : float -> float >> Round below to an integer value. floor f returns the greatest integer value less than or equal to f. The result is returned as a float. << val abs_float : float -> float >> abs_float f returns the absolute value of f. << val copysign : float -> float -> float >> copysign x y returns a float whose absolute value is that of x and whose sign is that of y. If x is nan, returns nan. If y is nan, returns either x or -. x, but it is not specified which. Since: 4.00 << val mod_float : float -> float -> float >> mod_float a b returns the remainder of a with respect to b. The returned value is a -. n *. b, where n is the quotient a /. b rounded towards zero to an integer. << val frexp : float -> float * int >> frexp f returns the pair of the significant and the exponent of f. When f is zero, the significant x and the exponent n of f are equal to zero. When f is non-zero, they are defined by f = x *. 2 ** n and 0.5 <= x < 1.0. << val ldexp : float -> int -> float >> ldexp x n returns x *. 2 ** n. << val modf : float -> float * float >> modf f returns the pair of the fractional and integral part of f. << val float : int -> float >> Same as float_of_int[28.2]. << val float_of_int : int -> float >> Convert an integer to floating-point. << val truncate : float -> int >> Same as int_of_float[28.2]. << val int_of_float : float -> int >> Truncate the given floating-point number to an integer. The result is unspecified if the argument is nan or falls outside the range of representable integers. << val infinity : float >> Positive infinity. << val neg_infinity : float >> Negative infinity. << val nan : float >> A special floating-point value denoting the result of an undefined operation such as 0.0 /. 0.0. Stands for ’not a number’. Any floating-point operation with nan as argument returns nan as result, unless otherwise specified in IEEE 754 standard. As for floating-point comparisons, =, <, <=, > and >= return false and <> returns true if one or both of their arguments is nan. nan is a quiet NaN since 5.1; it was a signaling NaN before. << val max_float : float >> The largest positive finite value of type float. << val min_float : float >> The smallest positive, non-zero, non-denormalized value of type float. << val epsilon_float : float >> The difference between 1.0 and the smallest exactly representable floating-point number greater than 1.0. << type fpclass = | FP_normal >> Normal number, none of the below << | FP_subnormal >> Number very close to 0.0, has reduced precision << | FP_zero >> Number is 0.0 or -0.0 << | FP_infinite >> Number is positive or negative infinity << | FP_nan >> Not a number: result of an undefined operation The five classes of floating-point numbers, as determined by the classify_float[28.2] function. << val classify_float : float -> fpclass >> Return the class of the given floating-point number: normal, subnormal, zero, infinite, or not a number. String operations ================= More string operations are provided in module String[28.2]. << val (^) : string -> string -> string >> String concatenation. Right-associative operator, see Ocaml_operators[29.61] for more information. Raises Invalid_argument if the result is longer then than Sys.max_string_length[29.56] bytes. Character operations ==================== More character operations are provided in module Char[28.2]. << val int_of_char : char -> int >> Return the ASCII code of the argument. << val char_of_int : int -> char >> Return the character with the given ASCII code. Raises Invalid_argument if the argument is outside the range 0–255. Unit operations =============== << val ignore : 'a -> unit >> Discard the value of its argument and return (). For instance, ignore(f x) discards the result of the side-effecting function f. It is equivalent to f x; (), except that the latter may generate a compiler warning; writing ignore(f x) instead avoids the warning. String conversion functions =========================== << val string_of_bool : bool -> string >> Return the string representation of a boolean. As the returned values may be shared, the user should not modify them directly. << val bool_of_string_opt : string -> bool option >> Convert the given string to a boolean. Return None if the string is not "true" or "false". Since: 4.05 << val bool_of_string : string -> bool >> Same as bool_of_string_opt[28.2], but raise Invalid_argument "bool_of_string" instead of returning None. << val string_of_int : int -> string >> Return the string representation of an integer, in decimal. << val int_of_string_opt : string -> int option >> Convert the given string to an integer. The string is read in decimal (by default, or if the string begins with 0u), in hexadecimal (if it begins with 0x or 0X), in octal (if it begins with 0o or 0O), or in binary (if it begins with 0b or 0B). The 0u prefix reads the input as an unsigned integer in the range [0, 2*max_int+1]. If the input exceeds max_int[28.2] it is converted to the signed integer min_int + input - max_int - 1. The _ (underscore) character can appear anywhere in the string and is ignored. Return None if the given string is not a valid representation of an integer, or if the integer represented exceeds the range of integers representable in type int. Since: 4.05 << val int_of_string : string -> int >> Same as int_of_string_opt[28.2], but raise Failure "int_of_string" instead of returning None. << val string_of_float : float -> string >> Return a string representation of a floating-point number. This conversion can involve a loss of precision. For greater control over the manner in which the number is printed, see Printf[28.2]. << val float_of_string_opt : string -> float option >> Convert the given string to a float. The string is read in decimal (by default) or in hexadecimal (marked by 0x or 0X). The format of decimal floating-point numbers is [-] dd.ddd (e|E) [+|-] dd , where d stands for a decimal digit. The format of hexadecimal floating-point numbers is [-] 0(x|X) hh.hhh (p|P) [+|-] dd , where h stands for an hexadecimal digit and d for a decimal digit. In both cases, at least one of the integer and fractional parts must be given; the exponent part is optional. The _ (underscore) character can appear anywhere in the string and is ignored. Depending on the execution platforms, other representations of floating-point numbers can be accepted, but should not be relied upon. Return None if the given string is not a valid representation of a float. Since: 4.05 << val float_of_string : string -> float >> Same as float_of_string_opt[28.2], but raise Failure "float_of_string" instead of returning None. Pair operations =============== << val fst : 'a * 'b -> 'a >> Return the first component of a pair. << val snd : 'a * 'b -> 'b >> Return the second component of a pair. List operations =============== More list operations are provided in module List[28.2]. << val (@) : 'a list -> 'a list -> 'a list >> l0 @ l1 appends l1 to l0. Same function as List.append[29.32]. Right-associative operator, see Ocaml_operators[29.61] for more information. Since: 5.1 this function is tail-recursive. Input/output ============ Note: all input/output functions can raise Sys_error when the system calls they invoke fail. << type in_channel >> The type of input channel. << type out_channel >> The type of output channel. << val stdin : in_channel >> The standard input for the process. << val stdout : out_channel >> The standard output for the process. << val stderr : out_channel >> The standard error output for the process. Output functions on standard output ----------------------------------- << val print_char : char -> unit >> Print a character on standard output. << val print_string : string -> unit >> Print a string on standard output. << val print_bytes : bytes -> unit >> Print a byte sequence on standard output. Since: 4.02 << val print_int : int -> unit >> Print an integer, in decimal, on standard output. << val print_float : float -> unit >> Print a floating-point number, in decimal, on standard output. The conversion of the number to a string uses string_of_float[28.2] and can involve a loss of precision. << val print_endline : string -> unit >> Print a string, followed by a newline character, on standard output and flush standard output. << val print_newline : unit -> unit >> Print a newline character on standard output, and flush standard output. This can be used to simulate line buffering of standard output. Output functions on standard error ---------------------------------- << val prerr_char : char -> unit >> Print a character on standard error. << val prerr_string : string -> unit >> Print a string on standard error. << val prerr_bytes : bytes -> unit >> Print a byte sequence on standard error. Since: 4.02 << val prerr_int : int -> unit >> Print an integer, in decimal, on standard error. << val prerr_float : float -> unit >> Print a floating-point number, in decimal, on standard error. The conversion of the number to a string uses string_of_float[28.2] and can involve a loss of precision. << val prerr_endline : string -> unit >> Print a string, followed by a newline character on standard error and flush standard error. << val prerr_newline : unit -> unit >> Print a newline character on standard error, and flush standard error. Input functions on standard input --------------------------------- << val read_line : unit -> string >> Flush standard output, then read characters from standard input until a newline character is encountered. Return the string of all characters read, without the newline character at the end. Raises End_of_file if the end of the file is reached at the beginning of line. << val read_int_opt : unit -> int option >> Flush standard output, then read one line from standard input and convert it to an integer. Return None if the line read is not a valid representation of an integer. Since: 4.05 << val read_int : unit -> int >> Same as read_int_opt[28.2], but raise Failure "int_of_string" instead of returning None. << val read_float_opt : unit -> float option >> Flush standard output, then read one line from standard input and convert it to a floating-point number. Return None if the line read is not a valid representation of a floating-point number. Since: 4.05 << val read_float : unit -> float >> Same as read_float_opt[28.2], but raise Failure "float_of_string" instead of returning None. General output functions ------------------------ << type open_flag = | Open_rdonly >> open for reading. << | Open_wronly >> open for writing. << | Open_append >> open for appending: always write at end of file. << | Open_creat >> create the file if it does not exist. << | Open_trunc >> empty the file if it already exists. << | Open_excl >> fail if Open_creat and the file already exists. << | Open_binary >> open in binary mode (no conversion). << | Open_text >> open in text mode (may perform conversions). << | Open_nonblock >> open in non-blocking mode. Opening modes for open_out_gen[28.2] and open_in_gen[28.2]. << val open_out : string -> out_channel >> Open the named file for writing, and return a new output channel on that file, positioned at the beginning of the file. The file is truncated to zero length if it already exists. It is created if it does not already exists. << val open_out_bin : string -> out_channel >> Same as open_out[28.2], but the file is opened in binary mode, so that no translation takes place during writes. On operating systems that do not distinguish between text mode and binary mode, this function behaves like open_out[28.2]. << val open_out_gen : open_flag list -> int -> string -> out_channel >> open_out_gen mode perm filename opens the named file for writing, as described above. The extra argument mode specifies the opening mode. The extra argument perm specifies the file permissions, in case the file must be created. open_out[28.2] and open_out_bin[28.2] are special cases of this function. << val flush : out_channel -> unit >> Flush the buffer associated with the given output channel, performing all pending writes on that channel. Interactive programs must be careful about flushing standard output and standard error at the right time. << val flush_all : unit -> unit >> Flush all open output channels; ignore errors. << val output_char : out_channel -> char -> unit >> Write the character on the given output channel. << val output_string : out_channel -> string -> unit >> Write the string on the given output channel. << val output_bytes : out_channel -> bytes -> unit >> Write the byte sequence on the given output channel. Since: 4.02 << val output : out_channel -> bytes -> int -> int -> unit >> output oc buf pos len writes len characters from byte sequence buf, starting at offset pos, to the given output channel oc. Raises Invalid_argument if pos and len do not designate a valid range of buf. << val output_substring : out_channel -> string -> int -> int -> unit >> Same as output but take a string as argument instead of a byte sequence. Since: 4.02 << val output_byte : out_channel -> int -> unit >> Write one 8-bit integer (as the single character with that code) on the given output channel. The given integer is taken modulo 256. << val output_binary_int : out_channel -> int -> unit >> Write one integer in binary format (4 bytes, big-endian) on the given output channel. The given integer is taken modulo 2^32. The only reliable way to read it back is through the input_binary_int[28.2] function. The format is compatible across all machines for a given version of OCaml. << val output_value : out_channel -> 'a -> unit >> Write the representation of a structured value of any type to a channel. Circularities and sharing inside the value are detected and preserved. The object can be read back, by the function input_value[28.2]. See the description of module Marshal[28.2] for more information. output_value[28.2] is equivalent to Marshal.to_channel[29.35] with an empty list of flags. << val seek_out : out_channel -> int -> unit >> seek_out chan pos sets the current writing position to pos for channel chan. This works only for regular files. On files of other kinds (such as terminals, pipes and sockets), the behavior is unspecified. << val pos_out : out_channel -> int >> Return the current writing position for the given channel. Does not work on channels opened with the Open_append flag (returns unspecified results). For files opened in text mode under Windows, the returned position is approximate (owing to end-of-line conversion); in particular, saving the current position with pos_out, then going back to this position using seek_out will not work. For this programming idiom to work reliably and portably, the file must be opened in binary mode. << val out_channel_length : out_channel -> int >> Return the size (number of characters) of the regular file on which the given channel is opened. If the channel is opened on a file that is not a regular file, the result is meaningless. << val close_out : out_channel -> unit >> Close the given channel, flushing all buffered write operations. Output functions raise a Sys_error exception when they are applied to a closed output channel, except close_out and flush, which do nothing when applied to an already closed channel. Note that close_out may raise Sys_error if the operating system signals an error when flushing or closing. << val close_out_noerr : out_channel -> unit >> Same as close_out, but ignore all errors. << val set_binary_mode_out : out_channel -> bool -> unit >> set_binary_mode_out oc true sets the channel oc to binary mode: no translations take place during output. set_binary_mode_out oc false sets the channel oc to text mode: depending on the operating system, some translations may take place during output. For instance, under Windows, end-of-lines will be translated from \n to \r\n. This function has no effect under operating systems that do not distinguish between text mode and binary mode. General input functions ----------------------- << val open_in : string -> in_channel >> Open the named file for reading, and return a new input channel on that file, positioned at the beginning of the file. << val open_in_bin : string -> in_channel >> Same as open_in[28.2], but the file is opened in binary mode, so that no translation takes place during reads. On operating systems that do not distinguish between text mode and binary mode, this function behaves like open_in[28.2]. << val open_in_gen : open_flag list -> int -> string -> in_channel >> open_in_gen mode perm filename opens the named file for reading, as described above. The extra arguments mode and perm specify the opening mode and file permissions. open_in[28.2] and open_in_bin[28.2] are special cases of this function. << val input_char : in_channel -> char >> Read one character from the given input channel. Raises End_of_file if there are no more characters to read. << val input_line : in_channel -> string >> Read characters from the given input channel, until a newline character is encountered. Return the string of all characters read, without the newline character at the end. Raises End_of_file if the end of the file is reached at the beginning of line. << val input : in_channel -> bytes -> int -> int -> int >> input ic buf pos len reads up to len characters from the given channel ic, storing them in byte sequence buf, starting at character number pos. It returns the actual number of characters read, between 0 and len (inclusive). A return value of 0 means that the end of file was reached. A return value between 0 and len exclusive means that not all requested len characters were read, either because no more characters were available at that time, or because the implementation found it convenient to do a partial read; input must be called again to read the remaining characters, if desired. (See also really_input[28.2] for reading exactly len characters.) Exception Invalid_argument "input" is raised if pos and len do not designate a valid range of buf. << val really_input : in_channel -> bytes -> int -> int -> unit >> really_input ic buf pos len reads len characters from channel ic, storing them in byte sequence buf, starting at character number pos. Raises - End_of_file if the end of file is reached before len characters have been read. - Invalid_argument if pos and len do not designate a valid range of buf. << val really_input_string : in_channel -> int -> string >> really_input_string ic len reads len characters from channel ic and returns them in a new string. Since: 4.02 Raises End_of_file if the end of file is reached before len characters have been read. << val input_byte : in_channel -> int >> Same as input_char[28.2], but return the 8-bit integer representing the character. Raises End_of_file if the end of file was reached. << val input_binary_int : in_channel -> int >> Read an integer encoded in binary format (4 bytes, big-endian) from the given input channel. See output_binary_int[28.2]. Raises End_of_file if the end of file was reached while reading the integer. << val input_value : in_channel -> 'a >> Read the representation of a structured value, as produced by output_value[28.2], and return the corresponding value. This function is identical to Marshal.from_channel[29.35]; see the description of module Marshal[28.2] for more information, in particular concerning the lack of type safety. << val seek_in : in_channel -> int -> unit >> seek_in chan pos sets the current reading position to pos for channel chan. This works only for regular files. On files of other kinds, the behavior is unspecified. << val pos_in : in_channel -> int >> Return the current reading position for the given channel. For files opened in text mode under Windows, the returned position is approximate (owing to end-of-line conversion); in particular, saving the current position with pos_in, then going back to this position using seek_in will not work. For this programming idiom to work reliably and portably, the file must be opened in binary mode. << val in_channel_length : in_channel -> int >> Return the size (number of characters) of the regular file on which the given channel is opened. If the channel is opened on a file that is not a regular file, the result is meaningless. The returned size does not take into account the end-of-line translations that can be performed when reading from a channel opened in text mode. << val close_in : in_channel -> unit >> Close the given channel. Input functions raise a Sys_error exception when they are applied to a closed input channel, except close_in, which does nothing when applied to an already closed channel. << val close_in_noerr : in_channel -> unit >> Same as close_in, but ignore all errors. << val set_binary_mode_in : in_channel -> bool -> unit >> set_binary_mode_in ic true sets the channel ic to binary mode: no translations take place during input. set_binary_mode_out ic false sets the channel ic to text mode: depending on the operating system, some translations may take place during input. For instance, under Windows, end-of-lines will be translated from \r\n to \n. This function has no effect under operating systems that do not distinguish between text mode and binary mode. Operations on large files ------------------------- << module LargeFile : >>  sig << val seek_out : out_channel -> int64 -> unit >> << val pos_out : out_channel -> int64 >> << val out_channel_length : out_channel -> int64 >> << val seek_in : in_channel -> int64 -> unit >> << val pos_in : in_channel -> int64 >> << val in_channel_length : in_channel -> int64 >>  end Operations on large files. This sub-module provides 64-bit variants of the channel functions that manipulate file positions and file sizes. By representing positions and sizes by 64-bit integers (type int64) instead of regular integers (type int), these alternate functions allow operating on files whose sizes are greater than max_int. References ========== << type 'a ref = { mutable contents : 'a ; } >> The type of references (mutable indirection cells) containing a value of type 'a. << val ref : 'a -> 'a ref >> Return a fresh reference containing the given value. << val (!) : 'a ref -> 'a >> !r returns the current contents of reference r. Equivalent to fun r -> r.contents. Unary operator, see Ocaml_operators[29.61] for more information. << val (:=) : 'a ref -> 'a -> unit >> r := a stores the value of a in reference r. Equivalent to fun r v -> r.contents <- v. Right-associative operator, see Ocaml_operators[29.61] for more information. << val incr : int ref -> unit >> Increment the integer contained in the given reference. Equivalent to fun r -> r := succ !r. << val decr : int ref -> unit >> Decrement the integer contained in the given reference. Equivalent to fun r -> r := pred !r. Result type =========== << type ('a, 'b) result = | Ok of 'a | Error of 'b >> Since: 4.03 Operations on format strings ============================ Format strings are character strings with special lexical conventions that defines the functionality of formatted input/output functions. Format strings are used to read data with formatted input functions from module Scanf[28.2] and to print data with formatted output functions from modules Printf[28.2] and Format[28.2]. Format strings are made of three kinds of entities: - conversions specifications, introduced by the special character '%' followed by one or more characters specifying what kind of argument to read or print, - formatting indications, introduced by the special character '@' followed by one or more characters specifying how to read or print the argument, - plain characters that are regular characters with usual lexical conventions. Plain characters specify string literals to be read in the input or printed in the output. There is an additional lexical rule to escape the special characters '%' and '@' in format strings: if a special character follows a '%' character, it is treated as a plain character. In other words, "%%" is considered as a plain '%' and "%@" as a plain '@'. For more information about conversion specifications and formatting indications available, read the documentation of modules Scanf[28.2], Printf[28.2] and Format[28.2]. Format strings have a general and highly polymorphic type ('a, 'b, 'c, 'd, 'e, 'f) format6. The two simplified types, format and format4 below are included for backward compatibility with earlier releases of OCaml. The meaning of format string type parameters is as follows: - 'a is the type of the parameters of the format for formatted output functions (printf-style functions); 'a is the type of the values read by the format for formatted input functions (scanf-style functions). - 'b is the type of input source for formatted input functions and the type of output target for formatted output functions. For printf-style functions from module Printf[28.2], 'b is typically out_channel; for printf-style functions from module Format[28.2], 'b is typically Format.formatter[29.22]; for scanf-style functions from module Scanf[28.2], 'b is typically Scanf.Scanning.in_channel[29.48]. Type argument 'b is also the type of the first argument given to user’s defined printing functions for %a and %t conversions, and user’s defined reading functions for %r conversion. - 'c is the type of the result of the %a and %t printing functions, and also the type of the argument transmitted to the first argument of kprintf-style functions or to the kscanf-style functions. - 'd is the type of parameters for the scanf-style functions. - 'e is the type of the receiver function for the scanf-style functions. - 'f is the final result type of a formatted input/output function invocation: for the printf-style functions, it is typically unit; for the scanf-style functions, it is typically the result type of the receiver function. << type ('a, 'b, 'c, 'd, 'e, 'f) format6 = ('a, 'b, 'c, 'd, 'e, 'f) CamlinternalFormatBasics.format6 >> << type ('a, 'b, 'c, 'd) format4 = ('a, 'b, 'c, 'c, 'c, 'd) format6 >> << type ('a, 'b, 'c) format = ('a, 'b, 'c, 'c) format4 >> << val string_of_format : ('a, 'b, 'c, 'd, 'e, 'f) format6 -> string >> Converts a format string into a string. << val format_of_string : ('a, 'b, 'c, 'd, 'e, 'f) format6 -> ('a, 'b, 'c, 'd, 'e, 'f) format6 >> format_of_string s returns a format string read from the string literal s. Note: format_of_string can not convert a string argument that is not a literal. If you need this functionality, use the more general Scanf.format_from_string[29.48] function. << val (^^) : ('a, 'b, 'c, 'd, 'e, 'f) format6 -> ('f, 'b, 'c, 'e, 'g, 'h) format6 -> ('a, 'b, 'c, 'd, 'g, 'h) format6 >> f1 ^^ f2 catenates format strings f1 and f2. The result is a format string that behaves as the concatenation of format strings f1 and f2: in case of formatted output, it accepts arguments from f1, then arguments from f2; in case of formatted input, it returns results from f1, then results from f2. Right-associative operator, see Ocaml_operators[29.61] for more information. Program termination =================== << val exit : int -> 'a >> Terminate the process, returning the given status code to the operating system: usually 0 to indicate no errors, and a small positive integer to indicate failure. All open output channels are flushed with flush_all. The callbacks registered with Domain.at_exit[29.14] are called followed by those registered with at_exit[28.2]. An implicit exit 0 is performed each time a program terminates normally. An implicit exit 2 is performed if the program terminates early because of an uncaught exception. << val at_exit : (unit -> unit) -> unit >> Register the given function to be called at program termination time. The functions registered with at_exit will be called when the program does any of the following: - executes exit[28.2] - terminates, either normally or because of an uncaught exception - executes the C function caml_shutdown. The functions are called in ’last in, first out’ order: the function most recently added with at_exit is called first. Standard library modules ========================= << module Arg : >> Arg << module Array : >> Array << module ArrayLabels : >> ArrayLabels << module Atomic : >> Atomic << module Bigarray : >> Bigarray << module Bool : >> Bool << module Buffer : >> Buffer << module Bytes : >> Bytes << module BytesLabels : >> BytesLabels << module Callback : >> Callback << module Char : >> Char << module Complex : >> Complex << module Condition : >> Condition << module Digest : >> Digest << module Domain : >> Domain Alert unstable. The Domain interface may change in incompatible ways in the future. << module Dynarray : >> Dynarray << module Effect : >> Effect Alert unstable. The Effect interface may change in incompatible ways in the future. << module Either : >> Either << module Ephemeron : >> Ephemeron << module Filename : >> Filename << module Float : >> Float << module Format : >> Format << module Fun : >> Fun << module Gc : >> Gc << module Hashtbl : >> Hashtbl << module In_channel : >> In_channel << module Int : >> Int << module Int32 : >> Int32 << module Int64 : >> Int64 << module Lazy : >> Lazy << module Lexing : >> Lexing << module List : >> List << module ListLabels : >> ListLabels << module Map : >> Map << module Marshal : >> Marshal << module MoreLabels : >> MoreLabels << module Mutex : >> Mutex << module Nativeint : >> Nativeint << module Obj : >> Obj << module Oo : >> Oo << module Option : >> Option << module Out_channel : >> Out_channel << module Parsing : >> Parsing << module Printexc : >> Printexc << module Printf : >> Printf << module Queue : >> Queue << module Random : >> Random << module Result : >> Result << module Scanf : >> Scanf << module Semaphore : >> Semaphore << module Seq : >> Seq << module Set : >> Set << module Stack : >> Stack << module StdLabels : >> StdLabels << module String : >> String << module StringLabels : >> StringLabels << module Sys : >> Sys << module Type : >> Type << module Uchar : >> Uchar << module Unit : >> Unit << module Weak : >> Weak Chapter 29  The standard library ************************************ This chapter describes the functions provided by the OCaml standard library. The modules from the standard library are automatically linked with the user’s object code files by the ocamlc command. Hence, these modules can be used in standalone programs without having to add any .cmo file on the command line for the linking phase. Similarly, in interactive use, these globals can be used in toplevel phrases without having to load any .cmo file in memory. Unlike the core Stdlib module, submodules are not automatically “opened” when compilation starts, or when the toplevel system is launched. Hence it is necessary to use qualified identifiers to refer to the functions provided by these modules, or to add open directives. 29.1 Module Arg : Parsing of command line arguments. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This module provides a general mechanism for extracting options and arguments from the command line to the program. For example: << let usage_msg = "append [-verbose] [] ... -o " let verbose = ref false let input_files = ref [] let output_file = ref "" let anon_fun filename = input_files := filename::!input_files let speclist = [("-verbose", Arg.Set verbose, "Output debug information"); ("-o", Arg.Set_string output_file, "Set output file name")] let () = Arg.parse speclist anon_fun usage_msg; (* Main functionality here *) >> Syntax of command lines: A keyword is a character string starting with a -. An option is a keyword alone or followed by an argument. The types of keywords are: Unit, Bool, Set, Clear, String, Set_string, Int, Set_int, Float, Set_float, Tuple, Symbol, Rest, Rest_all and Expand. Unit, Set and Clear keywords take no argument. A Rest or Rest_all keyword takes the remainder of the command line as arguments. (More explanations below.) Every other keyword takes the following word on the command line as argument. For compatibility with GNU getopt_long, keyword=arg is also allowed. Arguments not preceded by a keyword are called anonymous arguments. Examples (cmd is assumed to be the command name): - cmd -flag (a unit option) - cmd -int 1 (an int option with argument 1) - cmd -string foobar (a string option with argument "foobar") - cmd -float 12.34 (a float option with argument 12.34) - cmd a b c (three anonymous arguments: "a", "b", and "c") - cmd a b – c d (two anonymous arguments and a rest option with two arguments) Rest takes a function that is called repeatedly for each remaining command line argument. Rest_all takes a function that is called once, with the list of all remaining arguments. Note that if no arguments follow a Rest keyword then the function is not called at all whereas the function for a Rest_all keyword is called with an empty list. Alert unsynchronized_access. The Arg module relies on a mutable global state, parsing functions should only be called from a single domain. << type spec = | Unit of (unit -> unit) >> Call the function with unit argument << | Bool of (bool -> unit) >> Call the function with a bool argument << | Set of bool ref >> Set the reference to true << | Clear of bool ref >> Set the reference to false << | String of (string -> unit) >> Call the function with a string argument << | Set_string of string ref >> Set the reference to the string argument << | Int of (int -> unit) >> Call the function with an int argument << | Set_int of int ref >> Set the reference to the int argument << | Float of (float -> unit) >> Call the function with a float argument << | Set_float of float ref >> Set the reference to the float argument << | Tuple of spec list >> Take several arguments according to the spec list << | Symbol of string list * (string -> unit) >> Take one of the symbols as argument and call the function with the symbol << | Rest of (string -> unit) >> Stop interpreting keywords and call the function with each remaining argument << | Rest_all of (string list -> unit) >> Stop interpreting keywords and call the function with all remaining arguments << | Expand of (string -> string array) >> If the remaining arguments to process are of the form ["-foo"; "arg"] @ rest where "foo" is registered as Expand f, then the arguments f "arg" @ rest are processed. Only allowed in parse_and_expand_argv_dynamic. The concrete type describing the behavior associated with a keyword. << type key = string >> << type doc = string >> << type usage_msg = string >> << type anon_fun = string -> unit >> << val parse : (key * spec * doc) list -> anon_fun -> usage_msg -> unit >> Arg.parse speclist anon_fun usage_msg parses the command line. speclist is a list of triples (key, spec, doc). key is the option keyword, it must start with a '-' character. spec gives the option type and the function to call when this option is found on the command line. doc is a one-line description of this option. anon_fun is called on anonymous arguments. The functions in spec and anon_fun are called in the same order as their arguments appear on the command line. If an error occurs, Arg.parse exits the program, after printing to standard error an error message as follows: - The reason for the error: unknown option, invalid or missing argument, etc. - usage_msg - The list of options, each followed by the corresponding doc string. Beware: options that have an empty doc string will not be included in the list. For the user to be able to specify anonymous arguments starting with a -, include for example ("-", String anon_fun, doc) in speclist. By default, parse recognizes two unit options, -help and –help, which will print to standard output usage_msg and the list of options, and exit the program. You can override this behaviour by specifying your own -help and –help options in speclist. << val parse_dynamic : (key * spec * doc) list ref -> anon_fun -> usage_msg -> unit >> Same as Arg.parse[29.1], except that the speclist argument is a reference and may be updated during the parsing. A typical use for this feature is to parse command lines of the form: - command subcommand options where the list of options depends on the value of the subcommand argument. Since: 4.01 << val parse_argv : ?current:int ref -> string array -> (key * spec * doc) list -> anon_fun -> usage_msg -> unit >> Arg.parse_argv ~current args speclist anon_fun usage_msg parses the array args as if it were the command line. It uses and updates the value of ~current (if given), or Arg.current[29.1]. You must set it before calling parse_argv. The initial value of current is the index of the program name (argument 0) in the array. If an error occurs, Arg.parse_argv raises Arg.Bad[29.1] with the error message as argument. If option -help or –help is given, Arg.parse_argv raises Arg.Help[29.1] with the help message as argument. << val parse_argv_dynamic : ?current:int ref -> string array -> (key * spec * doc) list ref -> anon_fun -> string -> unit >> Same as Arg.parse_argv[29.1], except that the speclist argument is a reference and may be updated during the parsing. See Arg.parse_dynamic[29.1]. Since: 4.01 << val parse_and_expand_argv_dynamic : int ref -> string array ref -> (key * spec * doc) list ref -> anon_fun -> string -> unit >> Same as Arg.parse_argv_dynamic[29.1], except that the argv argument is a reference and may be updated during the parsing of Expand arguments. See Arg.parse_argv_dynamic[29.1]. Since: 4.05 << val parse_expand : (key * spec * doc) list -> anon_fun -> usage_msg -> unit >> Same as Arg.parse[29.1], except that the Expand arguments are allowed and the Arg.current[29.1] reference is not updated. Since: 4.05 << exception Help of string >> Raised by Arg.parse_argv when the user asks for help. << exception Bad of string >> Functions in spec or anon_fun can raise Arg.Bad with an error message to reject invalid arguments. Arg.Bad is also raised by Arg.parse_argv[29.1] in case of an error. << val usage : (key * spec * doc) list -> usage_msg -> unit >> Arg.usage speclist usage_msg prints to standard error an error message that includes the list of valid options. This is the same message that Arg.parse[29.1] prints in case of error. speclist and usage_msg are the same as for Arg.parse[29.1]. << val usage_string : (key * spec * doc) list -> usage_msg -> string >> Returns the message that would have been printed by Arg.usage[29.1], if provided with the same parameters. << val align : ?limit:int -> (key * spec * doc) list -> (key * spec * doc) list >> Align the documentation strings by inserting spaces at the first alignment separator (tab or, if tab is not found, space), according to the length of the keyword. Use a alignment separator as the first character in a doc string if you want to align the whole string. The doc strings corresponding to Symbol arguments are aligned on the next line. << val current : int ref >> Position (in Sys.argv[29.56]) of the argument being processed. You can change this value, e.g. to force Arg.parse[29.1] to skip some arguments. Arg.parse[29.1] uses the initial value of Arg.current[29.1] as the index of argument 0 (the program name) and starts parsing arguments at the next element. << val read_arg : string -> string array >> Arg.read_arg file reads newline-terminated command line arguments from file file. Since: 4.05 << val read_arg0 : string -> string array >> Identical to Arg.read_arg[29.1] but assumes null character terminated command line arguments. Since: 4.05 << val write_arg : string -> string array -> unit >> Arg.write_arg file args writes the arguments args newline-terminated into the file file. If any of the arguments in args contains a newline, use Arg.write_arg0[29.1] instead. Since: 4.05 << val write_arg0 : string -> string array -> unit >> Identical to Arg.write_arg[29.1] but uses the null character for terminator instead of newline. Since: 4.05 29.2 Module Array : Array operations. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The labeled version of this module can be used as described in the StdLabels[29.53] module. << type 'a t = 'a array >> An alias for the type of arrays. << val length : 'a array -> int >> Return the length (number of elements) of the given array. << val get : 'a array -> int -> 'a >> get a n returns the element number n of array a. The first element has number 0. The last element has number length a - 1. You can also write a.(n) instead of get a n. Raises Invalid_argument if n is outside the range 0 to (length a - 1). << val set : 'a array -> int -> 'a -> unit >> set a n x modifies array a in place, replacing element number n with x. You can also write a.(n) <- x instead of set a n x. Raises Invalid_argument if n is outside the range 0 to length a - 1. << val make : int -> 'a -> 'a array >> make n x returns a fresh array of length n, initialized with x. All the elements of this new array are initially physically equal to x (in the sense of the == predicate). Consequently, if x is mutable, it is shared among all elements of the array, and modifying x through one of the array entries will modify all other entries at the same time. Raises Invalid_argument if n < 0 or n > Sys.max_array_length. If the value of x is a floating-point number, then the maximum size is only Sys.max_array_length / 2. << val create_float : int -> float array >> create_float n returns a fresh float array of length n, with uninitialized data. Since: 4.03 << val init : int -> (int -> 'a) -> 'a array >> init n f returns a fresh array of length n, with element number i initialized to the result of f i. In other terms, init n f tabulates the results of f applied in order to the integers 0 to n-1. Raises Invalid_argument if n < 0 or n > Sys.max_array_length. If the return type of f is float, then the maximum size is only Sys.max_array_length / 2. << val make_matrix : int -> int -> 'a -> 'a array array >> make_matrix dimx dimy e returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy. All the elements of this new matrix are initially physically equal to e. The element (x,y) of a matrix m is accessed with the notation m.(x).(y). Raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_array_length[29.56]. If the value of e is a floating-point number, then the maximum size is only Sys.max_array_length / 2. << val init_matrix : int -> int -> (int -> int -> 'a) -> 'a array array >> init_matrix dimx dimy f returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy, where the element at index (x,y) is initialized with f x y. The element (x,y) of a matrix m is accessed with the notation m.(x).(y). Since: 5.2 Raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_array_length[29.56]. If the return type of f is float, then the maximum size is only Sys.max_array_length / 2. << val append : 'a array -> 'a array -> 'a array >> append v1 v2 returns a fresh array containing the concatenation of the arrays v1 and v2. Raises Invalid_argument if length v1 + length v2 > Sys.max_array_length. << val concat : 'a array list -> 'a array >> Same as Array.append[29.2], but concatenates a list of arrays. << val sub : 'a array -> int -> int -> 'a array >> sub a pos len returns a fresh array of length len, containing the elements number pos to pos + len - 1 of array a. Raises Invalid_argument if pos and len do not designate a valid subarray of a; that is, if pos < 0, or len < 0, or pos + len > length a. << val copy : 'a array -> 'a array >> copy a returns a copy of a, that is, a fresh array containing the same elements as a. << val fill : 'a array -> int -> int -> 'a -> unit >> fill a pos len x modifies the array a in place, storing x in elements number pos to pos + len - 1. Raises Invalid_argument if pos and len do not designate a valid subarray of a. << val blit : 'a array -> int -> 'a array -> int -> int -> unit >> blit src src_pos dst dst_pos len copies len elements from array src, starting at element number src_pos, to array dst, starting at element number dst_pos. It works correctly even if src and dst are the same array, and the source and destination chunks overlap. Raises Invalid_argument if src_pos and len do not designate a valid subarray of src, or if dst_pos and len do not designate a valid subarray of dst. << val to_list : 'a array -> 'a list >> to_list a returns the list of all the elements of a. << val of_list : 'a list -> 'a array >> of_list l returns a fresh array containing the elements of l. Raises Invalid_argument if the length of l is greater than Sys.max_array_length. Iterators ========= << val iter : ('a -> unit) -> 'a array -> unit >> iter f a applies function f in turn to all the elements of a. It is equivalent to f a.(0); f a.(1); ...; f a.(length a - 1); (). << val iteri : (int -> 'a -> unit) -> 'a array -> unit >> Same as Array.iter[29.2], but the function is applied to the index of the element as first argument, and the element itself as second argument. << val map : ('a -> 'b) -> 'a array -> 'b array >> map f a applies function f to all the elements of a, and builds an array with the results returned by f: [| f a.(0); f a.(1); ...; f a.(length a - 1) |]. << val map_inplace : ('a -> 'a) -> 'a array -> unit >> map_inplace f a applies function f to all elements of a, and updates their values in place. Since: 5.1 << val mapi : (int -> 'a -> 'b) -> 'a array -> 'b array >> Same as Array.map[29.2], but the function is applied to the index of the element as first argument, and the element itself as second argument. << val mapi_inplace : (int -> 'a -> 'a) -> 'a array -> unit >> Same as Array.map_inplace[29.2], but the function is applied to the index of the element as first argument, and the element itself as second argument. Since: 5.1 << val fold_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a array -> 'acc >> fold_left f init a computes f (... (f (f init a.(0)) a.(1)) ...) a.(n-1), where n is the length of the array a. << val fold_left_map : ('acc -> 'a -> 'acc * 'b) -> 'acc -> 'a array -> 'acc * 'b array >> fold_left_map is a combination of Array.fold_left[29.2] and Array.map[29.2] that threads an accumulator through calls to f. Since: 4.13 << val fold_right : ('a -> 'acc -> 'acc) -> 'a array -> 'acc -> 'acc >> fold_right f a init computes f a.(0) (f a.(1) ( ... (f a.(n-1) init) ...)), where n is the length of the array a. Iterators on two arrays ======================= << val iter2 : ('a -> 'b -> unit) -> 'a array -> 'b array -> unit >> iter2 f a b applies function f to all the elements of a and b. Since: 4.03 (4.05 in ArrayLabels) Raises Invalid_argument if the arrays are not the same size. << val map2 : ('a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array >> map2 f a b applies function f to all the elements of a and b, and builds an array with the results returned by f: [| f a.(0) b.(0); ...; f a.(length a - 1) b.(length b - 1)|]. Since: 4.03 (4.05 in ArrayLabels) Raises Invalid_argument if the arrays are not the same size. Array scanning ============== << val for_all : ('a -> bool) -> 'a array -> bool >> for_all f [|a1; ...; an|] checks if all elements of the array satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an). Since: 4.03 << val exists : ('a -> bool) -> 'a array -> bool >> exists f [|a1; ...; an|] checks if at least one element of the array satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an). Since: 4.03 << val for_all2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool >> Same as Array.for_all[29.2], but for a two-argument predicate. Since: 4.11 Raises Invalid_argument if the two arrays have different lengths. << val exists2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool >> Same as Array.exists[29.2], but for a two-argument predicate. Since: 4.11 Raises Invalid_argument if the two arrays have different lengths. << val mem : 'a -> 'a array -> bool >> mem a set is true if and only if a is structurally equal to an element of set (i.e. there is an x in set such that compare a x = 0). Since: 4.03 << val memq : 'a -> 'a array -> bool >> Same as Array.mem[29.2], but uses physical equality instead of structural equality to compare array elements. Since: 4.03 << val find_opt : ('a -> bool) -> 'a array -> 'a option >> find_opt f a returns the first element of the array a that satisfies the predicate f, or None if there is no value that satisfies f in the array a. Since: 4.13 << val find_index : ('a -> bool) -> 'a array -> int option >> find_index f a returns Some i, where i is the index of the first element of the array a that satisfies f x, if there is such an element. It returns None if there is no such element. Since: 5.1 << val find_map : ('a -> 'b option) -> 'a array -> 'b option >> find_map f a applies f to the elements of a in order, and returns the first result of the form Some v, or None if none exist. Since: 4.13 << val find_mapi : (int -> 'a -> 'b option) -> 'a array -> 'b option >> Same as find_map, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 5.1 Arrays of pairs =============== << val split : ('a * 'b) array -> 'a array * 'b array >> split [|(a1,b1); ...; (an,bn)|] is ([|a1; ...; an|], [|b1; ...; bn|]). Since: 4.13 << val combine : 'a array -> 'b array -> ('a * 'b) array >> combine [|a1; ...; an|] [|b1; ...; bn|] is [|(a1,b1); ...; (an,bn)|]. Raise Invalid_argument if the two arrays have different lengths. Since: 4.13 Sorting and shuffling ===================== << val sort : ('a -> 'a -> int) -> 'a array -> unit >> Sort an array in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see below for a complete specification). For example, compare[28.2] is a suitable comparison function. After calling sort, the array is sorted in place in increasing order. sort is guaranteed to run in constant heap space and (at most) logarithmic stack space. The current implementation uses Heap Sort. It runs in constant stack space. Specification of the comparison function: Let a be the array and cmp the comparison function. The following must be true for all x, y, z in a : - cmp x y > 0 if and only if cmp y x < 0 - if cmp x y >= 0 and cmp y z >= 0 then cmp x z >= 0 When sort returns, a contains the same elements as before, reordered in such a way that for all i and j valid indices of a : - cmp a.(i) a.(j) >= 0 if and only if i >= j << val stable_sort : ('a -> 'a -> int) -> 'a array -> unit >> Same as Array.sort[29.2], but the sorting algorithm is stable (i.e. elements that compare equal are kept in their original order) and not guaranteed to run in constant heap space. The current implementation uses Merge Sort. It uses a temporary array of length n/2, where n is the length of the array. It is usually faster than the current implementation of Array.sort[29.2]. << val fast_sort : ('a -> 'a -> int) -> 'a array -> unit >> Same as Array.sort[29.2] or Array.stable_sort[29.2], whichever is faster on typical input. << val shuffle : rand:(int -> int) -> 'a array -> unit >> shuffle rand a randomly permutes a’s element using rand for randomness. The distribution of permutations is uniform. rand must be such that a call to rand n returns a uniformly distributed random number in the range [0;n-1]. Random.int[29.46] can be used for this (do not forget to initialize[29.46] the generator). Since: 5.2 Arrays and Sequences ==================== << val to_seq : 'a array -> 'a Seq.t >> Iterate on the array, in increasing order. Modifications of the array during iteration will be reflected in the sequence. Since: 4.07 << val to_seqi : 'a array -> (int * 'a) Seq.t >> Iterate on the array, in increasing order, yielding indices along elements. Modifications of the array during iteration will be reflected in the sequence. Since: 4.07 << val of_seq : 'a Seq.t -> 'a array >> Create an array from the generator Since: 4.07 Arrays and concurrency safety ============================= Care must be taken when concurrently accessing arrays from multiple domains: accessing an array will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results. Atomicity --------- Every array operation that accesses more than one array element is not atomic. This includes iteration, scanning, sorting, splitting and combining arrays. For example, consider the following program: << let size = 100_000_000 let a = Array.make size 1 let d1 = Domain.spawn (fun () -> Array.iteri (fun i x -> a.(i) <- x + 1) a ) let d2 = Domain.spawn (fun () -> Array.iteri (fun i x -> a.(i) <- 2 * x + 1) a ) let () = Domain.join d1; Domain.join d2 >> After executing this code, each field of the array a is either 2, 3, 4 or 5. If atomicity is required, then the user must implement their own synchronization (for example, using Mutex.t[29.37]). Data races ---------- If two domains only access disjoint parts of the array, then the observed behaviour is the equivalent to some sequential interleaving of the operations from the two domains. A data race is said to occur when two domains access the same array element without synchronization and at least one of the accesses is a write. In the absence of data races, the observed behaviour is equivalent to some sequential interleaving of the operations from different domains. Whenever possible, data races should be avoided by using synchronization to mediate the accesses to the array elements. Indeed, in the presence of data races, programs will not crash but the observed behaviour may not be equivalent to any sequential interleaving of operations from different domains. Nevertheless, even in the presence of data races, a read operation will return the value of some prior write to that location (with a few exceptions for float arrays). Float arrays ------------ Float arrays have two supplementary caveats in the presence of data races. First, the blit operation might copy an array byte-by-byte. Data races between such a blit operation and another operation might produce surprising values due to tearing: partial writes interleaved with other operations can create float values that would not exist with a sequential execution. For instance, at the end of << let zeros = Array.make size 0. let max_floats = Array.make size Float.max_float let res = Array.copy zeros let d1 = Domain.spawn (fun () -> Array.blit zeros 0 res 0 size) let d2 = Domain.spawn (fun () -> Array.blit max_floats 0 res 0 size) let () = Domain.join d1; Domain.join d2 >> the res array might contain values that are neither 0. nor max_float. Second, on 32-bit architectures, getting or setting a field involves two separate memory accesses. In the presence of data races, the user may observe tearing on any operation. 29.3 Module ArrayLabels : Array operations. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The labeled version of this module can be used as described in the StdLabels[29.53] module. << type 'a t = 'a array >> An alias for the type of arrays. << val length : 'a array -> int >> Return the length (number of elements) of the given array. << val get : 'a array -> int -> 'a >> get a n returns the element number n of array a. The first element has number 0. The last element has number length a - 1. You can also write a.(n) instead of get a n. Raises Invalid_argument if n is outside the range 0 to (length a - 1). << val set : 'a array -> int -> 'a -> unit >> set a n x modifies array a in place, replacing element number n with x. You can also write a.(n) <- x instead of set a n x. Raises Invalid_argument if n is outside the range 0 to length a - 1. << val make : int -> 'a -> 'a array >> make n x returns a fresh array of length n, initialized with x. All the elements of this new array are initially physically equal to x (in the sense of the == predicate). Consequently, if x is mutable, it is shared among all elements of the array, and modifying x through one of the array entries will modify all other entries at the same time. Raises Invalid_argument if n < 0 or n > Sys.max_array_length. If the value of x is a floating-point number, then the maximum size is only Sys.max_array_length / 2. << val create_float : int -> float array >> create_float n returns a fresh float array of length n, with uninitialized data. Since: 4.03 << val init : int -> f:(int -> 'a) -> 'a array >> init n ~f returns a fresh array of length n, with element number i initialized to the result of f i. In other terms, init n ~f tabulates the results of f applied in order to the integers 0 to n-1. Raises Invalid_argument if n < 0 or n > Sys.max_array_length. If the return type of f is float, then the maximum size is only Sys.max_array_length / 2. << val make_matrix : dimx:int -> dimy:int -> 'a -> 'a array array >> make_matrix ~dimx ~dimy e returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy. All the elements of this new matrix are initially physically equal to e. The element (x,y) of a matrix m is accessed with the notation m.(x).(y). Raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_array_length[29.56]. If the value of e is a floating-point number, then the maximum size is only Sys.max_array_length / 2. << val init_matrix : dimx:int -> dimy:int -> f:(int -> int -> 'a) -> 'a array array >> init_matrix ~dimx ~dimy ~f returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy, where the element at index (x,y) is initialized with f x y. The element (x,y) of a matrix m is accessed with the notation m.(x).(y). Since: 5.2 Raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_array_length[29.56]. If the return type of f is float, then the maximum size is only Sys.max_array_length / 2. << val append : 'a array -> 'a array -> 'a array >> append v1 v2 returns a fresh array containing the concatenation of the arrays v1 and v2. Raises Invalid_argument if length v1 + length v2 > Sys.max_array_length. << val concat : 'a array list -> 'a array >> Same as ArrayLabels.append[29.3], but concatenates a list of arrays. << val sub : 'a array -> pos:int -> len:int -> 'a array >> sub a ~pos ~len returns a fresh array of length len, containing the elements number pos to pos + len - 1 of array a. Raises Invalid_argument if pos and len do not designate a valid subarray of a; that is, if pos < 0, or len < 0, or pos + len > length a. << val copy : 'a array -> 'a array >> copy a returns a copy of a, that is, a fresh array containing the same elements as a. << val fill : 'a array -> pos:int -> len:int -> 'a -> unit >> fill a ~pos ~len x modifies the array a in place, storing x in elements number pos to pos + len - 1. Raises Invalid_argument if pos and len do not designate a valid subarray of a. << val blit : src:'a array -> src_pos:int -> dst:'a array -> dst_pos:int -> len:int -> unit >> blit ~src ~src_pos ~dst ~dst_pos ~len copies len elements from array src, starting at element number src_pos, to array dst, starting at element number dst_pos. It works correctly even if src and dst are the same array, and the source and destination chunks overlap. Raises Invalid_argument if src_pos and len do not designate a valid subarray of src, or if dst_pos and len do not designate a valid subarray of dst. << val to_list : 'a array -> 'a list >> to_list a returns the list of all the elements of a. << val of_list : 'a list -> 'a array >> of_list l returns a fresh array containing the elements of l. Raises Invalid_argument if the length of l is greater than Sys.max_array_length. Iterators ========= << val iter : f:('a -> unit) -> 'a array -> unit >> iter ~f a applies function f in turn to all the elements of a. It is equivalent to f a.(0); f a.(1); ...; f a.(length a - 1); (). << val iteri : f:(int -> 'a -> unit) -> 'a array -> unit >> Same as ArrayLabels.iter[29.3], but the function is applied to the index of the element as first argument, and the element itself as second argument. << val map : f:('a -> 'b) -> 'a array -> 'b array >> map ~f a applies function f to all the elements of a, and builds an array with the results returned by f: [| f a.(0); f a.(1); ...; f a.(length a - 1) |]. << val map_inplace : f:('a -> 'a) -> 'a array -> unit >> map_inplace ~f a applies function f to all elements of a, and updates their values in place. Since: 5.1 << val mapi : f:(int -> 'a -> 'b) -> 'a array -> 'b array >> Same as ArrayLabels.map[29.3], but the function is applied to the index of the element as first argument, and the element itself as second argument. << val mapi_inplace : f:(int -> 'a -> 'a) -> 'a array -> unit >> Same as ArrayLabels.map_inplace[29.3], but the function is applied to the index of the element as first argument, and the element itself as second argument. Since: 5.1 << val fold_left : f:('acc -> 'a -> 'acc) -> init:'acc -> 'a array -> 'acc >> fold_left ~f ~init a computes f (... (f (f init a.(0)) a.(1)) ...) a.(n-1), where n is the length of the array a. << val fold_left_map : f:('acc -> 'a -> 'acc * 'b) -> init:'acc -> 'a array -> 'acc * 'b array >> fold_left_map is a combination of ArrayLabels.fold_left[29.3] and ArrayLabels.map[29.3] that threads an accumulator through calls to f. Since: 4.13 << val fold_right : f:('a -> 'acc -> 'acc) -> 'a array -> init:'acc -> 'acc >> fold_right ~f a ~init computes f a.(0) (f a.(1) ( ... (f a.(n-1) init) ...)), where n is the length of the array a. Iterators on two arrays ======================= << val iter2 : f:('a -> 'b -> unit) -> 'a array -> 'b array -> unit >> iter2 ~f a b applies function f to all the elements of a and b. Since: 4.05 Raises Invalid_argument if the arrays are not the same size. << val map2 : f:('a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array >> map2 ~f a b applies function f to all the elements of a and b, and builds an array with the results returned by f: [| f a.(0) b.(0); ...; f a.(length a - 1) b.(length b - 1)|]. Since: 4.05 Raises Invalid_argument if the arrays are not the same size. Array scanning ============== << val for_all : f:('a -> bool) -> 'a array -> bool >> for_all ~f [|a1; ...; an|] checks if all elements of the array satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an). Since: 4.03 << val exists : f:('a -> bool) -> 'a array -> bool >> exists ~f [|a1; ...; an|] checks if at least one element of the array satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an). Since: 4.03 << val for_all2 : f:('a -> 'b -> bool) -> 'a array -> 'b array -> bool >> Same as ArrayLabels.for_all[29.3], but for a two-argument predicate. Since: 4.11 Raises Invalid_argument if the two arrays have different lengths. << val exists2 : f:('a -> 'b -> bool) -> 'a array -> 'b array -> bool >> Same as ArrayLabels.exists[29.3], but for a two-argument predicate. Since: 4.11 Raises Invalid_argument if the two arrays have different lengths. << val mem : 'a -> set:'a array -> bool >> mem a ~set is true if and only if a is structurally equal to an element of set (i.e. there is an x in set such that compare a x = 0). Since: 4.03 << val memq : 'a -> set:'a array -> bool >> Same as ArrayLabels.mem[29.3], but uses physical equality instead of structural equality to compare array elements. Since: 4.03 << val find_opt : f:('a -> bool) -> 'a array -> 'a option >> find_opt ~f a returns the first element of the array a that satisfies the predicate f, or None if there is no value that satisfies f in the array a. Since: 4.13 << val find_index : f:('a -> bool) -> 'a array -> int option >> find_index ~f a returns Some i, where i is the index of the first element of the array a that satisfies f x, if there is such an element. It returns None if there is no such element. Since: 5.1 << val find_map : f:('a -> 'b option) -> 'a array -> 'b option >> find_map ~f a applies f to the elements of a in order, and returns the first result of the form Some v, or None if none exist. Since: 4.13 << val find_mapi : f:(int -> 'a -> 'b option) -> 'a array -> 'b option >> Same as find_map, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 5.1 Arrays of pairs =============== << val split : ('a * 'b) array -> 'a array * 'b array >> split [|(a1,b1); ...; (an,bn)|] is ([|a1; ...; an|], [|b1; ...; bn|]). Since: 4.13 << val combine : 'a array -> 'b array -> ('a * 'b) array >> combine [|a1; ...; an|] [|b1; ...; bn|] is [|(a1,b1); ...; (an,bn)|]. Raise Invalid_argument if the two arrays have different lengths. Since: 4.13 Sorting and shuffling ===================== << val sort : cmp:('a -> 'a -> int) -> 'a array -> unit >> Sort an array in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see below for a complete specification). For example, compare[28.2] is a suitable comparison function. After calling sort, the array is sorted in place in increasing order. sort is guaranteed to run in constant heap space and (at most) logarithmic stack space. The current implementation uses Heap Sort. It runs in constant stack space. Specification of the comparison function: Let a be the array and cmp the comparison function. The following must be true for all x, y, z in a : - cmp x y > 0 if and only if cmp y x < 0 - if cmp x y >= 0 and cmp y z >= 0 then cmp x z >= 0 When sort returns, a contains the same elements as before, reordered in such a way that for all i and j valid indices of a : - cmp a.(i) a.(j) >= 0 if and only if i >= j << val stable_sort : cmp:('a -> 'a -> int) -> 'a array -> unit >> Same as ArrayLabels.sort[29.3], but the sorting algorithm is stable (i.e. elements that compare equal are kept in their original order) and not guaranteed to run in constant heap space. The current implementation uses Merge Sort. It uses a temporary array of length n/2, where n is the length of the array. It is usually faster than the current implementation of ArrayLabels.sort[29.3]. << val fast_sort : cmp:('a -> 'a -> int) -> 'a array -> unit >> Same as ArrayLabels.sort[29.3] or ArrayLabels.stable_sort[29.3], whichever is faster on typical input. << val shuffle : rand:(int -> int) -> 'a array -> unit >> shuffle ~rand a randomly permutes a’s element using rand for randomness. The distribution of permutations is uniform. rand must be such that a call to rand n returns a uniformly distributed random number in the range [0;n-1]. Random.int[29.46] can be used for this (do not forget to initialize[29.46] the generator). Since: 5.2 Arrays and Sequences ==================== << val to_seq : 'a array -> 'a Seq.t >> Iterate on the array, in increasing order. Modifications of the array during iteration will be reflected in the sequence. Since: 4.07 << val to_seqi : 'a array -> (int * 'a) Seq.t >> Iterate on the array, in increasing order, yielding indices along elements. Modifications of the array during iteration will be reflected in the sequence. Since: 4.07 << val of_seq : 'a Seq.t -> 'a array >> Create an array from the generator Since: 4.07 Arrays and concurrency safety ============================= Care must be taken when concurrently accessing arrays from multiple domains: accessing an array will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results. Atomicity --------- Every array operation that accesses more than one array element is not atomic. This includes iteration, scanning, sorting, splitting and combining arrays. For example, consider the following program: << let size = 100_000_000 let a = ArrayLabels.make size 1 let d1 = Domain.spawn (fun () -> ArrayLabels.iteri ~f:(fun i x -> a.(i) <- x + 1) a ) let d2 = Domain.spawn (fun () -> ArrayLabels.iteri ~f:(fun i x -> a.(i) <- 2 * x + 1) a ) let () = Domain.join d1; Domain.join d2 >> After executing this code, each field of the array a is either 2, 3, 4 or 5. If atomicity is required, then the user must implement their own synchronization (for example, using Mutex.t[29.37]). Data races ---------- If two domains only access disjoint parts of the array, then the observed behaviour is the equivalent to some sequential interleaving of the operations from the two domains. A data race is said to occur when two domains access the same array element without synchronization and at least one of the accesses is a write. In the absence of data races, the observed behaviour is equivalent to some sequential interleaving of the operations from different domains. Whenever possible, data races should be avoided by using synchronization to mediate the accesses to the array elements. Indeed, in the presence of data races, programs will not crash but the observed behaviour may not be equivalent to any sequential interleaving of operations from different domains. Nevertheless, even in the presence of data races, a read operation will return the value of some prior write to that location (with a few exceptions for float arrays). Float arrays ------------ Float arrays have two supplementary caveats in the presence of data races. First, the blit operation might copy an array byte-by-byte. Data races between such a blit operation and another operation might produce surprising values due to tearing: partial writes interleaved with other operations can create float values that would not exist with a sequential execution. For instance, at the end of << let zeros = Array.make size 0. let max_floats = Array.make size Float.max_float let res = Array.copy zeros let d1 = Domain.spawn (fun () -> Array.blit zeros 0 res 0 size) let d2 = Domain.spawn (fun () -> Array.blit max_floats 0 res 0 size) let () = Domain.join d1; Domain.join d2 >> the res array might contain values that are neither 0. nor max_float. Second, on 32-bit architectures, getting or setting a field involves two separate memory accesses. In the presence of data races, the user may observe tearing on any operation. 29.4 Module Atomic : Atomic references. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* See the examples[29.4] below. See ’Memory model: The hard bits’ chapter in the manual. Since: 4.12 << type !'a t >> An atomic (mutable) reference to a value of type 'a. << val make : 'a -> 'a t >> Create an atomic reference. << val make_contended : 'a -> 'a t >> Create an atomic reference that is alone on a cache line. It occupies 4-16x the memory of one allocated with make v. The primary purpose is to prevent false-sharing and the resulting performance degradation. When a CPU performs an atomic operation, it temporarily takes ownership of an entire cache line that contains the atomic reference. If multiple atomic references share the same cache line, modifying these disjoint memory regions simultaneously becomes impossible, which can create a bottleneck. Hence, as a general guideline, if an atomic reference is experiencing contention, assigning it its own cache line may enhance performance. << val get : 'a t -> 'a >> Get the current value of the atomic reference. << val set : 'a t -> 'a -> unit >> Set a new value for the atomic reference. << val exchange : 'a t -> 'a -> 'a >> Set a new value for the atomic reference, and return the current value. << val compare_and_set : 'a t -> 'a -> 'a -> bool >> compare_and_set r seen v sets the new value of r to v only if its current value is physically equal to seen – the comparison and the set occur atomically. Returns true if the comparison succeeded (so the set happened) and false otherwise. << val fetch_and_add : int t -> int -> int >> fetch_and_add r n atomically increments the value of r by n, and returns the current value (before the increment). << val incr : int t -> unit >> incr r atomically increments the value of r by 1. << val decr : int t -> unit >> decr r atomically decrements the value of r by 1. Examples ======== Basic Thread Coordination ------------------------- A basic use case is to have global counters that are updated in a thread-safe way, for example to keep some sorts of metrics over IOs performed by the program. Another basic use case is to coordinate the termination of threads in a given program, for example when one thread finds an answer, or when the program is shut down by the user. Here, for example, we’re going to try to find a number whose hash satisfies a basic property. To do that, we’ll run multiple threads which will try random numbers until they find one that works. Of course the output below is a sample run and will change every time the program is run. << (* use for termination *) let stop_all_threads = Atomic.make false (* total number of individual attempts to find a number *) let num_attempts = Atomic.make 0 (* find a number that satisfies [p], by... trying random numbers until one fits. *) let find_number_where (p:int -> bool) = let rand = Random.State.make_self_init() in while not (Atomic.get stop_all_threads) do let n = Random.State.full_int rand max_int in ignore (Atomic.fetch_and_add num_attempts 1 : int); if p (Hashtbl.hash n) then ( Printf.printf "found %d (hash=%d)\n%!" n (Hashtbl.hash n); Atomic.set stop_all_threads true; (* signal all threads to stop *) ) done;; (* run multiple domains to search for a [n] where [hash n <= 100] *) let () = let criterion n = n <= 100 in let threads = Array.init 8 (fun _ -> Domain.spawn (fun () -> find_number_where criterion)) in Array.iter Domain.join threads; Printf.printf "total number of attempts: %d\n%!" (Atomic.get num_attempts) ;; - : unit = () found 1651745641680046833 (hash=33) total number of attempts: 30230350 >> Treiber Stack ------------- Another example is a basic Treiber stack[ https://en.wikipedia.org/wiki/Treiber_stack] (a thread-safe stack) that can be safely shared between threads. Note how both push and pop are recursive, because they attempt to swap the new stack (with one more, or one fewer, element) with the old stack. This is optimistic concurrency: each iteration of, say, push stack x gets the old stack l, and hopes that by the time it tries to replace l with x::l, nobody else has had time to modify the list. If the compare_and_set fails it means we were too optimistic, and must try again. << type 'a stack = 'a list Atomic.t let rec push (stack: _ stack) elt : unit = let cur = Atomic.get stack in let success = Atomic.compare_and_set stack cur (elt :: cur) in if not success then push stack elt let rec pop (stack: _ stack) : _ option = let cur = Atomic.get stack in match cur with | [] -> None | x :: tail -> let success = Atomic.compare_and_set stack cur tail in if success then Some x else pop stack # let st = Atomic.make [] # push st 1 - : unit = () # push st 2 - : unit = () # pop st - : int option = Some 2 # pop st - : int option = Some 1 # pop st - : int option = None >> 29.5 Module Bigarray : Large, multi-dimensional, numerical arrays. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This module implements multi-dimensional arrays of integers and floating-point numbers, thereafter referred to as ’Bigarrays’, to distinguish them from the standard OCaml arrays described in Array[29.2]. The implementation allows efficient sharing of large numerical arrays between OCaml code and C or Fortran numerical libraries. The main differences between ’Bigarrays’ and standard OCaml arrays are as follows: - Bigarrays are not limited in size, unlike OCaml arrays. (Normal float arrays are limited to 2,097,151 elements on a 32-bit platform, and normal arrays of other types to 4,194,303 elements.) - Bigarrays are multi-dimensional. Any number of dimensions between 0 and 16 is supported. In contrast, OCaml arrays are mono-dimensional and require encoding multi-dimensional arrays as arrays of arrays. - Bigarrays can only contain integers and floating-point numbers, while OCaml arrays can contain arbitrary OCaml data types. - Bigarrays provide more space-efficient storage of integer and floating-point elements than normal OCaml arrays, in particular because they support ’small’ types such as single-precision floats and 8 and 16-bit integers, in addition to the standard OCaml types of double-precision floats and 32 and 64-bit integers. - The memory layout of Bigarrays is entirely compatible with that of arrays in C and Fortran, allowing large arrays to be passed back and forth between OCaml code and C / Fortran code with no data copying at all. - Bigarrays support interesting high-level operations that normal arrays do not provide efficiently, such as extracting sub-arrays and ’slicing’ a multi-dimensional array along certain dimensions, all without any copying. Users of this module are encouraged to do open Bigarray in their source, then refer to array types and operations via short dot notation, e.g. Array1.t or Array2.sub. Bigarrays support all the OCaml ad-hoc polymorphic operations: - comparisons (=, <>, <=, etc, as well as compare[28.2]); - hashing (module Hash); - and structured input-output (the functions from the Marshal[29.35] module, as well as output_value[28.2] and input_value[28.2]). Element kinds ============= Bigarrays can contain elements of the following kinds: - IEEE half precision (16 bits) floating-point numbers (Bigarray.float16_elt[29.5]), - IEEE single precision (32 bits) floating-point numbers (Bigarray.float32_elt[29.5]), - IEEE double precision (64 bits) floating-point numbers (Bigarray.float64_elt[29.5]), - IEEE single precision (2 * 32 bits) floating-point complex numbers (Bigarray.complex32_elt[29.5]), - IEEE double precision (2 * 64 bits) floating-point complex numbers (Bigarray.complex64_elt[29.5]), - 8-bit integers (signed or unsigned) (Bigarray.int8_signed_elt[29.5] or Bigarray.int8_unsigned_elt[29.5]), - 16-bit integers (signed or unsigned) (Bigarray.int16_signed_elt[29.5] or Bigarray.int16_unsigned_elt[29.5]), - OCaml integers (signed, 31 bits on 32-bit architectures, 63 bits on 64-bit architectures) (Bigarray.int_elt[29.5]), - 32-bit signed integers (Bigarray.int32_elt[29.5]), - 64-bit signed integers (Bigarray.int64_elt[29.5]), - platform-native signed integers (32 bits on 32-bit architectures, 64 bits on 64-bit architectures) (Bigarray.nativeint_elt[29.5]). Each element kind is represented at the type level by one of the *_elt types defined below (defined with a single constructor instead of abstract types for technical injectivity reasons). << type float16_elt = | Float16_elt >> << type float32_elt = | Float32_elt >> << type float64_elt = | Float64_elt >> << type int8_signed_elt = | Int8_signed_elt >> << type int8_unsigned_elt = | Int8_unsigned_elt >> << type int16_signed_elt = | Int16_signed_elt >> << type int16_unsigned_elt = | Int16_unsigned_elt >> << type int32_elt = | Int32_elt >> << type int64_elt = | Int64_elt >> << type int_elt = | Int_elt >> << type nativeint_elt = | Nativeint_elt >> << type complex32_elt = | Complex32_elt >> << type complex64_elt = | Complex64_elt >> << type ('a, 'b) kind = | Float32 : (float, float32_elt) kind | Float64 : (float, float64_elt) kind | Int8_signed : (int, int8_signed_elt) kind | Int8_unsigned : (int, int8_unsigned_elt) kind | Int16_signed : (int, int16_signed_elt) kind | Int16_unsigned : (int, int16_unsigned_elt) kind | Int32 : (int32, int32_elt) kind | Int64 : (int64, int64_elt) kind | Int : (int, int_elt) kind | Nativeint : (nativeint, nativeint_elt) kind | Complex32 : (Complex.t, complex32_elt) kind | Complex64 : (Complex.t, complex64_elt) kind | Char : (char, int8_unsigned_elt) kind | Float16 : (float, float16_elt) kind >> To each element kind is associated an OCaml type, which is the type of OCaml values that can be stored in the Bigarray or read back from it. This type is not necessarily the same as the type of the array elements proper: for instance, a Bigarray whose elements are of kind float32_elt contains 32-bit single precision floats, but reading or writing one of its elements from OCaml uses the OCaml type float, which is 64-bit double precision floats. The GADT type ('a, 'b) kind captures this association of an OCaml type 'a for values read or written in the Bigarray, and of an element kind 'b which represents the actual contents of the Bigarray. Its constructors list all possible associations of OCaml types with element kinds, and are re-exported below for backward-compatibility reasons. Using a generalized algebraic datatype (GADT) here allows writing well-typed polymorphic functions whose return type depend on the argument type, such as: << let zero : type a b. (a, b) kind -> a = function | Float32 -> 0.0 | Complex32 -> Complex.zero | Float64 -> 0.0 | Complex64 -> Complex.zero | Float16 -> 0.0 | Int8_signed -> 0 | Int8_unsigned -> 0 | Int16_signed -> 0 | Int16_unsigned -> 0 | Int32 -> 0l | Int64 -> 0L | Int -> 0 | Nativeint -> 0n | Char -> '\000' >> Since: 5.2 Constructor Float16 for the GADT. << val float16 : (float, float16_elt) kind >> See Bigarray.char[29.5]. Since: 5.2 << val float32 : (float, float32_elt) kind >> See Bigarray.char[29.5]. << val float64 : (float, float64_elt) kind >> See Bigarray.char[29.5]. << val complex32 : (Complex.t, complex32_elt) kind >> See Bigarray.char[29.5]. << val complex64 : (Complex.t, complex64_elt) kind >> See Bigarray.char[29.5]. << val int8_signed : (int, int8_signed_elt) kind >> See Bigarray.char[29.5]. << val int8_unsigned : (int, int8_unsigned_elt) kind >> See Bigarray.char[29.5]. << val int16_signed : (int, int16_signed_elt) kind >> See Bigarray.char[29.5]. << val int16_unsigned : (int, int16_unsigned_elt) kind >> See Bigarray.char[29.5]. << val int : (int, int_elt) kind >> See Bigarray.char[29.5]. << val int32 : (int32, int32_elt) kind >> See Bigarray.char[29.5]. << val int64 : (int64, int64_elt) kind >> See Bigarray.char[29.5]. << val nativeint : (nativeint, nativeint_elt) kind >> See Bigarray.char[29.5]. << val char : (char, int8_unsigned_elt) kind >> As shown by the types of the values above, Bigarrays of kind float16_elt, float32_elt and float64_elt are accessed using the OCaml type float. Bigarrays of complex kinds complex32_elt, complex64_elt are accessed with the OCaml type Complex.t[29.12]. Bigarrays of integer kinds are accessed using the smallest OCaml integer type large enough to represent the array elements: int for 8- and 16-bit integer Bigarrays, as well as OCaml-integer Bigarrays; int32 for 32-bit integer Bigarrays; int64 for 64-bit integer Bigarrays; and nativeint for platform-native integer Bigarrays. Finally, Bigarrays of kind int8_unsigned_elt can also be accessed as arrays of characters instead of arrays of small integers, by using the kind value char instead of int8_unsigned. << val kind_size_in_bytes : ('a, 'b) kind -> int >> kind_size_in_bytes k is the number of bytes used to store an element of type k. Since: 4.03 Array layouts ============= << type c_layout = | C_layout_typ >> See Bigarray.fortran_layout[29.5]. << type fortran_layout = | Fortran_layout_typ >> To facilitate interoperability with existing C and Fortran code, this library supports two different memory layouts for Bigarrays, one compatible with the C conventions, the other compatible with the Fortran conventions. In the C-style layout, array indices start at 0, and multi-dimensional arrays are laid out in row-major format. That is, for a two-dimensional array, all elements of row 0 are contiguous in memory, followed by all elements of row 1, etc. In other terms, the array elements at (x,y) and (x, y+1) are adjacent in memory. In the Fortran-style layout, array indices start at 1, and multi-dimensional arrays are laid out in column-major format. That is, for a two-dimensional array, all elements of column 0 are contiguous in memory, followed by all elements of column 1, etc. In other terms, the array elements at (x,y) and (x+1, y) are adjacent in memory. Each layout style is identified at the type level by the phantom types Bigarray.c_layout[29.5] and Bigarray.fortran_layout[29.5] respectively. Supported layouts ----------------- The GADT type 'a layout represents one of the two supported memory layouts: C-style or Fortran-style. Its constructors are re-exported as values below for backward-compatibility reasons. << type 'a layout = | C_layout : c_layout layout | Fortran_layout : fortran_layout layout >> << val c_layout : c_layout layout >> << val fortran_layout : fortran_layout layout >> Generic arrays (of arbitrarily many dimensions) =============================================== << module Genarray : >>  sig << type (!'a, !'b, !'c) t >> The type Genarray.t is the type of Bigarrays with variable numbers of dimensions. Any number of dimensions between 0 and 16 is supported. The three type parameters to Genarray.t identify the array element kind and layout, as follows: - the first parameter, 'a, is the OCaml type for accessing array elements (float, int, int32, int64, nativeint); - the second parameter, 'b, is the actual kind of array elements (float32_elt, float64_elt, int8_signed_elt, int8_unsigned_elt, etc); - the third parameter, 'c, identifies the array layout (c_layout or fortran_layout). For instance, (float, float32_elt, fortran_layout) Genarray.t is the type of generic Bigarrays containing 32-bit floats in Fortran layout; reads and writes in this array use the OCaml type float. << val create : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> int array -> ('a, 'b, 'c) t >> Genarray.create kind layout dimensions returns a new Bigarray whose element kind is determined by the parameter kind (one of float32, float64, int8_signed, etc) and whose layout is determined by the parameter layout (one of c_layout or fortran_layout). The dimensions parameter is an array of integers that indicate the size of the Bigarray in each dimension. The length of dimensions determines the number of dimensions of the Bigarray. For instance, Genarray.create int32 c_layout [|4;6;8|] returns a fresh Bigarray of 32-bit integers, in C layout, having three dimensions, the three dimensions being 4, 6 and 8 respectively. Bigarrays returned by Genarray.create are not initialized: the initial values of array elements is unspecified. Genarray.create raises Invalid_argument if the number of dimensions is not in the range 0 to 16 inclusive, or if one of the dimensions is negative. << val init : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> int array -> (int array -> 'a) -> ('a, 'b, 'c) t >> Genarray.init kind layout dimensions f returns a new Bigarray b whose element kind is determined by the parameter kind (one of float32, float64, int8_signed, etc) and whose layout is determined by the parameter layout (one of c_layout or fortran_layout). The dimensions parameter is an array of integers that indicate the size of the Bigarray in each dimension. The length of dimensions determines the number of dimensions of the Bigarray. Each element Genarray.get b i is initialized to the result of f i. In other words, Genarray.init kind layout dimensions f tabulates the results of f applied to the indices of a new Bigarray whose layout is described by kind, layout and dimensions. The index array i may be shared and mutated between calls to f. For instance, Genarray.init int c_layout [|2; 1; 3|] (Array.fold_left (+) 0) returns a fresh Bigarray of integers, in C layout, having three dimensions (2, 1, 3, respectively), with the element values 0, 1, 2, 1, 2, 3. Genarray.init raises Invalid_argument if the number of dimensions is not in the range 0 to 16 inclusive, or if one of the dimensions is negative. Since: 4.12 << val num_dims : ('a, 'b, 'c) t -> int >> Return the number of dimensions of the given Bigarray. << val dims : ('a, 'b, 'c) t -> int array >> Genarray.dims a returns all dimensions of the Bigarray a, as an array of integers of length Genarray.num_dims a. << val nth_dim : ('a, 'b, 'c) t -> int -> int >> Genarray.nth_dim a n returns the n-th dimension of the Bigarray a. The first dimension corresponds to n = 0; the second dimension corresponds to n = 1; the last dimension, to n = Genarray.num_dims a - 1. Raises Invalid_argument if n is less than 0 or greater or equal than Genarray.num_dims a. << val kind : ('a, 'b, 'c) t -> ('a, 'b) Bigarray.kind >> Return the kind of the given Bigarray. << val layout : ('a, 'b, 'c) t -> 'c Bigarray.layout >> Return the layout of the given Bigarray. << val change_layout : ('a, 'b, 'c) t -> 'd Bigarray.layout -> ('a, 'b, 'd) t >> Genarray.change_layout a layout returns a Bigarray with the specified layout, sharing the data with a (and hence having the same dimensions as a). No copying of elements is involved: the new array and the original array share the same storage space. The dimensions are reversed, such that get v [| a; b |] in C layout becomes get v [| b+1; a+1 |] in Fortran layout. Since: 4.04 << val size_in_bytes : ('a, 'b, 'c) t -> int >> size_in_bytes a is the number of elements in a multiplied by a’s Bigarray.kind_size_in_bytes[29.5]. Since: 4.03 << val get : ('a, 'b, 'c) t -> int array -> 'a >> Read an element of a generic Bigarray. Genarray.get a [|i1; ...; iN|] returns the element of a whose coordinates are i1 in the first dimension, i2 in the second dimension, ..., iN in the N-th dimension. If a has C layout, the coordinates must be greater or equal than 0 and strictly less than the corresponding dimensions of a. If a has Fortran layout, the coordinates must be greater or equal than 1 and less or equal than the corresponding dimensions of a. If N > 3, alternate syntax is provided: you can write a.{i1, i2, ..., iN} instead of Genarray.get a [|i1; ...; iN|]. (The syntax a.{...} with one, two or three coordinates is reserved for accessing one-, two- and three-dimensional arrays as described below.) Raises Invalid_argument if the array a does not have exactly N dimensions, or if the coordinates are outside the array bounds. << val set : ('a, 'b, 'c) t -> int array -> 'a -> unit >> Assign an element of a generic Bigarray. Genarray.set a [|i1; ...; iN|] v stores the value v in the element of a whose coordinates are i1 in the first dimension, i2 in the second dimension, ..., iN in the N-th dimension. The array a must have exactly N dimensions, and all coordinates must lie inside the array bounds, as described for Genarray.get; otherwise, Invalid_argument is raised. If N > 3, alternate syntax is provided: you can write a.{i1, i2, ..., iN} <- v instead of Genarray.set a [|i1; ...; iN|] v. (The syntax a.{...} <- v with one, two or three coordinates is reserved for updating one-, two- and three-dimensional arrays as described below.) << val sub_left : ('a, 'b, Bigarray.c_layout) t -> int -> int -> ('a, 'b, Bigarray.c_layout) t >> Extract a sub-array of the given Bigarray by restricting the first (left-most) dimension. Genarray.sub_left a ofs len returns a Bigarray with the same number of dimensions as a, and the same dimensions as a, except the first dimension, which corresponds to the interval [ofs ... ofs + len - 1] of the first dimension of a. No copying of elements is involved: the sub-array and the original array share the same storage space. In other terms, the element at coordinates [|i1; ...; iN|] of the sub-array is identical to the element at coordinates [|i1+ofs; ...; iN|] of the original array a. Genarray.sub_left applies only to Bigarrays in C layout. Raises Invalid_argument if ofs and len do not designate a valid sub-array of a, that is, if ofs < 0, or len < 0, or ofs + len > Genarray.nth_dim a 0. << val sub_right : ('a, 'b, Bigarray.fortran_layout) t -> int -> int -> ('a, 'b, Bigarray.fortran_layout) t >> Extract a sub-array of the given Bigarray by restricting the last (right-most) dimension. Genarray.sub_right a ofs len returns a Bigarray with the same number of dimensions as a, and the same dimensions as a, except the last dimension, which corresponds to the interval [ofs ... ofs + len - 1] of the last dimension of a. No copying of elements is involved: the sub-array and the original array share the same storage space. In other terms, the element at coordinates [|i1; ...; iN|] of the sub-array is identical to the element at coordinates [|i1; ...; iN+ofs|] of the original array a. Genarray.sub_right applies only to Bigarrays in Fortran layout. Raises Invalid_argument if ofs and len do not designate a valid sub-array of a, that is, if ofs < 1, or len < 0, or ofs + len > Genarray.nth_dim a (Genarray.num_dims a - 1). << val slice_left : ('a, 'b, Bigarray.c_layout) t -> int array -> ('a, 'b, Bigarray.c_layout) t >> Extract a sub-array of lower dimension from the given Bigarray by fixing one or several of the first (left-most) coordinates. Genarray.slice_left a [|i1; ... ; iM|] returns the ’slice’ of a obtained by setting the first M coordinates to i1, ..., iM. If a has N dimensions, the slice has dimension N - M, and the element at coordinates [|j1; ...; j(N-M)|] in the slice is identical to the element at coordinates [|i1; ...; iM; j1; ...; j(N-M)|] in the original array a. No copying of elements is involved: the slice and the original array share the same storage space. Genarray.slice_left applies only to Bigarrays in C layout. Raises Invalid_argument if M >= N, or if [|i1; ... ; iM|] is outside the bounds of a. << val slice_right : ('a, 'b, Bigarray.fortran_layout) t -> int array -> ('a, 'b, Bigarray.fortran_layout) t >> Extract a sub-array of lower dimension from the given Bigarray by fixing one or several of the last (right-most) coordinates. Genarray.slice_right a [|i1; ... ; iM|] returns the ’slice’ of a obtained by setting the last M coordinates to i1, ..., iM. If a has N dimensions, the slice has dimension N - M, and the element at coordinates [|j1; ...; j(N-M)|] in the slice is identical to the element at coordinates [|j1; ...; j(N-M); i1; ...; iM|] in the original array a. No copying of elements is involved: the slice and the original array share the same storage space. Genarray.slice_right applies only to Bigarrays in Fortran layout. Raises Invalid_argument if M >= N, or if [|i1; ... ; iM|] is outside the bounds of a. << val blit : ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit >> Copy all elements of a Bigarray in another Bigarray. Genarray.blit src dst copies all elements of src into dst. Both arrays src and dst must have the same number of dimensions and equal dimensions. Copying a sub-array of src to a sub-array of dst can be achieved by applying Genarray.blit to sub-array or slices of src and dst. << val fill : ('a, 'b, 'c) t -> 'a -> unit >> Set all elements of a Bigarray to a given value. Genarray.fill a v stores the value v in all elements of the Bigarray a. Setting only some elements of a to v can be achieved by applying Genarray.fill to a sub-array or a slice of a.  end Zero-dimensional arrays ======================= << module Array0 : >>  sig << type (!'a, !'b, !'c) t >> The type of zero-dimensional Bigarrays whose elements have OCaml type 'a, representation kind 'b, and memory layout 'c. << val create : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> ('a, 'b, 'c) t >> Array0.create kind layout returns a new Bigarray of zero dimension. kind and layout determine the array element kind and the array layout as described for Bigarray.Genarray.create[29.5]. << val init : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> 'a -> ('a, 'b, 'c) t >> Array0.init kind layout v behaves like Array0.create kind layout except that the element is additionally initialized to the value v. Since: 4.12 << val kind : ('a, 'b, 'c) t -> ('a, 'b) Bigarray.kind >> Return the kind of the given Bigarray. << val layout : ('a, 'b, 'c) t -> 'c Bigarray.layout >> Return the layout of the given Bigarray. << val change_layout : ('a, 'b, 'c) t -> 'd Bigarray.layout -> ('a, 'b, 'd) t >> Array0.change_layout a layout returns a Bigarray with the specified layout, sharing the data with a. No copying of elements is involved: the new array and the original array share the same storage space. Since: 4.06 << val size_in_bytes : ('a, 'b, 'c) t -> int >> size_in_bytes a is a’s Bigarray.kind_size_in_bytes[29.5]. << val get : ('a, 'b, 'c) t -> 'a >> Array0.get a returns the only element in a. << val set : ('a, 'b, 'c) t -> 'a -> unit >> Array0.set a x v stores the value v in a. << val blit : ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit >> Copy the first Bigarray to the second Bigarray. See Bigarray.Genarray.blit[29.5] for more details. << val fill : ('a, 'b, 'c) t -> 'a -> unit >> Fill the given Bigarray with the given value. See Bigarray.Genarray.fill[29.5] for more details. << val of_value : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> 'a -> ('a, 'b, 'c) t >> Build a zero-dimensional Bigarray initialized from the given value.  end Zero-dimensional arrays. The Array0 structure provides operations similar to those of Bigarray.Genarray[29.5], but specialized to the case of zero-dimensional arrays that only contain a single scalar value. Statically knowing the number of dimensions of the array allows faster operations, and more precise static type-checking. Since: 4.05 One-dimensional arrays ====================== << module Array1 : >>  sig << type (!'a, !'b, !'c) t >> The type of one-dimensional Bigarrays whose elements have OCaml type 'a, representation kind 'b, and memory layout 'c. << val create : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> int -> ('a, 'b, 'c) t >> Array1.create kind layout dim returns a new Bigarray of one dimension, whose size is dim. kind and layout determine the array element kind and the array layout as described for Bigarray.Genarray.create[29.5]. << val init : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> int -> (int -> 'a) -> ('a, 'b, 'c) t >> Array1.init kind layout dim f returns a new Bigarray b of one dimension, whose size is dim. kind and layout determine the array element kind and the array layout as described for Bigarray.Genarray.create[29.5]. Each element Array1.get b i of the array is initialized to the result of f i. In other words, Array1.init kind layout dimensions f tabulates the results of f applied to the indices of a new Bigarray whose layout is described by kind, layout and dim. Since: 4.12 << val dim : ('a, 'b, 'c) t -> int >> Return the size (dimension) of the given one-dimensional Bigarray. << val kind : ('a, 'b, 'c) t -> ('a, 'b) Bigarray.kind >> Return the kind of the given Bigarray. << val layout : ('a, 'b, 'c) t -> 'c Bigarray.layout >> Return the layout of the given Bigarray. << val change_layout : ('a, 'b, 'c) t -> 'd Bigarray.layout -> ('a, 'b, 'd) t >> Array1.change_layout a layout returns a Bigarray with the specified layout, sharing the data with a (and hence having the same dimension as a). No copying of elements is involved: the new array and the original array share the same storage space. Since: 4.06 << val size_in_bytes : ('a, 'b, 'c) t -> int >> size_in_bytes a is the number of elements in a multiplied by a’s Bigarray.kind_size_in_bytes[29.5]. Since: 4.03 << val get : ('a, 'b, 'c) t -> int -> 'a >> Array1.get a x, or alternatively a.{x}, returns the element of a at index x. x must be greater or equal than 0 and strictly less than Array1.dim a if a has C layout. If a has Fortran layout, x must be greater or equal than 1 and less or equal than Array1.dim a. Otherwise, Invalid_argument is raised. << val set : ('a, 'b, 'c) t -> int -> 'a -> unit >> Array1.set a x v, also written a.{x} <- v, stores the value v at index x in a. x must be inside the bounds of a as described in Bigarray.Array1.get[29.5]; otherwise, Invalid_argument is raised. << val sub : ('a, 'b, 'c) t -> int -> int -> ('a, 'b, 'c) t >> Extract a sub-array of the given one-dimensional Bigarray. See Bigarray.Genarray.sub_left[29.5] for more details. << val slice : ('a, 'b, 'c) t -> int -> ('a, 'b, 'c) Bigarray.Array0.t >> Extract a scalar (zero-dimensional slice) of the given one-dimensional Bigarray. The integer parameter is the index of the scalar to extract. See Bigarray.Genarray.slice_left[29.5] and Bigarray.Genarray.slice_right[29.5] for more details. Since: 4.05 << val blit : ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit >> Copy the first Bigarray to the second Bigarray. See Bigarray.Genarray.blit[29.5] for more details. << val fill : ('a, 'b, 'c) t -> 'a -> unit >> Fill the given Bigarray with the given value. See Bigarray.Genarray.fill[29.5] for more details. << val of_array : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> 'a array -> ('a, 'b, 'c) t >> Build a one-dimensional Bigarray initialized from the given array. << val unsafe_get : ('a, 'b, 'c) t -> int -> 'a >> Like Bigarray.Array1.get[29.5], but bounds checking is not always performed. Use with caution and only when the program logic guarantees that the access is within bounds. << val unsafe_set : ('a, 'b, 'c) t -> int -> 'a -> unit >> Like Bigarray.Array1.set[29.5], but bounds checking is not always performed. Use with caution and only when the program logic guarantees that the access is within bounds.  end One-dimensional arrays. The Array1 structure provides operations similar to those of Bigarray.Genarray[29.5], but specialized to the case of one-dimensional arrays. (The Bigarray.Array2[29.5] and Bigarray.Array3[29.5] structures below provide operations specialized for two- and three-dimensional arrays.) Statically knowing the number of dimensions of the array allows faster operations, and more precise static type-checking. Two-dimensional arrays ====================== << module Array2 : >>  sig << type (!'a, !'b, !'c) t >> The type of two-dimensional Bigarrays whose elements have OCaml type 'a, representation kind 'b, and memory layout 'c. << val create : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> int -> int -> ('a, 'b, 'c) t >> Array2.create kind layout dim1 dim2 returns a new Bigarray of two dimensions, whose size is dim1 in the first dimension and dim2 in the second dimension. kind and layout determine the array element kind and the array layout as described for Bigarray.Genarray.create[29.5]. << val init : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> int -> int -> (int -> int -> 'a) -> ('a, 'b, 'c) t >> Array2.init kind layout dim1 dim2 f returns a new Bigarray b of two dimensions, whose size is dim2 in the first dimension and dim2 in the second dimension. kind and layout determine the array element kind and the array layout as described for Bigarray.Genarray.create[29.5]. Each element Array2.get b i j of the array is initialized to the result of f i j. In other words, Array2.init kind layout dim1 dim2 f tabulates the results of f applied to the indices of a new Bigarray whose layout is described by kind, layout, dim1 and dim2. Since: 4.12 << val dim1 : ('a, 'b, 'c) t -> int >> Return the first dimension of the given two-dimensional Bigarray. << val dim2 : ('a, 'b, 'c) t -> int >> Return the second dimension of the given two-dimensional Bigarray. << val kind : ('a, 'b, 'c) t -> ('a, 'b) Bigarray.kind >> Return the kind of the given Bigarray. << val layout : ('a, 'b, 'c) t -> 'c Bigarray.layout >> Return the layout of the given Bigarray. << val change_layout : ('a, 'b, 'c) t -> 'd Bigarray.layout -> ('a, 'b, 'd) t >> Array2.change_layout a layout returns a Bigarray with the specified layout, sharing the data with a (and hence having the same dimensions as a). No copying of elements is involved: the new array and the original array share the same storage space. The dimensions are reversed, such that get v [| a; b |] in C layout becomes get v [| b+1; a+1 |] in Fortran layout. Since: 4.06 << val size_in_bytes : ('a, 'b, 'c) t -> int >> size_in_bytes a is the number of elements in a multiplied by a’s Bigarray.kind_size_in_bytes[29.5]. Since: 4.03 << val get : ('a, 'b, 'c) t -> int -> int -> 'a >> Array2.get a x y, also written a.{x,y}, returns the element of a at coordinates (x, y). x and y must be within the bounds of a, as described for Bigarray.Genarray.get[29.5]; otherwise, Invalid_argument is raised. << val set : ('a, 'b, 'c) t -> int -> int -> 'a -> unit >> Array2.set a x y v, or alternatively a.{x,y} <- v, stores the value v at coordinates (x, y) in a. x and y must be within the bounds of a, as described for Bigarray.Genarray.set[29.5]; otherwise, Invalid_argument is raised. << val sub_left : ('a, 'b, Bigarray.c_layout) t -> int -> int -> ('a, 'b, Bigarray.c_layout) t >> Extract a two-dimensional sub-array of the given two-dimensional Bigarray by restricting the first dimension. See Bigarray.Genarray.sub_left[29.5] for more details. Array2.sub_left applies only to arrays with C layout. << val sub_right : ('a, 'b, Bigarray.fortran_layout) t -> int -> int -> ('a, 'b, Bigarray.fortran_layout) t >> Extract a two-dimensional sub-array of the given two-dimensional Bigarray by restricting the second dimension. See Bigarray.Genarray.sub_right[29.5] for more details. Array2.sub_right applies only to arrays with Fortran layout. << val slice_left : ('a, 'b, Bigarray.c_layout) t -> int -> ('a, 'b, Bigarray.c_layout) Bigarray.Array1.t >> Extract a row (one-dimensional slice) of the given two-dimensional Bigarray. The integer parameter is the index of the row to extract. See Bigarray.Genarray.slice_left[29.5] for more details. Array2.slice_left applies only to arrays with C layout. << val slice_right : ('a, 'b, Bigarray.fortran_layout) t -> int -> ('a, 'b, Bigarray.fortran_layout) Bigarray.Array1.t >> Extract a column (one-dimensional slice) of the given two-dimensional Bigarray. The integer parameter is the index of the column to extract. See Bigarray.Genarray.slice_right[29.5] for more details. Array2.slice_right applies only to arrays with Fortran layout. << val blit : ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit >> Copy the first Bigarray to the second Bigarray. See Bigarray.Genarray.blit[29.5] for more details. << val fill : ('a, 'b, 'c) t -> 'a -> unit >> Fill the given Bigarray with the given value. See Bigarray.Genarray.fill[29.5] for more details. << val of_array : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> 'a array array -> ('a, 'b, 'c) t >> Build a two-dimensional Bigarray initialized from the given array of arrays. << val unsafe_get : ('a, 'b, 'c) t -> int -> int -> 'a >> Like Bigarray.Array2.get[29.5], but bounds checking is not always performed. << val unsafe_set : ('a, 'b, 'c) t -> int -> int -> 'a -> unit >> Like Bigarray.Array2.set[29.5], but bounds checking is not always performed.  end Two-dimensional arrays. The Array2 structure provides operations similar to those of Bigarray.Genarray[29.5], but specialized to the case of two-dimensional arrays. Three-dimensional arrays ======================== << module Array3 : >>  sig << type (!'a, !'b, !'c) t >> The type of three-dimensional Bigarrays whose elements have OCaml type 'a, representation kind 'b, and memory layout 'c. << val create : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> int -> int -> int -> ('a, 'b, 'c) t >> Array3.create kind layout dim1 dim2 dim3 returns a new Bigarray of three dimensions, whose size is dim1 in the first dimension, dim2 in the second dimension, and dim3 in the third. kind and layout determine the array element kind and the array layout as described for Bigarray.Genarray.create[29.5]. << val init : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> int -> int -> int -> (int -> int -> int -> 'a) -> ('a, 'b, 'c) t >> Array3.init kind layout dim1 dim2 dim3 f returns a new Bigarray b of three dimensions, whose size is dim1 in the first dimension, dim2 in the second dimension, and dim3 in the third. kind and layout determine the array element kind and the array layout as described for Bigarray.Genarray.create[29.5]. Each element Array3.get b i j k of the array is initialized to the result of f i j k. In other words, Array3.init kind layout dim1 dim2 dim3 f tabulates the results of f applied to the indices of a new Bigarray whose layout is described by kind, layout, dim1, dim2 and dim3. Since: 4.12 << val dim1 : ('a, 'b, 'c) t -> int >> Return the first dimension of the given three-dimensional Bigarray. << val dim2 : ('a, 'b, 'c) t -> int >> Return the second dimension of the given three-dimensional Bigarray. << val dim3 : ('a, 'b, 'c) t -> int >> Return the third dimension of the given three-dimensional Bigarray. << val kind : ('a, 'b, 'c) t -> ('a, 'b) Bigarray.kind >> Return the kind of the given Bigarray. << val layout : ('a, 'b, 'c) t -> 'c Bigarray.layout >> Return the layout of the given Bigarray. << val change_layout : ('a, 'b, 'c) t -> 'd Bigarray.layout -> ('a, 'b, 'd) t >> Array3.change_layout a layout returns a Bigarray with the specified layout, sharing the data with a (and hence having the same dimensions as a). No copying of elements is involved: the new array and the original array share the same storage space. The dimensions are reversed, such that get v [| a; b; c |] in C layout becomes get v [| c+1; b+1; a+1 |] in Fortran layout. Since: 4.06 << val size_in_bytes : ('a, 'b, 'c) t -> int >> size_in_bytes a is the number of elements in a multiplied by a’s Bigarray.kind_size_in_bytes[29.5]. Since: 4.03 << val get : ('a, 'b, 'c) t -> int -> int -> int -> 'a >> Array3.get a x y z, also written a.{x,y,z}, returns the element of a at coordinates (x, y, z). x, y and z must be within the bounds of a, as described for Bigarray.Genarray.get[29.5]; otherwise, Invalid_argument is raised. << val set : ('a, 'b, 'c) t -> int -> int -> int -> 'a -> unit >> Array3.set a x y v, or alternatively a.{x,y,z} <- v, stores the value v at coordinates (x, y, z) in a. x, y and z must be within the bounds of a, as described for Bigarray.Genarray.set[29.5]; otherwise, Invalid_argument is raised. << val sub_left : ('a, 'b, Bigarray.c_layout) t -> int -> int -> ('a, 'b, Bigarray.c_layout) t >> Extract a three-dimensional sub-array of the given three-dimensional Bigarray by restricting the first dimension. See Bigarray.Genarray.sub_left[29.5] for more details. Array3.sub_left applies only to arrays with C layout. << val sub_right : ('a, 'b, Bigarray.fortran_layout) t -> int -> int -> ('a, 'b, Bigarray.fortran_layout) t >> Extract a three-dimensional sub-array of the given three-dimensional Bigarray by restricting the second dimension. See Bigarray.Genarray.sub_right[29.5] for more details. Array3.sub_right applies only to arrays with Fortran layout. << val slice_left_1 : ('a, 'b, Bigarray.c_layout) t -> int -> int -> ('a, 'b, Bigarray.c_layout) Bigarray.Array1.t >> Extract a one-dimensional slice of the given three-dimensional Bigarray by fixing the first two coordinates. The integer parameters are the coordinates of the slice to extract. See Bigarray.Genarray.slice_left[29.5] for more details. Array3.slice_left_1 applies only to arrays with C layout. << val slice_right_1 : ('a, 'b, Bigarray.fortran_layout) t -> int -> int -> ('a, 'b, Bigarray.fortran_layout) Bigarray.Array1.t >> Extract a one-dimensional slice of the given three-dimensional Bigarray by fixing the last two coordinates. The integer parameters are the coordinates of the slice to extract. See Bigarray.Genarray.slice_right[29.5] for more details. Array3.slice_right_1 applies only to arrays with Fortran layout. << val slice_left_2 : ('a, 'b, Bigarray.c_layout) t -> int -> ('a, 'b, Bigarray.c_layout) Bigarray.Array2.t >> Extract a two-dimensional slice of the given three-dimensional Bigarray by fixing the first coordinate. The integer parameter is the first coordinate of the slice to extract. See Bigarray.Genarray.slice_left[29.5] for more details. Array3.slice_left_2 applies only to arrays with C layout. << val slice_right_2 : ('a, 'b, Bigarray.fortran_layout) t -> int -> ('a, 'b, Bigarray.fortran_layout) Bigarray.Array2.t >> Extract a two-dimensional slice of the given three-dimensional Bigarray by fixing the last coordinate. The integer parameter is the coordinate of the slice to extract. See Bigarray.Genarray.slice_right[29.5] for more details. Array3.slice_right_2 applies only to arrays with Fortran layout. << val blit : ('a, 'b, 'c) t -> ('a, 'b, 'c) t -> unit >> Copy the first Bigarray to the second Bigarray. See Bigarray.Genarray.blit[29.5] for more details. << val fill : ('a, 'b, 'c) t -> 'a -> unit >> Fill the given Bigarray with the given value. See Bigarray.Genarray.fill[29.5] for more details. << val of_array : ('a, 'b) Bigarray.kind -> 'c Bigarray.layout -> 'a array array array -> ('a, 'b, 'c) t >> Build a three-dimensional Bigarray initialized from the given array of arrays of arrays. << val unsafe_get : ('a, 'b, 'c) t -> int -> int -> int -> 'a >> Like Bigarray.Array3.get[29.5], but bounds checking is not always performed. << val unsafe_set : ('a, 'b, 'c) t -> int -> int -> int -> 'a -> unit >> Like Bigarray.Array3.set[29.5], but bounds checking is not always performed.  end Three-dimensional arrays. The Array3 structure provides operations similar to those of Bigarray.Genarray[29.5], but specialized to the case of three-dimensional arrays. Coercions between generic Bigarrays and fixed-dimension Bigarrays ================================================================= << val genarray_of_array0 : ('a, 'b, 'c) Array0.t -> ('a, 'b, 'c) Genarray.t >> Return the generic Bigarray corresponding to the given zero-dimensional Bigarray. Since: 4.05 << val genarray_of_array1 : ('a, 'b, 'c) Array1.t -> ('a, 'b, 'c) Genarray.t >> Return the generic Bigarray corresponding to the given one-dimensional Bigarray. << val genarray_of_array2 : ('a, 'b, 'c) Array2.t -> ('a, 'b, 'c) Genarray.t >> Return the generic Bigarray corresponding to the given two-dimensional Bigarray. << val genarray_of_array3 : ('a, 'b, 'c) Array3.t -> ('a, 'b, 'c) Genarray.t >> Return the generic Bigarray corresponding to the given three-dimensional Bigarray. << val array0_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array0.t >> Return the zero-dimensional Bigarray corresponding to the given generic Bigarray. Since: 4.05 Raises Invalid_argument if the generic Bigarray does not have exactly zero dimension. << val array1_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array1.t >> Return the one-dimensional Bigarray corresponding to the given generic Bigarray. Raises Invalid_argument if the generic Bigarray does not have exactly one dimension. << val array2_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array2.t >> Return the two-dimensional Bigarray corresponding to the given generic Bigarray. Raises Invalid_argument if the generic Bigarray does not have exactly two dimensions. << val array3_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array3.t >> Return the three-dimensional Bigarray corresponding to the given generic Bigarray. Raises Invalid_argument if the generic Bigarray does not have exactly three dimensions. Re-shaping Bigarrays ==================== << val reshape : ('a, 'b, 'c) Genarray.t -> int array -> ('a, 'b, 'c) Genarray.t >> reshape b [|d1;...;dN|] converts the Bigarray b to a N-dimensional array of dimensions d1...dN. The returned array and the original array b share their data and have the same layout. For instance, assuming that b is a one-dimensional array of dimension 12, reshape b [|3;4|] returns a two-dimensional array b' of dimensions 3 and 4. If b has C layout, the element (x,y) of b' corresponds to the element x * 3 + y of b. If b has Fortran layout, the element (x,y) of b' corresponds to the element x + (y - 1) * 4 of b. The returned Bigarray must have exactly the same number of elements as the original Bigarray b. That is, the product of the dimensions of b must be equal to i1 * ... * iN. Otherwise, Invalid_argument is raised. << val reshape_0 : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array0.t >> Specialized version of Bigarray.reshape[29.5] for reshaping to zero-dimensional arrays. Since: 4.05 << val reshape_1 : ('a, 'b, 'c) Genarray.t -> int -> ('a, 'b, 'c) Array1.t >> Specialized version of Bigarray.reshape[29.5] for reshaping to one-dimensional arrays. << val reshape_2 : ('a, 'b, 'c) Genarray.t -> int -> int -> ('a, 'b, 'c) Array2.t >> Specialized version of Bigarray.reshape[29.5] for reshaping to two-dimensional arrays. << val reshape_3 : ('a, 'b, 'c) Genarray.t -> int -> int -> int -> ('a, 'b, 'c) Array3.t >> Specialized version of Bigarray.reshape[29.5] for reshaping to three-dimensional arrays. Bigarrays and concurrency safety ================================ Care must be taken when concurrently accessing bigarrays from multiple domains: accessing a bigarray will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results. Atomicity --------- Every bigarray operation that accesses more than one array element is not atomic. This includes slicing, bliting, and filling bigarrays. For example, consider the following program: << open Bigarray let size = 100_000_000 let a = Array1.init Int C_layout size (fun _ -> 1) let update f a () = for i = 0 to size - 1 do a.{i} <- f a.{i} done let d1 = Domain.spawn (update (fun x -> x + 1) a) let d2 = Domain.spawn (update (fun x -> 2 * x + 1) a) let () = Domain.join d1; Domain.join d2 >> After executing this code, each field of the bigarray a is either 2, 3, 4 or 5. If atomicity is required, then the user must implement their own synchronization (for example, using Mutex.t[29.37]). Data races ---------- If two domains only access disjoint parts of the bigarray, then the observed behaviour is the equivalent to some sequential interleaving of the operations from the two domains. A data race is said to occur when two domains access the same bigarray element without synchronization and at least one of the accesses is a write. In the absence of data races, the observed behaviour is equivalent to some sequential interleaving of the operations from different domains. Whenever possible, data races should be avoided by using synchronization to mediate the accesses to the bigarray elements. Indeed, in the presence of data races, programs will not crash but the observed behaviour may not be equivalent to any sequential interleaving of operations from different domains. Tearing ------- Bigarrays have a distinct caveat in the presence of data races: concurrent bigarray operations might produce surprising values due to tearing. More precisely, the interleaving of partial writes and reads might create values that would not exist with a sequential execution. For instance, at the end of << let res = Array1.init Complex64 c_layout size (fun _ -> Complex.zero) let d1 = Domain.spawn (fun () -> Array1.fill res Complex.one) let d2 = Domain.spawn (fun () -> Array1.fill res Complex.i) let () = Domain.join d1; Domain.join d2 >> the res bigarray might contain values that are neither Complex.i nor Complex.one (for instance 1 + i). 29.6 Module Bool : Boolean values. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Since: 4.08 Booleans ======== << type t = bool = | false | true >> The type of booleans (truth values). The constructors false and true are included here so that they have paths, but they are not intended to be used in user-defined data types. << val not : bool -> bool >> not b is the boolean negation of b. << val (&&) : bool -> bool -> bool >> e0 && e1 is the lazy boolean conjunction of expressions e0 and e1. If e0 evaluates to false, e1 is not evaluated. Right-associative operator at precedence level 3/11. << val (||) : bool -> bool -> bool >> e0 || e1 is the lazy boolean disjunction of expressions e0 and e1. If e0 evaluates to true, e1 is not evaluated. Right-associative operator at precedence level 2/11. Predicates and comparisons ========================== << val equal : bool -> bool -> bool >> equal b0 b1 is true if and only if b0 and b1 are both true or both false. << val compare : bool -> bool -> int >> compare b0 b1 is a total order on boolean values. false is smaller than true. Converting ========== << val to_int : bool -> int >> to_int b is 0 if b is false and 1 if b is true. << val to_float : bool -> float >> to_float b is 0. if b is false and 1. if b is true. << val to_string : bool -> string >> to_string b is "true" if b is true and "false" if b is false. << val seeded_hash : int -> bool -> int >> A seeded hash function for booleans, with the same output value as Hashtbl.seeded_hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded[29.25]. Since: 5.1 << val hash : bool -> int >> An unseeded hash function for booleans, with the same output value as Hashtbl.hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.Make[29.25]. Since: 5.1 29.7 Module Buffer : Extensible buffers. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This module implements buffers that automatically expand as necessary. It provides accumulative concatenation of strings in linear time (instead of quadratic time when strings are concatenated pairwise). For example: << let concat_strings ss = let b = Buffer.create 16 in List.iter (Buffer.add_string b) ss; Buffer.contents b >> Alert unsynchronized_access. Unsynchronized accesses to buffers are a programming error. Unsynchronized accesses Unsynchronized accesses to a buffer may lead to an invalid buffer state. Thus, concurrent accesses to a buffer must be synchronized (for instance with a Mutex.t[29.37]). << type t >> The abstract type of buffers. << val create : int -> t >> create n returns a fresh buffer, initially empty. The n parameter is the initial size of the internal byte sequence that holds the buffer contents. That byte sequence is automatically reallocated when more than n characters are stored in the buffer, but shrinks back to n characters when reset is called. For best performance, n should be of the same order of magnitude as the number of characters that are expected to be stored in the buffer (for instance, 80 for a buffer that holds one output line). Nothing bad will happen if the buffer grows beyond that limit, however. In doubt, take n = 16 for instance. If n is not between 1 and Sys.max_string_length[29.56], it will be clipped to that interval. << val contents : t -> string >> Return a copy of the current contents of the buffer. The buffer itself is unchanged. << val to_bytes : t -> bytes >> Return a copy of the current contents of the buffer. The buffer itself is unchanged. Since: 4.02 << val sub : t -> int -> int -> string >> Buffer.sub b off len returns a copy of len bytes from the current contents of the buffer b, starting at offset off. Raises Invalid_argument if off and len do not designate a valid range of b. << val blit : t -> int -> bytes -> int -> int -> unit >> Buffer.blit src srcoff dst dstoff len copies len characters from the current contents of the buffer src, starting at offset srcoff to dst, starting at character dstoff. Since: 3.11.2 Raises Invalid_argument if srcoff and len do not designate a valid range of src, or if dstoff and len do not designate a valid range of dst. << val nth : t -> int -> char >> Get the n-th character of the buffer. Raises Invalid_argument if index out of bounds << val length : t -> int >> Return the number of characters currently contained in the buffer. << val clear : t -> unit >> Empty the buffer. << val reset : t -> unit >> Empty the buffer and deallocate the internal byte sequence holding the buffer contents, replacing it with the initial internal byte sequence of length n that was allocated by Buffer.create[29.7] n. For long-lived buffers that may have grown a lot, reset allows faster reclamation of the space used by the buffer. << val output_buffer : out_channel -> t -> unit >> output_buffer oc b writes the current contents of buffer b on the output channel oc. << val truncate : t -> int -> unit >> truncate b len truncates the length of b to len Note: the internal byte sequence is not shortened. Since: 4.05 Raises Invalid_argument if len < 0 or len > length b. Appending ========= Note: all add_* operations can raise Failure if the internal byte sequence of the buffer would need to grow beyond Sys.max_string_length[29.56]. << val add_char : t -> char -> unit >> add_char b c appends the character c at the end of buffer b. << val add_utf_8_uchar : t -> Uchar.t -> unit >> add_utf_8_uchar b u appends the UTF-8[https://tools.ietf.org/html/rfc3629] encoding of u at the end of buffer b. Since: 4.06 << val add_utf_16le_uchar : t -> Uchar.t -> unit >> add_utf_16le_uchar b u appends the UTF-16LE[https://tools.ietf.org/html/rfc2781] encoding of u at the end of buffer b. Since: 4.06 << val add_utf_16be_uchar : t -> Uchar.t -> unit >> add_utf_16be_uchar b u appends the UTF-16BE[https://tools.ietf.org/html/rfc2781] encoding of u at the end of buffer b. Since: 4.06 << val add_string : t -> string -> unit >> add_string b s appends the string s at the end of buffer b. << val add_bytes : t -> bytes -> unit >> add_bytes b s appends the byte sequence s at the end of buffer b. Since: 4.02 << val add_substring : t -> string -> int -> int -> unit >> add_substring b s ofs len takes len characters from offset ofs in string s and appends them at the end of buffer b. Raises Invalid_argument if ofs and len do not designate a valid range of s. << val add_subbytes : t -> bytes -> int -> int -> unit >> add_subbytes b s ofs len takes len characters from offset ofs in byte sequence s and appends them at the end of buffer b. Since: 4.02 Raises Invalid_argument if ofs and len do not designate a valid range of s. << val add_substitute : t -> (string -> string) -> string -> unit >> add_substitute b f s appends the string pattern s at the end of buffer b with substitution. The substitution process looks for variable references in the pattern and substitutes each variable reference with its value, as obtained by applying the mapping f to the variable name. Inside the string pattern, a variable reference is a non-escaped $ immediately followed by a variable name, which is one of the following: - a non empty sequence of alphanumeric or _ characters, - an arbitrary sequence of characters enclosed by a pair of matching parentheses or curly brackets. An escaped $ character is a $ that immediately follows a backslash character; the two characters together stand for a plain $. << val add_buffer : t -> t -> unit >> add_buffer b1 b2 appends the current contents of buffer b2 at the end of buffer b1. b2 is not modified. << val add_channel : t -> in_channel -> int -> unit >> add_channel b ic n reads at most n characters from the input channel ic and stores them at the end of buffer b. Raises - End_of_file if the channel contains fewer than n characters. In this case, the characters are still added to the buffer, so as to avoid loss of data. - Invalid_argument if len < 0 or len > Sys.max_string_length. Buffers and Sequences ===================== << val to_seq : t -> char Seq.t >> Iterate on the buffer, in increasing order. The behavior is not specified if the buffer is modified during iteration. Since: 4.07 << val to_seqi : t -> (int * char) Seq.t >> Iterate on the buffer, in increasing order, yielding indices along chars. The behavior is not specified if the buffer is modified during iteration. Since: 4.07 << val add_seq : t -> char Seq.t -> unit >> Add chars to the buffer Since: 4.07 << val of_seq : char Seq.t -> t >> Create a buffer from the generator Since: 4.07 Binary encoding of integers =========================== The functions in this section append binary encodings of integers to buffers. Little-endian (resp. big-endian) encoding means that least (resp. most) significant bytes are stored first. Big-endian is also known as network byte order. Native-endian encoding is either little-endian or big-endian depending on Sys.big_endian[29.56]. 32-bit and 64-bit integers are represented by the int32 and int64 types, which can be interpreted either as signed or unsigned numbers. 8-bit and 16-bit integers are represented by the int type, which has more bits than the binary encoding. Functions that encode these values truncate their inputs to their least significant bytes. << val add_uint8 : t -> int -> unit >> add_uint8 b i appends a binary unsigned 8-bit integer i to b. Since: 4.08 << val add_int8 : t -> int -> unit >> add_int8 b i appends a binary signed 8-bit integer i to b. Since: 4.08 << val add_uint16_ne : t -> int -> unit >> add_uint16_ne b i appends a binary native-endian unsigned 16-bit integer i to b. Since: 4.08 << val add_uint16_be : t -> int -> unit >> add_uint16_be b i appends a binary big-endian unsigned 16-bit integer i to b. Since: 4.08 << val add_uint16_le : t -> int -> unit >> add_uint16_le b i appends a binary little-endian unsigned 16-bit integer i to b. Since: 4.08 << val add_int16_ne : t -> int -> unit >> add_int16_ne b i appends a binary native-endian signed 16-bit integer i to b. Since: 4.08 << val add_int16_be : t -> int -> unit >> add_int16_be b i appends a binary big-endian signed 16-bit integer i to b. Since: 4.08 << val add_int16_le : t -> int -> unit >> add_int16_le b i appends a binary little-endian signed 16-bit integer i to b. Since: 4.08 << val add_int32_ne : t -> int32 -> unit >> add_int32_ne b i appends a binary native-endian 32-bit integer i to b. Since: 4.08 << val add_int32_be : t -> int32 -> unit >> add_int32_be b i appends a binary big-endian 32-bit integer i to b. Since: 4.08 << val add_int32_le : t -> int32 -> unit >> add_int32_le b i appends a binary little-endian 32-bit integer i to b. Since: 4.08 << val add_int64_ne : t -> int64 -> unit >> add_int64_ne b i appends a binary native-endian 64-bit integer i to b. Since: 4.08 << val add_int64_be : t -> int64 -> unit >> add_int64_be b i appends a binary big-endian 64-bit integer i to b. Since: 4.08 << val add_int64_le : t -> int64 -> unit >> add_int64_ne b i appends a binary little-endian 64-bit integer i to b. Since: 4.08 29.8 Module Bytes : Byte sequence operations. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* A byte sequence is a mutable data structure that contains a fixed-length sequence of bytes. Each byte can be indexed in constant time for reading or writing. Given a byte sequence s of length l, we can access each of the l bytes of s via its index in the sequence. Indexes start at 0, and we will call an index valid in s if it falls within the range [0...l-1] (inclusive). A position is the point between two bytes or at the beginning or end of the sequence. We call a position valid in s if it falls within the range [0...l] (inclusive). Note that the byte at index n is between positions n and n+1. Two parameters start and len are said to designate a valid range of s if len >= 0 and start and start+len are valid positions in s. Byte sequences can be modified in place, for instance via the set and blit functions described below. See also strings (module String[29.54]), which are almost the same data structure, but cannot be modified in place. Bytes are represented by the OCaml type char. The labeled version of this module can be used as described in the StdLabels[29.53] module. Since: 4.02 << val length : bytes -> int >> Return the length (number of bytes) of the argument. << val get : bytes -> int -> char >> get s n returns the byte at index n in argument s. Raises Invalid_argument if n is not a valid index in s. << val set : bytes -> int -> char -> unit >> set s n c modifies s in place, replacing the byte at index n with c. Raises Invalid_argument if n is not a valid index in s. << val create : int -> bytes >> create n returns a new byte sequence of length n. The sequence is uninitialized and contains arbitrary bytes. Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val make : int -> char -> bytes >> make n c returns a new byte sequence of length n, filled with the byte c. Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val init : int -> (int -> char) -> bytes >> init n f returns a fresh byte sequence of length n, with character i initialized to the result of f i (in increasing index order). Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val empty : bytes >> A byte sequence of size 0. << val copy : bytes -> bytes >> Return a new byte sequence that contains the same bytes as the argument. << val of_string : string -> bytes >> Return a new byte sequence that contains the same bytes as the given string. << val to_string : bytes -> string >> Return a new string that contains the same bytes as the given byte sequence. << val sub : bytes -> int -> int -> bytes >> sub s pos len returns a new byte sequence of length len, containing the subsequence of s that starts at position pos and has length len. Raises Invalid_argument if pos and len do not designate a valid range of s. << val sub_string : bytes -> int -> int -> string >> Same as Bytes.sub[29.8] but return a string instead of a byte sequence. << val extend : bytes -> int -> int -> bytes >> extend s left right returns a new byte sequence that contains the bytes of s, with left uninitialized bytes prepended and right uninitialized bytes appended to it. If left or right is negative, then bytes are removed (instead of appended) from the corresponding side of s. Since: 4.05 in BytesLabels Raises Invalid_argument if the result length is negative or longer than Sys.max_string_length[29.56] bytes. << val fill : bytes -> int -> int -> char -> unit >> fill s pos len c modifies s in place, replacing len characters with c, starting at pos. Raises Invalid_argument if pos and len do not designate a valid range of s. << val blit : bytes -> int -> bytes -> int -> int -> unit >> blit src src_pos dst dst_pos len copies len bytes from byte sequence src, starting at index src_pos, to byte sequence dst, starting at index dst_pos. It works correctly even if src and dst are the same byte sequence, and the source and destination intervals overlap. Raises Invalid_argument if src_pos and len do not designate a valid range of src, or if dst_pos and len do not designate a valid range of dst. << val blit_string : string -> int -> bytes -> int -> int -> unit >> blit_string src src_pos dst dst_pos len copies len bytes from string src, starting at index src_pos, to byte sequence dst, starting at index dst_pos. Since: 4.05 in BytesLabels Raises Invalid_argument if src_pos and len do not designate a valid range of src, or if dst_pos and len do not designate a valid range of dst. << val concat : bytes -> bytes list -> bytes >> concat sep sl concatenates the list of byte sequences sl, inserting the separator byte sequence sep between each, and returns the result as a new byte sequence. Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val cat : bytes -> bytes -> bytes >> cat s1 s2 concatenates s1 and s2 and returns the result as a new byte sequence. Since: 4.05 in BytesLabels Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val iter : (char -> unit) -> bytes -> unit >> iter f s applies function f in turn to all the bytes of s. It is equivalent to f (get s 0); f (get s 1); ...; f (get s (length s - 1)); (). << val iteri : (int -> char -> unit) -> bytes -> unit >> Same as Bytes.iter[29.8], but the function is applied to the index of the byte as first argument and the byte itself as second argument. << val map : (char -> char) -> bytes -> bytes >> map f s applies function f in turn to all the bytes of s (in increasing index order) and stores the resulting bytes in a new sequence that is returned as the result. << val mapi : (int -> char -> char) -> bytes -> bytes >> mapi f s calls f with each character of s and its index (in increasing index order) and stores the resulting bytes in a new sequence that is returned as the result. << val fold_left : ('acc -> char -> 'acc) -> 'acc -> bytes -> 'acc >> fold_left f x s computes f (... (f (f x (get s 0)) (get s 1)) ...) (get s (n-1)), where n is the length of s. Since: 4.13 << val fold_right : (char -> 'acc -> 'acc) -> bytes -> 'acc -> 'acc >> fold_right f s x computes f (get s 0) (f (get s 1) ( ... (f (get s (n-1)) x) ...)), where n is the length of s. Since: 4.13 << val for_all : (char -> bool) -> bytes -> bool >> for_all p s checks if all characters in s satisfy the predicate p. Since: 4.13 << val exists : (char -> bool) -> bytes -> bool >> exists p s checks if at least one character of s satisfies the predicate p. Since: 4.13 << val trim : bytes -> bytes >> Return a copy of the argument, without leading and trailing whitespace. The bytes regarded as whitespace are the ASCII characters ' ', '\012', '\n', '\r', and '\t'. << val escaped : bytes -> bytes >> Return a copy of the argument, with special characters represented by escape sequences, following the lexical conventions of OCaml. All characters outside the ASCII printable range (32..126) are escaped, as well as backslash and double-quote. Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val index : bytes -> char -> int >> index s c returns the index of the first occurrence of byte c in s. Raises Not_found if c does not occur in s. << val index_opt : bytes -> char -> int option >> index_opt s c returns the index of the first occurrence of byte c in s or None if c does not occur in s. Since: 4.05 << val rindex : bytes -> char -> int >> rindex s c returns the index of the last occurrence of byte c in s. Raises Not_found if c does not occur in s. << val rindex_opt : bytes -> char -> int option >> rindex_opt s c returns the index of the last occurrence of byte c in s or None if c does not occur in s. Since: 4.05 << val index_from : bytes -> int -> char -> int >> index_from s i c returns the index of the first occurrence of byte c in s after position i. index s c is equivalent to index_from s 0 c. Raises - Invalid_argument if i is not a valid position in s. - Not_found if c does not occur in s after position i. << val index_from_opt : bytes -> int -> char -> int option >> index_from_opt s i c returns the index of the first occurrence of byte c in s after position i or None if c does not occur in s after position i. index_opt s c is equivalent to index_from_opt s 0 c. Since: 4.05 Raises Invalid_argument if i is not a valid position in s. << val rindex_from : bytes -> int -> char -> int >> rindex_from s i c returns the index of the last occurrence of byte c in s before position i+1. rindex s c is equivalent to rindex_from s (length s - 1) c. Raises - Invalid_argument if i+1 is not a valid position in s. - Not_found if c does not occur in s before position i+1. << val rindex_from_opt : bytes -> int -> char -> int option >> rindex_from_opt s i c returns the index of the last occurrence of byte c in s before position i+1 or None if c does not occur in s before position i+1. rindex_opt s c is equivalent to rindex_from s (length s - 1) c. Since: 4.05 Raises Invalid_argument if i+1 is not a valid position in s. << val contains : bytes -> char -> bool >> contains s c tests if byte c appears in s. << val contains_from : bytes -> int -> char -> bool >> contains_from s start c tests if byte c appears in s after position start. contains s c is equivalent to contains_from s 0 c. Raises Invalid_argument if start is not a valid position in s. << val rcontains_from : bytes -> int -> char -> bool >> rcontains_from s stop c tests if byte c appears in s before position stop+1. Raises Invalid_argument if stop < 0 or stop+1 is not a valid position in s. << val uppercase_ascii : bytes -> bytes >> Return a copy of the argument, with all lowercase letters translated to uppercase, using the US-ASCII character set. Since: 4.03 (4.05 in BytesLabels) << val lowercase_ascii : bytes -> bytes >> Return a copy of the argument, with all uppercase letters translated to lowercase, using the US-ASCII character set. Since: 4.03 (4.05 in BytesLabels) << val capitalize_ascii : bytes -> bytes >> Return a copy of the argument, with the first character set to uppercase, using the US-ASCII character set. Since: 4.03 (4.05 in BytesLabels) << val uncapitalize_ascii : bytes -> bytes >> Return a copy of the argument, with the first character set to lowercase, using the US-ASCII character set. Since: 4.03 (4.05 in BytesLabels) << type t = bytes >> An alias for the type of byte sequences. << val compare : t -> t -> int >> The comparison function for byte sequences, with the same specification as compare[28.2]. Along with the type t, this function compare allows the module Bytes to be passed as argument to the functors Set.Make[29.50] and Map.Make[29.34]. << val equal : t -> t -> bool >> The equality function for byte sequences. Since: 4.03 (4.05 in BytesLabels) << val starts_with : prefix:bytes -> bytes -> bool >> starts_with ~prefix s is true if and only if s starts with prefix. Since: 4.13 << val ends_with : suffix:bytes -> bytes -> bool >> ends_with ~suffix s is true if and only if s ends with suffix. Since: 4.13 Unsafe conversions (for advanced users) ======================================= This section describes unsafe, low-level conversion functions between bytes and string. They do not copy the internal data; used improperly, they can break the immutability invariant on strings provided by the -safe-string option. They are available for expert library authors, but for most purposes you should use the always-correct Bytes.to_string[29.8] and Bytes.of_string[29.8] instead. << val unsafe_to_string : bytes -> string >> Unsafely convert a byte sequence into a string. To reason about the use of unsafe_to_string, it is convenient to consider an "ownership" discipline. A piece of code that manipulates some data "owns" it; there are several disjoint ownership modes, including: - Unique ownership: the data may be accessed and mutated - Shared ownership: the data has several owners, that may only access it, not mutate it. Unique ownership is linear: passing the data to another piece of code means giving up ownership (we cannot write the data again). A unique owner may decide to make the data shared (giving up mutation rights on it), but shared data may not become uniquely-owned again. unsafe_to_string s can only be used when the caller owns the byte sequence s – either uniquely or as shared immutable data. The caller gives up ownership of s, and gains ownership of the returned string. There are two valid use-cases that respect this ownership discipline: 1. Creating a string by initializing and mutating a byte sequence that is never changed after initialization is performed. << let string_init len f : string = let s = Bytes.create len in for i = 0 to len - 1 do Bytes.set s i (f i) done; Bytes.unsafe_to_string s >> This function is safe because the byte sequence s will never be accessed or mutated after unsafe_to_string is called. The string_init code gives up ownership of s, and returns the ownership of the resulting string to its caller. Note that it would be unsafe if s was passed as an additional parameter to the function f as it could escape this way and be mutated in the future – string_init would give up ownership of s to pass it to f, and could not call unsafe_to_string safely. We have provided the String.init[29.54], String.map[29.54] and String.mapi[29.54] functions to cover most cases of building new strings. You should prefer those over to_string or unsafe_to_string whenever applicable. 2. Temporarily giving ownership of a byte sequence to a function that expects a uniquely owned string and returns ownership back, so that we can mutate the sequence again after the call ended. << let bytes_length (s : bytes) = String.length (Bytes.unsafe_to_string s) >> In this use-case, we do not promise that s will never be mutated after the call to bytes_length s. The String.length[29.54] function temporarily borrows unique ownership of the byte sequence (and sees it as a string), but returns this ownership back to the caller, which may assume that s is still a valid byte sequence after the call. Note that this is only correct because we know that String.length[29.54] does not capture its argument – it could escape by a side-channel such as a memoization combinator. The caller may not mutate s while the string is borrowed (it has temporarily given up ownership). This affects concurrent programs, but also higher-order functions: if String.length[29.54] returned a closure to be called later, s should not be mutated until this closure is fully applied and returns ownership. << val unsafe_of_string : string -> bytes >> Unsafely convert a shared string to a byte sequence that should not be mutated. The same ownership discipline that makes unsafe_to_string correct applies to unsafe_of_string: you may use it if you were the owner of the string value, and you will own the return bytes in the same mode. In practice, unique ownership of string values is extremely difficult to reason about correctly. You should always assume strings are shared, never uniquely owned. For example, string literals are implicitly shared by the compiler, so you never uniquely own them. << let incorrect = Bytes.unsafe_of_string "hello" let s = Bytes.of_string "hello" >> The first declaration is incorrect, because the string literal "hello" could be shared by the compiler with other parts of the program, and mutating incorrect is a bug. You must always use the second version, which performs a copy and is thus correct. Assuming unique ownership of strings that are not string literals, but are (partly) built from string literals, is also incorrect. For example, mutating unsafe_of_string ("foo" ^ s) could mutate the shared string "foo" – assuming a rope-like representation of strings. More generally, functions operating on strings will assume shared ownership, they do not preserve unique ownership. It is thus incorrect to assume unique ownership of the result of unsafe_of_string. The only case we have reasonable confidence is safe is if the produced bytes is shared – used as an immutable byte sequence. This is possibly useful for incremental migration of low-level programs that manipulate immutable sequences of bytes (for example Marshal.from_bytes[29.35]) and previously used the string type for this purpose. << val split_on_char : char -> bytes -> bytes list >> split_on_char sep s returns the list of all (possibly empty) subsequences of s that are delimited by the sep character. If s is empty, the result is the singleton list [empty]. The function’s output is specified by the following invariants: - The list is not empty. - Concatenating its elements using sep as a separator returns a byte sequence equal to the input (Bytes.concat (Bytes.make 1 sep) (Bytes.split_on_char sep s) = s). - No byte sequence in the result contains the sep character. Since: 4.13 Iterators ========= << val to_seq : t -> char Seq.t >> Iterate on the string, in increasing index order. Modifications of the string during iteration will be reflected in the sequence. Since: 4.07 << val to_seqi : t -> (int * char) Seq.t >> Iterate on the string, in increasing order, yielding indices along chars Since: 4.07 << val of_seq : char Seq.t -> t >> Create a string from the generator Since: 4.07 UTF codecs and validations ========================== UTF-8 ----- << val get_utf_8_uchar : t -> int -> Uchar.utf_decode >> get_utf_8_uchar b i decodes an UTF-8 character at index i in b. << val set_utf_8_uchar : t -> int -> Uchar.t -> int >> set_utf_8_uchar b i u UTF-8 encodes u at index i in b and returns the number of bytes n that were written starting at i. If n is 0 there was not enough space to encode u at i and b was left untouched. Otherwise a new character can be encoded at i + n. << val is_valid_utf_8 : t -> bool >> is_valid_utf_8 b is true if and only if b contains valid UTF-8 data. UTF-16BE -------- << val get_utf_16be_uchar : t -> int -> Uchar.utf_decode >> get_utf_16be_uchar b i decodes an UTF-16BE character at index i in b. << val set_utf_16be_uchar : t -> int -> Uchar.t -> int >> set_utf_16be_uchar b i u UTF-16BE encodes u at index i in b and returns the number of bytes n that were written starting at i. If n is 0 there was not enough space to encode u at i and b was left untouched. Otherwise a new character can be encoded at i + n. << val is_valid_utf_16be : t -> bool >> is_valid_utf_16be b is true if and only if b contains valid UTF-16BE data. UTF-16LE -------- << val get_utf_16le_uchar : t -> int -> Uchar.utf_decode >> get_utf_16le_uchar b i decodes an UTF-16LE character at index i in b. << val set_utf_16le_uchar : t -> int -> Uchar.t -> int >> set_utf_16le_uchar b i u UTF-16LE encodes u at index i in b and returns the number of bytes n that were written starting at i. If n is 0 there was not enough space to encode u at i and b was left untouched. Otherwise a new character can be encoded at i + n. << val is_valid_utf_16le : t -> bool >> is_valid_utf_16le b is true if and only if b contains valid UTF-16LE data. Binary encoding/decoding of integers ==================================== The functions in this section binary encode and decode integers to and from byte sequences. All following functions raise Invalid_argument if the space needed at index i to decode or encode the integer is not available. Little-endian (resp. big-endian) encoding means that least (resp. most) significant bytes are stored first. Big-endian is also known as network byte order. Native-endian encoding is either little-endian or big-endian depending on Sys.big_endian[29.56]. 32-bit and 64-bit integers are represented by the int32 and int64 types, which can be interpreted either as signed or unsigned numbers. 8-bit and 16-bit integers are represented by the int type, which has more bits than the binary encoding. These extra bits are handled as follows: - Functions that decode signed (resp. unsigned) 8-bit or 16-bit integers represented by int values sign-extend (resp. zero-extend) their result. - Functions that encode 8-bit or 16-bit integers represented by int values truncate their input to their least significant bytes. << val get_uint8 : bytes -> int -> int >> get_uint8 b i is b’s unsigned 8-bit integer starting at byte index i. Since: 4.08 << val get_int8 : bytes -> int -> int >> get_int8 b i is b’s signed 8-bit integer starting at byte index i. Since: 4.08 << val get_uint16_ne : bytes -> int -> int >> get_uint16_ne b i is b’s native-endian unsigned 16-bit integer starting at byte index i. Since: 4.08 << val get_uint16_be : bytes -> int -> int >> get_uint16_be b i is b’s big-endian unsigned 16-bit integer starting at byte index i. Since: 4.08 << val get_uint16_le : bytes -> int -> int >> get_uint16_le b i is b’s little-endian unsigned 16-bit integer starting at byte index i. Since: 4.08 << val get_int16_ne : bytes -> int -> int >> get_int16_ne b i is b’s native-endian signed 16-bit integer starting at byte index i. Since: 4.08 << val get_int16_be : bytes -> int -> int >> get_int16_be b i is b’s big-endian signed 16-bit integer starting at byte index i. Since: 4.08 << val get_int16_le : bytes -> int -> int >> get_int16_le b i is b’s little-endian signed 16-bit integer starting at byte index i. Since: 4.08 << val get_int32_ne : bytes -> int -> int32 >> get_int32_ne b i is b’s native-endian 32-bit integer starting at byte index i. Since: 4.08 << val get_int32_be : bytes -> int -> int32 >> get_int32_be b i is b’s big-endian 32-bit integer starting at byte index i. Since: 4.08 << val get_int32_le : bytes -> int -> int32 >> get_int32_le b i is b’s little-endian 32-bit integer starting at byte index i. Since: 4.08 << val get_int64_ne : bytes -> int -> int64 >> get_int64_ne b i is b’s native-endian 64-bit integer starting at byte index i. Since: 4.08 << val get_int64_be : bytes -> int -> int64 >> get_int64_be b i is b’s big-endian 64-bit integer starting at byte index i. Since: 4.08 << val get_int64_le : bytes -> int -> int64 >> get_int64_le b i is b’s little-endian 64-bit integer starting at byte index i. Since: 4.08 << val set_uint8 : bytes -> int -> int -> unit >> set_uint8 b i v sets b’s unsigned 8-bit integer starting at byte index i to v. Since: 4.08 << val set_int8 : bytes -> int -> int -> unit >> set_int8 b i v sets b’s signed 8-bit integer starting at byte index i to v. Since: 4.08 << val set_uint16_ne : bytes -> int -> int -> unit >> set_uint16_ne b i v sets b’s native-endian unsigned 16-bit integer starting at byte index i to v. Since: 4.08 << val set_uint16_be : bytes -> int -> int -> unit >> set_uint16_be b i v sets b’s big-endian unsigned 16-bit integer starting at byte index i to v. Since: 4.08 << val set_uint16_le : bytes -> int -> int -> unit >> set_uint16_le b i v sets b’s little-endian unsigned 16-bit integer starting at byte index i to v. Since: 4.08 << val set_int16_ne : bytes -> int -> int -> unit >> set_int16_ne b i v sets b’s native-endian signed 16-bit integer starting at byte index i to v. Since: 4.08 << val set_int16_be : bytes -> int -> int -> unit >> set_int16_be b i v sets b’s big-endian signed 16-bit integer starting at byte index i to v. Since: 4.08 << val set_int16_le : bytes -> int -> int -> unit >> set_int16_le b i v sets b’s little-endian signed 16-bit integer starting at byte index i to v. Since: 4.08 << val set_int32_ne : bytes -> int -> int32 -> unit >> set_int32_ne b i v sets b’s native-endian 32-bit integer starting at byte index i to v. Since: 4.08 << val set_int32_be : bytes -> int -> int32 -> unit >> set_int32_be b i v sets b’s big-endian 32-bit integer starting at byte index i to v. Since: 4.08 << val set_int32_le : bytes -> int -> int32 -> unit >> set_int32_le b i v sets b’s little-endian 32-bit integer starting at byte index i to v. Since: 4.08 << val set_int64_ne : bytes -> int -> int64 -> unit >> set_int64_ne b i v sets b’s native-endian 64-bit integer starting at byte index i to v. Since: 4.08 << val set_int64_be : bytes -> int -> int64 -> unit >> set_int64_be b i v sets b’s big-endian 64-bit integer starting at byte index i to v. Since: 4.08 << val set_int64_le : bytes -> int -> int64 -> unit >> set_int64_le b i v sets b’s little-endian 64-bit integer starting at byte index i to v. Since: 4.08 Byte sequences and concurrency safety ===================================== Care must be taken when concurrently accessing byte sequences from multiple domains: accessing a byte sequence will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results. Atomicity --------- Every byte sequence operation that accesses more than one byte is not atomic. This includes iteration and scanning. For example, consider the following program: << let size = 100_000_000 let b = Bytes.make size ' ' let update b f () = Bytes.iteri (fun i x -> Bytes.set b i (Char.chr (f (Char.code x)))) b let d1 = Domain.spawn (update b (fun x -> x + 1)) let d2 = Domain.spawn (update b (fun x -> 2 * x + 1)) let () = Domain.join d1; Domain.join d2 >> the bytes sequence b may contain a non-deterministic mixture of '!', 'A', 'B', and 'C' values. After executing this code, each byte of the sequence b is either '!', 'A', 'B', or 'C'. If atomicity is required, then the user must implement their own synchronization (for example, using Mutex.t[29.37]). Data races ---------- If two domains only access disjoint parts of a byte sequence, then the observed behaviour is the equivalent to some sequential interleaving of the operations from the two domains. A data race is said to occur when two domains access the same byte without synchronization and at least one of the accesses is a write. In the absence of data races, the observed behaviour is equivalent to some sequential interleaving of the operations from different domains. Whenever possible, data races should be avoided by using synchronization to mediate the accesses to the elements of the sequence. Indeed, in the presence of data races, programs will not crash but the observed behaviour may not be equivalent to any sequential interleaving of operations from different domains. Nevertheless, even in the presence of data races, a read operation will return the value of some prior write to that location. Mixed-size accesses -------------------- Another subtle point is that if a data race involves mixed-size writes and reads to the same location, the order in which those writes and reads are observed by domains is not specified. For instance, the following code write sequentially a 32-bit integer and a char to the same index << let b = Bytes.make 10 '\000' let d1 = Domain.spawn (fun () -> Bytes.set_int32_ne b 0 100; b.[0] <- 'd' ) >> In this situation, a domain that observes the write of ’d’ to b.0 is not guaranteed to also observe the write to indices 1, 2, or 3. 29.9 Module BytesLabels : Byte sequence operations. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* A byte sequence is a mutable data structure that contains a fixed-length sequence of bytes. Each byte can be indexed in constant time for reading or writing. Given a byte sequence s of length l, we can access each of the l bytes of s via its index in the sequence. Indexes start at 0, and we will call an index valid in s if it falls within the range [0...l-1] (inclusive). A position is the point between two bytes or at the beginning or end of the sequence. We call a position valid in s if it falls within the range [0...l] (inclusive). Note that the byte at index n is between positions n and n+1. Two parameters start and len are said to designate a valid range of s if len >= 0 and start and start+len are valid positions in s. Byte sequences can be modified in place, for instance via the set and blit functions described below. See also strings (module String[29.54]), which are almost the same data structure, but cannot be modified in place. Bytes are represented by the OCaml type char. The labeled version of this module can be used as described in the StdLabels[29.53] module. Since: 4.02 << val length : bytes -> int >> Return the length (number of bytes) of the argument. << val get : bytes -> int -> char >> get s n returns the byte at index n in argument s. Raises Invalid_argument if n is not a valid index in s. << val set : bytes -> int -> char -> unit >> set s n c modifies s in place, replacing the byte at index n with c. Raises Invalid_argument if n is not a valid index in s. << val create : int -> bytes >> create n returns a new byte sequence of length n. The sequence is uninitialized and contains arbitrary bytes. Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val make : int -> char -> bytes >> make n c returns a new byte sequence of length n, filled with the byte c. Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val init : int -> f:(int -> char) -> bytes >> init n f returns a fresh byte sequence of length n, with character i initialized to the result of f i (in increasing index order). Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val empty : bytes >> A byte sequence of size 0. << val copy : bytes -> bytes >> Return a new byte sequence that contains the same bytes as the argument. << val of_string : string -> bytes >> Return a new byte sequence that contains the same bytes as the given string. << val to_string : bytes -> string >> Return a new string that contains the same bytes as the given byte sequence. << val sub : bytes -> pos:int -> len:int -> bytes >> sub s ~pos ~len returns a new byte sequence of length len, containing the subsequence of s that starts at position pos and has length len. Raises Invalid_argument if pos and len do not designate a valid range of s. << val sub_string : bytes -> pos:int -> len:int -> string >> Same as BytesLabels.sub[29.9] but return a string instead of a byte sequence. << val extend : bytes -> left:int -> right:int -> bytes >> extend s ~left ~right returns a new byte sequence that contains the bytes of s, with left uninitialized bytes prepended and right uninitialized bytes appended to it. If left or right is negative, then bytes are removed (instead of appended) from the corresponding side of s. Since: 4.05 in BytesLabels Raises Invalid_argument if the result length is negative or longer than Sys.max_string_length[29.56] bytes. << val fill : bytes -> pos:int -> len:int -> char -> unit >> fill s ~pos ~len c modifies s in place, replacing len characters with c, starting at pos. Raises Invalid_argument if pos and len do not designate a valid range of s. << val blit : src:bytes -> src_pos:int -> dst:bytes -> dst_pos:int -> len:int -> unit >> blit ~src ~src_pos ~dst ~dst_pos ~len copies len bytes from byte sequence src, starting at index src_pos, to byte sequence dst, starting at index dst_pos. It works correctly even if src and dst are the same byte sequence, and the source and destination intervals overlap. Raises Invalid_argument if src_pos and len do not designate a valid range of src, or if dst_pos and len do not designate a valid range of dst. << val blit_string : src:string -> src_pos:int -> dst:bytes -> dst_pos:int -> len:int -> unit >> blit_string ~src ~src_pos ~dst ~dst_pos ~len copies len bytes from string src, starting at index src_pos, to byte sequence dst, starting at index dst_pos. Since: 4.05 in BytesLabels Raises Invalid_argument if src_pos and len do not designate a valid range of src, or if dst_pos and len do not designate a valid range of dst. << val concat : sep:bytes -> bytes list -> bytes >> concat ~sep sl concatenates the list of byte sequences sl, inserting the separator byte sequence sep between each, and returns the result as a new byte sequence. Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val cat : bytes -> bytes -> bytes >> cat s1 s2 concatenates s1 and s2 and returns the result as a new byte sequence. Since: 4.05 in BytesLabels Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val iter : f:(char -> unit) -> bytes -> unit >> iter ~f s applies function f in turn to all the bytes of s. It is equivalent to f (get s 0); f (get s 1); ...; f (get s (length s - 1)); (). << val iteri : f:(int -> char -> unit) -> bytes -> unit >> Same as BytesLabels.iter[29.9], but the function is applied to the index of the byte as first argument and the byte itself as second argument. << val map : f:(char -> char) -> bytes -> bytes >> map ~f s applies function f in turn to all the bytes of s (in increasing index order) and stores the resulting bytes in a new sequence that is returned as the result. << val mapi : f:(int -> char -> char) -> bytes -> bytes >> mapi ~f s calls f with each character of s and its index (in increasing index order) and stores the resulting bytes in a new sequence that is returned as the result. << val fold_left : f:('acc -> char -> 'acc) -> init:'acc -> bytes -> 'acc >> fold_left f x s computes f (... (f (f x (get s 0)) (get s 1)) ...) (get s (n-1)), where n is the length of s. Since: 4.13 << val fold_right : f:(char -> 'acc -> 'acc) -> bytes -> init:'acc -> 'acc >> fold_right f s x computes f (get s 0) (f (get s 1) ( ... (f (get s (n-1)) x) ...)), where n is the length of s. Since: 4.13 << val for_all : f:(char -> bool) -> bytes -> bool >> for_all p s checks if all characters in s satisfy the predicate p. Since: 4.13 << val exists : f:(char -> bool) -> bytes -> bool >> exists p s checks if at least one character of s satisfies the predicate p. Since: 4.13 << val trim : bytes -> bytes >> Return a copy of the argument, without leading and trailing whitespace. The bytes regarded as whitespace are the ASCII characters ' ', '\012', '\n', '\r', and '\t'. << val escaped : bytes -> bytes >> Return a copy of the argument, with special characters represented by escape sequences, following the lexical conventions of OCaml. All characters outside the ASCII printable range (32..126) are escaped, as well as backslash and double-quote. Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val index : bytes -> char -> int >> index s c returns the index of the first occurrence of byte c in s. Raises Not_found if c does not occur in s. << val index_opt : bytes -> char -> int option >> index_opt s c returns the index of the first occurrence of byte c in s or None if c does not occur in s. Since: 4.05 << val rindex : bytes -> char -> int >> rindex s c returns the index of the last occurrence of byte c in s. Raises Not_found if c does not occur in s. << val rindex_opt : bytes -> char -> int option >> rindex_opt s c returns the index of the last occurrence of byte c in s or None if c does not occur in s. Since: 4.05 << val index_from : bytes -> int -> char -> int >> index_from s i c returns the index of the first occurrence of byte c in s after position i. index s c is equivalent to index_from s 0 c. Raises - Invalid_argument if i is not a valid position in s. - Not_found if c does not occur in s after position i. << val index_from_opt : bytes -> int -> char -> int option >> index_from_opt s i c returns the index of the first occurrence of byte c in s after position i or None if c does not occur in s after position i. index_opt s c is equivalent to index_from_opt s 0 c. Since: 4.05 Raises Invalid_argument if i is not a valid position in s. << val rindex_from : bytes -> int -> char -> int >> rindex_from s i c returns the index of the last occurrence of byte c in s before position i+1. rindex s c is equivalent to rindex_from s (length s - 1) c. Raises - Invalid_argument if i+1 is not a valid position in s. - Not_found if c does not occur in s before position i+1. << val rindex_from_opt : bytes -> int -> char -> int option >> rindex_from_opt s i c returns the index of the last occurrence of byte c in s before position i+1 or None if c does not occur in s before position i+1. rindex_opt s c is equivalent to rindex_from s (length s - 1) c. Since: 4.05 Raises Invalid_argument if i+1 is not a valid position in s. << val contains : bytes -> char -> bool >> contains s c tests if byte c appears in s. << val contains_from : bytes -> int -> char -> bool >> contains_from s start c tests if byte c appears in s after position start. contains s c is equivalent to contains_from s 0 c. Raises Invalid_argument if start is not a valid position in s. << val rcontains_from : bytes -> int -> char -> bool >> rcontains_from s stop c tests if byte c appears in s before position stop+1. Raises Invalid_argument if stop < 0 or stop+1 is not a valid position in s. << val uppercase_ascii : bytes -> bytes >> Return a copy of the argument, with all lowercase letters translated to uppercase, using the US-ASCII character set. Since: 4.05 << val lowercase_ascii : bytes -> bytes >> Return a copy of the argument, with all uppercase letters translated to lowercase, using the US-ASCII character set. Since: 4.05 << val capitalize_ascii : bytes -> bytes >> Return a copy of the argument, with the first character set to uppercase, using the US-ASCII character set. Since: 4.05 << val uncapitalize_ascii : bytes -> bytes >> Return a copy of the argument, with the first character set to lowercase, using the US-ASCII character set. Since: 4.05 << type t = bytes >> An alias for the type of byte sequences. << val compare : t -> t -> int >> The comparison function for byte sequences, with the same specification as compare[28.2]. Along with the type t, this function compare allows the module Bytes to be passed as argument to the functors Set.Make[29.50] and Map.Make[29.34]. << val equal : t -> t -> bool >> The equality function for byte sequences. Since: 4.05 << val starts_with : prefix:bytes -> bytes -> bool >> starts_with ~prefix s is true if and only if s starts with prefix. Since: 4.13 << val ends_with : suffix:bytes -> bytes -> bool >> ends_with ~suffix s is true if and only if s ends with suffix. Since: 4.13 Unsafe conversions (for advanced users) ======================================= This section describes unsafe, low-level conversion functions between bytes and string. They do not copy the internal data; used improperly, they can break the immutability invariant on strings provided by the -safe-string option. They are available for expert library authors, but for most purposes you should use the always-correct BytesLabels.to_string[29.9] and BytesLabels.of_string[29.9] instead. << val unsafe_to_string : bytes -> string >> Unsafely convert a byte sequence into a string. To reason about the use of unsafe_to_string, it is convenient to consider an "ownership" discipline. A piece of code that manipulates some data "owns" it; there are several disjoint ownership modes, including: - Unique ownership: the data may be accessed and mutated - Shared ownership: the data has several owners, that may only access it, not mutate it. Unique ownership is linear: passing the data to another piece of code means giving up ownership (we cannot write the data again). A unique owner may decide to make the data shared (giving up mutation rights on it), but shared data may not become uniquely-owned again. unsafe_to_string s can only be used when the caller owns the byte sequence s – either uniquely or as shared immutable data. The caller gives up ownership of s, and gains ownership of the returned string. There are two valid use-cases that respect this ownership discipline: 1. Creating a string by initializing and mutating a byte sequence that is never changed after initialization is performed. << let string_init len f : string = let s = Bytes.create len in for i = 0 to len - 1 do Bytes.set s i (f i) done; Bytes.unsafe_to_string s >> This function is safe because the byte sequence s will never be accessed or mutated after unsafe_to_string is called. The string_init code gives up ownership of s, and returns the ownership of the resulting string to its caller. Note that it would be unsafe if s was passed as an additional parameter to the function f as it could escape this way and be mutated in the future – string_init would give up ownership of s to pass it to f, and could not call unsafe_to_string safely. We have provided the String.init[29.54], String.map[29.54] and String.mapi[29.54] functions to cover most cases of building new strings. You should prefer those over to_string or unsafe_to_string whenever applicable. 2. Temporarily giving ownership of a byte sequence to a function that expects a uniquely owned string and returns ownership back, so that we can mutate the sequence again after the call ended. << let bytes_length (s : bytes) = String.length (Bytes.unsafe_to_string s) >> In this use-case, we do not promise that s will never be mutated after the call to bytes_length s. The String.length[29.54] function temporarily borrows unique ownership of the byte sequence (and sees it as a string), but returns this ownership back to the caller, which may assume that s is still a valid byte sequence after the call. Note that this is only correct because we know that String.length[29.54] does not capture its argument – it could escape by a side-channel such as a memoization combinator. The caller may not mutate s while the string is borrowed (it has temporarily given up ownership). This affects concurrent programs, but also higher-order functions: if String.length[29.54] returned a closure to be called later, s should not be mutated until this closure is fully applied and returns ownership. << val unsafe_of_string : string -> bytes >> Unsafely convert a shared string to a byte sequence that should not be mutated. The same ownership discipline that makes unsafe_to_string correct applies to unsafe_of_string: you may use it if you were the owner of the string value, and you will own the return bytes in the same mode. In practice, unique ownership of string values is extremely difficult to reason about correctly. You should always assume strings are shared, never uniquely owned. For example, string literals are implicitly shared by the compiler, so you never uniquely own them. << let incorrect = Bytes.unsafe_of_string "hello" let s = Bytes.of_string "hello" >> The first declaration is incorrect, because the string literal "hello" could be shared by the compiler with other parts of the program, and mutating incorrect is a bug. You must always use the second version, which performs a copy and is thus correct. Assuming unique ownership of strings that are not string literals, but are (partly) built from string literals, is also incorrect. For example, mutating unsafe_of_string ("foo" ^ s) could mutate the shared string "foo" – assuming a rope-like representation of strings. More generally, functions operating on strings will assume shared ownership, they do not preserve unique ownership. It is thus incorrect to assume unique ownership of the result of unsafe_of_string. The only case we have reasonable confidence is safe is if the produced bytes is shared – used as an immutable byte sequence. This is possibly useful for incremental migration of low-level programs that manipulate immutable sequences of bytes (for example Marshal.from_bytes[29.35]) and previously used the string type for this purpose. << val split_on_char : sep:char -> bytes -> bytes list >> split_on_char sep s returns the list of all (possibly empty) subsequences of s that are delimited by the sep character. If s is empty, the result is the singleton list [empty]. The function’s output is specified by the following invariants: - The list is not empty. - Concatenating its elements using sep as a separator returns a byte sequence equal to the input (Bytes.concat (Bytes.make 1 sep) (Bytes.split_on_char sep s) = s). - No byte sequence in the result contains the sep character. Since: 4.13 Iterators ========= << val to_seq : t -> char Seq.t >> Iterate on the string, in increasing index order. Modifications of the string during iteration will be reflected in the sequence. Since: 4.07 << val to_seqi : t -> (int * char) Seq.t >> Iterate on the string, in increasing order, yielding indices along chars Since: 4.07 << val of_seq : char Seq.t -> t >> Create a string from the generator Since: 4.07 UTF codecs and validations ========================== UTF-8 ----- << val get_utf_8_uchar : t -> int -> Uchar.utf_decode >> get_utf_8_uchar b i decodes an UTF-8 character at index i in b. << val set_utf_8_uchar : t -> int -> Uchar.t -> int >> set_utf_8_uchar b i u UTF-8 encodes u at index i in b and returns the number of bytes n that were written starting at i. If n is 0 there was not enough space to encode u at i and b was left untouched. Otherwise a new character can be encoded at i + n. << val is_valid_utf_8 : t -> bool >> is_valid_utf_8 b is true if and only if b contains valid UTF-8 data. UTF-16BE -------- << val get_utf_16be_uchar : t -> int -> Uchar.utf_decode >> get_utf_16be_uchar b i decodes an UTF-16BE character at index i in b. << val set_utf_16be_uchar : t -> int -> Uchar.t -> int >> set_utf_16be_uchar b i u UTF-16BE encodes u at index i in b and returns the number of bytes n that were written starting at i. If n is 0 there was not enough space to encode u at i and b was left untouched. Otherwise a new character can be encoded at i + n. << val is_valid_utf_16be : t -> bool >> is_valid_utf_16be b is true if and only if b contains valid UTF-16BE data. UTF-16LE -------- << val get_utf_16le_uchar : t -> int -> Uchar.utf_decode >> get_utf_16le_uchar b i decodes an UTF-16LE character at index i in b. << val set_utf_16le_uchar : t -> int -> Uchar.t -> int >> set_utf_16le_uchar b i u UTF-16LE encodes u at index i in b and returns the number of bytes n that were written starting at i. If n is 0 there was not enough space to encode u at i and b was left untouched. Otherwise a new character can be encoded at i + n. << val is_valid_utf_16le : t -> bool >> is_valid_utf_16le b is true if and only if b contains valid UTF-16LE data. Binary encoding/decoding of integers ==================================== The functions in this section binary encode and decode integers to and from byte sequences. All following functions raise Invalid_argument if the space needed at index i to decode or encode the integer is not available. Little-endian (resp. big-endian) encoding means that least (resp. most) significant bytes are stored first. Big-endian is also known as network byte order. Native-endian encoding is either little-endian or big-endian depending on Sys.big_endian[29.56]. 32-bit and 64-bit integers are represented by the int32 and int64 types, which can be interpreted either as signed or unsigned numbers. 8-bit and 16-bit integers are represented by the int type, which has more bits than the binary encoding. These extra bits are handled as follows: - Functions that decode signed (resp. unsigned) 8-bit or 16-bit integers represented by int values sign-extend (resp. zero-extend) their result. - Functions that encode 8-bit or 16-bit integers represented by int values truncate their input to their least significant bytes. << val get_uint8 : bytes -> int -> int >> get_uint8 b i is b’s unsigned 8-bit integer starting at byte index i. Since: 4.08 << val get_int8 : bytes -> int -> int >> get_int8 b i is b’s signed 8-bit integer starting at byte index i. Since: 4.08 << val get_uint16_ne : bytes -> int -> int >> get_uint16_ne b i is b’s native-endian unsigned 16-bit integer starting at byte index i. Since: 4.08 << val get_uint16_be : bytes -> int -> int >> get_uint16_be b i is b’s big-endian unsigned 16-bit integer starting at byte index i. Since: 4.08 << val get_uint16_le : bytes -> int -> int >> get_uint16_le b i is b’s little-endian unsigned 16-bit integer starting at byte index i. Since: 4.08 << val get_int16_ne : bytes -> int -> int >> get_int16_ne b i is b’s native-endian signed 16-bit integer starting at byte index i. Since: 4.08 << val get_int16_be : bytes -> int -> int >> get_int16_be b i is b’s big-endian signed 16-bit integer starting at byte index i. Since: 4.08 << val get_int16_le : bytes -> int -> int >> get_int16_le b i is b’s little-endian signed 16-bit integer starting at byte index i. Since: 4.08 << val get_int32_ne : bytes -> int -> int32 >> get_int32_ne b i is b’s native-endian 32-bit integer starting at byte index i. Since: 4.08 << val get_int32_be : bytes -> int -> int32 >> get_int32_be b i is b’s big-endian 32-bit integer starting at byte index i. Since: 4.08 << val get_int32_le : bytes -> int -> int32 >> get_int32_le b i is b’s little-endian 32-bit integer starting at byte index i. Since: 4.08 << val get_int64_ne : bytes -> int -> int64 >> get_int64_ne b i is b’s native-endian 64-bit integer starting at byte index i. Since: 4.08 << val get_int64_be : bytes -> int -> int64 >> get_int64_be b i is b’s big-endian 64-bit integer starting at byte index i. Since: 4.08 << val get_int64_le : bytes -> int -> int64 >> get_int64_le b i is b’s little-endian 64-bit integer starting at byte index i. Since: 4.08 << val set_uint8 : bytes -> int -> int -> unit >> set_uint8 b i v sets b’s unsigned 8-bit integer starting at byte index i to v. Since: 4.08 << val set_int8 : bytes -> int -> int -> unit >> set_int8 b i v sets b’s signed 8-bit integer starting at byte index i to v. Since: 4.08 << val set_uint16_ne : bytes -> int -> int -> unit >> set_uint16_ne b i v sets b’s native-endian unsigned 16-bit integer starting at byte index i to v. Since: 4.08 << val set_uint16_be : bytes -> int -> int -> unit >> set_uint16_be b i v sets b’s big-endian unsigned 16-bit integer starting at byte index i to v. Since: 4.08 << val set_uint16_le : bytes -> int -> int -> unit >> set_uint16_le b i v sets b’s little-endian unsigned 16-bit integer starting at byte index i to v. Since: 4.08 << val set_int16_ne : bytes -> int -> int -> unit >> set_int16_ne b i v sets b’s native-endian signed 16-bit integer starting at byte index i to v. Since: 4.08 << val set_int16_be : bytes -> int -> int -> unit >> set_int16_be b i v sets b’s big-endian signed 16-bit integer starting at byte index i to v. Since: 4.08 << val set_int16_le : bytes -> int -> int -> unit >> set_int16_le b i v sets b’s little-endian signed 16-bit integer starting at byte index i to v. Since: 4.08 << val set_int32_ne : bytes -> int -> int32 -> unit >> set_int32_ne b i v sets b’s native-endian 32-bit integer starting at byte index i to v. Since: 4.08 << val set_int32_be : bytes -> int -> int32 -> unit >> set_int32_be b i v sets b’s big-endian 32-bit integer starting at byte index i to v. Since: 4.08 << val set_int32_le : bytes -> int -> int32 -> unit >> set_int32_le b i v sets b’s little-endian 32-bit integer starting at byte index i to v. Since: 4.08 << val set_int64_ne : bytes -> int -> int64 -> unit >> set_int64_ne b i v sets b’s native-endian 64-bit integer starting at byte index i to v. Since: 4.08 << val set_int64_be : bytes -> int -> int64 -> unit >> set_int64_be b i v sets b’s big-endian 64-bit integer starting at byte index i to v. Since: 4.08 << val set_int64_le : bytes -> int -> int64 -> unit >> set_int64_le b i v sets b’s little-endian 64-bit integer starting at byte index i to v. Since: 4.08 Byte sequences and concurrency safety ===================================== Care must be taken when concurrently accessing byte sequences from multiple domains: accessing a byte sequence will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results. Atomicity --------- Every byte sequence operation that accesses more than one byte is not atomic. This includes iteration and scanning. For example, consider the following program: << let size = 100_000_000 let b = Bytes.make size ' ' let update b f () = Bytes.iteri (fun i x -> Bytes.set b i (Char.chr (f (Char.code x)))) b let d1 = Domain.spawn (update b (fun x -> x + 1)) let d2 = Domain.spawn (update b (fun x -> 2 * x + 1)) let () = Domain.join d1; Domain.join d2 >> the bytes sequence b may contain a non-deterministic mixture of '!', 'A', 'B', and 'C' values. After executing this code, each byte of the sequence b is either '!', 'A', 'B', or 'C'. If atomicity is required, then the user must implement their own synchronization (for example, using Mutex.t[29.37]). Data races ---------- If two domains only access disjoint parts of a byte sequence, then the observed behaviour is the equivalent to some sequential interleaving of the operations from the two domains. A data race is said to occur when two domains access the same byte without synchronization and at least one of the accesses is a write. In the absence of data races, the observed behaviour is equivalent to some sequential interleaving of the operations from different domains. Whenever possible, data races should be avoided by using synchronization to mediate the accesses to the elements of the sequence. Indeed, in the presence of data races, programs will not crash but the observed behaviour may not be equivalent to any sequential interleaving of operations from different domains. Nevertheless, even in the presence of data races, a read operation will return the value of some prior write to that location. Mixed-size accesses -------------------- Another subtle point is that if a data race involves mixed-size writes and reads to the same location, the order in which those writes and reads are observed by domains is not specified. For instance, the following code write sequentially a 32-bit integer and a char to the same index << let b = Bytes.make 10 '\000' let d1 = Domain.spawn (fun () -> Bytes.set_int32_ne b 0 100; b.[0] <- 'd' ) >> In this situation, a domain that observes the write of ’d’ to b.0 is not guaranteed to also observe the write to indices 1, 2, or 3. 29.10 Module Callback : Registering OCaml values with the C runtime. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This module allows OCaml values to be registered with the C runtime under a symbolic name, so that C code can later call back registered OCaml functions, or raise registered OCaml exceptions. << val register : string -> 'a -> unit >> Callback.register n v registers the value v under the name n. C code can later retrieve a handle to v by calling caml_named_value(n). << val register_exception : string -> exn -> unit >> Callback.register_exception n exn registers the exception contained in the exception value exn under the name n. C code can later retrieve a handle to the exception by calling caml_named_value(n). The exception value thus obtained is suitable for passing as first argument to raise_constant or raise_with_arg. 29.11 Module Char : Character operations. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* << val code : char -> int >> Return the ASCII code of the argument. << val chr : int -> char >> Return the character with the given ASCII code. Raises Invalid_argument if the argument is outside the range 0–255. << val escaped : char -> string >> Return a string representing the given character, with special characters escaped following the lexical conventions of OCaml. All characters outside the ASCII printable range (32..126) are escaped, as well as backslash, double-quote, and single-quote. << val lowercase_ascii : char -> char >> Convert the given character to its equivalent lowercase character, using the US-ASCII character set. Since: 4.03 << val uppercase_ascii : char -> char >> Convert the given character to its equivalent uppercase character, using the US-ASCII character set. Since: 4.03 << type t = char >> An alias for the type of characters. << val compare : t -> t -> int >> The comparison function for characters, with the same specification as compare[28.2]. Along with the type t, this function compare allows the module Char to be passed as argument to the functors Set.Make[29.50] and Map.Make[29.34]. << val equal : t -> t -> bool >> The equal function for chars. Since: 4.03 << val seeded_hash : int -> t -> int >> A seeded hash function for characters, with the same output value as Hashtbl.seeded_hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded[29.25]. Since: 5.1 << val hash : t -> int >> An unseeded hash function for characters, with the same output value as Hashtbl.hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.Make[29.25]. Since: 5.1 29.12 Module Complex : Complex numbers. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module provides arithmetic operations on complex numbers. Complex numbers are represented by their real and imaginary parts (cartesian representation). Each part is represented by a double-precision floating-point number (type float). << type t = { re : float ; im : float ; } >> The type of complex numbers. re is the real part and im the imaginary part. << val zero : t >> The complex number 0. << val one : t >> The complex number 1. << val i : t >> The complex number i. << val neg : t -> t >> Unary negation. << val conj : t -> t >> Conjugate: given the complex x + i.y, returns x - i.y. << val add : t -> t -> t >> Addition << val sub : t -> t -> t >> Subtraction << val mul : t -> t -> t >> Multiplication << val inv : t -> t >> Multiplicative inverse (1/z). << val div : t -> t -> t >> Division << val sqrt : t -> t >> Square root. The result x + i.y is such that x > 0 or x = 0 and y >= 0. This function has a discontinuity along the negative real axis. << val norm2 : t -> float >> Norm squared: given x + i.y, returns x^2 + y^2. << val norm : t -> float >> Norm: given x + i.y, returns sqrt(x^2 + y^2). << val arg : t -> float >> Argument. The argument of a complex number is the angle in the complex plane between the positive real axis and a line passing through zero and the number. This angle ranges from -pi to pi. This function has a discontinuity along the negative real axis. << val polar : float -> float -> t >> polar norm arg returns the complex having norm norm and argument arg. << val exp : t -> t >> Exponentiation. exp z returns e to the z power. << val log : t -> t >> Natural logarithm (in base e). << val pow : t -> t -> t >> Power function. pow z1 z2 returns z1 to the z2 power. 29.13 Module Condition : Condition variables. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Condition variables are useful when several threads wish to access a shared data structure that is protected by a mutex (a mutual exclusion lock). A condition variable is a communication channel. On the receiver side, one or more threads can indicate that they wish to wait for a certain property to become true. On the sender side, a thread can signal that this property has become true, causing one (or more) waiting threads to be woken up. For instance, in the implementation of a queue data structure, if a thread that wishes to extract an element finds that the queue is currently empty, then this thread waits for the queue to become nonempty. A thread that inserts an element into the queue signals that the queue has become nonempty. A condition variable is used for this purpose. This communication channel conveys the information that the property "the queue is nonempty" is true, or more accurately, may be true. (We explain below why the receiver of a signal cannot be certain that the property holds.) To continue the example of the queue, assuming that the queue has a fixed maximum capacity, then a thread that wishes to insert an element may find that the queue is full. Then, this thread must wait for the queue to become not full, and a thread that extracts an element of the queue signals that the queue has become not full. Another condition variable is used for this purpose. In short, a condition variable c is used to convey the information that a certain property P about a shared data structure D, protected by a mutex m, may be true. Condition variables provide an efficient alternative to busy-waiting. When one wishes to wait for the property P to be true, instead of writing a busy-waiting loop: << Mutex.lock m; while not P do Mutex.unlock m; Mutex.lock m done; ; Mutex.unlock m >> one uses Condition.wait[29.13] in the body of the loop, as follows: << Mutex.lock m; while not P do Condition.wait c m done; ; Mutex.unlock m >> The busy-waiting loop is inefficient because the waiting thread consumes processing time and creates contention of the mutex m. Calling Condition.wait[29.13] allows the waiting thread to be suspended, so it does not consume any computing resources while waiting. With a condition variable c, exactly one mutex m is associated. This association is implicit: the mutex m is not explicitly passed as an argument to Condition.create[29.13]. It is up to the programmer to know, for each condition variable c, which is the associated mutex m. With a mutex m, several condition variables can be associated. In the example of the bounded queue, one condition variable is used to indicate that the queue is nonempty, and another condition variable is used to indicate that the queue is not full. With a condition variable c, exactly one logical property P should be associated. Examples of such properties include "the queue is nonempty" and "the queue is not full". It is up to the programmer to keep track, for each condition variable, of the corresponding property P. A signal is sent on the condition variable c as an indication that the property P is true, or may be true. On the receiving end, however, a thread that is woken up cannot assume that P is true; after a call to Condition.wait[29.13] terminates, one must explicitly test whether P is true. There are several reasons why this is so. One reason is that, between the moment when the signal is sent and the moment when a waiting thread receives the signal and is scheduled, the property P may be falsified by some other thread that is able to acquire the mutex m and alter the data structure D. Another reason is that spurious wakeups may occur: a waiting thread can be woken up even if no signal was sent. Here is a complete example, where a mutex protects a sequential unbounded queue, and where a condition variable is used to signal that the queue is nonempty. << type 'a safe_queue = { queue : 'a Queue.t; mutex : Mutex.t; nonempty : Condition.t } let create () = { queue = Queue.create(); mutex = Mutex.create(); nonempty = Condition.create() } let add v q = Mutex.lock q.mutex; let was_empty = Queue.is_empty q.queue in Queue.add v q.queue; if was_empty then Condition.broadcast q.nonempty; Mutex.unlock q.mutex let take q = Mutex.lock q.mutex; while Queue.is_empty q.queue do Condition.wait q.nonempty q.mutex done; let v = Queue.take q.queue in (* cannot fail since queue is nonempty *) Mutex.unlock q.mutex; v >> Because the call to Condition.broadcast[29.13] takes place inside the critical section, the following property holds whenever the mutex is unlocked: if the queue is nonempty, then no thread is waiting, or, in other words, if some thread is waiting, then the queue must be empty. This is a desirable property: if a thread that attempts to execute a take operation could remain suspended even though the queue is nonempty, that would be a problematic situation, known as a deadlock. << type t >> The type of condition variables. << val create : unit -> t >> create() creates and returns a new condition variable. This condition variable should be associated (in the programmer’s mind) with a certain mutex m and with a certain property P of the data structure that is protected by the mutex m. << val wait : t -> Mutex.t -> unit >> The call wait c m is permitted only if m is the mutex associated with the condition variable c, and only if m is currently locked. This call atomically unlocks the mutex m and suspends the current thread on the condition variable c. This thread can later be woken up after the condition variable c has been signaled via Condition.signal[29.13] or Condition.broadcast[29.13]; however, it can also be woken up for no reason. The mutex m is locked again before wait returns. One cannot assume that the property P associated with the condition variable c holds when wait returns; one must explicitly test whether P holds after calling wait. << val signal : t -> unit >> signal c wakes up one of the threads waiting on the condition variable c, if there is one. If there is none, this call has no effect. It is recommended to call signal c inside a critical section, that is, while the mutex m associated with c is locked. << val broadcast : t -> unit >> broadcast c wakes up all threads waiting on the condition variable c. If there are none, this call has no effect. It is recommended to call broadcast c inside a critical section, that is, while the mutex m associated with c is locked. 29.14 Module Domain *=*=*=*=*=*=*=*=*=*=* Alert unstable. The Domain interface may change in incompatible ways in the future. Domains. See ’Parallel programming’ chapter in the manual. << type !'a t >> A domain of type 'a t runs independently, eventually producing a result of type ’a, or an exception << val spawn : (unit -> 'a) -> 'a t >> spawn f creates a new domain that runs in parallel with the current domain. Raises Failure if the program has insufficient resources to create another domain. << val join : 'a t -> 'a >> join d blocks until domain d runs to completion. If d results in a value, then that is returned by join d. If d raises an uncaught exception, then that is re-raised by join d. << type id = private int >> Domains have unique integer identifiers << val get_id : 'a t -> id >> get_id d returns the identifier of the domain d << val self : unit -> id >> self () is the identifier of the currently running domain << val before_first_spawn : (unit -> unit) -> unit >> before_first_spawn f registers f to be called before the first domain is spawned by the program. The functions registered with before_first_spawn are called on the main (initial) domain. The functions registered with before_first_spawn are called in ’first in, first out’ order: the oldest function added with before_first_spawn is called first. Raises Invalid_argument if the program has already spawned a domain. << val at_exit : (unit -> unit) -> unit >> at_exit f registers f to be called when the current domain exits. Note that at_exit callbacks are domain-local and only apply to the calling domain. The registered functions are called in ’last in, first out’ order: the function most recently added with at_exit is called first. An example: << let temp_file_key = Domain.DLS.new_key (fun _ -> let tmp = snd (Filename.open_temp_file "" "") in Domain.at_exit (fun () -> close_out_noerr tmp); tmp) >> The snippet above creates a key that when retrieved for the first time will open a temporary file and register an at_exit callback to close it, thus guaranteeing the descriptor is not leaked in case the current domain exits. << val cpu_relax : unit -> unit >> If busy-waiting, calling cpu_relax () between iterations will improve performance on some CPU architectures << val is_main_domain : unit -> bool >> is_main_domain () returns true if called from the initial domain. << val recommended_domain_count : unit -> int >> The recommended maximum number of domains which should be running simultaneously (including domains already running). The value returned is at least 1. << module DLS : >>  sig Domain-local Storage << type 'a key >> Type of a DLS key << val new_key : ?split_from_parent:('a -> 'a) -> (unit -> 'a) -> 'a key >> new_key f returns a new key bound to initialiser f for accessing , domain-local variables. If split_from_parent is not provided, the value for a new domain will be computed on-demand by the new domain: the first get call will call the initializer f and store that value. Warning. f may be called several times if another call to get occurs during initialization on the same domain. Only the ’first’ value computed will be used, the other now-useless values will be discarded. Your initialization function should support this situation, or contain logic to detect this case and fail. If split_from_parent is provided, spawning a domain will derive the child value (for this key) from the parent value. This computation happens in the parent domain and it always happens, regardless of whether the child domain will use it. If the splitting function is expensive or requires child-side computation, consider using 'a Lazy.t key: << let init () = ... let split_from_parent parent_value = ... parent-side computation ...; lazy ( ... child-side computation ... ) let key = Domain.DLS.new_key ~split_from_parent init let get () = Lazy.force (Domain.DLS.get key) >> In this case a part of the computation happens on the child domain; in particular, it can access parent_value concurrently with the parent domain, which may require explicit synchronization to avoid data races. << val get : 'a key -> 'a >> get k returns v if a value v is associated to the key k on the calling domain’s domain-local state. Sets k’s value with its initialiser and returns it otherwise. << val set : 'a key -> 'a -> unit >> set k v updates the calling domain’s domain-local state to associate the key k with value v. It overwrites any previous values associated to k, which cannot be restored later.  end 29.15 Module Digest : Message digest. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module provides functions to compute ’digests’, also known as ’hashes’, of arbitrary-length strings or files. The supported hashing algorithms are BLAKE2 and MD5. Basic functions =============== The functions in this section use the MD5 hash function to produce 128-bit digests (16 bytes). MD5 is not cryptographically secure. Hence, these functions should not be used for security-sensitive applications. The BLAKE2 functions below are cryptographically secure. << type t = string >> The type of digests: 16-byte strings. << val compare : t -> t -> int >> The comparison function for 16-byte digests, with the same specification as compare[28.2] and the implementation shared with String.compare[29.54]. Along with the type t, this function compare allows the module Digest to be passed as argument to the functors Set.Make[29.50] and Map.Make[29.34]. Since: 4.00 << val equal : t -> t -> bool >> The equal function for 16-byte digests. Since: 4.03 << val string : string -> t >> Return the digest of the given string. << val bytes : bytes -> t >> Return the digest of the given byte sequence. Since: 4.02 << val substring : string -> int -> int -> t >> Digest.substring s ofs len returns the digest of the substring of s starting at index ofs and containing len characters. << val subbytes : bytes -> int -> int -> t >> Digest.subbytes s ofs len returns the digest of the subsequence of s starting at index ofs and containing len bytes. Since: 4.02 << val channel : in_channel -> int -> t >> If len is nonnegative, Digest.channel ic len reads len characters from channel ic and returns their digest, or raises End_of_file if end-of-file is reached before len characters are read. If len is negative, Digest.channel ic len reads all characters from ic until end-of-file is reached and return their digest. << val file : string -> t >> Return the digest of the file whose name is given. << val output : out_channel -> t -> unit >> Write a digest on the given output channel. << val input : in_channel -> t >> Read a digest from the given input channel. << val to_hex : t -> string >> Return the printable hexadecimal representation of the given digest. Raises Invalid_argument if the argument is not exactly 16 bytes. << val of_hex : string -> t >> Convert a hexadecimal representation back into the corresponding digest. Since: 5.2 Raises Invalid_argument if the argument is not exactly 32 hexadecimal characters. << val from_hex : string -> t >> Same function as Digest.of_hex[29.15]. Since: 4.00 Generic interface ================= << module type S = >>  sig << type t = string >> The type of digests. << val hash_length : int >> The length of digests, in bytes. << val compare : t -> t -> int >> Compare two digests, with the same specification as compare[28.2]. << val equal : t -> t -> bool >> Test two digests for equality. << val string : string -> t >> Return the digest of the given string. << val bytes : bytes -> t >> Return the digest of the given byte sequence. << val substring : string -> int -> int -> t >> substring s ofs len returns the digest of the substring of s starting at index ofs and containing len characters. << val subbytes : bytes -> int -> int -> t >> subbytes s ofs len returns the digest of the subsequence of s starting at index ofs and containing len bytes. << val channel : in_channel -> int -> t >> Read characters from the channel and return their digest. See Digest.channel[29.15] for the full specification. << val file : string -> t >> Return the digest of the file whose name is given. << val output : out_channel -> t -> unit >> Write a digest on the given output channel. << val input : in_channel -> t >> Read a digest from the given input channel. << val to_hex : t -> string >> Return the printable hexadecimal representation of the given digest. Raises Invalid_argument if the length of the argument is not hash_length, << val of_hex : string -> t >> Convert a hexadecimal representation back into the corresponding digest. Raises Invalid_argument if the length of the argument is not 2 * hash_length, or if the arguments contains non-hexadecimal characters.  end The signature for a hash function that produces digests of length hash_length from character strings, byte arrays, and files. Since: 5.2 Specific hash functions ======================= << module BLAKE128 : >> S BLAKE128 is the BLAKE2b hash function producing 128-bit (16-byte) digests. It is cryptographically secure. However, the small size of the digests enables brute-force attacks in 2{^64} attempts. Since: 5.2 << module BLAKE256 : >> S BLAKE256 is the BLAKE2b hash function producing 256-bit (32-byte) digests. It is cryptographically secure, and the digests are large enough to thwart brute-force attacks. Since: 5.2 << module BLAKE512 : >> S BLAKE512 is the BLAKE2b hash function producing 512-bit (64-byte) digests. It is cryptographically secure, and the digests are large enough to thwart brute-force attacks. Since: 5.2 << module MD5 : >> S MD5 is the MD5 hash function. It produces 128-bit (16-byte) digests and is not cryptographically secure at all. It should be used only for compatibility with earlier designs that mandate the use of MD5. Since: 5.2 29.16 Module Dynarray : Dynamic arrays. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The Array[29.2] module provide arrays of fixed length. Dynarray[29.16] provides arrays whose length can change over time, by adding or removing elements at the end of the array. This is typically used to accumulate elements whose number is not known in advance or changes during computation, while also providing fast access to elements at arbitrary positions. << let dynarray_of_list li = let arr = Dynarray.create () in List.iter (fun v -> Dynarray.add_last arr v) li; arr >> The Buffer[29.7] module provides similar features, but it is specialized for accumulating characters into a dynamically-resized string. The Stack[29.52] module provides a last-in first-out data structure that can be easily implemented on top of dynamic arrays. Warning. In their current implementation, the memory layout of dynamic arrays differs from the one of Array[29.2]s. See the Memory Layout[29.16] section for more information. Since: 5.2 Alert unsynchronized_access. Unsynchronized accesses to dynamic arrays are a programming error. Unsynchronized accesses Concurrent accesses to dynamic arrays must be synchronized (for instance with a Mutex.t[29.37]). Unsynchronized accesses to a dynamic array are a programming error that may lead to an invalid dynamic array state, on which some operations would fail with an Invalid_argument exception. Dynamic arrays ============== << type !'a t >> A dynamic array containing values of type 'a. A dynamic array a provides constant-time get and set operations on indices between 0 and Dynarray.length a - 1 included. Its Dynarray.length[29.16] may change over time by adding or removing elements to the end of the array. We say that an index into a dynarray a is valid if it is in 0 .. length a - 1 and invalid otherwise. << val create : unit -> 'a t >> create () is a new, empty array. << val make : int -> 'a -> 'a t >> make n x is a new array of length n, filled with x. Raises Invalid_argument if n < 0 or n > Sys.max_array_length. << val init : int -> (int -> 'a) -> 'a t >> init n f is a new array a of length n, such that get a i is f i. In other words, the elements of a are f 0, then f 1, then f 2... and f (n - 1) last, evaluated in that order. This is similar to Array.init[29.2]. Raises Invalid_argument if n < 0 or n > Sys.max_array_length. << val get : 'a t -> int -> 'a >> get a i is the i-th element of a, starting with index 0. Raises Invalid_argument if the index is invalid << val set : 'a t -> int -> 'a -> unit >> set a i x sets the i-th element of a to be x. i must be a valid index. set does not add new elements to the array – see Dynarray.add_last[29.16] to add an element. Raises Invalid_argument if the index is invalid. << val length : 'a t -> int >> length a is the number of elements in the array. << val is_empty : 'a t -> bool >> is_empty a is true if a is empty, that is, if length a = 0. << val get_last : 'a t -> 'a >> get_last a is the element of a at index length a - 1. Raises Invalid_argument if a is empty. << val find_last : 'a t -> 'a option >> find_last a is None if a is empty and Some (get_last a) otherwise. << val copy : 'a t -> 'a t >> copy a is a shallow copy of a, a new array containing the same elements as a. Adding elements =============== Note: all operations adding elements raise Invalid_argument if the length needs to grow beyond Sys.max_array_length[29.56]. << val add_last : 'a t -> 'a -> unit >> add_last a x adds the element x at the end of the array a. << val append_array : 'a t -> 'a array -> unit >> append_array a b adds all elements of b at the end of a, in the order they appear in b. For example: << let a = Dynarray.of_list [1;2] in Dynarray.append_array a [|3; 4|]; assert (Dynarray.to_list a = [1; 2; 3; 4]) >> << val append_list : 'a t -> 'a list -> unit >> Like Dynarray.append_array[29.16] but with a list. << val append : 'a t -> 'a t -> unit >> append a b is like append_array a b, but b is itself a dynamic array instead of a fixed-size array. Warning: append a a is a programming error because it iterates on a and adds elements to it at the same time – see the Iteration[29.16] section below. It fails with Invalid_argument. If you really want to append a copy of a to itself, you can use Dynarray.append_array a (Dynarray.to_array a) which copies a into a temporary array. << val append_seq : 'a t -> 'a Seq.t -> unit >> Like Dynarray.append_array[29.16] but with a sequence. Warning: append_seq a (to_seq_reentrant a) simultaneously traverses a and adds element to it; the ordering of those operations is unspecified, and may result in an infinite loop – the new elements may in turn be produced by to_seq_reentrant a and get added again and again. << val append_iter : 'a t -> (('a -> unit) -> 'x -> unit) -> 'x -> unit >> append_iter a iter x adds each element of x to the end of a. This is iter (add_last a) x. For example, append_iter a List.iter [1;2;3] would add elements 1, 2, and then 3 at the end of a. append_iter a Queue.iter q adds elements from the queue q. Removing elements ================= << val pop_last_opt : 'a t -> 'a option >> pop_last_opt a removes and returns the last element of a, or None if the array is empty. << val pop_last : 'a t -> 'a >> pop_last a removes and returns the last element of a. Raises Not_found on an empty array. << val remove_last : 'a t -> unit >> remove_last a removes the last element of a, if any. It does nothing if a is empty. << val truncate : 'a t -> int -> unit >> truncate a n truncates a to have at most n elements. It removes elements whose index is greater or equal to n. It does nothing if n >= length a. truncate a n is equivalent to: << if n < 0 then invalid_argument "..."; while length a > n do remove_last a done >> Raises Invalid_argument if n < 0. << val clear : 'a t -> unit >> clear a is truncate a 0, it removes all the elements of a. Iteration ========= The iteration functions traverse the elements of a dynamic array. Traversals of a are computed in increasing index order: from the element of index 0 to the element of index length a - 1. It is a programming error to change the length of an array (by adding or removing elements) during an iteration on the array. Any iteration function will fail with Invalid_argument if it detects such a length change. << val iter : ('a -> unit) -> 'a t -> unit >> iter f a calls f on each element of a. << val iteri : (int -> 'a -> unit) -> 'a t -> unit >> iteri f a calls f i x for each x at index i in a. << val map : ('a -> 'b) -> 'a t -> 'b t >> map f a is a new array of elements of the form f x for each element x of a. For example, if the elements of a are x0, x1, x2, then the elements of b are f x0, f x1, f x2. << val mapi : (int -> 'a -> 'b) -> 'a t -> 'b t >> mapi f a is a new array of elements of the form f i x for each element x of a at index i. For example, if the elements of a are x0, x1, x2, then the elements of b are f 0 x0, f 1 x1, f 2 x2. << val fold_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a t -> 'acc >> fold_left f acc a folds f over a in order, starting with accumulator acc. For example, if the elements of a are x0, x1, then fold f acc a is << let acc = f acc x0 in let acc = f acc x1 in acc >> << val fold_right : ('a -> 'acc -> 'acc) -> 'a t -> 'acc -> 'acc >> fold_right f a acc computes f x0 (f x1 (... (f xn acc) ...)) where x0, x1, ..., xn are the elements of a. << val exists : ('a -> bool) -> 'a t -> bool >> exists f a is true if some element of a satisfies f. For example, if the elements of a are x0, x1, x2, then exists f a is f x0 || f x1 || f x2. << val for_all : ('a -> bool) -> 'a t -> bool >> for_all f a is true if all elements of a satisfy f. This includes the case where a is empty. For example, if the elements of a are x0, x1, then exists f a is f x0 && f x1 && f x2. << val filter : ('a -> bool) -> 'a t -> 'a t >> filter f a is a new array of all the elements of a that satisfy f. In other words, it is an array b such that, for each element x in a in order, x is added to b if f x is true. For example, filter (fun x -> x >= 0) a is a new array of all non-negative elements of a, in order. << val filter_map : ('a -> 'b option) -> 'a t -> 'b t >> filter_map f a is a new array of elements y such that f x is Some y for an element x of a. In others words, it is an array b such that, for each element x of a in order: - if f x = Some y, then y is added to b, - if f x = None, then no element is added to b. For example, filter_map int_of_string_opt inputs returns a new array of integers read from the strings in inputs, ignoring strings that cannot be converted to integers. Conversions to other data structures ==================================== Note: the of_* functions raise Invalid_argument if the length needs to grow beyond Sys.max_array_length[29.56]. The to_* functions, except those specifically marked "reentrant", iterate on their dynarray argument. In particular it is a programming error if the length of the dynarray changes during their execution, and the conversion functions raise Invalid_argument if they observe such a change. << val of_array : 'a array -> 'a t >> of_array arr returns a dynamic array corresponding to the fixed-sized array a. Operates in O(n) time by making a copy. << val to_array : 'a t -> 'a array >> to_array a returns a fixed-sized array corresponding to the dynamic array a. This always allocate a new array and copies elements into it. << val of_list : 'a list -> 'a t >> of_list l is the array containing the elements of l in the same order. << val to_list : 'a t -> 'a list >> to_list a is a list with the elements contained in the array a. << val of_seq : 'a Seq.t -> 'a t >> of_seq seq is an array containing the same elements as seq. It traverses seq once and will terminate only if seq is finite. << val to_seq : 'a t -> 'a Seq.t >> to_seq a is the sequence of elements get a 0, get a 1... get a (length a - 1). << val to_seq_reentrant : 'a t -> 'a Seq.t >> to_seq_reentrant a is a reentrant variant of Dynarray.to_seq[29.16], in the sense that one may still access its elements after the length of a has changed. Demanding the i-th element of the resulting sequence (which can happen zero, one or several times) will access the i-th element of a at the time of the demand. The sequence stops if a has less than i elements at this point. << val to_seq_rev : 'a t -> 'a Seq.t >> to_seq_rev a is the sequence of elements get a (l - 1), get a (l - 2)... get a 0, where l is length a at the time to_seq_rev is invoked. << val to_seq_rev_reentrant : 'a t -> 'a Seq.t >> to_seq_rev_reentrant a is a reentrant variant of Dynarray.to_seq_rev[29.16], in the sense that one may still access its elements after the length of a has changed. Elements that have been removed from the array by the time they are demanded in the sequence are skipped. Advanced topics for performance =============================== Backing array, capacity ----------------------- Internally, a dynamic array uses a backing array (a fixed-size array as provided by the Array[29.2] module) whose length is greater or equal to the length of the dynamic array. We define the capacity of a dynamic array as the length of its backing array. The capacity of a dynamic array is relevant in advanced scenarios, when reasoning about the performance of dynamic array programs: - The memory usage of a dynamic array is proportional to its capacity, rather than its length. - When there is no empty space left at the end of the backing array, adding elements requires allocating a new, larger backing array. The implementation uses a standard exponential reallocation strategy which guarantees amortized constant-time operation; in particular, the total capacity of all backing arrays allocated over the lifetime of a dynamic array is at worst proportional to the total number of elements added. In other words, users need not care about capacity and reallocations, and they will get reasonable behavior by default. However, in some performance-sensitive scenarios the functions below can help control memory usage or guarantee an optimal number of reallocations. << val capacity : 'a t -> int >> capacity a is the length of a’s backing array. << val ensure_capacity : 'a t -> int -> unit >> ensure_capacity a n makes sure that the capacity of a is at least n. Raises Invalid_argument if the requested capacity is outside the range 0 .. Sys.max_array_length. An example would be to reimplement Dynarray.of_array[29.16] without using Dynarray.init[29.16]: << let of_array arr = let a = Dynarray.create () in Dynarray.ensure_capacity a (Array.length arr); Array.iter (fun v -> add_last a v) arr >> Using ensure_capacity guarantees that at most one reallocation will take place, instead of possibly several. Without this ensure_capacity hint, the number of resizes would be logarithmic in the length of arr, creating a constant-factor slowdown noticeable when arr is large. << val ensure_extra_capacity : 'a t -> int -> unit >> ensure_extra_capacity a n is ensure_capacity a (length a + n), it makes sure that a has room for n extra items. Raises Invalid_argument if the total requested capacity is outside the range 0 .. Sys.max_array_length. A use case would be to implement Dynarray.append_array[29.16]: << let append_array a arr = ensure_extra_capacity a (Array.length arr); Array.iter (fun v -> add_last a v) arr >> << val fit_capacity : 'a t -> unit >> fit_capacity a reallocates a backing array if necessary, so that the resulting capacity is exactly length a, with no additional empty space at the end. This can be useful to make sure there is no memory wasted on a long-lived array. Note that calling fit_capacity breaks the amortized complexity guarantees provided by the default reallocation strategy. Calling it repeatedly on an array may have quadratic complexity, both in time and in total number of words allocated. If you know that a dynamic array has reached its final length, which will remain fixed in the future, it is sufficient to call to_array and only keep the resulting fixed-size array. fit_capacity is useful when you need to keep a dynamic array for eventual future resizes. << val set_capacity : 'a t -> int -> unit >> set_capacity a n reallocates a backing array if necessary, so that the resulting capacity is exactly n. In particular, all elements of index n or greater are removed. Like Dynarray.fit_capacity[29.16], this function breaks the amortized complexity guarantees provided by the reallocation strategy. Calling it repeatedly on an array may have quadratic complexity, both in time and in total number of words allocated. This is an advanced function; in particular, Dynarray.ensure_capacity[29.16] should be preferred to increase the capacity, as it preserves those amortized guarantees. Raises Invalid_argument if n < 0. << val reset : 'a t -> unit >> reset a clears a and replaces its backing array by an empty array. It is equivalent to set_capacity a 0 or clear a; fit_capacity a. No leaks: preservation of memory liveness ----------------------------------------- The user-provided values reachable from a dynamic array a are exactly the elements in the positions 0 to length a - 1. In particular, no user-provided values are "leaked" by being present in the backing array in position length a or later. Memory layout of dynarrays -------------------------- In the current implementation, the backing array of an 'a Dynarray.t is not an 'a array, but something with the same representation as an 'a option array or 'a ref array. Each element is in a "box", allocated when the element is first added to the array – see the implementation for more details. Using an 'a array would be delicate, as there is no obvious type-correct way to represent the empty space at the end of the backing array – using user-provided values would either complicate the API or violate the no leaks[29.16] guarantee. The constraint of remaining memory-safe under unsynchronized concurrent usage makes it even more difficult. Various unsafe ways to do this have been discussed, with no consensus on a standard implementation so far. On a realistic automated-theorem-proving program that relies heavily on dynamic arrays, we measured the overhead of this extra "boxing" as at most 25%. We believe that the overhead for most uses of dynarray is much smaller, negligible in many cases, but you may still prefer to use your own specialized implementation for performance. (If you know that you do not need the no leaks[noleaks] guarantee, you can also speed up deleting elements.) Code examples ============= Min-heaps for mutable priority queues ------------------------------------- We can use dynamic arrays to implement a mutable priority queue. A priority queue provides a function to add elements, and a function to extract the minimum element – according to some comparison function. << (* We present our priority queues as a functor parametrized on the comparison function. *) module Heap (Elem : Map.OrderedType) : sig type t val create : unit -> t val add : t -> Elem.t -> unit val pop_min : t -> Elem.t option end = struct (* Our priority queues are implemented using the standard "min heap" data structure, a dynamic array representing a binary tree. *) type t = Elem.t Dynarray.t let create = Dynarray.create (* The node of index [i] has as children the nodes of index [2 * i + 1] and [2 * i + 2] -- if they are valid indices in the dynarray. *) let left_child i = 2 * i + 1 let right_child i = 2 * i + 2 let parent_node i = (i - 1) / 2 (* We use indexing operators for convenient notations. *) let ( .!() ) = Dynarray.get let ( .!()<- ) = Dynarray.set (* Auxiliary functions to compare and swap two elements in the dynamic array. *) let order h i j = Elem.compare h.!(i) h.!(j) let swap h i j = let v = h.!(i) in h.!(i) <- h.!(j); h.!(j) <- v (* We say that a heap respects the "heap ordering" if the value of each node is smaller than the value of its children. The algorithm manipulates arrays that respect the heap algorithm, except for one node whose value may be too small or too large. The auxiliary functions [heap_up] and [heap_down] take such a misplaced value, and move it "up" (respectively: "down") the tree by permuting it with its parent value (respectively: a child value) until the heap ordering is restored. *) let rec heap_up h i = if i = 0 then () else let parent = parent_node i in if order h i parent < 0 then (swap h i parent; heap_up h parent) and heap_down h ~len i = let left, right = left_child i, right_child i in if left >= len then () (* no child, stop *) else let smallest = if right >= len then left (* no right child *) else if order h left right < 0 then left else right in if order h i smallest > 0 then (swap h i smallest; heap_down h ~len smallest) let add h s = let i = Dynarray.length h in Dynarray.add_last h s; heap_up h i let pop_min h = if Dynarray.is_empty h then None else begin (* Standard trick: swap the 'best' value at index 0 with the last value of the array. *) let last = Dynarray.length h - 1 in swap h 0 last; (* At this point [pop_last] returns the 'best' value, and leaves a heap with one misplaced element at position 0. *) let best = Dynarray.pop_last h in (* Restore the heap ordering -- does nothing if the heap is empty. *) heap_down h ~len:last 0; Some best end end >> The production code from which this example was inspired includes logic to free the backing array when the heap becomes empty, only in the case where the capacity is above a certain threshold. This can be done by calling the following function from pop: << let shrink h = if Dynarray.length h = 0 && Dynarray.capacity h > 1 lsl 18 then Dynarray.reset h >> The Heap functor can be used to implement a sorting function, by adding all elements into a priority queue and then extracting them in order. << let heap_sort (type a) cmp li = let module Heap = Heap(struct type t = a let compare = cmp end) in let heap = Heap.create () in List.iter (Heap.add heap) li; List.map (fun _ -> Heap.pop_min heap |> Option.get) li >> 29.17 Module Effect *=*=*=*=*=*=*=*=*=*=* Alert unstable. The Effect interface may change in incompatible ways in the future. Effects. See ’Language extensions/Effect handlers’ section in the manual. << type _ t = .. >> The type of effects. << exception Unhandled : 'a t -> exn >> Unhandled e is raised when effect e is performed and there is no handler for it. << exception Continuation_already_resumed >> Exception raised when a continuation is continued or discontinued more than once. << val perform : 'a t -> 'a >> perform e performs an effect e. Raises Unhandled if there is no handler for e. << module Deep : >>  sig Deep handlers << type ('a, 'b) continuation >> ('a,'b) continuation is a delimited continuation that expects a 'a value and returns a 'b value. << val continue : ('a, 'b) continuation -> 'a -> 'b >> continue k x resumes the continuation k by passing x to k. Raises Continuation_already_resumed if the continuation has already been resumed. << val discontinue : ('a, 'b) continuation -> exn -> 'b >> discontinue k e resumes the continuation k by raising the exception e in k. Raises Continuation_already_resumed if the continuation has already been resumed. << val discontinue_with_backtrace : ('a, 'b) continuation -> exn -> Printexc.raw_backtrace -> 'b >> discontinue_with_backtrace k e bt resumes the continuation k by raising the exception e in k using bt as the origin for the exception. Raises Continuation_already_resumed if the continuation has already been resumed. << type ('a, 'b) handler = { retc : 'a -> 'b ; exnc : exn -> 'b ; effc : 'c. 'c Effect.t -> (('c, 'b) continuation -> 'b) option ; } >> ('a,'b) handler is a handler record with three fields – retc is the value handler, exnc handles exceptions, and effc handles the effects performed by the computation enclosed by the handler. << val match_with : ('c -> 'a) -> 'c -> ('a, 'b) handler -> 'b >> match_with f v h runs the computation f v in the handler h. << type 'a effect_handler = { effc : 'b. 'b Effect.t -> (('b, 'a) continuation -> 'a) option ; } >> 'a effect_handler is a deep handler with an identity value handler fun x -> x and an exception handler that raises any exception fun e -> raise e. << val try_with : ('b -> 'a) -> 'b -> 'a effect_handler -> 'a >> try_with f v h runs the computation f v under the handler h. << val get_callstack : ('a, 'b) continuation -> int -> Printexc.raw_backtrace >> get_callstack c n returns a description of the top of the call stack on the continuation c, with at most n entries.  end << module Shallow : >>  sig << type ('a, 'b) continuation >> ('a,'b) continuation is a delimited continuation that expects a 'a value and returns a 'b value. << val fiber : ('a -> 'b) -> ('a, 'b) continuation >> fiber f constructs a continuation that runs the computation f. << type ('a, 'b) handler = { retc : 'a -> 'b ; exnc : exn -> 'b ; effc : 'c. 'c Effect.t -> (('c, 'a) continuation -> 'b) option ; } >> ('a,'b) handler is a handler record with three fields – retc is the value handler, exnc handles exceptions, and effc handles the effects performed by the computation enclosed by the handler. << val continue_with : ('c, 'a) continuation -> 'c -> ('a, 'b) handler -> 'b >> continue_with k v h resumes the continuation k with value v with the handler h. Raises Continuation_already_resumed if the continuation has already been resumed. << val discontinue_with : ('c, 'a) continuation -> exn -> ('a, 'b) handler -> 'b >> discontinue_with k e h resumes the continuation k by raising the exception e with the handler h. Raises Continuation_already_resumed if the continuation has already been resumed. << val discontinue_with_backtrace : ('a, 'b) continuation -> exn -> Printexc.raw_backtrace -> ('b, 'c) handler -> 'c >> discontinue_with k e bt h resumes the continuation k by raising the exception e with the handler h using the raw backtrace bt as the origin of the exception. Raises Continuation_already_resumed if the continuation has already been resumed. << val get_callstack : ('a, 'b) continuation -> int -> Printexc.raw_backtrace >> get_callstack c n returns a description of the top of the call stack on the continuation c, with at most n entries.  end 29.18 Module Either : Either type. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Either is the simplest and most generic sum/variant type: a value of ('a, 'b) Either.t is either a Left (v : 'a) or a Right (v : 'b). It is a natural choice in the API of generic functions where values could fall in two different cases, possibly at different types, without assigning a specific meaning to what each case should be. For example: << List.partition_map: ('a -> ('b, 'c) Either.t) -> 'a list -> 'b list * 'c list >> If you are looking for a parametrized type where one alternative means success and the other means failure, you should use the more specific type Result.t[29.47]. Since: 4.12 << type ('a, 'b) t = | Left of 'a | Right of 'b >> A value of ('a, 'b) Either.t contains either a value of 'a or a value of 'b << val left : 'a -> ('a, 'b) t >> left v is Left v. << val right : 'b -> ('a, 'b) t >> right v is Right v. << val is_left : ('a, 'b) t -> bool >> is_left (Left v) is true, is_left (Right v) is false. << val is_right : ('a, 'b) t -> bool >> is_right (Left v) is false, is_right (Right v) is true. << val find_left : ('a, 'b) t -> 'a option >> find_left (Left v) is Some v, find_left (Right _) is None << val find_right : ('a, 'b) t -> 'b option >> find_right (Right v) is Some v, find_right (Left _) is None << val map_left : ('a1 -> 'a2) -> ('a1, 'b) t -> ('a2, 'b) t >> map_left f e is Left (f v) if e is Left v and e if e is Right _. << val map_right : ('b1 -> 'b2) -> ('a, 'b1) t -> ('a, 'b2) t >> map_right f e is Right (f v) if e is Right v and e if e is Left _. << val map : left:('a1 -> 'a2) -> right:('b1 -> 'b2) -> ('a1, 'b1) t -> ('a2, 'b2) t >> map ~left ~right (Left v) is Left (left v), map ~left ~right (Right v) is Right (right v). << val fold : left:('a -> 'c) -> right:('b -> 'c) -> ('a, 'b) t -> 'c >> fold ~left ~right (Left v) is left v, and fold ~left ~right (Right v) is right v. << val iter : left:('a -> unit) -> right:('b -> unit) -> ('a, 'b) t -> unit >> iter ~left ~right (Left v) is left v, and iter ~left ~right (Right v) is right v. << val for_all : left:('a -> bool) -> right:('b -> bool) -> ('a, 'b) t -> bool >> for_all ~left ~right (Left v) is left v, and for_all ~left ~right (Right v) is right v. << val equal : left:('a -> 'a -> bool) -> right:('b -> 'b -> bool) -> ('a, 'b) t -> ('a, 'b) t -> bool >> equal ~left ~right e0 e1 tests equality of e0 and e1 using left and right to respectively compare values wrapped by Left _ and Right _. << val compare : left:('a -> 'a -> int) -> right:('b -> 'b -> int) -> ('a, 'b) t -> ('a, 'b) t -> int >> compare ~left ~right e0 e1 totally orders e0 and e1 using left and right to respectively compare values wrapped by Left _ and Right _. Left _ values are smaller than Right _ values. 29.19 Module Ephemeron : Ephemerons and weak hash tables. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Ephemerons and weak hash tables are useful when one wants to cache or memorize the computation of a function, as long as the arguments and the function are used, without creating memory leaks by continuously keeping old computation results that are not useful anymore because one argument or the function is freed. An implementation using Hashtbl.t[29.25] is not suitable because all associations would keep the arguments and the result in memory. Ephemerons can also be used for "adding" a field to an arbitrary boxed OCaml value: you can attach some information to a value created by an external library without memory leaks. Ephemerons hold some keys and one or no data. They are all boxed OCaml values. The keys of an ephemeron have the same behavior as weak pointers according to the garbage collector. In fact OCaml weak pointers are implemented as ephemerons without data. The keys and data of an ephemeron are said to be full if they point to a value, or empty if the value has never been set, has been unset, or was erased by the GC. In the function that accesses the keys or data these two states are represented by the option type. The data is considered by the garbage collector alive if all the full keys are alive and if the ephemeron is alive. When one of the keys is not considered alive anymore by the GC, the data is emptied from the ephemeron. The data could be alive for another reason and in that case the GC will not free it, but the ephemeron will not hold the data anymore. The ephemerons complicate the notion of liveness of values, because it is not anymore an equivalence with the reachability from root value by usual pointers (not weak and not ephemerons). With ephemerons the notion of liveness is constructed by the least fixpoint of: A value is alive if: - it is a root value - it is reachable from alive value by usual pointers - it is the data of an alive ephemeron with all its full keys alive Notes: - All the types defined in this module cannot be marshaled using output_value[28.2] or the functions of the Marshal[29.35] module. Ephemerons are defined in a language agnostic way in this paper: B. Hayes, Ephemerons: A New Finalization Mechanism, OOPSLA’97 Since: 4.03 Alert unsynchronized_access. Unsynchronized accesses to weak hash tables are a programming error. Unsynchronized accesses Unsynchronized accesses to a weak hash table may lead to an invalid weak hash table state. Thus, concurrent accesses to a buffer must be synchronized (for instance with a Mutex.t[29.37]). << module type S = >>  sig Propose the same interface as usual hash table. However since the bindings are weak, even if mem h k is true, a subsequent find h k may raise Not_found because the garbage collector can run between the two. << type key >> << type !'a t >> << val create : int -> 'a t >> << val clear : 'a t -> unit >> << val reset : 'a t -> unit >> << val copy : 'a t -> 'a t >> << val add : 'a t -> key -> 'a -> unit >> << val remove : 'a t -> key -> unit >> << val find : 'a t -> key -> 'a >> << val find_opt : 'a t -> key -> 'a option >> << val find_all : 'a t -> key -> 'a list >> << val replace : 'a t -> key -> 'a -> unit >> << val mem : 'a t -> key -> bool >> << val length : 'a t -> int >> << val stats : 'a t -> Hashtbl.statistics >> << val add_seq : 'a t -> (key * 'a) Seq.t -> unit >> << val replace_seq : 'a t -> (key * 'a) Seq.t -> unit >> << val of_seq : (key * 'a) Seq.t -> 'a t >> << val clean : 'a t -> unit >> remove all dead bindings. Done automatically during automatic resizing. << val stats_alive : 'a t -> Hashtbl.statistics >> same as Hashtbl.SeededS.stats[29.25] but only count the alive bindings  end The output signature of the functors Ephemeron.K1.Make[29.19] and Ephemeron.K2.Make[29.19]. These hash tables are weak in the keys. If all the keys of a binding are alive the binding is kept, but if one of the keys of the binding is dead then the binding is removed. << module type SeededS = >>  sig << type key >> << type !'a t >> << val create : ?random:bool -> int -> 'a t >> << val clear : 'a t -> unit >> << val reset : 'a t -> unit >> << val copy : 'a t -> 'a t >> << val add : 'a t -> key -> 'a -> unit >> << val remove : 'a t -> key -> unit >> << val find : 'a t -> key -> 'a >> << val find_opt : 'a t -> key -> 'a option >> << val find_all : 'a t -> key -> 'a list >> << val replace : 'a t -> key -> 'a -> unit >> << val mem : 'a t -> key -> bool >> << val length : 'a t -> int >> << val stats : 'a t -> Hashtbl.statistics >> << val add_seq : 'a t -> (key * 'a) Seq.t -> unit >> << val replace_seq : 'a t -> (key * 'a) Seq.t -> unit >> << val of_seq : (key * 'a) Seq.t -> 'a t >> << val clean : 'a t -> unit >> remove all dead bindings. Done automatically during automatic resizing. << val stats_alive : 'a t -> Hashtbl.statistics >> same as Hashtbl.SeededS.stats[29.25] but only count the alive bindings  end The output signature of the functors Ephemeron.K1.MakeSeeded[29.19] and Ephemeron.K2.MakeSeeded[29.19]. << module K1 : >>  sig << type ('k, 'd) t >> an ephemeron with one key << val make : 'k -> 'd -> ('k, 'd) t >> Ephemeron.K1.make k d creates an ephemeron with key k and data d. << val query : ('k, 'd) t -> 'k -> 'd option >> Ephemeron.K1.query eph key returns Some x (where x is the ephemeron’s data) if key is physically equal to eph’s key, and None if eph is empty or key is not equal to eph’s key. << module Make : >> functor (H : Hashtbl.HashedType) -> Ephemeron.S with type key = H.t Functor building an implementation of a weak hash table << module MakeSeeded : >> functor (H : Hashtbl.SeededHashedType) -> Ephemeron.SeededS with type key = H.t Functor building an implementation of a weak hash table. The seed is similar to the one of Hashtbl.MakeSeeded[29.25]. << module Bucket : >>  sig << type ('k, 'd) t >> A bucket is a mutable "list" of ephemerons. << val make : unit -> ('k, 'd) t >> Create a new bucket. << val add : ('k, 'd) t -> 'k -> 'd -> unit >> Add an ephemeron to the bucket. << val remove : ('k, 'd) t -> 'k -> unit >> remove b k removes from b the most-recently added ephemeron with key k, or does nothing if there is no such ephemeron. << val find : ('k, 'd) t -> 'k -> 'd option >> Returns the data of the most-recently added ephemeron with the given key, or None if there is no such ephemeron. << val length : ('k, 'd) t -> int >> Returns an upper bound on the length of the bucket. << val clear : ('k, 'd) t -> unit >> Remove all ephemerons from the bucket.  end  end Ephemerons with one key. << module K2 : >>  sig << type ('k1, 'k2, 'd) t >> an ephemeron with two keys << val make : 'k1 -> 'k2 -> 'd -> ('k1, 'k2, 'd) t >> Same as Ephemeron.K1.make[29.19] << val query : ('k1, 'k2, 'd) t -> 'k1 -> 'k2 -> 'd option >> Same as Ephemeron.K1.query[29.19] << module Make : >> functor (H1 : Hashtbl.HashedType) -> functor (H2 : Hashtbl.HashedType) -> Ephemeron.S with type key = H1.t * H2.t Functor building an implementation of a weak hash table << module MakeSeeded : >> functor (H1 : Hashtbl.SeededHashedType) -> functor (H2 : Hashtbl.SeededHashedType) -> Ephemeron.SeededS with type key = H1.t * H2.t Functor building an implementation of a weak hash table. The seed is similar to the one of Hashtbl.MakeSeeded[29.25]. << module Bucket : >>  sig << type ('k1, 'k2, 'd) t >> A bucket is a mutable "list" of ephemerons. << val make : unit -> ('k1, 'k2, 'd) t >> Create a new bucket. << val add : ('k1, 'k2, 'd) t -> 'k1 -> 'k2 -> 'd -> unit >> Add an ephemeron to the bucket. << val remove : ('k1, 'k2, 'd) t -> 'k1 -> 'k2 -> unit >> remove b k1 k2 removes from b the most-recently added ephemeron with keys k1 and k2, or does nothing if there is no such ephemeron. << val find : ('k1, 'k2, 'd) t -> 'k1 -> 'k2 -> 'd option >> Returns the data of the most-recently added ephemeron with the given keys, or None if there is no such ephemeron. << val length : ('k1, 'k2, 'd) t -> int >> Returns an upper bound on the length of the bucket. << val clear : ('k1, 'k2, 'd) t -> unit >> Remove all ephemerons from the bucket.  end  end Ephemerons with two keys. << module Kn : >>  sig << type ('k, 'd) t >> an ephemeron with an arbitrary number of keys of the same type << val make : 'k array -> 'd -> ('k, 'd) t >> Same as Ephemeron.K1.make[29.19] << val query : ('k, 'd) t -> 'k array -> 'd option >> Same as Ephemeron.K1.query[29.19] << module Make : >> functor (H : Hashtbl.HashedType) -> Ephemeron.S with type key = H.t array Functor building an implementation of a weak hash table << module MakeSeeded : >> functor (H : Hashtbl.SeededHashedType) -> Ephemeron.SeededS with type key = H.t array Functor building an implementation of a weak hash table. The seed is similar to the one of Hashtbl.MakeSeeded[29.25]. << module Bucket : >>  sig << type ('k, 'd) t >> A bucket is a mutable "list" of ephemerons. << val make : unit -> ('k, 'd) t >> Create a new bucket. << val add : ('k, 'd) t -> 'k array -> 'd -> unit >> Add an ephemeron to the bucket. << val remove : ('k, 'd) t -> 'k array -> unit >> remove b k removes from b the most-recently added ephemeron with keys k, or does nothing if there is no such ephemeron. << val find : ('k, 'd) t -> 'k array -> 'd option >> Returns the data of the most-recently added ephemeron with the given keys, or None if there is no such ephemeron. << val length : ('k, 'd) t -> int >> Returns an upper bound on the length of the bucket. << val clear : ('k, 'd) t -> unit >> Remove all ephemerons from the bucket.  end  end Ephemerons with arbitrary number of keys of the same type. 29.20 Module Filename : Operations on file names. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* << val current_dir_name : string >> The conventional name for the current directory (e.g. . in Unix). << val parent_dir_name : string >> The conventional name for the parent of the current directory (e.g. .. in Unix). << val dir_sep : string >> The directory separator (e.g. / in Unix). Since: 3.11.2 << val concat : string -> string -> string >> concat dir file returns a file name that designates file file in directory dir. << val is_relative : string -> bool >> Return true if the file name is relative to the current directory, false if it is absolute (i.e. in Unix, starts with /). << val is_implicit : string -> bool >> Return true if the file name is relative and does not start with an explicit reference to the current directory (./ or ../ in Unix), false if it starts with an explicit reference to the root directory or the current directory. << val check_suffix : string -> string -> bool >> check_suffix name suff returns true if the filename name ends with the suffix suff. Under Windows ports (including Cygwin), comparison is case-insensitive, relying on String.lowercase_ascii. Note that this does not match exactly the interpretation of case-insensitive filename equivalence from Windows. << val chop_suffix : string -> string -> string >> chop_suffix name suff removes the suffix suff from the filename name. Raises Invalid_argument if name does not end with the suffix suff. << val chop_suffix_opt : suffix:string -> string -> string option >> chop_suffix_opt ~suffix filename removes the suffix from the filename if possible, or returns None if the filename does not end with the suffix. Under Windows ports (including Cygwin), comparison is case-insensitive, relying on String.lowercase_ascii. Note that this does not match exactly the interpretation of case-insensitive filename equivalence from Windows. Since: 4.08 << val extension : string -> string >> extension name is the shortest suffix ext of name0 where: - name0 is the longest suffix of name that does not contain a directory separator; - ext starts with a period; - ext is preceded by at least one non-period character in name0. If such a suffix does not exist, extension name is the empty string. Since: 4.04 << val remove_extension : string -> string >> Return the given file name without its extension, as defined in Filename.extension[29.20]. If the extension is empty, the function returns the given file name. The following invariant holds for any file name s: remove_extension s ^ extension s = s Since: 4.04 << val chop_extension : string -> string >> Same as Filename.remove_extension[29.20], but raise Invalid_argument if the given name has an empty extension. << val basename : string -> string >> Split a file name into directory name / base file name. If name is a valid file name, then concat (dirname name) (basename name) returns a file name which is equivalent to name. Moreover, after setting the current directory to dirname name (with Sys.chdir[29.56]), references to basename name (which is a relative file name) designate the same file as name before the call to Sys.chdir[29.56]. This function conforms to the specification of POSIX.1-2008 for the basename utility. << val dirname : string -> string >> See Filename.basename[29.20]. This function conforms to the specification of POSIX.1-2008 for the dirname utility. << val null : string >> null is "/dev/null" on POSIX and "NUL" on Windows. It represents a file on the OS that discards all writes and returns end of file on reads. Since: 4.10 << val temp_file : ?temp_dir:string -> string -> string -> string >> temp_file prefix suffix returns the name of a fresh temporary file in the temporary directory. The base name of the temporary file is formed by concatenating prefix, then a suitably chosen integer number, then suffix. The optional argument temp_dir indicates the temporary directory to use, defaulting to the current result of Filename.get_temp_dir_name[29.20]. The temporary file is created empty, with permissions 0o600 (readable and writable only by the file owner). The file is guaranteed to be different from any other file that existed when temp_file was called. Before 3.11.2 no ?temp_dir optional argument Raises Sys_error if the file could not be created. << val open_temp_file : ?mode:open_flag list -> ?perms:int -> ?temp_dir:string -> string -> string -> string * out_channel >> Same as Filename.temp_file[29.20], but returns both the name of a fresh temporary file, and an output channel opened (atomically) on this file. This function is more secure than temp_file: there is no risk that the temporary file will be modified (e.g. replaced by a symbolic link) before the program opens it. The optional argument mode is a list of additional flags to control the opening of the file. It can contain one or several of Open_append, Open_binary, and Open_text. The default is [Open_text] (open in text mode). The file is created with permissions perms (defaults to readable and writable only by the file owner, 0o600). Before 4.03 no ?perms optional argument Before 3.11.2 no ?temp_dir optional argument Raises Sys_error if the file could not be opened. << val temp_dir : ?temp_dir:string -> ?perms:int -> string -> string -> string >> temp_dir prefix suffix creates and returns the name of a fresh temporary directory with permissions perms (defaults to 0o700) inside temp_dir. The base name of the temporary directory is formed by concatenating prefix, then a suitably chosen integer number, then suffix. The optional argument temp_dir indicates the temporary directory to use, defaulting to the current result of Filename.get_temp_dir_name[29.20]. The temporary directory is created empty, with permissions 0o700 (readable, writable, and searchable only by the file owner). The directory is guaranteed to be different from any other directory that existed when temp_dir was called. If temp_dir does not exist, this function does not create it. Instead, it raises Sys_error. Since: 5.1 Raises Sys_error if the directory could not be created. << val get_temp_dir_name : unit -> string >> The name of the temporary directory: Under Unix, the value of the TMPDIR environment variable, or "/tmp" if the variable is not set. Under Windows, the value of the TEMP environment variable, or "." if the variable is not set. The temporary directory can be changed with Filename.set_temp_dir_name[29.20]. Since: 4.00 << val set_temp_dir_name : string -> unit >> Change the temporary directory returned by Filename.get_temp_dir_name[29.20] and used by Filename.temp_file[29.20] and Filename.open_temp_file[29.20]. The temporary directory is a domain-local value which is inherited by child domains. Since: 4.00 << val quote : string -> string >> Return a quoted version of a file name, suitable for use as one argument in a command line, escaping all meta-characters. Warning: under Windows, the output is only suitable for use with programs that follow the standard Windows quoting conventions. << val quote_command : string -> ?stdin:string -> ?stdout:string -> ?stderr:string -> string list -> string >> quote_command cmd args returns a quoted command line, suitable for use as an argument to Sys.command[29.56], Unix.system[??], and the Unix.open_process[??] functions. The string cmd is the command to call. The list args is the list of arguments to pass to this command. It can be empty. The optional arguments ?stdin and ?stdout and ?stderr are file names used to redirect the standard input, the standard output, or the standard error of the command. If ~stdin:f is given, a redirection < f is performed and the standard input of the command reads from file f. If ~stdout:f is given, a redirection > f is performed and the standard output of the command is written to file f. If ~stderr:f is given, a redirection 2> f is performed and the standard error of the command is written to file f. If both ~stdout:f and ~stderr:f are given, with the exact same file name f, a 2>&1 redirection is performed so that the standard output and the standard error of the command are interleaved and redirected to the same file f. Under Unix and Cygwin, the command, the arguments, and the redirections if any are quoted using Filename.quote[29.20], then concatenated. Under Win32, additional quoting is performed as required by the cmd.exe shell that is called by Sys.command[29.56]. Since: 4.10 Raises Failure if the command cannot be escaped on the current platform. 29.21 Module Float : Floating-point arithmetic. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* OCaml’s floating-point numbers follow the IEEE 754 standard, using double precision (64 bits) numbers. Floating-point operations never raise an exception on overflow, underflow, division by zero, etc. Instead, special IEEE numbers are returned as appropriate, such as infinity for 1.0 /. 0.0, neg_infinity for -1.0 /. 0.0, and nan (’not a number’) for 0.0 /. 0.0. These special numbers then propagate through floating-point computations as expected: for instance, 1.0 /. infinity is 0.0, basic arithmetic operations (+., -., *., /.) with nan as an argument return nan, ... Since: 4.07 << val zero : float >> The floating point 0. Since: 4.08 << val one : float >> The floating-point 1. Since: 4.08 << val minus_one : float >> The floating-point -1. Since: 4.08 << val neg : float -> float >> Unary negation. << val add : float -> float -> float >> Floating-point addition. << val sub : float -> float -> float >> Floating-point subtraction. << val mul : float -> float -> float >> Floating-point multiplication. << val div : float -> float -> float >> Floating-point division. << val fma : float -> float -> float -> float >> fma x y z returns x * y + z, with a best effort for computing this expression with a single rounding, using either hardware instructions (providing full IEEE compliance) or a software emulation. On 64-bit Cygwin, 64-bit mingw-w64 and MSVC 2017 and earlier, this function may be emulated owing to known bugs on limitations on these platforms. Note: since software emulation of the fma is costly, make sure that you are using hardware fma support if performance matters. Since: 4.08 << val rem : float -> float -> float >> rem a b returns the remainder of a with respect to b. The returned value is a -. n *. b, where n is the quotient a /. b rounded towards zero to an integer. << val succ : float -> float >> succ x returns the floating point number right after x i.e., the smallest floating-point number greater than x. See also Float.next_after[29.21]. Since: 4.08 << val pred : float -> float >> pred x returns the floating-point number right before x i.e., the greatest floating-point number smaller than x. See also Float.next_after[29.21]. Since: 4.08 << val abs : float -> float >> abs f returns the absolute value of f. << val infinity : float >> Positive infinity. << val neg_infinity : float >> Negative infinity. << val nan : float >> A special floating-point value denoting the result of an undefined operation such as 0.0 /. 0.0. Stands for ’not a number’. Any floating-point operation with nan as argument returns nan as result, unless otherwise specified in IEEE 754 standard. As for floating-point comparisons, =, <, <=, > and >= return false and <> returns true if one or both of their arguments is nan. nan is quiet_nan since 5.1; it was a signaling NaN before. << val signaling_nan : float >> Signaling NaN. The corresponding signals do not raise OCaml exception, but the value can be useful for interoperability with C libraries. Since: 5.1 << val quiet_nan : float >> Quiet NaN. Since: 5.1 << val pi : float >> The constant pi. << val max_float : float >> The largest positive finite value of type float. << val min_float : float >> The smallest positive, non-zero, non-denormalized value of type float. << val epsilon : float >> The difference between 1.0 and the smallest exactly representable floating-point number greater than 1.0. << val is_finite : float -> bool >> is_finite x is true if and only if x is finite i.e., not infinite and not Float.nan[29.21]. Since: 4.08 << val is_infinite : float -> bool >> is_infinite x is true if and only if x is Float.infinity[29.21] or Float.neg_infinity[29.21]. Since: 4.08 << val is_nan : float -> bool >> is_nan x is true if and only if x is not a number (see Float.nan[29.21]). Since: 4.08 << val is_integer : float -> bool >> is_integer x is true if and only if x is an integer. Since: 4.08 << val of_int : int -> float >> Convert an integer to floating-point. << val to_int : float -> int >> Truncate the given floating-point number to an integer. The result is unspecified if the argument is nan or falls outside the range of representable integers. << val of_string : string -> float >> Convert the given string to a float. The string is read in decimal (by default) or in hexadecimal (marked by 0x or 0X). The format of decimal floating-point numbers is [-] dd.ddd (e|E) [+|-] dd , where d stands for a decimal digit. The format of hexadecimal floating-point numbers is [-] 0(x|X) hh.hhh (p|P) [+|-] dd , where h stands for an hexadecimal digit and d for a decimal digit. In both cases, at least one of the integer and fractional parts must be given; the exponent part is optional. The _ (underscore) character can appear anywhere in the string and is ignored. Depending on the execution platforms, other representations of floating-point numbers can be accepted, but should not be relied upon. Raises Failure if the given string is not a valid representation of a float. << val of_string_opt : string -> float option >> Same as of_string, but returns None instead of raising. << val to_string : float -> string >> Return a string representation of a floating-point number. This conversion can involve a loss of precision. For greater control over the manner in which the number is printed, see Printf[29.44]. This function is an alias for string_of_float[28.2]. << type fpclass = fpclass = | FP_normal >> Normal number, none of the below << | FP_subnormal >> Number very close to 0.0, has reduced precision << | FP_zero >> Number is 0.0 or -0.0 << | FP_infinite >> Number is positive or negative infinity << | FP_nan >> Not a number: result of an undefined operation The five classes of floating-point numbers, as determined by the Float.classify_float[29.21] function. << val classify_float : float -> fpclass >> Return the class of the given floating-point number: normal, subnormal, zero, infinite, or not a number. << val pow : float -> float -> float >> Exponentiation. << val sqrt : float -> float >> Square root. << val cbrt : float -> float >> Cube root. Since: 4.13 << val exp : float -> float >> Exponential. << val exp2 : float -> float >> Base 2 exponential function. Since: 4.13 << val log : float -> float >> Natural logarithm. << val log10 : float -> float >> Base 10 logarithm. << val log2 : float -> float >> Base 2 logarithm. Since: 4.13 << val expm1 : float -> float >> expm1 x computes exp x -. 1.0, giving numerically-accurate results even if x is close to 0.0. << val log1p : float -> float >> log1p x computes log(1.0 +. x) (natural logarithm), giving numerically-accurate results even if x is close to 0.0. << val cos : float -> float >> Cosine. Argument is in radians. << val sin : float -> float >> Sine. Argument is in radians. << val tan : float -> float >> Tangent. Argument is in radians. << val acos : float -> float >> Arc cosine. The argument must fall within the range [-1.0, 1.0]. Result is in radians and is between 0.0 and pi. << val asin : float -> float >> Arc sine. The argument must fall within the range [-1.0, 1.0]. Result is in radians and is between -pi/2 and pi/2. << val atan : float -> float >> Arc tangent. Result is in radians and is between -pi/2 and pi/2. << val atan2 : float -> float -> float >> atan2 y x returns the arc tangent of y /. x. The signs of x and y are used to determine the quadrant of the result. Result is in radians and is between -pi and pi. << val hypot : float -> float -> float >> hypot x y returns sqrt(x *. x +. y *. y), that is, the length of the hypotenuse of a right-angled triangle with sides of length x and y, or, equivalently, the distance of the point (x,y) to origin. If one of x or y is infinite, returns infinity even if the other is nan. << val cosh : float -> float >> Hyperbolic cosine. Argument is in radians. << val sinh : float -> float >> Hyperbolic sine. Argument is in radians. << val tanh : float -> float >> Hyperbolic tangent. Argument is in radians. << val acosh : float -> float >> Hyperbolic arc cosine. The argument must fall within the range [1.0, inf]. Result is in radians and is between 0.0 and inf. Since: 4.13 << val asinh : float -> float >> Hyperbolic arc sine. The argument and result range over the entire real line. Result is in radians. Since: 4.13 << val atanh : float -> float >> Hyperbolic arc tangent. The argument must fall within the range [-1.0, 1.0]. Result is in radians and ranges over the entire real line. Since: 4.13 << val erf : float -> float >> Error function. The argument ranges over the entire real line. The result is always within [-1.0, 1.0]. Since: 4.13 << val erfc : float -> float >> Complementary error function (erfc x = 1 - erf x). The argument ranges over the entire real line. The result is always within [-1.0, 1.0]. Since: 4.13 << val trunc : float -> float >> trunc x rounds x to the nearest integer whose absolute value is less than or equal to x. Since: 4.08 << val round : float -> float >> round x rounds x to the nearest integer with ties (fractional values of 0.5) rounded away from zero, regardless of the current rounding direction. If x is an integer, +0., -0., nan, or infinite, x itself is returned. On 64-bit mingw-w64, this function may be emulated owing to a bug in the C runtime library (CRT) on this platform. Since: 4.08 << val ceil : float -> float >> Round above to an integer value. ceil f returns the least integer value greater than or equal to f. The result is returned as a float. << val floor : float -> float >> Round below to an integer value. floor f returns the greatest integer value less than or equal to f. The result is returned as a float. << val next_after : float -> float -> float >> next_after x y returns the next representable floating-point value following x in the direction of y. More precisely, if y is greater (resp. less) than x, it returns the smallest (resp. largest) representable number greater (resp. less) than x. If x equals y, the function returns y. If x or y is nan, a nan is returned. Note that next_after max_float infinity = infinity and that next_after 0. infinity is the smallest denormalized positive number. If x is the smallest denormalized positive number, next_after x 0. = 0. Since: 4.08 << val copy_sign : float -> float -> float >> copy_sign x y returns a float whose absolute value is that of x and whose sign is that of y. If x is nan, returns nan. If y is nan, returns either x or -. x, but it is not specified which. << val sign_bit : float -> bool >> sign_bit x is true if and only if the sign bit of x is set. For example sign_bit 1. and signbit 0. are false while sign_bit (-1.) and sign_bit (-0.) are true. Since: 4.08 << val frexp : float -> float * int >> frexp f returns the pair of the significant and the exponent of f. When f is zero, the significant x and the exponent n of f are equal to zero. When f is non-zero, they are defined by f = x *. 2 ** n and 0.5 <= x < 1.0. << val ldexp : float -> int -> float >> ldexp x n returns x *. 2 ** n. << val modf : float -> float * float >> modf f returns the pair of the fractional and integral part of f. << type t = float >> An alias for the type of floating-point numbers. << val compare : t -> t -> int >> compare x y returns 0 if x is equal to y, a negative integer if x is less than y, and a positive integer if x is greater than y. compare treats nan as equal to itself and less than any other float value. This treatment of nan ensures that compare defines a total ordering relation. << val equal : t -> t -> bool >> The equal function for floating-point numbers, compared using Float.compare[29.21]. << val min : t -> t -> t >> min x y returns the minimum of x and y. It returns nan when x or y is nan. Moreover min (-0.) (+0.) = -0. Since: 4.08 << val max : float -> float -> float >> max x y returns the maximum of x and y. It returns nan when x or y is nan. Moreover max (-0.) (+0.) = +0. Since: 4.08 << val min_max : float -> float -> float * float >> min_max x y is (min x y, max x y), just more efficient. Since: 4.08 << val min_num : t -> t -> t >> min_num x y returns the minimum of x and y treating nan as missing values. If both x and y are nan, nan is returned. Moreover min_num (-0.) (+0.) = -0. Since: 4.08 << val max_num : t -> t -> t >> max_num x y returns the maximum of x and y treating nan as missing values. If both x and y are nan nan is returned. Moreover max_num (-0.) (+0.) = +0. Since: 4.08 << val min_max_num : float -> float -> float * float >> min_max_num x y is (min_num x y, max_num x y), just more efficient. Note that in particular min_max_num x nan = (x, x) and min_max_num nan y = (y, y). Since: 4.08 << val seeded_hash : int -> t -> int >> A seeded hash function for floats, with the same output value as Hashtbl.seeded_hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded[29.25]. Since: 5.1 << val hash : t -> int >> An unseeded hash function for floats, with the same output value as Hashtbl.hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.Make[29.25]. << module Array : >>  sig << type t = floatarray >> The type of float arrays with packed representation. Since: 4.08 << val length : t -> int >> Return the length (number of elements) of the given floatarray. << val get : t -> int -> float >> get a n returns the element number n of floatarray a. Raises Invalid_argument if n is outside the range 0 to (length a - 1). << val set : t -> int -> float -> unit >> set a n x modifies floatarray a in place, replacing element number n with x. Raises Invalid_argument if n is outside the range 0 to (length a - 1). << val make : int -> float -> t >> make n x returns a fresh floatarray of length n, initialized with x. Raises Invalid_argument if n < 0 or n > Sys.max_floatarray_length. << val create : int -> t >> create n returns a fresh floatarray of length n, with uninitialized data. Raises Invalid_argument if n < 0 or n > Sys.max_floatarray_length. << val init : int -> (int -> float) -> t >> init n f returns a fresh floatarray of length n, with element number i initialized to the result of f i. In other terms, init n f tabulates the results of f applied to the integers 0 to n-1. Raises Invalid_argument if n < 0 or n > Sys.max_floatarray_length. << val make_matrix : int -> int -> float -> t array >> make_matrix dimx dimy e returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy, where all elements are initialized with e. Since: 5.2 Raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_floatarray_length[29.56]. << val init_matrix : int -> int -> (int -> int -> float) -> t array >> init_matrix dimx dimy f returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy, where the element at index (x,y) is initialized with f x y. Since: 5.2 Raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_floatarray_length[29.56]. << val append : t -> t -> t >> append v1 v2 returns a fresh floatarray containing the concatenation of the floatarrays v1 and v2. Raises Invalid_argument if length v1 + length v2 > Sys.max_floatarray_length. << val concat : t list -> t >> Same as Float.Array.append[29.21], but concatenates a list of floatarrays. << val sub : t -> int -> int -> t >> sub a pos len returns a fresh floatarray of length len, containing the elements number pos to pos + len - 1 of floatarray a. Raises Invalid_argument if pos and len do not designate a valid subarray of a; that is, if pos < 0, or len < 0, or pos + len > length a. << val copy : t -> t >> copy a returns a copy of a, that is, a fresh floatarray containing the same elements as a. << val fill : t -> int -> int -> float -> unit >> fill a pos len x modifies the floatarray a in place, storing x in elements number pos to pos + len - 1. Raises Invalid_argument if pos and len do not designate a valid subarray of a. << val blit : t -> int -> t -> int -> int -> unit >> blit src src_pos dst dst_pos len copies len elements from floatarray src, starting at element number src_pos, to floatarray dst, starting at element number dst_pos. It works correctly even if src and dst are the same floatarray, and the source and destination chunks overlap. Raises Invalid_argument if src_pos and len do not designate a valid subarray of src, or if dst_pos and len do not designate a valid subarray of dst. << val to_list : t -> float list >> to_list a returns the list of all the elements of a. << val of_list : float list -> t >> of_list l returns a fresh floatarray containing the elements of l. Raises Invalid_argument if the length of l is greater than Sys.max_floatarray_length. Iterators ========= << val iter : (float -> unit) -> t -> unit >> iter f a applies function f in turn to all the elements of a. It is equivalent to f a.(0); f a.(1); ...; f a.(length a - 1); (). << val iteri : (int -> float -> unit) -> t -> unit >> Same as Float.Array.iter[29.21], but the function is applied with the index of the element as first argument, and the element itself as second argument. << val map : (float -> float) -> t -> t >> map f a applies function f to all the elements of a, and builds a floatarray with the results returned by f. << val map_inplace : (float -> float) -> t -> unit >> map_inplace f a applies function f to all elements of a, and updates their values in place. Since: 5.1 << val mapi : (int -> float -> float) -> t -> t >> Same as Float.Array.map[29.21], but the function is applied to the index of the element as first argument, and the element itself as second argument. << val mapi_inplace : (int -> float -> float) -> t -> unit >> Same as Float.Array.map_inplace[29.21], but the function is applied to the index of the element as first argument, and the element itself as second argument. Since: 5.1 << val fold_left : ('acc -> float -> 'acc) -> 'acc -> t -> 'acc >> fold_left f x init computes f (... (f (f x init.(0)) init.(1)) ...) init.(n-1), where n is the length of the floatarray init. << val fold_right : (float -> 'acc -> 'acc) -> t -> 'acc -> 'acc >> fold_right f a init computes f a.(0) (f a.(1) ( ... (f a.(n-1) init) ...)), where n is the length of the floatarray a. Iterators on two arrays ======================= << val iter2 : (float -> float -> unit) -> t -> t -> unit >> Array.iter2 f a b applies function f to all the elements of a and b. Raises Invalid_argument if the floatarrays are not the same size. << val map2 : (float -> float -> float) -> t -> t -> t >> map2 f a b applies function f to all the elements of a and b, and builds a floatarray with the results returned by f: [| f a.(0) b.(0); ...; f a.(length a - 1) b.(length b - 1)|]. Raises Invalid_argument if the floatarrays are not the same size. Array scanning ============== << val for_all : (float -> bool) -> t -> bool >> for_all f [|a1; ...; an|] checks if all elements of the floatarray satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an). << val exists : (float -> bool) -> t -> bool >> exists f [|a1; ...; an|] checks if at least one element of the floatarray satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an). << val mem : float -> t -> bool >> mem a set is true if and only if there is an element of set that is structurally equal to a, i.e. there is an x in set such that compare a x = 0. << val mem_ieee : float -> t -> bool >> Same as Float.Array.mem[29.21], but uses IEEE equality instead of structural equality. Array searching =============== << val find_opt : (float -> bool) -> t -> float option >> << val find_index : (float -> bool) -> t -> int option >> find_index f a returns Some i, where i is the index of the first element of the array a that satisfies f x, if there is such an element. It returns None if there is no such element. Since: 5.1 << val find_map : (float -> 'a option) -> t -> 'a option >> << val find_mapi : (int -> float -> 'a option) -> t -> 'a option >> Same as find_map, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 5.1 Sorting and shuffling ===================== << val sort : (float -> float -> int) -> t -> unit >> Sort a floatarray in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see below for a complete specification). For example, compare[28.2] is a suitable comparison function. After calling sort, the array is sorted in place in increasing order. sort is guaranteed to run in constant heap space and (at most) logarithmic stack space. The current implementation uses Heap Sort. It runs in constant stack space. Specification of the comparison function: Let a be the floatarray and cmp the comparison function. The following must be true for all x, y, z in a : - cmp x y > 0 if and only if cmp y x < 0 - if cmp x y >= 0 and cmp y z >= 0 then cmp x z >= 0 When sort returns, a contains the same elements as before, reordered in such a way that for all i and j valid indices of a : - cmp a.(i) a.(j) >= 0 if and only if i >= j << val stable_sort : (float -> float -> int) -> t -> unit >> Same as Float.Array.sort[29.21], but the sorting algorithm is stable (i.e. elements that compare equal are kept in their original order) and not guaranteed to run in constant heap space. The current implementation uses Merge Sort. It uses a temporary floatarray of length n/2, where n is the length of the floatarray. It is usually faster than the current implementation of Float.Array.sort[29.21]. << val fast_sort : (float -> float -> int) -> t -> unit >> Same as Float.Array.sort[29.21] or Float.Array.stable_sort[29.21], whichever is faster on typical input. << val shuffle : rand:(int -> int) -> t -> unit >> shuffle rand a randomly permutes a’s elements using rand for randomness. The distribution of permutations is uniform. rand must be such that a call to rand n returns a uniformly distributed random number in the range [0;n-1]. Random.int[29.46] can be used for this (do not forget to initialize[29.46] the generator). Since: 5.2 Float arrays and Sequences ========================== << val to_seq : t -> float Seq.t >> Iterate on the floatarray, in increasing order. Modifications of the floatarray during iteration will be reflected in the sequence. << val to_seqi : t -> (int * float) Seq.t >> Iterate on the floatarray, in increasing order, yielding indices along elements. Modifications of the floatarray during iteration will be reflected in the sequence. << val of_seq : float Seq.t -> t >> Create an array from the generator. << val map_to_array : (float -> 'a) -> t -> 'a array >> map_to_array f a applies function f to all the elements of a, and builds an array with the results returned by f: [| f a.(0); f a.(1); ...; f a.(length a - 1) |]. << val map_from_array : ('a -> float) -> 'a array -> t >> map_from_array f a applies function f to all the elements of a, and builds a floatarray with the results returned by f. Arrays and concurrency safety ============================= Care must be taken when concurrently accessing float arrays from multiple domains: accessing an array will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results. Atomicity --------- Every float array operation that accesses more than one array element is not atomic. This includes iteration, scanning, sorting, splitting and combining arrays. For example, consider the following program: << let size = 100_000_000 let a = Float.Array.make size 1. let update a f () = Float.Array.iteri (fun i x -> Float.Array.set a i (f x)) a let d1 = Domain.spawn (update a (fun x -> x +. 1.)) let d2 = Domain.spawn (update a (fun x -> 2. *. x +. 1.)) let () = Domain.join d1; Domain.join d2 >> After executing this code, each field of the float array a is either 2., 3., 4. or 5.. If atomicity is required, then the user must implement their own synchronization (for example, using Mutex.t[29.37]). Data races ---------- If two domains only access disjoint parts of the array, then the observed behaviour is the equivalent to some sequential interleaving of the operations from the two domains. A data race is said to occur when two domains access the same array element without synchronization and at least one of the accesses is a write. In the absence of data races, the observed behaviour is equivalent to some sequential interleaving of the operations from different domains. Whenever possible, data races should be avoided by using synchronization to mediate the accesses to the array elements. Indeed, in the presence of data races, programs will not crash but the observed behaviour may not be equivalent to any sequential interleaving of operations from different domains. Nevertheless, even in the presence of data races, a read operation will return the value of some prior write to that location with a few exceptions. Tearing -------- Float arrays have two supplementary caveats in the presence of data races. First, the blit operation might copy an array byte-by-byte. Data races between such a blit operation and another operation might produce surprising values due to tearing: partial writes interleaved with other operations can create float values that would not exist with a sequential execution. For instance, at the end of << let zeros = Float.Array.make size 0. let max_floats = Float.Array.make size Float.max_float let res = Float.Array.copy zeros let d1 = Domain.spawn (fun () -> Float.Array.blit zeros 0 res 0 size) let d2 = Domain.spawn (fun () -> Float.Array.blit max_floats 0 res 0 size) let () = Domain.join d1; Domain.join d2 >> the res float array might contain values that are neither 0. nor max_float. Second, on 32-bit architectures, getting or setting a field involves two separate memory accesses. In the presence of data races, the user may observe tearing on any operation.  end Float arrays with packed representation. << module ArrayLabels : >>  sig << type t = floatarray >> The type of float arrays with packed representation. Since: 4.08 << val length : t -> int >> Return the length (number of elements) of the given floatarray. << val get : t -> int -> float >> get a n returns the element number n of floatarray a. Raises Invalid_argument if n is outside the range 0 to (length a - 1). << val set : t -> int -> float -> unit >> set a n x modifies floatarray a in place, replacing element number n with x. Raises Invalid_argument if n is outside the range 0 to (length a - 1). << val make : int -> float -> t >> make n x returns a fresh floatarray of length n, initialized with x. Raises Invalid_argument if n < 0 or n > Sys.max_floatarray_length. << val create : int -> t >> create n returns a fresh floatarray of length n, with uninitialized data. Raises Invalid_argument if n < 0 or n > Sys.max_floatarray_length. << val init : int -> f:(int -> float) -> t >> init n ~f returns a fresh floatarray of length n, with element number i initialized to the result of f i. In other terms, init n ~f tabulates the results of f applied to the integers 0 to n-1. Raises Invalid_argument if n < 0 or n > Sys.max_floatarray_length. << val make_matrix : dimx:int -> dimy:int -> float -> t array >> make_matrix ~dimx ~dimy e returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy, where all elements are initialized with e. Since: 5.2 Raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_floatarray_length[29.56]. << val init_matrix : dimx:int -> dimy:int -> f:(int -> int -> float) -> t array >> init_matrix ~dimx ~dimy ~f returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy, where the element at index (x,y) is initialized with f x y. Since: 5.2 Raises Invalid_argument if dimx or dimy is negative or greater than Sys.max_floatarray_length[29.56]. << val append : t -> t -> t >> append v1 v2 returns a fresh floatarray containing the concatenation of the floatarrays v1 and v2. Raises Invalid_argument if length v1 + length v2 > Sys.max_floatarray_length. << val concat : t list -> t >> Same as Float.ArrayLabels.append[29.21], but concatenates a list of floatarrays. << val sub : t -> pos:int -> len:int -> t >> sub a ~pos ~len returns a fresh floatarray of length len, containing the elements number pos to pos + len - 1 of floatarray a. Raises Invalid_argument if pos and len do not designate a valid subarray of a; that is, if pos < 0, or len < 0, or pos + len > length a. << val copy : t -> t >> copy a returns a copy of a, that is, a fresh floatarray containing the same elements as a. << val fill : t -> pos:int -> len:int -> float -> unit >> fill a ~pos ~len x modifies the floatarray a in place, storing x in elements number pos to pos + len - 1. Raises Invalid_argument if pos and len do not designate a valid subarray of a. << val blit : src:t -> src_pos:int -> dst:t -> dst_pos:int -> len:int -> unit >> blit ~src ~src_pos ~dst ~dst_pos ~len copies len elements from floatarray src, starting at element number src_pos, to floatarray dst, starting at element number dst_pos. It works correctly even if src and dst are the same floatarray, and the source and destination chunks overlap. Raises Invalid_argument if src_pos and len do not designate a valid subarray of src, or if dst_pos and len do not designate a valid subarray of dst. << val to_list : t -> float list >> to_list a returns the list of all the elements of a. << val of_list : float list -> t >> of_list l returns a fresh floatarray containing the elements of l. Raises Invalid_argument if the length of l is greater than Sys.max_floatarray_length. Iterators ========= << val iter : f:(float -> unit) -> t -> unit >> iter ~f a applies function f in turn to all the elements of a. It is equivalent to f a.(0); f a.(1); ...; f a.(length a - 1); (). << val iteri : f:(int -> float -> unit) -> t -> unit >> Same as Float.ArrayLabels.iter[29.21], but the function is applied with the index of the element as first argument, and the element itself as second argument. << val map : f:(float -> float) -> t -> t >> map ~f a applies function f to all the elements of a, and builds a floatarray with the results returned by f. << val map_inplace : f:(float -> float) -> t -> unit >> map_inplace f a applies function f to all elements of a, and updates their values in place. Since: 5.1 << val mapi : f:(int -> float -> float) -> t -> t >> Same as Float.ArrayLabels.map[29.21], but the function is applied to the index of the element as first argument, and the element itself as second argument. << val mapi_inplace : f:(int -> float -> float) -> t -> unit >> Same as Float.ArrayLabels.map_inplace[29.21], but the function is applied to the index of the element as first argument, and the element itself as second argument. Since: 5.1 << val fold_left : f:('acc -> float -> 'acc) -> init:'acc -> t -> 'acc >> fold_left ~f x ~init computes f (... (f (f x init.(0)) init.(1)) ...) init.(n-1), where n is the length of the floatarray init. << val fold_right : f:(float -> 'acc -> 'acc) -> t -> init:'acc -> 'acc >> fold_right f a init computes f a.(0) (f a.(1) ( ... (f a.(n-1) init) ...)), where n is the length of the floatarray a. Iterators on two arrays ======================= << val iter2 : f:(float -> float -> unit) -> t -> t -> unit >> Array.iter2 ~f a b applies function f to all the elements of a and b. Raises Invalid_argument if the floatarrays are not the same size. << val map2 : f:(float -> float -> float) -> t -> t -> t >> map2 ~f a b applies function f to all the elements of a and b, and builds a floatarray with the results returned by f: [| f a.(0) b.(0); ...; f a.(length a - 1) b.(length b - 1)|]. Raises Invalid_argument if the floatarrays are not the same size. Array scanning ============== << val for_all : f:(float -> bool) -> t -> bool >> for_all ~f [|a1; ...; an|] checks if all elements of the floatarray satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an). << val exists : f:(float -> bool) -> t -> bool >> exists f [|a1; ...; an|] checks if at least one element of the floatarray satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an). << val mem : float -> set:t -> bool >> mem a ~set is true if and only if there is an element of set that is structurally equal to a, i.e. there is an x in set such that compare a x = 0. << val mem_ieee : float -> set:t -> bool >> Same as Float.ArrayLabels.mem[29.21], but uses IEEE equality instead of structural equality. Array searching =============== << val find_opt : f:(float -> bool) -> t -> float option >> << val find_index : f:(float -> bool) -> t -> int option >> find_index ~f a returns Some i, where i is the index of the first element of the array a that satisfies f x, if there is such an element. It returns None if there is no such element. Since: 5.1 << val find_map : f:(float -> 'a option) -> t -> 'a option >> << val find_mapi : f:(int -> float -> 'a option) -> t -> 'a option >> Same as find_map, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 5.1 Sorting and shuffling ===================== << val sort : cmp:(float -> float -> int) -> t -> unit >> Sort a floatarray in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see below for a complete specification). For example, compare[28.2] is a suitable comparison function. After calling sort, the array is sorted in place in increasing order. sort is guaranteed to run in constant heap space and (at most) logarithmic stack space. The current implementation uses Heap Sort. It runs in constant stack space. Specification of the comparison function: Let a be the floatarray and cmp the comparison function. The following must be true for all x, y, z in a : - cmp x y > 0 if and only if cmp y x < 0 - if cmp x y >= 0 and cmp y z >= 0 then cmp x z >= 0 When sort returns, a contains the same elements as before, reordered in such a way that for all i and j valid indices of a : - cmp a.(i) a.(j) >= 0 if and only if i >= j << val stable_sort : cmp:(float -> float -> int) -> t -> unit >> Same as Float.ArrayLabels.sort[29.21], but the sorting algorithm is stable (i.e. elements that compare equal are kept in their original order) and not guaranteed to run in constant heap space. The current implementation uses Merge Sort. It uses a temporary floatarray of length n/2, where n is the length of the floatarray. It is usually faster than the current implementation of Float.ArrayLabels.sort[29.21]. << val fast_sort : cmp:(float -> float -> int) -> t -> unit >> Same as Float.ArrayLabels.sort[29.21] or Float.ArrayLabels.stable_sort[29.21], whichever is faster on typical input. << val shuffle : rand:(int -> int) -> t -> unit >> shuffle ~rand a randomly permutes a’s elements using rand for randomness. The distribution of permutations is uniform. rand must be such that a call to rand n returns a uniformly distributed random number in the range [0;n-1]. Random.int[29.46] can be used for this (do not forget to initialize[29.46] the generator). Since: 5.2 Float arrays and Sequences ========================== << val to_seq : t -> float Seq.t >> Iterate on the floatarray, in increasing order. Modifications of the floatarray during iteration will be reflected in the sequence. << val to_seqi : t -> (int * float) Seq.t >> Iterate on the floatarray, in increasing order, yielding indices along elements. Modifications of the floatarray during iteration will be reflected in the sequence. << val of_seq : float Seq.t -> t >> Create an array from the generator. << val map_to_array : f:(float -> 'a) -> t -> 'a array >> map_to_array ~f a applies function f to all the elements of a, and builds an array with the results returned by f: [| f a.(0); f a.(1); ...; f a.(length a - 1) |]. << val map_from_array : f:('a -> float) -> 'a array -> t >> map_from_array ~f a applies function f to all the elements of a, and builds a floatarray with the results returned by f. Arrays and concurrency safety ============================= Care must be taken when concurrently accessing float arrays from multiple domains: accessing an array will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results. Atomicity --------- Every float array operation that accesses more than one array element is not atomic. This includes iteration, scanning, sorting, splitting and combining arrays. For example, consider the following program: << let size = 100_000_000 let a = Float.ArrayLabels.make size 1. let update a f () = Float.ArrayLabels.iteri ~f:(fun i x -> Float.Array.set a i (f x)) a let d1 = Domain.spawn (update a (fun x -> x +. 1.)) let d2 = Domain.spawn (update a (fun x -> 2. *. x +. 1.)) let () = Domain.join d1; Domain.join d2 >> After executing this code, each field of the float array a is either 2., 3., 4. or 5.. If atomicity is required, then the user must implement their own synchronization (for example, using Mutex.t[29.37]). Data races ---------- If two domains only access disjoint parts of the array, then the observed behaviour is the equivalent to some sequential interleaving of the operations from the two domains. A data race is said to occur when two domains access the same array element without synchronization and at least one of the accesses is a write. In the absence of data races, the observed behaviour is equivalent to some sequential interleaving of the operations from different domains. Whenever possible, data races should be avoided by using synchronization to mediate the accesses to the array elements. Indeed, in the presence of data races, programs will not crash but the observed behaviour may not be equivalent to any sequential interleaving of operations from different domains. Nevertheless, even in the presence of data races, a read operation will return the value of some prior write to that location with a few exceptions. Tearing -------- Float arrays have two supplementary caveats in the presence of data races. First, the blit operation might copy an array byte-by-byte. Data races between such a blit operation and another operation might produce surprising values due to tearing: partial writes interleaved with other operations can create float values that would not exist with a sequential execution. For instance, at the end of << let zeros = Float.Array.make size 0. let max_floats = Float.Array.make size Float.max_float let res = Float.Array.copy zeros let d1 = Domain.spawn (fun () -> Float.Array.blit zeros 0 res 0 size) let d2 = Domain.spawn (fun () -> Float.Array.blit max_floats 0 res 0 size) let () = Domain.join d1; Domain.join d2 >> the res float array might contain values that are neither 0. nor max_float. Second, on 32-bit architectures, getting or setting a field involves two separate memory accesses. In the presence of data races, the user may observe tearing on any operation.  end Float arrays with packed representation (labeled functions). 29.22 Module Format : Pretty-printing. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= If you are new to this module, see the examples[29.4] below. This module implements a pretty-printing facility to format values within ’pretty-printing boxes’[29.22] and ’semantic tags’[29.22] combined with a set of printf-like functions[29.22]. The pretty-printer splits lines at specified break hints[29.22], and indents lines according to the box structure. Similarly, semantic tags[29.22] can be used to decouple text presentation from its contents. This pretty-printing facility is implemented as an overlay on top of abstract formatters[29.22] which provide basic output functions. Some formatters are predefined, notably: - Format.std_formatter[29.22] outputs to stdout[28.2] - Format.err_formatter[29.22] outputs to stderr[28.2] Most functions in the Format[29.22] module come in two variants: a short version that operates on the current domain’s standard formatter as obtained using Format.get_std_formatter[29.22] and the generic version prefixed by pp_ that takes a formatter as its first argument. For the version that operates on the current domain’s standard formatter, the call to Format.get_std_formatter[29.22] is delayed until the last argument is received. More formatters can be created with Format.formatter_of_out_channel[29.22], Format.formatter_of_buffer[29.22], Format.formatter_of_symbolic_output_buffer[29.22] or using custom formatters[29.22]. Warning: Since formatters[29.22] contain mutable state, it is not thread-safe to use the same formatter on multiple domains in parallel without synchronization. If multiple domains write to the same output channel using the predefined formatters (as obtained by Format.get_std_formatter[29.22] or Format.get_err_formatter[29.22]), the output from the domains will be interleaved with each other at points where the formatters are flushed, such as with Format.print_flush[29.22]. This synchronization is not performed by formatters obtained from Format.formatter_of_out_channel[29.22] (on the standard out channels or others). Introduction ============ You may consider this module as providing an extension to the printf facility to provide automatic line splitting. The addition of pretty-printing annotations to your regular printf format strings gives you fancy indentation and line breaks. Pretty-printing annotations are described below in the documentation of the function Format.fprintf[29.22]. You may also use the explicit pretty-printing box management and printing functions provided by this module. This style is more basic but more verbose than the concise fprintf format strings. For instance, the sequence open_box 0; print_string "x ="; print_space (); print_int 1; close_box (); print_newline () that prints x = 1 within a pretty-printing box, can be abbreviated as printf "@[%s@ %i@]@." "x =" 1, or even shorter printf "@[x =@ %i@]@." 1. Rule of thumb for casual users of this library: - use simple pretty-printing boxes (as obtained by open_box 0); - use simple break hints as obtained by print_cut () that outputs a simple break hint, or by print_space () that outputs a space indicating a break hint; - once a pretty-printing box is open, display its material with basic printing functions (e. g. print_int and print_string); - when the material for a pretty-printing box has been printed, call close_box () to close the box; - at the end of pretty-printing, flush the pretty-printer to display all the remaining material, e.g. evaluate print_newline (). The behavior of pretty-printing commands is unspecified if there is no open pretty-printing box. Each box opened by one of the open_ functions below must be closed using close_box for proper formatting. Otherwise, some of the material printed in the boxes may not be output, or may be formatted incorrectly. In case of interactive use, each phrase is executed in the initial state of the standard pretty-printer: after each phrase execution, the interactive system closes all open pretty-printing boxes, flushes all pending text, and resets the standard pretty-printer. Warning: mixing calls to pretty-printing functions of this module with calls to Stdlib[28.2] low level output functions is error prone. The pretty-printing functions output material that is delayed in the pretty-printer queue and stacks in order to compute proper line splitting. In contrast, basic I/O output functions write directly in their output device. As a consequence, the output of a basic I/O function may appear before the output of a pretty-printing function that has been called before. For instance, Stdlib.print_string "<"; Format.print_string "PRETTY"; Stdlib.print_string ">"; Format.print_string "TEXT"; leads to output <>PRETTYTEXT. Formatters ========== << type formatter >> Abstract data corresponding to a pretty-printer (also called a formatter) and all its machinery. See also [29.22]. Pretty-printing boxes ===================== The pretty-printing engine uses the concepts of pretty-printing box and break hint to drive indentation and line splitting behavior of the pretty-printer. Each different pretty-printing box kind introduces a specific line splitting policy: - within an horizontal box, break hints never split the line (but the line may be split in a box nested deeper), - within a vertical box, break hints always split the line, - within an horizontal/vertical box, if the box fits on the current line then break hints never split the line, otherwise break hint always split the line, - within a compacting box, a break hint never splits the line, unless there is no more room on the current line. Note that line splitting policy is box specific: the policy of a box does not rule the policy of inner boxes. For instance, if a vertical box is nested in an horizontal box, all break hints within the vertical box will split the line. Moreover, opening a box after the maximum indentation limit[29.22] splits the line whether or not the box would end up fitting on the line. << val pp_open_box : formatter -> int -> unit >> << val open_box : int -> unit >> pp_open_box ppf d opens a new compacting pretty-printing box with offset d in the formatter ppf. Within this box, the pretty-printer prints as much as possible material on every line. A break hint splits the line if there is no more room on the line to print the remainder of the box. Within this box, the pretty-printer emphasizes the box structure: if a structural box does not fit fully on a simple line, a break hint also splits the line if the splitting “moves to the left” (i.e. the new line gets an indentation smaller than the one of the current line). This box is the general purpose pretty-printing box. If the pretty-printer splits the line in the box, offset d is added to the current indentation. << val pp_close_box : formatter -> unit -> unit >> << val close_box : unit -> unit >> Closes the most recently open pretty-printing box. << val pp_open_hbox : formatter -> unit -> unit >> << val open_hbox : unit -> unit >> pp_open_hbox ppf () opens a new ’horizontal’ pretty-printing box. This box prints material on a single line. Break hints in a horizontal box never split the line. (Line splitting may still occur inside boxes nested deeper). << val pp_open_vbox : formatter -> int -> unit >> << val open_vbox : int -> unit >> pp_open_vbox ppf d opens a new ’vertical’ pretty-printing box with offset d. This box prints material on as many lines as break hints in the box. Every break hint in a vertical box splits the line. If the pretty-printer splits the line in the box, d is added to the current indentation. << val pp_open_hvbox : formatter -> int -> unit >> << val open_hvbox : int -> unit >> pp_open_hvbox ppf d opens a new ’horizontal/vertical’ pretty-printing box with offset d. This box behaves as an horizontal box if it fits on a single line, otherwise it behaves as a vertical box. If the pretty-printer splits the line in the box, d is added to the current indentation. << val pp_open_hovbox : formatter -> int -> unit >> << val open_hovbox : int -> unit >> pp_open_hovbox ppf d opens a new ’horizontal-or-vertical’ pretty-printing box with offset d. This box prints material as much as possible on every line. A break hint splits the line if there is no more room on the line to print the remainder of the box. If the pretty-printer splits the line in the box, d is added to the current indentation. Formatting functions ==================== << val pp_print_string : formatter -> string -> unit >> << val print_string : string -> unit >> pp_print_string ppf s prints s in the current pretty-printing box. << val pp_print_bytes : formatter -> bytes -> unit >> << val print_bytes : bytes -> unit >> pp_print_bytes ppf b prints b in the current pretty-printing box. Since: 4.13 << val pp_print_as : formatter -> int -> string -> unit >> << val print_as : int -> string -> unit >> pp_print_as ppf len s prints s in the current pretty-printing box. The pretty-printer formats s as if it were of length len. << val pp_print_int : formatter -> int -> unit >> << val print_int : int -> unit >> Print an integer in the current pretty-printing box. << val pp_print_float : formatter -> float -> unit >> << val print_float : float -> unit >> Print a floating point number in the current pretty-printing box. << val pp_print_char : formatter -> char -> unit >> << val print_char : char -> unit >> Print a character in the current pretty-printing box. << val pp_print_bool : formatter -> bool -> unit >> << val print_bool : bool -> unit >> Print a boolean in the current pretty-printing box. << val pp_print_nothing : formatter -> unit -> unit >> Print nothing. Since: 5.2 Break hints =========== A ’break hint’ tells the pretty-printer to output some space or split the line whichever way is more appropriate to the current pretty-printing box splitting rules. Break hints are used to separate printing items and are mandatory to let the pretty-printer correctly split lines and indent items. Simple break hints are: - the ’space’: output a space or split the line if appropriate, - the ’cut’: split the line if appropriate. Note: the notions of space and line splitting are abstract for the pretty-printing engine, since those notions can be completely redefined by the programmer. However, in the pretty-printer default setting, “output a space” simply means printing a space character (ASCII code 32) and “split the line” means printing a newline character (ASCII code 10). << val pp_print_space : formatter -> unit -> unit >> << val print_space : unit -> unit >> pp_print_space ppf () emits a ’space’ break hint: the pretty-printer may split the line at this point, otherwise it prints one space. pp_print_space ppf () is equivalent to pp_print_break ppf 1 0. << val pp_print_cut : formatter -> unit -> unit >> << val print_cut : unit -> unit >> pp_print_cut ppf () emits a ’cut’ break hint: the pretty-printer may split the line at this point, otherwise it prints nothing. pp_print_cut ppf () is equivalent to pp_print_break ppf 0 0. << val pp_print_break : formatter -> int -> int -> unit >> << val print_break : int -> int -> unit >> pp_print_break ppf nspaces offset emits a ’full’ break hint: the pretty-printer may split the line at this point, otherwise it prints nspaces spaces. If the pretty-printer splits the line, offset is added to the current indentation. << val pp_print_custom_break : formatter -> fits:string * int * string -> breaks:string * int * string -> unit >> pp_print_custom_break ppf ~fits:(s1, n, s2) ~breaks:(s3, m, s4) emits a custom break hint: the pretty-printer may split the line at this point. If it does not split the line, then the s1 is emitted, then n spaces, then s2. If it splits the line, then it emits the s3 string, then an indent (according to the box rules), then an offset of m spaces, then the s4 string. While n and m are handled by formatter_out_functions.out_indent, the strings will be handled by formatter_out_functions.out_string. This allows for a custom formatter that handles indentation distinctly, for example, outputs
    tags or   entities. The custom break is useful if you want to change which visible (non-whitespace) characters are printed in case of break or no break. For example, when printing a list [a; b; c] , you might want to add a trailing semicolon when it is printed vertically: << [ a; b; c; ] >> You can do this as follows: << printf "@[[@;<0 2>@[a;@,b;@,c@]%t]@]@\n" (pp_print_custom_break ~fits:("", 0, "") ~breaks:(";", 0, "")) >> Since: 4.08 << val pp_force_newline : formatter -> unit -> unit >> << val force_newline : unit -> unit >> Force a new line in the current pretty-printing box. The pretty-printer must split the line at this point, Not the normal way of pretty-printing, since imperative line splitting may interfere with current line counters and box size calculation. Using break hints within an enclosing vertical box is a better alternative. << val pp_print_if_newline : formatter -> unit -> unit >> << val print_if_newline : unit -> unit >> Execute the next formatting command if the preceding line has just been split. Otherwise, ignore the next formatting command. Pretty-printing termination =========================== << val pp_print_flush : formatter -> unit -> unit >> << val print_flush : unit -> unit >> End of pretty-printing: resets the pretty-printer to initial state. All open pretty-printing boxes are closed, all pending text is printed. In addition, the pretty-printer low level output device is flushed to ensure that all pending text is really displayed. Note: never use print_flush in the normal course of a pretty-printing routine, since the pretty-printer uses a complex buffering machinery to properly indent the output; manually flushing those buffers at random would conflict with the pretty-printer strategy and result to poor rendering. Only consider using print_flush when displaying all pending material is mandatory (for instance in case of interactive use when you want the user to read some text) and when resetting the pretty-printer state will not disturb further pretty-printing. Warning: If the output device of the pretty-printer is an output channel, repeated calls to print_flush means repeated calls to flush[28.2] to flush the out channel; these explicit flush calls could foil the buffering strategy of output channels and could dramatically impact efficiency. << val pp_print_newline : formatter -> unit -> unit >> << val print_newline : unit -> unit >> End of pretty-printing: resets the pretty-printer to initial state. All open pretty-printing boxes are closed, all pending text is printed. Equivalent to Format.print_flush[29.22] with a new line emitted on the pretty-printer low-level output device immediately before the device is flushed. See corresponding words of caution for Format.print_flush[29.22]. Note: this is not the normal way to output a new line; the preferred method is using break hints within a vertical pretty-printing box. Margin ====== << val pp_infinity : int >> pp_infinity is the maximal size of the margin. Its exact value is implementation dependent but is guaranteed to be greater than 10^9. Since: 5.2 << val pp_set_margin : formatter -> int -> unit >> << val set_margin : int -> unit >> pp_set_margin ppf d sets the right margin to d (in characters): the pretty-printer splits lines that overflow the right margin according to the break hints given. Setting the margin to d means that the formatting engine aims at printing at most d-1 characters per line. Nothing happens if d is smaller than 2. If d >= Format.pp_infinity[29.22], the right margin is set to Format.pp_infinity[29.22] - 1. If d is less than the current maximum indentation limit, the maximum indentation limit is decreased while trying to preserve a minimal ratio max_indent/margin>=50% and if possible the current difference margin - max_indent. See also Format.pp_set_geometry[29.22]. << val pp_get_margin : formatter -> unit -> int >> << val get_margin : unit -> int >> Returns the position of the right margin. Maximum indentation limit ========================= << val pp_set_max_indent : formatter -> int -> unit >> << val set_max_indent : int -> unit >> pp_set_max_indent ppf d sets the maximum indentation limit of lines to d (in characters): once this limit is reached, new pretty-printing boxes are rejected to the left, unless the enclosing box fully fits on the current line. As an illustration, << set_margin 10; set_max_indent 5; printf "@[123456@[7@]89A@]@." >> yields << 123456 789A >> because the nested box "@[7@]" is opened after the maximum indentation limit (7>5) and its parent box does not fit on the current line. Either decreasing the length of the parent box to make it fit on a line: << printf "@[123456@[7@]89@]@." >> or opening an intermediary box before the maximum indentation limit which fits on the current line << printf "@[123@[456@[7@]89@]A@]@." >> avoids the rejection to the left of the inner boxes and print respectively "123456789" and "123456789A" . Note also that vertical boxes never fit on a line whereas horizontal boxes always fully fit on the current line. Opening a box may split a line whereas the contents may have fit. If this behavior is problematic, it can be curtailed by setting the maximum indentation limit to margin - 1. Note that setting the maximum indentation limit to margin is invalid. Nothing happens if d is smaller than 2. If d is greater than the current margin, it is ignored, and the current maximum indentation limit is kept. See also Format.pp_set_geometry[29.22]. << val pp_get_max_indent : formatter -> unit -> int >> << val get_max_indent : unit -> int >> Return the maximum indentation limit (in characters). Geometry ========= Geometric functions can be used to manipulate simultaneously the coupled variables, margin and maximum indentation limit. << type geometry = { max_indent : int ; margin : int ; } >> Since: 4.08 << val check_geometry : geometry -> bool >> Check if the formatter geometry is valid: 1 < max_indent < margin < Format.pp_infinity[29.22] Since: 4.08 << val pp_set_geometry : formatter -> max_indent:int -> margin:int -> unit >> << val set_geometry : max_indent:int -> margin:int -> unit >> << val pp_safe_set_geometry : formatter -> max_indent:int -> margin:int -> unit >> << val safe_set_geometry : max_indent:int -> margin:int -> unit >> pp_set_geometry ppf ~max_indent ~margin sets both the margin and maximum indentation limit for ppf. When 1 < max_indent < margin < Format.pp_infinity[29.22], pp_set_geometry ppf ~max_indent ~margin is equivalent to pp_set_margin ppf margin; pp_set_max_indent ppf max_indent; and avoids the subtly incorrect pp_set_max_indent ppf max_indent; pp_set_margin ppf margin; Outside of this domain, pp_set_geometry raises an invalid argument exception whereas pp_safe_set_geometry does nothing. Since: 4.08 << val pp_update_geometry : formatter -> (geometry -> geometry) -> unit >> pp_update_geometry ppf (fun geo -> { geo with ... }) lets you update a formatter’s geometry in a way that is robust to extension of the geometry record with new fields. Raises an invalid argument exception if the returned geometry does not satisfy Format.check_geometry[29.22]. Since: 4.11 << val update_geometry : (geometry -> geometry) -> unit >> << val pp_get_geometry : formatter -> unit -> geometry >> << val get_geometry : unit -> geometry >> Return the current geometry of the formatter Since: 4.08 Maximum formatting depth ======================== The maximum formatting depth is the maximum number of pretty-printing boxes simultaneously open. Material inside boxes nested deeper is printed as an ellipsis (more precisely as the text returned by Format.get_ellipsis_text[29.22] ()). << val pp_set_max_boxes : formatter -> int -> unit >> << val set_max_boxes : int -> unit >> pp_set_max_boxes ppf max sets the maximum number of pretty-printing boxes simultaneously open. Material inside boxes nested deeper is printed as an ellipsis (more precisely as the text returned by Format.get_ellipsis_text[29.22] ()). Nothing happens if max is smaller than 2. << val pp_get_max_boxes : formatter -> unit -> int >> << val get_max_boxes : unit -> int >> Returns the maximum number of pretty-printing boxes allowed before ellipsis. << val pp_over_max_boxes : formatter -> unit -> bool >> << val over_max_boxes : unit -> bool >> Tests if the maximum number of pretty-printing boxes allowed have already been opened. Tabulation boxes ================ A tabulation box prints material on lines divided into cells of fixed length. A tabulation box provides a simple way to display vertical columns of left adjusted text. This box features command set_tab to define cell boundaries, and command print_tab to move from cell to cell and split the line when there is no more cells to print on the line. Note: printing within tabulation box is line directed, so arbitrary line splitting inside a tabulation box leads to poor rendering. Yet, controlled use of tabulation boxes allows simple printing of columns within module Format[29.22]. << val pp_open_tbox : formatter -> unit -> unit >> << val open_tbox : unit -> unit >> open_tbox () opens a new tabulation box. This box prints lines separated into cells of fixed width. Inside a tabulation box, special tabulation markers defines points of interest on the line (for instance to delimit cell boundaries). Function Format.set_tab[29.22] sets a tabulation marker at insertion point. A tabulation box features specific tabulation breaks to move to next tabulation marker or split the line. Function Format.print_tbreak[29.22] prints a tabulation break. << val pp_close_tbox : formatter -> unit -> unit >> << val close_tbox : unit -> unit >> Closes the most recently opened tabulation box. << val pp_set_tab : formatter -> unit -> unit >> << val set_tab : unit -> unit >> Sets a tabulation marker at current insertion point. << val pp_print_tab : formatter -> unit -> unit >> << val print_tab : unit -> unit >> print_tab () emits a ’next’ tabulation break hint: if not already set on a tabulation marker, the insertion point moves to the first tabulation marker on the right, or the pretty-printer splits the line and insertion point moves to the leftmost tabulation marker. It is equivalent to print_tbreak 0 0. << val pp_print_tbreak : formatter -> int -> int -> unit >> << val print_tbreak : int -> int -> unit >> print_tbreak nspaces offset emits a ’full’ tabulation break hint. If not already set on a tabulation marker, the insertion point moves to the first tabulation marker on the right and the pretty-printer prints nspaces spaces. If there is no next tabulation marker on the right, the pretty-printer splits the line at this point, then insertion point moves to the leftmost tabulation marker of the box. If the pretty-printer splits the line, offset is added to the current indentation. Ellipsis ======== << val pp_set_ellipsis_text : formatter -> string -> unit >> << val set_ellipsis_text : string -> unit >> Set the text of the ellipsis printed when too many pretty-printing boxes are open (a single dot, ., by default). << val pp_get_ellipsis_text : formatter -> unit -> string >> << val get_ellipsis_text : unit -> string >> Return the text of the ellipsis. Semantic tags ============= << type stag = .. >> Semantic tags (or simply tags) are user’s defined annotations to associate user’s specific operations to printed entities. Common usage of semantic tags is text decoration to get specific font or text size rendering for a display device, or marking delimitation of entities (e.g. HTML or TeX elements or terminal escape sequences). More sophisticated usage of semantic tags could handle dynamic modification of the pretty-printer behavior to properly print the material within some specific tags. For instance, we can define an RGB tag like so: << type stag += RGB of {r:int;g:int;b:int} >> In order to properly delimit printed entities, a semantic tag must be opened before and closed after the entity. Semantic tags must be properly nested like parentheses using Format.pp_open_stag[29.22] and Format.pp_close_stag[29.22]. Tag specific operations occur any time a tag is opened or closed, At each occurrence, two kinds of operations are performed tag-marking and tag-printing: - The tag-marking operation is the simpler tag specific operation: it simply writes a tag specific string into the output device of the formatter. Tag-marking does not interfere with line-splitting computation. - The tag-printing operation is the more involved tag specific operation: it can print arbitrary material to the formatter. Tag-printing is tightly linked to the current pretty-printer operations. Roughly speaking, tag-marking is commonly used to get a better rendering of texts in the rendering device, while tag-printing allows fine tuning of printing routines to print the same entity differently according to the semantic tags (i.e. print additional material or even omit parts of the output). More precisely: when a semantic tag is opened or closed then both and successive ’tag-printing’ and ’tag-marking’ operations occur: - Tag-printing a semantic tag means calling the formatter specific function print_open_stag (resp. print_close_stag) with the name of the tag as argument: that tag-printing function can then print any regular material to the formatter (so that this material is enqueued as usual in the formatter queue for further line splitting computation). - Tag-marking a semantic tag means calling the formatter specific function mark_open_stag (resp. mark_close_stag) with the name of the tag as argument: that tag-marking function can then return the ’tag-opening marker’ (resp. ‘tag-closing marker’) for direct output into the output device of the formatter. Being written directly into the output device of the formatter, semantic tag marker strings are not considered as part of the printing material that drives line splitting (in other words, the length of the strings corresponding to tag markers is considered as zero for line splitting). Thus, semantic tag handling is in some sense transparent to pretty-printing and does not interfere with usual indentation. Hence, a single pretty-printing routine can output both simple ’verbatim’ material or richer decorated output depending on the treatment of tags. By default, tags are not active, hence the output is not decorated with tag information. Once set_tags is set to true, the pretty-printer engine honors tags and decorates the output accordingly. Default tag-marking functions behave the HTML way: string tags[29.22] are enclosed in "<" and ">" while other tags are ignored; hence, opening marker for tag string "t" is "" and closing marker is "". Default tag-printing functions just do nothing. Tag-marking and tag-printing functions are user definable and can be set by calling Format.set_formatter_stag_functions[29.22]. Semantic tag operations may be set on or off with Format.set_tags[29.22]. Tag-marking operations may be set on or off with Format.set_mark_tags[29.22]. Tag-printing operations may be set on or off with Format.set_print_tags[29.22]. Since: 4.08 << type tag = string >> << type stag += >> << | String_tag of tag >> String_tag s is a string tag s. String tags can be inserted either by explicitly using the constructor String_tag or by using the dedicated format syntax "@{ ... @}". Since: 4.08 << val pp_open_stag : formatter -> stag -> unit >> << val open_stag : stag -> unit >> pp_open_stag ppf t opens the semantic tag named t. The print_open_stag tag-printing function of the formatter is called with t as argument; then the opening tag marker for t, as given by mark_open_stag t, is written into the output device of the formatter. Since: 4.08 << val pp_close_stag : formatter -> unit -> unit >> << val close_stag : unit -> unit >> pp_close_stag ppf () closes the most recently opened semantic tag t. The closing tag marker, as given by mark_close_stag t, is written into the output device of the formatter; then the print_close_stag tag-printing function of the formatter is called with t as argument. Since: 4.08 << val pp_set_tags : formatter -> bool -> unit >> << val set_tags : bool -> unit >> pp_set_tags ppf b turns on or off the treatment of semantic tags (default is off). << val pp_set_print_tags : formatter -> bool -> unit >> << val set_print_tags : bool -> unit >> pp_set_print_tags ppf b turns on or off the tag-printing operations. << val pp_set_mark_tags : formatter -> bool -> unit >> << val set_mark_tags : bool -> unit >> pp_set_mark_tags ppf b turns on or off the tag-marking operations. << val pp_get_print_tags : formatter -> unit -> bool >> << val get_print_tags : unit -> bool >> Return the current status of tag-printing operations. << val pp_get_mark_tags : formatter -> unit -> bool >> << val get_mark_tags : unit -> bool >> Return the current status of tag-marking operations. << val pp_set_formatter_out_channel : formatter -> out_channel -> unit >> Redirecting the standard formatter output ========================================= << val set_formatter_out_channel : out_channel -> unit >> Redirect the standard pretty-printer output to the given channel. (All the output functions of the standard formatter are set to the default output functions printing to the given channel.) set_formatter_out_channel is equivalent to Format.pp_set_formatter_out_channel[29.22] std_formatter. << val pp_set_formatter_output_functions : formatter -> (string -> int -> int -> unit) -> (unit -> unit) -> unit >> << val set_formatter_output_functions : (string -> int -> int -> unit) -> (unit -> unit) -> unit >> pp_set_formatter_output_functions ppf out flush redirects the standard pretty-printer output functions to the functions out and flush. The out function performs all the pretty-printer string output. It is called with a string s, a start position p, and a number of characters n; it is supposed to output characters p to p + n - 1 of s. The flush function is called whenever the pretty-printer is flushed (via conversion %!, or pretty-printing indications @? or @., or using low level functions print_flush or print_newline). << val pp_get_formatter_output_functions : formatter -> unit -> (string -> int -> int -> unit) * (unit -> unit) >> << val get_formatter_output_functions : unit -> (string -> int -> int -> unit) * (unit -> unit) >> Return the current output functions of the standard pretty-printer. Redefining formatter output =========================== The Format module is versatile enough to let you completely redefine the meaning of pretty-printing output: you may provide your own functions to define how to handle indentation, line splitting, and even printing of all the characters that have to be printed! Redefining output functions --------------------------- << type formatter_out_functions = { out_string : string -> int -> int -> unit ; out_flush : unit -> unit ; out_newline : unit -> unit ; out_spaces : int -> unit ; out_indent : int -> unit ; >> Since: 4.06 << } >> The set of output functions specific to a formatter: - the out_string function performs all the pretty-printer string output. It is called with a string s, a start position p, and a number of characters n; it is supposed to output characters p to p + n - 1 of s. - the out_flush function flushes the pretty-printer output device. - out_newline is called to open a new line when the pretty-printer splits the line. - the out_spaces function outputs spaces when a break hint leads to spaces instead of a line split. It is called with the number of spaces to output. - the out_indent function performs new line indentation when the pretty-printer splits the line. It is called with the indentation value of the new line. By default: - fields out_string and out_flush are output device specific; (e.g. output_string[28.2] and flush[28.2] for a out_channel[28.2] device, or Buffer.add_substring and ignore[28.2] for a Buffer.t output device), - field out_newline is equivalent to out_string "\n" 0 1; - fields out_spaces and out_indent are equivalent to out_string (String.make n ' ') 0 n. Since: 4.01 << val pp_set_formatter_out_functions : formatter -> formatter_out_functions -> unit >> << val set_formatter_out_functions : formatter_out_functions -> unit >> pp_set_formatter_out_functions ppf out_funs Set all the pretty-printer output functions of ppf to those of argument out_funs, This way, you can change the meaning of indentation (which can be something else than just printing space characters) and the meaning of new lines opening (which can be connected to any other action needed by the application at hand). Reasonable defaults for functions out_spaces and out_newline are respectively out_funs.out_string (String.make n ' ') 0 n and out_funs.out_string "\n" 0 1. Since: 4.01 << val pp_get_formatter_out_functions : formatter -> unit -> formatter_out_functions >> << val get_formatter_out_functions : unit -> formatter_out_functions >> Return the current output functions of the pretty-printer, including line splitting and indentation functions. Useful to record the current setting and restore it afterwards. Since: 4.01 Redefining semantic tag operations ================================== << type formatter_stag_functions = { mark_open_stag : stag -> string ; mark_close_stag : stag -> string ; print_open_stag : stag -> unit ; print_close_stag : stag -> unit ; } >> The semantic tag handling functions specific to a formatter: mark versions are the ’tag-marking’ functions that associate a string marker to a tag in order for the pretty-printing engine to write those markers as 0 length tokens in the output device of the formatter. print versions are the ’tag-printing’ functions that can perform regular printing when a tag is closed or opened. Since: 4.08 << val pp_set_formatter_stag_functions : formatter -> formatter_stag_functions -> unit >> << val set_formatter_stag_functions : formatter_stag_functions -> unit >> pp_set_formatter_stag_functions ppf tag_funs changes the meaning of opening and closing semantic tag operations to use the functions in tag_funs when printing on ppf. When opening a semantic tag with name t, the string t is passed to the opening tag-marking function (the mark_open_stag field of the record tag_funs), that must return the opening tag marker for that name. When the next call to close_stag () happens, the semantic tag name t is sent back to the closing tag-marking function (the mark_close_stag field of record tag_funs), that must return a closing tag marker for that name. The print_ field of the record contains the tag-printing functions that are called at tag opening and tag closing time, to output regular material in the pretty-printer queue. Since: 4.08 << val pp_get_formatter_stag_functions : formatter -> unit -> formatter_stag_functions >> << val get_formatter_stag_functions : unit -> formatter_stag_functions >> Return the current semantic tag operation functions of the standard pretty-printer. Since: 4.08 Defining formatters =================== Defining new formatters permits unrelated output of material in parallel on several output devices. All the parameters of a formatter are local to the formatter: right margin, maximum indentation limit, maximum number of pretty-printing boxes simultaneously open, ellipsis, and so on, are specific to each formatter and may be fixed independently. For instance, given a Buffer.t[29.7] buffer b, Format.formatter_of_buffer[29.22] b returns a new formatter using buffer b as its output device. Similarly, given a out_channel[28.2] output channel oc, Format.formatter_of_out_channel[29.22] oc returns a new formatter using channel oc as its output device. Alternatively, given out_funs, a complete set of output functions for a formatter, then Format.formatter_of_out_functions[29.22] out_funs computes a new formatter using those functions for output. << val formatter_of_out_channel : out_channel -> formatter >> formatter_of_out_channel oc returns a new formatter writing to the corresponding output channel oc. << val synchronized_formatter_of_out_channel : out_channel -> formatter Domain.DLS.key >> synchronized_formatter_of_out_channel oc returns the key to the domain-local state that holds the domain-local formatter for writing to the corresponding output channel oc. When the formatter is used with multiple domains, the output from the domains will be interleaved with each other at points where the formatter is flushed, such as with Format.print_flush[29.22]. Alert unstable << val std_formatter : formatter >> The initial domain’s standard formatter to write to standard output. It is defined as Format.formatter_of_out_channel[29.22] stdout[28.2]. << val get_std_formatter : unit -> formatter >> get_std_formatter () returns the current domain’s standard formatter used to write to standard output. Since: 5.0 << val err_formatter : formatter >> The initial domain’s formatter to write to standard error. It is defined as Format.formatter_of_out_channel[29.22] stderr[28.2]. << val get_err_formatter : unit -> formatter >> get_err_formatter () returns the current domain’s formatter used to write to standard error. Since: 5.0 << val formatter_of_buffer : Buffer.t -> formatter >> formatter_of_buffer b returns a new formatter writing to buffer b. At the end of pretty-printing, the formatter must be flushed using Format.pp_print_flush[29.22] or Format.pp_print_newline[29.22], to print all the pending material into the buffer. << val stdbuf : Buffer.t >> The initial domain’s string buffer in which str_formatter writes. << val get_stdbuf : unit -> Buffer.t >> get_stdbuf () returns the current domain’s string buffer in which the current domain’s string formatter writes. Since: 5.0 << val str_formatter : formatter >> The initial domain’s formatter to output to the Format.stdbuf[29.22] string buffer. str_formatter is defined as Format.formatter_of_buffer[29.22] Format.stdbuf[29.22]. << val get_str_formatter : unit -> formatter >> The current domain’s formatter to output to the current domains string buffer. Since: 5.0 << val flush_str_formatter : unit -> string >> Returns the material printed with str_formatter of the current domain, flushes the formatter and resets the corresponding buffer. << val make_formatter : (string -> int -> int -> unit) -> (unit -> unit) -> formatter >> make_formatter out flush returns a new formatter that outputs with function out, and flushes with function flush. For instance, << make_formatter (Stdlib.output_substring oc) (fun () -> Stdlib.flush oc) >> returns a formatter to the out_channel[28.2] oc. << val make_synchronized_formatter : (string -> int -> int -> unit) -> (unit -> unit) -> formatter Domain.DLS.key >> make_synchronized_formatter out flush returns the key to the domain-local state that holds the domain-local formatter that outputs with function out, and flushes with function flush. When the formatter is used with multiple domains, the output from the domains will be interleaved with each other at points where the formatter is flushed, such as with Format.print_flush[29.22]. Since: 5.0 Alert unstable << val formatter_of_out_functions : formatter_out_functions -> formatter >> formatter_of_out_functions out_funs returns a new formatter that writes with the set of output functions out_funs. See definition of type Format.formatter_out_functions[29.22] for the meaning of argument out_funs. Since: 4.06 Symbolic pretty-printing ------------------------ Symbolic pretty-printing is pretty-printing using a symbolic formatter, i.e. a formatter that outputs symbolic pretty-printing items. When using a symbolic formatter, all regular pretty-printing activities occur but output material is symbolic and stored in a buffer of output items. At the end of pretty-printing, flushing the output buffer allows post-processing of symbolic output before performing low level output operations. In practice, first define a symbolic output buffer b using: - let sob = make_symbolic_output_buffer (). Then define a symbolic formatter with: - let ppf = formatter_of_symbolic_output_buffer sob Use symbolic formatter ppf as usual, and retrieve symbolic items at end of pretty-printing by flushing symbolic output buffer sob with: - flush_symbolic_output_buffer sob. << type symbolic_output_item = | Output_flush >> symbolic flush command << | Output_newline >> symbolic newline command << | Output_string of string >> Output_string s: symbolic output for string s << | Output_spaces of int >> Output_spaces n: symbolic command to output n spaces << | Output_indent of int >> Output_indent i: symbolic indentation of size i Items produced by symbolic pretty-printers Since: 4.06 << type symbolic_output_buffer >> The output buffer of a symbolic pretty-printer. Since: 4.06 << val make_symbolic_output_buffer : unit -> symbolic_output_buffer >> make_symbolic_output_buffer () returns a fresh buffer for symbolic output. Since: 4.06 << val clear_symbolic_output_buffer : symbolic_output_buffer -> unit >> clear_symbolic_output_buffer sob resets buffer sob. Since: 4.06 << val get_symbolic_output_buffer : symbolic_output_buffer -> symbolic_output_item list >> get_symbolic_output_buffer sob returns the contents of buffer sob. Since: 4.06 << val flush_symbolic_output_buffer : symbolic_output_buffer -> symbolic_output_item list >> flush_symbolic_output_buffer sob returns the contents of buffer sob and resets buffer sob. flush_symbolic_output_buffer sob is equivalent to let items = get_symbolic_output_buffer sob in clear_symbolic_output_buffer sob; items Since: 4.06 << val add_symbolic_output_item : symbolic_output_buffer -> symbolic_output_item -> unit >> add_symbolic_output_item sob itm adds item itm to buffer sob. Since: 4.06 << val formatter_of_symbolic_output_buffer : symbolic_output_buffer -> formatter >> formatter_of_symbolic_output_buffer sob returns a symbolic formatter that outputs to symbolic_output_buffer sob. Since: 4.06 Convenience formatting functions. ================================= << val pp_print_iter : ?pp_sep:(formatter -> unit -> unit) -> (('a -> unit) -> 'b -> unit) -> (formatter -> 'a -> unit) -> formatter -> 'b -> unit >> pp_print_iter ~pp_sep iter pp_v ppf v formats on ppf the iterations of iter over a collection v of values using pp_v. Iterations are separated by pp_sep (defaults to Format.pp_print_cut[29.22]). Since: 5.1 << val pp_print_list : ?pp_sep:(formatter -> unit -> unit) -> (formatter -> 'a -> unit) -> formatter -> 'a list -> unit >> pp_print_list ?pp_sep pp_v ppf l prints items of list l, using pp_v to print each item, and calling pp_sep between items (pp_sep defaults to Format.pp_print_cut[29.22]). Does nothing on empty lists. Since: 4.02 << val pp_print_array : ?pp_sep:(formatter -> unit -> unit) -> (formatter -> 'a -> unit) -> formatter -> 'a array -> unit >> pp_print_array ?pp_sep pp_v ppf a prints items of array a, using pp_v to print each item, and calling pp_sep between items (pp_sep defaults to Format.pp_print_cut[29.22]). Does nothing on empty arrays. If a is mutated after pp_print_array is called, the printed values may not be what is expected because Format can delay the printing. This can be avoided by flushing ppf. Since: 5.1 << val pp_print_seq : ?pp_sep:(formatter -> unit -> unit) -> (formatter -> 'a -> unit) -> formatter -> 'a Seq.t -> unit >> pp_print_seq ?pp_sep pp_v ppf s prints items of sequence s, using pp_v to print each item, and calling pp_sep between items (pp_sep defaults to Format.pp_print_cut[29.22]. Does nothing on empty sequences. This function does not terminate on infinite sequences. Since: 4.12 << val pp_print_text : formatter -> string -> unit >> pp_print_text ppf s prints s with spaces and newlines respectively printed using Format.pp_print_space[29.22] and Format.pp_force_newline[29.22]. Since: 4.02 << val pp_print_option : ?none:(formatter -> unit -> unit) -> (formatter -> 'a -> unit) -> formatter -> 'a option -> unit >> pp_print_option ?none pp_v ppf o prints o on ppf using pp_v if o is Some v and none if it is None. none prints nothing by default. Since: 4.08 << val pp_print_result : ok:(formatter -> 'a -> unit) -> error:(formatter -> 'e -> unit) -> formatter -> ('a, 'e) result -> unit >> pp_print_result ~ok ~error ppf r prints r on ppf using ok if r is Ok _ and error if r is Error _. Since: 4.08 << val pp_print_either : left:(formatter -> 'a -> unit) -> right:(formatter -> 'b -> unit) -> formatter -> ('a, 'b) Either.t -> unit >> pp_print_either ~left ~right ppf e prints e on ppf using left if e is Either.Left _ and right if e is Either.Right _. Since: 4.13 Formatted pretty-printing ========================= Module Format provides a complete set of printf like functions for pretty-printing using format string specifications. Specific annotations may be added in the format strings to give pretty-printing commands to the pretty-printing engine. Those annotations are introduced in the format strings using the @ character. For instance, @ means a space break, @, means a cut, @[ opens a new box, and @] closes the last open box. << val fprintf : formatter -> ('a, formatter, unit) format -> 'a >> fprintf ff fmt arg1 ... argN formats the arguments arg1 to argN according to the format string fmt, and outputs the resulting string on the formatter ff. The format string fmt is a character string which contains three types of objects: plain characters and conversion specifications as specified in the Printf[29.44] module, and pretty-printing indications specific to the Format module. The pretty-printing indication characters are introduced by a @ character, and their meanings are: - @[: open a pretty-printing box. The type and offset of the box may be optionally specified with the following syntax: the < character, followed by an optional box type indication, then an optional integer offset, and the closing > character. Pretty-printing box type is one of h, v, hv, b, or hov. ’h’ stands for an ’horizontal’ pretty-printing box, ’v’ stands for a ’vertical’ pretty-printing box, ’hv’ stands for an ’horizontal/vertical’ pretty-printing box, ’b’ stands for an ’horizontal-or-vertical’ pretty-printing box demonstrating indentation, ’hov’ stands a simple ’horizontal-or-vertical’ pretty-printing box. For instance, @[ opens an ’horizontal-or-vertical’ pretty-printing box with indentation 2 as obtained with open_hovbox 2. For more details about pretty-printing boxes, see the various box opening functions open_*box. - @]: close the most recently opened pretty-printing box. - @,: output a ’cut’ break hint, as with print_cut (). - @ : output a ’space’ break hint, as with print_space (). - @;: output a ’full’ break hint as with print_break. The nspaces and offset parameters of the break hint may be optionally specified with the following syntax: the < character, followed by an integer nspaces value, then an integer offset, and a closing > character. If no parameters are provided, the full break defaults to a ’space’ break hint. - @.: flush the pretty-printer and split the line, as with print_newline (). - @: print the following item as if it were of length n. Hence, printf "@<0>%s" arg prints arg as a zero length string. If @ is not followed by a conversion specification, then the following character of the format is printed as if it were of length n. - @{: open a semantic tag. The name of the tag may be optionally specified with the following syntax: the < character, followed by an optional string specification, and the closing > character. The string specification is any character string that does not contain the closing character '>'. If omitted, the tag name defaults to the empty string. For more details about semantic tags, see the functions Format.open_stag[29.22] and Format.close_stag[29.22]. - @}: close the most recently opened semantic tag. - @?: flush the pretty-printer as with print_flush (). This is equivalent to the conversion %!. - @\n: force a newline, as with force_newline (), not the normal way of pretty-printing, you should prefer using break hints inside a vertical pretty-printing box. Note: To prevent the interpretation of a @ character as a pretty-printing indication, escape it with a % character. Old quotation mode @@ is deprecated since it is not compatible with formatted input interpretation of character '@'. Example: printf "@[%s@ %d@]@." "x =" 1 is equivalent to open_box (); print_string "x ="; print_space (); print_int 1; close_box (); print_newline (). It prints x = 1 within a pretty-printing ’horizontal-or-vertical’ box. << val printf : ('a, formatter, unit) format -> 'a >> Same as fprintf above, but output on get_std_formatter (). It is defined similarly to fun fmt -> fprintf (get_std_formatter ()) fmt but delays calling get_std_formatter until after the final argument required by the format is received. When used with multiple domains, the output from the domains will be interleaved with each other at points where the formatter is flushed, such as with Format.print_flush[29.22]. << val eprintf : ('a, formatter, unit) format -> 'a >> Same as fprintf above, but output on get_err_formatter (). It is defined similarly to fun fmt -> fprintf (get_err_formatter ()) fmt but delays calling get_err_formatter until after the final argument required by the format is received. When used with multiple domains, the output from the domains will be interleaved with each other at points where the formatter is flushed, such as with Format.print_flush[29.22]. << val sprintf : ('a, unit, string) format -> 'a >> Same as printf above, but instead of printing on a formatter, returns a string containing the result of formatting the arguments. Note that the pretty-printer queue is flushed at the end of each call to sprintf. Note that if your format string contains a %a, you should use asprintf. In case of multiple and related calls to sprintf to output material on a single string, you should consider using fprintf with the predefined formatter str_formatter and call flush_str_formatter () to get the final result. Alternatively, you can use Format.fprintf with a formatter writing to a buffer of your own: flushing the formatter and the buffer at the end of pretty-printing returns the desired string. << val asprintf : ('a, formatter, unit, string) format4 -> 'a >> Same as printf above, but instead of printing on a formatter, returns a string containing the result of formatting the arguments. The type of asprintf is general enough to interact nicely with %a conversions. Since: 4.01 << val dprintf : ('a, formatter, unit, formatter -> unit) format4 -> 'a >> Same as Format.fprintf[29.22], except the formatter is the last argument. dprintf "..." a b c is a function of type formatter -> unit which can be given to a format specifier %t. This can be used as a replacement for Format.asprintf[29.22] to delay formatting decisions. Using the string returned by Format.asprintf[29.22] in a formatting context forces formatting decisions to be taken in isolation, and the final string may be created prematurely. Format.dprintf[29.22] allows delay of formatting decisions until the final formatting context is known. For example: << let t = Format.dprintf "%i@ %i@ %i" 1 2 3 in ... Format.printf "@[%t@]" t >> Since: 4.08 << val ifprintf : formatter -> ('a, formatter, unit) format -> 'a >> Same as fprintf above, but does not print anything. Useful to ignore some material when conditionally printing. Since: 3.10 Formatted Pretty-Printing with continuations. << val kfprintf : (formatter -> 'a) -> formatter -> ('b, formatter, unit, 'a) format4 -> 'b >> Same as fprintf above, but instead of returning immediately, passes the formatter to its first argument at the end of printing. << val kdprintf : ((formatter -> unit) -> 'a) -> ('b, formatter, unit, 'a) format4 -> 'b >> Same as Format.dprintf[29.22] above, but instead of returning immediately, passes the suspended printer to its first argument at the end of printing. Since: 4.08 << val ikfprintf : (formatter -> 'a) -> formatter -> ('b, formatter, unit, 'a) format4 -> 'b >> Same as kfprintf above, but does not print anything. Useful to ignore some material when conditionally printing. Since: 3.12 << val ksprintf : (string -> 'a) -> ('b, unit, string, 'a) format4 -> 'b >> Same as sprintf above, but instead of returning the string, passes it to the first argument. << val kasprintf : (string -> 'a) -> ('b, formatter, unit, 'a) format4 -> 'b >> Same as asprintf above, but instead of returning the string, passes it to the first argument. Since: 4.03 Examples ======== A few warmup examples to get an idea of how Format is used. We have a list l of pairs (int * bool), which the toplevel prints for us: << # let l = List.init 20 (fun n -> n, n mod 2 = 0) val l : (int * bool) list = [(0, true); (1, false); (2, true); (3, false); (4, true); (5, false); (6, true); (7, false); (8, true); (9, false); (10, true); (11, false); (12, true); (13, false); (14, true); (15, false); (16, true); (17, false); (18, true); (19, false)] >> If we want to print it ourself without the toplevel magic, we can try this: << # let pp_pair out (x,y) = Format.fprintf out "(%d, %b)" x y val pp_pair : Format.formatter -> int * bool -> unit = # Format.printf "l: [@[%a@]]@." Format.(pp_print_list ~pp_sep:(fun out () -> fprintf out ";@ ") pp_pair) l l: [(0, true); (1, false); (2, true); (3, false); (4, true); (5, false); (6, true); (7, false); (8, true); (9, false); (10, true); (11, false); (12, true); (13, false); (14, true); (15, false); (16, true); (17, false); (18, true); (19, false)] >> What this does, briefly, is: - pp_pair prints a pair bool*int surrounded in "(" ")". It takes a formatter (into which formatting happens), and the pair itself. When printing is done it returns (). - Format.printf "l = [@[%a@]]@." ... l is like printf, but with additional formatting instructions (denoted with "@"). The pair "@[" and "@]" is a "horizontal-or-vertical box". - "@." ends formatting with a newline. It is similar to "\n" but is also aware of the Format.formatter’s state. Do not use "\n" with Format. - "%a" is a formatting instruction, like "%d" or "%s" for printf. However, where "%d" prints an integer and "%s" prints a string, "%a" takes a printer (of type Format.formatter -> 'a -> unit) and a value (of type 'a) and applies the printer to the value. This is key to compositionality of printers. - We build a list printer using Format.pp_print_list ~pp_sep:(...) pp_pair. pp_print_list takes an element printer and returns a list printer. The ?pp_sep optional argument, if provided, is called in between each element to print a separator. - Here, for a separator, we use (fun out () -> Format.fprintf out ";@ "). It prints ";", and then "@ " which is a breaking space (either it prints " ", or it prints a newline if the box is about to overflow). This "@ " is responsible for the list printing splitting into several lines. If we omit "@ ", we get an ugly single-line print: << # Format.printf "l: [@[%a@]]@." Format.(pp_print_list ~pp_sep:(fun out () -> fprintf out "; ") pp_pair) l l: [(0, true); (1, false); (2, true); (* ... *); (18, true); (19, false)] - : unit = () >> Generally, it is good practice to define custom printers for important types in your program. If, for example, you were to define basic geometry types like so: << type point = { x: float; y: float; } type rectangle = { ll: point; (* lower left *) ur: point; (* upper right *) } >> For debugging purpose, or to display information in logs, or on the console, it would be convenient to define printers for these types. Here is an example of to do it. Note that "%.3f" is a float printer up to 3 digits of precision after the dot; "%f" would print as many digits as required, which is somewhat verbose; "%h" is an hexadecimal float printer. << let pp_point out (p:point) = Format.fprintf out "{ @[x=%.3f;@ y=%.3f@] }" p.x p.y let pp_rectangle out (r:rectangle) = Format.fprintf out "{ @[ll=%a;@ ur=%a@] }" pp_point r.ll pp_point r.ur >> In the .mli file, we could have: << val pp_point : Format.formatter -> point -> unit val pp_rectangle : Format.formatter -> rectangle -> unit >> These printers can now be used with "%a" inside other printers. << # Format.printf "some rectangle: %a@." (Format.pp_print_option pp_rectangle) (Some {ll={x=1.; y=2.}; ur={x=42.; y=500.12345}}) some rectangle: { l={ x=1.000; y=2.000 }; ur={ x=42.000; y=500.123 } } # Format.printf "no rectangle: %a@." (Format.pp_option pp_rectangle) None no rectangle: >> See how we combine pp_print_option (option printer) and our newly defined rectangle printer, like we did with pp_print_list earlier. For a more extensive tutorial, see "Using the Format module"[ https://caml.inria.fr/resources/doc/guides/format.en.html]. A final note: the Format module is a starting point. The OCaml ecosystem has libraries that makes formatting easier and more expressive, with more combinators, more concise names, etc. An example of such a library is Fmt[ https://erratique.ch/software/fmt]. Automatic deriving of pretty-printers from type definitions is also possible, using https://github.com/ocaml-ppx/ppx_deriving[ ppx_deriving.show] or similar ppx derivers. 29.23 Module Fun : Function manipulation. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Since: 4.08 Combinators =========== << val id : 'a -> 'a >> id is the identity function. For any argument x, id x is x. << val const : 'a -> 'b -> 'a >> const c is a function that always returns the value c. For any argument x, (const c) x is c. << val compose : ('b -> 'c) -> ('a -> 'b) -> 'a -> 'c >> compose f g is a function composition of applying g then f. For any arguments f, g, and x, compose f g x is f (g x). Since: 5.2 << val flip : ('a -> 'b -> 'c) -> 'b -> 'a -> 'c >> flip f reverses the argument order of the binary function f. For any arguments x and y, (flip f) x y is f y x. << val negate : ('a -> bool) -> 'a -> bool >> negate p is the negation of the predicate function p. For any argument x, (negate p) x is not (p x). Exception handling ================== << val protect : finally:(unit -> unit) -> (unit -> 'a) -> 'a >> protect ~finally work invokes work () and then finally () before work () returns with its value or an exception. In the latter case the exception is re-raised after finally (). If finally () raises an exception, then the exception Fun.Finally_raised[29.23] is raised instead. protect can be used to enforce local invariants whether work () returns normally or raises an exception. However, it does not protect against unexpected exceptions raised inside finally () such as Out_of_memory[28.2], Stack_overflow[28.2], or asynchronous exceptions raised by signal handlers (e.g. Sys.Break[29.56]). Note: It is a programming error if other kinds of exceptions are raised by finally, as any exception raised in work () will be lost in the event of a Fun.Finally_raised[29.23] exception. Therefore, one should make sure to handle those inside the finally. << exception Finally_raised of exn >> Finally_raised exn is raised by protect ~finally work when finally raises an exception exn. This exception denotes either an unexpected exception or a programming error. As a general rule, one should not catch a Finally_raised exception except as part of a catch-all handler. 29.24 Module Gc : Memory management control and statistics; finalised values. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* << type stat = { minor_words : float ; >> Number of words allocated in the minor heap since the program was started. << promoted_words : float ; >> Number of words allocated in the minor heap that survived a minor collection and were moved to the major heap since the program was started. << major_words : float ; >> Number of words allocated in the major heap, including the promoted words, since the program was started. << minor_collections : int ; >> Number of minor collections since the program was started. << major_collections : int ; >> Number of major collection cycles completed since the program was started. << heap_words : int ; >> Total size of the major heap, in words. << heap_chunks : int ; >> Number of contiguous pieces of memory that make up the major heap. This metrics is currently not available in OCaml 5: the field value is always 0. << live_words : int ; >> Number of words of live data in the major heap, including the header words. Note that "live" words refers to every word in the major heap that isn’t currently known to be collectable, which includes words that have become unreachable by the program after the start of the previous gc cycle. It is typically much simpler and more predictable to call Gc.full_major[29.24] (or Gc.compact[29.24]) then computing gc stats, as then "live" words has the simple meaning of "reachable by the program". One caveat is that a single call to Gc.full_major[29.24] will not reclaim values that have a finaliser from Gc.finalise[29.24] (this does not apply to Gc.finalise_last[29.24]). If this caveat matters, simply call Gc.full_major[29.24] twice instead of once. << live_blocks : int ; >> Number of live blocks in the major heap. See live_words for a caveat about what "live" means. << free_words : int ; >> Number of words in the free list. << free_blocks : int ; >> Number of blocks in the free list. This metrics is currently not available in OCaml 5: the field value is always 0. << largest_free : int ; >> Size (in words) of the largest block in the free list. This metrics is currently not available in OCaml 5: the field value is always 0. << fragments : int ; >> Number of wasted words due to fragmentation. These are 1-words free blocks placed between two live blocks. They are not available for allocation. << compactions : int ; >> Number of heap compactions since the program was started. << top_heap_words : int ; >> Maximum size reached by the major heap, in words. << stack_size : int ; >> Current size of the stack, in words. This metrics is currently not available in OCaml 5: the field value is always 0. Since: 3.12 << forced_major_collections : int ; >> Number of forced full major collections completed since the program was started. Since: 4.12 << } >> The memory management counters are returned in a stat record. These counters give values for the whole program. The total amount of memory allocated by the program since it was started is (in words) minor_words + major_words - promoted_words. Multiply by the word size (4 on a 32-bit machine, 8 on a 64-bit machine) to get the number of bytes. << type control = { minor_heap_size : int ; >> The size (in words) of the minor heap. Changing this parameter will trigger a minor collection. The total size of the minor heap used by this program is the sum of the heap sizes of the active domains. Default: 256k. << major_heap_increment : int ; >> How much to add to the major heap when increasing it. If this number is less than or equal to 1000, it is a percentage of the current heap size (i.e. setting it to 100 will double the heap size at each increase). If it is more than 1000, it is a fixed number of words that will be added to the heap. Default: 15. << space_overhead : int ; >> The major GC speed is computed from this parameter. This is the memory that will be "wasted" because the GC does not immediately collect unreachable blocks. It is expressed as a percentage of the memory used for live data. The GC will work more (use more CPU time and collect blocks more eagerly) if space_overhead is smaller. Default: 120. << verbose : int ; >> This value controls the GC messages on standard error output. It is a sum of some of the following flags, to print messages on the corresponding events: - 0x001 Start and end of major GC cycle. - 0x002 Minor collection and major GC slice. - 0x004 Growing and shrinking of the heap. - 0x008 Resizing of stacks and memory manager tables. - 0x010 Heap compaction. - 0x020 Change of GC parameters. - 0x040 Computation of major GC slice size. - 0x080 Calling of finalisation functions. - 0x100 Bytecode executable and shared library search at start-up. - 0x200 Computation of compaction-triggering condition. - 0x400 Output GC statistics at program exit. Default: 0. << max_overhead : int ; >> Heap compaction is triggered when the estimated amount of "wasted" memory is more than max_overhead percent of the amount of live data. If max_overhead is set to 0, heap compaction is triggered at the end of each major GC cycle (this setting is intended for testing purposes only). If max_overhead >= 1000000, compaction is never triggered. Default: 500. << stack_limit : int ; >> The maximum size of the fiber stacks (in words). Default: 1024k. << allocation_policy : int ; >> The policy used for allocating in the major heap. This option is ignored in OCaml 5.x. Prior to OCaml 5.0, possible values were 0, 1 and 2. - 0 was the next-fit policy - 1 was the first-fit policy (since OCaml 3.11) - 2 was the best-fit policy (since OCaml 4.10) Since: 3.11 << window_size : int ; >> The size of the window used by the major GC for smoothing out variations in its workload. This is an integer between 1 and 50. Default: 1. Since: 4.03 << custom_major_ratio : int ; >> Target ratio of floating garbage to major heap size for out-of-heap memory held by custom values located in the major heap. The GC speed is adjusted to try to use this much memory for dead values that are not yet collected. Expressed as a percentage of major heap size. The default value keeps the out-of-heap floating garbage about the same size as the in-heap overhead. Note: this only applies to values allocated with caml_alloc_custom_mem (e.g. bigarrays). Default: 44. Since: 4.08 << custom_minor_ratio : int ; >> Bound on floating garbage for out-of-heap memory held by custom values in the minor heap. A minor GC is triggered when this much memory is held by custom values located in the minor heap. Expressed as a percentage of minor heap size. Note: this only applies to values allocated with caml_alloc_custom_mem (e.g. bigarrays). Default: 100. Since: 4.08 << custom_minor_max_size : int ; >> Maximum amount of out-of-heap memory for each custom value allocated in the minor heap. Custom values that hold more than this many bytes are allocated on the major heap. Note: this only applies to values allocated with caml_alloc_custom_mem (e.g. bigarrays). Default: 70000 bytes. Since: 4.08 << } >> The GC parameters are given as a control record. Note that these parameters can also be initialised by setting the OCAMLRUNPARAM environment variable. See the documentation of ocamlrun. << val stat : unit -> stat >> Return the current values of the memory management counters in a stat record that represent the program’s total memory stats. This function causes a full major collection. << val quick_stat : unit -> stat >> Same as stat except that live_words, live_blocks, free_words, free_blocks, largest_free, and fragments are set to 0. Due to per-domain buffers it may only represent the state of the program’s total memory usage since the last minor collection or major cycle. This function is much faster than stat because it does not need to trigger a full major collection. << val counters : unit -> float * float * float >> Return (minor_words, promoted_words, major_words) for the current domain or potentially previous domains. This function is as fast as quick_stat. << val minor_words : unit -> float >> Number of words allocated in the minor heap by this domain or potentially previous domains. This number is accurate in byte-code programs, but only an approximation in programs compiled to native code. In native code this function does not allocate. Since: 4.04 << val get : unit -> control >> Return the current values of the GC parameters in a control record. Alert unsynchronized_access. GC parameters are a mutable global state. << val set : control -> unit >> set r changes the GC parameters according to the control record r. The normal usage is: Gc.set { (Gc.get()) with Gc.verbose = 0x00d } Alert unsynchronized_access. GC parameters are a mutable global state. << val minor : unit -> unit >> Trigger a minor collection. << val major_slice : int -> int >> major_slice n Do a minor collection and a slice of major collection. n is the size of the slice: the GC will do enough work to free (on average) n words of memory. If n = 0, the GC will try to do enough work to ensure that the next automatic slice has no work to do. This function returns an unspecified integer (currently: 0). << val major : unit -> unit >> Do a minor collection and finish the current major collection cycle. << val full_major : unit -> unit >> Do a minor collection, finish the current major collection cycle, and perform a complete new cycle. This will collect all currently unreachable blocks. << val compact : unit -> unit >> Perform a full major collection and compact the heap. Note that heap compaction is a lengthy operation. << val print_stat : out_channel -> unit >> Print the current values of the memory management counters (in human-readable form) of the total program into the channel argument. << val allocated_bytes : unit -> float >> Return the number of bytes allocated by this domain and potentially a previous domain. It is returned as a float to avoid overflow problems with int on 32-bit machines. << val get_minor_free : unit -> int >> Return the current size of the free space inside the minor heap of this domain. Since: 4.03 << val finalise : ('a -> unit) -> 'a -> unit >> finalise f v registers f as a finalisation function for v. v must be heap-allocated. f will be called with v as argument at some point between the first time v becomes unreachable (including through weak pointers) and the time v is collected by the GC. Several functions can be registered for the same value, or even several instances of the same function. Each instance will be called once (or never, if the program terminates before v becomes unreachable). The GC will call the finalisation functions in the order of deallocation. When several values become unreachable at the same time (i.e. during the same GC cycle), the finalisation functions will be called in the reverse order of the corresponding calls to finalise. If finalise is called in the same order as the values are allocated, that means each value is finalised before the values it depends upon. Of course, this becomes false if additional dependencies are introduced by assignments. In the presence of multiple OCaml threads it should be assumed that any particular finaliser may be executed in any of the threads. Anything reachable from the closure of finalisation functions is considered reachable, so the following code will not work as expected: - let v = ... in Gc.finalise (fun _ -> ...v...) v Instead you should make sure that v is not in the closure of the finalisation function by writing: - let f = fun x -> ... let v = ... in Gc.finalise f v The f function can use all features of OCaml, including assignments that make the value reachable again. It can also loop forever (in this case, the other finalisation functions will not be called during the execution of f, unless it calls finalise_release). It can call finalise on v or other values to register other functions or even itself. It can raise an exception; in this case the exception will interrupt whatever the program was doing when the function was called. finalise will raise Invalid_argument if v is not guaranteed to be heap-allocated. Some examples of values that are not heap-allocated are integers, constant constructors, booleans, the empty array, the empty list, the unit value. The exact list of what is heap-allocated or not is implementation-dependent. Some constant values can be heap-allocated but never deallocated during the lifetime of the program, for example a list of integer constants; this is also implementation-dependent. Note that values of types float are sometimes allocated and sometimes not, so finalising them is unsafe, and finalise will also raise Invalid_argument for them. Values of type 'a Lazy.t (for any 'a) are like float in this respect, except that the compiler sometimes optimizes them in a way that prevents finalise from detecting them. In this case, it will not raise Invalid_argument, but you should still avoid calling finalise on lazy values. The results of calling String.make[29.54], Bytes.make[29.8], Bytes.create[29.8], Array.make[29.2], and ref[28.2] are guaranteed to be heap-allocated and non-constant except when the length argument is 0. << val finalise_last : (unit -> unit) -> 'a -> unit >> same as Gc.finalise[29.24] except the value is not given as argument. So you can’t use the given value for the computation of the finalisation function. The benefit is that the function is called after the value is unreachable for the last time instead of the first time. So contrary to Gc.finalise[29.24] the value will never be reachable again or used again. In particular every weak pointer and ephemeron that contained this value as key or data is unset before running the finalisation function. Moreover the finalisation functions attached with Gc.finalise[29.24] are always called before the finalisation functions attached with Gc.finalise_last[29.24]. Since: 4.04 << val finalise_release : unit -> unit >> A finalisation function may call finalise_release to tell the GC that it can launch the next finalisation function without waiting for the current one to return. << type alarm >> An alarm is a piece of data that calls a user function at the end of major GC cycle. The following functions are provided to create and delete alarms. << val create_alarm : (unit -> unit) -> alarm >> create_alarm f will arrange for f to be called at the end of major GC cycles, not caused by f itself, starting with the current cycle or the next one. f will run on the same domain that created the alarm, until the domain exits or delete_alarm is called. A value of type alarm is returned that you can use to call delete_alarm. It is not guaranteed that the Gc alarm runs at the end of every major GC cycle, but it is guaranteed that it will run eventually. As an example, here is a crude way to interrupt a function if the memory consumption of the program exceeds a given limit in MB, suitable for use in the toplevel: << let run_with_memory_limit (limit : int) (f : unit -> 'a) : 'a = let limit_memory () = let mem = Gc.(quick_stat ()).heap_words in if mem / (1024 * 1024) > limit / (Sys.word_size / 8) then raise Out_of_memory in let alarm = Gc.create_alarm limit_memory in Fun.protect f ~finally:(fun () -> Gc.delete_alarm alarm ; Gc.compact ()) >> << val delete_alarm : alarm -> unit >> delete_alarm a will stop the calls to the function associated to a. Calling delete_alarm a again has no effect. << val eventlog_pause : unit -> unit >> Deprecated. Use Runtime_events.pause instead. << val eventlog_resume : unit -> unit >> Deprecated. Use Runtime_events.resume instead. << module Memprof : >>  sig << type t >> the type of a profile << type allocation_source = | Normal | Marshal | Custom >> << type allocation = private { n_samples : int ; >> The number of samples in this block (>= 1). << size : int ; >> The size of the block, in words, excluding the header. << source : allocation_source ; >> The cause of the allocation; Marshal cannot be produced since OCaml 5. << callstack : Printexc.raw_backtrace ; >> The callstack for the allocation. << } >> The type of metadata associated with allocations. This is the type of records passed to the callback triggered by the sampling of an allocation. << type ('minor, 'major) tracker = { alloc_minor : allocation -> 'minor option ; alloc_major : allocation -> 'major option ; promote : 'minor -> 'major option ; dealloc_minor : 'minor -> unit ; dealloc_major : 'major -> unit ; } >> A ('minor, 'major) tracker describes how memprof should track sampled blocks over their lifetime, keeping a user-defined piece of metadata for each of them: 'minor is the type of metadata to keep for minor blocks, and 'major the type of metadata for major blocks. The member functions in a tracker are called callbacks. If an allocation or promotion callback raises an exception or returns None, memprof stops tracking the corresponding block. << val null_tracker : ('minor, 'major) tracker >> Default callbacks simply return None or () << val start : sampling_rate:float -> ?callstack_size:int -> ('minor, 'major) tracker -> t >> Start a profile with the given parameters. Raises an exception if a profile is already sampling in the current domain. Sampling begins immediately. The parameter sampling_rate is the sampling rate in samples per word (including headers). Usually, with cheap callbacks, a rate of 1e-4 has no visible effect on performance, and 1e-3 causes the program to run a few percent slower. The parameter callstack_size is the length of the callstack recorded at every sample. Its default is max_int. The parameter tracker determines how to track sampled blocks over their lifetime in the minor and major heap. Sampling is temporarily disabled on the current thread when calling a callback, so callbacks do not need to be re-entrant if the program is single-threaded and single-domain. However, if threads or multiple domains are used, it is possible that several callbacks will run in parallel. In this case, callback functions must be re-entrant. Note that a callback may be postponed slightly after the actual event. The callstack passed to an allocation callback always accurately reflects the allocation, but the program state may have evolved between the allocation and the call to the callback. If a new thread or domain is created when profiling is active, the child thread or domain joins that profile (using the same sampling_rate, callstack_size, and tracker callbacks). An allocation callback is generally run by the thread which allocated the block. If the thread exits or the profile is stopped before the callback is called, the callback may be run by a different thread. Each callback is generally run by the domain which allocated the block. If the domain terminates or the profile is stopped before the callback is called, the callback may be run by a different domain. Different domains may run different profiles simultaneously. << val stop : unit -> unit >> Stop sampling for the current profile. Fails if no profile is sampling in the current domain. Stops sampling in all threads and domains sharing the profile. Callbacks from a profile may run after stop is called, until discard is applied to the profile. A profile is implicitly stopped (but not discarded) if all domains and threads sampling for it are terminated. << val discard : t -> unit >> Discards all profiling state for a stopped profile, which prevents any more callbacks for it. Raises an exception if called on a profile which has not been stopped.  end Memprof is a profiling engine which randomly samples allocated memory words. Every allocated word has a probability of being sampled equal to a configurable sampling rate. Once a block is sampled, it becomes tracked. A tracked block triggers a user-defined callback as soon as it is allocated, promoted or deallocated. Since blocks are composed of several words, a block can potentially be sampled several times. If a block is sampled several times, then each of the callbacks is called once for each event of this block: the multiplicity is given in the n_samples field of the allocation structure. This engine makes it possible to implement a low-overhead memory profiler as an OCaml library. Note: this API is EXPERIMENTAL. It may change without prior notice. 29.25 Module Hashtbl : Hash tables and hash functions. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Hash tables are hashed association tables, with in-place modification. Because most operations on a hash table modify their input, they’re more commonly used in imperative code. The lookup of the value associated with a key (see Hashtbl.find[29.25], Hashtbl.find_opt[29.25]) is normally very fast, often faster than the equivalent lookup in Map[29.34]. The functors Hashtbl.Make[29.25] and Hashtbl.MakeSeeded[29.25] can be used when performance or flexibility are key. The user provides custom equality and hash functions for the key type, and obtains a custom hash table type for this particular type of key. Warning a hash table is only as good as the hash function. A bad hash function will turn the table into a degenerate association list, with linear time lookup instead of constant time lookup. The polymorphic Hashtbl.t[29.25] hash table is useful in simpler cases or in interactive environments. It uses the polymorphic Hashtbl.hash[29.25] function defined in the OCaml runtime (at the time of writing, it’s SipHash), as well as the polymorphic equality (=). See the examples section[29.4]. Alert unsynchronized_access. Unsynchronized accesses to hash tables are a programming error. Unsynchronized accesses Unsynchronized accesses to a hash table may lead to an invalid hash table state. Thus, concurrent accesses to a hash tables must be synchronized (for instance with a Mutex.t[29.37]). Generic interface ================= << type (!'a, !'b) t >> The type of hash tables from type 'a to type 'b. << val create : ?random:bool -> int -> ('a, 'b) t >> Hashtbl.create n creates a new, empty hash table, with initial size n. For best results, n should be on the order of the expected number of elements that will be in the table. The table grows as needed, so n is just an initial guess. The optional ~random parameter (a boolean) controls whether the internal organization of the hash table is randomized at each execution of Hashtbl.create or deterministic over all executions. A hash table that is created with ~random set to false uses a fixed hash function (Hashtbl.hash[29.25]) to distribute keys among buckets. As a consequence, collisions between keys happen deterministically. In Web-facing applications or other security-sensitive applications, the deterministic collision patterns can be exploited by a malicious user to create a denial-of-service attack: the attacker sends input crafted to create many collisions in the table, slowing the application down. A hash table that is created with ~random set to true uses the seeded hash function Hashtbl.seeded_hash[29.25] with a seed that is randomly chosen at hash table creation time. In effect, the hash function used is randomly selected among 2^{30} different hash functions. All these hash functions have different collision patterns, rendering ineffective the denial-of-service attack described above. However, because of randomization, enumerating all elements of the hash table using Hashtbl.fold[29.25] or Hashtbl.iter[29.25] is no longer deterministic: elements are enumerated in different orders at different runs of the program. If no ~random parameter is given, hash tables are created in non-random mode by default. This default can be changed either programmatically by calling Hashtbl.randomize[29.25] or by setting the R flag in the OCAMLRUNPARAM environment variable. Before 4.00 the ~random parameter was not present and all hash tables were created in non-randomized mode. << val clear : ('a, 'b) t -> unit >> Empty a hash table. Use reset instead of clear to shrink the size of the bucket table to its initial size. << val reset : ('a, 'b) t -> unit >> Empty a hash table and shrink the size of the bucket table to its initial size. Since: 4.00 << val copy : ('a, 'b) t -> ('a, 'b) t >> Return a copy of the given hashtable. << val add : ('a, 'b) t -> 'a -> 'b -> unit >> Hashtbl.add tbl key data adds a binding of key to data in table tbl. Warning: Previous bindings for key are not removed, but simply hidden. That is, after performing Hashtbl.remove[29.25] tbl key, the previous binding for key, if any, is restored. (Same behavior as with association lists.) If you desire the classic behavior of replacing elements, see Hashtbl.replace[29.25]. << val find : ('a, 'b) t -> 'a -> 'b >> Hashtbl.find tbl x returns the current binding of x in tbl, or raises Not_found if no such binding exists. << val find_opt : ('a, 'b) t -> 'a -> 'b option >> Hashtbl.find_opt tbl x returns the current binding of x in tbl, or None if no such binding exists. Since: 4.05 << val find_all : ('a, 'b) t -> 'a -> 'b list >> Hashtbl.find_all tbl x returns the list of all data associated with x in tbl. The current binding is returned first, then the previous bindings, in reverse order of introduction in the table. << val mem : ('a, 'b) t -> 'a -> bool >> Hashtbl.mem tbl x checks if x is bound in tbl. << val remove : ('a, 'b) t -> 'a -> unit >> Hashtbl.remove tbl x removes the current binding of x in tbl, restoring the previous binding if it exists. It does nothing if x is not bound in tbl. << val replace : ('a, 'b) t -> 'a -> 'b -> unit >> Hashtbl.replace tbl key data replaces the current binding of key in tbl by a binding of key to data. If key is unbound in tbl, a binding of key to data is added to tbl. This is functionally equivalent to Hashtbl.remove[29.25] tbl key followed by Hashtbl.add[29.25] tbl key data. << val iter : ('a -> 'b -> unit) -> ('a, 'b) t -> unit >> Hashtbl.iter f tbl applies f to all bindings in table tbl. f receives the key as first argument, and the associated value as second argument. Each binding is presented exactly once to f. The order in which the bindings are passed to f is unspecified. However, if the table contains several bindings for the same key, they are passed to f in reverse order of introduction, that is, the most recent binding is passed first. If the hash table was created in non-randomized mode, the order in which the bindings are enumerated is reproducible between successive runs of the program, and even between minor versions of OCaml. For randomized hash tables, the order of enumeration is entirely random. The behavior is not specified if the hash table is modified by f during the iteration. << val filter_map_inplace : ('a -> 'b -> 'b option) -> ('a, 'b) t -> unit >> Hashtbl.filter_map_inplace f tbl applies f to all bindings in table tbl and update each binding depending on the result of f. If f returns None, the binding is discarded. If it returns Some new_val, the binding is update to associate the key to new_val. Other comments for Hashtbl.iter[29.25] apply as well. Since: 4.03 << val fold : ('a -> 'b -> 'acc -> 'acc) -> ('a, 'b) t -> 'acc -> 'acc >> Hashtbl.fold f tbl init computes (f kN dN ... (f k1 d1 init)...), where k1 ... kN are the keys of all bindings in tbl, and d1 ... dN are the associated values. Each binding is presented exactly once to f. The order in which the bindings are passed to f is unspecified. However, if the table contains several bindings for the same key, they are passed to f in reverse order of introduction, that is, the most recent binding is passed first. If the hash table was created in non-randomized mode, the order in which the bindings are enumerated is reproducible between successive runs of the program, and even between minor versions of OCaml. For randomized hash tables, the order of enumeration is entirely random. The behavior is not specified if the hash table is modified by f during the iteration. << val length : ('a, 'b) t -> int >> Hashtbl.length tbl returns the number of bindings in tbl. It takes constant time. Multiple bindings are counted once each, so Hashtbl.length gives the number of times Hashtbl.iter calls its first argument. << val randomize : unit -> unit >> After a call to Hashtbl.randomize(), hash tables are created in randomized mode by default: Hashtbl.create[29.25] returns randomized hash tables, unless the ~random:false optional parameter is given. The same effect can be achieved by setting the R parameter in the OCAMLRUNPARAM environment variable. It is recommended that applications or Web frameworks that need to protect themselves against the denial-of-service attack described in Hashtbl.create[29.25] call Hashtbl.randomize() at initialization time before any domains are created. Note that once Hashtbl.randomize() was called, there is no way to revert to the non-randomized default behavior of Hashtbl.create[29.25]. This is intentional. Non-randomized hash tables can still be created using Hashtbl.create ~random:false. Since: 4.00 << val is_randomized : unit -> bool >> Return true if the tables are currently created in randomized mode by default, false otherwise. Since: 4.03 << val rebuild : ?random:bool -> ('a, 'b) t -> ('a, 'b) t >> Return a copy of the given hashtable. Unlike Hashtbl.copy[29.25], Hashtbl.rebuild[29.25] h re-hashes all the (key, value) entries of the original table h. The returned hash table is randomized if h was randomized, or the optional random parameter is true, or if the default is to create randomized hash tables; see Hashtbl.create[29.25] for more information. Hashtbl.rebuild[29.25] can safely be used to import a hash table built by an old version of the Hashtbl[29.25] module, then marshaled to persistent storage. After unmarshaling, apply Hashtbl.rebuild[29.25] to produce a hash table for the current version of the Hashtbl[29.25] module. Since: 4.12 << type statistics = { num_bindings : int ; >> Number of bindings present in the table. Same value as returned by Hashtbl.length[29.25]. << num_buckets : int ; >> Number of buckets in the table. << max_bucket_length : int ; >> Maximal number of bindings per bucket. << bucket_histogram : int array ; >> Histogram of bucket sizes. This array histo has length max_bucket_length + 1. The value of histo.(i) is the number of buckets whose size is i. << } >> Since: 4.00 << val stats : ('a, 'b) t -> statistics >> Hashtbl.stats tbl returns statistics about the table tbl: number of buckets, size of the biggest bucket, distribution of buckets by size. Since: 4.00 Hash tables and Sequences ========================= << val to_seq : ('a, 'b) t -> ('a * 'b) Seq.t >> Iterate on the whole table. The order in which the bindings appear in the sequence is unspecified. However, if the table contains several bindings for the same key, they appear in reversed order of introduction, that is, the most recent binding appears first. The behavior is not specified if the hash table is modified during the iteration. Since: 4.07 << val to_seq_keys : ('a, 'b) t -> 'a Seq.t >> Same as Seq.map fst (to_seq m) Since: 4.07 << val to_seq_values : ('a, 'b) t -> 'b Seq.t >> Same as Seq.map snd (to_seq m) Since: 4.07 << val add_seq : ('a, 'b) t -> ('a * 'b) Seq.t -> unit >> Add the given bindings to the table, using Hashtbl.add[29.25] Since: 4.07 << val replace_seq : ('a, 'b) t -> ('a * 'b) Seq.t -> unit >> Add the given bindings to the table, using Hashtbl.replace[29.25] Since: 4.07 << val of_seq : ('a * 'b) Seq.t -> ('a, 'b) t >> Build a table from the given bindings. The bindings are added in the same order they appear in the sequence, using Hashtbl.replace_seq[29.25], which means that if two pairs have the same key, only the latest one will appear in the table. Since: 4.07 Functorial interface ==================== The functorial interface allows the use of specific comparison and hash functions, either for performance/security concerns, or because keys are not hashable/comparable with the polymorphic builtins. For instance, one might want to specialize a table for integer keys: << module IntHash = struct type t = int let equal i j = i=j let hash i = i land max_int end module IntHashtbl = Hashtbl.Make(IntHash) let h = IntHashtbl.create 17 in IntHashtbl.add h 12 "hello" >> This creates a new module IntHashtbl, with a new type 'a IntHashtbl.t of tables from int to 'a. In this example, h contains string values so its type is string IntHashtbl.t. Note that the new type 'a IntHashtbl.t is not compatible with the type ('a,'b) Hashtbl.t of the generic interface. For example, Hashtbl.length h would not type-check, you must use IntHashtbl.length. << module type HashedType = >>  sig << type t >> The type of the hashtable keys. << val equal : t -> t -> bool >> The equality predicate used to compare keys. << val hash : t -> int >> A hashing function on keys. It must be such that if two keys are equal according to equal, then they have identical hash values as computed by hash. Examples: suitable (equal, hash) pairs for arbitrary key types include - ((=), Hashtbl.HashedType.hash[29.25]) for comparing objects by structure (provided objects do not contain floats) - ((fun x y -> compare x y = 0), Hashtbl.HashedType.hash[29.25]) for comparing objects by structure and handling nan[28.2] correctly - ((==), Hashtbl.HashedType.hash[29.25]) for comparing objects by physical equality (e.g. for mutable or cyclic objects).  end The input signature of the functor Hashtbl.Make[29.25]. << module type S = >>  sig << type key >> << type !'a t >> << val create : int -> 'a t >> << val clear : 'a t -> unit >> << val reset : 'a t -> unit >> Since: 4.00 << val copy : 'a t -> 'a t >> << val add : 'a t -> key -> 'a -> unit >> << val remove : 'a t -> key -> unit >> << val find : 'a t -> key -> 'a >> << val find_opt : 'a t -> key -> 'a option >> Since: 4.05 << val find_all : 'a t -> key -> 'a list >> << val replace : 'a t -> key -> 'a -> unit >> << val mem : 'a t -> key -> bool >> << val iter : (key -> 'a -> unit) -> 'a t -> unit >> << val filter_map_inplace : (key -> 'a -> 'a option) -> 'a t -> unit >> Since: 4.03 << val fold : (key -> 'a -> 'acc -> 'acc) -> 'a t -> 'acc -> 'acc >> << val length : 'a t -> int >> << val stats : 'a t -> Hashtbl.statistics >> Since: 4.00 << val to_seq : 'a t -> (key * 'a) Seq.t >> Since: 4.07 << val to_seq_keys : 'a t -> key Seq.t >> Since: 4.07 << val to_seq_values : 'a t -> 'a Seq.t >> Since: 4.07 << val add_seq : 'a t -> (key * 'a) Seq.t -> unit >> Since: 4.07 << val replace_seq : 'a t -> (key * 'a) Seq.t -> unit >> Since: 4.07 << val of_seq : (key * 'a) Seq.t -> 'a t >> Since: 4.07  end The output signature of the functor Hashtbl.Make[29.25]. << module Make : >> functor (H : HashedType) -> S with type key = H.t Functor building an implementation of the hashtable structure. The functor Hashtbl.Make returns a structure containing a type key of keys and a type 'a t of hash tables associating data of type 'a to keys of type key. The operations perform similarly to those of the generic interface, but use the hashing and equality functions specified in the functor argument H instead of generic equality and hashing. Since the hash function is not seeded, the create operation of the result structure always returns non-randomized hash tables. << module type SeededHashedType = >>  sig << type t >> The type of the hashtable keys. << val equal : t -> t -> bool >> The equality predicate used to compare keys. << val seeded_hash : int -> t -> int >> A seeded hashing function on keys. The first argument is the seed. It must be the case that if equal x y is true, then seeded_hash seed x = seeded_hash seed y for any value of seed. A suitable choice for seeded_hash is the function Hashtbl.seeded_hash[29.25] below.  end The input signature of the functor Hashtbl.MakeSeeded[29.25]. Since: 4.00 << module type SeededS = >>  sig << type key >> << type !'a t >> << val create : ?random:bool -> int -> 'a t >> << val clear : 'a t -> unit >> << val reset : 'a t -> unit >> << val copy : 'a t -> 'a t >> << val add : 'a t -> key -> 'a -> unit >> << val remove : 'a t -> key -> unit >> << val find : 'a t -> key -> 'a >> << val find_opt : 'a t -> key -> 'a option >> Since: 4.05 << val find_all : 'a t -> key -> 'a list >> << val replace : 'a t -> key -> 'a -> unit >> << val mem : 'a t -> key -> bool >> << val iter : (key -> 'a -> unit) -> 'a t -> unit >> << val filter_map_inplace : (key -> 'a -> 'a option) -> 'a t -> unit >> Since: 4.03 << val fold : (key -> 'a -> 'acc -> 'acc) -> 'a t -> 'acc -> 'acc >> << val length : 'a t -> int >> << val stats : 'a t -> Hashtbl.statistics >> << val to_seq : 'a t -> (key * 'a) Seq.t >> Since: 4.07 << val to_seq_keys : 'a t -> key Seq.t >> Since: 4.07 << val to_seq_values : 'a t -> 'a Seq.t >> Since: 4.07 << val add_seq : 'a t -> (key * 'a) Seq.t -> unit >> Since: 4.07 << val replace_seq : 'a t -> (key * 'a) Seq.t -> unit >> Since: 4.07 << val of_seq : (key * 'a) Seq.t -> 'a t >> Since: 4.07  end The output signature of the functor Hashtbl.MakeSeeded[29.25]. Since: 4.00 << module MakeSeeded : >> functor (H : SeededHashedType) -> SeededS with type key = H.t Functor building an implementation of the hashtable structure. The functor Hashtbl.MakeSeeded returns a structure containing a type key of keys and a type 'a t of hash tables associating data of type 'a to keys of type key. The operations perform similarly to those of the generic interface, but use the seeded hashing and equality functions specified in the functor argument H instead of generic equality and hashing. The create operation of the result structure supports the ~random optional parameter and returns randomized hash tables if ~random:true is passed or if randomization is globally on (see Hashtbl.randomize[29.25]). Since: 4.00 The polymorphic hash functions ============================== << val hash : 'a -> int >> Hashtbl.hash x associates a nonnegative integer to any value of any type. It is guaranteed that if x = y or Stdlib.compare x y = 0, then hash x = hash y. Moreover, hash always terminates, even on cyclic structures. << val seeded_hash : int -> 'a -> int >> A variant of Hashtbl.hash[29.25] that is further parameterized by an integer seed. Since: 4.00 << val hash_param : int -> int -> 'a -> int >> Hashtbl.hash_param meaningful total x computes a hash value for x, with the same properties as for hash. The two extra integer parameters meaningful and total give more precise control over hashing. Hashing performs a breadth-first, left-to-right traversal of the structure x, stopping after meaningful meaningful nodes were encountered, or total nodes (meaningful or not) were encountered. If total as specified by the user exceeds a certain value, currently 256, then it is capped to that value. Meaningful nodes are: integers; floating-point numbers; strings; characters; booleans; and constant constructors. Larger values of meaningful and total means that more nodes are taken into account to compute the final hash value, and therefore collisions are less likely to happen. However, hashing takes longer. The parameters meaningful and total govern the tradeoff between accuracy and speed. As default choices, Hashtbl.hash[29.25] and Hashtbl.seeded_hash[29.25] take meaningful = 10 and total = 100. << val seeded_hash_param : int -> int -> int -> 'a -> int >> A variant of Hashtbl.hash_param[29.25] that is further parameterized by an integer seed. Usage: Hashtbl.seeded_hash_param meaningful total seed x. Since: 4.00 Examples ======== Basic Example ------------- << (* 0...99 *) let seq = Seq.ints 0 |> Seq.take 100 (* build from Seq.t *) # let tbl = seq |> Seq.map (fun x -> x, string_of_int x) |> Hashtbl.of_seq val tbl : (int, string) Hashtbl.t = # Hashtbl.length tbl - : int = 100 # Hashtbl.find_opt tbl 32 - : string option = Some "32" # Hashtbl.find_opt tbl 166 - : string option = None # Hashtbl.replace tbl 166 "one six six" - : unit = () # Hashtbl.find_opt tbl 166 - : string option = Some "one six six" # Hashtbl.length tbl - : int = 101 >> Counting Elements ----------------- Given a sequence of elements (here, a Seq.t[29.49]), we want to count how many times each distinct element occurs in the sequence. A simple way to do this, assuming the elements are comparable and hashable, is to use a hash table that maps elements to their number of occurrences. Here we illustrate that principle using a sequence of (ascii) characters (type char). We use a custom Char_tbl specialized for char. << # module Char_tbl = Hashtbl.Make(struct type t = char let equal = Char.equal let hash = Hashtbl.hash end) (* count distinct occurrences of chars in [seq] *) # let count_chars (seq : char Seq.t) : _ list = let counts = Char_tbl.create 16 in Seq.iter (fun c -> let count_c = Char_tbl.find_opt counts c |> Option.value ~default:0 in Char_tbl.replace counts c (count_c + 1)) seq; (* turn into a list *) Char_tbl.fold (fun c n l -> (c,n) :: l) counts [] |> List.sort (fun (c1,_)(c2,_) -> Char.compare c1 c2) val count_chars : Char_tbl.key Seq.t -> (Char.t * int) list = (* basic seq from a string *) # let seq = String.to_seq "hello world, and all the camels in it!" val seq : char Seq.t = # count_chars seq - : (Char.t * int) list = [(' ', 7); ('!', 1); (',', 1); ('a', 3); ('c', 1); ('d', 2); ('e', 3); ('h', 2); ('i', 2); ('l', 6); ('m', 1); ('n', 2); ('o', 2); ('r', 1); ('s', 1); ('t', 2); ('w', 1)] (* "abcabcabc..." *) # let seq2 = Seq.cycle (String.to_seq "abc") |> Seq.take 31 val seq2 : char Seq.t = # String.of_seq seq2 - : String.t = "abcabcabcabcabcabcabcabcabcabca" # count_chars seq2 - : (Char.t * int) list = [('a', 11); ('b', 10); ('c', 10)] >> 29.26 Module In_channel : Input channels. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module provides functions for working with input channels. See the example section[29.4] below. Since: 4.14 Channels ======== << type t = in_channel >> The type of input channel. << type open_flag = open_flag = | Open_rdonly >> open for reading. << | Open_wronly >> open for writing. << | Open_append >> open for appending: always write at end of file. << | Open_creat >> create the file if it does not exist. << | Open_trunc >> empty the file if it already exists. << | Open_excl >> fail if Open_creat and the file already exists. << | Open_binary >> open in binary mode (no conversion). << | Open_text >> open in text mode (may perform conversions). << | Open_nonblock >> open in non-blocking mode. Opening modes for In_channel.open_gen[29.26]. << val stdin : t >> The standard input for the process. << val open_bin : string -> t >> Open the named file for reading, and return a new input channel on that file, positioned at the beginning of the file. << val open_text : string -> t >> Same as In_channel.open_bin[29.26], but the file is opened in text mode, so that newline translation takes place during reads. On operating systems that do not distinguish between text mode and binary mode, this function behaves like In_channel.open_bin[29.26]. << val open_gen : open_flag list -> int -> string -> t >> open_gen mode perm filename opens the named file for reading, as described above. The extra arguments mode and perm specify the opening mode and file permissions. In_channel.open_text[29.26] and In_channel.open_bin[29.26] are special cases of this function. << val with_open_bin : string -> (t -> 'a) -> 'a >> with_open_bin fn f opens a channel ic on file fn and returns f ic. After f returns, either with a value or by raising an exception, ic is guaranteed to be closed. << val with_open_text : string -> (t -> 'a) -> 'a >> Like In_channel.with_open_bin[29.26], but the channel is opened in text mode (see In_channel.open_text[29.26]). << val with_open_gen : open_flag list -> int -> string -> (t -> 'a) -> 'a >> Like In_channel.with_open_bin[29.26], but can specify the opening mode and file permission, in case the file must be created (see In_channel.open_gen[29.26]). << val close : t -> unit >> Close the given channel. Input functions raise a Sys_error exception when they are applied to a closed input channel, except In_channel.close[29.26], which does nothing when applied to an already closed channel. << val close_noerr : t -> unit >> Same as In_channel.close[29.26], but ignore all errors. Input ===== << val input_char : t -> char option >> Read one character from the given input channel. Returns None if there are no more characters to read. << val input_byte : t -> int option >> Same as In_channel.input_char[29.26], but return the 8-bit integer representing the character. Returns None if the end of file was reached. << val input_line : t -> string option >> input_line ic reads characters from ic until a newline or the end of file is reached. Returns the string of all characters read, without the newline (if any). Returns None if the end of the file has been reached. In particular, this will be the case if the last line of input is empty. A newline is the character \n unless the file is open in text mode and Sys.win32[29.56] is true in which case it is the sequence of characters \r\n. << val really_input_string : t -> int -> string option >> really_input_string ic len reads len characters from channel ic and returns them in a new string. Returns None if the end of file is reached before len characters have been read. If the same channel is read concurrently by multiple threads, the returned string is not guaranteed to contain contiguous characters from the input. << val input_all : t -> string >> input_all ic reads all remaining data from ic. If the same channel is read concurrently by multiple threads, the returned string is not guaranteed to contain contiguous characters from the input. << val input_lines : t -> string list >> input_lines ic reads lines using In_channel.input_line[29.26] until the end of file is reached. It returns the list of all lines read, in the order they were read. The newline characters that terminate lines are not included in the returned strings. Empty lines produce empty strings. Since: 5.1 Advanced input ============== << val input : t -> bytes -> int -> int -> int >> input ic buf pos len reads up to len characters from the given channel ic, storing them in byte sequence buf, starting at character number pos. It returns the actual number of characters read, between 0 and len (inclusive). A return value of 0 means that the end of file was reached. Use In_channel.really_input[29.26] to read exactly len characters. Raises Invalid_argument if pos and len do not designate a valid range of buf. << val input_bigarray : t -> ('a, Bigarray.int8_unsigned_elt, Bigarray.c_layout) Bigarray.Array1.t -> int -> int -> int >> Same as In_channel.input[29.26], but read the data into a bigarray. Since: 5.2 << val really_input : t -> bytes -> int -> int -> unit option >> really_input ic buf pos len reads len characters from channel ic, storing them in byte sequence buf, starting at character number pos. Returns None if the end of file is reached before len characters have been read. If the same channel is read concurrently by multiple threads, the bytes read by really_input are not guaranteed to be contiguous. Raises Invalid_argument if pos and len do not designate a valid range of buf. << val really_input_bigarray : t -> ('a, Bigarray.int8_unsigned_elt, Bigarray.c_layout) Bigarray.Array1.t -> int -> int -> unit option >> Same as In_channel.really_input[29.26], but read the data into a bigarray. Since: 5.2 << val fold_lines : ('acc -> string -> 'acc) -> 'acc -> t -> 'acc >> fold_lines f init ic reads lines from ic using In_channel.input_line[29.26] until the end of file is reached, and successively passes each line to function f in the style of a fold. More precisely, if lines l1, ..., lN are read, fold_lines f init ic computes f (... (f (f init l1) l2) ...) lN. If f has no side effects, this is equivalent to List.fold_left f init (In_channel.input_lines ic), but is more efficient since it does not construct the list of all lines read. Since: 5.1 Seeking ======= << val seek : t -> int64 -> unit >> seek chan pos sets the current reading position to pos for channel chan. This works only for regular files. On files of other kinds, the behavior is unspecified. << val pos : t -> int64 >> Return the current reading position for the given channel. For files opened in text mode under Windows, the returned position is approximate (owing to end-of-line conversion); in particular, saving the current position with In_channel.pos[29.26], then going back to this position using In_channel.seek[29.26] will not work. For this programming idiom to work reliably and portably, the file must be opened in binary mode. Attributes ========== << val length : t -> int64 >> Return the size (number of characters) of the regular file on which the given channel is opened. If the channel is opened on a file that is not a regular file, the result is meaningless. The returned size does not take into account the end-of-line translations that can be performed when reading from a channel opened in text mode. << val set_binary_mode : t -> bool -> unit >> set_binary_mode ic true sets the channel ic to binary mode: no translations take place during input. set_binary_mode ic false sets the channel ic to text mode: depending on the operating system, some translations may take place during input. For instance, under Windows, end-of-lines will be translated from \r\n to \n. This function has no effect under operating systems that do not distinguish between text mode and binary mode. << val is_binary_mode : t -> bool >> is_binary_mode ic returns whether the channel ic is in binary mode (see In_channel.set_binary_mode[29.26]). Since: 5.2 << val isatty : t -> bool >> isatty ic is true if ic refers to a terminal or console window, false otherwise. Since: 5.1 Examples ======== Reading the contents of a file: << let read_file file = In_channel.with_open_bin file In_channel.input_all >> Reading a line from stdin: << let user_input () = In_channel.input_line In_channel.stdin >> 29.27 Module Int : Integer values. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Integers are Sys.int_size[29.56] bits wide and use two’s complement representation. All operations are taken modulo 2^Sys.int_size. They do not fail on overflow. Since: 4.08 Integers ======== << type t = int >> The type for integer values. << val zero : int >> zero is the integer 0. << val one : int >> one is the integer 1. << val minus_one : int >> minus_one is the integer -1. << val neg : int -> int >> neg x is ~-x. << val add : int -> int -> int >> add x y is the addition x + y. << val sub : int -> int -> int >> sub x y is the subtraction x - y. << val mul : int -> int -> int >> mul x y is the multiplication x * y. << val div : int -> int -> int >> div x y is the division x / y. See (/)[28.2] for details. << val rem : int -> int -> int >> rem x y is the remainder x mod y. See (mod)[28.2] for details. << val succ : int -> int >> succ x is add x 1. << val pred : int -> int >> pred x is sub x 1. << val abs : int -> int >> abs x is the absolute value of x. That is x if x is positive and neg x if x is negative. Warning. This may be negative if the argument is Int.min_int[29.27]. << val max_int : int >> max_int is the greatest representable integer, 2^Sys.int_size − 1-1. << val min_int : int >> min_int is the smallest representable integer, -2^Sys.int_size − 1. << val logand : int -> int -> int >> logand x y is the bitwise logical and of x and y. << val logor : int -> int -> int >> logor x y is the bitwise logical or of x and y. << val logxor : int -> int -> int >> logxor x y is the bitwise logical exclusive or of x and y. << val lognot : int -> int >> lognot x is the bitwise logical negation of x. << val shift_left : int -> int -> int >> shift_left x n shifts x to the left by n bits. The result is unspecified if n < 0 or n > Sys.int_size[29.56]. << val shift_right : int -> int -> int >> shift_right x n shifts x to the right by n bits. This is an arithmetic shift: the sign bit of x is replicated and inserted in the vacated bits. The result is unspecified if n < 0 or n > Sys.int_size[29.56]. << val shift_right_logical : int -> int -> int >> shift_right x n shifts x to the right by n bits. This is a logical shift: zeroes are inserted in the vacated bits regardless of the sign of x. The result is unspecified if n < 0 or n > Sys.int_size[29.56]. Predicates and comparisons ========================== << val equal : int -> int -> bool >> equal x y is true if and only if x = y. << val compare : int -> int -> int >> compare x y is compare[28.2] x y but more efficient. << val min : int -> int -> int >> Return the smaller of the two arguments. Since: 4.13 << val max : int -> int -> int >> Return the greater of the two arguments. Since: 4.13 Converting ========== << val to_float : int -> float >> to_float x is x as a floating point number. << val of_float : float -> int >> of_float x truncates x to an integer. The result is unspecified if the argument is nan or falls outside the range of representable integers. << val to_string : int -> string >> to_string x is the written representation of x in decimal. << val seeded_hash : int -> int -> int >> A seeded hash function for ints, with the same output value as Hashtbl.seeded_hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded[29.25]. Since: 5.1 << val hash : int -> int >> An unseeded hash function for ints, with the same output value as Hashtbl.hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.Make[29.25]. Since: 5.1 29.28 Module Int32 : 32-bit integers. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module provides operations on the type int32 of signed 32-bit integers. Unlike the built-in int type, the type int32 is guaranteed to be exactly 32-bit wide on all platforms. All arithmetic operations over int32 are taken modulo 2^32. Performance notice: values of type int32 occupy more memory space than values of type int, and arithmetic operations on int32 are generally slower than those on int. Use int32 only when the application requires exact 32-bit arithmetic. Literals for 32-bit integers are suffixed by l: << let zero: int32 = 0l let one: int32 = 1l let m_one: int32 = -1l >> << val zero : int32 >> The 32-bit integer 0. << val one : int32 >> The 32-bit integer 1. << val minus_one : int32 >> The 32-bit integer -1. << val neg : int32 -> int32 >> Unary negation. << val add : int32 -> int32 -> int32 >> Addition. << val sub : int32 -> int32 -> int32 >> Subtraction. << val mul : int32 -> int32 -> int32 >> Multiplication. << val div : int32 -> int32 -> int32 >> Integer division. This division rounds the real quotient of its arguments towards zero, as specified for (/)[28.2]. Raises Division_by_zero if the second argument is zero. << val unsigned_div : int32 -> int32 -> int32 >> Same as Int32.div[29.28], except that arguments and result are interpreted as unsigned 32-bit integers. Since: 4.08 << val rem : int32 -> int32 -> int32 >> Integer remainder. If y is not zero, the result of Int32.rem x y satisfies the following property: x = Int32.add (Int32.mul (Int32.div x y) y) (Int32.rem x y). If y = 0, Int32.rem x y raises Division_by_zero. << val unsigned_rem : int32 -> int32 -> int32 >> Same as Int32.rem[29.28], except that arguments and result are interpreted as unsigned 32-bit integers. Since: 4.08 << val succ : int32 -> int32 >> Successor. Int32.succ x is Int32.add x Int32.one. << val pred : int32 -> int32 >> Predecessor. Int32.pred x is Int32.sub x Int32.one. << val abs : int32 -> int32 >> abs x is the absolute value of x. On min_int this is min_int itself and thus remains negative. << val max_int : int32 >> The greatest representable 32-bit integer, 2^31 - 1. << val min_int : int32 >> The smallest representable 32-bit integer, -2^31. << val logand : int32 -> int32 -> int32 >> Bitwise logical and. << val logor : int32 -> int32 -> int32 >> Bitwise logical or. << val logxor : int32 -> int32 -> int32 >> Bitwise logical exclusive or. << val lognot : int32 -> int32 >> Bitwise logical negation. << val shift_left : int32 -> int -> int32 >> Int32.shift_left x y shifts x to the left by y bits. The result is unspecified if y < 0 or y >= 32. << val shift_right : int32 -> int -> int32 >> Int32.shift_right x y shifts x to the right by y bits. This is an arithmetic shift: the sign bit of x is replicated and inserted in the vacated bits. The result is unspecified if y < 0 or y >= 32. << val shift_right_logical : int32 -> int -> int32 >> Int32.shift_right_logical x y shifts x to the right by y bits. This is a logical shift: zeroes are inserted in the vacated bits regardless of the sign of x. The result is unspecified if y < 0 or y >= 32. << val of_int : int -> int32 >> Convert the given integer (type int) to a 32-bit integer (type int32). On 64-bit platforms, the argument is taken modulo 2^32. << val to_int : int32 -> int >> Convert the given 32-bit integer (type int32) to an integer (type int). On 32-bit platforms, the 32-bit integer is taken modulo 2^31, i.e. the high-order bit is lost during the conversion. On 64-bit platforms, the conversion is exact. << val unsigned_to_int : int32 -> int option >> Same as Int32.to_int[29.28], but interprets the argument as an unsigned integer. Returns None if the unsigned value of the argument cannot fit into an int. Since: 4.08 << val of_float : float -> int32 >> Convert the given floating-point number to a 32-bit integer, discarding the fractional part (truncate towards 0). If the truncated floating-point number is outside the range [Int32.min_int[29.28], Int32.max_int[29.28]], no exception is raised, and an unspecified, platform-dependent integer is returned. << val to_float : int32 -> float >> Convert the given 32-bit integer to a floating-point number. << val of_string : string -> int32 >> Convert the given string to a 32-bit integer. The string is read in decimal (by default, or if the string begins with 0u) or in hexadecimal, octal or binary if the string begins with 0x, 0o or 0b respectively. The 0u prefix reads the input as an unsigned integer in the range [0, 2*Int32.max_int+1]. If the input exceeds Int32.max_int[29.28] it is converted to the signed integer Int32.min_int + input - Int32.max_int - 1. The _ (underscore) character can appear anywhere in the string and is ignored. Raises Failure if the given string is not a valid representation of an integer, or if the integer represented exceeds the range of integers representable in type int32. << val of_string_opt : string -> int32 option >> Same as of_string, but return None instead of raising. Since: 4.05 << val to_string : int32 -> string >> Return the string representation of its argument, in signed decimal. << val bits_of_float : float -> int32 >> Return the internal representation of the given float according to the IEEE 754 floating-point ’single format’ bit layout. Bit 31 of the result represents the sign of the float; bits 30 to 23 represent the (biased) exponent; bits 22 to 0 represent the mantissa. << val float_of_bits : int32 -> float >> Return the floating-point number whose internal representation, according to the IEEE 754 floating-point ’single format’ bit layout, is the given int32. << type t = int32 >> An alias for the type of 32-bit integers. << val compare : t -> t -> int >> The comparison function for 32-bit integers, with the same specification as compare[28.2]. Along with the type t, this function compare allows the module Int32 to be passed as argument to the functors Set.Make[29.50] and Map.Make[29.34]. << val unsigned_compare : t -> t -> int >> Same as Int32.compare[29.28], except that arguments are interpreted as unsigned 32-bit integers. Since: 4.08 << val equal : t -> t -> bool >> The equal function for int32s. Since: 4.03 << val min : t -> t -> t >> Return the smaller of the two arguments. Since: 4.13 << val max : t -> t -> t >> Return the greater of the two arguments. Since: 4.13 << val seeded_hash : int -> t -> int >> A seeded hash function for 32-bit ints, with the same output value as Hashtbl.seeded_hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded[29.25]. Since: 5.1 << val hash : t -> int >> An unseeded hash function for 32-bit ints, with the same output value as Hashtbl.hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.Make[29.25]. Since: 5.1 29.29 Module Int64 : 64-bit integers. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module provides operations on the type int64 of signed 64-bit integers. Unlike the built-in int type, the type int64 is guaranteed to be exactly 64-bit wide on all platforms. All arithmetic operations over int64 are taken modulo 2^64 Performance notice: values of type int64 occupy more memory space than values of type int, and arithmetic operations on int64 are generally slower than those on int. Use int64 only when the application requires exact 64-bit arithmetic. Literals for 64-bit integers are suffixed by L: << let zero: int64 = 0L let one: int64 = 1L let m_one: int64 = -1L >> << val zero : int64 >> The 64-bit integer 0. << val one : int64 >> The 64-bit integer 1. << val minus_one : int64 >> The 64-bit integer -1. << val neg : int64 -> int64 >> Unary negation. << val add : int64 -> int64 -> int64 >> Addition. << val sub : int64 -> int64 -> int64 >> Subtraction. << val mul : int64 -> int64 -> int64 >> Multiplication. << val div : int64 -> int64 -> int64 >> Integer division. Raises Division_by_zero if the second argument is zero. This division rounds the real quotient of its arguments towards zero, as specified for (/)[28.2]. << val unsigned_div : int64 -> int64 -> int64 >> Same as Int64.div[29.29], except that arguments and result are interpreted as unsigned 64-bit integers. Since: 4.08 << val rem : int64 -> int64 -> int64 >> Integer remainder. If y is not zero, the result of Int64.rem x y satisfies the following property: x = Int64.add (Int64.mul (Int64.div x y) y) (Int64.rem x y). If y = 0, Int64.rem x y raises Division_by_zero. << val unsigned_rem : int64 -> int64 -> int64 >> Same as Int64.rem[29.29], except that arguments and result are interpreted as unsigned 64-bit integers. Since: 4.08 << val succ : int64 -> int64 >> Successor. Int64.succ x is Int64.add x Int64.one. << val pred : int64 -> int64 >> Predecessor. Int64.pred x is Int64.sub x Int64.one. << val abs : int64 -> int64 >> abs x is the absolute value of x. On min_int this is min_int itself and thus remains negative. << val max_int : int64 >> The greatest representable 64-bit integer, 2^63 - 1. << val min_int : int64 >> The smallest representable 64-bit integer, -2^63. << val logand : int64 -> int64 -> int64 >> Bitwise logical and. << val logor : int64 -> int64 -> int64 >> Bitwise logical or. << val logxor : int64 -> int64 -> int64 >> Bitwise logical exclusive or. << val lognot : int64 -> int64 >> Bitwise logical negation. << val shift_left : int64 -> int -> int64 >> Int64.shift_left x y shifts x to the left by y bits. The result is unspecified if y < 0 or y >= 64. << val shift_right : int64 -> int -> int64 >> Int64.shift_right x y shifts x to the right by y bits. This is an arithmetic shift: the sign bit of x is replicated and inserted in the vacated bits. The result is unspecified if y < 0 or y >= 64. << val shift_right_logical : int64 -> int -> int64 >> Int64.shift_right_logical x y shifts x to the right by y bits. This is a logical shift: zeroes are inserted in the vacated bits regardless of the sign of x. The result is unspecified if y < 0 or y >= 64. << val of_int : int -> int64 >> Convert the given integer (type int) to a 64-bit integer (type int64). << val to_int : int64 -> int >> Convert the given 64-bit integer (type int64) to an integer (type int). On 64-bit platforms, the 64-bit integer is taken modulo 2^63, i.e. the high-order bit is lost during the conversion. On 32-bit platforms, the 64-bit integer is taken modulo 2^31, i.e. the top 33 bits are lost during the conversion. << val unsigned_to_int : int64 -> int option >> Same as Int64.to_int[29.29], but interprets the argument as an unsigned integer. Returns None if the unsigned value of the argument cannot fit into an int. Since: 4.08 << val of_float : float -> int64 >> Convert the given floating-point number to a 64-bit integer, discarding the fractional part (truncate towards 0). If the truncated floating-point number is outside the range [Int64.min_int[29.29], Int64.max_int[29.29]], no exception is raised, and an unspecified, platform-dependent integer is returned. << val to_float : int64 -> float >> Convert the given 64-bit integer to a floating-point number. << val of_int32 : int32 -> int64 >> Convert the given 32-bit integer (type int32) to a 64-bit integer (type int64). << val to_int32 : int64 -> int32 >> Convert the given 64-bit integer (type int64) to a 32-bit integer (type int32). The 64-bit integer is taken modulo 2^32, i.e. the top 32 bits are lost during the conversion. << val of_nativeint : nativeint -> int64 >> Convert the given native integer (type nativeint) to a 64-bit integer (type int64). << val to_nativeint : int64 -> nativeint >> Convert the given 64-bit integer (type int64) to a native integer. On 32-bit platforms, the 64-bit integer is taken modulo 2^32. On 64-bit platforms, the conversion is exact. << val of_string : string -> int64 >> Convert the given string to a 64-bit integer. The string is read in decimal (by default, or if the string begins with 0u) or in hexadecimal, octal or binary if the string begins with 0x, 0o or 0b respectively. The 0u prefix reads the input as an unsigned integer in the range [0, 2*Int64.max_int+1]. If the input exceeds Int64.max_int[29.29] it is converted to the signed integer Int64.min_int + input - Int64.max_int - 1. The _ (underscore) character can appear anywhere in the string and is ignored. Raises Failure if the given string is not a valid representation of an integer, or if the integer represented exceeds the range of integers representable in type int64. << val of_string_opt : string -> int64 option >> Same as of_string, but return None instead of raising. Since: 4.05 << val to_string : int64 -> string >> Return the string representation of its argument, in decimal. << val bits_of_float : float -> int64 >> Return the internal representation of the given float according to the IEEE 754 floating-point ’double format’ bit layout. Bit 63 of the result represents the sign of the float; bits 62 to 52 represent the (biased) exponent; bits 51 to 0 represent the mantissa. << val float_of_bits : int64 -> float >> Return the floating-point number whose internal representation, according to the IEEE 754 floating-point ’double format’ bit layout, is the given int64. << type t = int64 >> An alias for the type of 64-bit integers. << val compare : t -> t -> int >> The comparison function for 64-bit integers, with the same specification as compare[28.2]. Along with the type t, this function compare allows the module Int64 to be passed as argument to the functors Set.Make[29.50] and Map.Make[29.34]. << val unsigned_compare : t -> t -> int >> Same as Int64.compare[29.29], except that arguments are interpreted as unsigned 64-bit integers. Since: 4.08 << val equal : t -> t -> bool >> The equal function for int64s. Since: 4.03 << val min : t -> t -> t >> Return the smaller of the two arguments. Since: 4.13 << val max : t -> t -> t >> Return the greater of the two arguments. Since: 4.13 << val seeded_hash : int -> t -> int >> A seeded hash function for 64-bit ints, with the same output value as Hashtbl.seeded_hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded[29.25]. Since: 5.1 << val hash : t -> int >> An unseeded hash function for 64-bit ints, with the same output value as Hashtbl.hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.Make[29.25]. Since: 5.1 29.30 Module Lazy : Deferred computations. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= << type 'a t = 'a CamlinternalLazy.t >> A value of type 'a Lazy.t is a deferred computation, called a suspension, that has a result of type 'a. The special expression syntax lazy (expr) makes a suspension of the computation of expr, without computing expr itself yet. "Forcing" the suspension will then compute expr and return its result. Matching a suspension with the special pattern syntax lazy(pattern) also computes the underlying expression and tries to bind it to pattern: << let lazy_option_map f x = match x with | lazy (Some x) -> Some (Lazy.force f x) | _ -> None >> Note: If lazy patterns appear in multiple cases in a pattern-matching, lazy expressions may be forced even outside of the case ultimately selected by the pattern matching. In the example above, the suspension x is always computed. Note: lazy_t is the built-in type constructor used by the compiler for the lazy keyword. You should not use it directly. Always use Lazy.t instead. Note: Lazy.force is not concurrency-safe. If you use this module with multiple fibers, systhreads or domains, then you will need to add some locks. The module however ensures memory-safety, and hence, concurrently accessing this module will not lead to a crash but the behaviour is unspecified. Note: if the program is compiled with the -rectypes option, ill-founded recursive definitions of the form let rec x = lazy x or let rec x = lazy(lazy(...(lazy x))) are accepted by the type-checker and lead, when forced, to ill-formed values that trigger infinite loops in the garbage collector and other parts of the run-time system. Without the -rectypes option, such ill-founded recursive definitions are rejected by the type-checker. << exception Undefined >> Raised when forcing a suspension concurrently from multiple fibers, systhreads or domains, or when the suspension tries to force itself recursively. << val force : 'a t -> 'a >> force x forces the suspension x and returns its result. If x has already been forced, Lazy.force x returns the same value again without recomputing it. If it raised an exception, the same exception is raised again. Raises Undefined (see Lazy.Undefined[29.30]). Iterators ========= << val map : ('a -> 'b) -> 'a t -> 'b t >> map f x returns a suspension that, when forced, forces x and applies f to its value. It is equivalent to lazy (f (Lazy.force x)). Since: 4.13 Reasoning on already-forced suspensions ======================================= << val is_val : 'a t -> bool >> is_val x returns true if x has already been forced and did not raise an exception. Since: 4.00 << val from_val : 'a -> 'a t >> from_val v evaluates v first (as any function would) and returns an already-forced suspension of its result. It is the same as let x = v in lazy x, but uses dynamic tests to optimize suspension creation in some cases. Since: 4.00 << val map_val : ('a -> 'b) -> 'a t -> 'b t >> map_val f x applies f directly if x is already forced, otherwise it behaves as map f x. When x is already forced, this behavior saves the construction of a suspension, but on the other hand it performs more work eagerly that may not be useful if you never force the function result. If f raises an exception, it will be raised immediately when is_val x, or raised only when forcing the thunk otherwise. If map_val f x does not raise an exception, then is_val (map_val f x) is equal to is_val x. Since: 4.13 Advanced ======== The following definitions are for advanced uses only; they require familiarity with the lazy compilation scheme to be used appropriately. << val from_fun : (unit -> 'a) -> 'a t >> from_fun f is the same as lazy (f ()) but slightly more efficient. It should only be used if the function f is already defined. In particular it is always less efficient to write from_fun (fun () -> expr) than lazy expr. Since: 4.00 << val force_val : 'a t -> 'a >> force_val x forces the suspension x and returns its result. If x has already been forced, force_val x returns the same value again without recomputing it. If the computation of x raises an exception, it is unspecified whether force_val x raises the same exception or Lazy.Undefined[29.30]. Raises - Undefined if the forcing of x tries to force x itself recursively. - Undefined (see Lazy.Undefined[29.30]). 29.31 Module Lexing : The run-time library for lexers generated by ocamllex. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Positions ========= << type position = { pos_fname : string ; pos_lnum : int ; pos_bol : int ; pos_cnum : int ; } >> A value of type position describes a point in a source file. pos_fname is the file name; pos_lnum is the line number; pos_bol is the offset of the beginning of the line (number of characters between the beginning of the lexbuf and the beginning of the line); pos_cnum is the offset of the position (number of characters between the beginning of the lexbuf and the position). The difference between pos_cnum and pos_bol is the character offset within the line (i.e. the column number, assuming each character is one column wide). See the documentation of type lexbuf for information about how the lexing engine will manage positions. << val dummy_pos : position >> A value of type position, guaranteed to be different from any valid position. Lexer buffers ============= << type lexbuf = { refill_buff : lexbuf -> unit ; mutable lex_buffer : bytes ; mutable lex_buffer_len : int ; mutable lex_abs_pos : int ; mutable lex_start_pos : int ; mutable lex_curr_pos : int ; mutable lex_last_pos : int ; mutable lex_last_action : int ; mutable lex_eof_reached : bool ; mutable lex_mem : int array ; mutable lex_start_p : position ; mutable lex_curr_p : position ; } >> The type of lexer buffers. A lexer buffer is the argument passed to the scanning functions defined by the generated scanners. The lexer buffer holds the current state of the scanner, plus a function to refill the buffer from the input. Lexers can optionally maintain the lex_curr_p and lex_start_p position fields. This "position tracking" mode is the default, and it corresponds to passing ~with_position:true to functions that create lexer buffers. In this mode, the lexing engine and lexer actions are co-responsible for properly updating the position fields, as described in the next paragraph. When the mode is explicitly disabled (with ~with_position:false), the lexing engine will not touch the position fields and the lexer actions should be careful not to do it either; the lex_curr_p and lex_start_p field will then always hold the dummy_pos invalid position. Not tracking positions avoids allocations and memory writes and can significantly improve the performance of the lexer in contexts where lex_start_p and lex_curr_p are not needed. Position tracking mode works as follows. At each token, the lexing engine will copy lex_curr_p to lex_start_p, then change the pos_cnum field of lex_curr_p by updating it with the number of characters read since the start of the lexbuf. The other fields are left unchanged by the lexing engine. In order to keep them accurate, they must be initialised before the first use of the lexbuf, and updated by the relevant lexer actions (i.e. at each end of line – see also new_line). << val from_channel : ?with_positions:bool -> in_channel -> lexbuf >> Create a lexer buffer on the given input channel. Lexing.from_channel inchan returns a lexer buffer which reads from the input channel inchan, at the current reading position. << val from_string : ?with_positions:bool -> string -> lexbuf >> Create a lexer buffer which reads from the given string. Reading starts from the first character in the string. An end-of-input condition is generated when the end of the string is reached. << val from_function : ?with_positions:bool -> (bytes -> int -> int) -> lexbuf >> Create a lexer buffer with the given function as its reading method. When the scanner needs more characters, it will call the given function, giving it a byte sequence s and a byte count n. The function should put n bytes or fewer in s, starting at index 0, and return the number of bytes provided. A return value of 0 means end of input. << val set_position : lexbuf -> position -> unit >> Set the initial tracked input position for lexbuf to a custom value. Ignores pos_fname. See Lexing.set_filename[29.31] for changing this field. Since: 4.11 << val set_filename : lexbuf -> string -> unit >> Set filename in the initial tracked position to file in lexbuf. Since: 4.11 << val with_positions : lexbuf -> bool >> Tell whether the lexer buffer keeps track of position fields lex_curr_p / lex_start_p, as determined by the corresponding optional argument for functions that create lexer buffers (whose default value is true). When with_positions is false, lexer actions should not modify position fields. Doing it nevertheless could re-enable the with_position mode and degrade performances. Functions for lexer semantic actions ==================================== The following functions can be called from the semantic actions of lexer definitions (the ML code enclosed in braces that computes the value returned by lexing functions). They give access to the character string matched by the regular expression associated with the semantic action. These functions must be applied to the argument lexbuf, which, in the code generated by ocamllex, is bound to the lexer buffer passed to the parsing function. << val lexeme : lexbuf -> string >> Lexing.lexeme lexbuf returns the string matched by the regular expression. << val lexeme_char : lexbuf -> int -> char >> Lexing.lexeme_char lexbuf i returns character number i in the matched string. << val lexeme_start : lexbuf -> int >> Lexing.lexeme_start lexbuf returns the offset in the input stream of the first character of the matched string. The first character of the stream has offset 0. << val lexeme_end : lexbuf -> int >> Lexing.lexeme_end lexbuf returns the offset in the input stream of the character following the last character of the matched string. The first character of the stream has offset 0. << val lexeme_start_p : lexbuf -> position >> Like lexeme_start, but return a complete position instead of an offset. When position tracking is disabled, the function returns dummy_pos. << val lexeme_end_p : lexbuf -> position >> Like lexeme_end, but return a complete position instead of an offset. When position tracking is disabled, the function returns dummy_pos. << val new_line : lexbuf -> unit >> Update the lex_curr_p field of the lexbuf to reflect the start of a new line. You can call this function in the semantic action of the rule that matches the end-of-line character. The function does nothing when position tracking is disabled. Since: 3.11 Miscellaneous functions ======================= << val flush_input : lexbuf -> unit >> Discard the contents of the buffer and reset the current position to 0. The next use of the lexbuf will trigger a refill. 29.32 Module List : List operations. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Some functions are flagged as not tail-recursive. A tail-recursive function uses constant stack space, while a non-tail-recursive function uses stack space proportional to the length of its list argument, which can be a problem with very long lists. When the function takes several list arguments, an approximate formula giving stack usage (in some unspecified constant unit) is shown in parentheses. The above considerations can usually be ignored if your lists are not longer than about 10000 elements. The labeled version of this module can be used as described in the StdLabels[29.53] module. << type 'a t = 'a list = | [] | (::) of 'a * 'a list >> An alias for the type of lists. << val length : 'a list -> int >> Return the length (number of elements) of the given list. << val compare_lengths : 'a list -> 'b list -> int >> Compare the lengths of two lists. compare_lengths l1 l2 is equivalent to compare (length l1) (length l2), except that the computation stops after reaching the end of the shortest list. Since: 4.05 << val compare_length_with : 'a list -> int -> int >> Compare the length of a list to an integer. compare_length_with l len is equivalent to compare (length l) len, except that the computation stops after at most len iterations on the list. Since: 4.05 << val is_empty : 'a list -> bool >> is_empty l is true if and only if l has no elements. It is equivalent to compare_length_with l 0 = 0. Since: 5.1 << val cons : 'a -> 'a list -> 'a list >> cons x xs is x :: xs Since: 4.03 (4.05 in ListLabels) << val hd : 'a list -> 'a >> Return the first element of the given list. Raises Failure if the list is empty. << val tl : 'a list -> 'a list >> Return the given list without its first element. Raises Failure if the list is empty. << val nth : 'a list -> int -> 'a >> Return the n-th element of the given list. The first element (head of the list) is at position 0. Raises - Failure if the list is too short. - Invalid_argument if n is negative. << val nth_opt : 'a list -> int -> 'a option >> Return the n-th element of the given list. The first element (head of the list) is at position 0. Return None if the list is too short. Since: 4.05 Raises Invalid_argument if n is negative. << val rev : 'a list -> 'a list >> List reversal. << val init : int -> (int -> 'a) -> 'a list >> init len f is [f 0; f 1; ...; f (len-1)], evaluated left to right. Since: 4.06 Raises Invalid_argument if len < 0. << val append : 'a list -> 'a list -> 'a list >> append l0 l1 appends l1 to l0. Same function as the infix operator @. Since: 5.1 this function is tail-recursive. << val rev_append : 'a list -> 'a list -> 'a list >> rev_append l1 l2 reverses l1 and concatenates it with l2. This is equivalent to (List.rev[29.32] l1) @ l2. << val concat : 'a list list -> 'a list >> Concatenate a list of lists. The elements of the argument are all concatenated together (in the same order) to give the result. Not tail-recursive (length of the argument + length of the longest sub-list). << val flatten : 'a list list -> 'a list >> Same as List.concat[29.32]. Not tail-recursive (length of the argument + length of the longest sub-list). Comparison ========== << val equal : ('a -> 'a -> bool) -> 'a list -> 'a list -> bool >> equal eq [a1; ...; an] [b1; ..; bm] holds when the two input lists have the same length, and for each pair of elements ai, bi at the same position we have eq ai bi. Note: the eq function may be called even if the lists have different length. If you know your equality function is costly, you may want to check List.compare_lengths[29.32] first. Since: 4.12 << val compare : ('a -> 'a -> int) -> 'a list -> 'a list -> int >> compare cmp [a1; ...; an] [b1; ...; bm] performs a lexicographic comparison of the two input lists, using the same 'a -> 'a -> int interface as compare[28.2]: - a1 :: l1 is smaller than a2 :: l2 (negative result) if a1 is smaller than a2, or if they are equal (0 result) and l1 is smaller than l2 - the empty list [] is strictly smaller than non-empty lists Note: the cmp function will be called even if the lists have different lengths. Since: 4.12 Iterators ========= << val iter : ('a -> unit) -> 'a list -> unit >> iter f [a1; ...; an] applies function f in turn to [a1; ...; an]. It is equivalent to f a1; f a2; ...; f an. << val iteri : (int -> 'a -> unit) -> 'a list -> unit >> Same as List.iter[29.32], but the function is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 4.00 << val map : ('a -> 'b) -> 'a list -> 'b list >> map f [a1; ...; an] applies function f to a1, ..., an, and builds the list [f a1; ...; f an] with the results returned by f. << val mapi : (int -> 'a -> 'b) -> 'a list -> 'b list >> Same as List.map[29.32], but the function is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 4.00 << val rev_map : ('a -> 'b) -> 'a list -> 'b list >> rev_map f l gives the same result as List.rev[29.32] (List.map[29.32] f l), but is more efficient. << val filter_map : ('a -> 'b option) -> 'a list -> 'b list >> filter_map f l applies f to every element of l, filters out the None elements and returns the list of the arguments of the Some elements. Since: 4.08 << val concat_map : ('a -> 'b list) -> 'a list -> 'b list >> concat_map f l gives the same result as List.concat[29.32] (List.map[29.32] f l). Tail-recursive. Since: 4.10 << val fold_left_map : ('acc -> 'a -> 'acc * 'b) -> 'acc -> 'a list -> 'acc * 'b list >> fold_left_map is a combination of fold_left and map that threads an accumulator through calls to f. Since: 4.11 << val fold_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a list -> 'acc >> fold_left f init [b1; ...; bn] is f (... (f (f init b1) b2) ...) bn. << val fold_right : ('a -> 'acc -> 'acc) -> 'a list -> 'acc -> 'acc >> fold_right f [a1; ...; an] init is f a1 (f a2 (... (f an init) ...)). Not tail-recursive. Iterators on two lists ====================== << val iter2 : ('a -> 'b -> unit) -> 'a list -> 'b list -> unit >> iter2 f [a1; ...; an] [b1; ...; bn] calls in turn f a1 b1; ...; f an bn. Raises Invalid_argument if the two lists are determined to have different lengths. << val map2 : ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list >> map2 f [a1; ...; an] [b1; ...; bn] is [f a1 b1; ...; f an bn]. Raises Invalid_argument if the two lists are determined to have different lengths. << val rev_map2 : ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list >> rev_map2 f l1 l2 gives the same result as List.rev[29.32] (List.map2[29.32] f l1 l2), but is more efficient. << val fold_left2 : ('acc -> 'a -> 'b -> 'acc) -> 'acc -> 'a list -> 'b list -> 'acc >> fold_left2 f init [a1; ...; an] [b1; ...; bn] is f (... (f (f init a1 b1) a2 b2) ...) an bn. Raises Invalid_argument if the two lists are determined to have different lengths. << val fold_right2 : ('a -> 'b -> 'acc -> 'acc) -> 'a list -> 'b list -> 'acc -> 'acc >> fold_right2 f [a1; ...; an] [b1; ...; bn] init is f a1 b1 (f a2 b2 (... (f an bn init) ...)). Raises Invalid_argument if the two lists are determined to have different lengths. Not tail-recursive. List scanning ============= << val for_all : ('a -> bool) -> 'a list -> bool >> for_all f [a1; ...; an] checks if all elements of the list satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an) for a non-empty list and true if the list is empty. << val exists : ('a -> bool) -> 'a list -> bool >> exists f [a1; ...; an] checks if at least one element of the list satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an) for a non-empty list and false if the list is empty. << val for_all2 : ('a -> 'b -> bool) -> 'a list -> 'b list -> bool >> Same as List.for_all[29.32], but for a two-argument predicate. Raises Invalid_argument if the two lists are determined to have different lengths. << val exists2 : ('a -> 'b -> bool) -> 'a list -> 'b list -> bool >> Same as List.exists[29.32], but for a two-argument predicate. Raises Invalid_argument if the two lists are determined to have different lengths. << val mem : 'a -> 'a list -> bool >> mem a set is true if and only if a is equal to an element of set. << val memq : 'a -> 'a list -> bool >> Same as List.mem[29.32], but uses physical equality instead of structural equality to compare list elements. List searching ============== << val find : ('a -> bool) -> 'a list -> 'a >> find f l returns the first element of the list l that satisfies the predicate f. Raises Not_found if there is no value that satisfies f in the list l. << val find_opt : ('a -> bool) -> 'a list -> 'a option >> find f l returns the first element of the list l that satisfies the predicate f. Returns None if there is no value that satisfies f in the list l. Since: 4.05 << val find_index : ('a -> bool) -> 'a list -> int option >> find_index f xs returns Some i, where i is the index of the first element of the list xs that satisfies f x, if there is such an element. It returns None if there is no such element. Since: 5.1 << val find_map : ('a -> 'b option) -> 'a list -> 'b option >> find_map f l applies f to the elements of l in order, and returns the first result of the form Some v, or None if none exist. Since: 4.10 << val find_mapi : (int -> 'a -> 'b option) -> 'a list -> 'b option >> Same as find_map, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 5.1 << val filter : ('a -> bool) -> 'a list -> 'a list >> filter f l returns all the elements of the list l that satisfy the predicate f. The order of the elements in the input list is preserved. << val find_all : ('a -> bool) -> 'a list -> 'a list >> find_all is another name for List.filter[29.32]. << val filteri : (int -> 'a -> bool) -> 'a list -> 'a list >> Same as List.filter[29.32], but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 4.11 << val partition : ('a -> bool) -> 'a list -> 'a list * 'a list >> partition f l returns a pair of lists (l1, l2), where l1 is the list of all the elements of l that satisfy the predicate f, and l2 is the list of all the elements of l that do not satisfy f. The order of the elements in the input list is preserved. << val partition_map : ('a -> ('b, 'c) Either.t) -> 'a list -> 'b list * 'c list >> partition_map f l returns a pair of lists (l1, l2) such that, for each element x of the input list l: - if f x is Left y1, then y1 is in l1, and - if f x is Right y2, then y2 is in l2. The output elements are included in l1 and l2 in the same relative order as the corresponding input elements in l. In particular, partition_map (fun x -> if f x then Left x else Right x) l is equivalent to partition f l. Since: 4.12 Association lists ================= << val assoc : 'a -> ('a * 'b) list -> 'b >> assoc a l returns the value associated with key a in the list of pairs l. That is, assoc a [ ...; (a,b); ...] = b if (a,b) is the leftmost binding of a in list l. Raises Not_found if there is no value associated with a in the list l. << val assoc_opt : 'a -> ('a * 'b) list -> 'b option >> assoc_opt a l returns the value associated with key a in the list of pairs l. That is, assoc_opt a [ ...; (a,b); ...] = Some b if (a,b) is the leftmost binding of a in list l. Returns None if there is no value associated with a in the list l. Since: 4.05 << val assq : 'a -> ('a * 'b) list -> 'b >> Same as List.assoc[29.32], but uses physical equality instead of structural equality to compare keys. << val assq_opt : 'a -> ('a * 'b) list -> 'b option >> Same as List.assoc_opt[29.32], but uses physical equality instead of structural equality to compare keys. Since: 4.05 << val mem_assoc : 'a -> ('a * 'b) list -> bool >> Same as List.assoc[29.32], but simply return true if a binding exists, and false if no bindings exist for the given key. << val mem_assq : 'a -> ('a * 'b) list -> bool >> Same as List.mem_assoc[29.32], but uses physical equality instead of structural equality to compare keys. << val remove_assoc : 'a -> ('a * 'b) list -> ('a * 'b) list >> remove_assoc a l returns the list of pairs l without the first pair with key a, if any. Not tail-recursive. << val remove_assq : 'a -> ('a * 'b) list -> ('a * 'b) list >> Same as List.remove_assoc[29.32], but uses physical equality instead of structural equality to compare keys. Not tail-recursive. Lists of pairs ============== << val split : ('a * 'b) list -> 'a list * 'b list >> Transform a list of pairs into a pair of lists: split [(a1,b1); ...; (an,bn)] is ([a1; ...; an], [b1; ...; bn]). Not tail-recursive. << val combine : 'a list -> 'b list -> ('a * 'b) list >> Transform a pair of lists into a list of pairs: combine [a1; ...; an] [b1; ...; bn] is [(a1,b1); ...; (an,bn)]. Raises Invalid_argument if the two lists have different lengths. Not tail-recursive. Sorting ======= << val sort : ('a -> 'a -> int) -> 'a list -> 'a list >> Sort a list in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see Array.sort for a complete specification). For example, compare[28.2] is a suitable comparison function. The resulting list is sorted in increasing order. List.sort[29.32] is guaranteed to run in constant heap space (in addition to the size of the result list) and logarithmic stack space. The current implementation uses Merge Sort. It runs in constant heap space and logarithmic stack space. << val stable_sort : ('a -> 'a -> int) -> 'a list -> 'a list >> Same as List.sort[29.32], but the sorting algorithm is guaranteed to be stable (i.e. elements that compare equal are kept in their original order). The current implementation uses Merge Sort. It runs in constant heap space and logarithmic stack space. << val fast_sort : ('a -> 'a -> int) -> 'a list -> 'a list >> Same as List.sort[29.32] or List.stable_sort[29.32], whichever is faster on typical input. << val sort_uniq : ('a -> 'a -> int) -> 'a list -> 'a list >> Same as List.sort[29.32], but also remove duplicates. Since: 4.02 (4.03 in ListLabels) << val merge : ('a -> 'a -> int) -> 'a list -> 'a list -> 'a list >> Merge two lists: Assuming that l1 and l2 are sorted according to the comparison function cmp, merge cmp l1 l2 will return a sorted list containing all the elements of l1 and l2. If several elements compare equal, the elements of l1 will be before the elements of l2. Not tail-recursive (sum of the lengths of the arguments). Lists and Sequences =================== << val to_seq : 'a list -> 'a Seq.t >> Iterate on the list. Since: 4.07 << val of_seq : 'a Seq.t -> 'a list >> Create a list from a sequence. Since: 4.07 29.33 Module ListLabels : List operations. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Some functions are flagged as not tail-recursive. A tail-recursive function uses constant stack space, while a non-tail-recursive function uses stack space proportional to the length of its list argument, which can be a problem with very long lists. When the function takes several list arguments, an approximate formula giving stack usage (in some unspecified constant unit) is shown in parentheses. The above considerations can usually be ignored if your lists are not longer than about 10000 elements. The labeled version of this module can be used as described in the StdLabels[29.53] module. << type 'a t = 'a list = | [] | (::) of 'a * 'a list >> An alias for the type of lists. << val length : 'a list -> int >> Return the length (number of elements) of the given list. << val compare_lengths : 'a list -> 'b list -> int >> Compare the lengths of two lists. compare_lengths l1 l2 is equivalent to compare (length l1) (length l2), except that the computation stops after reaching the end of the shortest list. Since: 4.05 << val compare_length_with : 'a list -> len:int -> int >> Compare the length of a list to an integer. compare_length_with l len is equivalent to compare (length l) len, except that the computation stops after at most len iterations on the list. Since: 4.05 << val is_empty : 'a list -> bool >> is_empty l is true if and only if l has no elements. It is equivalent to compare_length_with l 0 = 0. Since: 5.1 << val cons : 'a -> 'a list -> 'a list >> cons x xs is x :: xs Since: 4.05 << val hd : 'a list -> 'a >> Return the first element of the given list. Raises Failure if the list is empty. << val tl : 'a list -> 'a list >> Return the given list without its first element. Raises Failure if the list is empty. << val nth : 'a list -> int -> 'a >> Return the n-th element of the given list. The first element (head of the list) is at position 0. Raises - Failure if the list is too short. - Invalid_argument if n is negative. << val nth_opt : 'a list -> int -> 'a option >> Return the n-th element of the given list. The first element (head of the list) is at position 0. Return None if the list is too short. Since: 4.05 Raises Invalid_argument if n is negative. << val rev : 'a list -> 'a list >> List reversal. << val init : len:int -> f:(int -> 'a) -> 'a list >> init ~len ~f is [f 0; f 1; ...; f (len-1)], evaluated left to right. Since: 4.06 Raises Invalid_argument if len < 0. << val append : 'a list -> 'a list -> 'a list >> append l0 l1 appends l1 to l0. Same function as the infix operator @. Since: 5.1 this function is tail-recursive. << val rev_append : 'a list -> 'a list -> 'a list >> rev_append l1 l2 reverses l1 and concatenates it with l2. This is equivalent to (ListLabels.rev[29.33] l1) @ l2. << val concat : 'a list list -> 'a list >> Concatenate a list of lists. The elements of the argument are all concatenated together (in the same order) to give the result. Not tail-recursive (length of the argument + length of the longest sub-list). << val flatten : 'a list list -> 'a list >> Same as ListLabels.concat[29.33]. Not tail-recursive (length of the argument + length of the longest sub-list). Comparison ========== << val equal : eq:('a -> 'a -> bool) -> 'a list -> 'a list -> bool >> equal eq [a1; ...; an] [b1; ..; bm] holds when the two input lists have the same length, and for each pair of elements ai, bi at the same position we have eq ai bi. Note: the eq function may be called even if the lists have different length. If you know your equality function is costly, you may want to check ListLabels.compare_lengths[29.33] first. Since: 4.12 << val compare : cmp:('a -> 'a -> int) -> 'a list -> 'a list -> int >> compare cmp [a1; ...; an] [b1; ...; bm] performs a lexicographic comparison of the two input lists, using the same 'a -> 'a -> int interface as compare[28.2]: - a1 :: l1 is smaller than a2 :: l2 (negative result) if a1 is smaller than a2, or if they are equal (0 result) and l1 is smaller than l2 - the empty list [] is strictly smaller than non-empty lists Note: the cmp function will be called even if the lists have different lengths. Since: 4.12 Iterators ========= << val iter : f:('a -> unit) -> 'a list -> unit >> iter ~f [a1; ...; an] applies function f in turn to [a1; ...; an]. It is equivalent to f a1; f a2; ...; f an. << val iteri : f:(int -> 'a -> unit) -> 'a list -> unit >> Same as ListLabels.iter[29.33], but the function is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 4.00 << val map : f:('a -> 'b) -> 'a list -> 'b list >> map ~f [a1; ...; an] applies function f to a1, ..., an, and builds the list [f a1; ...; f an] with the results returned by f. << val mapi : f:(int -> 'a -> 'b) -> 'a list -> 'b list >> Same as ListLabels.map[29.33], but the function is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 4.00 << val rev_map : f:('a -> 'b) -> 'a list -> 'b list >> rev_map ~f l gives the same result as ListLabels.rev[29.33] (ListLabels.map[29.33] f l), but is more efficient. << val filter_map : f:('a -> 'b option) -> 'a list -> 'b list >> filter_map ~f l applies f to every element of l, filters out the None elements and returns the list of the arguments of the Some elements. Since: 4.08 << val concat_map : f:('a -> 'b list) -> 'a list -> 'b list >> concat_map ~f l gives the same result as ListLabels.concat[29.33] (ListLabels.map[29.33] f l). Tail-recursive. Since: 4.10 << val fold_left_map : f:('acc -> 'a -> 'acc * 'b) -> init:'acc -> 'a list -> 'acc * 'b list >> fold_left_map is a combination of fold_left and map that threads an accumulator through calls to f. Since: 4.11 << val fold_left : f:('acc -> 'a -> 'acc) -> init:'acc -> 'a list -> 'acc >> fold_left ~f ~init [b1; ...; bn] is f (... (f (f init b1) b2) ...) bn. << val fold_right : f:('a -> 'acc -> 'acc) -> 'a list -> init:'acc -> 'acc >> fold_right ~f [a1; ...; an] ~init is f a1 (f a2 (... (f an init) ...)). Not tail-recursive. Iterators on two lists ====================== << val iter2 : f:('a -> 'b -> unit) -> 'a list -> 'b list -> unit >> iter2 ~f [a1; ...; an] [b1; ...; bn] calls in turn f a1 b1; ...; f an bn. Raises Invalid_argument if the two lists are determined to have different lengths. << val map2 : f:('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list >> map2 ~f [a1; ...; an] [b1; ...; bn] is [f a1 b1; ...; f an bn]. Raises Invalid_argument if the two lists are determined to have different lengths. << val rev_map2 : f:('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list >> rev_map2 ~f l1 l2 gives the same result as ListLabels.rev[29.33] (ListLabels.map2[29.33] f l1 l2), but is more efficient. << val fold_left2 : f:('acc -> 'a -> 'b -> 'acc) -> init:'acc -> 'a list -> 'b list -> 'acc >> fold_left2 ~f ~init [a1; ...; an] [b1; ...; bn] is f (... (f (f init a1 b1) a2 b2) ...) an bn. Raises Invalid_argument if the two lists are determined to have different lengths. << val fold_right2 : f:('a -> 'b -> 'acc -> 'acc) -> 'a list -> 'b list -> init:'acc -> 'acc >> fold_right2 ~f [a1; ...; an] [b1; ...; bn] ~init is f a1 b1 (f a2 b2 (... (f an bn init) ...)). Raises Invalid_argument if the two lists are determined to have different lengths. Not tail-recursive. List scanning ============= << val for_all : f:('a -> bool) -> 'a list -> bool >> for_all ~f [a1; ...; an] checks if all elements of the list satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an) for a non-empty list and true if the list is empty. << val exists : f:('a -> bool) -> 'a list -> bool >> exists ~f [a1; ...; an] checks if at least one element of the list satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an) for a non-empty list and false if the list is empty. << val for_all2 : f:('a -> 'b -> bool) -> 'a list -> 'b list -> bool >> Same as ListLabels.for_all[29.33], but for a two-argument predicate. Raises Invalid_argument if the two lists are determined to have different lengths. << val exists2 : f:('a -> 'b -> bool) -> 'a list -> 'b list -> bool >> Same as ListLabels.exists[29.33], but for a two-argument predicate. Raises Invalid_argument if the two lists are determined to have different lengths. << val mem : 'a -> set:'a list -> bool >> mem a ~set is true if and only if a is equal to an element of set. << val memq : 'a -> set:'a list -> bool >> Same as ListLabels.mem[29.33], but uses physical equality instead of structural equality to compare list elements. List searching ============== << val find : f:('a -> bool) -> 'a list -> 'a >> find ~f l returns the first element of the list l that satisfies the predicate f. Raises Not_found if there is no value that satisfies f in the list l. << val find_opt : f:('a -> bool) -> 'a list -> 'a option >> find ~f l returns the first element of the list l that satisfies the predicate f. Returns None if there is no value that satisfies f in the list l. Since: 4.05 << val find_index : f:('a -> bool) -> 'a list -> int option >> find_index ~f xs returns Some i, where i is the index of the first element of the list xs that satisfies f x, if there is such an element. It returns None if there is no such element. Since: 5.1 << val find_map : f:('a -> 'b option) -> 'a list -> 'b option >> find_map ~f l applies f to the elements of l in order, and returns the first result of the form Some v, or None if none exist. Since: 4.10 << val find_mapi : f:(int -> 'a -> 'b option) -> 'a list -> 'b option >> Same as find_map, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 5.1 << val filter : f:('a -> bool) -> 'a list -> 'a list >> filter ~f l returns all the elements of the list l that satisfy the predicate f. The order of the elements in the input list is preserved. << val find_all : f:('a -> bool) -> 'a list -> 'a list >> find_all is another name for ListLabels.filter[29.33]. << val filteri : f:(int -> 'a -> bool) -> 'a list -> 'a list >> Same as ListLabels.filter[29.33], but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. Since: 4.11 << val partition : f:('a -> bool) -> 'a list -> 'a list * 'a list >> partition ~f l returns a pair of lists (l1, l2), where l1 is the list of all the elements of l that satisfy the predicate f, and l2 is the list of all the elements of l that do not satisfy f. The order of the elements in the input list is preserved. << val partition_map : f:('a -> ('b, 'c) Either.t) -> 'a list -> 'b list * 'c list >> partition_map f l returns a pair of lists (l1, l2) such that, for each element x of the input list l: - if f x is Left y1, then y1 is in l1, and - if f x is Right y2, then y2 is in l2. The output elements are included in l1 and l2 in the same relative order as the corresponding input elements in l. In particular, partition_map (fun x -> if f x then Left x else Right x) l is equivalent to partition f l. Since: 4.12 Association lists ================= << val assoc : 'a -> ('a * 'b) list -> 'b >> assoc a l returns the value associated with key a in the list of pairs l. That is, assoc a [ ...; (a,b); ...] = b if (a,b) is the leftmost binding of a in list l. Raises Not_found if there is no value associated with a in the list l. << val assoc_opt : 'a -> ('a * 'b) list -> 'b option >> assoc_opt a l returns the value associated with key a in the list of pairs l. That is, assoc_opt a [ ...; (a,b); ...] = Some b if (a,b) is the leftmost binding of a in list l. Returns None if there is no value associated with a in the list l. Since: 4.05 << val assq : 'a -> ('a * 'b) list -> 'b >> Same as ListLabels.assoc[29.33], but uses physical equality instead of structural equality to compare keys. << val assq_opt : 'a -> ('a * 'b) list -> 'b option >> Same as ListLabels.assoc_opt[29.33], but uses physical equality instead of structural equality to compare keys. Since: 4.05 << val mem_assoc : 'a -> map:('a * 'b) list -> bool >> Same as ListLabels.assoc[29.33], but simply return true if a binding exists, and false if no bindings exist for the given key. << val mem_assq : 'a -> map:('a * 'b) list -> bool >> Same as ListLabels.mem_assoc[29.33], but uses physical equality instead of structural equality to compare keys. << val remove_assoc : 'a -> ('a * 'b) list -> ('a * 'b) list >> remove_assoc a l returns the list of pairs l without the first pair with key a, if any. Not tail-recursive. << val remove_assq : 'a -> ('a * 'b) list -> ('a * 'b) list >> Same as ListLabels.remove_assoc[29.33], but uses physical equality instead of structural equality to compare keys. Not tail-recursive. Lists of pairs ============== << val split : ('a * 'b) list -> 'a list * 'b list >> Transform a list of pairs into a pair of lists: split [(a1,b1); ...; (an,bn)] is ([a1; ...; an], [b1; ...; bn]). Not tail-recursive. << val combine : 'a list -> 'b list -> ('a * 'b) list >> Transform a pair of lists into a list of pairs: combine [a1; ...; an] [b1; ...; bn] is [(a1,b1); ...; (an,bn)]. Raises Invalid_argument if the two lists have different lengths. Not tail-recursive. Sorting ======= << val sort : cmp:('a -> 'a -> int) -> 'a list -> 'a list >> Sort a list in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see Array.sort for a complete specification). For example, compare[28.2] is a suitable comparison function. The resulting list is sorted in increasing order. ListLabels.sort[29.33] is guaranteed to run in constant heap space (in addition to the size of the result list) and logarithmic stack space. The current implementation uses Merge Sort. It runs in constant heap space and logarithmic stack space. << val stable_sort : cmp:('a -> 'a -> int) -> 'a list -> 'a list >> Same as ListLabels.sort[29.33], but the sorting algorithm is guaranteed to be stable (i.e. elements that compare equal are kept in their original order). The current implementation uses Merge Sort. It runs in constant heap space and logarithmic stack space. << val fast_sort : cmp:('a -> 'a -> int) -> 'a list -> 'a list >> Same as ListLabels.sort[29.33] or ListLabels.stable_sort[29.33], whichever is faster on typical input. << val sort_uniq : cmp:('a -> 'a -> int) -> 'a list -> 'a list >> Same as ListLabels.sort[29.33], but also remove duplicates. Since: 4.03 << val merge : cmp:('a -> 'a -> int) -> 'a list -> 'a list -> 'a list >> Merge two lists: Assuming that l1 and l2 are sorted according to the comparison function cmp, merge ~cmp l1 l2 will return a sorted list containing all the elements of l1 and l2. If several elements compare equal, the elements of l1 will be before the elements of l2. Not tail-recursive (sum of the lengths of the arguments). Lists and Sequences =================== << val to_seq : 'a list -> 'a Seq.t >> Iterate on the list. Since: 4.07 << val of_seq : 'a Seq.t -> 'a list >> Create a list from a sequence. Since: 4.07 29.34 Module Map : Association tables over ordered types. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module implements applicative association tables, also known as finite maps or dictionaries, given a total ordering function over the keys. All operations over maps are purely applicative (no side-effects). The implementation uses balanced binary trees, and therefore searching and insertion take time logarithmic in the size of the map. For instance: << module IntPairs = struct type t = int * int let compare (x0,y0) (x1,y1) = match Stdlib.compare x0 x1 with 0 -> Stdlib.compare y0 y1 | c -> c end module PairsMap = Map.Make(IntPairs) let m = PairsMap.(empty |> add (0,1) "hello" |> add (1,0) "world") >> This creates a new module PairsMap, with a new type 'a PairsMap.t of maps from int * int to 'a. In this example, m contains string values so its type is string PairsMap.t. << module type OrderedType = >>  sig << type t >> The type of the map keys. << val compare : t -> t -> int >> A total ordering function over the keys. This is a two-argument function f such that f e1 e2 is zero if the keys e1 and e2 are equal, f e1 e2 is strictly negative if e1 is smaller than e2, and f e1 e2 is strictly positive if e1 is greater than e2. Example: a suitable ordering function is the generic structural comparison function compare[28.2].  end Input signature of the functor Map.Make[29.34]. << module type S = >>  sig Maps ==== << type key >> The type of the map keys. << type !+'a t >> The type of maps from type key to type 'a. << val empty : 'a t >> The empty map. << val add : key -> 'a -> 'a t -> 'a t >> add key data m returns a map containing the same bindings as m, plus a binding of key to data. If key was already bound in m to a value that is physically equal to data, m is returned unchanged (the result of the function is then physically equal to m). Otherwise, the previous binding of key in m disappears. Before 4.03 Physical equality was not ensured. << val add_to_list : key -> 'a -> 'a list t -> 'a list t >> add_to_list key data m is m with key mapped to l such that l is data :: Map.find key m if key was bound in m and [v] otherwise. Since: 5.1 << val update : key -> ('a option -> 'a option) -> 'a t -> 'a t >> update key f m returns a map containing the same bindings as m, except for the binding of key. Depending on the value of y where y is f (find_opt key m), the binding of key is added, removed or updated. If y is None, the binding is removed if it exists; otherwise, if y is Some z then key is associated to z in the resulting map. If key was already bound in m to a value that is physically equal to z, m is returned unchanged (the result of the function is then physically equal to m). Since: 4.06 << val singleton : key -> 'a -> 'a t >> singleton x y returns the one-element map that contains a binding y for x. Since: 3.12 << val remove : key -> 'a t -> 'a t >> remove x m returns a map containing the same bindings as m, except for x which is unbound in the returned map. If x was not in m, m is returned unchanged (the result of the function is then physically equal to m). Before 4.03 Physical equality was not ensured. << val merge : (key -> 'a option -> 'b option -> 'c option) -> 'a t -> 'b t -> 'c t >> merge f m1 m2 computes a map whose keys are a subset of the keys of m1 and of m2. The presence of each such binding, and the corresponding value, is determined with the function f. In terms of the find_opt operation, we have find_opt x (merge f m1 m2) = f x (find_opt x m1) (find_opt x m2) for any key x, provided that f x None None = None. Since: 3.12 << val union : (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t >> union f m1 m2 computes a map whose keys are a subset of the keys of m1 and of m2. When the same binding is defined in both arguments, the function f is used to combine them. This is a special case of merge: union f m1 m2 is equivalent to merge f' m1 m2, where - f' _key None None = None - f' _key (Some v) None = Some v - f' _key None (Some v) = Some v - f' key (Some v1) (Some v2) = f key v1 v2 Since: 4.03 << val cardinal : 'a t -> int >> Return the number of bindings of a map. Since: 3.12 Bindings ======== << val bindings : 'a t -> (key * 'a) list >> Return the list of all bindings of the given map. The returned list is sorted in increasing order of keys with respect to the ordering Ord.compare, where Ord is the argument given to Map.Make[29.34]. Since: 3.12 << val min_binding : 'a t -> key * 'a >> Return the binding with the smallest key in a given map (with respect to the Ord.compare ordering), or raise Not_found if the map is empty. Since: 3.12 << val min_binding_opt : 'a t -> (key * 'a) option >> Return the binding with the smallest key in the given map (with respect to the Ord.compare ordering), or None if the map is empty. Since: 4.05 << val max_binding : 'a t -> key * 'a >> Same as Map.S.min_binding[29.34], but returns the binding with the largest key in the given map. Since: 3.12 << val max_binding_opt : 'a t -> (key * 'a) option >> Same as Map.S.min_binding_opt[29.34], but returns the binding with the largest key in the given map. Since: 4.05 << val choose : 'a t -> key * 'a >> Return one binding of the given map, or raise Not_found if the map is empty. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps. Since: 3.12 << val choose_opt : 'a t -> (key * 'a) option >> Return one binding of the given map, or None if the map is empty. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps. Since: 4.05 Searching ========= << val find : key -> 'a t -> 'a >> find x m returns the current value of x in m, or raises Not_found if no binding for x exists. << val find_opt : key -> 'a t -> 'a option >> find_opt x m returns Some v if the current value of x in m is v, or None if no binding for x exists. Since: 4.05 << val find_first : (key -> bool) -> 'a t -> key * 'a >> find_first f m, where f is a monotonically increasing function, returns the binding of m with the lowest key k such that f k, or raises Not_found if no such key exists. For example, find_first (fun k -> Ord.compare k x >= 0) m will return the first binding k, v of m where Ord.compare k x >= 0 (intuitively: k >= x), or raise Not_found if x is greater than any element of m. Since: 4.05 << val find_first_opt : (key -> bool) -> 'a t -> (key * 'a) option >> find_first_opt f m, where f is a monotonically increasing function, returns an option containing the binding of m with the lowest key k such that f k, or None if no such key exists. Since: 4.05 << val find_last : (key -> bool) -> 'a t -> key * 'a >> find_last f m, where f is a monotonically decreasing function, returns the binding of m with the highest key k such that f k, or raises Not_found if no such key exists. Since: 4.05 << val find_last_opt : (key -> bool) -> 'a t -> (key * 'a) option >> find_last_opt f m, where f is a monotonically decreasing function, returns an option containing the binding of m with the highest key k such that f k, or None if no such key exists. Since: 4.05 Traversing ========== << val iter : (key -> 'a -> unit) -> 'a t -> unit >> iter f m applies f to all bindings in map m. f receives the key as first argument, and the associated value as second argument. The bindings are passed to f in increasing order with respect to the ordering over the type of the keys. << val fold : (key -> 'a -> 'acc -> 'acc) -> 'a t -> 'acc -> 'acc >> fold f m init computes (f kN dN ... (f k1 d1 init)...), where k1 ... kN are the keys of all bindings in m (in increasing order), and d1 ... dN are the associated data. Transforming ============ << val map : ('a -> 'b) -> 'a t -> 'b t >> map f m returns a map with same domain as m, where the associated value a of all bindings of m has been replaced by the result of the application of f to a. The bindings are passed to f in increasing order with respect to the ordering over the type of the keys. << val mapi : (key -> 'a -> 'b) -> 'a t -> 'b t >> Same as Map.S.map[29.34], but the function receives as arguments both the key and the associated value for each binding of the map. << val filter : (key -> 'a -> bool) -> 'a t -> 'a t >> filter f m returns the map with all the bindings in m that satisfy predicate p. If every binding in m satisfies f, m is returned unchanged (the result of the function is then physically equal to m) Before 4.03 Physical equality was not ensured. Since: 3.12 << val filter_map : (key -> 'a -> 'b option) -> 'a t -> 'b t >> filter_map f m applies the function f to every binding of m, and builds a map from the results. For each binding (k, v) in the input map: - if f k v is None then k is not in the result, - if f k v is Some v' then the binding (k, v') is in the output map. For example, the following function on maps whose values are lists << filter_map (fun _k li -> match li with [] -> None | _::tl -> Some tl) m >> drops all bindings of m whose value is an empty list, and pops the first element of each value that is non-empty. Since: 4.11 << val partition : (key -> 'a -> bool) -> 'a t -> 'a t * 'a t >> partition f m returns a pair of maps (m1, m2), where m1 contains all the bindings of m that satisfy the predicate f, and m2 is the map with all the bindings of m that do not satisfy f. Since: 3.12 << val split : key -> 'a t -> 'a t * 'a option * 'a t >> split x m returns a triple (l, data, r), where l is the map with all the bindings of m whose key is strictly less than x; r is the map with all the bindings of m whose key is strictly greater than x; data is None if m contains no binding for x, or Some v if m binds v to x. Since: 3.12 Predicates and comparisons ========================== << val is_empty : 'a t -> bool >> Test whether a map is empty or not. << val mem : key -> 'a t -> bool >> mem x m returns true if m contains a binding for x, and false otherwise. << val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool >> equal cmp m1 m2 tests whether the maps m1 and m2 are equal, that is, contain equal keys and associate them with equal data. cmp is the equality predicate used to compare the data associated with the keys. << val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int >> Total ordering between maps. The first argument is a total ordering used to compare data associated with equal keys in the two maps. << val for_all : (key -> 'a -> bool) -> 'a t -> bool >> for_all f m checks if all the bindings of the map satisfy the predicate f. Since: 3.12 << val exists : (key -> 'a -> bool) -> 'a t -> bool >> exists f m checks if at least one binding of the map satisfies the predicate f. Since: 3.12 Converting ========== << val to_list : 'a t -> (key * 'a) list >> to_list m is Map.S.bindings[29.34] m. Since: 5.1 << val of_list : (key * 'a) list -> 'a t >> of_list bs adds the bindings of bs to the empty map, in list order (if a key is bound twice in bs the last one takes over). Since: 5.1 << val to_seq : 'a t -> (key * 'a) Seq.t >> Iterate on the whole map, in ascending order of keys Since: 4.07 << val to_rev_seq : 'a t -> (key * 'a) Seq.t >> Iterate on the whole map, in descending order of keys Since: 4.12 << val to_seq_from : key -> 'a t -> (key * 'a) Seq.t >> to_seq_from k m iterates on a subset of the bindings of m, in ascending order of keys, from key k or above. Since: 4.07 << val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t >> Add the given bindings to the map, in order. Since: 4.07 << val of_seq : (key * 'a) Seq.t -> 'a t >> Build a map from the given bindings Since: 4.07  end Output signature of the functor Map.Make[29.34]. << module Make : >> functor (Ord : OrderedType) -> S with type key = Ord.t Functor building an implementation of the map structure given a totally ordered type. 29.35 Module Marshal : Marshaling of data structures. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module provides functions to encode arbitrary data structures as sequences of bytes, which can then be written on a file or sent over a pipe or network connection. The bytes can then be read back later, possibly in another process, and decoded back into a data structure. The format for the byte sequences is compatible across all machines for a given version of OCaml. Warning: marshaling is currently not type-safe. The type of marshaled data is not transmitted along the value of the data, making it impossible to check that the data read back possesses the type expected by the context. In particular, the result type of the Marshal.from_* functions is given as 'a, but this is misleading: the returned OCaml value does not possess type 'a for all 'a; it has one, unique type which cannot be determined at compile-time. The programmer should explicitly give the expected type of the returned value, using the following syntax: - (Marshal.from_channel chan : type). Anything can happen at run-time if the object in the file does not belong to the given type. Values of extensible variant types, for example exceptions (of extensible type exn), returned by the unmarshaller should not be pattern-matched over through match ... with or try ... with, because unmarshalling does not preserve the information required for matching their constructors. Structural equalities with other extensible variant values does not work either. Most other uses such as Printexc.to_string, will still work as expected. The representation of marshaled values is not human-readable, and uses bytes that are not printable characters. Therefore, input and output channels used in conjunction with Marshal.to_channel and Marshal.from_channel must be opened in binary mode, using e.g. open_out_bin or open_in_bin; channels opened in text mode will cause unmarshaling errors on platforms where text channels behave differently than binary channels, e.g. Windows. << type extern_flags = | No_sharing >> Don’t preserve sharing << | Closures >> Send function closures << | Compat_32 >> Ensure 32-bit compatibility The flags to the Marshal.to_* functions below. << val to_channel : out_channel -> 'a -> extern_flags list -> unit >> Marshal.to_channel chan v flags writes the representation of v on channel chan. The flags argument is a possibly empty list of flags that governs the marshaling behavior with respect to sharing, functional values, and compatibility between 32- and 64-bit platforms. If flags does not contain Marshal.No_sharing, circularities and sharing inside the value v are detected and preserved in the sequence of bytes produced. In particular, this guarantees that marshaling always terminates. Sharing between values marshaled by successive calls to Marshal.to_channel is neither detected nor preserved, though. If flags contains Marshal.No_sharing, sharing is ignored. This results in faster marshaling if v contains no shared substructures, but may cause slower marshaling and larger byte representations if v actually contains sharing, or even non-termination if v contains cycles. If flags does not contain Marshal.Closures, marshaling fails when it encounters a functional value inside v: only ’pure’ data structures, containing neither functions nor objects, can safely be transmitted between different programs. If flags contains Marshal.Closures, functional values will be marshaled as a the position in the code of the program together with the values corresponding to the free variables captured in the closure. In this case, the output of marshaling can only be read back in processes that run exactly the same program, with exactly the same compiled code. (This is checked at un-marshaling time, using an MD5 digest of the code transmitted along with the code position.) The exact definition of which free variables are captured in a closure is not specified and can vary between bytecode and native code (and according to optimization flags). In particular, a function value accessing a global reference may or may not include the reference in its closure. If it does, unmarshaling the corresponding closure will create a new reference, different from the global one. If flags contains Marshal.Compat_32, marshaling fails when it encounters an integer value outside the range -2^30, 2^30-1 of integers that are representable on a 32-bit platform. This ensures that marshaled data generated on a 64-bit platform can be safely read back on a 32-bit platform. If flags does not contain Marshal.Compat_32, integer values outside the range -2^30, 2^30-1 are marshaled, and can be read back on a 64-bit platform, but will cause an error at un-marshaling time when read back on a 32-bit platform. The Mashal.Compat_32 flag only matters when marshaling is performed on a 64-bit platform; it has no effect if marshaling is performed on a 32-bit platform. Raises Failure if chan is not in binary mode. << val to_bytes : 'a -> extern_flags list -> bytes >> Marshal.to_bytes v flags returns a byte sequence containing the representation of v. The flags argument has the same meaning as for Marshal.to_channel[29.35]. Since: 4.02 << val to_string : 'a -> extern_flags list -> string >> Same as to_bytes but return the result as a string instead of a byte sequence. << val to_buffer : bytes -> int -> int -> 'a -> extern_flags list -> int >> Marshal.to_buffer buff ofs len v flags marshals the value v, storing its byte representation in the sequence buff, starting at index ofs, and writing at most len bytes. It returns the number of bytes actually written to the sequence. If the byte representation of v does not fit in len characters, the exception Failure is raised. << val from_channel : in_channel -> 'a >> Marshal.from_channel chan reads from channel chan the byte representation of a structured value, as produced by one of the Marshal.to_* functions, and reconstructs and returns the corresponding value. Raises - End_of_file if chan is already at the end of the file. - Failure if the end of the file is reached during unmarshalling itself or if chan is not in binary mode. << val from_bytes : bytes -> int -> 'a >> Marshal.from_bytes buff ofs unmarshals a structured value like Marshal.from_channel[29.35] does, except that the byte representation is not read from a channel, but taken from the byte sequence buff, starting at position ofs. The byte sequence is not mutated. Since: 4.02 << val from_string : string -> int -> 'a >> Same as from_bytes but take a string as argument instead of a byte sequence. << val header_size : int >> The bytes representing a marshaled value are composed of a fixed-size header and a variable-sized data part, whose size can be determined from the header. Marshal.header_size[29.35] is the size, in bytes, of the header. Marshal.data_size[29.35] buff ofs is the size, in bytes, of the data part, assuming a valid header is stored in buff starting at position ofs. Finally, Marshal.total_size[29.35] buff ofs is the total size, in bytes, of the marshaled value. Both Marshal.data_size[29.35] and Marshal.total_size[29.35] raise Failure if buff, ofs does not contain a valid header. To read the byte representation of a marshaled value into a byte sequence, the program needs to read first Marshal.header_size[29.35] bytes into the sequence, then determine the length of the remainder of the representation using Marshal.data_size[29.35], make sure the sequence is large enough to hold the remaining data, then read it, and finally call Marshal.from_bytes[29.35] to unmarshal the value. << val data_size : bytes -> int -> int >> See Marshal.header_size[29.35]. << val total_size : bytes -> int -> int >> See Marshal.header_size[29.35]. Marshal and domain safety ========================= Care must be taken when marshaling a mutable value that may be modified by a different domain. Mutating a value that is being marshaled (i.e., turned into a sequence of bytes) is a programming error and might result in suprising values (when unmarshaling) due to tearing, since marshaling involves byte-per-byte copy. 29.36 Module MoreLabels : Extra labeled libraries. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This meta-module provides labelized versions of the MoreLabels.Hashtbl[29.36], MoreLabels.Map[29.36] and MoreLabels.Set[29.36] modules. This module is intended to be used through open MoreLabels which replaces MoreLabels.Hashtbl[29.36], MoreLabels.Map[29.36], and MoreLabels.Set[29.36] with their labeled counterparts. For example: << open MoreLabels Hashtbl.iter ~f:(fun ~key ~data -> g key data) table >> << module Hashtbl : >>  sig Hash tables and hash functions. Hash tables are hashed association tables, with in-place modification. Because most operations on a hash table modify their input, they’re more commonly used in imperative code. The lookup of the value associated with a key (see MoreLabels.Hashtbl.find[29.36], MoreLabels.Hashtbl.find_opt[29.36]) is normally very fast, often faster than the equivalent lookup in MoreLabels.Map[29.36]. The functors MoreLabels.Hashtbl.Make[29.36] and MoreLabels.Hashtbl.MakeSeeded[29.36] can be used when performance or flexibility are key. The user provides custom equality and hash functions for the key type, and obtains a custom hash table type for this particular type of key. Warning a hash table is only as good as the hash function. A bad hash function will turn the table into a degenerate association list, with linear time lookup instead of constant time lookup. The polymorphic MoreLabels.Hashtbl.t[29.36] hash table is useful in simpler cases or in interactive environments. It uses the polymorphic MoreLabels.Hashtbl.hash[29.36] function defined in the OCaml runtime (at the time of writing, it’s SipHash), as well as the polymorphic equality (=). See the examples section[29.4]. Unsynchronized accesses Unsynchronized accesses to a hash table may lead to an invalid hash table state. Thus, concurrent accesses to a hash tables must be synchronized (for instance with a Mutex.t[29.37]). Generic interface ================= << type ('a, 'b) t = ('a, 'b) Hashtbl.t >> The type of hash tables from type 'a to type 'b. << val create : ?random:bool -> int -> ('a, 'b) t >> Hashtbl.create n creates a new, empty hash table, with initial size n. For best results, n should be on the order of the expected number of elements that will be in the table. The table grows as needed, so n is just an initial guess. The optional ~random parameter (a boolean) controls whether the internal organization of the hash table is randomized at each execution of Hashtbl.create or deterministic over all executions. A hash table that is created with ~random set to false uses a fixed hash function (MoreLabels.Hashtbl.hash[29.36]) to distribute keys among buckets. As a consequence, collisions between keys happen deterministically. In Web-facing applications or other security-sensitive applications, the deterministic collision patterns can be exploited by a malicious user to create a denial-of-service attack: the attacker sends input crafted to create many collisions in the table, slowing the application down. A hash table that is created with ~random set to true uses the seeded hash function MoreLabels.Hashtbl.seeded_hash[29.36] with a seed that is randomly chosen at hash table creation time. In effect, the hash function used is randomly selected among 2^{30} different hash functions. All these hash functions have different collision patterns, rendering ineffective the denial-of-service attack described above. However, because of randomization, enumerating all elements of the hash table using MoreLabels.Hashtbl.fold[29.36] or MoreLabels.Hashtbl.iter[29.36] is no longer deterministic: elements are enumerated in different orders at different runs of the program. If no ~random parameter is given, hash tables are created in non-random mode by default. This default can be changed either programmatically by calling MoreLabels.Hashtbl.randomize[29.36] or by setting the R flag in the OCAMLRUNPARAM environment variable. Before 4.00 the ~random parameter was not present and all hash tables were created in non-randomized mode. << val clear : ('a, 'b) t -> unit >> Empty a hash table. Use reset instead of clear to shrink the size of the bucket table to its initial size. << val reset : ('a, 'b) t -> unit >> Empty a hash table and shrink the size of the bucket table to its initial size. Since: 4.00 << val copy : ('a, 'b) t -> ('a, 'b) t >> Return a copy of the given hashtable. << val add : ('a, 'b) t -> key:'a -> data:'b -> unit >> Hashtbl.add tbl ~key ~data adds a binding of key to data in table tbl. Warning: Previous bindings for key are not removed, but simply hidden. That is, after performing MoreLabels.Hashtbl.remove[29.36] tbl key, the previous binding for key, if any, is restored. (Same behavior as with association lists.) If you desire the classic behavior of replacing elements, see MoreLabels.Hashtbl.replace[29.36]. << val find : ('a, 'b) t -> 'a -> 'b >> Hashtbl.find tbl x returns the current binding of x in tbl, or raises Not_found if no such binding exists. << val find_opt : ('a, 'b) t -> 'a -> 'b option >> Hashtbl.find_opt tbl x returns the current binding of x in tbl, or None if no such binding exists. Since: 4.05 << val find_all : ('a, 'b) t -> 'a -> 'b list >> Hashtbl.find_all tbl x returns the list of all data associated with x in tbl. The current binding is returned first, then the previous bindings, in reverse order of introduction in the table. << val mem : ('a, 'b) t -> 'a -> bool >> Hashtbl.mem tbl x checks if x is bound in tbl. << val remove : ('a, 'b) t -> 'a -> unit >> Hashtbl.remove tbl x removes the current binding of x in tbl, restoring the previous binding if it exists. It does nothing if x is not bound in tbl. << val replace : ('a, 'b) t -> key:'a -> data:'b -> unit >> Hashtbl.replace tbl ~key ~data replaces the current binding of key in tbl by a binding of key to data. If key is unbound in tbl, a binding of key to data is added to tbl. This is functionally equivalent to MoreLabels.Hashtbl.remove[29.36] tbl key followed by MoreLabels.Hashtbl.add[29.36] tbl key data. << val iter : f:(key:'a -> data:'b -> unit) -> ('a, 'b) t -> unit >> Hashtbl.iter ~f tbl applies f to all bindings in table tbl. f receives the key as first argument, and the associated value as second argument. Each binding is presented exactly once to f. The order in which the bindings are passed to f is unspecified. However, if the table contains several bindings for the same key, they are passed to f in reverse order of introduction, that is, the most recent binding is passed first. If the hash table was created in non-randomized mode, the order in which the bindings are enumerated is reproducible between successive runs of the program, and even between minor versions of OCaml. For randomized hash tables, the order of enumeration is entirely random. The behavior is not specified if the hash table is modified by f during the iteration. << val filter_map_inplace : f:(key:'a -> data:'b -> 'b option) -> ('a, 'b) t -> unit >> Hashtbl.filter_map_inplace ~f tbl applies f to all bindings in table tbl and update each binding depending on the result of f. If f returns None, the binding is discarded. If it returns Some new_val, the binding is update to associate the key to new_val. Other comments for MoreLabels.Hashtbl.iter[29.36] apply as well. Since: 4.03 << val fold : f:(key:'a -> data:'b -> 'acc -> 'acc) -> ('a, 'b) t -> init:'acc -> 'acc >> Hashtbl.fold ~f tbl ~init computes (f kN dN ... (f k1 d1 init)...), where k1 ... kN are the keys of all bindings in tbl, and d1 ... dN are the associated values. Each binding is presented exactly once to f. The order in which the bindings are passed to f is unspecified. However, if the table contains several bindings for the same key, they are passed to f in reverse order of introduction, that is, the most recent binding is passed first. If the hash table was created in non-randomized mode, the order in which the bindings are enumerated is reproducible between successive runs of the program, and even between minor versions of OCaml. For randomized hash tables, the order of enumeration is entirely random. The behavior is not specified if the hash table is modified by f during the iteration. << val length : ('a, 'b) t -> int >> Hashtbl.length tbl returns the number of bindings in tbl. It takes constant time. Multiple bindings are counted once each, so Hashtbl.length gives the number of times Hashtbl.iter calls its first argument. << val randomize : unit -> unit >> After a call to Hashtbl.randomize(), hash tables are created in randomized mode by default: MoreLabels.Hashtbl.create[29.36] returns randomized hash tables, unless the ~random:false optional parameter is given. The same effect can be achieved by setting the R parameter in the OCAMLRUNPARAM environment variable. It is recommended that applications or Web frameworks that need to protect themselves against the denial-of-service attack described in MoreLabels.Hashtbl.create[29.36] call Hashtbl.randomize() at initialization time before any domains are created. Note that once Hashtbl.randomize() was called, there is no way to revert to the non-randomized default behavior of MoreLabels.Hashtbl.create[29.36]. This is intentional. Non-randomized hash tables can still be created using Hashtbl.create ~random:false. Since: 4.00 << val is_randomized : unit -> bool >> Return true if the tables are currently created in randomized mode by default, false otherwise. Since: 4.03 << val rebuild : ?random:bool -> ('a, 'b) t -> ('a, 'b) t >> Return a copy of the given hashtable. Unlike MoreLabels.Hashtbl.copy[29.36], MoreLabels.Hashtbl.rebuild[29.36] h re-hashes all the (key, value) entries of the original table h. The returned hash table is randomized if h was randomized, or the optional random parameter is true, or if the default is to create randomized hash tables; see MoreLabels.Hashtbl.create[29.36] for more information. MoreLabels.Hashtbl.rebuild[29.36] can safely be used to import a hash table built by an old version of the MoreLabels.Hashtbl[29.36] module, then marshaled to persistent storage. After unmarshaling, apply MoreLabels.Hashtbl.rebuild[29.36] to produce a hash table for the current version of the MoreLabels.Hashtbl[29.36] module. Since: 4.12 << type statistics = Hashtbl.statistics = { num_bindings : int ; >> Number of bindings present in the table. Same value as returned by MoreLabels.Hashtbl.length[29.36]. << num_buckets : int ; >> Number of buckets in the table. << max_bucket_length : int ; >> Maximal number of bindings per bucket. << bucket_histogram : int array ; >> Histogram of bucket sizes. This array histo has length max_bucket_length + 1. The value of histo.(i) is the number of buckets whose size is i. << } >> Since: 4.00 << val stats : ('a, 'b) t -> statistics >> Hashtbl.stats tbl returns statistics about the table tbl: number of buckets, size of the biggest bucket, distribution of buckets by size. Since: 4.00 Hash tables and Sequences ========================= << val to_seq : ('a, 'b) t -> ('a * 'b) Seq.t >> Iterate on the whole table. The order in which the bindings appear in the sequence is unspecified. However, if the table contains several bindings for the same key, they appear in reversed order of introduction, that is, the most recent binding appears first. The behavior is not specified if the hash table is modified during the iteration. Since: 4.07 << val to_seq_keys : ('a, 'b) t -> 'a Seq.t >> Same as Seq.map fst (to_seq m) Since: 4.07 << val to_seq_values : ('a, 'b) t -> 'b Seq.t >> Same as Seq.map snd (to_seq m) Since: 4.07 << val add_seq : ('a, 'b) t -> ('a * 'b) Seq.t -> unit >> Add the given bindings to the table, using MoreLabels.Hashtbl.add[29.36] Since: 4.07 << val replace_seq : ('a, 'b) t -> ('a * 'b) Seq.t -> unit >> Add the given bindings to the table, using MoreLabels.Hashtbl.replace[29.36] Since: 4.07 << val of_seq : ('a * 'b) Seq.t -> ('a, 'b) t >> Build a table from the given bindings. The bindings are added in the same order they appear in the sequence, using MoreLabels.Hashtbl.replace_seq[29.36], which means that if two pairs have the same key, only the latest one will appear in the table. Since: 4.07 Functorial interface ==================== The functorial interface allows the use of specific comparison and hash functions, either for performance/security concerns, or because keys are not hashable/comparable with the polymorphic builtins. For instance, one might want to specialize a table for integer keys: << module IntHash = struct type t = int let equal i j = i=j let hash i = i land max_int end module IntHashtbl = Hashtbl.Make(IntHash) let h = IntHashtbl.create 17 in IntHashtbl.add h 12 "hello" >> This creates a new module IntHashtbl, with a new type 'a IntHashtbl.t of tables from int to 'a. In this example, h contains string values so its type is string IntHashtbl.t. Note that the new type 'a IntHashtbl.t is not compatible with the type ('a,'b) Hashtbl.t of the generic interface. For example, Hashtbl.length h would not type-check, you must use IntHashtbl.length. << module type HashedType = >>  sig << type t >> The type of the hashtable keys. << val equal : t -> t -> bool >> The equality predicate used to compare keys. << val hash : t -> int >> A hashing function on keys. It must be such that if two keys are equal according to equal, then they have identical hash values as computed by hash. Examples: suitable (equal, hash) pairs for arbitrary key types include - ((=), MoreLabels.Hashtbl.HashedType.hash[29.36]) for comparing objects by structure (provided objects do not contain floats) - ((fun x y -> compare x y = 0), MoreLabels.Hashtbl.HashedType.hash[29.36]) for comparing objects by structure and handling nan[28.2] correctly - ((==), MoreLabels.Hashtbl.HashedType.hash[29.36]) for comparing objects by physical equality (e.g. for mutable or cyclic objects).  end The input signature of the functor MoreLabels.Hashtbl.Make[29.36]. << module type S = >>  sig << type key >> << type !'a t >> << val create : int -> 'a t >> << val clear : 'a t -> unit >> << val reset : 'a t -> unit >> Since: 4.00 << val copy : 'a t -> 'a t >> << val add : 'a t -> key:key -> data:'a -> unit >> << val remove : 'a t -> key -> unit >> << val find : 'a t -> key -> 'a >> << val find_opt : 'a t -> key -> 'a option >> Since: 4.05 << val find_all : 'a t -> key -> 'a list >> << val replace : 'a t -> key:key -> data:'a -> unit >> << val mem : 'a t -> key -> bool >> << val iter : f:(key:key -> data:'a -> unit) -> 'a t -> unit >> << val filter_map_inplace : f:(key:key -> data:'a -> 'a option) -> 'a t -> unit >> Since: 4.03 << val fold : f:(key:key -> data:'a -> 'acc -> 'acc) -> 'a t -> init:'acc -> 'acc >> << val length : 'a t -> int >> << val stats : 'a t -> MoreLabels.Hashtbl.statistics >> Since: 4.00 << val to_seq : 'a t -> (key * 'a) Seq.t >> Since: 4.07 << val to_seq_keys : 'a t -> key Seq.t >> Since: 4.07 << val to_seq_values : 'a t -> 'a Seq.t >> Since: 4.07 << val add_seq : 'a t -> (key * 'a) Seq.t -> unit >> Since: 4.07 << val replace_seq : 'a t -> (key * 'a) Seq.t -> unit >> Since: 4.07 << val of_seq : (key * 'a) Seq.t -> 'a t >> Since: 4.07  end The output signature of the functor MoreLabels.Hashtbl.Make[29.36]. << module Make : >> functor (H : HashedType) -> S with type key = H.t and type 'a t = 'a Hashtbl.Make(H).t Functor building an implementation of the hashtable structure. The functor Hashtbl.Make returns a structure containing a type key of keys and a type 'a t of hash tables associating data of type 'a to keys of type key. The operations perform similarly to those of the generic interface, but use the hashing and equality functions specified in the functor argument H instead of generic equality and hashing. Since the hash function is not seeded, the create operation of the result structure always returns non-randomized hash tables. << module type SeededHashedType = >>  sig << type t >> The type of the hashtable keys. << val equal : t -> t -> bool >> The equality predicate used to compare keys. << val seeded_hash : int -> t -> int >> A seeded hashing function on keys. The first argument is the seed. It must be the case that if equal x y is true, then seeded_hash seed x = seeded_hash seed y for any value of seed. A suitable choice for seeded_hash is the function MoreLabels.Hashtbl.seeded_hash[29.36] below.  end The input signature of the functor MoreLabels.Hashtbl.MakeSeeded[29.36]. Since: 4.00 << module type SeededS = >>  sig << type key >> << type !'a t >> << val create : ?random:bool -> int -> 'a t >> << val clear : 'a t -> unit >> << val reset : 'a t -> unit >> << val copy : 'a t -> 'a t >> << val add : 'a t -> key:key -> data:'a -> unit >> << val remove : 'a t -> key -> unit >> << val find : 'a t -> key -> 'a >> << val find_opt : 'a t -> key -> 'a option >> Since: 4.05 << val find_all : 'a t -> key -> 'a list >> << val replace : 'a t -> key:key -> data:'a -> unit >> << val mem : 'a t -> key -> bool >> << val iter : f:(key:key -> data:'a -> unit) -> 'a t -> unit >> << val filter_map_inplace : f:(key:key -> data:'a -> 'a option) -> 'a t -> unit >> Since: 4.03 << val fold : f:(key:key -> data:'a -> 'acc -> 'acc) -> 'a t -> init:'acc -> 'acc >> << val length : 'a t -> int >> << val stats : 'a t -> MoreLabels.Hashtbl.statistics >> << val to_seq : 'a t -> (key * 'a) Seq.t >> Since: 4.07 << val to_seq_keys : 'a t -> key Seq.t >> Since: 4.07 << val to_seq_values : 'a t -> 'a Seq.t >> Since: 4.07 << val add_seq : 'a t -> (key * 'a) Seq.t -> unit >> Since: 4.07 << val replace_seq : 'a t -> (key * 'a) Seq.t -> unit >> Since: 4.07 << val of_seq : (key * 'a) Seq.t -> 'a t >> Since: 4.07  end The output signature of the functor MoreLabels.Hashtbl.MakeSeeded[29.36]. Since: 4.00 << module MakeSeeded : >> functor (H : SeededHashedType) -> SeededS with type key = H.t and type 'a t = 'a Hashtbl.MakeSeeded(H).t Functor building an implementation of the hashtable structure. The functor Hashtbl.MakeSeeded returns a structure containing a type key of keys and a type 'a t of hash tables associating data of type 'a to keys of type key. The operations perform similarly to those of the generic interface, but use the seeded hashing and equality functions specified in the functor argument H instead of generic equality and hashing. The create operation of the result structure supports the ~random optional parameter and returns randomized hash tables if ~random:true is passed or if randomization is globally on (see MoreLabels.Hashtbl.randomize[29.36]). Since: 4.00 The polymorphic hash functions ============================== << val hash : 'a -> int >> Hashtbl.hash x associates a nonnegative integer to any value of any type. It is guaranteed that if x = y or Stdlib.compare x y = 0, then hash x = hash y. Moreover, hash always terminates, even on cyclic structures. << val seeded_hash : int -> 'a -> int >> A variant of MoreLabels.Hashtbl.hash[29.36] that is further parameterized by an integer seed. Since: 4.00 << val hash_param : int -> int -> 'a -> int >> Hashtbl.hash_param meaningful total x computes a hash value for x, with the same properties as for hash. The two extra integer parameters meaningful and total give more precise control over hashing. Hashing performs a breadth-first, left-to-right traversal of the structure x, stopping after meaningful meaningful nodes were encountered, or total nodes (meaningful or not) were encountered. If total as specified by the user exceeds a certain value, currently 256, then it is capped to that value. Meaningful nodes are: integers; floating-point numbers; strings; characters; booleans; and constant constructors. Larger values of meaningful and total means that more nodes are taken into account to compute the final hash value, and therefore collisions are less likely to happen. However, hashing takes longer. The parameters meaningful and total govern the tradeoff between accuracy and speed. As default choices, MoreLabels.Hashtbl.hash[29.36] and MoreLabels.Hashtbl.seeded_hash[29.36] take meaningful = 10 and total = 100. << val seeded_hash_param : int -> int -> int -> 'a -> int >> A variant of MoreLabels.Hashtbl.hash_param[29.36] that is further parameterized by an integer seed. Usage: Hashtbl.seeded_hash_param meaningful total seed x. Since: 4.00 Examples ======== Basic Example ------------- << (* 0...99 *) let seq = Seq.ints 0 |> Seq.take 100 (* build from Seq.t *) # let tbl = seq |> Seq.map (fun x -> x, string_of_int x) |> Hashtbl.of_seq val tbl : (int, string) Hashtbl.t = # Hashtbl.length tbl - : int = 100 # Hashtbl.find_opt tbl 32 - : string option = Some "32" # Hashtbl.find_opt tbl 166 - : string option = None # Hashtbl.replace tbl 166 "one six six" - : unit = () # Hashtbl.find_opt tbl 166 - : string option = Some "one six six" # Hashtbl.length tbl - : int = 101 >> Counting Elements ----------------- Given a sequence of elements (here, a Seq.t[29.49]), we want to count how many times each distinct element occurs in the sequence. A simple way to do this, assuming the elements are comparable and hashable, is to use a hash table that maps elements to their number of occurrences. Here we illustrate that principle using a sequence of (ascii) characters (type char). We use a custom Char_tbl specialized for char. << # module Char_tbl = Hashtbl.Make(struct type t = char let equal = Char.equal let hash = Hashtbl.hash end) (* count distinct occurrences of chars in [seq] *) # let count_chars (seq : char Seq.t) : _ list = let counts = Char_tbl.create 16 in Seq.iter (fun c -> let count_c = Char_tbl.find_opt counts c |> Option.value ~default:0 in Char_tbl.replace counts c (count_c + 1)) seq; (* turn into a list *) Char_tbl.fold (fun c n l -> (c,n) :: l) counts [] |> List.sort (fun (c1,_)(c2,_) -> Char.compare c1 c2) val count_chars : Char_tbl.key Seq.t -> (Char.t * int) list = (* basic seq from a string *) # let seq = String.to_seq "hello world, and all the camels in it!" val seq : char Seq.t = # count_chars seq - : (Char.t * int) list = [(' ', 7); ('!', 1); (',', 1); ('a', 3); ('c', 1); ('d', 2); ('e', 3); ('h', 2); ('i', 2); ('l', 6); ('m', 1); ('n', 2); ('o', 2); ('r', 1); ('s', 1); ('t', 2); ('w', 1)] (* "abcabcabc..." *) # let seq2 = Seq.cycle (String.to_seq "abc") |> Seq.take 31 val seq2 : char Seq.t = # String.of_seq seq2 - : String.t = "abcabcabcabcabcabcabcabcabcabca" # count_chars seq2 - : (Char.t * int) list = [('a', 11); ('b', 10); ('c', 10)] >>  end << module Map : >>  sig Association tables over ordered types. This module implements applicative association tables, also known as finite maps or dictionaries, given a total ordering function over the keys. All operations over maps are purely applicative (no side-effects). The implementation uses balanced binary trees, and therefore searching and insertion take time logarithmic in the size of the map. For instance: << module IntPairs = struct type t = int * int let compare (x0,y0) (x1,y1) = match Stdlib.compare x0 x1 with 0 -> Stdlib.compare y0 y1 | c -> c end module PairsMap = Map.Make(IntPairs) let m = PairsMap.(empty |> add (0,1) "hello" |> add (1,0) "world") >> This creates a new module PairsMap, with a new type 'a PairsMap.t of maps from int * int to 'a. In this example, m contains string values so its type is string PairsMap.t. << module type OrderedType = >>  sig << type t >> The type of the map keys. << val compare : t -> t -> int >> A total ordering function over the keys. This is a two-argument function f such that f e1 e2 is zero if the keys e1 and e2 are equal, f e1 e2 is strictly negative if e1 is smaller than e2, and f e1 e2 is strictly positive if e1 is greater than e2. Example: a suitable ordering function is the generic structural comparison function compare[28.2].  end Input signature of the functor MoreLabels.Map.Make[29.36]. << module type S = >>  sig Maps ==== << type key >> The type of the map keys. << type !+'a t >> The type of maps from type key to type 'a. << val empty : 'a t >> The empty map. << val add : key:key -> data:'a -> 'a t -> 'a t >> add ~key ~data m returns a map containing the same bindings as m, plus a binding of key to data. If key was already bound in m to a value that is physically equal to data, m is returned unchanged (the result of the function is then physically equal to m). Otherwise, the previous binding of key in m disappears. Before 4.03 Physical equality was not ensured. << val add_to_list : key:key -> data:'a -> 'a list t -> 'a list t >> add_to_list ~key ~data m is m with key mapped to l such that l is data :: Map.find key m if key was bound in m and [v] otherwise. Since: 5.1 << val update : key:key -> f:('a option -> 'a option) -> 'a t -> 'a t >> update ~key ~f m returns a map containing the same bindings as m, except for the binding of key. Depending on the value of y where y is f (find_opt key m), the binding of key is added, removed or updated. If y is None, the binding is removed if it exists; otherwise, if y is Some z then key is associated to z in the resulting map. If key was already bound in m to a value that is physically equal to z, m is returned unchanged (the result of the function is then physically equal to m). Since: 4.06 << val singleton : key -> 'a -> 'a t >> singleton x y returns the one-element map that contains a binding y for x. Since: 3.12 << val remove : key -> 'a t -> 'a t >> remove x m returns a map containing the same bindings as m, except for x which is unbound in the returned map. If x was not in m, m is returned unchanged (the result of the function is then physically equal to m). Before 4.03 Physical equality was not ensured. << val merge : f:(key -> 'a option -> 'b option -> 'c option) -> 'a t -> 'b t -> 'c t >> merge ~f m1 m2 computes a map whose keys are a subset of the keys of m1 and of m2. The presence of each such binding, and the corresponding value, is determined with the function f. In terms of the find_opt operation, we have find_opt x (merge f m1 m2) = f x (find_opt x m1) (find_opt x m2) for any key x, provided that f x None None = None. Since: 3.12 << val union : f:(key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t >> union ~f m1 m2 computes a map whose keys are a subset of the keys of m1 and of m2. When the same binding is defined in both arguments, the function f is used to combine them. This is a special case of merge: union f m1 m2 is equivalent to merge f' m1 m2, where - f' _key None None = None - f' _key (Some v) None = Some v - f' _key None (Some v) = Some v - f' key (Some v1) (Some v2) = f key v1 v2 Since: 4.03 << val cardinal : 'a t -> int >> Return the number of bindings of a map. Since: 3.12 Bindings ======== << val bindings : 'a t -> (key * 'a) list >> Return the list of all bindings of the given map. The returned list is sorted in increasing order of keys with respect to the ordering Ord.compare, where Ord is the argument given to MoreLabels.Map.Make[29.36]. Since: 3.12 << val min_binding : 'a t -> key * 'a >> Return the binding with the smallest key in a given map (with respect to the Ord.compare ordering), or raise Not_found if the map is empty. Since: 3.12 << val min_binding_opt : 'a t -> (key * 'a) option >> Return the binding with the smallest key in the given map (with respect to the Ord.compare ordering), or None if the map is empty. Since: 4.05 << val max_binding : 'a t -> key * 'a >> Same as MoreLabels.Map.S.min_binding[29.36], but returns the binding with the largest key in the given map. Since: 3.12 << val max_binding_opt : 'a t -> (key * 'a) option >> Same as MoreLabels.Map.S.min_binding_opt[29.36], but returns the binding with the largest key in the given map. Since: 4.05 << val choose : 'a t -> key * 'a >> Return one binding of the given map, or raise Not_found if the map is empty. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps. Since: 3.12 << val choose_opt : 'a t -> (key * 'a) option >> Return one binding of the given map, or None if the map is empty. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps. Since: 4.05 Searching ========= << val find : key -> 'a t -> 'a >> find x m returns the current value of x in m, or raises Not_found if no binding for x exists. << val find_opt : key -> 'a t -> 'a option >> find_opt x m returns Some v if the current value of x in m is v, or None if no binding for x exists. Since: 4.05 << val find_first : f:(key -> bool) -> 'a t -> key * 'a >> find_first ~f m, where f is a monotonically increasing function, returns the binding of m with the lowest key k such that f k, or raises Not_found if no such key exists. For example, find_first (fun k -> Ord.compare k x >= 0) m will return the first binding k, v of m where Ord.compare k x >= 0 (intuitively: k >= x), or raise Not_found if x is greater than any element of m. Since: 4.05 << val find_first_opt : f:(key -> bool) -> 'a t -> (key * 'a) option >> find_first_opt ~f m, where f is a monotonically increasing function, returns an option containing the binding of m with the lowest key k such that f k, or None if no such key exists. Since: 4.05 << val find_last : f:(key -> bool) -> 'a t -> key * 'a >> find_last ~f m, where f is a monotonically decreasing function, returns the binding of m with the highest key k such that f k, or raises Not_found if no such key exists. Since: 4.05 << val find_last_opt : f:(key -> bool) -> 'a t -> (key * 'a) option >> find_last_opt ~f m, where f is a monotonically decreasing function, returns an option containing the binding of m with the highest key k such that f k, or None if no such key exists. Since: 4.05 Traversing ========== << val iter : f:(key:key -> data:'a -> unit) -> 'a t -> unit >> iter ~f m applies f to all bindings in map m. f receives the key as first argument, and the associated value as second argument. The bindings are passed to f in increasing order with respect to the ordering over the type of the keys. << val fold : f:(key:key -> data:'a -> 'acc -> 'acc) -> 'a t -> init:'acc -> 'acc >> fold ~f m ~init computes (f kN dN ... (f k1 d1 init)...), where k1 ... kN are the keys of all bindings in m (in increasing order), and d1 ... dN are the associated data. Transforming ============ << val map : f:('a -> 'b) -> 'a t -> 'b t >> map ~f m returns a map with same domain as m, where the associated value a of all bindings of m has been replaced by the result of the application of f to a. The bindings are passed to f in increasing order with respect to the ordering over the type of the keys. << val mapi : f:(key -> 'a -> 'b) -> 'a t -> 'b t >> Same as MoreLabels.Map.S.map[29.36], but the function receives as arguments both the key and the associated value for each binding of the map. << val filter : f:(key -> 'a -> bool) -> 'a t -> 'a t >> filter ~f m returns the map with all the bindings in m that satisfy predicate p. If every binding in m satisfies f, m is returned unchanged (the result of the function is then physically equal to m) Before 4.03 Physical equality was not ensured. Since: 3.12 << val filter_map : f:(key -> 'a -> 'b option) -> 'a t -> 'b t >> filter_map ~f m applies the function f to every binding of m, and builds a map from the results. For each binding (k, v) in the input map: - if f k v is None then k is not in the result, - if f k v is Some v' then the binding (k, v') is in the output map. For example, the following function on maps whose values are lists << filter_map (fun _k li -> match li with [] -> None | _::tl -> Some tl) m >> drops all bindings of m whose value is an empty list, and pops the first element of each value that is non-empty. Since: 4.11 << val partition : f:(key -> 'a -> bool) -> 'a t -> 'a t * 'a t >> partition ~f m returns a pair of maps (m1, m2), where m1 contains all the bindings of m that satisfy the predicate f, and m2 is the map with all the bindings of m that do not satisfy f. Since: 3.12 << val split : key -> 'a t -> 'a t * 'a option * 'a t >> split x m returns a triple (l, data, r), where l is the map with all the bindings of m whose key is strictly less than x; r is the map with all the bindings of m whose key is strictly greater than x; data is None if m contains no binding for x, or Some v if m binds v to x. Since: 3.12 Predicates and comparisons ========================== << val is_empty : 'a t -> bool >> Test whether a map is empty or not. << val mem : key -> 'a t -> bool >> mem x m returns true if m contains a binding for x, and false otherwise. << val equal : cmp:('a -> 'a -> bool) -> 'a t -> 'a t -> bool >> equal ~cmp m1 m2 tests whether the maps m1 and m2 are equal, that is, contain equal keys and associate them with equal data. cmp is the equality predicate used to compare the data associated with the keys. << val compare : cmp:('a -> 'a -> int) -> 'a t -> 'a t -> int >> Total ordering between maps. The first argument is a total ordering used to compare data associated with equal keys in the two maps. << val for_all : f:(key -> 'a -> bool) -> 'a t -> bool >> for_all ~f m checks if all the bindings of the map satisfy the predicate f. Since: 3.12 << val exists : f:(key -> 'a -> bool) -> 'a t -> bool >> exists ~f m checks if at least one binding of the map satisfies the predicate f. Since: 3.12 Converting ========== << val to_list : 'a t -> (key * 'a) list >> to_list m is MoreLabels.Map.S.bindings[29.36] m. Since: 5.1 << val of_list : (key * 'a) list -> 'a t >> of_list bs adds the bindings of bs to the empty map, in list order (if a key is bound twice in bs the last one takes over). Since: 5.1 << val to_seq : 'a t -> (key * 'a) Seq.t >> Iterate on the whole map, in ascending order of keys Since: 4.07 << val to_rev_seq : 'a t -> (key * 'a) Seq.t >> Iterate on the whole map, in descending order of keys Since: 4.12 << val to_seq_from : key -> 'a t -> (key * 'a) Seq.t >> to_seq_from k m iterates on a subset of the bindings of m, in ascending order of keys, from key k or above. Since: 4.07 << val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t >> Add the given bindings to the map, in order. Since: 4.07 << val of_seq : (key * 'a) Seq.t -> 'a t >> Build a map from the given bindings Since: 4.07  end Output signature of the functor MoreLabels.Map.Make[29.36]. << module Make : >> functor (Ord : OrderedType) -> S with type key = Ord.t and type 'a t = 'a Map.Make(Ord).t Functor building an implementation of the map structure given a totally ordered type.  end << module Set : >>  sig Sets over ordered types. This module implements the set data structure, given a total ordering function over the set elements. All operations over sets are purely applicative (no side-effects). The implementation uses balanced binary trees, and is therefore reasonably efficient: insertion and membership take time logarithmic in the size of the set, for instance. The MoreLabels.Set.Make[29.36] functor constructs implementations for any type, given a compare function. For instance: << module IntPairs = struct type t = int * int let compare (x0,y0) (x1,y1) = match Stdlib.compare x0 x1 with 0 -> Stdlib.compare y0 y1 | c -> c end module PairsSet = Set.Make(IntPairs) let m = PairsSet.(empty |> add (2,3) |> add (5,7) |> add (11,13)) >> This creates a new module PairsSet, with a new type PairsSet.t of sets of int * int. << module type OrderedType = >>  sig << type t >> The type of the set elements. << val compare : t -> t -> int >> A total ordering function over the set elements. This is a two-argument function f such that f e1 e2 is zero if the elements e1 and e2 are equal, f e1 e2 is strictly negative if e1 is smaller than e2, and f e1 e2 is strictly positive if e1 is greater than e2. Example: a suitable ordering function is the generic structural comparison function compare[28.2].  end Input signature of the functor MoreLabels.Set.Make[29.36]. << module type S = >>  sig Sets ==== << type elt >> The type of the set elements. << type t >> The type of sets. << val empty : t >> The empty set. << val add : elt -> t -> t >> add x s returns a set containing all elements of s, plus x. If x was already in s, s is returned unchanged (the result of the function is then physically equal to s). Before 4.03 Physical equality was not ensured. << val singleton : elt -> t >> singleton x returns the one-element set containing only x. << val remove : elt -> t -> t >> remove x s returns a set containing all elements of s, except x. If x was not in s, s is returned unchanged (the result of the function is then physically equal to s). Before 4.03 Physical equality was not ensured. << val union : t -> t -> t >> Set union. << val inter : t -> t -> t >> Set intersection. << val disjoint : t -> t -> bool >> Test if two sets are disjoint. Since: 4.08 << val diff : t -> t -> t >> Set difference: diff s1 s2 contains the elements of s1 that are not in s2. << val cardinal : t -> int >> Return the number of elements of a set. Elements ======== << val elements : t -> elt list >> Return the list of all elements of the given set. The returned list is sorted in increasing order with respect to the ordering Ord.compare, where Ord is the argument given to MoreLabels.Set.Make[29.36]. << val min_elt : t -> elt >> Return the smallest element of the given set (with respect to the Ord.compare ordering), or raise Not_found if the set is empty. << val min_elt_opt : t -> elt option >> Return the smallest element of the given set (with respect to the Ord.compare ordering), or None if the set is empty. Since: 4.05 << val max_elt : t -> elt >> Same as MoreLabels.Set.S.min_elt[29.36], but returns the largest element of the given set. << val max_elt_opt : t -> elt option >> Same as MoreLabels.Set.S.min_elt_opt[29.36], but returns the largest element of the given set. Since: 4.05 << val choose : t -> elt >> Return one element of the given set, or raise Not_found if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets. << val choose_opt : t -> elt option >> Return one element of the given set, or None if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets. Since: 4.05 Searching ========= << val find : elt -> t -> elt >> find x s returns the element of s equal to x (according to Ord.compare), or raise Not_found if no such element exists. Since: 4.01 << val find_opt : elt -> t -> elt option >> find_opt x s returns the element of s equal to x (according to Ord.compare), or None if no such element exists. Since: 4.05 << val find_first : f:(elt -> bool) -> t -> elt >> find_first ~f s, where f is a monotonically increasing function, returns the lowest element e of s such that f e, or raises Not_found if no such element exists. For example, find_first (fun e -> Ord.compare e x >= 0) s will return the first element e of s where Ord.compare e x >= 0 (intuitively: e >= x), or raise Not_found if x is greater than any element of s. Since: 4.05 << val find_first_opt : f:(elt -> bool) -> t -> elt option >> find_first_opt ~f s, where f is a monotonically increasing function, returns an option containing the lowest element e of s such that f e, or None if no such element exists. Since: 4.05 << val find_last : f:(elt -> bool) -> t -> elt >> find_last ~f s, where f is a monotonically decreasing function, returns the highest element e of s such that f e, or raises Not_found if no such element exists. Since: 4.05 << val find_last_opt : f:(elt -> bool) -> t -> elt option >> find_last_opt ~f s, where f is a monotonically decreasing function, returns an option containing the highest element e of s such that f e, or None if no such element exists. Since: 4.05 Traversing ========== << val iter : f:(elt -> unit) -> t -> unit >> iter ~f s applies f in turn to all elements of s. The elements of s are presented to f in increasing order with respect to the ordering over the type of the elements. << val fold : f:(elt -> 'acc -> 'acc) -> t -> init:'acc -> 'acc >> fold ~f s init computes (f xN ... (f x2 (f x1 init))...), where x1 ... xN are the elements of s, in increasing order. Transforming ============ << val map : f:(elt -> elt) -> t -> t >> map ~f s is the set whose elements are f a0,f a1... f aN, where a0,a1...aN are the elements of s. The elements are passed to f in increasing order with respect to the ordering over the type of the elements. If no element of s is changed by f, s is returned unchanged. (If each output of f is physically equal to its input, the returned set is physically equal to s.) Since: 4.04 << val filter : f:(elt -> bool) -> t -> t >> filter ~f s returns the set of all elements in s that satisfy predicate f. If f satisfies every element in s, s is returned unchanged (the result of the function is then physically equal to s). Before 4.03 Physical equality was not ensured. << val filter_map : f:(elt -> elt option) -> t -> t >> filter_map ~f s returns the set of all v such that f x = Some v for some element x of s. For example, << filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s >> is the set of halves of the even elements of s. If no element of s is changed or dropped by f (if f x = Some x for each element x), then s is returned unchanged: the result of the function is then physically equal to s. Since: 4.11 << val partition : f:(elt -> bool) -> t -> t * t >> partition ~f s returns a pair of sets (s1, s2), where s1 is the set of all the elements of s that satisfy the predicate f, and s2 is the set of all the elements of s that do not satisfy f. << val split : elt -> t -> t * bool * t >> split x s returns a triple (l, present, r), where l is the set of elements of s that are strictly less than x; r is the set of elements of s that are strictly greater than x; present is false if s contains no element equal to x, or true if s contains an element equal to x. Predicates and comparisons ========================== << val is_empty : t -> bool >> Test whether a set is empty or not. << val mem : elt -> t -> bool >> mem x s tests whether x belongs to the set s. << val equal : t -> t -> bool >> equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements. << val compare : t -> t -> int >> Total ordering between sets. Can be used as the ordering function for doing sets of sets. << val subset : t -> t -> bool >> subset s1 s2 tests whether the set s1 is a subset of the set s2. << val for_all : f:(elt -> bool) -> t -> bool >> for_all ~f s checks if all elements of the set satisfy the predicate f. << val exists : f:(elt -> bool) -> t -> bool >> exists ~f s checks if at least one element of the set satisfies the predicate f. Converting ========== << val to_list : t -> elt list >> to_list s is MoreLabels.Set.S.elements[29.36] s. Since: 5.1 << val of_list : elt list -> t >> of_list l creates a set from a list of elements. This is usually more efficient than folding add over the list, except perhaps for lists with many duplicated elements. Since: 4.02 << val to_seq_from : elt -> t -> elt Seq.t >> to_seq_from x s iterates on a subset of the elements of s in ascending order, from x or above. Since: 4.07 << val to_seq : t -> elt Seq.t >> Iterate on the whole set, in ascending order Since: 4.07 << val to_rev_seq : t -> elt Seq.t >> Iterate on the whole set, in descending order Since: 4.12 << val add_seq : elt Seq.t -> t -> t >> Add the given elements to the set, in order. Since: 4.07 << val of_seq : elt Seq.t -> t >> Build a set from the given bindings Since: 4.07  end Output signature of the functor MoreLabels.Set.Make[29.36]. << module Make : >> functor (Ord : OrderedType) -> S with type elt = Ord.t and type t = Set.Make(Ord).t Functor building an implementation of the set structure given a totally ordered type.  end 29.37 Module Mutex : Locks for mutual exclusion. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Mutexes (mutual-exclusion locks) are used to implement critical sections and protect shared mutable data structures against concurrent accesses. The typical use is (if m is the mutex associated with the data structure D): << Mutex.lock m; (* Critical section that operates over D *); Mutex.unlock m >> << type t >> The type of mutexes. << val create : unit -> t >> Return a new mutex. << val lock : t -> unit >> Lock the given mutex. Only one thread can have the mutex locked at any time. A thread that attempts to lock a mutex already locked by another thread will suspend until the other thread unlocks the mutex. Before 4.12 Sys_error was not raised for recursive locking (platform-dependent behaviour) Raises Sys_error if the mutex is already locked by the thread calling Mutex.lock[29.37]. << val try_lock : t -> bool >> Same as Mutex.lock[29.37], but does not suspend the calling thread if the mutex is already locked: just return false immediately in that case. If the mutex is unlocked, lock it and return true. << val unlock : t -> unit >> Unlock the given mutex. Other threads suspended trying to lock the mutex will restart. The mutex must have been previously locked by the thread that calls Mutex.unlock[29.37]. Before 4.12 Sys_error was not raised when unlocking an unlocked mutex or when unlocking a mutex from a different thread. Raises Sys_error if the mutex is unlocked or was locked by another thread. << val protect : t -> (unit -> 'a) -> 'a >> protect mutex f runs f() in a critical section where mutex is locked (using Mutex.lock[29.37]); it then takes care of releasing mutex, whether f() returned a value or raised an exception. The unlocking operation is guaranteed to always takes place, even in the event an asynchronous exception (e.g. Sys.Break[29.56]) is raised in some signal handler. Since: 5.1 29.38 Module Nativeint : Processor-native integers. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module provides operations on the type nativeint of signed 32-bit integers (on 32-bit platforms) or signed 64-bit integers (on 64-bit platforms). This integer type has exactly the same width as that of a pointer type in the C compiler. All arithmetic operations over nativeint are taken modulo 2^32 or 2^64 depending on the word size of the architecture. Performance notice: values of type nativeint occupy more memory space than values of type int, and arithmetic operations on nativeint are generally slower than those on int. Use nativeint only when the application requires the extra bit of precision over the int type. Literals for native integers are suffixed by n: << let zero: nativeint = 0n let one: nativeint = 1n let m_one: nativeint = -1n >> << val zero : nativeint >> The native integer 0. << val one : nativeint >> The native integer 1. << val minus_one : nativeint >> The native integer -1. << val neg : nativeint -> nativeint >> Unary negation. << val add : nativeint -> nativeint -> nativeint >> Addition. << val sub : nativeint -> nativeint -> nativeint >> Subtraction. << val mul : nativeint -> nativeint -> nativeint >> Multiplication. << val div : nativeint -> nativeint -> nativeint >> Integer division. This division rounds the real quotient of its arguments towards zero, as specified for (/)[28.2]. Raises Division_by_zero if the second argument is zero. << val unsigned_div : nativeint -> nativeint -> nativeint >> Same as Nativeint.div[29.38], except that arguments and result are interpreted as unsigned native integers. Since: 4.08 << val rem : nativeint -> nativeint -> nativeint >> Integer remainder. If y is not zero, the result of Nativeint.rem x y satisfies the following properties: Nativeint.zero <= Nativeint.rem x y < Nativeint.abs y and x = Nativeint.add (Nativeint.mul (Nativeint.div x y) y) (Nativeint.rem x y). If y = 0, Nativeint.rem x y raises Division_by_zero. << val unsigned_rem : nativeint -> nativeint -> nativeint >> Same as Nativeint.rem[29.38], except that arguments and result are interpreted as unsigned native integers. Since: 4.08 << val succ : nativeint -> nativeint >> Successor. Nativeint.succ x is Nativeint.add x Nativeint.one. << val pred : nativeint -> nativeint >> Predecessor. Nativeint.pred x is Nativeint.sub x Nativeint.one. << val abs : nativeint -> nativeint >> abs x is the absolute value of x. On min_int this is min_int itself and thus remains negative. << val size : int >> The size in bits of a native integer. This is equal to 32 on a 32-bit platform and to 64 on a 64-bit platform. << val max_int : nativeint >> The greatest representable native integer, either 2^31 - 1 on a 32-bit platform, or 2^63 - 1 on a 64-bit platform. << val min_int : nativeint >> The smallest representable native integer, either -2^31 on a 32-bit platform, or -2^63 on a 64-bit platform. << val logand : nativeint -> nativeint -> nativeint >> Bitwise logical and. << val logor : nativeint -> nativeint -> nativeint >> Bitwise logical or. << val logxor : nativeint -> nativeint -> nativeint >> Bitwise logical exclusive or. << val lognot : nativeint -> nativeint >> Bitwise logical negation. << val shift_left : nativeint -> int -> nativeint >> Nativeint.shift_left x y shifts x to the left by y bits. The result is unspecified if y < 0 or y >= bitsize, where bitsize is 32 on a 32-bit platform and 64 on a 64-bit platform. << val shift_right : nativeint -> int -> nativeint >> Nativeint.shift_right x y shifts x to the right by y bits. This is an arithmetic shift: the sign bit of x is replicated and inserted in the vacated bits. The result is unspecified if y < 0 or y >= bitsize. << val shift_right_logical : nativeint -> int -> nativeint >> Nativeint.shift_right_logical x y shifts x to the right by y bits. This is a logical shift: zeroes are inserted in the vacated bits regardless of the sign of x. The result is unspecified if y < 0 or y >= bitsize. << val of_int : int -> nativeint >> Convert the given integer (type int) to a native integer (type nativeint). << val to_int : nativeint -> int >> Convert the given native integer (type nativeint) to an integer (type int). The high-order bit is lost during the conversion. << val unsigned_to_int : nativeint -> int option >> Same as Nativeint.to_int[29.38], but interprets the argument as an unsigned integer. Returns None if the unsigned value of the argument cannot fit into an int. Since: 4.08 << val of_float : float -> nativeint >> Convert the given floating-point number to a native integer, discarding the fractional part (truncate towards 0). If the truncated floating-point number is outside the range [Nativeint.min_int[29.38], Nativeint.max_int[29.38]], no exception is raised, and an unspecified, platform-dependent integer is returned. << val to_float : nativeint -> float >> Convert the given native integer to a floating-point number. << val of_int32 : int32 -> nativeint >> Convert the given 32-bit integer (type int32) to a native integer. << val to_int32 : nativeint -> int32 >> Convert the given native integer to a 32-bit integer (type int32). On 64-bit platforms, the 64-bit native integer is taken modulo 2^32, i.e. the top 32 bits are lost. On 32-bit platforms, the conversion is exact. << val of_string : string -> nativeint >> Convert the given string to a native integer. The string is read in decimal (by default, or if the string begins with 0u) or in hexadecimal, octal or binary if the string begins with 0x, 0o or 0b respectively. The 0u prefix reads the input as an unsigned integer in the range [0, 2*Nativeint.max_int+1]. If the input exceeds Nativeint.max_int[29.38] it is converted to the signed integer Int64.min_int + input - Nativeint.max_int - 1. Raises Failure if the given string is not a valid representation of an integer, or if the integer represented exceeds the range of integers representable in type nativeint. << val of_string_opt : string -> nativeint option >> Same as of_string, but return None instead of raising. Since: 4.05 << val to_string : nativeint -> string >> Return the string representation of its argument, in decimal. << type t = nativeint >> An alias for the type of native integers. << val compare : t -> t -> int >> The comparison function for native integers, with the same specification as compare[28.2]. Along with the type t, this function compare allows the module Nativeint to be passed as argument to the functors Set.Make[29.50] and Map.Make[29.34]. << val unsigned_compare : t -> t -> int >> Same as Nativeint.compare[29.38], except that arguments are interpreted as unsigned native integers. Since: 4.08 << val equal : t -> t -> bool >> The equal function for native ints. Since: 4.03 << val min : t -> t -> t >> Return the smaller of the two arguments. Since: 4.13 << val max : t -> t -> t >> Return the greater of the two arguments. Since: 4.13 << val seeded_hash : int -> t -> int >> A seeded hash function for native ints, with the same output value as Hashtbl.seeded_hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded[29.25]. Since: 5.1 << val hash : t -> int >> An unseeded hash function for native ints, with the same output value as Hashtbl.hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.Make[29.25]. Since: 5.1 29.39 Module Oo : Operations on objects *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* << val copy : (< .. > as 'a) -> 'a >> Oo.copy o returns a copy of object o, that is a fresh object with the same methods and instance variables as o. Alert unsynchronized_access. Unsynchronized accesses to mutable objects are a programming error. << val id : < .. > -> int >> Return an integer identifying this object, unique for the current execution of the program. The generic comparison and hashing functions are based on this integer. When an object is obtained by unmarshaling, the id is refreshed, and thus different from the original object. As a consequence, the internal invariants of data structures such as hash table or sets containing objects are broken after unmarshaling the data structures. 29.40 Module Option : Option values. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Option values explicitly indicate the presence or absence of a value. Since: 4.08 Options ======= << type 'a t = 'a option = | None | Some of 'a >> The type for option values. Either None or a value Some v. << val none : 'a option >> none is None. << val some : 'a -> 'a option >> some v is Some v. << val value : 'a option -> default:'a -> 'a >> value o ~default is v if o is Some v and default otherwise. << val get : 'a option -> 'a >> get o is v if o is Some v and raise otherwise. Raises Invalid_argument if o is None. << val bind : 'a option -> ('a -> 'b option) -> 'b option >> bind o f is f v if o is Some v and None if o is None. << val join : 'a option option -> 'a option >> join oo is Some v if oo is Some (Some v) and None otherwise. << val map : ('a -> 'b) -> 'a option -> 'b option >> map f o is None if o is None and Some (f v) if o is Some v. << val fold : none:'a -> some:('b -> 'a) -> 'b option -> 'a >> fold ~none ~some o is none if o is None and some v if o is Some v. << val iter : ('a -> unit) -> 'a option -> unit >> iter f o is f v if o is Some v and () otherwise. Predicates and comparisons ========================== << val is_none : 'a option -> bool >> is_none o is true if and only if o is None. << val is_some : 'a option -> bool >> is_some o is true if and only if o is Some o. << val equal : ('a -> 'a -> bool) -> 'a option -> 'a option -> bool >> equal eq o0 o1 is true if and only if o0 and o1 are both None or if they are Some v0 and Some v1 and eq v0 v1 is true. << val compare : ('a -> 'a -> int) -> 'a option -> 'a option -> int >> compare cmp o0 o1 is a total order on options using cmp to compare values wrapped by Some _. None is smaller than Some _ values. Converting ========== << val to_result : none:'e -> 'a option -> ('a, 'e) result >> to_result ~none o is Ok v if o is Some v and Error none otherwise. << val to_list : 'a option -> 'a list >> to_list o is [] if o is None and [v] if o is Some v. << val to_seq : 'a option -> 'a Seq.t >> to_seq o is o as a sequence. None is the empty sequence and Some v is the singleton sequence containing v. 29.41 Module Out_channel : Output channels. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module provides functions for working with output channels. See the example section[29.4] below. Since: 4.14 Channels ======== << type t = out_channel >> The type of output channel. << type open_flag = open_flag = | Open_rdonly >> open for reading. << | Open_wronly >> open for writing. << | Open_append >> open for appending: always write at end of file. << | Open_creat >> create the file if it does not exist. << | Open_trunc >> empty the file if it already exists. << | Open_excl >> fail if Open_creat and the file already exists. << | Open_binary >> open in binary mode (no conversion). << | Open_text >> open in text mode (may perform conversions). << | Open_nonblock >> open in non-blocking mode. Opening modes for Out_channel.open_gen[29.41]. << val stdout : t >> The standard output for the process. << val stderr : t >> The standard error output for the process. << val open_bin : string -> t >> Open the named file for writing, and return a new output channel on that file, positioned at the beginning of the file. The file is truncated to zero length if it already exists. It is created if it does not already exists. << val open_text : string -> t >> Same as Out_channel.open_bin[29.41], but the file is opened in text mode, so that newline translation takes place during writes. On operating systems that do not distinguish between text mode and binary mode, this function behaves like Out_channel.open_bin[29.41]. << val open_gen : open_flag list -> int -> string -> t >> open_gen mode perm filename opens the named file for writing, as described above. The extra argument mode specifies the opening mode. The extra argument perm specifies the file permissions, in case the file must be created. Out_channel.open_text[29.41] and Out_channel.open_bin[29.41] are special cases of this function. << val with_open_bin : string -> (t -> 'a) -> 'a >> with_open_bin fn f opens a channel oc on file fn and returns f oc. After f returns, either with a value or by raising an exception, oc is guaranteed to be closed. << val with_open_text : string -> (t -> 'a) -> 'a >> Like Out_channel.with_open_bin[29.41], but the channel is opened in text mode (see Out_channel.open_text[29.41]). << val with_open_gen : open_flag list -> int -> string -> (t -> 'a) -> 'a >> Like Out_channel.with_open_bin[29.41], but can specify the opening mode and file permission, in case the file must be created (see Out_channel.open_gen[29.41]). << val close : t -> unit >> Close the given channel, flushing all buffered write operations. Output functions raise a Sys_error exception when they are applied to a closed output channel, except Out_channel.close[29.41] and Out_channel.flush[29.41], which do nothing when applied to an already closed channel. Note that Out_channel.close[29.41] may raise Sys_error if the operating system signals an error when flushing or closing. << val close_noerr : t -> unit >> Same as Out_channel.close[29.41], but ignore all errors. Output ====== << val output_char : t -> char -> unit >> Write the character on the given output channel. << val output_byte : t -> int -> unit >> Write one 8-bit integer (as the single character with that code) on the given output channel. The given integer is taken modulo 256. << val output_string : t -> string -> unit >> Write the string on the given output channel. << val output_bytes : t -> bytes -> unit >> Write the byte sequence on the given output channel. Advanced output =============== << val output : t -> bytes -> int -> int -> unit >> output oc buf pos len writes len characters from byte sequence buf, starting at offset pos, to the given output channel oc. Raises Invalid_argument if pos and len do not designate a valid range of buf. << val output_substring : t -> string -> int -> int -> unit >> Same as Out_channel.output[29.41] but take a string as argument instead of a byte sequence. << val output_bigarray : t -> ('a, Bigarray.int8_unsigned_elt, Bigarray.c_layout) Bigarray.Array1.t -> int -> int -> unit >> Same as Out_channel.output[29.41] but take the data from a bigarray. Since: 5.2 Flushing ======== << val flush : t -> unit >> Flush the buffer associated with the given output channel, performing all pending writes on that channel. Interactive programs must be careful about flushing standard output and standard error at the right time. << val flush_all : unit -> unit >> Flush all open output channels; ignore errors. Seeking ======= << val seek : t -> int64 -> unit >> seek chan pos sets the current writing position to pos for channel chan. This works only for regular files. On files of other kinds (such as terminals, pipes and sockets), the behavior is unspecified. << val pos : t -> int64 >> Return the current writing position for the given channel. Does not work on channels opened with the Open_append flag (returns unspecified results). For files opened in text mode under Windows, the returned position is approximate (owing to end-of-line conversion); in particular, saving the current position with Out_channel.pos[29.41], then going back to this position using Out_channel.seek[29.41] will not work. For this programming idiom to work reliably and portably, the file must be opened in binary mode. Attributes ========== << val length : t -> int64 >> Return the size (number of characters) of the regular file on which the given channel is opened. If the channel is opened on a file that is not a regular file, the result is meaningless. << val set_binary_mode : t -> bool -> unit >> set_binary_mode oc true sets the channel oc to binary mode: no translations take place during output. set_binary_mode oc false sets the channel oc to text mode: depending on the operating system, some translations may take place during output. For instance, under Windows, end-of-lines will be translated from \n to \r\n. This function has no effect under operating systems that do not distinguish between text mode and binary mode. << val is_binary_mode : t -> bool >> is_binary_mode oc returns whether the channel oc is in binary mode (see Out_channel.set_binary_mode[29.41]). Since: 5.2 << val set_buffered : t -> bool -> unit >> set_buffered oc true sets the channel oc to buffered mode. In this mode, data output on oc will be buffered until either the internal buffer is full or the function Out_channel.flush[29.41] or Out_channel.flush_all[29.41] is called, at which point it will be sent to the output device. set_buffered oc false sets the channel oc to unbuffered mode. In this mode, data output on oc will be sent to the output device immediately. All channels are open in buffered mode by default. << val is_buffered : t -> bool >> is_buffered oc returns whether the channel oc is buffered (see Out_channel.set_buffered[29.41]). << val isatty : t -> bool >> isatty oc is true if oc refers to a terminal or console window, false otherwise. Since: 5.1 Examples ======== Writing the contents of a file: << let write_file file s = Out_channel.with_open_bin file (fun oc -> Out_channel.output_string oc s)) >> 29.42 Module Parsing : The run-time library for parsers generated by *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= ocamlyacc. *=*=*=*=*= << val symbol_start : unit -> int >> symbol_start and Parsing.symbol_end[29.42] are to be called in the action part of a grammar rule only. They return the offset of the string that matches the left-hand side of the rule: symbol_start() returns the offset of the first character; symbol_end() returns the offset after the last character. The first character in a file is at offset 0. << val symbol_end : unit -> int >> See Parsing.symbol_start[29.42]. << val rhs_start : int -> int >> Same as Parsing.symbol_start[29.42] and Parsing.symbol_end[29.42], but return the offset of the string matching the nth item on the right-hand side of the rule, where n is the integer parameter to rhs_start and rhs_end. n is 1 for the leftmost item. << val rhs_end : int -> int >> See Parsing.rhs_start[29.42]. << val symbol_start_pos : unit -> Lexing.position >> Same as symbol_start, but return a position instead of an offset. << val symbol_end_pos : unit -> Lexing.position >> Same as symbol_end, but return a position instead of an offset. << val rhs_start_pos : int -> Lexing.position >> Same as rhs_start, but return a position instead of an offset. << val rhs_end_pos : int -> Lexing.position >> Same as rhs_end, but return a position instead of an offset. << val clear_parser : unit -> unit >> Empty the parser stack. Call it just after a parsing function has returned, to remove all pointers from the parser stack to structures that were built by semantic actions during parsing. This is optional, but lowers the memory requirements of the programs. << exception Parse_error >> Raised when a parser encounters a syntax error. Can also be raised from the action part of a grammar rule, to initiate error recovery. << val set_trace : bool -> bool >> Control debugging support for ocamlyacc-generated parsers. After Parsing.set_trace true, the pushdown automaton that executes the parsers prints a trace of its actions (reading a token, shifting a state, reducing by a rule) on standard output. Parsing.set_trace false turns this debugging trace off. The boolean returned is the previous state of the trace flag. Since: 3.11 29.43 Module Printexc : Facilities for printing exceptions and inspecting *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* current call stack. *=*=*=*=*=*=*=*=*=* << type t = exn = .. >> The type of exception values. << val to_string : exn -> string >> Printexc.to_string e returns a string representation of the exception e. << val to_string_default : exn -> string >> Printexc.to_string_default e returns a string representation of the exception e, ignoring all registered exception printers. Since: 4.09 << val print : ('a -> 'b) -> 'a -> 'b >> Printexc.print fn x applies fn to x and returns the result. If the evaluation of fn x raises any exception, the name of the exception is printed on standard error output, and the exception is raised again. The typical use is to catch and report exceptions that escape a function application. << val catch : ('a -> 'b) -> 'a -> 'b >> Deprecated. This function is no longer needed.Printexc.catch fn x is similar to Printexc.print[29.43], but aborts the program with exit code 2 after printing the uncaught exception. This function is deprecated: the runtime system is now able to print uncaught exceptions as precisely as Printexc.catch does. Moreover, calling Printexc.catch makes it harder to track the location of the exception using the debugger or the stack backtrace facility. So, do not use Printexc.catch in new code. << val print_backtrace : out_channel -> unit >> Printexc.print_backtrace oc prints an exception backtrace on the output channel oc. The backtrace lists the program locations where the most-recently raised exception was raised and where it was propagated through function calls. If the call is not inside an exception handler, the returned backtrace is unspecified. If the call is after some exception-catching code (before in the handler, or in a when-guard during the matching of the exception handler), the backtrace may correspond to a later exception than the handled one. Since: 3.11 << val get_backtrace : unit -> string >> Printexc.get_backtrace () returns a string containing the same exception backtrace that Printexc.print_backtrace would print. Same restriction usage than Printexc.print_backtrace[29.43]. Since: 3.11 << val record_backtrace : bool -> unit >> Printexc.record_backtrace b turns recording of exception backtraces on (if b = true) or off (if b = false). Initially, backtraces are not recorded, unless the b flag is given to the program through the OCAMLRUNPARAM variable. Since: 3.11 << val backtrace_status : unit -> bool >> Printexc.backtrace_status() returns true if exception backtraces are currently recorded, false if not. Since: 3.11 << val register_printer : (exn -> string option) -> unit >> Printexc.register_printer fn registers fn as an exception printer. The printer should return None or raise an exception if it does not know how to convert the passed exception, and Some s with s the resulting string if it can convert the passed exception. Exceptions raised by the printer are ignored. When converting an exception into a string, the printers will be invoked in the reverse order of their registrations, until a printer returns a Some s value (if no such printer exists, the runtime will use a generic printer). When using this mechanism, one should be aware that an exception backtrace is attached to the thread that saw it raised, rather than to the exception itself. Practically, it means that the code related to fn should not use the backtrace if it has itself raised an exception before. Since: 3.11.2 << val use_printers : exn -> string option >> Printexc.use_printers e returns None if there are no registered printers and Some s with else as the resulting string otherwise. Since: 4.09 Raw backtraces ============== << type raw_backtrace >> The type raw_backtrace stores a backtrace in a low-level format, which can be converted to usable form using raw_backtrace_entries and backtrace_slots_of_raw_entry below. Converting backtraces to backtrace_slots is slower than capturing the backtraces. If an application processes many backtraces, it can be useful to use raw_backtrace to avoid or delay conversion. Raw backtraces cannot be marshalled. If you need marshalling, you should use the array returned by the backtrace_slots function of the next section. Since: 4.01 << type raw_backtrace_entry = private int >> A raw_backtrace_entry is an element of a raw_backtrace. Each raw_backtrace_entry is an opaque integer, whose value is not stable between different programs, or even between different runs of the same binary. A raw_backtrace_entry can be converted to a usable form using backtrace_slots_of_raw_entry below. Note that, due to inlining, a single raw_backtrace_entry may convert to several backtrace_slots. Since the values of a raw_backtrace_entry are not stable, they cannot be marshalled. If they are to be converted, the conversion must be done by the process that generated them. Again due to inlining, there may be multiple distinct raw_backtrace_entry values that convert to equal backtrace_slots. However, if two raw_backtrace_entrys are equal as integers, then they represent the same backtrace_slots. Since: 4.12 << val raw_backtrace_entries : raw_backtrace -> raw_backtrace_entry array >> Since: 4.12 << val get_raw_backtrace : unit -> raw_backtrace >> Printexc.get_raw_backtrace () returns the same exception backtrace that Printexc.print_backtrace would print, but in a raw format. Same restriction usage than Printexc.print_backtrace[29.43]. Since: 4.01 << val print_raw_backtrace : out_channel -> raw_backtrace -> unit >> Print a raw backtrace in the same format Printexc.print_backtrace uses. Since: 4.01 << val raw_backtrace_to_string : raw_backtrace -> string >> Return a string from a raw backtrace, in the same format Printexc.get_backtrace uses. Since: 4.01 << val raise_with_backtrace : exn -> raw_backtrace -> 'a >> Reraise the exception using the given raw_backtrace for the origin of the exception Since: 4.05 Current call stack ================== << val get_callstack : int -> raw_backtrace >> Printexc.get_callstack n returns a description of the top of the call stack on the current program point (for the current thread), with at most n entries. (Note: this function is not related to exceptions at all, despite being part of the Printexc module.) Since: 4.01 Uncaught exceptions =================== << val default_uncaught_exception_handler : exn -> raw_backtrace -> unit >> Printexc.default_uncaught_exception_handler prints the exception and backtrace on standard error output. Since: 4.11 << val set_uncaught_exception_handler : (exn -> raw_backtrace -> unit) -> unit >> Printexc.set_uncaught_exception_handler fn registers fn as the handler for uncaught exceptions. The default handler is Printexc.default_uncaught_exception_handler[29.43]. Note that when fn is called all the functions registered with at_exit[28.2] have already been called. Because of this you must make sure any output channel fn writes on is flushed. Also note that exceptions raised by user code in the interactive toplevel are not passed to this function as they are caught by the toplevel itself. If fn raises an exception, both the exceptions passed to fn and raised by fn will be printed with their respective backtrace. Since: 4.02 Manipulation of backtrace information ===================================== These functions are used to traverse the slots of a raw backtrace and extract information from them in a programmer-friendly format. << type backtrace_slot >> The abstract type backtrace_slot represents a single slot of a backtrace. Since: 4.02 << val backtrace_slots : raw_backtrace -> backtrace_slot array option >> Returns the slots of a raw backtrace, or None if none of them contain useful information. In the return array, the slot at index 0 corresponds to the most recent function call, raise, or primitive get_backtrace call in the trace. Some possible reasons for returning None are as follow: - none of the slots in the trace come from modules compiled with debug information (-g) - the program is a bytecode program that has not been linked with debug information enabled (ocamlc -g) Since: 4.02 << val backtrace_slots_of_raw_entry : raw_backtrace_entry -> backtrace_slot array option >> Returns the slots of a single raw backtrace entry, or None if this entry lacks debug information. Slots are returned in the same order as backtrace_slots: the slot at index 0 is the most recent call, raise, or primitive, and subsequent slots represent callers. Since: 4.12 << type location = { filename : string ; line_number : int ; start_char : int ; end_char : int ; end_line : int ; >> Since: 5.2 << end_col : int ; >> Since: 5.2 << } >> The type of location information found in backtraces. start_char and end_char are positions relative to the beginning of line_number. end_col is relative to the beginning of end_line. Since: 4.02 << module Slot : >>  sig << type t = Printexc.backtrace_slot >> << val is_raise : t -> bool >> is_raise slot is true when slot refers to a raising point in the code, and false when it comes from a simple function call. Since: 4.02 << val is_inline : t -> bool >> is_inline slot is true when slot refers to a call that got inlined by the compiler, and false when it comes from any other context. Since: 4.04 << val location : t -> Printexc.location option >> location slot returns the location information of the slot, if available, and None otherwise. Some possible reasons for failing to return a location are as follow: - the slot corresponds to a compiler-inserted raise - the slot corresponds to a part of the program that has not been compiled with debug information (-g) Since: 4.02 << val name : t -> string option >> name slot returns the name of the function or definition enclosing the location referred to by the slot. name slot returns None if the name is unavailable, which may happen for the same reasons as location returning None. Since: 4.11 << val format : int -> t -> string option >> format pos slot returns the string representation of slot as raw_backtrace_to_string would format it, assuming it is the pos-th element of the backtrace: the 0-th element is pretty-printed differently than the others. Whole-backtrace printing functions also skip some uninformative slots; in that case, format pos slot returns None. Since: 4.02  end Since: 4.02 Raw backtrace slots =================== << type raw_backtrace_slot >> This type is used to iterate over the slots of a raw_backtrace. For most purposes, backtrace_slots_of_raw_entry is easier to use. Like raw_backtrace_entry, values of this type are process-specific and must absolutely not be marshalled, and are unsafe to use for this reason (marshalling them may not fail, but un-marshalling and using the result will result in undefined behavior). Elements of this type can still be compared and hashed: when two elements are equal, then they represent the same source location (the converse is not necessarily true in presence of inlining, for example). Since: 4.02 << val raw_backtrace_length : raw_backtrace -> int >> raw_backtrace_length bckt returns the number of slots in the backtrace bckt. Since: 4.02 << val get_raw_backtrace_slot : raw_backtrace -> int -> raw_backtrace_slot >> get_raw_backtrace_slot bckt pos returns the slot in position pos in the backtrace bckt. Since: 4.02 << val convert_raw_backtrace_slot : raw_backtrace_slot -> backtrace_slot >> Extracts the user-friendly backtrace_slot from a low-level raw_backtrace_slot. Since: 4.02 << val get_raw_backtrace_next_slot : raw_backtrace_slot -> raw_backtrace_slot option >> get_raw_backtrace_next_slot slot returns the next slot inlined, if any. Sample code to iterate over all frames (inlined and non-inlined): << (* Iterate over inlined frames *) let rec iter_raw_backtrace_slot f slot = f slot; match get_raw_backtrace_next_slot slot with | None -> () | Some slot' -> iter_raw_backtrace_slot f slot' (* Iterate over stack frames *) let iter_raw_backtrace f bt = for i = 0 to raw_backtrace_length bt - 1 do iter_raw_backtrace_slot f (get_raw_backtrace_slot bt i) done >> Since: 4.04 Exception slots =============== << val exn_slot_id : exn -> int >> Printexc.exn_slot_id returns an integer which uniquely identifies the constructor used to create the exception value exn (in the current runtime). Since: 4.02 << val exn_slot_name : exn -> string >> Printexc.exn_slot_name exn returns the internal name of the constructor used to create the exception value exn. Since: 4.02 29.44 Module Printf : Formatted output functions. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* << val fprintf : out_channel -> ('a, out_channel, unit) format -> 'a >> fprintf outchan format arg1 ... argN formats the arguments arg1 to argN according to the format string format, and outputs the resulting string on the channel outchan. The format string is a character string which contains two types of objects: plain characters, which are simply copied to the output channel, and conversion specifications, each of which causes conversion and printing of arguments. Conversion specifications have the following form: % [flags] [width] [.precision] type In short, a conversion specification consists in the % character, followed by optional modifiers and a type which is made of one or two characters. The types and their meanings are: - d, i: convert an integer argument to signed decimal. The flag # adds underscores to large values for readability. - u, n, l, L, or N: convert an integer argument to unsigned decimal. Warning: n, l, L, and N are used for scanf, and should not be used for printf. The flag # adds underscores to large values for readability. - x: convert an integer argument to unsigned hexadecimal, using lowercase letters. The flag # adds a 0x prefix to non zero values. - X: convert an integer argument to unsigned hexadecimal, using uppercase letters. The flag # adds a 0X prefix to non zero values. - o: convert an integer argument to unsigned octal. The flag # adds a 0 prefix to non zero values. - s: insert a string argument. - S: convert a string argument to OCaml syntax (double quotes, escapes). - c: insert a character argument. - C: convert a character argument to OCaml syntax (single quotes, escapes). - f: convert a floating-point argument to decimal notation, in the style dddd.ddd. - F: convert a floating-point argument to OCaml syntax (dddd. or dddd.ddd or d.ddd e+-dd). Converts to hexadecimal with the # flag (see h). - e or E: convert a floating-point argument to decimal notation, in the style d.ddd e+-dd (mantissa and exponent). - g or G: convert a floating-point argument to decimal notation, in style f or e, E (whichever is more compact). Moreover, any trailing zeros are removed from the fractional part of the result and the decimal-point character is removed if there is no fractional part remaining. - h or H: convert a floating-point argument to hexadecimal notation, in the style 0xh.hhhh p+-dd (hexadecimal mantissa, exponent in decimal and denotes a power of 2). - B: convert a boolean argument to the string true or false - b: convert a boolean argument (deprecated; do not use in new programs). - ld, li, lu, lx, lX, lo: convert an int32 argument to the format specified by the second letter (decimal, hexadecimal, etc). - nd, ni, nu, nx, nX, no: convert a nativeint argument to the format specified by the second letter. - Ld, Li, Lu, Lx, LX, Lo: convert an int64 argument to the format specified by the second letter. - a: user-defined printer. Take two arguments and apply the first one to outchan (the current output channel) and to the second argument. The first argument must therefore have type out_channel -> 'b -> unit and the second 'b. The output produced by the function is inserted in the output of fprintf at the current point. - t: same as %a, but take only one argument (with type out_channel -> unit) and apply it to outchan. - { fmt %}: convert a format string argument to its type digest. The argument must have the same type as the internal format string fmt. - ( fmt %): format string substitution. Take a format string argument and substitute it to the internal format string fmt to print following arguments. The argument must have the same type as the internal format string fmt. - !: take no argument and flush the output. - %: take no argument and output one % character. - @: take no argument and output one @ character. - ,: take no argument and output nothing: a no-op delimiter for conversion specifications. The optional flags are: - -: left-justify the output (default is right justification). - 0: for numerical conversions, pad with zeroes instead of spaces. - +: for signed numerical conversions, prefix number with a + sign if positive. - space: for signed numerical conversions, prefix number with a space if positive. - #: request an alternate formatting style for the integer types and the floating-point type F. The optional width is an integer indicating the minimal width of the result. For instance, %6d prints an integer, prefixing it with spaces to fill at least 6 characters. The optional precision is a dot . followed by an integer indicating how many digits follow the decimal point in the %f, %e, %E, %h, and %H conversions or the maximum number of significant digits to appear for the %F, %g and %G conversions. For instance, %.4f prints a float with 4 fractional digits. The integer in a width or precision can also be specified as *, in which case an extra integer argument is taken to specify the corresponding width or precision. This integer argument precedes immediately the argument to print. For instance, %.*f prints a float with as many fractional digits as the value of the argument given before the float. << val printf : ('a, out_channel, unit) format -> 'a >> Same as Printf.fprintf[29.44], but output on stdout. << val eprintf : ('a, out_channel, unit) format -> 'a >> Same as Printf.fprintf[29.44], but output on stderr. << val sprintf : ('a, unit, string) format -> 'a >> Same as Printf.fprintf[29.44], but instead of printing on an output channel, return a string containing the result of formatting the arguments. << val bprintf : Buffer.t -> ('a, Buffer.t, unit) format -> 'a >> Same as Printf.fprintf[29.44], but instead of printing on an output channel, append the formatted arguments to the given extensible buffer (see module Buffer[29.7]). << val ifprintf : 'b -> ('a, 'b, 'c, unit) format4 -> 'a >> Same as Printf.fprintf[29.44], but does not print anything. Useful to ignore some material when conditionally printing. Since: 3.10 << val ibprintf : Buffer.t -> ('a, Buffer.t, unit) format -> 'a >> Same as Printf.bprintf[29.44], but does not print anything. Useful to ignore some material when conditionally printing. Since: 4.11 Formatted output functions with continuations. << val kfprintf : (out_channel -> 'd) -> out_channel -> ('a, out_channel, unit, 'd) format4 -> 'a >> Same as fprintf, but instead of returning immediately, passes the out channel to its first argument at the end of printing. Since: 3.09 << val ikfprintf : ('b -> 'd) -> 'b -> ('a, 'b, 'c, 'd) format4 -> 'a >> Same as kfprintf above, but does not print anything. Useful to ignore some material when conditionally printing. Since: 4.01 << val ksprintf : (string -> 'd) -> ('a, unit, string, 'd) format4 -> 'a >> Same as sprintf above, but instead of returning the string, passes it to the first argument. Since: 3.09 << val kbprintf : (Buffer.t -> 'd) -> Buffer.t -> ('a, Buffer.t, unit, 'd) format4 -> 'a >> Same as bprintf, but instead of returning immediately, passes the buffer to its first argument at the end of printing. Since: 3.10 << val ikbprintf : (Buffer.t -> 'd) -> Buffer.t -> ('a, Buffer.t, unit, 'd) format4 -> 'a >> Same as kbprintf above, but does not print anything. Useful to ignore some material when conditionally printing. Since: 4.11 Deprecated << val kprintf : (string -> 'b) -> ('a, unit, string, 'b) format4 -> 'a >> Deprecated. Use Printf.ksprintf instead.A deprecated synonym for ksprintf. 29.45 Module Queue : First-in first-out queues. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module implements queues (FIFOs), with in-place modification. See the example section[29.4] below. Alert unsynchronized_access. Unsynchronized accesses to queues are a programming error. Unsynchronized accesses Unsynchronized accesses to a queue may lead to an invalid queue state. Thus, concurrent accesses to queues must be synchronized (for instance with a Mutex.t[29.37]). << type !'a t >> The type of queues containing elements of type 'a. << exception Empty >> Raised when Queue.take[29.45] or Queue.peek[29.45] is applied to an empty queue. << val create : unit -> 'a t >> Return a new queue, initially empty. << val add : 'a -> 'a t -> unit >> add x q adds the element x at the end of the queue q. << val push : 'a -> 'a t -> unit >> push is a synonym for add. << val take : 'a t -> 'a >> take q removes and returns the first element in queue q, or raises Queue.Empty[29.45] if the queue is empty. << val take_opt : 'a t -> 'a option >> take_opt q removes and returns the first element in queue q, or returns None if the queue is empty. Since: 4.08 << val pop : 'a t -> 'a >> pop is a synonym for take. << val peek : 'a t -> 'a >> peek q returns the first element in queue q, without removing it from the queue, or raises Queue.Empty[29.45] if the queue is empty. << val peek_opt : 'a t -> 'a option >> peek_opt q returns the first element in queue q, without removing it from the queue, or returns None if the queue is empty. Since: 4.08 << val top : 'a t -> 'a >> top is a synonym for peek. << val clear : 'a t -> unit >> Discard all elements from a queue. << val copy : 'a t -> 'a t >> Return a copy of the given queue. << val is_empty : 'a t -> bool >> Return true if the given queue is empty, false otherwise. << val length : 'a t -> int >> Return the number of elements in a queue. << val iter : ('a -> unit) -> 'a t -> unit >> iter f q applies f in turn to all elements of q, from the least recently entered to the most recently entered. The queue itself is unchanged. << val fold : ('acc -> 'a -> 'acc) -> 'acc -> 'a t -> 'acc >> fold f accu q is equivalent to List.fold_left f accu l, where l is the list of q’s elements. The queue remains unchanged. << val transfer : 'a t -> 'a t -> unit >> transfer q1 q2 adds all of q1’s elements at the end of the queue q2, then clears q1. It is equivalent to the sequence iter (fun x -> add x q2) q1; clear q1, but runs in constant time. Iterators ========= << val to_seq : 'a t -> 'a Seq.t >> Iterate on the queue, in front-to-back order. The behavior is not specified if the queue is modified during the iteration. Since: 4.07 << val add_seq : 'a t -> 'a Seq.t -> unit >> Add the elements from a sequence to the end of the queue. Since: 4.07 << val of_seq : 'a Seq.t -> 'a t >> Create a queue from a sequence. Since: 4.07 Examples ======== Basic Example ------------- A basic example: << # let q = Queue.create () val q : '_weak1 Queue.t = # Queue.push 1 q; Queue.push 2 q; Queue.push 3 q - : unit = () # Queue.length q - : int = 3 # Queue.pop q - : int = 1 # Queue.pop q - : int = 2 # Queue.pop q - : int = 3 # Queue.pop q Exception: Stdlib.Queue.Empty. >> Search Through a Graph ---------------------- For a more elaborate example, a classic algorithmic use of queues is to implement a BFS (breadth-first search) through a graph. << type graph = { edges: (int, int list) Hashtbl.t } (* Search in graph [g] using BFS, starting from node [start]. It returns the first node that satisfies [p], or [None] if no node reachable from [start] satisfies [p]. *) let search_for ~(g:graph) ~(start:int) (p:int -> bool) : int option = let to_explore = Queue.create() in let explored = Hashtbl.create 16 in Queue.push start to_explore; let rec loop () = if Queue.is_empty to_explore then None else (* node to explore *) let node = Queue.pop to_explore in explore_node node and explore_node node = if not (Hashtbl.mem explored node) then ( if p node then Some node (* found *) else ( Hashtbl.add explored node (); let children = Hashtbl.find_opt g.edges node |> Option.value ~default:[] in List.iter (fun child -> Queue.push child to_explore) children; loop() ) ) else loop() in loop() (* a sample graph *) let my_graph: graph = let edges = List.to_seq [ 1, [2;3]; 2, [10; 11]; 3, [4;5]; 5, [100]; 11, [0; 20]; ] |> Hashtbl.of_seq in {edges} # search_for ~g:my_graph ~start:1 (fun x -> x = 30) - : int option = None # search_for ~g:my_graph ~start:1 (fun x -> x >= 15) - : int option = Some 20 # search_for ~g:my_graph ~start:1 (fun x -> x >= 50) - : int option = Some 100 >> 29.46 Module Random : Pseudo-random number generators (PRNG). *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* With multiple domains, each domain has its own generator that evolves independently of the generators of other domains. When a domain is created, its generator is initialized by splitting the state of the generator associated with the parent domain. In contrast, all threads within a domain share the same domain-local generator. Independent generators can be created with the Random.split[29.46] function and used with the functions from the Random.State[29.46] module. Before 5.0 Random value generation used a different algorithm. This affects all the functions in this module which return random values. Basic functions =============== << val init : int -> unit >> Initialize the domain-local generator, using the argument as a seed. The same seed will always yield the same sequence of numbers. << val full_init : int array -> unit >> Same as Random.init[29.46] but takes more data as seed. << val self_init : unit -> unit >> Initialize the domain-local generator with a random seed chosen in a system-dependent way. If /dev/urandom is available on the host machine, it is used to provide a highly random initial seed. Otherwise, a less random seed is computed from system parameters (current time, process IDs, domain-local state). << val bits : unit -> int >> Return 30 random bits in a nonnegative integer. << val int : int -> int >> Random.int bound returns a random integer between 0 (inclusive) and bound (exclusive). bound must be greater than 0 and less than 2^30. Raises Invalid_argument if bound <= 0 or bound >= 2^30. << val full_int : int -> int >> Random.full_int bound returns a random integer between 0 (inclusive) and bound (exclusive). bound may be any positive integer. If bound is less than 2^31, then Random.full_int bound yields identical output across systems with varying int sizes. If bound is less than 2^30, then Random.full_int bound is equal to Random.int[29.46] bound. If bound is at least 2^30 (on 64-bit systems, or non-standard environments such as JavaScript), then Random.full_int returns a value whereas Random.int[29.46] raises Invalid_argument[28.2]. Since: 4.13 Raises Invalid_argument if bound <= 0. << val int_in_range : min:int -> max:int -> int >> Random.int_in_range ~min ~max returns a random integer between min (inclusive) and max (inclusive). Both min and max are allowed to be negative; min must be less than or equal to max. If both bounds fit in 32-bit signed integers (that is, if -2^31 <= min and max < 2^31), then int_in_range yields identical output across systems with varying int sizes. Since: 5.2 Raises Invalid_argument if min > max. << val int32 : Int32.t -> Int32.t >> Random.int32 bound returns a random integer between 0 (inclusive) and bound (exclusive). bound must be greater than 0. Raises Invalid_argument if bound <= 0. << val int32_in_range : min:int32 -> max:int32 -> int32 >> Random.int32_in_range ~min ~max returns a random integer between min (inclusive) and max (inclusive). Both min and max are allowed to be negative; min must be less than or equal to max. Since: 5.2 Raises Invalid_argument if min > max. << val nativeint : Nativeint.t -> Nativeint.t >> Random.nativeint bound returns a random integer between 0 (inclusive) and bound (exclusive). bound must be greater than 0. Raises Invalid_argument if bound <= 0. << val nativeint_in_range : min:nativeint -> max:nativeint -> nativeint >> Random.nativeint_in_range ~min ~max returns a random integer between min (inclusive) and max (inclusive). Both min and max are allowed to be negative; min must be less than or equal to max. Since: 5.2 Raises Invalid_argument if min > max. << val int64 : Int64.t -> Int64.t >> Random.int64 bound returns a random integer between 0 (inclusive) and bound (exclusive). bound must be greater than 0. Raises Invalid_argument if bound <= 0. << val int64_in_range : min:int64 -> max:int64 -> int64 >> Random.int64_in_range ~min ~max returns a random integer between min (inclusive) and max (inclusive). Both min and max are allowed to be negative; min must be less than or equal to max. Since: 5.2 Raises Invalid_argument if min > max. << val float : float -> float >> Random.float bound returns a random floating-point number between 0 and bound (inclusive). If bound is negative, the result is negative or zero. If bound is 0, the result is 0. << val bool : unit -> bool >> Random.bool () returns true or false with probability 0.5 each. << val bits32 : unit -> Int32.t >> Random.bits32 () returns 32 random bits as an integer between Int32.min_int[29.28] and Int32.max_int[29.28]. Since: 4.14 << val bits64 : unit -> Int64.t >> Random.bits64 () returns 64 random bits as an integer between Int64.min_int[29.29] and Int64.max_int[29.29]. Since: 4.14 << val nativebits : unit -> Nativeint.t >> Random.nativebits () returns 32 or 64 random bits (depending on the bit width of the platform) as an integer between Nativeint.min_int[29.38] and Nativeint.max_int[29.38]. Since: 4.14 Advanced functions ================== The functions from module Random.State[29.46] manipulate the current state of the random generator explicitly. This allows using one or several deterministic PRNGs, even in a multi-threaded program, without interference from other parts of the program. << module State : >>  sig << type t >> The type of PRNG states. << val make : int array -> t >> Create a new state and initialize it with the given seed. << val make_self_init : unit -> t >> Create a new state and initialize it with a random seed chosen in a system-dependent way. The seed is obtained as described in Random.self_init[29.46]. << val copy : t -> t >> Return a copy of the given state. << val bits : t -> int >> << val int : t -> int -> int >> << val full_int : t -> int -> int >> << val int_in_range : t -> min:int -> max:int -> int >> << val int32 : t -> Int32.t -> Int32.t >> << val int32_in_range : t -> min:int32 -> max:int32 -> int32 >> << val nativeint : t -> Nativeint.t -> Nativeint.t >> << val nativeint_in_range : t -> min:nativeint -> max:nativeint -> nativeint >> << val int64 : t -> Int64.t -> Int64.t >> << val int64_in_range : t -> min:int64 -> max:int64 -> int64 >> << val float : t -> float -> float >> << val bool : t -> bool >> << val bits32 : t -> Int32.t >> << val bits64 : t -> Int64.t >> << val nativebits : t -> Nativeint.t >> These functions are the same as the basic functions, except that they use (and update) the given PRNG state instead of the default one. << val split : t -> t >> Draw a fresh PRNG state from the given PRNG state. (The given PRNG state is modified.) The new PRNG is statistically independent from the given PRNG. Data can be drawn from both PRNGs, in any order, without risk of correlation. Both PRNGs can be split later, arbitrarily many times. Since: 5.0 << val to_binary_string : t -> string >> Serializes the PRNG state into an immutable sequence of bytes. See Random.State.of_binary_string[29.46] for deserialization. The string type is intended here for serialization only, the encoding is not human-readable and may not be printable. Note that the serialization format may differ across OCaml versions. Since: 5.1 << val of_binary_string : string -> t >> Deserializes a byte sequence obtained by calling Random.State.to_binary_string[29.46]. The resulting PRNG state will produce the same random numbers as the state that was passed as input to Random.State.to_binary_string[29.46]. Since: 5.1 Raises Failure if the input is not in the expected format. Note that the serialization format may differ across OCaml versions. Unlike the functions provided by the Marshal[29.35] module, this function either produces a valid state or fails cleanly with a Failure exception. It can be safely used on user-provided, untrusted inputs.  end << val get_state : unit -> State.t >> get_state() returns a fresh copy of the current state of the domain-local generator (which is used by the basic functions). << val set_state : State.t -> unit >> set_state s updates the current state of the domain-local generator (which is used by the basic functions) by copying the state s into it. << val split : unit -> State.t >> Draw a fresh PRNG state from the current state of the domain-local generator used by the default functions. (The state of the domain-local generator is modified.) See Random.State.split[29.46]. Since: 5.0 29.47 Module Result : Result values. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Result values handle computation results and errors in an explicit and declarative manner without resorting to exceptions. Since: 4.08 Results ======= << type ('a, 'e) t = ('a, 'e) result = | Ok of 'a | Error of 'e >> The type for result values. Either a value Ok v or an error Error e. << val ok : 'a -> ('a, 'e) result >> ok v is Ok v. << val error : 'e -> ('a, 'e) result >> error e is Error e. << val value : ('a, 'e) result -> default:'a -> 'a >> value r ~default is v if r is Ok v and default otherwise. << val get_ok : ('a, 'e) result -> 'a >> get_ok r is v if r is Ok v and raise otherwise. Raises Invalid_argument if r is Error _. << val get_error : ('a, 'e) result -> 'e >> get_error r is e if r is Error e and raise otherwise. Raises Invalid_argument if r is Ok _. << val bind : ('a, 'e) result -> ('a -> ('b, 'e) result) -> ('b, 'e) result >> bind r f is f v if r is Ok v and r if r is Error _. << val join : (('a, 'e) result, 'e) result -> ('a, 'e) result >> join rr is r if rr is Ok r and rr if rr is Error _. << val map : ('a -> 'b) -> ('a, 'e) result -> ('b, 'e) result >> map f r is Ok (f v) if r is Ok v and r if r is Error _. << val map_error : ('e -> 'f) -> ('a, 'e) result -> ('a, 'f) result >> map_error f r is Error (f e) if r is Error e and r if r is Ok _. << val fold : ok:('a -> 'c) -> error:('e -> 'c) -> ('a, 'e) result -> 'c >> fold ~ok ~error r is ok v if r is Ok v and error e if r is Error e. << val iter : ('a -> unit) -> ('a, 'e) result -> unit >> iter f r is f v if r is Ok v and () otherwise. << val iter_error : ('e -> unit) -> ('a, 'e) result -> unit >> iter_error f r is f e if r is Error e and () otherwise. Predicates and comparisons ========================== << val is_ok : ('a, 'e) result -> bool >> is_ok r is true if and only if r is Ok _. << val is_error : ('a, 'e) result -> bool >> is_error r is true if and only if r is Error _. << val equal : ok:('a -> 'a -> bool) -> error:('e -> 'e -> bool) -> ('a, 'e) result -> ('a, 'e) result -> bool >> equal ~ok ~error r0 r1 tests equality of r0 and r1 using ok and error to respectively compare values wrapped by Ok _ and Error _. << val compare : ok:('a -> 'a -> int) -> error:('e -> 'e -> int) -> ('a, 'e) result -> ('a, 'e) result -> int >> compare ~ok ~error r0 r1 totally orders r0 and r1 using ok and error to respectively compare values wrapped by Ok _ and Error _. Ok _ values are smaller than Error _ values. Converting ========== << val to_option : ('a, 'e) result -> 'a option >> to_option r is r as an option, mapping Ok v to Some v and Error _ to None. << val to_list : ('a, 'e) result -> 'a list >> to_list r is [v] if r is Ok v and [] otherwise. << val to_seq : ('a, 'e) result -> 'a Seq.t >> to_seq r is r as a sequence. Ok v is the singleton sequence containing v and Error _ is the empty sequence. 29.48 Module Scanf : Formatted input functions. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Alert unsynchronized_access. Unsynchronized accesses to Scanning.in_channel are a programming error. Introduction ============ Functional input with format strings ------------------------------------ The module Scanf[29.48] provides formatted input functions or scanners. The formatted input functions can read from any kind of input, including strings, files, or anything that can return characters. The more general source of characters is named a formatted input channel (or scanning buffer) and has type Scanf.Scanning.in_channel[29.48]. The more general formatted input function reads from any scanning buffer and is named bscanf. Generally speaking, the formatted input functions have 3 arguments: - the first argument is a source of characters for the input, - the second argument is a format string that specifies the values to read, - the third argument is a receiver function that is applied to the values read. Hence, a typical call to the formatted input function Scanf.bscanf[29.48] is bscanf ic fmt f, where: - ic is a source of characters (typically a formatted input channel with type Scanf.Scanning.in_channel[29.48]), - fmt is a format string (the same format strings as those used to print material with module Printf[29.44] or Format[29.22]), - f is a function that has as many arguments as the number of values to read in the input according to fmt. A simple example ---------------- As suggested above, the expression bscanf ic "%d" f reads a decimal integer n from the source of characters ic and returns f n. For instance, - if we use stdin as the source of characters (Scanf.Scanning.stdin[29.48] is the predefined formatted input channel that reads from standard input), - if we define the receiver f as let f x = x + 1, then bscanf Scanning.stdin "%d" f reads an integer n from the standard input and returns f n (that is n + 1). Thus, if we evaluate bscanf stdin "%d" f, and then enter 41 at the keyboard, the result we get is 42. Formatted input as a functional feature --------------------------------------- The OCaml scanning facility is reminiscent of the corresponding C feature. However, it is also largely different, simpler, and yet more powerful: the formatted input functions are higher-order functionals and the parameter passing mechanism is just the regular function application not the variable assignment based mechanism which is typical for formatted input in imperative languages; the OCaml format strings also feature useful additions to easily define complex tokens; as expected within a functional programming language, the formatted input functions also support polymorphism, in particular arbitrary interaction with polymorphic user-defined scanners. Furthermore, the OCaml formatted input facility is fully type-checked at compile time. Unsynchronized accesses Unsynchronized accesses to a Scanf.Scanning.in_channel[29.48] may lead to an invalid Scanf.Scanning.in_channel[29.48] state. Thus, concurrent accesses to Scanf.Scanning.in_channel[29.48]s must be synchronized (for instance with a Mutex.t[29.37]). Formatted input channel ======================= << module Scanning : >>  sig << type in_channel >> The notion of input channel for the Scanf[29.48] module: those channels provide all the machinery necessary to read from any source of characters, including a in_channel[28.2] value. A Scanf.Scanning.in_channel value is also called a formatted input channel or equivalently a scanning buffer. The type Scanf.Scanning.scanbuf[29.48] below is an alias for Scanning.in_channel. Note that a Scanning.in_channel is not concurrency-safe: concurrent use may produce arbitrary values or exceptions. Since: 3.12 << type scanbuf = in_channel >> The type of scanning buffers. A scanning buffer is the source from which a formatted input function gets characters. The scanning buffer holds the current state of the scan, plus a function to get the next char from the input, and a token buffer to store the string matched so far. Note: a scanning action may often require to examine one character in advance; when this ’lookahead’ character does not belong to the token read, it is stored back in the scanning buffer and becomes the next character yet to be read. << val stdin : in_channel >> The standard input notion for the Scanf[29.48] module. Scanning.stdin is the Scanf.Scanning.in_channel[29.48] formatted input channel attached to stdin[28.2]. Note: in the interactive system, when input is read from stdin[28.2], the newline character that triggers evaluation is part of the input; thus, the scanning specifications must properly skip this additional newline character (for instance, simply add a '\n' as the last character of the format string). Since: 3.12 << type file_name = string >> A convenient alias to designate a file name. Since: 4.00 << val open_in : file_name -> in_channel >> Scanning.open_in fname returns a Scanf.Scanning.in_channel[29.48] formatted input channel for bufferized reading in text mode from file fname. Note: open_in returns a formatted input channel that efficiently reads characters in large chunks; in contrast, from_channel below returns formatted input channels that must read one character at a time, leading to a much slower scanning rate. Since: 3.12 << val open_in_bin : file_name -> in_channel >> Scanning.open_in_bin fname returns a Scanf.Scanning.in_channel[29.48] formatted input channel for bufferized reading in binary mode from file fname. Since: 3.12 << val close_in : in_channel -> unit >> Closes the in_channel[28.2] associated with the given Scanf.Scanning.in_channel[29.48] formatted input channel. Since: 3.12 << val from_file : file_name -> in_channel >> An alias for Scanf.Scanning.open_in[29.48] above. << val from_file_bin : string -> in_channel >> An alias for Scanf.Scanning.open_in_bin[29.48] above. << val from_string : string -> in_channel >> Scanning.from_string s returns a Scanf.Scanning.in_channel[29.48] formatted input channel which reads from the given string. Reading starts from the first character in the string. The end-of-input condition is set when the end of the string is reached. << val from_function : (unit -> char) -> in_channel >> Scanning.from_function f returns a Scanf.Scanning.in_channel[29.48] formatted input channel with the given function as its reading method. When scanning needs one more character, the given function is called. When the function has no more character to provide, it must signal an end-of-input condition by raising the exception End_of_file. << val from_channel : in_channel -> in_channel >> Scanning.from_channel ic returns a Scanf.Scanning.in_channel[29.48] formatted input channel which reads from the regular in_channel[28.2] input channel ic argument. Reading starts at current reading position of ic. << val end_of_input : in_channel -> bool >> Scanning.end_of_input ic tests the end-of-input condition of the given Scanf.Scanning.in_channel[29.48] formatted input channel. << val beginning_of_input : in_channel -> bool >> Scanning.beginning_of_input ic tests the beginning of input condition of the given Scanf.Scanning.in_channel[29.48] formatted input channel. << val name_of_input : in_channel -> string >> Scanning.name_of_input ic returns the name of the character source for the given Scanf.Scanning.in_channel[29.48] formatted input channel. Since: 3.09  end Type of formatted input functions ================================= << type ('a, 'b, 'c, 'd) scanner = ('a, Scanning.in_channel, 'b, 'c, 'a -> 'd, 'd) format6 -> 'c >> The type of formatted input scanners: ('a, 'b, 'c, 'd) scanner is the type of a formatted input function that reads from some formatted input channel according to some format string; more precisely, if scan is some formatted input function, then scan ic fmt f applies f to all the arguments specified by format string fmt, when scan has read those arguments from the Scanf.Scanning.in_channel[29.48] formatted input channel ic. For instance, the Scanf.scanf[29.48] function below has type ('a, 'b, 'c, 'd) scanner, since it is a formatted input function that reads from Scanf.Scanning.stdin[29.48]: scanf fmt f applies f to the arguments specified by fmt, reading those arguments from stdin[28.2] as expected. If the format fmt has some %r indications, the corresponding formatted input functions must be provided before receiver function f. For instance, if read_elem is an input function for values of type t, then bscanf ic "%r;" read_elem f reads a value v of type t followed by a ';' character, and returns f v. Since: 3.10 << type ('a, 'b, 'c, 'd) scanner_opt = ('a, Scanning.in_channel, 'b, 'c, 'a -> 'd option, 'd) format6 -> 'c >> << exception Scan_failure of string >> When the input can not be read according to the format string specification, formatted input functions typically raise exception Scan_failure. The general formatted input function ==================================== << val bscanf : Scanning.in_channel -> ('a, 'b, 'c, 'd) scanner >> bscanf ic fmt r1 ... rN f reads characters from the Scanf.Scanning.in_channel[29.48] formatted input channel ic and converts them to values according to format string fmt. As a final step, receiver function f is applied to the values read and gives the result of the bscanf call. For instance, if f is the function fun s i -> i + 1, then Scanf.sscanf "x = 1" "%s = %i" f returns 2. Arguments r1 to rN are user-defined input functions that read the argument corresponding to the %r conversions specified in the format string. << val bscanf_opt : Scanning.in_channel -> ('a, 'b, 'c, 'd) scanner_opt >> Same as Scanf.bscanf[29.48], but returns None in case of scanning failure. Since: 5.0 Format string description ========================= The format string is a character string which contains three types of objects: - plain characters, which are simply matched with the characters of the input (with a special case for space and line feed, see [29.48]), - conversion specifications, each of which causes reading and conversion of one argument for the function f (see [29.48]), - scanning indications to specify boundaries of tokens (see scanning [29.48]). The space character in format strings ------------------------------------- As mentioned above, a plain character in the format string is just matched with the next character of the input; however, two characters are special exceptions to this rule: the space character (' ' or ASCII code 32) and the line feed character ('\n' or ASCII code 10). A space does not match a single space character, but any amount of ’whitespace’ in the input. More precisely, a space inside the format string matches any number of tab, space, line feed and carriage return characters. Similarly, a line feed character in the format string matches either a single line feed or a carriage return followed by a line feed. Matching any amount of whitespace, a space in the format string also matches no amount of whitespace at all; hence, the call bscanf ib "Price = %d $" (fun p -> p) succeeds and returns 1 when reading an input with various whitespace in it, such as Price = 1 $, Price = 1 $, or even Price=1$. Conversion specifications in format strings ------------------------------------------- Conversion specifications consist in the % character, followed by an optional flag, an optional field width, and followed by one or two conversion characters. The conversion characters and their meanings are: - d: reads an optionally signed decimal integer (0-9+). - i: reads an optionally signed integer (usual input conventions for decimal (0-9+), hexadecimal (0x[0-9a-f]+ and 0X[0-9A-F]+), octal (0o[0-7]+), and binary (0b[0-1]+) notations are understood). - u: reads an unsigned decimal integer. - x or X: reads an unsigned hexadecimal integer ([0-9a-fA-F]+). - o: reads an unsigned octal integer ([0-7]+). - s: reads a string argument that spreads as much as possible, until the following bounding condition holds: - a whitespace has been found (see [29.48]), - a scanning indication (see scanning [29.48]) has been encountered, - the end-of-input has been reached. Hence, this conversion always succeeds: it returns an empty string if the bounding condition holds when the scan begins. - S: reads a delimited string argument (delimiters and special escaped characters follow the lexical conventions of OCaml). - c: reads a single character. To test the current input character without reading it, specify a null field width, i.e. use specification %0c. Raise Invalid_argument, if the field width specification is greater than 1. - C: reads a single delimited character (delimiters and special escaped characters follow the lexical conventions of OCaml). - f, e, E, g, G: reads an optionally signed floating-point number in decimal notation, in the style dddd.ddd e/E+-dd. - h, H: reads an optionally signed floating-point number in hexadecimal notation. - F: reads a floating point number according to the lexical conventions of OCaml (hence the decimal point is mandatory if the exponent part is not mentioned). - B: reads a boolean argument (true or false). - b: reads a boolean argument (for backward compatibility; do not use in new programs). - ld, li, lu, lx, lX, lo: reads an int32 argument to the format specified by the second letter for regular integers. - nd, ni, nu, nx, nX, no: reads a nativeint argument to the format specified by the second letter for regular integers. - Ld, Li, Lu, Lx, LX, Lo: reads an int64 argument to the format specified by the second letter for regular integers. - [ range ]: reads characters that matches one of the characters mentioned in the range of characters range (or not mentioned in it, if the range starts with ^). Reads a string that can be empty, if the next input character does not match the range. The set of characters from c1 to c2 (inclusively) is denoted by c1-c2. Hence, %[0-9] returns a string representing a decimal number or an empty string if no decimal digit is found; similarly, %[0-9a-f] returns a string of hexadecimal digits. If a closing bracket appears in a range, it must occur as the first character of the range (or just after the ^ in case of range negation); hence []] matches a ] character and [^]] matches any character that is not ]. Use %% and %@ to include a % or a @ in a range. - r: user-defined reader. Takes the next ri formatted input function and applies it to the scanning buffer ib to read the next argument. The input function ri must therefore have type Scanning.in_channel -> 'a and the argument read has type 'a. - { fmt %}: reads a format string argument. The format string read must have the same type as the format string specification fmt. For instance, "%{ %i %}" reads any format string that can read a value of type int; hence, if s is the string "fmt:\"number is %u\"", then Scanf.sscanf s "fmt: %{%i%}" succeeds and returns the format string "number is %u". - ( fmt %): scanning sub-format substitution. Reads a format string rf in the input, then goes on scanning with rf instead of scanning with fmt. The format string rf must have the same type as the format string specification fmt that it replaces. For instance, "%( %i %)" reads any format string that can read a value of type int. The conversion returns the format string read rf, and then a value read using rf. Hence, if s is the string "\"%4d\"1234.00", then Scanf.sscanf s "%(%i%)" (fun fmt i -> fmt, i) evaluates to ("%4d", 1234). This behaviour is not mere format substitution, since the conversion returns the format string read as additional argument. If you need pure format substitution, use special flag _ to discard the extraneous argument: conversion %_( fmt %) reads a format string rf and then behaves the same as format string rf. Hence, if s is the string "\"%4d\"1234.00", then Scanf.sscanf s "%_(%i%)" is simply equivalent to Scanf.sscanf "1234.00" "%4d". - l: returns the number of lines read so far. - n: returns the number of characters read so far. - N or L: returns the number of tokens read so far. - !: matches the end of input condition. - %: matches one % character in the input. - @: matches one @ character in the input. - ,: does nothing. Following the % character that introduces a conversion, there may be the special flag _: the conversion that follows occurs as usual, but the resulting value is discarded. For instance, if f is the function fun i -> i + 1, and s is the string "x = 1", then Scanf.sscanf s "%_s = %i" f returns 2. The field width is composed of an optional integer literal indicating the maximal width of the token to read. For instance, %6d reads an integer, having at most 6 decimal digits; %4f reads a float with at most 4 characters; and %8[\000-\255] returns the next 8 characters (or all the characters still available, if fewer than 8 characters are available in the input). Notes: - as mentioned above, a %s conversion always succeeds, even if there is nothing to read in the input: in this case, it simply returns "". - in addition to the relevant digits, '_' characters may appear inside numbers (this is reminiscent to the usual OCaml lexical conventions). If stricter scanning is desired, use the range conversion facility instead of the number conversions. - the scanf facility is not intended for heavy duty lexical analysis and parsing. If it appears not expressive enough for your needs, several alternative exists: regular expressions (module Str[32.1]), stream parsers, ocamllex-generated lexers, ocamlyacc-generated parsers. Scanning indications in format strings -------------------------------------- Scanning indications appear just after the string conversions %s and %[ range ] to delimit the end of the token. A scanning indication is introduced by a @ character, followed by some plain character c. It means that the string token should end just before the next matching c (which is skipped). If no c character is encountered, the string token spreads as much as possible. For instance, "%s@\t" reads a string up to the next tab character or to the end of input. If a @ character appears anywhere else in the format string, it is treated as a plain character. Note: - As usual in format strings, % and @ characters must be escaped using %% and %@; this rule still holds within range specifications and scanning indications. For instance, format "%s@%%" reads a string up to the next % character, and format "%s@%@" reads a string up to the next @. - The scanning indications introduce slight differences in the syntax of Scanf[29.48] format strings, compared to those used for the Printf[29.44] module. However, the scanning indications are similar to those used in the Format[29.22] module; hence, when producing formatted text to be scanned by Scanf.bscanf[29.48], it is wise to use printing functions from the Format[29.22] module (or, if you need to use functions from Printf[29.44], banish or carefully double check the format strings that contain '@' characters). Exceptions during scanning -------------------------- Scanners may raise the following exceptions when the input cannot be read according to the format string: - Raise Scanf.Scan_failure[29.48] if the input does not match the format. - Raise Failure if a conversion to a number is not possible. - Raise End_of_file if the end of input is encountered while some more characters are needed to read the current conversion specification. - Raise Invalid_argument if the format string is invalid. Note: - as a consequence, scanning a %s conversion never raises exception End_of_file: if the end of input is reached the conversion succeeds and simply returns the characters read so far, or "" if none were ever read. Specialised formatted input functions ===================================== << val sscanf : string -> ('a, 'b, 'c, 'd) scanner >> Same as Scanf.bscanf[29.48], but reads from the given string. << val sscanf_opt : string -> ('a, 'b, 'c, 'd) scanner_opt >> Same as Scanf.sscanf[29.48], but returns None in case of scanning failure. Since: 5.0 << val scanf : ('a, 'b, 'c, 'd) scanner >> Same as Scanf.bscanf[29.48], but reads from the predefined formatted input channel Scanf.Scanning.stdin[29.48] that is connected to stdin[28.2]. << val scanf_opt : ('a, 'b, 'c, 'd) scanner_opt >> Same as Scanf.scanf[29.48], but returns None in case of scanning failure. Since: 5.0 << val kscanf : Scanning.in_channel -> (Scanning.in_channel -> exn -> 'd) -> ('a, 'b, 'c, 'd) scanner >> Same as Scanf.bscanf[29.48], but takes an additional function argument ef that is called in case of error: if the scanning process or some conversion fails, the scanning function aborts and calls the error handling function ef with the formatted input channel and the exception that aborted the scanning process as arguments. << val ksscanf : string -> (Scanning.in_channel -> exn -> 'd) -> ('a, 'b, 'c, 'd) scanner >> Same as Scanf.kscanf[29.48] but reads from the given string. Since: 4.02 Reading format strings from input ================================= << val bscanf_format : Scanning.in_channel -> ('a, 'b, 'c, 'd, 'e, 'f) format6 -> (('a, 'b, 'c, 'd, 'e, 'f) format6 -> 'g) -> 'g >> bscanf_format ic fmt f reads a format string token from the formatted input channel ic, according to the given format string fmt, and applies f to the resulting format string value. Since: 3.09 Raises Scan_failure if the format string value read does not have the same type as fmt. << val sscanf_format : string -> ('a, 'b, 'c, 'd, 'e, 'f) format6 -> (('a, 'b, 'c, 'd, 'e, 'f) format6 -> 'g) -> 'g >> Same as Scanf.bscanf_format[29.48], but reads from the given string. Since: 3.09 << val format_from_string : string -> ('a, 'b, 'c, 'd, 'e, 'f) format6 -> ('a, 'b, 'c, 'd, 'e, 'f) format6 >> format_from_string s fmt converts a string argument to a format string, according to the given format string fmt. Since: 3.10 Raises Scan_failure if s, considered as a format string, does not have the same type as fmt. << val unescaped : string -> string >> unescaped s return a copy of s with escape sequences (according to the lexical conventions of OCaml) replaced by their corresponding special characters. More precisely, Scanf.unescaped has the following property: for all string s, Scanf.unescaped (String.escaped s) = s. Always return a copy of the argument, even if there is no escape sequence in the argument. Since: 4.00 Raises Scan_failure if s is not properly escaped (i.e. s has invalid escape sequences or special characters that are not properly escaped). For instance, Scanf.unescaped "\"" will fail. 29.49 Module Seq : Sequences. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* A sequence of type 'a Seq.t can be thought of as a delayed list, that is, a list whose elements are computed only when they are demanded by a consumer. This allows sequences to be produced and transformed lazily (one element at a time) rather than eagerly (all elements at once). This also allows constructing conceptually infinite sequences. The type 'a Seq.t is defined as a synonym for unit -> 'a Seq.node. This is a function type: therefore, it is opaque. The consumer can query a sequence in order to request the next element (if there is one), but cannot otherwise inspect the sequence in any way. Because it is opaque, the type 'a Seq.t does not reveal whether a sequence is: - persistent, which means that the sequence can be used as many times as desired, producing the same elements every time, just like an immutable list; or - ephemeral, which means that the sequence is not persistent. Querying an ephemeral sequence might have an observable side effect, such as incrementing a mutable counter. As a common special case, an ephemeral sequence can be affine, which means that it must be queried at most once. It also does not reveal whether the elements of the sequence are: - pre-computed and stored in memory, which means that querying the sequence is cheap; - computed when first demanded and then stored in memory, which means that querying the sequence once can be expensive, but querying the same sequence again is cheap; or - re-computed every time they are demanded, which may or may not be cheap. It is up to the programmer to keep these distinctions in mind so as to understand the time and space requirements of sequences. For the sake of simplicity, most of the documentation that follows is written under the implicit assumption that the sequences at hand are persistent. We normally do not point out when or how many times each function is invoked, because that would be too verbose. For instance, in the description of map, we write: "if xs is the sequence x0; x1; ... then map f xs is the sequence f x0; f x1; ...". If we wished to be more explicit, we could point out that the transformation takes place on demand: that is, the elements of map f xs are computed only when they are demanded. In other words, the definition let ys = map f xs terminates immediately and does not invoke f. The function call f x0 takes place only when the first element of ys is demanded, via the function call ys(). Furthermore, calling ys() twice causes f x0 to be called twice as well. If one wishes for f to be applied at most once to each element of xs, even in scenarios where ys is queried more than once, then one should use let ys = memoize (map f xs). As a general rule, the functions that build sequences, such as map, filter, scan, take, etc., produce sequences whose elements are computed only on demand. The functions that eagerly consume sequences, such as is_empty, find, length, iter, fold_left, etc., are the functions that force computation to take place. When possible, we recommend using sequences rather than dispensers (functions of type unit -> 'a option that produce elements upon demand). Whereas sequences can be persistent or ephemeral, dispensers are always ephemeral, and are typically more difficult to work with than sequences. Two conversion functions, Seq.to_dispenser[29.49] and Seq.of_dispenser[29.49], are provided. Since: 4.07 << type 'a t = unit -> 'a node >> A sequence xs of type 'a t is a delayed list of elements of type 'a. Such a sequence is queried by performing a function application xs(). This function application returns a node, allowing the caller to determine whether the sequence is empty or nonempty, and in the latter case, to obtain its head and tail. << type 'a node = | Nil | Cons of 'a * 'a t >> A node is either Nil, which means that the sequence is empty, or Cons (x, xs), which means that x is the first element of the sequence and that xs is the remainder of the sequence. Consuming sequences =================== The functions in this section consume their argument, a sequence, either partially or completely: - is_empty and uncons consume the sequence down to depth 1. That is, they demand the first argument of the sequence, if there is one. - iter, fold_left, length, etc., consume the sequence all the way to its end. They terminate only if the sequence is finite. - for_all, exists, find, etc. consume the sequence down to a certain depth, which is a priori unpredictable. Similarly, among the functions that consume two sequences, one can distinguish two groups: - iter2 and fold_left2 consume both sequences all the way to the end, provided the sequences have the same length. - for_all2, exists2, equal, compare consume the sequences down to a certain depth, which is a priori unpredictable. The functions that consume two sequences can be applied to two sequences of distinct lengths: in that case, the excess elements in the longer sequence are ignored. (It may be the case that one excess element is demanded, even though this element is not used.) None of the functions in this section is lazy. These functions are consumers: they force some computation to take place. << val is_empty : 'a t -> bool >> is_empty xs determines whether the sequence xs is empty. It is recommended that the sequence xs be persistent. Indeed, is_empty xs demands the head of the sequence xs, so, if xs is ephemeral, it may be the case that xs cannot be used any more after this call has taken place. Since: 4.14 << val uncons : 'a t -> ('a * 'a t) option >> If xs is empty, then uncons xs is None. If xs is nonempty, then uncons xs is Some (x, ys) where x is the head of the sequence and ys its tail. Since: 4.14 << val length : 'a t -> int >> length xs is the length of the sequence xs. The sequence xs must be finite. Since: 4.14 << val iter : ('a -> unit) -> 'a t -> unit >> iter f xs invokes f x successively for every element x of the sequence xs, from left to right. It terminates only if the sequence xs is finite. << val fold_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a t -> 'acc >> fold_left f _ xs invokes f _ x successively for every element x of the sequence xs, from left to right. An accumulator of type 'a is threaded through the calls to f. It terminates only if the sequence xs is finite. << val iteri : (int -> 'a -> unit) -> 'a t -> unit >> iteri f xs invokes f i x successively for every element x located at index i in the sequence xs. It terminates only if the sequence xs is finite. iteri f xs is equivalent to iter (fun (i, x) -> f i x) (zip (ints 0) xs). Since: 4.14 << val fold_lefti : ('acc -> int -> 'a -> 'acc) -> 'acc -> 'a t -> 'acc >> fold_lefti f _ xs invokes f _ i x successively for every element x located at index i of the sequence xs. An accumulator of type 'b is threaded through the calls to f. It terminates only if the sequence xs is finite. fold_lefti f accu xs is equivalent to fold_left (fun accu (i, x) -> f accu i x) accu (zip (ints 0) xs). Since: 4.14 << val for_all : ('a -> bool) -> 'a t -> bool >> for_all p xs determines whether all elements x of the sequence xs satisfy p x. The sequence xs must be finite. Since: 4.14 << val exists : ('a -> bool) -> 'a t -> bool >> exists xs p determines whether at least one element x of the sequence xs satisfies p x. The sequence xs must be finite. Since: 4.14 << val find : ('a -> bool) -> 'a t -> 'a option >> find p xs returns Some x, where x is the first element of the sequence xs that satisfies p x, if there is such an element. It returns None if there is no such element. The sequence xs must be finite. Since: 4.14 << val find_index : ('a -> bool) -> 'a t -> int option >> find_index p xs returns Some i, where i is the index of the first element of the sequence xs that satisfies p x, if there is such an element. It returns None if there is no such element. The sequence xs must be finite. Since: 5.1 << val find_map : ('a -> 'b option) -> 'a t -> 'b option >> find_map f xs returns Some y, where x is the first element of the sequence xs such that f x = Some _, if there is such an element, and where y is defined by f x = Some y. It returns None if there is no such element. The sequence xs must be finite. Since: 4.14 << val find_mapi : (int -> 'a -> 'b option) -> 'a t -> 'b option >> Same as find_map, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument. The sequence xs must be finite. Since: 5.1 << val iter2 : ('a -> 'b -> unit) -> 'a t -> 'b t -> unit >> iter2 f xs ys invokes f x y successively for every pair (x, y) of elements drawn synchronously from the sequences xs and ys. If the sequences xs and ys have different lengths, then iteration stops as soon as one sequence is exhausted; the excess elements in the other sequence are ignored. Iteration terminates only if at least one of the sequences xs and ys is finite. iter2 f xs ys is equivalent to iter (fun (x, y) -> f x y) (zip xs ys). Since: 4.14 << val fold_left2 : ('acc -> 'a -> 'b -> 'acc) -> 'acc -> 'a t -> 'b t -> 'acc >> fold_left2 f _ xs ys invokes f _ x y successively for every pair (x, y) of elements drawn synchronously from the sequences xs and ys. An accumulator of type 'a is threaded through the calls to f. If the sequences xs and ys have different lengths, then iteration stops as soon as one sequence is exhausted; the excess elements in the other sequence are ignored. Iteration terminates only if at least one of the sequences xs and ys is finite. fold_left2 f accu xs ys is equivalent to fold_left (fun accu (x, y) -> f accu x y) (zip xs ys). Since: 4.14 << val for_all2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool >> for_all2 p xs ys determines whether all pairs (x, y) of elements drawn synchronously from the sequences xs and ys satisfy p x y. If the sequences xs and ys have different lengths, then iteration stops as soon as one sequence is exhausted; the excess elements in the other sequence are ignored. In particular, if xs or ys is empty, then for_all2 p xs ys is true. This is where for_all2 and equal differ: equal eq xs ys can be true only if xs and ys have the same length. At least one of the sequences xs and ys must be finite. for_all2 p xs ys is equivalent to for_all (fun b -> b) (map2 p xs ys). Since: 4.14 << val exists2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool >> exists2 p xs ys determines whether some pair (x, y) of elements drawn synchronously from the sequences xs and ys satisfies p x y. If the sequences xs and ys have different lengths, then iteration must stop as soon as one sequence is exhausted; the excess elements in the other sequence are ignored. At least one of the sequences xs and ys must be finite. exists2 p xs ys is equivalent to exists (fun b -> b) (map2 p xs ys). Since: 4.14 << val equal : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool >> Provided the function eq defines an equality on elements, equal eq xs ys determines whether the sequences xs and ys are pointwise equal. At least one of the sequences xs and ys must be finite. Since: 4.14 << val compare : ('a -> 'b -> int) -> 'a t -> 'b t -> int >> Provided the function cmp defines a preorder on elements, compare cmp xs ys compares the sequences xs and ys according to the lexicographic preorder. For more details on comparison functions, see Array.sort[29.2]. At least one of the sequences xs and ys must be finite. Since: 4.14 Constructing sequences ====================== The functions in this section are lazy: that is, they return sequences whose elements are computed only when demanded. << val empty : 'a t >> empty is the empty sequence. It has no elements. Its length is 0. << val return : 'a -> 'a t >> return x is the sequence whose sole element is x. Its length is 1. << val cons : 'a -> 'a t -> 'a t >> cons x xs is the sequence that begins with the element x, followed with the sequence xs. Writing cons (f()) xs causes the function call f() to take place immediately. For this call to be delayed until the sequence is queried, one must instead write (fun () -> Cons(f(), xs)). Since: 4.11 << val init : int -> (int -> 'a) -> 'a t >> init n f is the sequence f 0; f 1; ...; f (n-1). n must be nonnegative. If desired, the infinite sequence f 0; f 1; ... can be defined as map f (ints 0). Since: 4.14 Raises Invalid_argument if n is negative. << val unfold : ('b -> ('a * 'b) option) -> 'b -> 'a t >> unfold constructs a sequence out of a step function and an initial state. If f u is None then unfold f u is the empty sequence. If f u is Some (x, u') then unfold f u is the nonempty sequence cons x (unfold f u'). For example, unfold (function [] -> None | h :: t -> Some (h, t)) l is equivalent to List.to_seq l. Since: 4.11 << val repeat : 'a -> 'a t >> repeat x is the infinite sequence where the element x is repeated indefinitely. repeat x is equivalent to cycle (return x). Since: 4.14 << val forever : (unit -> 'a) -> 'a t >> forever f is an infinite sequence where every element is produced (on demand) by the function call f(). For instance, forever Random.bool is an infinite sequence of random bits. forever f is equivalent to map f (repeat ()). Since: 4.14 << val cycle : 'a t -> 'a t >> cycle xs is the infinite sequence that consists of an infinite number of repetitions of the sequence xs. If xs is an empty sequence, then cycle xs is empty as well. Consuming (a prefix of) the sequence cycle xs once can cause the sequence xs to be consumed more than once. Therefore, xs must be persistent. Since: 4.14 << val iterate : ('a -> 'a) -> 'a -> 'a t >> iterate f x is the infinite sequence whose elements are x, f x, f (f x), and so on. In other words, it is the orbit of the function f, starting at x. Since: 4.14 Transforming sequences ====================== The functions in this section are lazy: that is, they return sequences whose elements are computed only when demanded. << val map : ('a -> 'b) -> 'a t -> 'b t >> map f xs is the image of the sequence xs through the transformation f. If xs is the sequence x0; x1; ... then map f xs is the sequence f x0; f x1; .... << val mapi : (int -> 'a -> 'b) -> 'a t -> 'b t >> mapi is analogous to map, but applies the function f to an index and an element. mapi f xs is equivalent to map2 f (ints 0) xs. Since: 4.14 << val filter : ('a -> bool) -> 'a t -> 'a t >> filter p xs is the sequence of the elements x of xs that satisfy p x. In other words, filter p xs is the sequence xs, deprived of the elements x such that p x is false. << val filter_map : ('a -> 'b option) -> 'a t -> 'b t >> filter_map f xs is the sequence of the elements y such that f x = Some y, where x ranges over xs. filter_map f xs is equivalent to map Option.get (filter Option.is_some (map f xs)). << val scan : ('b -> 'a -> 'b) -> 'b -> 'a t -> 'b t >> If xs is a sequence [x0; x1; x2; ...], then scan f a0 xs is a sequence of accumulators [a0; a1; a2; ...] where a1 is f a0 x0, a2 is f a1 x1, and so on. Thus, scan f a0 xs is conceptually related to fold_left f a0 xs. However, instead of performing an eager iteration and immediately returning the final accumulator, it returns a sequence of accumulators. For instance, scan (+) 0 transforms a sequence of integers into the sequence of its partial sums. If xs has length n then scan f a0 xs has length n+1. Since: 4.14 << val take : int -> 'a t -> 'a t >> take n xs is the sequence of the first n elements of xs. If xs has fewer than n elements, then take n xs is equivalent to xs. n must be nonnegative. Since: 4.14 Raises Invalid_argument if n is negative. << val drop : int -> 'a t -> 'a t >> drop n xs is the sequence xs, deprived of its first n elements. If xs has fewer than n elements, then drop n xs is empty. n must be nonnegative. drop is lazy: the first n+1 elements of the sequence xs are demanded only when the first element of drop n xs is demanded. For this reason, drop 1 xs is not equivalent to tail xs, which queries xs immediately. Since: 4.14 Raises Invalid_argument if n is negative. << val take_while : ('a -> bool) -> 'a t -> 'a t >> take_while p xs is the longest prefix of the sequence xs where every element x satisfies p x. Since: 4.14 << val drop_while : ('a -> bool) -> 'a t -> 'a t >> drop_while p xs is the sequence xs, deprived of the prefix take_while p xs. Since: 4.14 << val group : ('a -> 'a -> bool) -> 'a t -> 'a t t >> Provided the function eq defines an equality on elements, group eq xs is the sequence of the maximal runs of adjacent duplicate elements of the sequence xs. Every element of group eq xs is a nonempty sequence of equal elements. The concatenation concat (group eq xs) is equal to xs. Consuming group eq xs, and consuming the sequences that it contains, can cause xs to be consumed more than once. Therefore, xs must be persistent. Since: 4.14 << val memoize : 'a t -> 'a t >> The sequence memoize xs has the same elements as the sequence xs. Regardless of whether xs is ephemeral or persistent, memoize xs is persistent: even if it is queried several times, xs is queried at most once. The construction of the sequence memoize xs internally relies on suspensions provided by the module Lazy[29.30]. These suspensions are not thread-safe. Therefore, the sequence memoize xs must not be queried by multiple threads concurrently. Since: 4.14 << exception Forced_twice >> This exception is raised when a sequence returned by Seq.once[29.49] (or a suffix of it) is queried more than once. Since: 4.14 << val once : 'a t -> 'a t >> The sequence once xs has the same elements as the sequence xs. Regardless of whether xs is ephemeral or persistent, once xs is an ephemeral sequence: it can be queried at most once. If it (or a suffix of it) is queried more than once, then the exception Forced_twice is raised. This can be useful, while debugging or testing, to ensure that a sequence is consumed at most once. Since: 4.14 Raises Forced_twice if once xs, or a suffix of it, is queried more than once. << val transpose : 'a t t -> 'a t t >> If xss is a matrix (a sequence of rows), then transpose xss is the sequence of the columns of the matrix xss. The rows of the matrix xss are not required to have the same length. The matrix xss is not required to be finite (in either direction). The matrix xss must be persistent. Since: 4.14 Combining sequences =================== << val append : 'a t -> 'a t -> 'a t >> append xs ys is the concatenation of the sequences xs and ys. Its elements are the elements of xs, followed by the elements of ys. Since: 4.11 << val concat : 'a t t -> 'a t >> If xss is a sequence of sequences, then concat xss is its concatenation. If xss is the sequence xs0; xs1; ... then concat xss is the sequence xs0 @ xs1 @ .... Since: 4.13 << val flat_map : ('a -> 'b t) -> 'a t -> 'b t >> flat_map f xs is equivalent to concat (map f xs). << val concat_map : ('a -> 'b t) -> 'a t -> 'b t >> concat_map f xs is equivalent to concat (map f xs). concat_map is an alias for flat_map. Since: 4.13 << val zip : 'a t -> 'b t -> ('a * 'b) t >> zip xs ys is the sequence of pairs (x, y) drawn synchronously from the sequences xs and ys. If the sequences xs and ys have different lengths, then the sequence ends as soon as one sequence is exhausted; the excess elements in the other sequence are ignored. zip xs ys is equivalent to map2 (fun a b -> (a, b)) xs ys. Since: 4.14 << val map2 : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t >> map2 f xs ys is the sequence of the elements f x y, where the pairs (x, y) are drawn synchronously from the sequences xs and ys. If the sequences xs and ys have different lengths, then the sequence ends as soon as one sequence is exhausted; the excess elements in the other sequence are ignored. map2 f xs ys is equivalent to map (fun (x, y) -> f x y) (zip xs ys). Since: 4.14 << val interleave : 'a t -> 'a t -> 'a t >> interleave xs ys is the sequence that begins with the first element of xs, continues with the first element of ys, and so on. When one of the sequences xs and ys is exhausted, interleave xs ys continues with the rest of the other sequence. Since: 4.14 << val sorted_merge : ('a -> 'a -> int) -> 'a t -> 'a t -> 'a t >> If the sequences xs and ys are sorted according to the total preorder cmp, then sorted_merge cmp xs ys is the sorted sequence obtained by merging the sequences xs and ys. For more details on comparison functions, see Array.sort[29.2]. Since: 4.14 << val product : 'a t -> 'b t -> ('a * 'b) t >> product xs ys is the Cartesian product of the sequences xs and ys. For every element x of xs and for every element y of ys, the pair (x, y) appears once as an element of product xs ys. The order in which the pairs appear is unspecified. The sequences xs and ys are not required to be finite. The sequences xs and ys must be persistent. Since: 4.14 << val map_product : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t >> The sequence map_product f xs ys is the image through f of the Cartesian product of the sequences xs and ys. For every element x of xs and for every element y of ys, the element f x y appears once as an element of map_product f xs ys. The order in which these elements appear is unspecified. The sequences xs and ys are not required to be finite. The sequences xs and ys must be persistent. map_product f xs ys is equivalent to map (fun (x, y) -> f x y) (product xs ys). Since: 4.14 Splitting a sequence into two sequences ======================================= << val unzip : ('a * 'b) t -> 'a t * 'b t >> unzip transforms a sequence of pairs into a pair of sequences. unzip xs is equivalent to (map fst xs, map snd xs). Querying either of the sequences returned by unzip xs causes xs to be queried. Therefore, querying both of them causes xs to be queried twice. Thus, xs must be persistent and cheap. If that is not the case, use unzip (memoize xs). Since: 4.14 << val split : ('a * 'b) t -> 'a t * 'b t >> split is an alias for unzip. Since: 4.14 << val partition_map : ('a -> ('b, 'c) Either.t) -> 'a t -> 'b t * 'c t >> partition_map f xs returns a pair of sequences (ys, zs), where: - ys is the sequence of the elements y such that f x = Left y, where x ranges over xs; - zs is the sequence of the elements z such that f x = Right z, where x ranges over xs. partition_map f xs is equivalent to a pair of filter_map Either.find_left (map f xs) and filter_map Either.find_right (map f xs). Querying either of the sequences returned by partition_map f xs causes xs to be queried. Therefore, querying both of them causes xs to be queried twice. Thus, xs must be persistent and cheap. If that is not the case, use partition_map f (memoize xs). Since: 4.14 << val partition : ('a -> bool) -> 'a t -> 'a t * 'a t >> partition p xs returns a pair of the subsequence of the elements of xs that satisfy p and the subsequence of the elements of xs that do not satisfy p. partition p xs is equivalent to filter p xs, filter (fun x -> not (p x)) xs. Consuming both of the sequences returned by partition p xs causes xs to be consumed twice and causes the function f to be applied twice to each element of the list. Therefore, f should be pure and cheap. Furthermore, xs should be persistent and cheap. If that is not the case, use partition p (memoize xs). Since: 4.14 Converting between sequences and dispensers =========================================== A dispenser is a representation of a sequence as a function of type unit -> 'a option. Every time this function is invoked, it returns the next element of the sequence. When there are no more elements, it returns None. A dispenser has mutable internal state, therefore is ephemeral: the sequence that it represents can be consumed at most once. << val of_dispenser : (unit -> 'a option) -> 'a t >> of_dispenser it is the sequence of the elements produced by the dispenser it. It is an ephemeral sequence: it can be consumed at most once. If a persistent sequence is needed, use memoize (of_dispenser it). Since: 4.14 << val to_dispenser : 'a t -> unit -> 'a option >> to_dispenser xs is a fresh dispenser on the sequence xs. This dispenser has mutable internal state, which is not protected by a lock; so, it must not be used by several threads concurrently. Since: 4.14 Sequences of integers ===================== << val ints : int -> int t >> ints i is the infinite sequence of the integers beginning at i and counting up. Since: 4.14 29.50 Module Set : Sets over ordered types. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* This module implements the set data structure, given a total ordering function over the set elements. All operations over sets are purely applicative (no side-effects). The implementation uses balanced binary trees, and is therefore reasonably efficient: insertion and membership take time logarithmic in the size of the set, for instance. The Set.Make[29.50] functor constructs implementations for any type, given a compare function. For instance: << module IntPairs = struct type t = int * int let compare (x0,y0) (x1,y1) = match Stdlib.compare x0 x1 with 0 -> Stdlib.compare y0 y1 | c -> c end module PairsSet = Set.Make(IntPairs) let m = PairsSet.(empty |> add (2,3) |> add (5,7) |> add (11,13)) >> This creates a new module PairsSet, with a new type PairsSet.t of sets of int * int. << module type OrderedType = >>  sig << type t >> The type of the set elements. << val compare : t -> t -> int >> A total ordering function over the set elements. This is a two-argument function f such that f e1 e2 is zero if the elements e1 and e2 are equal, f e1 e2 is strictly negative if e1 is smaller than e2, and f e1 e2 is strictly positive if e1 is greater than e2. Example: a suitable ordering function is the generic structural comparison function compare[28.2].  end Input signature of the functor Set.Make[29.50]. << module type S = >>  sig Sets ==== << type elt >> The type of the set elements. << type t >> The type of sets. << val empty : t >> The empty set. << val add : elt -> t -> t >> add x s returns a set containing all elements of s, plus x. If x was already in s, s is returned unchanged (the result of the function is then physically equal to s). Before 4.03 Physical equality was not ensured. << val singleton : elt -> t >> singleton x returns the one-element set containing only x. << val remove : elt -> t -> t >> remove x s returns a set containing all elements of s, except x. If x was not in s, s is returned unchanged (the result of the function is then physically equal to s). Before 4.03 Physical equality was not ensured. << val union : t -> t -> t >> Set union. << val inter : t -> t -> t >> Set intersection. << val disjoint : t -> t -> bool >> Test if two sets are disjoint. Since: 4.08 << val diff : t -> t -> t >> Set difference: diff s1 s2 contains the elements of s1 that are not in s2. << val cardinal : t -> int >> Return the number of elements of a set. Elements ======== << val elements : t -> elt list >> Return the list of all elements of the given set. The returned list is sorted in increasing order with respect to the ordering Ord.compare, where Ord is the argument given to Set.Make[29.50]. << val min_elt : t -> elt >> Return the smallest element of the given set (with respect to the Ord.compare ordering), or raise Not_found if the set is empty. << val min_elt_opt : t -> elt option >> Return the smallest element of the given set (with respect to the Ord.compare ordering), or None if the set is empty. Since: 4.05 << val max_elt : t -> elt >> Same as Set.S.min_elt[29.50], but returns the largest element of the given set. << val max_elt_opt : t -> elt option >> Same as Set.S.min_elt_opt[29.50], but returns the largest element of the given set. Since: 4.05 << val choose : t -> elt >> Return one element of the given set, or raise Not_found if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets. << val choose_opt : t -> elt option >> Return one element of the given set, or None if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets. Since: 4.05 Searching ========= << val find : elt -> t -> elt >> find x s returns the element of s equal to x (according to Ord.compare), or raise Not_found if no such element exists. Since: 4.01 << val find_opt : elt -> t -> elt option >> find_opt x s returns the element of s equal to x (according to Ord.compare), or None if no such element exists. Since: 4.05 << val find_first : (elt -> bool) -> t -> elt >> find_first f s, where f is a monotonically increasing function, returns the lowest element e of s such that f e, or raises Not_found if no such element exists. For example, find_first (fun e -> Ord.compare e x >= 0) s will return the first element e of s where Ord.compare e x >= 0 (intuitively: e >= x), or raise Not_found if x is greater than any element of s. Since: 4.05 << val find_first_opt : (elt -> bool) -> t -> elt option >> find_first_opt f s, where f is a monotonically increasing function, returns an option containing the lowest element e of s such that f e, or None if no such element exists. Since: 4.05 << val find_last : (elt -> bool) -> t -> elt >> find_last f s, where f is a monotonically decreasing function, returns the highest element e of s such that f e, or raises Not_found if no such element exists. Since: 4.05 << val find_last_opt : (elt -> bool) -> t -> elt option >> find_last_opt f s, where f is a monotonically decreasing function, returns an option containing the highest element e of s such that f e, or None if no such element exists. Since: 4.05 Traversing ========== << val iter : (elt -> unit) -> t -> unit >> iter f s applies f in turn to all elements of s. The elements of s are presented to f in increasing order with respect to the ordering over the type of the elements. << val fold : (elt -> 'acc -> 'acc) -> t -> 'acc -> 'acc >> fold f s init computes (f xN ... (f x2 (f x1 init))...), where x1 ... xN are the elements of s, in increasing order. Transforming ============ << val map : (elt -> elt) -> t -> t >> map f s is the set whose elements are f a0,f a1... f aN, where a0,a1...aN are the elements of s. The elements are passed to f in increasing order with respect to the ordering over the type of the elements. If no element of s is changed by f, s is returned unchanged. (If each output of f is physically equal to its input, the returned set is physically equal to s.) Since: 4.04 << val filter : (elt -> bool) -> t -> t >> filter f s returns the set of all elements in s that satisfy predicate f. If f satisfies every element in s, s is returned unchanged (the result of the function is then physically equal to s). Before 4.03 Physical equality was not ensured. << val filter_map : (elt -> elt option) -> t -> t >> filter_map f s returns the set of all v such that f x = Some v for some element x of s. For example, << filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s >> is the set of halves of the even elements of s. If no element of s is changed or dropped by f (if f x = Some x for each element x), then s is returned unchanged: the result of the function is then physically equal to s. Since: 4.11 << val partition : (elt -> bool) -> t -> t * t >> partition f s returns a pair of sets (s1, s2), where s1 is the set of all the elements of s that satisfy the predicate f, and s2 is the set of all the elements of s that do not satisfy f. << val split : elt -> t -> t * bool * t >> split x s returns a triple (l, present, r), where l is the set of elements of s that are strictly less than x; r is the set of elements of s that are strictly greater than x; present is false if s contains no element equal to x, or true if s contains an element equal to x. Predicates and comparisons ========================== << val is_empty : t -> bool >> Test whether a set is empty or not. << val mem : elt -> t -> bool >> mem x s tests whether x belongs to the set s. << val equal : t -> t -> bool >> equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements. << val compare : t -> t -> int >> Total ordering between sets. Can be used as the ordering function for doing sets of sets. << val subset : t -> t -> bool >> subset s1 s2 tests whether the set s1 is a subset of the set s2. << val for_all : (elt -> bool) -> t -> bool >> for_all f s checks if all elements of the set satisfy the predicate f. << val exists : (elt -> bool) -> t -> bool >> exists f s checks if at least one element of the set satisfies the predicate f. Converting ========== << val to_list : t -> elt list >> to_list s is Set.S.elements[29.50] s. Since: 5.1 << val of_list : elt list -> t >> of_list l creates a set from a list of elements. This is usually more efficient than folding add over the list, except perhaps for lists with many duplicated elements. Since: 4.02 << val to_seq_from : elt -> t -> elt Seq.t >> to_seq_from x s iterates on a subset of the elements of s in ascending order, from x or above. Since: 4.07 << val to_seq : t -> elt Seq.t >> Iterate on the whole set, in ascending order Since: 4.07 << val to_rev_seq : t -> elt Seq.t >> Iterate on the whole set, in descending order Since: 4.12 << val add_seq : elt Seq.t -> t -> t >> Add the given elements to the set, in order. Since: 4.07 << val of_seq : elt Seq.t -> t >> Build a set from the given bindings Since: 4.07  end Output signature of the functor Set.Make[29.50]. << module Make : >> functor (Ord : OrderedType) -> S with type elt = Ord.t Functor building an implementation of the set structure given a totally ordered type. 29.51 Module Semaphore : Semaphores *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* A semaphore is a thread synchronization device that can be used to control access to a shared resource. Two flavors of semaphores are provided: counting semaphores and binary semaphores. Since: 4.12 Counting semaphores ------------------- A counting semaphore is a counter that can be accessed concurrently by several threads. The typical use is to synchronize producers and consumers of a resource by counting how many units of the resource are available. The two basic operations on semaphores are: - "release" (also called "V", "post", "up", and "signal"), which increments the value of the counter. This corresponds to producing one more unit of the shared resource and making it available to others. - "acquire" (also called "P", "wait", "down", and "pend"), which waits until the counter is greater than zero and decrements it. This corresponds to consuming one unit of the shared resource. << module Counting : >>  sig << type t >> The type of counting semaphores. << val make : int -> t >> make n returns a new counting semaphore, with initial value n. The initial value n must be nonnegative. Raises Invalid_argument if n < 0 << val release : t -> unit >> release s increments the value of semaphore s. If other threads are waiting on s, one of them is restarted. If the current value of s is equal to max_int, the value of the semaphore is unchanged and a Sys_error exception is raised to signal overflow. Raises Sys_error if the value of the semaphore would overflow max_int << val acquire : t -> unit >> acquire s blocks the calling thread until the value of semaphore s is not zero, then atomically decrements the value of s and returns. << val try_acquire : t -> bool >> try_acquire s immediately returns false if the value of semaphore s is zero. Otherwise, the value of s is atomically decremented and try_acquire s returns true. << val get_value : t -> int >> get_value s returns the current value of semaphore s. The current value can be modified at any time by concurrent Semaphore.Counting.release[29.51] and Semaphore.Counting.acquire[29.51] operations. Hence, the get_value operation is racy, and its result should only be used for debugging or informational messages.  end Binary semaphores ----------------- Binary semaphores are a variant of counting semaphores where semaphores can only take two values, 0 and 1. A binary semaphore can be used to control access to a single shared resource, with value 1 meaning "resource is available" and value 0 meaning "resource is unavailable". The "release" operation of a binary semaphore sets its value to 1, and "acquire" waits until the value is 1 and sets it to 0. A binary semaphore can be used instead of a mutex (see module Mutex[29.37]) when the mutex discipline (of unlocking the mutex from the thread that locked it) is too restrictive. The "acquire" operation corresponds to locking the mutex, and the "release" operation to unlocking it, but "release" can be performed in a thread different than the one that performed the "acquire". Likewise, it is safe to release a binary semaphore that is already available. << module Binary : >>  sig << type t >> The type of binary semaphores. << val make : bool -> t >> make b returns a new binary semaphore. If b is true, the initial value of the semaphore is 1, meaning "available". If b is false, the initial value of the semaphore is 0, meaning "unavailable". << val release : t -> unit >> release s sets the value of semaphore s to 1, putting it in the "available" state. If other threads are waiting on s, one of them is restarted. << val acquire : t -> unit >> acquire s blocks the calling thread until the semaphore s has value 1 (is available), then atomically sets it to 0 and returns. << val try_acquire : t -> bool >> try_acquire s immediately returns false if the semaphore s has value 0. If s has value 1, its value is atomically set to 0 and try_acquire s returns true.  end 29.52 Module Stack : Last-in first-out stacks. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This module implements stacks (LIFOs), with in-place modification. Alert unsynchronized_access. Unsynchronized accesses to stacks are a programming error. Unsynchronized accesses Unsynchronized accesses to a stack may lead to an invalid queue state. Thus, concurrent accesses to stacks must be synchronized (for instance with a Mutex.t[29.37]). << type !'a t >> The type of stacks containing elements of type 'a. << exception Empty >> Raised when Stack.pop[29.52] or Stack.top[29.52] is applied to an empty stack. << val create : unit -> 'a t >> Return a new stack, initially empty. << val push : 'a -> 'a t -> unit >> push x s adds the element x at the top of stack s. << val pop : 'a t -> 'a >> pop s removes and returns the topmost element in stack s, or raises Stack.Empty[29.52] if the stack is empty. << val pop_opt : 'a t -> 'a option >> pop_opt s removes and returns the topmost element in stack s, or returns None if the stack is empty. Since: 4.08 << val drop : 'a t -> unit >> drop s removes the topmost element in stack s, or raises Stack.Empty[29.52] if the stack is empty. Since: 5.1 << val top : 'a t -> 'a >> top s returns the topmost element in stack s, or raises Stack.Empty[29.52] if the stack is empty. << val top_opt : 'a t -> 'a option >> top_opt s returns the topmost element in stack s, or None if the stack is empty. Since: 4.08 << val clear : 'a t -> unit >> Discard all elements from a stack. << val copy : 'a t -> 'a t >> Return a copy of the given stack. << val is_empty : 'a t -> bool >> Return true if the given stack is empty, false otherwise. << val length : 'a t -> int >> Return the number of elements in a stack. Time complexity O(1) << val iter : ('a -> unit) -> 'a t -> unit >> iter f s applies f in turn to all elements of s, from the element at the top of the stack to the element at the bottom of the stack. The stack itself is unchanged. << val fold : ('acc -> 'a -> 'acc) -> 'acc -> 'a t -> 'acc >> fold f accu s is (f (... (f (f accu x1) x2) ...) xn) where x1 is the top of the stack, x2 the second element, and xn the bottom element. The stack is unchanged. Since: 4.03 Stacks and Sequences ==================== << val to_seq : 'a t -> 'a Seq.t >> Iterate on the stack, top to bottom. It is safe to modify the stack during iteration. Since: 4.07 << val add_seq : 'a t -> 'a Seq.t -> unit >> Add the elements from the sequence on the top of the stack. Since: 4.07 << val of_seq : 'a Seq.t -> 'a t >> Create a stack from the sequence. Since: 4.07 29.53 Module StdLabels : Standard labeled libraries. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This meta-module provides versions of the StdLabels.Array[29.53], StdLabels.Bytes[29.53], StdLabels.List[29.53] and StdLabels.String[29.53] modules where function arguments are systematically labeled. It is intended to be opened at the top of source files, as shown below. << open StdLabels let to_upper = String.map ~f:Char.uppercase_ascii let seq len = List.init ~f:(fun i -> i) ~len let everything = Array.create_matrix ~dimx:42 ~dimy:42 42 >> << module Array : >> ArrayLabels << module Bytes : >> BytesLabels << module List : >> ListLabels << module String : >> StringLabels 29.54 Module String : Strings. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= A string s of length n is an indexable and immutable sequence of n bytes. For historical reasons these bytes are referred to as characters. The semantics of string functions is defined in terms of indices and positions. These are depicted and described as follows. <> - An index i of s is an integer in the range [0;n-1]. It represents the ith byte (character) of s which can be accessed using the constant time string indexing operator s.[i]. - A position i of s is an integer in the range [0;n]. It represents either the point at the beginning of the string, or the point between two indices, or the point at the end of the string. The ith byte index is between position i and i+1. Two integers start and len are said to define a valid substring of s if len >= 0 and start, start+len are positions of s. Unicode text. Strings being arbitrary sequences of bytes, they can hold any kind of textual encoding. However the recommended encoding for storing Unicode text in OCaml strings is UTF-8. This is the encoding used by Unicode escapes in string literals. For example the string "\u{1F42B}" is the UTF-8 encoding of the Unicode character U+1F42B. Past mutability. Before OCaml 4.02, strings used to be modifiable in place like Bytes.t[29.8] mutable sequences of bytes. OCaml 4 had various compiler flags and configuration options to support the transition period from mutable to immutable strings. Those options are no longer available, and strings are now always immutable. The labeled version of this module can be used as described in the StdLabels[29.53] module. Strings ======= << type t = string >> The type for strings. << val make : int -> char -> string >> make n c is a string of length n with each index holding the character c. Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val init : int -> (int -> char) -> string >> init n f is a string of length n with index i holding the character f i (called in increasing index order). Since: 4.02 Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val empty : string >> The empty string. Since: 4.13 << val length : string -> int >> length s is the length (number of bytes/characters) of s. << val get : string -> int -> char >> get s i is the character at index i in s. This is the same as writing s.[i]. Raises Invalid_argument if i not an index of s. << val of_bytes : bytes -> string >> Return a new string that contains the same bytes as the given byte sequence. Since: 4.13 << val to_bytes : string -> bytes >> Return a new byte sequence that contains the same bytes as the given string. Since: 4.13 << val blit : string -> int -> bytes -> int -> int -> unit >> Same as Bytes.blit_string[29.8] which should be preferred. Concatenating ============= Note. The (^)[28.2] binary operator concatenates two strings. << val concat : string -> string list -> string >> concat sep ss concatenates the list of strings ss, inserting the separator string sep between each. Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val cat : string -> string -> string >> cat s1 s2 concatenates s1 and s2 (s1 ^ s2). Since: 4.13 Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. Predicates and comparisons ========================== << val equal : t -> t -> bool >> equal s0 s1 is true if and only if s0 and s1 are character-wise equal. Since: 4.03 (4.05 in StringLabels) << val compare : t -> t -> int >> compare s0 s1 sorts s0 and s1 in lexicographical order. compare behaves like compare[28.2] on strings but may be more efficient. << val starts_with : prefix:string -> string -> bool >> starts_with ~prefix s is true if and only if s starts with prefix. Since: 4.13 << val ends_with : suffix:string -> string -> bool >> ends_with ~suffix s is true if and only if s ends with suffix. Since: 4.13 << val contains_from : string -> int -> char -> bool >> contains_from s start c is true if and only if c appears in s after position start. Raises Invalid_argument if start is not a valid position in s. << val rcontains_from : string -> int -> char -> bool >> rcontains_from s stop c is true if and only if c appears in s before position stop+1. Raises Invalid_argument if stop < 0 or stop+1 is not a valid position in s. << val contains : string -> char -> bool >> contains s c is String.contains_from[29.54] s 0 c. Extracting substrings ===================== << val sub : string -> int -> int -> string >> sub s pos len is a string of length len, containing the substring of s that starts at position pos and has length len. Raises Invalid_argument if pos and len do not designate a valid substring of s. << val split_on_char : char -> string -> string list >> split_on_char sep s is the list of all (possibly empty) substrings of s that are delimited by the character sep. If s is empty, the result is the singleton list [""]. The function’s result is specified by the following invariants: - The list is not empty. - Concatenating its elements using sep as a separator returns a string equal to the input (concat (make 1 sep) (split_on_char sep s) = s). - No string in the result contains the sep character. Since: 4.04 (4.05 in StringLabels) Transforming ============ << val map : (char -> char) -> string -> string >> map f s is the string resulting from applying f to all the characters of s in increasing order. Since: 4.00 << val mapi : (int -> char -> char) -> string -> string >> mapi f s is like String.map[29.54] but the index of the character is also passed to f. Since: 4.02 << val fold_left : ('acc -> char -> 'acc) -> 'acc -> string -> 'acc >> fold_left f x s computes f (... (f (f x s.[0]) s.[1]) ...) s.[n-1], where n is the length of the string s. Since: 4.13 << val fold_right : (char -> 'acc -> 'acc) -> string -> 'acc -> 'acc >> fold_right f s x computes f s.[0] (f s.[1] ( ... (f s.[n-1] x) ...)), where n is the length of the string s. Since: 4.13 << val for_all : (char -> bool) -> string -> bool >> for_all p s checks if all characters in s satisfy the predicate p. Since: 4.13 << val exists : (char -> bool) -> string -> bool >> exists p s checks if at least one character of s satisfies the predicate p. Since: 4.13 << val trim : string -> string >> trim s is s without leading and trailing whitespace. Whitespace characters are: ' ', '\x0C' (form feed), '\n', '\r', and '\t'. Since: 4.00 << val escaped : string -> string >> escaped s is s with special characters represented by escape sequences, following the lexical conventions of OCaml. All characters outside the US-ASCII printable range [0x20;0x7E] are escaped, as well as backslash (0x2F) and double-quote (0x22). The function Scanf.unescaped[29.48] is a left inverse of escaped, i.e. Scanf.unescaped (escaped s) = s for any string s (unless escaped s fails). Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val uppercase_ascii : string -> string >> uppercase_ascii s is s with all lowercase letters translated to uppercase, using the US-ASCII character set. Since: 4.03 (4.05 in StringLabels) << val lowercase_ascii : string -> string >> lowercase_ascii s is s with all uppercase letters translated to lowercase, using the US-ASCII character set. Since: 4.03 (4.05 in StringLabels) << val capitalize_ascii : string -> string >> capitalize_ascii s is s with the first character set to uppercase, using the US-ASCII character set. Since: 4.03 (4.05 in StringLabels) << val uncapitalize_ascii : string -> string >> uncapitalize_ascii s is s with the first character set to lowercase, using the US-ASCII character set. Since: 4.03 (4.05 in StringLabels) Traversing ========== << val iter : (char -> unit) -> string -> unit >> iter f s applies function f in turn to all the characters of s. It is equivalent to f s.[0]; f s.[1]; ...; f s.[length s - 1]; (). << val iteri : (int -> char -> unit) -> string -> unit >> iteri is like String.iter[29.54], but the function is also given the corresponding character index. Since: 4.00 Searching ========= << val index_from : string -> int -> char -> int >> index_from s i c is the index of the first occurrence of c in s after position i. Raises - Not_found if c does not occur in s after position i. - Invalid_argument if i is not a valid position in s. << val index_from_opt : string -> int -> char -> int option >> index_from_opt s i c is the index of the first occurrence of c in s after position i (if any). Since: 4.05 Raises Invalid_argument if i is not a valid position in s. << val rindex_from : string -> int -> char -> int >> rindex_from s i c is the index of the last occurrence of c in s before position i+1. Raises - Not_found if c does not occur in s before position i+1. - Invalid_argument if i+1 is not a valid position in s. << val rindex_from_opt : string -> int -> char -> int option >> rindex_from_opt s i c is the index of the last occurrence of c in s before position i+1 (if any). Since: 4.05 Raises Invalid_argument if i+1 is not a valid position in s. << val index : string -> char -> int >> index s c is String.index_from[29.54] s 0 c. << val index_opt : string -> char -> int option >> index_opt s c is String.index_from_opt[29.54] s 0 c. Since: 4.05 << val rindex : string -> char -> int >> rindex s c is String.rindex_from[29.54] s (length s - 1) c. << val rindex_opt : string -> char -> int option >> rindex_opt s c is String.rindex_from_opt[29.54] s (length s - 1) c. Since: 4.05 Strings and Sequences ===================== << val to_seq : t -> char Seq.t >> to_seq s is a sequence made of the string’s characters in increasing order. In "unsafe-string" mode, modifications of the string during iteration will be reflected in the sequence. Since: 4.07 << val to_seqi : t -> (int * char) Seq.t >> to_seqi s is like String.to_seq[29.54] but also tuples the corresponding index. Since: 4.07 << val of_seq : char Seq.t -> t >> of_seq s is a string made of the sequence’s characters. Since: 4.07 UTF decoding and validations ============================ UTF-8 ----- << val get_utf_8_uchar : t -> int -> Uchar.utf_decode >> get_utf_8_uchar b i decodes an UTF-8 character at index i in b. << val is_valid_utf_8 : t -> bool >> is_valid_utf_8 b is true if and only if b contains valid UTF-8 data. UTF-16BE -------- << val get_utf_16be_uchar : t -> int -> Uchar.utf_decode >> get_utf_16be_uchar b i decodes an UTF-16BE character at index i in b. << val is_valid_utf_16be : t -> bool >> is_valid_utf_16be b is true if and only if b contains valid UTF-16BE data. UTF-16LE -------- << val get_utf_16le_uchar : t -> int -> Uchar.utf_decode >> get_utf_16le_uchar b i decodes an UTF-16LE character at index i in b. << val is_valid_utf_16le : t -> bool >> is_valid_utf_16le b is true if and only if b contains valid UTF-16LE data. Binary decoding of integers =========================== The functions in this section binary decode integers from strings. All following functions raise Invalid_argument if the characters needed at index i to decode the integer are not available. Little-endian (resp. big-endian) encoding means that least (resp. most) significant bytes are stored first. Big-endian is also known as network byte order. Native-endian encoding is either little-endian or big-endian depending on Sys.big_endian[29.56]. 32-bit and 64-bit integers are represented by the int32 and int64 types, which can be interpreted either as signed or unsigned numbers. 8-bit and 16-bit integers are represented by the int type, which has more bits than the binary encoding. These extra bits are sign-extended (or zero-extended) for functions which decode 8-bit or 16-bit integers and represented them with int values. << val get_uint8 : string -> int -> int >> get_uint8 b i is b’s unsigned 8-bit integer starting at character index i. Since: 4.13 << val get_int8 : string -> int -> int >> get_int8 b i is b’s signed 8-bit integer starting at character index i. Since: 4.13 << val get_uint16_ne : string -> int -> int >> get_uint16_ne b i is b’s native-endian unsigned 16-bit integer starting at character index i. Since: 4.13 << val get_uint16_be : string -> int -> int >> get_uint16_be b i is b’s big-endian unsigned 16-bit integer starting at character index i. Since: 4.13 << val get_uint16_le : string -> int -> int >> get_uint16_le b i is b’s little-endian unsigned 16-bit integer starting at character index i. Since: 4.13 << val get_int16_ne : string -> int -> int >> get_int16_ne b i is b’s native-endian signed 16-bit integer starting at character index i. Since: 4.13 << val get_int16_be : string -> int -> int >> get_int16_be b i is b’s big-endian signed 16-bit integer starting at character index i. Since: 4.13 << val get_int16_le : string -> int -> int >> get_int16_le b i is b’s little-endian signed 16-bit integer starting at character index i. Since: 4.13 << val get_int32_ne : string -> int -> int32 >> get_int32_ne b i is b’s native-endian 32-bit integer starting at character index i. Since: 4.13 << val hash : t -> int >> An unseeded hash function for strings, with the same output value as Hashtbl.hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.Make[29.25]. Since: 5.0 << val seeded_hash : int -> t -> int >> A seeded hash function for strings, with the same output value as Hashtbl.seeded_hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded[29.25]. Since: 5.0 << val get_int32_be : string -> int -> int32 >> get_int32_be b i is b’s big-endian 32-bit integer starting at character index i. Since: 4.13 << val get_int32_le : string -> int -> int32 >> get_int32_le b i is b’s little-endian 32-bit integer starting at character index i. Since: 4.13 << val get_int64_ne : string -> int -> int64 >> get_int64_ne b i is b’s native-endian 64-bit integer starting at character index i. Since: 4.13 << val get_int64_be : string -> int -> int64 >> get_int64_be b i is b’s big-endian 64-bit integer starting at character index i. Since: 4.13 << val get_int64_le : string -> int -> int64 >> get_int64_le b i is b’s little-endian 64-bit integer starting at character index i. Since: 4.13 29.55 Module StringLabels : Strings. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= A string s of length n is an indexable and immutable sequence of n bytes. For historical reasons these bytes are referred to as characters. The semantics of string functions is defined in terms of indices and positions. These are depicted and described as follows. <> - An index i of s is an integer in the range [0;n-1]. It represents the ith byte (character) of s which can be accessed using the constant time string indexing operator s.[i]. - A position i of s is an integer in the range [0;n]. It represents either the point at the beginning of the string, or the point between two indices, or the point at the end of the string. The ith byte index is between position i and i+1. Two integers start and len are said to define a valid substring of s if len >= 0 and start, start+len are positions of s. Unicode text. Strings being arbitrary sequences of bytes, they can hold any kind of textual encoding. However the recommended encoding for storing Unicode text in OCaml strings is UTF-8. This is the encoding used by Unicode escapes in string literals. For example the string "\u{1F42B}" is the UTF-8 encoding of the Unicode character U+1F42B. Past mutability. Before OCaml 4.02, strings used to be modifiable in place like Bytes.t[29.8] mutable sequences of bytes. OCaml 4 had various compiler flags and configuration options to support the transition period from mutable to immutable strings. Those options are no longer available, and strings are now always immutable. The labeled version of this module can be used as described in the StdLabels[29.53] module. Strings ======= << type t = string >> The type for strings. << val make : int -> char -> string >> make n c is a string of length n with each index holding the character c. Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val init : int -> f:(int -> char) -> string >> init n ~f is a string of length n with index i holding the character f i (called in increasing index order). Since: 4.02 Raises Invalid_argument if n < 0 or n > Sys.max_string_length[29.56]. << val empty : string >> The empty string. Since: 4.13 << val length : string -> int >> length s is the length (number of bytes/characters) of s. << val get : string -> int -> char >> get s i is the character at index i in s. This is the same as writing s.[i]. Raises Invalid_argument if i not an index of s. << val of_bytes : bytes -> string >> Return a new string that contains the same bytes as the given byte sequence. Since: 4.13 << val to_bytes : string -> bytes >> Return a new byte sequence that contains the same bytes as the given string. Since: 4.13 << val blit : src:string -> src_pos:int -> dst:bytes -> dst_pos:int -> len:int -> unit >> Same as Bytes.blit_string[29.8] which should be preferred. Concatenating ============= Note. The (^)[28.2] binary operator concatenates two strings. << val concat : sep:string -> string list -> string >> concat ~sep ss concatenates the list of strings ss, inserting the separator string sep between each. Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val cat : string -> string -> string >> cat s1 s2 concatenates s1 and s2 (s1 ^ s2). Since: 4.13 Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. Predicates and comparisons ========================== << val equal : t -> t -> bool >> equal s0 s1 is true if and only if s0 and s1 are character-wise equal. Since: 4.05 << val compare : t -> t -> int >> compare s0 s1 sorts s0 and s1 in lexicographical order. compare behaves like compare[28.2] on strings but may be more efficient. << val starts_with : prefix:string -> string -> bool >> starts_with ~prefix s is true if and only if s starts with prefix. Since: 4.13 << val ends_with : suffix:string -> string -> bool >> ends_with ~suffix s is true if and only if s ends with suffix. Since: 4.13 << val contains_from : string -> int -> char -> bool >> contains_from s start c is true if and only if c appears in s after position start. Raises Invalid_argument if start is not a valid position in s. << val rcontains_from : string -> int -> char -> bool >> rcontains_from s stop c is true if and only if c appears in s before position stop+1. Raises Invalid_argument if stop < 0 or stop+1 is not a valid position in s. << val contains : string -> char -> bool >> contains s c is String.contains_from[29.54] s 0 c. Extracting substrings ===================== << val sub : string -> pos:int -> len:int -> string >> sub s ~pos ~len is a string of length len, containing the substring of s that starts at position pos and has length len. Raises Invalid_argument if pos and len do not designate a valid substring of s. << val split_on_char : sep:char -> string -> string list >> split_on_char ~sep s is the list of all (possibly empty) substrings of s that are delimited by the character sep. If s is empty, the result is the singleton list [""]. The function’s result is specified by the following invariants: - The list is not empty. - Concatenating its elements using sep as a separator returns a string equal to the input (concat (make 1 sep) (split_on_char sep s) = s). - No string in the result contains the sep character. Since: 4.05 Transforming ============ << val map : f:(char -> char) -> string -> string >> map f s is the string resulting from applying f to all the characters of s in increasing order. Since: 4.00 << val mapi : f:(int -> char -> char) -> string -> string >> mapi ~f s is like StringLabels.map[29.55] but the index of the character is also passed to f. Since: 4.02 << val fold_left : f:('acc -> char -> 'acc) -> init:'acc -> string -> 'acc >> fold_left f x s computes f (... (f (f x s.[0]) s.[1]) ...) s.[n-1], where n is the length of the string s. Since: 4.13 << val fold_right : f:(char -> 'acc -> 'acc) -> string -> init:'acc -> 'acc >> fold_right f s x computes f s.[0] (f s.[1] ( ... (f s.[n-1] x) ...)), where n is the length of the string s. Since: 4.13 << val for_all : f:(char -> bool) -> string -> bool >> for_all p s checks if all characters in s satisfy the predicate p. Since: 4.13 << val exists : f:(char -> bool) -> string -> bool >> exists p s checks if at least one character of s satisfies the predicate p. Since: 4.13 << val trim : string -> string >> trim s is s without leading and trailing whitespace. Whitespace characters are: ' ', '\x0C' (form feed), '\n', '\r', and '\t'. Since: 4.00 << val escaped : string -> string >> escaped s is s with special characters represented by escape sequences, following the lexical conventions of OCaml. All characters outside the US-ASCII printable range [0x20;0x7E] are escaped, as well as backslash (0x2F) and double-quote (0x22). The function Scanf.unescaped[29.48] is a left inverse of escaped, i.e. Scanf.unescaped (escaped s) = s for any string s (unless escaped s fails). Raises Invalid_argument if the result is longer than Sys.max_string_length[29.56] bytes. << val uppercase_ascii : string -> string >> uppercase_ascii s is s with all lowercase letters translated to uppercase, using the US-ASCII character set. Since: 4.05 << val lowercase_ascii : string -> string >> lowercase_ascii s is s with all uppercase letters translated to lowercase, using the US-ASCII character set. Since: 4.05 << val capitalize_ascii : string -> string >> capitalize_ascii s is s with the first character set to uppercase, using the US-ASCII character set. Since: 4.05 << val uncapitalize_ascii : string -> string >> uncapitalize_ascii s is s with the first character set to lowercase, using the US-ASCII character set. Since: 4.05 Traversing ========== << val iter : f:(char -> unit) -> string -> unit >> iter ~f s applies function f in turn to all the characters of s. It is equivalent to f s.[0]; f s.[1]; ...; f s.[length s - 1]; (). << val iteri : f:(int -> char -> unit) -> string -> unit >> iteri is like StringLabels.iter[29.55], but the function is also given the corresponding character index. Since: 4.00 Searching ========= << val index_from : string -> int -> char -> int >> index_from s i c is the index of the first occurrence of c in s after position i. Raises - Not_found if c does not occur in s after position i. - Invalid_argument if i is not a valid position in s. << val index_from_opt : string -> int -> char -> int option >> index_from_opt s i c is the index of the first occurrence of c in s after position i (if any). Since: 4.05 Raises Invalid_argument if i is not a valid position in s. << val rindex_from : string -> int -> char -> int >> rindex_from s i c is the index of the last occurrence of c in s before position i+1. Raises - Not_found if c does not occur in s before position i+1. - Invalid_argument if i+1 is not a valid position in s. << val rindex_from_opt : string -> int -> char -> int option >> rindex_from_opt s i c is the index of the last occurrence of c in s before position i+1 (if any). Since: 4.05 Raises Invalid_argument if i+1 is not a valid position in s. << val index : string -> char -> int >> index s c is String.index_from[29.54] s 0 c. << val index_opt : string -> char -> int option >> index_opt s c is String.index_from_opt[29.54] s 0 c. Since: 4.05 << val rindex : string -> char -> int >> rindex s c is String.rindex_from[29.54] s (length s - 1) c. << val rindex_opt : string -> char -> int option >> rindex_opt s c is String.rindex_from_opt[29.54] s (length s - 1) c. Since: 4.05 Strings and Sequences ===================== << val to_seq : t -> char Seq.t >> to_seq s is a sequence made of the string’s characters in increasing order. In "unsafe-string" mode, modifications of the string during iteration will be reflected in the sequence. Since: 4.07 << val to_seqi : t -> (int * char) Seq.t >> to_seqi s is like StringLabels.to_seq[29.55] but also tuples the corresponding index. Since: 4.07 << val of_seq : char Seq.t -> t >> of_seq s is a string made of the sequence’s characters. Since: 4.07 UTF decoding and validations ============================ UTF-8 ----- << val get_utf_8_uchar : t -> int -> Uchar.utf_decode >> get_utf_8_uchar b i decodes an UTF-8 character at index i in b. << val is_valid_utf_8 : t -> bool >> is_valid_utf_8 b is true if and only if b contains valid UTF-8 data. UTF-16BE -------- << val get_utf_16be_uchar : t -> int -> Uchar.utf_decode >> get_utf_16be_uchar b i decodes an UTF-16BE character at index i in b. << val is_valid_utf_16be : t -> bool >> is_valid_utf_16be b is true if and only if b contains valid UTF-16BE data. UTF-16LE -------- << val get_utf_16le_uchar : t -> int -> Uchar.utf_decode >> get_utf_16le_uchar b i decodes an UTF-16LE character at index i in b. << val is_valid_utf_16le : t -> bool >> is_valid_utf_16le b is true if and only if b contains valid UTF-16LE data. Binary decoding of integers =========================== The functions in this section binary decode integers from strings. All following functions raise Invalid_argument if the characters needed at index i to decode the integer are not available. Little-endian (resp. big-endian) encoding means that least (resp. most) significant bytes are stored first. Big-endian is also known as network byte order. Native-endian encoding is either little-endian or big-endian depending on Sys.big_endian[29.56]. 32-bit and 64-bit integers are represented by the int32 and int64 types, which can be interpreted either as signed or unsigned numbers. 8-bit and 16-bit integers are represented by the int type, which has more bits than the binary encoding. These extra bits are sign-extended (or zero-extended) for functions which decode 8-bit or 16-bit integers and represented them with int values. << val get_uint8 : string -> int -> int >> get_uint8 b i is b’s unsigned 8-bit integer starting at character index i. Since: 4.13 << val get_int8 : string -> int -> int >> get_int8 b i is b’s signed 8-bit integer starting at character index i. Since: 4.13 << val get_uint16_ne : string -> int -> int >> get_uint16_ne b i is b’s native-endian unsigned 16-bit integer starting at character index i. Since: 4.13 << val get_uint16_be : string -> int -> int >> get_uint16_be b i is b’s big-endian unsigned 16-bit integer starting at character index i. Since: 4.13 << val get_uint16_le : string -> int -> int >> get_uint16_le b i is b’s little-endian unsigned 16-bit integer starting at character index i. Since: 4.13 << val get_int16_ne : string -> int -> int >> get_int16_ne b i is b’s native-endian signed 16-bit integer starting at character index i. Since: 4.13 << val get_int16_be : string -> int -> int >> get_int16_be b i is b’s big-endian signed 16-bit integer starting at character index i. Since: 4.13 << val get_int16_le : string -> int -> int >> get_int16_le b i is b’s little-endian signed 16-bit integer starting at character index i. Since: 4.13 << val get_int32_ne : string -> int -> int32 >> get_int32_ne b i is b’s native-endian 32-bit integer starting at character index i. Since: 4.13 << val hash : t -> int >> An unseeded hash function for strings, with the same output value as Hashtbl.hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.Make[29.25]. Since: 5.0 << val seeded_hash : int -> t -> int >> A seeded hash function for strings, with the same output value as Hashtbl.seeded_hash[29.25]. This function allows this module to be passed as argument to the functor Hashtbl.MakeSeeded[29.25]. Since: 5.0 << val get_int32_be : string -> int -> int32 >> get_int32_be b i is b’s big-endian 32-bit integer starting at character index i. Since: 4.13 << val get_int32_le : string -> int -> int32 >> get_int32_le b i is b’s little-endian 32-bit integer starting at character index i. Since: 4.13 << val get_int64_ne : string -> int -> int64 >> get_int64_ne b i is b’s native-endian 64-bit integer starting at character index i. Since: 4.13 << val get_int64_be : string -> int -> int64 >> get_int64_be b i is b’s big-endian 64-bit integer starting at character index i. Since: 4.13 << val get_int64_le : string -> int -> int64 >> get_int64_le b i is b’s little-endian 64-bit integer starting at character index i. Since: 4.13 29.56 Module Sys : System interface. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Every function in this module raises Sys_error with an informative message when the underlying system call signal an error. << val argv : string array >> The command line arguments given to the process. The first element is the command name used to invoke the program. The following elements are the command-line arguments given to the program. << val executable_name : string >> The name of the file containing the executable currently running. This name may be absolute or relative to the current directory, depending on the platform and whether the program was compiled to bytecode or a native executable. << val file_exists : string -> bool >> Test if a file with the given name exists. << val is_directory : string -> bool >> Returns true if the given name refers to a directory, false if it refers to another kind of file. Since: 3.10 Raises Sys_error if no file exists with the given name. << val is_regular_file : string -> bool >> Returns true if the given name refers to a regular file, false if it refers to another kind of file. Since: 5.1 Raises Sys_error if no file exists with the given name. << val remove : string -> unit >> Remove the given file name from the file system. << val rename : string -> string -> unit >> Rename a file or directory. rename oldpath newpath renames the file or directory called oldpath, giving it newpath as its new name, moving it between (parent) directories if needed. If a file named newpath already exists, its contents will be replaced with those of oldpath. Depending on the operating system, the metadata (permissions, owner, etc) of newpath can either be preserved or be replaced by those of oldpath. Since: 4.06 concerning the "replace existing file" behavior << val getenv : string -> string >> Return the value associated to a variable in the process environment. Raises Not_found if the variable is unbound. << val getenv_opt : string -> string option >> Return the value associated to a variable in the process environment or None if the variable is unbound. Since: 4.05 << val command : string -> int >> Execute the given shell command and return its exit code. The argument of Sys.command[29.56] is generally the name of a command followed by zero, one or several arguments, separated by whitespace. The given argument is interpreted by a shell: either the Windows shell cmd.exe for the Win32 ports of OCaml, or the POSIX shell sh for other ports. It can contain shell builtin commands such as echo, and also special characters such as file redirections > and <, which will be honored by the shell. Conversely, whitespace or special shell characters occurring in command names or in their arguments must be quoted or escaped so that the shell does not interpret them. The quoting rules vary between the POSIX shell and the Windows shell. The Filename.quote_command[29.20] performs the appropriate quoting given a command name, a list of arguments, and optional file redirections. << val time : unit -> float >> Return the processor time, in seconds, used by the program since the beginning of execution. << val chdir : string -> unit >> Change the current working directory of the process. << val mkdir : string -> int -> unit >> Create a directory with the given permissions. Since: 4.12 << val rmdir : string -> unit >> Remove an empty directory. Since: 4.12 << val getcwd : unit -> string >> Return the current working directory of the process. << val readdir : string -> string array >> Return the names of all files present in the given directory. Names denoting the current directory and the parent directory ("." and ".." in Unix) are not returned. Each string in the result is a file name rather than a complete path. There is no guarantee that the name strings in the resulting array will appear in any specific order; they are not, in particular, guaranteed to appear in alphabetical order. << val interactive : bool ref >> This reference is initially set to false in standalone programs and to true if the code is being executed under the interactive toplevel system ocaml. Alert unsynchronized_access. The interactive status is a mutable global state. << val os_type : string >> Operating system currently executing the OCaml program. One of - "Unix" (for all Unix versions, including Linux and Mac OS X), - "Win32" (for MS-Windows, OCaml compiled with MSVC++ or MinGW-w64), - "Cygwin" (for MS-Windows, OCaml compiled with Cygwin). << type backend_type = | Native | Bytecode | Other of string >> Currently, the official distribution only supports Native and Bytecode, but it can be other backends with alternative compilers, for example, javascript. Since: 4.04 << val backend_type : backend_type >> Backend type currently executing the OCaml program. Since: 4.04 << val unix : bool >> True if Sys.os_type = "Unix". Since: 4.01 << val win32 : bool >> True if Sys.os_type = "Win32". Since: 4.01 << val cygwin : bool >> True if Sys.os_type = "Cygwin". Since: 4.01 << val word_size : int >> Size of one word on the machine currently executing the OCaml program, in bits: 32 or 64. << val int_size : int >> Size of int, in bits. It is 31 (resp. 63) when using OCaml on a 32-bit (resp. 64-bit) platform. It may differ for other implementations, e.g. it can be 32 bits when compiling to JavaScript. Since: 4.03 << val big_endian : bool >> Whether the machine currently executing the Caml program is big-endian. Since: 4.00 << val max_string_length : int >> Maximum length of strings and byte sequences. << val max_array_length : int >> Maximum length of a normal array (i.e. any array whose elements are not of type float). The maximum length of a float array is max_floatarray_length if OCaml was configured with –enable-flat-float-array and max_array_length if configured with –disable-flat-float-array. << val max_floatarray_length : int >> Maximum length of a floatarray. This is also the maximum length of a float array when OCaml is configured with –enable-flat-float-array. << val runtime_variant : unit -> string >> Return the name of the runtime variant the program is running on. This is normally the argument given to -runtime-variant at compile time, but for byte-code it can be changed after compilation. Since: 4.03 << val runtime_parameters : unit -> string >> Return the value of the runtime parameters, in the same format as the contents of the OCAMLRUNPARAM environment variable. Since: 4.03 Signal handling =============== << type signal_behavior = | Signal_default | Signal_ignore | Signal_handle of (int -> unit) >> What to do when receiving a signal: - Signal_default: take the default behavior (usually: abort the program) - Signal_ignore: ignore the signal - Signal_handle f: call function f, giving it the signal number as argument. << val signal : int -> signal_behavior -> signal_behavior >> Set the behavior of the system on receipt of a given signal. The first argument is the signal number. Return the behavior previously associated with the signal. If the signal number is invalid (or not available on your system), an Invalid_argument exception is raised. << val set_signal : int -> signal_behavior -> unit >> Same as Sys.signal[29.56] but return value is ignored. Signal numbers for the standard POSIX signals. ---------------------------------------------- << val sigabrt : int >> Abnormal termination << val sigalrm : int >> Timeout << val sigfpe : int >> Arithmetic exception << val sighup : int >> Hangup on controlling terminal << val sigill : int >> Invalid hardware instruction << val sigint : int >> Interactive interrupt (ctrl-C) << val sigkill : int >> Termination (cannot be ignored) << val sigpipe : int >> Broken pipe << val sigquit : int >> Interactive termination << val sigsegv : int >> Invalid memory reference << val sigterm : int >> Termination << val sigusr1 : int >> Application-defined signal 1 << val sigusr2 : int >> Application-defined signal 2 << val sigchld : int >> Child process terminated << val sigcont : int >> Continue << val sigstop : int >> Stop << val sigtstp : int >> Interactive stop << val sigttin : int >> Terminal read from background process << val sigttou : int >> Terminal write from background process << val sigvtalrm : int >> Timeout in virtual time << val sigprof : int >> Profiling interrupt << val sigbus : int >> Bus error Since: 4.03 << val sigpoll : int >> Pollable event Since: 4.03 << val sigsys : int >> Bad argument to routine Since: 4.03 << val sigtrap : int >> Trace/breakpoint trap Since: 4.03 << val sigurg : int >> Urgent condition on socket Since: 4.03 << val sigxcpu : int >> Timeout in cpu time Since: 4.03 << val sigxfsz : int >> File size limit exceeded Since: 4.03 << exception Break >> Exception raised on interactive interrupt if Sys.catch_break[29.56] is enabled. << val catch_break : bool -> unit >> catch_break governs whether interactive interrupt (ctrl-C) terminates the program or raises the Break exception. Call catch_break true to enable raising Break, and catch_break false to let the system terminate the program on user interrupt. Inside multi-threaded programs, the Break exception will arise in any one of the active threads, and will keep arising on further interactive interrupt until all threads are terminated. Use signal masks from Thread.sigmask to direct the interrupt towards a specific thread. << val ocaml_version : string >> ocaml_version is the version of OCaml. It is a string of the form "major.minor[.patchlevel][(+|~)additional-info]", where major, minor, and patchlevel are integers, and additional-info is an arbitrary string. The [.patchlevel] part was absent before version 3.08.0 and became mandatory from 3.08.0 onwards. The [(+|~)additional-info] part may be absent. << val development_version : bool >> true if this is a development version, false otherwise. Since: 4.14 << type extra_prefix = | Plus | Tilde >> << type extra_info = extra_prefix * string >> Since: 4.14 << type ocaml_release_info = { major : int ; minor : int ; patchlevel : int ; extra : extra_info option ; } >> Since: 4.14 << val ocaml_release : ocaml_release_info >> ocaml_release is the version of OCaml. Since: 4.14 << val enable_runtime_warnings : bool -> unit >> Control whether the OCaml runtime system can emit warnings on stderr. Currently, the only supported warning is triggered when a channel created by open_* functions is finalized without being closed. Runtime warnings are disabled by default. Since: 4.03 Alert unsynchronized_access. The status of runtime warnings is a mutable global state. << val runtime_warnings_enabled : unit -> bool >> Return whether runtime warnings are currently enabled. Since: 4.03 Alert unsynchronized_access. The status of runtime warnings is a mutable global state. Optimization ============ << val opaque_identity : 'a -> 'a >> For the purposes of optimization, opaque_identity behaves like an unknown (and thus possibly side-effecting) function. At runtime, opaque_identity disappears altogether. A typical use of this function is to prevent pure computations from being optimized away in benchmarking loops. For example: << for _round = 1 to 100_000 do ignore (Sys.opaque_identity (my_pure_computation ())) done >> Since: 4.03 << module Immediate64 : >>  sig This module allows to define a type t with the immediate64 attribute. This attribute means that the type is immediate on 64 bit architectures. On other architectures, it might or might not be immediate. << module type Non_immediate = >>  sig << type t >>  end << module type Immediate = >>  sig << type t >>  end << module Make : >> functor (Immediate : Immediate) -> functor (Non_immediate : Non_immediate) ->  sig << type t >> << type 'a repr = | Immediate : Sys.Immediate64.Immediate.t repr | Non_immediate : Sys.Immediate64.Non_immediate.t repr >> << val repr : t repr >>  end  end 29.57 Module Type : Type introspection. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Since: 5.1 Type equality witness ===================== << type (_, _) eq = | Equal : ('a, 'a) eq >> The purpose of eq is to represent type equalities that may not otherwise be known by the type checker (e.g. because they may depend on dynamic data). A value of type (a, b) eq represents the fact that types a and b are equal. If one has a value eq : (a, b) eq that proves types a and b are equal, one can use it to convert a value of type a to a value of type b by pattern matching on Equal: << let cast (type a) (type b) (Equal : (a, b) Type.eq) (a : a) : b = a >> At runtime, this function simply returns its second argument unchanged. Type identifiers ================ << module Id : >>  sig Type identifiers ================ << type !'a t >> The type for identifiers for type 'a. << val make : unit -> 'a t >> make () is a new type identifier. << val uid : 'a t -> int >> uid id is a runtime unique identifier for id. << val provably_equal : 'a t -> 'b t -> ('a, 'b) Type.eq option >> provably_equal i0 i1 is Some Equal if identifier i0 is equal to i1 and None otherwise. Example ======= The following shows how type identifiers can be used to implement a simple heterogeneous key-value dictionary. In contrast to Map[28.2] values whose keys map to a single, homogeneous type of values, this dictionary can associate a different type of value to each key. << (** Heterogeneous dictionaries. *) module Dict : sig type t (** The type for dictionaries. *) type 'a key (** The type for keys binding values of type ['a]. *) val key : unit -> 'a key (** [key ()] is a new dictionary key. *) val empty : t (** [empty] is the empty dictionary. *) val add : 'a key -> 'a -> t -> t (** [add k v d] is [d] with [k] bound to [v]. *) val remove : 'a key -> t -> t (** [remove k d] is [d] with the last binding of [k] removed. *) val find : 'a key -> t -> 'a option (** [find k d] is the binding of [k] in [d], if any. *) end = struct type 'a key = 'a Type.Id.t type binding = B : 'a key * 'a -> binding type t = (int * binding) list let key () = Type.Id.make () let empty = [] let add k v d = (Type.Id.uid k, B (k, v)) :: d let remove k d = List.remove_assoc (Type.Id.uid k) d let find : type a. a key -> t -> a option = fun k d -> match List.assoc_opt (Type.Id.uid k) d with | None -> None | Some (B (k', v)) -> match Type.Id.provably_equal k k' with | Some Type.Equal -> Some v | None -> assert false end >>  end Type identifiers. A type identifier is a value that denotes a type. Given two type identifiers, they can be tested for equality[29.57] to prove they denote the same type. Note that: - Unequal identifiers do not imply unequal types: a given type can be denoted by more than one identifier. - Type identifiers can be marshalled, but they get a new, distinct, identity on unmarshalling, so the equalities are lost. See an example[29.57] of use. 29.58 Module Uchar : Unicode characters. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Since: 4.03 << type t >> The type for Unicode characters. A value of this type represents a Unicode scalar value[http://unicode.org/glossary/#unicode_scalar_value] which is an integer in the ranges 0x0000...0xD7FF or 0xE000...0x10FFFF. << val min : t >> min is U+0000. << val max : t >> max is U+10FFFF. << val bom : t >> bom is U+FEFF, the byte order mark[http://unicode.org/glossary/#byte_order_mark] (BOM) character. Since: 4.06 << val rep : t >> rep is U+FFFD, the replacement[http://unicode.org/glossary/#replacement_character] character. Since: 4.06 << val succ : t -> t >> succ u is the scalar value after u in the set of Unicode scalar values. Raises Invalid_argument if u is Uchar.max[29.58]. << val pred : t -> t >> pred u is the scalar value before u in the set of Unicode scalar values. Raises Invalid_argument if u is Uchar.min[29.58]. << val is_valid : int -> bool >> is_valid n is true if and only if n is a Unicode scalar value (i.e. in the ranges 0x0000...0xD7FF or 0xE000...0x10FFFF). << val of_int : int -> t >> of_int i is i as a Unicode character. Raises Invalid_argument if i does not satisfy Uchar.is_valid[29.58]. << val to_int : t -> int >> to_int u is u as an integer. << val is_char : t -> bool >> is_char u is true if and only if u is a latin1 OCaml character. << val of_char : char -> t >> of_char c is c as a Unicode character. << val to_char : t -> char >> to_char u is u as an OCaml latin1 character. Raises Invalid_argument if u does not satisfy Uchar.is_char[29.58]. << val equal : t -> t -> bool >> equal u u' is u = u'. << val compare : t -> t -> int >> compare u u' is Stdlib.compare u u'. << val hash : t -> int >> hash u associates a non-negative integer to u. UTF codecs tools ================ << type utf_decode >> The type for UTF decode results. Values of this type represent the result of a Unicode Transformation Format decoding attempt. << val utf_decode_is_valid : utf_decode -> bool >> utf_decode_is_valid d is true if and only if d holds a valid decode. << val utf_decode_uchar : utf_decode -> t >> utf_decode_uchar d is the Unicode character decoded by d if utf_decode_is_valid d is true and Uchar.rep[29.58] otherwise. << val utf_decode_length : utf_decode -> int >> utf_decode_length d is the number of elements from the source that were consumed by the decode d. This is always strictly positive and smaller or equal to 4. The kind of source elements depends on the actual decoder; for the decoders of the standard library this function always returns a length in bytes. << val utf_decode : int -> t -> utf_decode >> utf_decode n u is a valid UTF decode for u that consumed n elements from the source for decoding. n must be positive and smaller or equal to 4 (this is not checked by the module). << val utf_decode_invalid : int -> utf_decode >> utf_decode_invalid n is an invalid UTF decode that consumed n elements from the source to error. n must be positive and smaller or equal to 4 (this is not checked by the module). The resulting decode has Uchar.rep[29.58] as the decoded Unicode character. << val utf_8_byte_length : t -> int >> utf_8_byte_length u is the number of bytes needed to encode u in UTF-8. << val utf_16_byte_length : t -> int >> utf_16_byte_length u is the number of bytes needed to encode u in UTF-16. 29.59 Module Unit : Unit values. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Since: 4.08 The unit type ============= << type t = unit = | () >> The unit type. The constructor () is included here so that it has a path, but it is not intended to be used in user-defined data types. << val equal : t -> t -> bool >> equal u1 u2 is true. << val compare : t -> t -> int >> compare u1 u2 is 0. << val to_string : t -> string >> to_string b is "()". 29.60 Module Weak : Arrays of weak pointers and hash sets of weak pointers. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Low-level functions =================== << type !'a t >> The type of arrays of weak pointers (weak arrays). A weak pointer is a value that the garbage collector may erase whenever the value is not used any more (through normal pointers) by the program. Note that finalisation functions are run before the weak pointers are erased, because the finalisation functions can make values alive again (before 4.03 the finalisation functions were run after). A weak pointer is said to be full if it points to a value, empty if the value was erased by the GC. Notes: - Integers are not allocated and cannot be stored in weak arrays. - Weak arrays cannot be marshaled using output_value[28.2] nor the functions of the Marshal[29.35] module. << val create : int -> 'a t >> Weak.create n returns a new weak array of length n. All the pointers are initially empty. Raises Invalid_argument if n is not comprised between zero and Obj.Ephemeron.max_ephe_length[??] (limits included). << val length : 'a t -> int >> Weak.length ar returns the length (number of elements) of ar. << val set : 'a t -> int -> 'a option -> unit >> Weak.set ar n (Some el) sets the nth cell of ar to be a (full) pointer to el; Weak.set ar n None sets the nth cell of ar to empty. Raises Invalid_argument if n is not in the range 0 to Weak.length[29.60] ar - 1. << val get : 'a t -> int -> 'a option >> Weak.get ar n returns None if the nth cell of ar is empty, Some x (where x is the value) if it is full. Raises Invalid_argument if n is not in the range 0 to Weak.length[29.60] ar - 1. << val get_copy : 'a t -> int -> 'a option >> Weak.get_copy ar n returns None if the nth cell of ar is empty, Some x (where x is a (shallow) copy of the value) if it is full. In addition to pitfalls with mutable values, the interesting difference with get is that get_copy does not prevent the incremental GC from erasing the value in its current cycle (get may delay the erasure to the next GC cycle). Raises Invalid_argument if n is not in the range 0 to Weak.length[29.60] ar - 1. If the element is a custom block it is not copied. << val check : 'a t -> int -> bool >> Weak.check ar n returns true if the nth cell of ar is full, false if it is empty. Note that even if Weak.check ar n returns true, a subsequent Weak.get[29.60] ar n can return None. Raises Invalid_argument if n is not in the range 0 to Weak.length[29.60] ar - 1. << val fill : 'a t -> int -> int -> 'a option -> unit >> Weak.fill ar ofs len el sets to el all pointers of ar from ofs to ofs + len - 1. Raises Invalid_argument if ofs and len do not designate a valid subarray of ar. << val blit : 'a t -> int -> 'a t -> int -> int -> unit >> Weak.blit ar1 off1 ar2 off2 len copies len weak pointers from ar1 (starting at off1) to ar2 (starting at off2). It works correctly even if ar1 and ar2 are the same. Raises Invalid_argument if off1 and len do not designate a valid subarray of ar1, or if off2 and len do not designate a valid subarray of ar2. Weak hash sets ============== A weak hash set is a hashed set of values. Each value may magically disappear from the set when it is not used by the rest of the program any more. This is normally used to share data structures without inducing memory leaks. Weak hash sets are defined on values from a Hashtbl.HashedType[29.25] module; the equal relation and hash function are taken from that module. We will say that v is an instance of x if equal x v is true. The equal relation must be able to work on a shallow copy of the values and give the same result as with the values themselves. Unsynchronized accesses Unsynchronized accesses to weak hash sets are a programming error. Unsynchronized accesses to a weak hash set may lead to an invalid weak hash set state. Thus, concurrent accesses to weak hash sets must be synchronized (for instance with a Mutex.t[29.37]). << module type S = >>  sig << type data >> The type of the elements stored in the table. << type t >> The type of tables that contain elements of type data. Note that weak hash sets cannot be marshaled using output_value[28.2] or the functions of the Marshal[29.35] module. << val create : int -> t >> create n creates a new empty weak hash set, of initial size n. The table will grow as needed. << val clear : t -> unit >> Remove all elements from the table. << val merge : t -> data -> data >> merge t x returns an instance of x found in t if any, or else adds x to t and return x. << val add : t -> data -> unit >> add t x adds x to t. If there is already an instance of x in t, it is unspecified which one will be returned by subsequent calls to find and merge. << val remove : t -> data -> unit >> remove t x removes from t one instance of x. Does nothing if there is no instance of x in t. << val find : t -> data -> data >> find t x returns an instance of x found in t. Raises Not_found if there is no such element. << val find_opt : t -> data -> data option >> find_opt t x returns an instance of x found in t or None if there is no such element. Since: 4.05 << val find_all : t -> data -> data list >> find_all t x returns a list of all the instances of x found in t. << val mem : t -> data -> bool >> mem t x returns true if there is at least one instance of x in t, false otherwise. << val iter : (data -> unit) -> t -> unit >> iter f t calls f on each element of t, in some unspecified order. It is not specified what happens if f tries to change t itself. << val fold : (data -> 'acc -> 'acc) -> t -> 'acc -> 'acc >> fold f t init computes (f d1 (... (f dN init))) where d1 ... dN are the elements of t in some unspecified order. It is not specified what happens if f tries to change t itself. << val count : t -> int >> Count the number of elements in the table. count t gives the same result as fold (fun _ n -> n+1) t 0 but does not delay the deallocation of the dead elements. << val stats : t -> int * int * int * int * int * int >> Return statistics on the table. The numbers are, in order: table length, number of entries, sum of bucket lengths, smallest bucket length, median bucket length, biggest bucket length.  end The output signature of the functor Weak.Make[29.60]. << module Make : >> functor (H : Hashtbl.HashedType) -> S with type data = H.t Functor building an implementation of the weak hash set structure. H.equal can’t be the physical equality, since only shallow copies of the elements in the set are given to it. 29.61 Ocaml_operators : Precedence level and associativity of operators *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* The following table lists the precedence level of all operator classes from the highest to the lowest precedence. A few other syntactic constructions are also listed as references. ----------------------------------------------- Operator class Associativity ----------------------------------------------- !... ~... – .···() .···[] .···{} – #... left function application left - -. – **... lsl lsr asr right *... /...%...mod land lor lxor left +...-... left :: right @...^... right =...<...>...|...&...$...!= left & && right or || right , – <- := right if – ; right ----------------------------------------------- Chapter 30  The compiler front-end ************************************** This chapter describes the OCaml front-end, which declares the abstract syntax tree used by the compiler, provides a way to parse, print and pretty-print OCaml code, and ultimately allows one to write abstract syntax tree preprocessors invoked via the -ppx flag (see chapters 13 and 16). It is important to note that the exported front-end interface follows the evolution of the OCaml language and implementation, and thus does not provide any backwards compatibility guarantees. The front-end is a part of compiler-libs library. Programs that use the compiler-libs library should be built as follows: << ocamlfind ocamlc other options -package compiler-libs.common other files ocamlfind ocamlopt other options -package compiler-libs.common other files >> Use of the ocamlfind utility is recommended. However, if this is not possible, an alternative method may be used: << ocamlc other options -I +compiler-libs ocamlcommon.cma other files ocamlopt other options -I +compiler-libs ocamlcommon.cmxa other files >> For interactive use of the compiler-libs library, start ocaml and type #load "compiler-libs/ocamlcommon.cma";;. 30.1 Module Ast_mapper : The interface of a -ppx rewriter *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* A -ppx rewriter is a program that accepts a serialized abstract syntax tree and outputs another, possibly modified, abstract syntax tree. This module encapsulates the interface between the compiler and the -ppx rewriters, handling such details as the serialization format, forwarding of command-line flags, and storing state. Ast_mapper.mapper[30.1] enables AST rewriting using open recursion. A typical mapper would be based on Ast_mapper.default_mapper[30.1], a deep identity mapper, and will fall back on it for handling the syntax it does not modify. For example: << open Asttypes open Parsetree open Ast_mapper let test_mapper argv = { default_mapper with expr = fun mapper expr -> match expr with | { pexp_desc = Pexp_extension ({ txt = "test" }, PStr [])} -> Ast_helper.Exp.constant (Pconst_integer ("42", None)) | other -> default_mapper.expr mapper other; } let () = register "ppx_test" test_mapper >> This -ppx rewriter, which replaces [%test] in expressions with the constant 42, can be compiled using ocamlc -o ppx_test -I +compiler-libs ocamlcommon.cma ppx_test.ml. Warning: this module is unstable and part of compiler-libs[30]. A generic Parsetree mapper ========================== << type mapper = { attribute : mapper -> Parsetree.attribute -> Parsetree.attribute ; attributes : mapper -> Parsetree.attribute list -> Parsetree.attribute list ; binding_op : mapper -> Parsetree.binding_op -> Parsetree.binding_op ; case : mapper -> Parsetree.case -> Parsetree.case ; cases : mapper -> Parsetree.case list -> Parsetree.case list ; class_declaration : mapper -> Parsetree.class_declaration -> Parsetree.class_declaration ; class_description : mapper -> Parsetree.class_description -> Parsetree.class_description ; class_expr : mapper -> Parsetree.class_expr -> Parsetree.class_expr ; class_field : mapper -> Parsetree.class_field -> Parsetree.class_field ; class_signature : mapper -> Parsetree.class_signature -> Parsetree.class_signature ; class_structure : mapper -> Parsetree.class_structure -> Parsetree.class_structure ; class_type : mapper -> Parsetree.class_type -> Parsetree.class_type ; class_type_declaration : mapper -> Parsetree.class_type_declaration -> Parsetree.class_type_declaration ; class_type_field : mapper -> Parsetree.class_type_field -> Parsetree.class_type_field ; constant : mapper -> Parsetree.constant -> Parsetree.constant ; constructor_declaration : mapper -> Parsetree.constructor_declaration -> Parsetree.constructor_declaration ; directive_argument : mapper -> Parsetree.directive_argument -> Parsetree.directive_argument ; expr : mapper -> Parsetree.expression -> Parsetree.expression ; extension : mapper -> Parsetree.extension -> Parsetree.extension ; extension_constructor : mapper -> Parsetree.extension_constructor -> Parsetree.extension_constructor ; include_declaration : mapper -> Parsetree.include_declaration -> Parsetree.include_declaration ; include_description : mapper -> Parsetree.include_description -> Parsetree.include_description ; label_declaration : mapper -> Parsetree.label_declaration -> Parsetree.label_declaration ; location : mapper -> Location.t -> Location.t ; module_binding : mapper -> Parsetree.module_binding -> Parsetree.module_binding ; module_declaration : mapper -> Parsetree.module_declaration -> Parsetree.module_declaration ; module_substitution : mapper -> Parsetree.module_substitution -> Parsetree.module_substitution ; module_expr : mapper -> Parsetree.module_expr -> Parsetree.module_expr ; module_type : mapper -> Parsetree.module_type -> Parsetree.module_type ; module_type_declaration : mapper -> Parsetree.module_type_declaration -> Parsetree.module_type_declaration ; open_declaration : mapper -> Parsetree.open_declaration -> Parsetree.open_declaration ; open_description : mapper -> Parsetree.open_description -> Parsetree.open_description ; pat : mapper -> Parsetree.pattern -> Parsetree.pattern ; payload : mapper -> Parsetree.payload -> Parsetree.payload ; signature : mapper -> Parsetree.signature -> Parsetree.signature ; signature_item : mapper -> Parsetree.signature_item -> Parsetree.signature_item ; structure : mapper -> Parsetree.structure -> Parsetree.structure ; structure_item : mapper -> Parsetree.structure_item -> Parsetree.structure_item ; toplevel_directive : mapper -> Parsetree.toplevel_directive -> Parsetree.toplevel_directive ; toplevel_phrase : mapper -> Parsetree.toplevel_phrase -> Parsetree.toplevel_phrase ; typ : mapper -> Parsetree.core_type -> Parsetree.core_type ; type_declaration : mapper -> Parsetree.type_declaration -> Parsetree.type_declaration ; type_extension : mapper -> Parsetree.type_extension -> Parsetree.type_extension ; type_exception : mapper -> Parsetree.type_exception -> Parsetree.type_exception ; type_kind : mapper -> Parsetree.type_kind -> Parsetree.type_kind ; value_binding : mapper -> Parsetree.value_binding -> Parsetree.value_binding ; value_description : mapper -> Parsetree.value_description -> Parsetree.value_description ; with_constraint : mapper -> Parsetree.with_constraint -> Parsetree.with_constraint ; } >> A mapper record implements one "method" per syntactic category, using an open recursion style: each method takes as its first argument the mapper to be applied to children in the syntax tree. << val default_mapper : mapper >> A default mapper, which implements a "deep identity" mapping. Apply mappers to compilation units ================================== << val tool_name : unit -> string >> Can be used within a ppx preprocessor to know which tool is calling it "ocamlc", "ocamlopt", "ocamldoc", "ocamldep", "ocaml", ... Some global variables that reflect command-line options are automatically synchronized between the calling tool and the ppx preprocessor: Clflags.include_dirs[??], Clflags.hidden_include_dirs[??], Load_path[??], Clflags.open_modules[??], Clflags.for_package[??], Clflags.debug[??]. << val apply : source:string -> target:string -> mapper -> unit >> Apply a mapper (parametrized by the unit name) to a dumped parsetree found in the source file and put the result in the target file. The structure or signature field of the mapper is applied to the implementation or interface. << val run_main : (string list -> mapper) -> unit >> Entry point to call to implement a standalone -ppx rewriter from a mapper, parametrized by the command line arguments. The current unit name can be obtained from Location.input_name[30.3]. This function implements proper error reporting for uncaught exceptions. Registration API ================ << val register_function : (string -> (string list -> mapper) -> unit) ref >> << val register : string -> (string list -> mapper) -> unit >> Apply the register_function. The default behavior is to run the mapper immediately, taking arguments from the process command line. This is to support a scenario where a mapper is linked as a stand-alone executable. It is possible to overwrite the register_function to define "-ppx drivers", which combine several mappers in a single process. Typically, a driver starts by defining register_function to a custom implementation, then lets ppx rewriters (linked statically or dynamically) register themselves, and then run all or some of them. It is also possible to have -ppx drivers apply rewriters to only specific parts of an AST. The first argument to register is a symbolic name to be used by the ppx driver. Convenience functions to write mappers ====================================== << val map_opt : ('a -> 'b) -> 'a option -> 'b option >> << val extension_of_error : Location.error -> Parsetree.extension >> Encode an error into an ’ocaml.error’ extension node which can be inserted in a generated Parsetree. The compiler will be responsible for reporting the error. << val attribute_of_warning : Location.t -> string -> Parsetree.attribute >> Encode a warning message into an ’ocaml.ppwarning’ attribute which can be inserted in a generated Parsetree. The compiler will be responsible for reporting the warning. Helper functions to call external mappers ========================================= << val add_ppx_context_str : tool_name:string -> Parsetree.structure -> Parsetree.structure >> Extract information from the current environment and encode it into an attribute which is prepended to the list of structure items in order to pass the information to an external processor. << val add_ppx_context_sig : tool_name:string -> Parsetree.signature -> Parsetree.signature >> Same as add_ppx_context_str, but for signatures. << val drop_ppx_context_str : restore:bool -> Parsetree.structure -> Parsetree.structure >> Drop the ocaml.ppx.context attribute from a structure. If restore is true, also restore the associated data in the current process. << val drop_ppx_context_sig : restore:bool -> Parsetree.signature -> Parsetree.signature >> Same as drop_ppx_context_str, but for signatures. Cookies ======= Cookies are used to pass information from a ppx processor to a further invocation of itself, when called from the OCaml toplevel (or other tools that support cookies). << val set_cookie : string -> Parsetree.expression -> unit >> << val get_cookie : string -> Parsetree.expression option >> 30.2 Module Asttypes : Auxiliary AST types used by parsetree and typedtree. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Warning: this module is unstable and part of compiler-libs[30]. << type constant = | Const_int of int | Const_char of char | Const_string of string * Location.t * string option | Const_float of string | Const_int32 of int32 | Const_int64 of int64 | Const_nativeint of nativeint >> << type rec_flag = | Nonrecursive | Recursive >> << type direction_flag = | Upto | Downto >> << type private_flag = | Private | Public >> << type mutable_flag = | Immutable | Mutable >> << type virtual_flag = | Virtual | Concrete >> << type override_flag = | Override | Fresh >> << type closed_flag = | Closed | Open >> << type label = string >> << type arg_label = | Nolabel | Labelled of string >> label:T -> ... << | Optional of string >> ?label:T -> ... << type 'a loc = 'a Location.loc = { txt : 'a ; loc : Location.t ; } >> << type variance = | Covariant | Contravariant | NoVariance >> << type injectivity = | Injective | NoInjectivity >> 30.3 Module Location : Source code locations (ranges of positions), used in *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* parsetree. *=*=*=*=*= Warning: this module is unstable and part of compiler-libs[30]. << type t = Warnings.loc = { loc_start : Lexing.position ; loc_end : Lexing.position ; loc_ghost : bool ; } >> Note on the use of Lexing.position in this module. If pos_fname = "", then use !input_name instead. If pos_lnum = -1, then pos_bol = 0. Use pos_cnum and re-parse the file to get the line and character numbers. Else all fields are correct. << val none : t >> An arbitrary value of type t; describes an empty ghost range. << val is_none : t -> bool >> True for Location.none, false any other location << val in_file : string -> t >> Return an empty ghost range located in a given file. << val init : Lexing.lexbuf -> string -> unit >> Set the file name and line number of the lexbuf to be the start of the named file. << val curr : Lexing.lexbuf -> t >> Get the location of the current token from the lexbuf. << val symbol_rloc : unit -> t >> << val symbol_gloc : unit -> t >> << val rhs_loc : int -> t >> rhs_loc n returns the location of the symbol at position n, starting at 1, in the current parser rule. << val rhs_interval : int -> int -> t >> << val get_pos_info : Lexing.position -> string * int * int >> file, line, char << type 'a loc = { txt : 'a ; loc : t ; } >> << val mknoloc : 'a -> 'a loc >> << val mkloc : 'a -> t -> 'a loc >> Input info ========== << val input_name : string ref >> << val input_lexbuf : Lexing.lexbuf option ref >> << val input_phrase_buffer : Buffer.t option ref >> Toplevel-specific functions =========================== << val echo_eof : unit -> unit >> << val separate_new_message : Format.formatter -> unit >> << val reset : unit -> unit >> Rewriting path =============== << val rewrite_absolute_path : string -> string >> rewrite_absolute_path path rewrites path to honor the BUILD_PATH_PREFIX_MAP variable if it is set. It does not check whether path is absolute or not. The result is as follows: - If BUILD_PATH_PREFIX_MAP is not set, just return path. - otherwise, rewrite using the mapping (and if there are no matching prefixes that will just return path). See the BUILD_PATH_PREFIX_MAP spec[ https://reproducible-builds.org/specs/build-path-prefix-map/ ] << val rewrite_find_first_existing : string -> string option >> rewrite_find_first_existing path uses a BUILD_PATH_PREFIX_MAP mapping and tries to find a source in mapping that maps to a result that exists in the file system. There are the following return values: - None, means either - BUILD_PATH_PREFIX_MAP is not set and path does not exists, or - no source prefixes of path in the mapping were found, - Some target, means target exists and either - BUILD_PATH_PREFIX_MAP is not set and target = path, or - target is the first file (in priority order) that path mapped to that exists in the file system. - Not_found raised, means some source prefixes in the map were found that matched path, but none of them existed in the file system. The caller should catch this and issue an appropriate error message. See the BUILD_PATH_PREFIX_MAP spec[ https://reproducible-builds.org/specs/build-path-prefix-map/ ] << val rewrite_find_all_existing_dirs : string -> string list >> rewrite_find_all_existing_dirs dir accumulates a list of existing directories, dirs, that are the result of mapping a potentially abstract directory, dir, over all the mapping pairs in the BUILD_PATH_PREFIX_MAP environment variable, if any. The list dirs will be in priority order (head as highest priority). The possible results are: - [], means either - BUILD_PATH_PREFIX_MAP is not set and dir is not an existing directory, or - if set, then there were no matching prefixes of dir. - Some dirs, means dirs are the directories found. Either - BUILD_PATH_PREFIX_MAP is not set and dirs = [dir], or - it was set and dirs are the mapped existing directories. - Not_found raised, means some source prefixes in the map were found that matched dir, but none of mapping results were existing directories (possibly due to misconfiguration). The caller should catch this and issue an appropriate error message. See the BUILD_PATH_PREFIX_MAP spec[ https://reproducible-builds.org/specs/build-path-prefix-map/ ] << val absolute_path : string -> string >> absolute_path path first makes an absolute path, s from path, prepending the current working directory if path was relative. Then s is rewritten using rewrite_absolute_path. Finally the result is normalized by eliminating instances of '.' or '..'. Printing locations ================== << val show_filename : string -> string >> In -absname mode, return the absolute path for this filename. Otherwise, returns the filename unchanged. << val print_filename : Format.formatter -> string -> unit >> << val print_loc : Format.formatter -> t -> unit >> << val print_locs : Format.formatter -> t list -> unit >> Toplevel-specific location highlighting ======================================= << val highlight_terminfo : Lexing.lexbuf -> Format.formatter -> t list -> unit >> Reporting errors and warnings ============================= The type of reports and report printers --------------------------------------- << type msg = (Format.formatter -> unit) loc >> << val msg : ?loc:t -> ('a, Format.formatter, unit, msg) format4 -> 'a >> << type report_kind = | Report_error | Report_warning of string | Report_warning_as_error of string | Report_alert of string | Report_alert_as_error of string >> << type report = { kind : report_kind ; main : msg ; sub : msg list ; } >> << type report_printer = { pp : report_printer -> Format.formatter -> report -> unit ; pp_report_kind : report_printer -> report -> Format.formatter -> report_kind -> unit ; pp_main_loc : report_printer -> report -> Format.formatter -> t -> unit ; pp_main_txt : report_printer -> report -> Format.formatter -> (Format.formatter -> unit) -> unit ; pp_submsgs : report_printer -> report -> Format.formatter -> msg list -> unit ; pp_submsg : report_printer -> report -> Format.formatter -> msg -> unit ; pp_submsg_loc : report_printer -> report -> Format.formatter -> t -> unit ; pp_submsg_txt : report_printer -> report -> Format.formatter -> (Format.formatter -> unit) -> unit ; } >> A printer for reports, defined using open-recursion. The goal is to make it easy to define new printers by re-using code from existing ones. Report printers used in the compiler ------------------------------------ << val batch_mode_printer : report_printer >> << val terminfo_toplevel_printer : Lexing.lexbuf -> report_printer >> << val best_toplevel_printer : unit -> report_printer >> Detects the terminal capabilities and selects an adequate printer Printing a report ----------------- << val print_report : Format.formatter -> report -> unit >> Display an error or warning report. << val report_printer : (unit -> report_printer) ref >> Hook for redefining the printer of reports. The hook is a unit -> report_printer and not simply a report_printer: this is useful so that it can detect the type of the output (a file, a terminal, ...) and select a printer accordingly. << val default_report_printer : unit -> report_printer >> Original report printer for use in hooks. Reporting warnings ================== Converting a Warnings.t into a report ------------------------------------- << val report_warning : t -> Warnings.t -> report option >> report_warning loc w produces a report for the given warning w, or None if the warning is not to be printed. << val warning_reporter : (t -> Warnings.t -> report option) ref >> Hook for intercepting warnings. << val default_warning_reporter : t -> Warnings.t -> report option >> Original warning reporter for use in hooks. Printing warnings ----------------- << val formatter_for_warnings : Format.formatter ref >> << val print_warning : t -> Format.formatter -> Warnings.t -> unit >> Prints a warning. This is simply the composition of report_warning and print_report. << val prerr_warning : t -> Warnings.t -> unit >> Same as print_warning, but uses !formatter_for_warnings as output formatter. Reporting alerts ================ Converting an Alert.t into a report ----------------------------------- << val report_alert : t -> Warnings.alert -> report option >> report_alert loc w produces a report for the given alert w, or None if the alert is not to be printed. << val alert_reporter : (t -> Warnings.alert -> report option) ref >> Hook for intercepting alerts. << val default_alert_reporter : t -> Warnings.alert -> report option >> Original alert reporter for use in hooks. Printing alerts --------------- << val print_alert : t -> Format.formatter -> Warnings.alert -> unit >> Prints an alert. This is simply the composition of report_alert and print_report. << val prerr_alert : t -> Warnings.alert -> unit >> Same as print_alert, but uses !formatter_for_warnings as output formatter. << val deprecated : ?def:t -> ?use:t -> t -> string -> unit >> Prints a deprecation alert. << val alert : ?def:t -> ?use:t -> kind:string -> t -> string -> unit >> Prints an arbitrary alert. << val auto_include_alert : string -> unit >> Prints an alert that -I +lib has been automatically added to the load path << val deprecated_script_alert : string -> unit >> deprecated_script_alert command prints an alert that command foo has been deprecated in favour of command ./foo Reporting errors ================ << type error = report >> An error is a report which report_kind must be Report_error. << val error : ?loc:t -> ?sub:msg list -> string -> error >> << val errorf : ?loc:t -> ?sub:msg list -> ('a, Format.formatter, unit, error) format4 -> 'a >> << val error_of_printer : ?loc:t -> ?sub:msg list -> (Format.formatter -> 'a -> unit) -> 'a -> error >> << val error_of_printer_file : (Format.formatter -> 'a -> unit) -> 'a -> error >> Automatically reporting errors for raised exceptions ==================================================== << val register_error_of_exn : (exn -> error option) -> unit >> Each compiler module which defines a custom type of exception which can surface as a user-visible error should register a "printer" for this exception using register_error_of_exn. The result of the printer is an error value containing a location, a message, and optionally sub-messages (each of them being located as well). << val error_of_exn : exn -> [ `Already_displayed | `Ok of error ] option >> << exception Error of error >> Raising Error e signals an error e; the exception will be caught and the error will be printed. << exception Already_displayed_error >> Raising Already_displayed_error signals an error which has already been printed. The exception will be caught, but nothing will be printed << val raise_errorf : ?loc:t -> ?sub:msg list -> ('a, Format.formatter, unit, 'b) format4 -> 'a >> << val report_exception : Format.formatter -> exn -> unit >> Reraise the exception if it is unknown. 30.4 Module Longident : Long identifiers, used in parsetree. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Warning: this module is unstable and part of compiler-libs[30]. To print a longident, see Pprintast.longident[30.7], using Format.asprintf[29.22] to convert to a string. << type t = | Lident of string | Ldot of t * string | Lapply of t * t >> << val flatten : t -> string list >> << val unflatten : string list -> t option >> For a non-empty list l, unflatten l is Some lid where lid is the long identifier created by concatenating the elements of l with Ldot. unflatten [] is None. << val last : t -> string >> << val parse : string -> t >> Deprecated. this function may misparse its input, use "Parse.longident" or "Longident.unflatten"This function is broken on identifiers that are not just "Word.Word.word"; for example, it returns incorrect results on infix operators and extended module paths. If you want to generate long identifiers that are a list of dot-separated identifiers, the function Longident.unflatten[30.4] is safer and faster. Longident.unflatten[30.4] is available since OCaml 4.06.0. If you want to parse any identifier correctly, use the long-identifiers functions from the Parse[30.5] module, in particular Parse.longident[30.5]. They are available since OCaml 4.11, and also provide proper input-location support. 30.5 Module Parse : Entry points in the parser *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Warning: this module is unstable and part of compiler-libs[30]. << val implementation : Lexing.lexbuf -> Parsetree.structure >> << val interface : Lexing.lexbuf -> Parsetree.signature >> << val toplevel_phrase : Lexing.lexbuf -> Parsetree.toplevel_phrase >> << val use_file : Lexing.lexbuf -> Parsetree.toplevel_phrase list >> << val core_type : Lexing.lexbuf -> Parsetree.core_type >> << val expression : Lexing.lexbuf -> Parsetree.expression >> << val pattern : Lexing.lexbuf -> Parsetree.pattern >> << val module_type : Lexing.lexbuf -> Parsetree.module_type >> << val module_expr : Lexing.lexbuf -> Parsetree.module_expr >> The functions below can be used to parse Longident safely. << val longident : Lexing.lexbuf -> Longident.t >> The function longident is guaranteed to parse all subclasses of Longident.t[30.4] used in OCaml: values, constructors, simple or extended module paths, and types or module types. However, this function accepts inputs which are not accepted by the compiler, because they combine functor applications and infix operators. In valid OCaml syntax, only value-level identifiers may end with infix operators Foo.( + ). Moreover, in value-level identifiers the module path Foo must be simple (M.N rather than F(X)): functor applications may only appear in type-level identifiers. As a consequence, a path such as F(X).( + ) is not a valid OCaml identifier; but it is accepted by this function. The next functions are specialized to a subclass of Longident.t[30.4] << val val_ident : Lexing.lexbuf -> Longident.t >> This function parses a syntactically valid path for a value. For instance, x, M.x, and (+.) are valid. Contrarily, M.A, F(X).x, and true are rejected. Longident for OCaml’s value cannot contain functor application. The last component of the Longident.t[30.4] is not capitalized, but can be an operator A.Path.To.(.%.%.(;..)<-) << val constr_ident : Lexing.lexbuf -> Longident.t >> This function parses a syntactically valid path for a variant constructor. For instance, A, M.A and M.(::) are valid, but both M.a and F(X).A are rejected. Longident for OCaml’s variant constructors cannot contain functor application. The last component of the Longident.t[30.4] is capitalized, or it may be one the special constructors: true,false,(),[],(::). Among those special constructors, only (::) can be prefixed by a module path (A.B.C.(::)). << val simple_module_path : Lexing.lexbuf -> Longident.t >> This function parses a syntactically valid path for a module. For instance, A, and M.A are valid, but both M.a and F(X).A are rejected. Longident for OCaml’s module cannot contain functor application. The last component of the Longident.t[30.4] is capitalized. << val extended_module_path : Lexing.lexbuf -> Longident.t >> This function parse syntactically valid path for an extended module. For instance, A.B and F(A).B are valid. Contrarily, (.%()) or [] are both rejected. The last component of the Longident.t[30.4] is capitalized. << val type_ident : Lexing.lexbuf -> Longident.t >> This function parse syntactically valid path for a type or a module type. For instance, A, t, M.t and F(X).t are valid. Contrarily, (.%()) or [] are both rejected. In path for type and module types, only operators and special constructors are rejected. 30.6 Module Parsetree : Abstract syntax tree produced by parsing *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Warning: this module is unstable and part of compiler-libs[30]. << type constant = | Pconst_integer of string * char option >> Integer constants such as 3 3l 3L 3n. Suffixes [g-z][G-Z] are accepted by the parser. Suffixes except 'l', 'L' and 'n' are rejected by the typechecker << | Pconst_char of char >> Character such as 'c'. << | Pconst_string of string * Location.t * string option >> Constant string such as "constant" or {delim|other constant|delim}. The location span the content of the string, without the delimiters. << | Pconst_float of string * char option >> Float constant such as 3.4, 2e5 or 1.4e-4. Suffixes g-zG-Z are accepted by the parser. Suffixes are rejected by the typechecker. << type location_stack = Location.t list >> Extension points ================ << type attribute = { attr_name : string Asttypes.loc ; attr_payload : payload ; attr_loc : Location.t ; } >> Attributes such as [@id ARG] and [@@id ARG]. Metadata containers passed around within the AST. The compiler ignores unknown attributes. << type extension = string Asttypes.loc * payload >> Extension points such as [%id ARG] and [%%id ARG]. Sub-language placeholder – rejected by the typechecker. << type attributes = attribute list >> << type payload = | PStr of structure | PSig of signature >> : SIG in an attribute or an extension point << | PTyp of core_type >> : T in an attribute or an extension point << | PPat of pattern * expression option >> ? P or ? P when E, in an attribute or an extension point Core language ============= Type expressions ---------------- << type core_type = { ptyp_desc : core_type_desc ; ptyp_loc : Location.t ; ptyp_loc_stack : location_stack ; ptyp_attributes : attributes ; >> ... [@id1] [@id2] << } >> << type core_type_desc = | Ptyp_any >> _ << | Ptyp_var of string >> A type variable such as 'a << | Ptyp_arrow of Asttypes.arg_label * core_type * core_type >> Ptyp_arrow(lbl, T1, T2) represents: - T1 -> T2 when lbl is Nolabel[??], - ~l:T1 -> T2 when lbl is Labelled[??], - ?l:T1 -> T2 when lbl is Optional[??]. << | Ptyp_tuple of core_type list >> Ptyp_tuple([T1 ; ... ; Tn]) represents a product type T1 * ... * Tn. Invariant: n >= 2. << | Ptyp_constr of Longident.t Asttypes.loc * core_type list >> Ptyp_constr(lident, l) represents: - tconstr when l=[], - T tconstr when l=[T], - (T1, ..., Tn) tconstr when l=[T1 ; ... ; Tn]. << | Ptyp_object of object_field list * Asttypes.closed_flag >> Ptyp_object([ l1:T1; ...; ln:Tn ], flag) represents: - < l1:T1; ...; ln:Tn > when flag is Closed[??], - < l1:T1; ...; ln:Tn; .. > when flag is Open[??]. << | Ptyp_class of Longident.t Asttypes.loc * core_type list >> Ptyp_class(tconstr, l) represents: - #tconstr when l=[], - T #tconstr when l=[T], - (T1, ..., Tn) #tconstr when l=[T1 ; ... ; Tn]. << | Ptyp_alias of core_type * string Asttypes.loc >> T as 'a. << | Ptyp_variant of row_field list * Asttypes.closed_flag * Asttypes.label list option >> Ptyp_variant([`A;`B], flag, labels) represents: - [ `A|`B ] when flag is Closed[??], and labels is None, - [> `A|`B ] when flag is Open[??], and labels is None, - [< `A|`B ] when flag is Closed[??], and labels is Some [], - [< `A|`B > `X `Y ] when flag is Closed[??], and labels is Some ["X";"Y"]. << | Ptyp_poly of string Asttypes.loc list * core_type >> 'a1 ... 'an. T Can only appear in the following context: - As the Parsetree.core_type[30.6] of a Ppat_constraint[??] node corresponding to a constraint on a let-binding: << let x : 'a1 ... 'an. T = e ... >> - Under Cfk_virtual[??] for methods (not values). - As the Parsetree.core_type[30.6] of a Pctf_method[??] node. - As the Parsetree.core_type[30.6] of a Pexp_poly[??] node. - As the pld_type[??] field of a Parsetree.label_declaration[30.6]. - As a Parsetree.core_type[30.6] of a Ptyp_object[??] node. - As the pval_type[??] field of a Parsetree.value_description[30.6]. << | Ptyp_package of package_type >> (module S). << | Ptyp_open of Longident.t Asttypes.loc * core_type >> M.(T) << | Ptyp_extension of extension >> [%id]. << type package_type = Longident.t Asttypes.loc * (Longident.t Asttypes.loc * core_type) list >> As Parsetree.package_type[30.6] typed values: - (S, []) represents (module S), - (S, [(t1, T1) ; ... ; (tn, Tn)]) represents (module S with type t1 = T1 and ... and tn = Tn). << type row_field = { prf_desc : row_field_desc ; prf_loc : Location.t ; prf_attributes : attributes ; } >> << type row_field_desc = | Rtag of Asttypes.label Asttypes.loc * bool * core_type list >> Rtag(`A, b, l) represents: - `A when b is true and l is [], - `A of T when b is false and l is [T], - `A of T1 & .. & Tn when b is false and l is [T1;...Tn], - `A of & T1 & .. & Tn when b is true and l is [T1;...Tn]. - The bool field is true if the tag contains a constant (empty) constructor. - & occurs when several types are used for the same constructor (see 4.2 in the manual) << | Rinherit of core_type >> [ | t ] << type object_field = { pof_desc : object_field_desc ; pof_loc : Location.t ; pof_attributes : attributes ; } >> << type object_field_desc = | Otag of Asttypes.label Asttypes.loc * core_type | Oinherit of core_type >> Patterns -------- << type pattern = { ppat_desc : pattern_desc ; ppat_loc : Location.t ; ppat_loc_stack : location_stack ; ppat_attributes : attributes ; >> ... [@id1] [@id2] << } >> << type pattern_desc = | Ppat_any >> The pattern _. << | Ppat_var of string Asttypes.loc >> A variable pattern such as x << | Ppat_alias of pattern * string Asttypes.loc >> An alias pattern such as P as 'a << | Ppat_constant of constant >> Patterns such as 1, 'a', "true", 1.0, 1l, 1L, 1n << | Ppat_interval of constant * constant >> Patterns such as 'a'..'z'. Other forms of interval are recognized by the parser but rejected by the type-checker. << | Ppat_tuple of pattern list >> Patterns (P1, ..., Pn). Invariant: n >= 2 << | Ppat_construct of Longident.t Asttypes.loc * (string Asttypes.loc list * pattern) option >> Ppat_construct(C, args) represents: - C when args is None, - C P when args is Some ([], P) - C (P1, ..., Pn) when args is Some ([], Ppat_tuple [P1; ...; Pn]) - C (type a b) P when args is Some ([a; b], P) << | Ppat_variant of Asttypes.label * pattern option >> Ppat_variant(`A, pat) represents: - `A when pat is None, - `A P when pat is Some P << | Ppat_record of (Longident.t Asttypes.loc * pattern) list * Asttypes.closed_flag >> Ppat_record([(l1, P1) ; ... ; (ln, Pn)], flag) represents: - { l1=P1; ...; ln=Pn } when flag is Closed[??] - { l1=P1; ...; ln=Pn; _} when flag is Open[??] Invariant: n > 0 << | Ppat_array of pattern list >> Pattern [| P1; ...; Pn |] << | Ppat_or of pattern * pattern >> Pattern P1 | P2 << | Ppat_constraint of pattern * core_type >> Pattern (P : T) << | Ppat_type of Longident.t Asttypes.loc >> Pattern #tconst << | Ppat_lazy of pattern >> Pattern lazy P << | Ppat_unpack of string option Asttypes.loc >> Ppat_unpack(s) represents: - (module P) when s is Some "P" - (module _) when s is None Note: (module P : S) is represented as Ppat_constraint(Ppat_unpack(Some "P"), Ptyp_package S) << | Ppat_exception of pattern >> Pattern exception P << | Ppat_extension of extension >> Pattern [%id] << | Ppat_open of Longident.t Asttypes.loc * pattern >> Pattern M.(P) Value expressions ----------------- << type expression = { pexp_desc : expression_desc ; pexp_loc : Location.t ; pexp_loc_stack : location_stack ; pexp_attributes : attributes ; >> ... [@id1] [@id2] << } >> << type expression_desc = | Pexp_ident of Longident.t Asttypes.loc >> Identifiers such as x and M.x << | Pexp_constant of constant >> Expressions constant such as 1, 'a', "true", 1.0, 1l, 1L, 1n << | Pexp_let of Asttypes.rec_flag * value_binding list * expression >> Pexp_let(flag, [(P1,E1) ; ... ; (Pn,En)], E) represents: - let P1 = E1 and ... and Pn = EN in E when flag is Nonrecursive[??], - let rec P1 = E1 and ... and Pn = EN in E when flag is Recursive[??]. << | Pexp_function of function_param list * type_constraint option * function_body >> Pexp_function ([P1; ...; Pn], C, body) represents any construct involving fun or function, including: - fun P1 ... Pn -> E when body = Pfunction_body E - fun P1 ... Pn -> function p1 -> e1 | ... | pm -> em when body = Pfunction_cases [ p1 -> e1; ...; pm -> em ] C represents a type constraint or coercion placed immediately before the arrow, e.g. fun P1 ... Pn : ty -> ... when C = Some (Pconstraint ty). A function must have parameters. Pexp_function (params, _, body) must have non-empty params or a Pfunction_cases _ body. << | Pexp_apply of expression * (Asttypes.arg_label * expression) list >> Pexp_apply(E0, [(l1, E1) ; ... ; (ln, En)]) represents E0 ~l1:E1 ... ~ln:En li can be Nolabel[??] (non labeled argument), Labelled[??] (labelled arguments) or Optional[??] (optional argument). Invariant: n > 0 << | Pexp_match of expression * case list >> match E0 with P1 -> E1 | ... | Pn -> En << | Pexp_try of expression * case list >> try E0 with P1 -> E1 | ... | Pn -> En << | Pexp_tuple of expression list >> Expressions (E1, ..., En) Invariant: n >= 2 << | Pexp_construct of Longident.t Asttypes.loc * expression option >> Pexp_construct(C, exp) represents: - C when exp is None, - C E when exp is Some E, - C (E1, ..., En) when exp is Some (Pexp_tuple[E1;...;En]) << | Pexp_variant of Asttypes.label * expression option >> Pexp_variant(`A, exp) represents - `A when exp is None - `A E when exp is Some E << | Pexp_record of (Longident.t Asttypes.loc * expression) list * expression option >> Pexp_record([(l1,P1) ; ... ; (ln,Pn)], exp0) represents - { l1=P1; ...; ln=Pn } when exp0 is None - { E0 with l1=P1; ...; ln=Pn } when exp0 is Some E0 Invariant: n > 0 << | Pexp_field of expression * Longident.t Asttypes.loc >> E.l << | Pexp_setfield of expression * Longident.t Asttypes.loc * expression >> E1.l <- E2 << | Pexp_array of expression list >> [| E1; ...; En |] << | Pexp_ifthenelse of expression * expression * expression option >> if E1 then E2 else E3 << | Pexp_sequence of expression * expression >> E1; E2 << | Pexp_while of expression * expression >> while E1 do E2 done << | Pexp_for of pattern * expression * expression * Asttypes.direction_flag * expression >> Pexp_for(i, E1, E2, direction, E3) represents: - for i = E1 to E2 do E3 done when direction is Upto[??] - for i = E1 downto E2 do E3 done when direction is Downto[??] << | Pexp_constraint of expression * core_type >> (E : T) << | Pexp_coerce of expression * core_type option * core_type >> Pexp_coerce(E, from, T) represents - (E :> T) when from is None, - (E : T0 :> T) when from is Some T0. << | Pexp_send of expression * Asttypes.label Asttypes.loc >> E # m << | Pexp_new of Longident.t Asttypes.loc >> new M.c << | Pexp_setinstvar of Asttypes.label Asttypes.loc * expression >> x <- 2 << | Pexp_override of (Asttypes.label Asttypes.loc * expression) list >> {< x1 = E1; ...; xn = En >} << | Pexp_letmodule of string option Asttypes.loc * module_expr * expression >> let module M = ME in E << | Pexp_letexception of extension_constructor * expression >> let exception C in E << | Pexp_assert of expression >> assert E. Note: assert false is treated in a special way by the type-checker. << | Pexp_lazy of expression >> lazy E << | Pexp_poly of expression * core_type option >> Used for method bodies. Can only be used as the expression under Cfk_concrete[??] for methods (not values). << | Pexp_object of class_structure >> object ... end << | Pexp_newtype of string Asttypes.loc * expression >> fun (type t) -> E << | Pexp_pack of module_expr >> (module ME). (module ME : S) is represented as Pexp_constraint(Pexp_pack ME, Ptyp_package S) << | Pexp_open of open_declaration * expression >> - M.(E) - let open M in E - let open! M in E << | Pexp_letop of letop >> - let* P = E0 in E1 - let* P0 = E00 and* P1 = E01 in E1 << | Pexp_extension of extension >> [%id] << | Pexp_unreachable >> . << type case = { pc_lhs : pattern ; pc_guard : expression option ; pc_rhs : expression ; } >> Values of type Parsetree.case[30.6] represents (P -> E) or (P when E0 -> E) << type letop = { let_ : binding_op ; ands : binding_op list ; body : expression ; } >> << type binding_op = { pbop_op : string Asttypes.loc ; pbop_pat : pattern ; pbop_exp : expression ; pbop_loc : Location.t ; } >> << type function_param_desc = | Pparam_val of Asttypes.arg_label * expression option * pattern >> Pparam_val (lbl, exp0, P) represents the parameter: - P when lbl is Nolabel[??] and exp0 is None - ~l:P when lbl is Labelled l[??] and exp0 is None - ?l:P when lbl is Optional l[??] and exp0 is None - ?l:(P = E0) when lbl is Optional l[??] and exp0 is Some E0 Note: If E0 is provided, only Optional[??] is allowed. << | Pparam_newtype of string Asttypes.loc >> Pparam_newtype x represents the parameter (type x). x carries the location of the identifier, whereas the pparam_loc on the enclosing function_param node is the location of the (type x) as a whole. Multiple parameters (type a b c) are represented as multiple Pparam_newtype nodes, let’s say: << [ { pparam_kind = Pparam_newtype a; pparam_loc = loc1 }; { pparam_kind = Pparam_newtype b; pparam_loc = loc2 }; { pparam_kind = Pparam_newtype c; pparam_loc = loc3 }; ] >> Here, the first loc loc1 is the location of (type a b c), and the subsequent locs loc2 and loc3 are the same as loc1, except marked as ghost locations. The locations on a, b, c, correspond to the variables a, b, and c in the source code. << type function_param = { pparam_loc : Location.t ; pparam_desc : function_param_desc ; } >> << type function_body = | Pfunction_body of expression | Pfunction_cases of case list * Location.t * attributes >> In Pfunction_cases (_, loc, attrs), the location extends from the start of the function keyword to the end of the last case. The compiler will only use typechecking-related attributes from attrs, e.g. enabling or disabling a warning. See the comment on Pexp_function[??]. << type type_constraint = | Pconstraint of core_type | Pcoerce of core_type option * core_type >> See the comment on Pexp_function[??]. Value descriptions ------------------ << type value_description = { pval_name : string Asttypes.loc ; pval_type : core_type ; pval_prim : string list ; pval_attributes : attributes ; >> ... [@@id1] [@@id2] << pval_loc : Location.t ; } >> Values of type Parsetree.value_description[30.6] represents: - val x: T, when pval_prim[??] is [] - external x: T = "s1" ... "sn" when pval_prim[??] is ["s1";..."sn"] Type declarations ----------------- << type type_declaration = { ptype_name : string Asttypes.loc ; ptype_params : (core_type * (Asttypes.variance * Asttypes.injectivity)) list ; >> ('a1,...'an) t << ptype_cstrs : (core_type * core_type * Location.t) list ; >> ... constraint T1=T1' ... constraint Tn=Tn' << ptype_kind : type_kind ; ptype_private : Asttypes.private_flag ; >> for = private ... << ptype_manifest : core_type option ; >> represents = T << ptype_attributes : attributes ; >> ... [@@id1] [@@id2] << ptype_loc : Location.t ; } >> Here are type declarations and their representation, for various ptype_kind[??] and ptype_manifest[??] values: - type t when type_kind is Ptype_abstract[??], and manifest is None, - type t = T0 when type_kind is Ptype_abstract[??], and manifest is Some T0, - type t = C of T | ... when type_kind is Ptype_variant[??], and manifest is None, - type t = T0 = C of T | ... when type_kind is Ptype_variant[??], and manifest is Some T0, - type t = {l: T; ...} when type_kind is Ptype_record[??], and manifest is None, - type t = T0 = {l : T; ...} when type_kind is Ptype_record[??], and manifest is Some T0, - type t = .. when type_kind is Ptype_open[??], and manifest is None. << type type_kind = | Ptype_abstract | Ptype_variant of constructor_declaration list | Ptype_record of label_declaration list >> Invariant: non-empty list << | Ptype_open >> << type label_declaration = { pld_name : string Asttypes.loc ; pld_mutable : Asttypes.mutable_flag ; pld_type : core_type ; pld_loc : Location.t ; pld_attributes : attributes ; >> l : T [@id1] [@id2] << } >> - { ...; l: T; ... } when pld_mutable[??] is Immutable[??], - { ...; mutable l: T; ... } when pld_mutable[??] is Mutable[??]. Note: T can be a Ptyp_poly[??]. << type constructor_declaration = { pcd_name : string Asttypes.loc ; pcd_vars : string Asttypes.loc list ; pcd_args : constructor_arguments ; pcd_res : core_type option ; pcd_loc : Location.t ; pcd_attributes : attributes ; >> C of ... [@id1] [@id2] << } >> << type constructor_arguments = | Pcstr_tuple of core_type list | Pcstr_record of label_declaration list >> Values of type Parsetree.constructor_declaration[30.6] represents the constructor arguments of: - C of T1 * ... * Tn when res = None, and args = Pcstr_tuple [T1; ... ; Tn], - C: T0 when res = Some T0, and args = Pcstr_tuple [], - C: T1 * ... * Tn -> T0 when res = Some T0, and args = Pcstr_tuple [T1; ... ; Tn], - C of {...} when res = None, and args = Pcstr_record [...], - C: {...} -> T0 when res = Some T0, and args = Pcstr_record [...]. << type type_extension = { ptyext_path : Longident.t Asttypes.loc ; ptyext_params : (core_type * (Asttypes.variance * Asttypes.injectivity)) list ; ptyext_constructors : extension_constructor list ; ptyext_private : Asttypes.private_flag ; ptyext_loc : Location.t ; ptyext_attributes : attributes ; >> ... @@id1 @@id2 << } >> Definition of new extensions constructors for the extensive sum type t (type t += ...). << type extension_constructor = { pext_name : string Asttypes.loc ; pext_kind : extension_constructor_kind ; pext_loc : Location.t ; pext_attributes : attributes ; >> C of ... [@id1] [@id2] << } >> << type type_exception = { ptyexn_constructor : extension_constructor ; ptyexn_loc : Location.t ; ptyexn_attributes : attributes ; >> ... [@@id1] [@@id2] << } >> Definition of a new exception (exception E). << type extension_constructor_kind = | Pext_decl of string Asttypes.loc list * constructor_arguments * core_type option >> Pext_decl(existentials, c_args, t_opt) describes a new extension constructor. It can be: - C of T1 * ... * Tn when: - existentials is [], - c_args is [T1; ...; Tn], - t_opt is None - C: T0 when - existentials is [], - c_args is [], - t_opt is Some T0. - C: T1 * ... * Tn -> T0 when - existentials is [], - c_args is [T1; ...; Tn], - t_opt is Some T0. - C: 'a... . T1 * ... * Tn -> T0 when - existentials is ['a;...], - c_args is [T1; ... ; Tn], - t_opt is Some T0. << | Pext_rebind of Longident.t Asttypes.loc >> Pext_rebind(D) re-export the constructor D with the new name C Class language ============== Type expressions for the class language --------------------------------------- << type class_type = { pcty_desc : class_type_desc ; pcty_loc : Location.t ; pcty_attributes : attributes ; >> ... [@id1] [@id2] << } >> << type class_type_desc = | Pcty_constr of Longident.t Asttypes.loc * core_type list >> - c - ['a1, ..., 'an] c << | Pcty_signature of class_signature >> object ... end << | Pcty_arrow of Asttypes.arg_label * core_type * class_type >> Pcty_arrow(lbl, T, CT) represents: - T -> CT when lbl is Nolabel[??], - ~l:T -> CT when lbl is Labelled l[??], - ?l:T -> CT when lbl is Optional l[??]. << | Pcty_extension of extension >> %id << | Pcty_open of open_description * class_type >> let open M in CT << type class_signature = { pcsig_self : core_type ; pcsig_fields : class_type_field list ; } >> Values of type class_signature represents: - object('selfpat) ... end - object ... end when pcsig_self[??] is Ptyp_any[??] << type class_type_field = { pctf_desc : class_type_field_desc ; pctf_loc : Location.t ; pctf_attributes : attributes ; >> ... [@@id1] [@@id2] << } >> << type class_type_field_desc = | Pctf_inherit of class_type >> inherit CT << | Pctf_val of (Asttypes.label Asttypes.loc * Asttypes.mutable_flag * Asttypes.virtual_flag * core_type) >> val x: T << | Pctf_method of (Asttypes.label Asttypes.loc * Asttypes.private_flag * Asttypes.virtual_flag * core_type) >> method x: T Note: T can be a Ptyp_poly[??]. << | Pctf_constraint of (core_type * core_type) >> constraint T1 = T2 << | Pctf_attribute of attribute >> [@@@id] << | Pctf_extension of extension >> [%%id] << type 'a class_infos = { pci_virt : Asttypes.virtual_flag ; pci_params : (core_type * (Asttypes.variance * Asttypes.injectivity)) list ; pci_name : string Asttypes.loc ; pci_expr : 'a ; pci_loc : Location.t ; pci_attributes : attributes ; >> ... [@@id1] [@@id2] << } >> Values of type class_expr class_infos represents: - class c = ... - class ['a1,...,'an] c = ... - class virtual c = ... They are also used for "class type" declaration. << type class_description = class_type class_infos >> << type class_type_declaration = class_type class_infos >> Value expressions for the class language ---------------------------------------- << type class_expr = { pcl_desc : class_expr_desc ; pcl_loc : Location.t ; pcl_attributes : attributes ; >> ... [@id1] [@id2] << } >> << type class_expr_desc = | Pcl_constr of Longident.t Asttypes.loc * core_type list >> c and ['a1, ..., 'an] c << | Pcl_structure of class_structure >> object ... end << | Pcl_fun of Asttypes.arg_label * expression option * pattern * class_expr >> Pcl_fun(lbl, exp0, P, CE) represents: - fun P -> CE when lbl is Nolabel[??] and exp0 is None, - fun ~l:P -> CE when lbl is Labelled l[??] and exp0 is None, - fun ?l:P -> CE when lbl is Optional l[??] and exp0 is None, - fun ?l:(P = E0) -> CE when lbl is Optional l[??] and exp0 is Some E0. << | Pcl_apply of class_expr * (Asttypes.arg_label * expression) list >> Pcl_apply(CE, [(l1,E1) ; ... ; (ln,En)]) represents CE ~l1:E1 ... ~ln:En. li can be empty (non labeled argument) or start with ? (optional argument). Invariant: n > 0 << | Pcl_let of Asttypes.rec_flag * value_binding list * class_expr >> Pcl_let(rec, [(P1, E1); ... ; (Pn, En)], CE) represents: - let P1 = E1 and ... and Pn = EN in CE when rec is Nonrecursive[??], - let rec P1 = E1 and ... and Pn = EN in CE when rec is Recursive[??]. << | Pcl_constraint of class_expr * class_type >> (CE : CT) << | Pcl_extension of extension >> [%id] << | Pcl_open of open_description * class_expr >> let open M in CE << type class_structure = { pcstr_self : pattern ; pcstr_fields : class_field list ; } >> Values of type Parsetree.class_structure[30.6] represents: - object(selfpat) ... end - object ... end when pcstr_self[??] is Ppat_any[??] << type class_field = { pcf_desc : class_field_desc ; pcf_loc : Location.t ; pcf_attributes : attributes ; >> ... [@@id1] [@@id2] << } >> << type class_field_desc = | Pcf_inherit of Asttypes.override_flag * class_expr * string Asttypes.loc option >> Pcf_inherit(flag, CE, s) represents: - inherit CE when flag is Fresh[??] and s is None, - inherit CE as x when flag is Fresh[??] and s is Some x, - inherit! CE when flag is Override[??] and s is None, - inherit! CE as x when flag is Override[??] and s is Some x << | Pcf_val of (Asttypes.label Asttypes.loc * Asttypes.mutable_flag * class_field_kind) >> Pcf_val(x,flag, kind) represents: - val x = E when flag is Immutable[??] and kind is Cfk_concrete(Fresh, E)[??] - val virtual x: T when flag is Immutable[??] and kind is Cfk_virtual(T)[??] - val mutable x = E when flag is Mutable[??] and kind is Cfk_concrete(Fresh, E)[??] - val mutable virtual x: T when flag is Mutable[??] and kind is Cfk_virtual(T)[??] << | Pcf_method of (Asttypes.label Asttypes.loc * Asttypes.private_flag * class_field_kind) >> - method x = E (E can be a Pexp_poly[??]) - method virtual x: T (T can be a Ptyp_poly[??]) << | Pcf_constraint of (core_type * core_type) >> constraint T1 = T2 << | Pcf_initializer of expression >> initializer E << | Pcf_attribute of attribute >> [@@@id] << | Pcf_extension of extension >> [%%id] << type class_field_kind = | Cfk_virtual of core_type | Cfk_concrete of Asttypes.override_flag * expression >> << type class_declaration = class_expr class_infos >> Module language =============== Type expressions for the module language ---------------------------------------- << type module_type = { pmty_desc : module_type_desc ; pmty_loc : Location.t ; pmty_attributes : attributes ; >> ... [@id1] [@id2] << } >> << type module_type_desc = | Pmty_ident of Longident.t Asttypes.loc >> Pmty_ident(S) represents S << | Pmty_signature of signature >> sig ... end << | Pmty_functor of functor_parameter * module_type >> functor(X : MT1) -> MT2 << | Pmty_with of module_type * with_constraint list >> MT with ... << | Pmty_typeof of module_expr >> module type of ME << | Pmty_extension of extension >> [%id] << | Pmty_alias of Longident.t Asttypes.loc >> (module M) << type functor_parameter = | Unit >> () << | Named of string option Asttypes.loc * module_type >> Named(name, MT) represents: - (X : MT) when name is Some X, - (_ : MT) when name is None << type signature = signature_item list >> << type signature_item = { psig_desc : signature_item_desc ; psig_loc : Location.t ; } >> << type signature_item_desc = | Psig_value of value_description >> - val x: T - external x: T = "s1" ... "sn" << | Psig_type of Asttypes.rec_flag * type_declaration list >> type t1 = ... and ... and tn = ... << | Psig_typesubst of type_declaration list >> type t1 := ... and ... and tn := ... << | Psig_typext of type_extension >> type t1 += ... << | Psig_exception of type_exception >> exception C of T << | Psig_module of module_declaration >> module X = M and module X : MT << | Psig_modsubst of module_substitution >> module X := M << | Psig_recmodule of module_declaration list >> module rec X1 : MT1 and ... and Xn : MTn << | Psig_modtype of module_type_declaration >> module type S = MT and module type S << | Psig_modtypesubst of module_type_declaration >> module type S := ... << | Psig_open of open_description >> open X << | Psig_include of include_description >> include MT << | Psig_class of class_description list >> class c1 : ... and ... and cn : ... << | Psig_class_type of class_type_declaration list >> class type ct1 = ... and ... and ctn = ... << | Psig_attribute of attribute >> [@@@id] << | Psig_extension of extension * attributes >> [%%id] << type module_declaration = { pmd_name : string option Asttypes.loc ; pmd_type : module_type ; pmd_attributes : attributes ; >> ... [@@id1] [@@id2] << pmd_loc : Location.t ; } >> Values of type module_declaration represents S : MT << type module_substitution = { pms_name : string Asttypes.loc ; pms_manifest : Longident.t Asttypes.loc ; pms_attributes : attributes ; >> ... [@@id1] [@@id2] << pms_loc : Location.t ; } >> Values of type module_substitution represents S := M << type module_type_declaration = { pmtd_name : string Asttypes.loc ; pmtd_type : module_type option ; pmtd_attributes : attributes ; >> ... [@@id1] [@@id2] << pmtd_loc : Location.t ; } >> Values of type module_type_declaration represents: - S = MT, - S for abstract module type declaration, when pmtd_type[??] is None. << type 'a open_infos = { popen_expr : 'a ; popen_override : Asttypes.override_flag ; popen_loc : Location.t ; popen_attributes : attributes ; } >> Values of type 'a open_infos represents: - open! X when popen_override[??] is Override[??] (silences the "used identifier shadowing" warning) - open X when popen_override[??] is Fresh[??] << type open_description = Longident.t Asttypes.loc open_infos >> Values of type open_description represents: - open M.N - open M(N).O << type open_declaration = module_expr open_infos >> Values of type open_declaration represents: - open M.N - open M(N).O - open struct ... end << type 'a include_infos = { pincl_mod : 'a ; pincl_loc : Location.t ; pincl_attributes : attributes ; } >> << type include_description = module_type include_infos >> Values of type include_description represents include MT << type include_declaration = module_expr include_infos >> Values of type include_declaration represents include ME << type with_constraint = | Pwith_type of Longident.t Asttypes.loc * type_declaration >> with type X.t = ... Note: the last component of the longident must match the name of the type_declaration. << | Pwith_module of Longident.t Asttypes.loc * Longident.t Asttypes.loc >> with module X.Y = Z << | Pwith_modtype of Longident.t Asttypes.loc * module_type >> with module type X.Y = Z << | Pwith_modtypesubst of Longident.t Asttypes.loc * module_type >> with module type X.Y := sig end << | Pwith_typesubst of Longident.t Asttypes.loc * type_declaration >> with type X.t := ..., same format as [Pwith_type] << | Pwith_modsubst of Longident.t Asttypes.loc * Longident.t Asttypes.loc >> with module X.Y := Z Value expressions for the module language ----------------------------------------- << type module_expr = { pmod_desc : module_expr_desc ; pmod_loc : Location.t ; pmod_attributes : attributes ; >> ... [@id1] [@id2] << } >> << type module_expr_desc = | Pmod_ident of Longident.t Asttypes.loc >> X << | Pmod_structure of structure >> struct ... end << | Pmod_functor of functor_parameter * module_expr >> functor(X : MT1) -> ME << | Pmod_apply of module_expr * module_expr >> ME1(ME2) << | Pmod_apply_unit of module_expr >> ME1() << | Pmod_constraint of module_expr * module_type >> (ME : MT) << | Pmod_unpack of expression >> (val E) << | Pmod_extension of extension >> [%id] << type structure = structure_item list >> << type structure_item = { pstr_desc : structure_item_desc ; pstr_loc : Location.t ; } >> << type structure_item_desc = | Pstr_eval of expression * attributes >> E << | Pstr_value of Asttypes.rec_flag * value_binding list >> Pstr_value(rec, [(P1, E1 ; ... ; (Pn, En))]) represents: - let P1 = E1 and ... and Pn = EN when rec is Nonrecursive[??], - let rec P1 = E1 and ... and Pn = EN when rec is Recursive[??]. << | Pstr_primitive of value_description >> - val x: T - external x: T = "s1" ... "sn" << | Pstr_type of Asttypes.rec_flag * type_declaration list >> type t1 = ... and ... and tn = ... << | Pstr_typext of type_extension >> type t1 += ... << | Pstr_exception of type_exception >> - exception C of T - exception C = M.X << | Pstr_module of module_binding >> module X = ME << | Pstr_recmodule of module_binding list >> module rec X1 = ME1 and ... and Xn = MEn << | Pstr_modtype of module_type_declaration >> module type S = MT << | Pstr_open of open_declaration >> open X << | Pstr_class of class_declaration list >> class c1 = ... and ... and cn = ... << | Pstr_class_type of class_type_declaration list >> class type ct1 = ... and ... and ctn = ... << | Pstr_include of include_declaration >> include ME << | Pstr_attribute of attribute >> [@@@id] << | Pstr_extension of extension * attributes >> [%%id] << type value_constraint = | Pvc_constraint of { locally_abstract_univars : string Asttypes.loc list ; typ : core_type ; } | Pvc_coercion of { ground : core_type option ; coercion : core_type ; } >> - Pvc_constraint { locally_abstract_univars=[]; typ} is a simple type constraint on a value binding: let x : typ - More generally, in Pvc_constraint { locally_abstract_univars; typ} locally_abstract_univars is the list of locally abstract type variables in let x: type a ... . typ - Pvc_coercion { ground=None; coercion } represents let x :> typ - Pvc_coercion { ground=Some g; coercion } represents let x : g :> typ << type value_binding = { pvb_pat : pattern ; pvb_expr : expression ; pvb_constraint : value_constraint option ; pvb_attributes : attributes ; pvb_loc : Location.t ; } >> let pat : type_constraint = exp << type module_binding = { pmb_name : string option Asttypes.loc ; pmb_expr : module_expr ; pmb_attributes : attributes ; pmb_loc : Location.t ; } >> Values of type module_binding represents module X = ME Toplevel ======== Toplevel phrases ---------------- << type toplevel_phrase = | Ptop_def of structure | Ptop_dir of toplevel_directive >> #use, #load ... << type toplevel_directive = { pdir_name : string Asttypes.loc ; pdir_arg : directive_argument option ; pdir_loc : Location.t ; } >> << type directive_argument = { pdira_desc : directive_argument_desc ; pdira_loc : Location.t ; } >> << type directive_argument_desc = | Pdir_string of string | Pdir_int of string * char option | Pdir_ident of Longident.t | Pdir_bool of bool >> 30.7 Module Pprintast : Pretty-printers for Parsetree[30.6] *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* Warning: this module is unstable and part of compiler-libs[30]. << type space_formatter = (unit, Format.formatter, unit) format >> << val longident : Format.formatter -> Longident.t -> unit >> << val expression : Format.formatter -> Parsetree.expression -> unit >> << val string_of_expression : Parsetree.expression -> string >> << val pattern : Format.formatter -> Parsetree.pattern -> unit >> << val core_type : Format.formatter -> Parsetree.core_type -> unit >> << val signature : Format.formatter -> Parsetree.signature -> unit >> << val structure : Format.formatter -> Parsetree.structure -> unit >> << val string_of_structure : Parsetree.structure -> string >> << val module_expr : Format.formatter -> Parsetree.module_expr -> unit >> << val toplevel_phrase : Format.formatter -> Parsetree.toplevel_phrase -> unit >> << val top_phrase : Format.formatter -> Parsetree.toplevel_phrase -> unit >> << val class_field : Format.formatter -> Parsetree.class_field -> unit >> << val class_type_field : Format.formatter -> Parsetree.class_type_field -> unit >> << val class_expr : Format.formatter -> Parsetree.class_expr -> unit >> << val class_type : Format.formatter -> Parsetree.class_type -> unit >> << val module_type : Format.formatter -> Parsetree.module_type -> unit >> << val structure_item : Format.formatter -> Parsetree.structure_item -> unit >> << val signature_item : Format.formatter -> Parsetree.signature_item -> unit >> << val binding : Format.formatter -> Parsetree.value_binding -> unit >> << val payload : Format.formatter -> Parsetree.payload -> unit >> << val tyvar_of_name : string -> string >> Turn a type variable name into a valid identifier, taking care of the special treatment required for the single quote character in second position, or for keywords by escaping them with \#. No-op on "_". << val tyvar : Format.formatter -> string -> unit >> Print a type variable name as a valid identifier, taking care of the special treatment required for the single quote character in second position, or for keywords by escaping them with \#. No-op on "_". Chapter 31  The unix library: Unix system calls *************************************************** The unix library makes many Unix system calls and system-related library functions available to OCaml programs. This chapter describes briefly the functions provided. Refer to sections 2 and 3 of the Unix manual for more details on the behavior of these functions. Not all functions are provided by all Unix variants. If some functions are not available, they will raise Invalid_arg when called. Programs that use the unix library must be linked as follows: << ocamlc other options -I +unix unix.cma other files ocamlopt other options -I +unix unix.cmxa other files >> For interactive use of the unix library, do: << ocamlmktop -o mytop -I +unix unix.cma ./mytop >> or (if dynamic linking of C libraries is supported on your platform), start ocaml and type << # #directory "+unix";; >> << # #load "unix.cma";; >>  Windows: The Cygwin port of OCaml fully implements all functions from the Unix module. The native Win32 ports implement a subset of them. Below is a list of the functions that are not implemented, or only partially implemented, by the Win32 ports. Functions not mentioned are fully implemented and behave as described previously in this chapter. ----------------------------------------------------------------- | Functions | Comment | ----------------------------------------------------------------- | fork |not implemented, use | | |create_process or threads| | | | |wait |not implemented, use | | |waitpid | |waitpid |can only wait for a given| | |PID, not any child | | |process | |getppid |not implemented | | |(meaningless under | | |Windows) | |nice |not implemented | |truncate, ftruncate |implemented (since | | |4.10.0) | |link |implemented (since 3.02) | |fchmod |not implemented | |chown, fchown |not implemented (make no | | |sense on a DOS file | | |system) | |umask |not implemented | |access |execute permission X_OK | | |cannot be tested, it just| | |tests for read permission| | |instead | |chroot |not implemented | |mkfifo |not implemented | |symlink, readlink |implemented (since | | |4.03.0) | |kill |partially implemented | | |(since 4.00.0): only the | | |sigkill signal is | | |implemented | |sigprocmask, sigpending, sigsuspend |not implemented (no | | |inter-process signals on | | |Windows | |pause |not implemented (no | | |inter-process signals in | | |Windows) | |alarm |not implemented | |times |partially implemented, | | |will not report timings | | |for child processes | |getitimer, setitimer |not implemented | |getuid, geteuid, getgid, getegid |always return 1 | |setuid, setgid, setgroups, initgroups|not implemented | |getgroups |always returns [|1|] | | |(since 2.00) | |getpwnam, getpwuid |always raise Not_found | |getgrnam, getgrgid |always raise Not_found | |type socket_domain |PF_INET is fully | | |supported; PF_INET6 is | | |fully supported (since | | |4.01.0); PF_UNIX is | | |supported since 4.14.0, | | |but only works on Windows| | |10 1803 and later. | |establish_server |not implemented; use | | |threads | |terminal functions (tc*) |not implemented | |setsid |not implemented | ----------------------------------------------------------------- Chapter 32  The str library: regular expressions and string processing ************************************************************************** The str library provides high-level string processing functions, some based on regular expressions. It is intended to support the kind of file processing that is usually performed with scripting languages such as awk, perl or sed. Programs that use the str library must be linked as follows: << ocamlc other options -I +str str.cma other files ocamlopt other options -I +str str.cmxa other files >> For interactive use of the str library, do: << ocamlmktop -o mytop str.cma ./mytop >> or (if dynamic linking of C libraries is supported on your platform), start ocaml and type << # #directory "+str";; >> << # #load "str.cma";; >> 32.1 Module Str : Regular expressions and high-level string processing *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Regular expressions =================== The Str[32.1] library provides regular expressions on sequences of bytes. It is, in general, unsuitable to match Unicode characters. << type regexp >> The type of compiled regular expressions. << val regexp : string -> regexp >> Compile a regular expression. The following constructs are recognized: - . Matches any character except newline. - * (postfix) Matches the preceding expression zero, one or several times - + (postfix) Matches the preceding expression one or several times - ? (postfix) Matches the preceding expression once or not at all - [..] Character set. Ranges are denoted with -, as in [a-z]. An initial ^, as in [^0-9], complements the set. To include a ] character in a set, make it the first character of the set. To include a - character in a set, make it the first or the last character of the set. - ^ Matches at beginning of line: either at the beginning of the matched string, or just after a ’\n’ character. - $ Matches at end of line: either at the end of the matched string, or just before a ’\n’ character. - \| (infix) Alternative between two expressions. - \(..\) Grouping and naming of the enclosed expression. - \1 The text matched by the first \(...\) expression (\2 for the second expression, and so on up to \9). - \b Matches word boundaries. - \ Quotes special characters. The special characters are $^\.*+?[]. In regular expressions you will often use backslash characters; it’s easier to use a quoted string literal {|...|} to avoid having to escape backslashes. For example, the following expression: << let r = Str.regexp {|hello \([A-Za-z]+\)|} in Str.replace_first r {|\1|} "hello world" >> returns the string "world". If you want a regular expression that matches a literal backslash character, you need to double it: Str.regexp {|\\|}. You can use regular string literals "..." too, however you will have to escape backslashes. The example above can be rewritten with a regular string literal as: << let r = Str.regexp "hello \\([A-Za-z]+\\)" in Str.replace_first r "\\1" "hello world" >> And the regular expression for matching a backslash becomes a quadruple backslash: Str.regexp "\\\\". << val regexp_case_fold : string -> regexp >> Same as regexp, but the compiled expression will match text in a case-insensitive way: uppercase and lowercase letters will be considered equivalent. << val quote : string -> string >> Str.quote s returns a regexp string that matches exactly s and nothing else. << val regexp_string : string -> regexp >> Str.regexp_string s returns a regular expression that matches exactly s and nothing else. << val regexp_string_case_fold : string -> regexp >> Str.regexp_string_case_fold is similar to Str.regexp_string[32.1], but the regexp matches in a case-insensitive way. String matching and searching ============================= << val string_match : regexp -> string -> int -> bool >> string_match r s start tests whether a substring of s that starts at position start matches the regular expression r. The first character of a string has position 0, as usual. << val search_forward : regexp -> string -> int -> int >> search_forward r s start searches the string s for a substring matching the regular expression r. The search starts at position start and proceeds towards the end of the string. Return the position of the first character of the matched substring. Raises Not_found if no substring matches. << val search_backward : regexp -> string -> int -> int >> search_backward r s last searches the string s for a substring matching the regular expression r. The search first considers substrings that start at position last and proceeds towards the beginning of string. Return the position of the first character of the matched substring. Raises Not_found if no substring matches. << val string_partial_match : regexp -> string -> int -> bool >> Similar to Str.string_match[32.1], but also returns true if the argument string is a prefix of a string that matches. This includes the case of a true complete match. << val matched_string : string -> string >> matched_string s returns the substring of s that was matched by the last call to one of the following matching or searching functions: - Str.string_match[32.1] - Str.search_forward[32.1] - Str.search_backward[32.1] - Str.string_partial_match[32.1] - Str.global_substitute[32.1] - Str.substitute_first[32.1] provided that none of the following functions was called in between: - Str.global_replace[32.1] - Str.replace_first[32.1] - Str.split[32.1] - Str.bounded_split[32.1] - Str.split_delim[32.1] - Str.bounded_split_delim[32.1] - Str.full_split[32.1] - Str.bounded_full_split[32.1] Note: in the case of global_substitute and substitute_first, a call to matched_string is only valid within the subst argument, not after global_substitute or substitute_first returns. The user must make sure that the parameter s is the same string that was passed to the matching or searching function. << val match_beginning : unit -> int >> match_beginning() returns the position of the first character of the substring that was matched by the last call to a matching or searching function (see Str.matched_string[32.1] for details). << val match_end : unit -> int >> match_end() returns the position of the character following the last character of the substring that was matched by the last call to a matching or searching function (see Str.matched_string[32.1] for details). << val matched_group : int -> string -> string >> matched_group n s returns the substring of s that was matched by the nth group \(...\) of the regular expression that was matched by the last call to a matching or searching function (see Str.matched_string[32.1] for details). When n is 0, it returns the substring matched by the whole regular expression. The user must make sure that the parameter s is the same string that was passed to the matching or searching function. Raises Not_found if the nth group of the regular expression was not matched. This can happen with groups inside alternatives \|, options ? or repetitions *. For instance, the empty string will match \(a\)*, but matched_group 1 "" will raise Not_found because the first group itself was not matched. << val group_beginning : int -> int >> group_beginning n returns the position of the first character of the substring that was matched by the nth group of the regular expression that was matched by the last call to a matching or searching function (see Str.matched_string[32.1] for details). Raises - Not_found if the nth group of the regular expression was not matched. - Invalid_argument if there are fewer than n groups in the regular expression. << val group_end : int -> int >> group_end n returns the position of the character following the last character of substring that was matched by the nth group of the regular expression that was matched by the last call to a matching or searching function (see Str.matched_string[32.1] for details). Raises - Not_found if the nth group of the regular expression was not matched. - Invalid_argument if there are fewer than n groups in the regular expression. Replacement =========== << val global_replace : regexp -> string -> string -> string >> global_replace regexp templ s returns a string identical to s, except that all substrings of s that match regexp have been replaced by templ. The replacement template templ can contain \1, \2, etc; these sequences will be replaced by the text matched by the corresponding group in the regular expression. \0 stands for the text matched by the whole regular expression. << val replace_first : regexp -> string -> string -> string >> Same as Str.global_replace[32.1], except that only the first substring matching the regular expression is replaced. << val global_substitute : regexp -> (string -> string) -> string -> string >> global_substitute regexp subst s returns a string identical to s, except that all substrings of s that match regexp have been replaced by the result of function subst. The function subst is called once for each matching substring, and receives s (the whole text) as argument. << val substitute_first : regexp -> (string -> string) -> string -> string >> Same as Str.global_substitute[32.1], except that only the first substring matching the regular expression is replaced. << val replace_matched : string -> string -> string >> replace_matched repl s returns the replacement text repl in which \1, \2, etc. have been replaced by the text matched by the corresponding groups in the regular expression that was matched by the last call to a matching or searching function (see Str.matched_string[32.1] for details). s must be the same string that was passed to the matching or searching function. Splitting ========= << val split : regexp -> string -> string list >> split r s splits s into substrings, taking as delimiters the substrings that match r, and returns the list of substrings. For instance, split (regexp "[ \t]+") s splits s into blank-separated words. An occurrence of the delimiter at the beginning or at the end of the string is ignored. << val bounded_split : regexp -> string -> int -> string list >> Same as Str.split[32.1], but splits into at most n substrings, where n is the extra integer parameter. << val split_delim : regexp -> string -> string list >> Same as Str.split[32.1] but occurrences of the delimiter at the beginning and at the end of the string are recognized and returned as empty strings in the result. For instance, split_delim (regexp " ") " abc " returns [""; "abc"; ""], while split with the same arguments returns ["abc"]. << val bounded_split_delim : regexp -> string -> int -> string list >> Same as Str.bounded_split[32.1], but occurrences of the delimiter at the beginning and at the end of the string are recognized and returned as empty strings in the result. << type split_result = | Text of string | Delim of string >> << val full_split : regexp -> string -> split_result list >> Same as Str.split_delim[32.1], but returns the delimiters as well as the substrings contained between delimiters. The former are tagged Delim in the result list; the latter are tagged Text. For instance, full_split (regexp "[{}]") "{ab}" returns [Delim "{"; Text "ab"; Delim "}"]. << val bounded_full_split : regexp -> string -> int -> split_result list >> Same as Str.bounded_split_delim[32.1], but returns the delimiters as well as the substrings contained between delimiters. The former are tagged Delim in the result list; the latter are tagged Text. Extracting substrings ===================== << val string_before : string -> int -> string >> string_before s n returns the substring of all characters of s that precede position n (excluding the character at position n). << val string_after : string -> int -> string >> string_after s n returns the substring of all characters of s that follow position n (including the character at position n). << val first_chars : string -> int -> string >> first_chars s n returns the first n characters of s. This is the same function as Str.string_before[32.1]. << val last_chars : string -> int -> string >> last_chars s n returns the last n characters of s. Chapter 33  The runtime_events library ****************************************** The runtime_events library provides an API for consuming runtime tracing and metrics information from the runtime. See chapter 25 for more information. Programs that use runtime_events must be linked as follows: << ocamlc -I +runtime_events other options unix.cma runtime_events.cma other files ocamlopt -I +runtime_events other options unix.cmxa runtime_events.cmxa other files >> Compilation units that use the runtime_events library must also be compiled with the -I +runtime_events option (see chapter 13). 33.1 Module Runtime_events : Runtime events - ring buffer-based runtime *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* tracing *=*=*=* This module enables users to enable and subscribe to tracing events from the Garbage Collector and other parts of the OCaml runtime. This can be useful for diagnostic or performance monitoring purposes. This module can be used to subscribe to events for the current process or external processes asynchronously. When enabled (either via setting the OCAML_RUNTIME_EVENTS_START environment variable or calling Runtime_events.start) a file with the pid of the process and extension .events will be created. By default this is in the current directory but can be over-ridden by the OCAML_RUNTIME_EVENTS_DIR environment variable. Each domain maintains its own ring buffer in a section of the larger file into which it emits events. There is additionally a set of C APIs in runtime_events.h that can enable zero-impact monitoring of the current process or bindings for other languages. The runtime events system’s behaviour can be controlled by the following environment variables: - OCAML_RUNTIME_EVENTS_START if set will cause the runtime events system to be started as part of the OCaml runtime initialization. - OCAML_RUNTIME_EVENTS_DIR sets the directory where the runtime events ring buffers will be located. If not present the program’s working directory will be used. - OCAML_RUNTIME_EVENTS_PRESERVE if set will prevent the OCaml runtime from removing its ring buffers when it terminates. This can help if monitoring very short running programs. << type runtime_counter = | EV_C_FORCE_MINOR_ALLOC_SMALL | EV_C_FORCE_MINOR_MAKE_VECT | EV_C_FORCE_MINOR_SET_MINOR_HEAP_SIZE | EV_C_FORCE_MINOR_MEMPROF | EV_C_MINOR_PROMOTED | EV_C_MINOR_ALLOCATED | EV_C_REQUEST_MAJOR_ALLOC_SHR | EV_C_REQUEST_MAJOR_ADJUST_GC_SPEED | EV_C_REQUEST_MINOR_REALLOC_REF_TABLE | EV_C_REQUEST_MINOR_REALLOC_EPHE_REF_TABLE | EV_C_REQUEST_MINOR_REALLOC_CUSTOM_TABLE | EV_C_MAJOR_HEAP_POOL_WORDS >> Total words in a Domain’s major heap pools. This is the sum of unallocated and live words in each pool. Since: 5.1 << | EV_C_MAJOR_HEAP_POOL_LIVE_WORDS >> Current live words in a Domain’s major heap pools. Since: 5.1 << | EV_C_MAJOR_HEAP_LARGE_WORDS >> Total words of a Domain’s major heap large allocations. A large allocation is an allocation larger than the largest sized pool. Since: 5.1 << | EV_C_MAJOR_HEAP_POOL_FRAG_WORDS >> Words in a Domain’s major heap pools lost to fragmentation. This is due to there not being a pool with the exact size of an allocation and a larger sized pool needing to be used. Since: 5.1 << | EV_C_MAJOR_HEAP_POOL_LIVE_BLOCKS >> Live blocks of a Domain’s major heap pools. Since: 5.1 << | EV_C_MAJOR_HEAP_LARGE_BLOCKS >> Live blocks of a Domain’s major heap large allocations. Since: 5.1 The type for counter events emitted by the runtime. << type runtime_phase = | EV_EXPLICIT_GC_SET | EV_EXPLICIT_GC_STAT | EV_EXPLICIT_GC_MINOR | EV_EXPLICIT_GC_MAJOR | EV_EXPLICIT_GC_FULL_MAJOR | EV_EXPLICIT_GC_COMPACT | EV_MAJOR | EV_MAJOR_SWEEP | EV_MAJOR_MARK_ROOTS | EV_MAJOR_MARK | EV_MINOR | EV_MINOR_LOCAL_ROOTS | EV_MINOR_FINALIZED | EV_EXPLICIT_GC_MAJOR_SLICE | EV_FINALISE_UPDATE_FIRST | EV_FINALISE_UPDATE_LAST | EV_INTERRUPT_REMOTE | EV_MAJOR_EPHE_MARK | EV_MAJOR_EPHE_SWEEP | EV_MAJOR_FINISH_MARKING | EV_MAJOR_GC_CYCLE_DOMAINS | EV_MAJOR_GC_PHASE_CHANGE | EV_MAJOR_GC_STW | EV_MAJOR_MARK_OPPORTUNISTIC | EV_MAJOR_SLICE | EV_MAJOR_FINISH_CYCLE | EV_MINOR_CLEAR | EV_MINOR_FINALIZERS_OLDIFY | EV_MINOR_GLOBAL_ROOTS | EV_MINOR_LEAVE_BARRIER | EV_STW_API_BARRIER | EV_STW_HANDLER | EV_STW_LEADER | EV_MAJOR_FINISH_SWEEPING | EV_MINOR_FINALIZERS_ADMIN | EV_MINOR_REMEMBERED_SET | EV_MINOR_REMEMBERED_SET_PROMOTE | EV_MINOR_LOCAL_ROOTS_PROMOTE | EV_DOMAIN_CONDITION_WAIT | EV_DOMAIN_RESIZE_HEAP_RESERVATION | EV_COMPACT | EV_COMPACT_EVACUATE | EV_COMPACT_FORWARD | EV_COMPACT_RELEASE >> The type for span events emitted by the runtime. << type lifecycle = | EV_RING_START | EV_RING_STOP | EV_RING_PAUSE | EV_RING_RESUME | EV_FORK_PARENT | EV_FORK_CHILD | EV_DOMAIN_SPAWN | EV_DOMAIN_TERMINATE >> Lifecycle events for the ring itself. << val lifecycle_name : lifecycle -> string >> Return a string representation of a given lifecycle event type. << val runtime_phase_name : runtime_phase -> string >> Return a string representation of a given runtime phase event type. << val runtime_counter_name : runtime_counter -> string >> Return a string representation of a given runtime counter type. << type cursor >> Type of the cursor used when consuming. << module Timestamp : >>  sig << type t >> Type for the int64 timestamp to allow for future changes. << val to_int64 : t -> int64 >>  end << module Type : >>  sig << type 'a t >> The type for a user event content type. << val unit : unit t >> An event that has no data associated with it. << type span = | Begin | End >> << val span : span t >> An event that has a beginning and an end. << val int : int t >> An event containing an integer value. << val register : encode:(bytes -> 'a -> int) -> decode:(bytes -> int -> 'a) -> 'a t >> Registers a custom type by providing an encoder and a decoder. The encoder writes the value in the provided buffer and returns the number of bytes written. The decoder gets a slice of the buffer of specified length, and returns the decoded value. The maximum value length is 1024 bytes.  end << module User : >>  sig User events is a way for libraries to provide runtime events that can be consumed by other tools. These events can carry known data types or custom values. The current maximum number of user events is 8192. << type tag = .. >> The type for a user event tag. Tags are used to discriminate between user events of the same type. << type 'value t >> The type for a user event. User events describe their tag, carried data type and an unique string-based name. << val register : string -> tag -> 'value Runtime_events.Type.t -> 'value t >> register name tag ty registers a new event with an unique name, carrying a tag and values of type ty. << val write : 'value t -> 'value -> unit >> write t v emits value v for event t. << val name : 'a t -> string >> name t is the unique identifying name of event t. << val tag : 'a t -> tag >> tag t is the associated tag of event t, when it is known. An event can be unknown if it was not registered in the consumer program.  end << module Callbacks : >>  sig << type t >> Type of callbacks. << val create : ?runtime_begin:(int -> Runtime_events.Timestamp.t -> Runtime_events.runtime_phase -> unit) -> ?runtime_end:(int -> Runtime_events.Timestamp.t -> Runtime_events.runtime_phase -> unit) -> ?runtime_counter:(int -> Runtime_events.Timestamp.t -> Runtime_events.runtime_counter -> int -> unit) -> ?alloc:(int -> Runtime_events.Timestamp.t -> int array -> unit) -> ?lifecycle:(int -> Runtime_events.Timestamp.t -> Runtime_events.lifecycle -> int option -> unit) -> ?lost_events:(int -> int -> unit) -> unit -> t >> Create a Callback that optionally subscribes to one or more runtime events. The first int supplied to callbacks is the ring buffer index. Each domain owns a single ring buffer for the duration of the domain’s existence. After a domain terminates, a newly spawned domain may take ownership of the ring buffer. A runtime_begin callback is called when the runtime enters a new phase (e.g a runtime_begin with EV_MINOR is called at the start of a minor GC). A runtime_end callback is called when the runtime leaves a certain phase. The runtime_counter callback is called when a counter is emitted by the runtime. lifecycle callbacks are called when the ring undergoes a change in lifecycle and a consumer may need to respond. alloc callbacks are currently only called on the instrumented runtime. lost_events callbacks are called if the consumer code detects some unconsumed events have been overwritten. << val add_user_event : 'a Runtime_events.Type.t -> (int -> Runtime_events.Timestamp.t -> 'a Runtime_events.User.t -> 'a -> unit) -> t -> t >> add_user_event ty callback t extends t to additionally subscribe to user events of type ty. When such an event happens, callback is called with the corresponding event and payload.  end << val start : unit -> unit >> start () will start the collection of events in the runtime if not already started. Events can be consumed by creating a cursor with create_cursor and providing a set of callbacks to be called for each type of event. << val pause : unit -> unit >> pause () will pause the collection of events in the runtime. Traces are collected if the program has called Runtime_events.start () or the OCAML_RUNTIME_EVENTS_START environment variable has been set. << val resume : unit -> unit >> resume () will resume the collection of events in the runtime. Traces are collected if the program has called Runtime_events.start () or the OCAML_RUNTIME_EVENTS_START environment variable has been set. << val create_cursor : (string * int) option -> cursor >> create_cursor path_pid creates a cursor to read from an runtime_events. Cursors can be created for runtime_events in and out of process. A runtime_events ring-buffer may have multiple cursors reading from it at any point in time and a program may have multiple cursors open concurrently (for example if multiple consumers want different sets of events). If path_pid is None then a cursor is created for the current process. Otherwise the pair contains a string path to the directory that contains the pid.events file and int pid for the runtime_events of an external process to monitor. << val free_cursor : cursor -> unit >> Free a previously created runtime_events cursor. << val read_poll : cursor -> Callbacks.t -> int option -> int >> read_poll cursor callbacks max_option calls the corresponding functions on callbacks for up to max_option events read off cursor’s runtime_events and returns the number of events read. Chapter 34  The threads library *********************************** The threads library allows concurrent programming in OCaml. It provides multiple threads of control (also called lightweight processes) that execute concurrently in the same memory space. Threads communicate by in-place modification of shared data structures, or by sending and receiving data on communication channels. The threads library is implemented on top of the threading facilities provided by the operating system: POSIX 1003.1c threads for Linux, MacOS, and other Unix-like systems; Win32 threads for Windows. Only one thread at a time is allowed to run OCaml code on a particular domain 9.5.1. Hence, opportunities for parallelism are limited to the parts of the program that run system or C library code. However, threads provide concurrency and can be used to structure programs as several communicating processes. Threads also efficiently support concurrent, overlapping I/O operations. Programs that use threads must be linked as follows: << ocamlc -I +unix -I +threads other options unix.cma threads.cma other files ocamlopt -I +unix -I +threads other options unix.cmxa threads.cmxa other files >> Compilation units that use the threads library must also be compiled with the -I +threads option (see chapter 13). 34.1 Module Thread : Lightweight threads for Posix 1003.1c and Win32. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* << type t >> The type of thread handles. Thread creation and termination =============================== << val create : ('a -> 'b) -> 'a -> t >> Thread.create funct arg creates a new thread of control, in which the function application funct arg is executed concurrently with the other threads of the domain. The application of Thread.create returns the handle of the newly created thread. The new thread terminates when the application funct arg returns, either normally or by raising the Thread.Exit[34.1] exception or by raising any other uncaught exception. In the last case, the uncaught exception is printed on standard error, but not propagated back to the parent thread. Similarly, the result of the application funct arg is discarded and not directly accessible to the parent thread. See also Domain.spawn[29.14] if you want parallel execution instead. << val self : unit -> t >> Return the handle for the thread currently executing. << val id : t -> int >> Return the identifier of the given thread. A thread identifier is an integer that identifies uniquely the thread. It can be used to build data structures indexed by threads. << exception Exit >> Exception raised by user code to initiate termination of the current thread. In a thread created by Thread.create[34.1] funct arg, if the Thread.Exit[34.1] exception reaches the top of the application funct arg, it has the effect of terminating the current thread silently. In other contexts, there is no implicit handling of the Thread.Exit[34.1] exception. << val exit : unit -> unit >> Deprecated. Use ’raise Thread.Exit’ instead.Raise the Thread.Exit[34.1] exception. In a thread created by Thread.create[34.1], this will cause the thread to terminate prematurely, unless the thread function handles the exception itself. Fun.protect[29.23] finalizers and catch-all exception handlers will be executed. To make it clear that an exception is raised and will trigger finalizers and catch-all exception handlers, it is recommended to write raise Thread.Exit instead of Thread.exit (). Before 5.0 A different implementation was used, not based on raising an exception, and not running finalizers and catch-all handlers. The previous implementation had a different behavior when called outside of a thread created by Thread.create. Suspending threads ================== << val delay : float -> unit >> delay d suspends the execution of the calling thread for d seconds. The other program threads continue to run during this time. << val join : t -> unit >> join th suspends the execution of the calling thread until the thread th has terminated. << val yield : unit -> unit >> Re-schedule the calling thread without suspending it. This function can be used to give scheduling hints, telling the scheduler that now is a good time to switch to other threads. Waiting for file descriptors or processes ========================================= The functions below are leftovers from an earlier, VM-based threading system. The Unix[??] module provides equivalent functionality, in a more general and more standard-conformant manner. It is recommended to use Unix[??] functions directly. << val wait_timed_read : Unix.file_descr -> float -> bool >> Deprecated. Use Unix.select instead.See Thread.wait_timed_write[34.1]. << val wait_timed_write : Unix.file_descr -> float -> bool >> Deprecated. Use Unix.select instead.Suspend the execution of the calling thread until at least one character or EOF is available for reading (wait_timed_read) or one character can be written without blocking (wait_timed_write) on the given Unix file descriptor. Wait for at most the amount of time given as second argument (in seconds). Return true if the file descriptor is ready for input/output and false if the timeout expired. The same functionality can be achieved with Unix.select[??]. << val select : Unix.file_descr list -> Unix.file_descr list -> Unix.file_descr list -> float -> Unix.file_descr list * Unix.file_descr list * Unix.file_descr list >> Deprecated. Use Unix.select instead.Same function as Unix.select[??]. Suspend the execution of the calling thread until input/output becomes possible on the given Unix file descriptors. The arguments and results have the same meaning as for Unix.select[??]. << val wait_pid : int -> int * Unix.process_status >> Deprecated. Use Unix.waitpid instead.Same function as Unix.waitpid[??]. wait_pid p suspends the execution of the calling thread until the process specified by the process identifier p terminates. Returns the pid of the child caught and its termination status, as per Unix.wait[??]. Management of signals ===================== Signal handling follows the POSIX thread model: signals generated by a thread are delivered to that thread; signals generated externally are delivered to one of the threads that does not block it. Each thread possesses a set of blocked signals, which can be modified using Thread.sigmask[34.1]. This set is inherited at thread creation time. Per-thread signal masks are supported only by the system thread library under Unix, but not under Win32, nor by the VM thread library. << val sigmask : Unix.sigprocmask_command -> int list -> int list >> sigmask cmd sigs changes the set of blocked signals for the calling thread. If cmd is SIG_SETMASK, blocked signals are set to those in the list sigs. If cmd is SIG_BLOCK, the signals in sigs are added to the set of blocked signals. If cmd is SIG_UNBLOCK, the signals in sigs are removed from the set of blocked signals. sigmask returns the set of previously blocked signals for the thread. << val wait_signal : int list -> int >> wait_signal sigs suspends the execution of the calling thread until the process receives one of the signals specified in the list sigs. It then returns the number of the signal received. Signal handlers attached to the signals in sigs will not be invoked. The signals sigs are expected to be blocked before calling wait_signal. Uncaught exceptions =================== << val default_uncaught_exception_handler : exn -> unit >> Thread.default_uncaught_exception_handler will print the thread’s id, exception and backtrace (if available). << val set_uncaught_exception_handler : (exn -> unit) -> unit >> Thread.set_uncaught_exception_handler fn registers fn as the handler for uncaught exceptions. If the newly set uncaught exception handler raise an exception, Thread.default_uncaught_exception_handler[34.1] will be called. 34.2 Module Event : First-class synchronous communication. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= This module implements synchronous inter-thread communications over channels. As in John Reppy’s Concurrent ML system, the communication events are first-class values: they can be built and combined independently before being offered for communication. << type 'a channel >> The type of communication channels carrying values of type 'a. << val new_channel : unit -> 'a channel >> Return a new channel. << type +'a event >> The type of communication events returning a result of type 'a. << val send : 'a channel -> 'a -> unit event >> send ch v returns the event consisting in sending the value v over the channel ch. The result value of this event is (). << val receive : 'a channel -> 'a event >> receive ch returns the event consisting in receiving a value from the channel ch. The result value of this event is the value received. << val always : 'a -> 'a event >> always v returns an event that is always ready for synchronization. The result value of this event is v. << val choose : 'a event list -> 'a event >> choose evl returns the event that is the alternative of all the events in the list evl. << val wrap : 'a event -> ('a -> 'b) -> 'b event >> wrap ev fn returns the event that performs the same communications as ev, then applies the post-processing function fn on the return value. << val wrap_abort : 'a event -> (unit -> unit) -> 'a event >> wrap_abort ev fn returns the event that performs the same communications as ev, but if it is not selected the function fn is called after the synchronization. << val guard : (unit -> 'a event) -> 'a event >> guard fn returns the event that, when synchronized, computes fn() and behaves as the resulting event. This enables computing events with side-effects at the time of the synchronization operation. << val sync : 'a event -> 'a >> ’Synchronize’ on an event: offer all the communication possibilities specified in the event to the outside world, and block until one of the communications succeed. The result value of that communication is returned. << val select : 'a event list -> 'a >> ’Synchronize’ on an alternative of events. select evl is shorthand for sync(choose evl). << val poll : 'a event -> 'a option >> Non-blocking version of Event.sync[34.2]: offer all the communication possibilities specified in the event to the outside world, and if one can take place immediately, perform it and return Some r where r is the result value of that communication. Otherwise, return None without blocking. Chapter 35  The dynlink library: dynamic loading and linking of object ************************************************************************** files ***** The dynlink library supports type-safe dynamic loading and linking of bytecode object files (.cmo and .cma files) in a running bytecode program, or of native plugins (usually .cmxs files) in a running native program. Type safety is ensured by limiting the set of modules from the running program that the loaded object file can access, and checking that the running program and the loaded object file have been compiled against the same interfaces for these modules. In native code, there are also some compatibility checks on the implementations (to avoid errors with cross-module optimizations); it might be useful to hide .cmx files when building native plugins so that they remain independent of the implementation of modules in the main program. Programs that use the dynlink library simply need to include the dynlink library directory with -I +dynlink and link dynlink.cma or dynlink.cmxa with their object files and other libraries. Note: in order to insure that the dynamically-loaded modules have access to all the libraries that are visible to the main program (and not just to the parts of those libraries that are actually used in the main program), programs using the dynlink library should be linked with -linkall. 35.1 Module Dynlink : Dynamic loading of .cmo, .cma and .cmxs files. *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= << val is_native : bool >> true if the program is native, false if the program is bytecode. Dynamic loading of compiled files ================================= << val loadfile : string -> unit >> In bytecode: load the given bytecode object file (.cmo file) or bytecode library file (.cma file), and link it with the running program. In native code: load the given OCaml plugin file (usually .cmxs), and link it with the running program. All toplevel expressions in the loaded compilation units are evaluated. No facilities are provided to access value names defined by the unit. Therefore, the unit must itself register its entry points with the main program (or a previously-loaded library) e.g. by modifying tables of functions. An exception will be raised if the given library defines toplevel modules whose names clash with modules existing either in the main program or a shared library previously loaded with loadfile. Modules from shared libraries previously loaded with loadfile_private are not included in this restriction. The compilation units loaded by this function are added to the "allowed units" list (see Dynlink.set_allowed_units[35.1]). << val loadfile_private : string -> unit >> Same as loadfile, except that the compilation units just loaded are hidden (cannot be referenced) from other modules dynamically loaded afterwards. An exception will be raised if the given library defines toplevel modules whose names clash with modules existing in either the main program or a shared library previously loaded with loadfile. Modules from shared libraries previously loaded with loadfile_private are not included in this restriction. An exception will also be raised if the given library defines toplevel modules whose name matches that of an interface depended on by a module existing in either the main program or a shared library previously loaded with loadfile. This applies even if such dependency is only a "module alias" dependency (i.e. just on the name rather than the contents of the interface). The compilation units loaded by this function are not added to the "allowed units" list (see Dynlink.set_allowed_units[35.1]) since they cannot be referenced from other compilation units. << val adapt_filename : string -> string >> In bytecode, the identity function. In native code, replace the last extension with .cmxs. Access control ============== << val set_allowed_units : string list -> unit >> Set the list of compilation units that may be referenced from units that are dynamically loaded in the future to be exactly the given value. Initially all compilation units composing the program currently running are available for reference from dynamically-linked units. set_allowed_units can be used to restrict access to a subset of these units, e.g. to the units that compose the API for dynamically-linked code, and prevent access to all other units, e.g. private, internal modules of the running program. Note that Dynlink.loadfile[35.1] changes the allowed-units list. << val allow_only : string list -> unit >> allow_only units sets the list of allowed units to be the intersection of the existing allowed units and the given list of units. As such it can never increase the set of allowed units. << val prohibit : string list -> unit >> prohibit units prohibits dynamically-linked units from referencing the units named in list units by removing such units from the allowed units list. This can be used to prevent access to selected units, e.g. private, internal modules of the running program. << val main_program_units : unit -> string list >> Return the list of compilation units that form the main program (i.e. are not dynamically linked). << val public_dynamically_loaded_units : unit -> string list >> Return the list of compilation units that have been dynamically loaded via loadfile (and not via loadfile_private). Note that compilation units loaded dynamically cannot be unloaded. << val all_units : unit -> string list >> Return the list of compilation units that form the main program together with those that have been dynamically loaded via loadfile (and not via loadfile_private). << val allow_unsafe_modules : bool -> unit >> Govern whether unsafe object files are allowed to be dynamically linked. A compilation unit is ’unsafe’ if it contains declarations of external functions, which can break type safety. By default, dynamic linking of unsafe object files is not allowed. In native code, this function does nothing; object files with external functions are always allowed to be dynamically linked. Error reporting =============== << type linking_error = private | Undefined_global of string | Unavailable_primitive of string | Uninitialized_global of string >> << type error = private | Not_a_bytecode_file of string | Inconsistent_import of string | Unavailable_unit of string | Unsafe_file | Linking_error of string * linking_error | Corrupted_interface of string | Cannot_open_dynamic_library of exn | Library's_module_initializers_failed of exn | Inconsistent_implementation of string | Module_already_loaded of string | Private_library_cannot_implement_interface of string >> << exception Error of error >> Errors in dynamic linking are reported by raising the Error exception with a description of the error. A common case is the dynamic library not being found on the system: this is reported via Cannot_open_dynamic_library (the enclosed exception may be platform-specific). << val error_message : error -> string >> Convert an error description to a printable message. Chapter 36  Recently removed or moved libraries (Graphics, Bigarray, Num, ***************************************************************************** LablTk) ******* This chapter describes three libraries which were formerly part of the OCaml distribution (Graphics, Num, and LablTk), and a library which has now become part of OCaml’s standard library, and is documented there (Bigarray). 36.1 The Graphics Library *=*=*=*=*=*=*=*=*=*=*=*=*=* Since OCaml 4.09, the graphics library is distributed as an external package. Its new home is: https://github.com/ocaml/graphics If you are using the opam package manager, you should install the corresponding graphics package: << opam install graphics >> Before OCaml 4.09, this package simply ensures that the graphics library was installed by the compiler, and starting from OCaml 4.09 this package effectively provides the graphics library. 36.2 The Bigarray Library *=*=*=*=*=*=*=*=*=*=*=*=*=* As of OCaml 4.07, the bigarray library has been integrated into OCaml’s standard library. The bigarray functionality may now be found in the standard library Bigarray module, except for the map_file function which is now part of the Unix library. The documentation has been integrated into the documentation for the standard library. The legacy bigarray library bundled with the compiler is a compatibility library with exactly the same interface as before, i.e. with map_file included. We strongly recommend that you port your code to use the standard library version instead, as the changes required are minimal. If you choose to use the compatibility library, you must link your programs as follows: << ocamlc other options bigarray.cma other files ocamlopt other options bigarray.cmxa other files >> For interactive use of the bigarray compatibility library, do: << ocamlmktop -o mytop bigarray.cma ./mytop >> or (if dynamic linking of C libraries is supported on your platform), start ocaml and type #load "bigarray.cma";;. 36.3 The Num Library *=*=*=*=*=*=*=*=*=*=*= The num library implements integer arithmetic and rational arithmetic in arbitrary precision. It was split off the core OCaml distribution starting with the 4.06.0 release, and can now be found at https://github.com/ocaml/num. New applications that need arbitrary-precision arithmetic should use the Zarith library (https://github.com/ocaml/Zarith) instead of the Num library, and older applications that already use Num are encouraged to switch to Zarith. Zarith delivers much better performance than Num and has a nicer API. 36.4 The Labltk Library and OCamlBrowser *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*= Since OCaml version 4.02, the OCamlBrowser tool and the Labltk library are distributed separately from the OCaml compiler. The project is now hosted at https://github.com/garrigue/labltk. Part: V ******* Indexes ******* Chapter 37  Index to the library ************************************ - ( * ), 28.2 - ( ** ), 28.2 - ( *. ), 28.2 - (&&), 28.2, 29.6 - (@), 28.2 - (@@), 28.2 - (!), 28.2 - (!=), 28.2 - (:=), 28.2 - (=), 28.2 - (==), 28.2 - (^), 28.2 - (^^), 28.2 - (>), 28.2 - (>=), 28.2 - (<), 28.2 - (<=), 28.2 - (<>), 28.2 - (-), 28.2 - (-.), 28.2 - (|>), 28.2 - (||), 28.2, 29.6 - (+), 28.2 - (+.), 28.2 - (/), 28.2 - (/.), 28.2 - (~-), 28.2 - (~-.), 28.2 - (~+), 28.2 - (~+.), 28.2 - (asr), 28.2 - (land), 28.2 - (lor), 28.2 - (lsl), 28.2 - (lsr), 28.2 - (lxor), 28.2 - (mod), 28.2 - __FILE__, 28.2 - __FUNCTION__, 28.2 - __LINE__, 28.2 - __LINE_OF__, 28.2 - __LOC__, 28.2 - __LOC_OF__, 28.2 - __MODULE__, 28.2 - __POS__, 28.2 - __POS_OF__, 28.2 - Already_displayed_error, 30.3 - Arg, 28.2, 29.1 - Array, 28.2, 29.2, 29.21, 29.53 - Array0, 29.5 - Array1, 29.5 - Array2, 29.5 - Array3, 29.5 - ArrayLabels, 28.2, 29.3, 29.21 - Assert_failure, 28.2 - Assert_failure, 11.7.8, 28.1 - Ast_mapper, 30.1 - Asttypes, 30.2 - Atomic, 28.2, 29.4 - abs, 28.2, 29.21, 29.27, 29.28, 29.29, 29.38 - abs_float, 28.2 - absolute_path, 30.3 - acos, 28.2, 29.21 - acosh, 28.2, 29.21 - acquire, 29.51, 29.51 - adapt_filename, 35.1 - add, 29.12, 29.19, 29.19, 29.19, 29.19, 29.19, 29.21, 29.25, 29.25, 29.25, 29.27, 29.28, 29.29, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.38, 29.45, 29.50, 29.60 - add_buffer, 29.7 - add_bytes, 29.7 - add_channel, 29.7 - add_char, 29.7 - add_int16_be, 29.7 - add_int16_le, 29.7 - add_int16_ne, 29.7 - add_int32_be, 29.7 - add_int32_le, 29.7 - add_int32_ne, 29.7 - add_int64_be, 29.7 - add_int64_le, 29.7 - add_int64_ne, 29.7 - add_int8, 29.7 - add_last, 29.16 - add_ppx_context_sig, 30.1 - add_ppx_context_str, 30.1 - add_seq, 29.7, 29.19, 29.19, 29.25, 29.25, 29.25, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.45, 29.50, 29.52 - add_string, 29.7 - add_subbytes, 29.7 - add_substitute, 29.7 - add_substring, 29.7 - add_symbolic_output_item, 29.22 - add_to_list, 29.34, 29.36 - add_uint16_be, 29.7 - add_uint16_le, 29.7 - add_uint16_ne, 29.7 - add_uint8, 29.7 - add_user_event, 33.1 - add_utf_16be_uchar, 29.7 - add_utf_16le_uchar, 29.7 - add_utf_8_uchar, 29.7 - alarm, 29.24 - alert, 30.3 - alert_reporter, 30.3 - align, 29.1 - all_units, 35.1 - allocated_bytes, 29.24 - allocation, 29.24 - allocation_source, 29.24 - allow_only, 35.1 - allow_unsafe_modules, 35.1 - always, 34.2 - anon_fun, 29.1 - append, 29.2, 29.3, 29.16, 29.21, 29.21, 29.32, 29.33, 29.49 - append_array, 29.16 - append_iter, 29.16 - append_list, 29.16 - append_seq, 29.16 - apply, 30.1 - arg, 29.12 - arg_label, 30.2 - argv, 29.56 - array, 28.1 - array0_of_genarray, 29.5 - array1_of_genarray, 29.5 - array2_of_genarray, 29.5 - array3_of_genarray, 29.5 - asin, 28.2, 29.21 - asinh, 28.2, 29.21 - asprintf, 29.22 - assoc, 29.32, 29.33 - assoc_opt, 29.32, 29.33 - assq, 29.32, 29.33 - assq_opt, 29.32, 29.33 - at_exit, 28.2, 29.14 - atan, 28.2, 29.21 - atan2, 28.2, 29.21 - atanh, 28.2, 29.21 - attribute, 30.6 - attribute_of_warning, 30.1 - attributes, 30.6 - auto_include_alert, 30.3 - Bad, 29.1 - Bigarray, 28.2, 29.5 - Binary, 29.51 - BLAKE128, 29.15 - BLAKE256, 29.15 - BLAKE512, 29.15 - Bool, 28.2, 29.6 - Break, 29.56 - Bucket, 29.19, 29.19, 29.19 - Buffer, 28.2, 29.7 - Bytes, 28.2, 29.8, 29.53 - BytesLabels, 28.2, 29.9 - backend_type, 29.56, 29.56 - backtrace_slot, 29.43 - backtrace_slots, 29.43 - backtrace_slots_of_raw_entry, 29.43 - backtrace_status, 29.43 - basename, 29.20 - batch_mode_printer, 30.3 - before_first_spawn, 29.14 - beginning_of_input, 29.48 - best_toplevel_printer, 30.3 - big_endian, 29.56 - bind, 29.40, 29.47 - binding, 30.7 - binding_op, 30.6 - bindings, 29.34, 29.36 - bits, 29.46, 29.46 - bits_of_float, 29.28, 29.29 - bits32, 29.46, 29.46 - bits64, 29.46, 29.46 - blit, 29.2, 29.3, 29.5, 29.5, 29.5, 29.5, 29.5, 29.7, 29.8, 29.9, 29.21, 29.21, 29.54, 29.55, 29.60 - blit_string, 29.8, 29.9 - bom, 29.58 - bool, 28.1, 29.46, 29.46 - bool_of_string, 28.2 - bool_of_string_opt, 28.2 - bounded_full_split, 32.1 - bounded_split, 32.1 - bounded_split_delim, 32.1 - bprintf, 29.44 - broadcast, 29.13 - bscanf, 29.48 - bscanf_format, 29.48 - bscanf_opt, 29.48 - bytes, 28.1, 29.15, 29.15 - Callback, 28.2, 29.10 - Callbacks, 33.1 - Char, 28.2, 29.11 - Complex, 28.2, 29.12 - Condition, 28.2, 29.13 - Continuation_already_resumed, 29.17 - Counting, 29.51 - c_layout, 29.5, 29.5 - capacity, 29.16 - capitalize_ascii, 29.8, 29.9, 29.54, 29.55 - cardinal, 29.34, 29.36, 29.36, 29.50 - case, 30.6 - cat, 29.8, 29.9, 29.54, 29.55 - catch, 29.43 - catch_break, 29.56 - cbrt, 29.21 - ceil, 28.2, 29.21 - change_layout, 29.5, 29.5, 29.5, 29.5, 29.5 - channel, 29.15, 29.15, 34.2 - char, 28.1, 29.5 - char_of_int, 28.2 - chdir, 29.56 - check, 29.60 - check_geometry, 29.22 - check_suffix, 29.20 - choose, 29.34, 29.36, 29.36, 29.50, 34.2 - choose_opt, 29.34, 29.36, 29.36, 29.50 - chop_extension, 29.20 - chop_suffix, 29.20 - chop_suffix_opt, 29.20 - chr, 29.11 - class_declaration, 30.6 - class_description, 30.6 - class_expr, 30.6, 30.7 - class_expr_desc, 30.6 - class_field, 30.6, 30.7 - class_field_desc, 30.6 - class_field_kind, 30.6 - class_infos, 30.6 - class_signature, 30.6 - class_structure, 30.6 - class_type, 30.6, 30.7 - class_type_declaration, 30.6 - class_type_desc, 30.6 - class_type_field, 30.6, 30.7 - class_type_field_desc, 30.6 - classify_float, 28.2, 29.21 - clean, 29.19, 29.19 - clear, 29.7, 29.16, 29.19, 29.19, 29.19, 29.19, 29.19, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36, 29.45, 29.52, 29.60 - clear_parser, 29.42 - clear_symbolic_output_buffer, 29.22 - close, 29.26, 29.41 - close_box, 29.22 - close_in, 28.2, 29.48 - close_in_noerr, 28.2 - close_noerr, 29.26, 29.41 - close_out, 28.2 - close_out_noerr, 28.2 - close_stag, 29.22 - close_tbox, 29.22 - closed_flag, 30.2 - code, 29.11 - combine, 29.2, 29.3, 29.32, 29.33 - command, 29.56 - compact, 29.24 - compare, 28.2, 29.6, 29.8, 29.9, 29.11, 29.15, 29.15, 29.18, 29.21, 29.27, 29.28, 29.29, 29.32, 29.33, 29.34, 29.34, 29.36, 29.36, 29.36, 29.36, 29.38, 29.40, 29.47, 29.49, 29.50, 29.50, 29.54, 29.55, 29.58, 29.59 - compare_and_set, 29.4 - compare_length_with, 29.32, 29.33 - compare_lengths, 29.32, 29.33 - complex32, 29.5 - complex32_elt, 29.5 - complex64, 29.5 - complex64_elt, 29.5 - compose, 29.23 - concat, 29.2, 29.3, 29.8, 29.9, 29.20, 29.21, 29.21, 29.32, 29.33, 29.49, 29.54, 29.55 - concat_map, 29.32, 29.33, 29.49 - conj, 29.12 - cons, 29.32, 29.33, 29.49 - const, 29.23 - constant, 30.2, 30.6 - constr_ident, 30.5 - constructor_arguments, 30.6 - constructor_declaration, 30.6 - contains, 29.8, 29.9, 29.54, 29.55 - contains_from, 29.8, 29.9, 29.54, 29.55 - contents, 29.7 - continuation, 29.17, 29.17 - continue, 29.17 - continue_with, 29.17 - control, 29.24 - convert_raw_backtrace_slot, 29.43 - copy, 29.2, 29.3, 29.8, 29.9, 29.16, 29.19, 29.19, 29.21, 29.21, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36, 29.39, 29.45, 29.46, 29.52 - copy_sign, 29.21 - copysign, 28.2 - core_type, 30.5, 30.6, 30.7 - core_type_desc, 30.6 - cos, 28.2, 29.21 - cosh, 28.2, 29.21 - count, 29.60 - counters, 29.24 - cpu_relax, 29.14 - create, 29.5, 29.5, 29.5, 29.5, 29.5, 29.7, 29.8, 29.9, 29.13, 29.16, 29.19, 29.19, 29.21, 29.21, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36, 29.37, 29.45, 29.52, 29.60, 29.60, 33.1, 34.1 - create_alarm, 29.24 - create_cursor, 33.1 - create_float, 29.2, 29.3 - curr, 30.3 - current, 29.1 - current_dir_name, 29.20 - cursor, 33.1 - cycle, 29.49 - cygwin, 29.56 - Deep, 29.17 - Digest, 28.2, 29.15 - Division_by_zero, 28.2 - Division_by_zero, 28.1 - DLS, 29.14 - Domain, 28.2, 29.14 - Dynarray, 28.2, 29.16 - Dynlink, 35.1 - data, 29.60 - data_size, 29.35 - decr, 28.2, 29.4 - default_alert_reporter, 30.3 - default_mapper, 30.1 - default_report_printer, 30.3 - default_uncaught_exception_handler, 29.43, 34.1 - default_warning_reporter, 30.3 - delay, 34.1 - delete_alarm, 29.24 - deprecated, 30.3 - deprecated_script_alert, 30.3 - development_version, 29.56 - diff, 29.36, 29.50 - dim, 29.5 - dim1, 29.5, 29.5 - dim2, 29.5, 29.5 - dim3, 29.5 - dims, 29.5 - dir_sep, 29.20 - direction_flag, 30.2 - directive_argument, 30.6 - directive_argument_desc, 30.6 - dirname, 29.20 - discard, 29.24 - discontinue, 29.17 - discontinue_with, 29.17 - discontinue_with_backtrace, 29.17, 29.17 - disjoint, 29.36, 29.50 - div, 29.12, 29.21, 29.27, 29.28, 29.29, 29.38 - doc, 29.1 - dprintf, 29.22 - drop, 29.49, 29.52 - drop_ppx_context_sig, 30.1 - drop_ppx_context_str, 30.1 - drop_while, 29.49 - dummy_pos, 29.31 - Effect, 28.2, 29.17 - Either, 28.2, 29.18 - Empty, 29.45, 29.52 - End_of_file, 28.2 - End_of_file, 28.1 - Ephemeron, 28.2, 29.19 - Error, 30.3, 35.1 - Event, 34.2 - Exit, 28.2, 34.1 - echo_eof, 30.3 - effect_handler, 29.17 - elements, 29.36, 29.50 - elt, 29.36, 29.50 - empty, 29.8, 29.9, 29.34, 29.36, 29.36, 29.49, 29.50, 29.54, 29.55 - enable_runtime_warnings, 29.56 - end_of_input, 29.48 - ends_with, 29.8, 29.9, 29.54, 29.55 - ensure_capacity, 29.16 - ensure_extra_capacity, 29.16 - eprintf, 29.22, 29.44 - epsilon, 29.21 - epsilon_float, 28.2 - eq, 29.57 - equal, 29.6, 29.8, 29.9, 29.11, 29.15, 29.15, 29.18, 29.21, 29.25, 29.25, 29.27, 29.28, 29.29, 29.32, 29.33, 29.34, 29.36, 29.36, 29.36, 29.36, 29.38, 29.40, 29.47, 29.49, 29.50, 29.54, 29.55, 29.58, 29.59 - erf, 29.21 - erfc, 29.21 - err_formatter, 29.22 - error, 29.47, 30.3, 30.3, 35.1 - error_message, 35.1 - error_of_exn, 30.3 - error_of_printer, 30.3 - error_of_printer_file, 30.3 - errorf, 30.3 - escaped, 29.8, 29.9, 29.11, 29.54, 29.55 - event, 34.2 - eventlog_pause, 29.24 - eventlog_resume, 29.24 - exchange, 29.4 - executable_name, 29.56 - exists, 29.2, 29.3, 29.8, 29.9, 29.16, 29.21, 29.21, 29.32, 29.33, 29.34, 29.36, 29.36, 29.49, 29.50, 29.54, 29.55 - exists2, 29.2, 29.3, 29.32, 29.33, 29.49 - exit, 28.2, 34.1 - exn, 28.1 - exn_slot_id, 29.43 - exn_slot_name, 29.43 - exp, 28.2, 29.12, 29.21 - exp2, 29.21 - expm1, 28.2, 29.21 - expression, 30.5, 30.6, 30.7 - expression_desc, 30.6 - extend, 29.8, 29.9 - extended_module_path, 30.5 - extension, 29.20, 30.6 - extension_constructor, 30.6 - extension_constructor_kind, 30.6 - extension_of_error, 30.1 - extern_flags, 29.35 - extra_info, 29.56 - extra_prefix, 29.56 - Failure, 28.1, 28.2 - Filename, 28.2, 29.20 - Finally_raised, 29.23 - Float, 28.2, 29.21 - Forced_twice, 29.49 - Format, 28.2, 29.22 - Fun, 28.2, 29.23 - failwith, 28.2 - fast_sort, 29.2, 29.3, 29.21, 29.21, 29.32, 29.33 - fetch_and_add, 29.4 - fiber, 29.17 - file, 29.15, 29.15 - file_exists, 29.56 - file_name, 29.48 - fill, 29.2, 29.3, 29.5, 29.5, 29.5, 29.5, 29.5, 29.8, 29.9, 29.21, 29.21, 29.60 - filter, 29.16, 29.32, 29.33, 29.34, 29.36, 29.36, 29.49, 29.50 - filter_map, 29.16, 29.32, 29.33, 29.34, 29.36, 29.36, 29.49, 29.50 - filter_map_inplace, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36 - filteri, 29.32, 29.33 - finalise, 29.24 - finalise_last, 29.24 - finalise_release, 29.24 - find, 29.19, 29.19, 29.19, 29.19, 29.19, 29.25, 29.25, 29.25, 29.32, 29.33, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.49, 29.50, 29.60 - find_all, 29.19, 29.19, 29.25, 29.25, 29.25, 29.32, 29.33, 29.36, 29.36, 29.36, 29.60 - find_first, 29.34, 29.36, 29.36, 29.50 - find_first_opt, 29.34, 29.36, 29.36, 29.50 - find_index, 29.2, 29.3, 29.21, 29.21, 29.32, 29.33, 29.49 - find_last, 29.16, 29.34, 29.36, 29.36, 29.50 - find_last_opt, 29.34, 29.36, 29.36, 29.50 - find_left, 29.18 - find_map, 29.2, 29.3, 29.21, 29.21, 29.32, 29.33, 29.49 - find_mapi, 29.2, 29.3, 29.21, 29.21, 29.32, 29.33, 29.49 - find_opt, 29.2, 29.3, 29.19, 29.19, 29.21, 29.21, 29.25, 29.25, 29.25, 29.32, 29.33, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.50, 29.60 - find_right, 29.18 - first_chars, 32.1 - fit_capacity, 29.16 - flat_map, 29.49 - flatten, 29.32, 29.33, 30.4 - flip, 29.23 - float, 28.1, 28.2, 29.46, 29.46 - float_of_bits, 29.28, 29.29 - float_of_int, 28.2 - float_of_string, 28.2 - float_of_string_opt, 28.2 - float16, 29.5 - float16_elt, 29.5 - float32, 29.5 - float32_elt, 29.5 - float64, 29.5 - float64_elt, 29.5 - floor, 28.2, 29.21 - flush, 28.2, 29.41 - flush_all, 28.2, 29.41 - flush_input, 29.31 - flush_str_formatter, 29.22 - flush_symbolic_output_buffer, 29.22 - fma, 29.21 - fold, 29.18, 29.25, 29.25, 29.25, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.40, 29.45, 29.47, 29.50, 29.52, 29.60 - fold_left, 29.2, 29.3, 29.8, 29.9, 29.16, 29.21, 29.21, 29.32, 29.33, 29.49, 29.54, 29.55 - fold_left_map, 29.2, 29.3, 29.32, 29.33 - fold_left2, 29.32, 29.33, 29.49 - fold_lefti, 29.49 - fold_lines, 29.26 - fold_right, 29.2, 29.3, 29.8, 29.9, 29.16, 29.21, 29.21, 29.32, 29.33, 29.54, 29.55 - fold_right2, 29.32, 29.33 - for_all, 29.2, 29.3, 29.8, 29.9, 29.16, 29.18, 29.21, 29.21, 29.32, 29.33, 29.34, 29.36, 29.36, 29.49, 29.50, 29.54, 29.55 - for_all2, 29.2, 29.3, 29.32, 29.33, 29.49 - force, 11.6, 29.30 - force_newline, 29.22 - force_val, 29.30 - forever, 29.49 - format, 28.2, 29.43 - format_from_string, 29.48 - format_of_string, 28.2 - format4, 28.1, 28.2 - format6, 28.2 - formatter, 29.22 - formatter_for_warnings, 30.3 - formatter_of_buffer, 29.22 - formatter_of_out_channel, 29.22 - formatter_of_out_functions, 29.22 - formatter_of_symbolic_output_buffer, 29.22 - formatter_out_functions, 29.22 - formatter_stag_functions, 29.22 - fortran_layout, 29.5, 29.5 - fpclass, 28.2, 29.21 - fprintf, 29.22, 29.44 - free_cursor, 33.1 - frexp, 28.2, 29.21 - from_bytes, 29.35 - from_channel, 29.31, 29.35, 29.48 - from_file, 29.48 - from_file_bin, 29.48 - from_fun, 29.30 - from_function, 29.31, 29.48 - from_hex, 29.15 - from_string, 29.31, 29.35, 29.48 - from_val, 29.30 - fst, 28.2 - full_init, 29.46 - full_int, 29.46, 29.46 - full_major, 29.24 - full_split, 32.1 - function_body, 30.6 - function_param, 30.6 - function_param_desc, 30.6 - functor_parameter, 30.6 - Gc, 28.2, 29.24 - Genarray, 29.5 - genarray_of_array0, 29.5 - genarray_of_array1, 29.5 - genarray_of_array2, 29.5 - genarray_of_array3, 29.5 - geometry, 29.22 - get, 29.2, 29.3, 29.4, 29.5, 29.5, 29.5, 29.5, 29.5, 29.8, 29.9, 29.14, 29.16, 29.21, 29.21, 29.24, 29.40, 29.54, 29.55, 29.60 - get_backtrace, 29.43 - get_callstack, 29.17, 29.17, 29.43 - get_cookie, 30.1 - get_copy, 29.60 - get_ellipsis_text, 29.22 - get_err_formatter, 29.22 - get_error, 29.47 - get_formatter_out_functions, 29.22 - get_formatter_output_functions, 29.22 - get_formatter_stag_functions, 29.22 - get_geometry, 29.22 - get_id, 29.14 - get_int16_be, 29.8, 29.9, 29.54, 29.55 - get_int16_le, 29.8, 29.9, 29.54, 29.55 - get_int16_ne, 29.8, 29.9, 29.54, 29.55 - get_int32_be, 29.8, 29.9, 29.54, 29.55 - get_int32_le, 29.8, 29.9, 29.54, 29.55 - get_int32_ne, 29.8, 29.9, 29.54, 29.55 - get_int64_be, 29.8, 29.9, 29.54, 29.55 - get_int64_le, 29.8, 29.9, 29.54, 29.55 - get_int64_ne, 29.8, 29.9, 29.54, 29.55 - get_int8, 29.8, 29.9, 29.54, 29.55 - get_last, 29.16 - get_margin, 29.22 - get_mark_tags, 29.22 - get_max_boxes, 29.22 - get_max_indent, 29.22 - get_minor_free, 29.24 - get_ok, 29.47 - get_pos_info, 30.3 - get_print_tags, 29.22 - get_raw_backtrace, 29.43 - get_raw_backtrace_next_slot, 29.43 - get_raw_backtrace_slot, 29.43 - get_state, 29.46 - get_std_formatter, 29.22 - get_stdbuf, 29.22 - get_str_formatter, 29.22 - get_symbolic_output_buffer, 29.22 - get_temp_dir_name, 29.20 - get_uint16_be, 29.8, 29.9, 29.54, 29.55 - get_uint16_le, 29.8, 29.9, 29.54, 29.55 - get_uint16_ne, 29.8, 29.9, 29.54, 29.55 - get_uint8, 29.8, 29.9, 29.54, 29.55 - get_utf_16be_uchar, 29.8, 29.9, 29.54, 29.55 - get_utf_16le_uchar, 29.8, 29.9, 29.54, 29.55 - get_utf_8_uchar, 29.8, 29.9, 29.54, 29.55 - get_value, 29.51 - getcwd, 29.56 - getenv, 29.56 - getenv_opt, 29.56 - global_replace, 32.1 - global_substitute, 32.1 - group, 29.49 - group_beginning, 32.1 - group_end, 32.1 - guard, 34.2 - HashedType, 29.25, 29.36 - Hashtbl, 28.2, 29.25, 29.36 - Help, 29.1 - handler, 29.17, 29.17 - hash, 29.6, 29.11, 29.21, 29.25, 29.25, 29.27, 29.28, 29.29, 29.36, 29.36, 29.38, 29.54, 29.55, 29.58 - hash_length, 29.15 - hash_param, 29.25, 29.36 - hd, 29.32, 29.33 - header_size, 29.35 - highlight_terminfo, 30.3 - hypot, 28.2, 29.21 - Id, 29.57 - Immediate, 29.56 - Immediate64, 29.56 - In_channel, 28.2, 29.26 - Int, 28.2, 29.27 - Int32, 28.2, 29.28 - Int64, 28.2, 29.29 - Invalid_argument, 28.2 - Invalid_argument, 28.1 - i, 29.12 - ibprintf, 29.44 - id, 29.14, 29.23, 29.39, 34.1 - ifprintf, 29.22, 29.44 - ignore, 28.2 - ikbprintf, 29.44 - ikfprintf, 29.22, 29.44 - implementation, 30.5 - in_channel, 28.2, 29.48 - in_channel_length, 28.2, 28.2 - in_file, 30.3 - include_declaration, 30.6 - include_description, 30.6 - include_infos, 30.6 - incr, 28.2, 29.4 - index, 29.8, 29.9, 29.54, 29.55 - index_from, 29.8, 29.9, 29.54, 29.55 - index_from_opt, 29.8, 29.9, 29.54, 29.55 - index_opt, 29.8, 29.9, 29.54, 29.55 - infinity, 28.2, 29.21 - init, 29.2, 29.3, 29.5, 29.5, 29.5, 29.5, 29.5, 29.8, 29.9, 29.16, 29.21, 29.21, 29.32, 29.33, 29.46, 29.49, 29.54, 29.55, 30.3 - init_matrix, 29.2, 29.3, 29.21, 29.21 - injectivity, 30.2 - input, 28.2, 29.15, 29.15, 29.26 - input_all, 29.26 - input_bigarray, 29.26 - input_binary_int, 28.2 - input_byte, 28.2, 29.26 - input_char, 28.2, 29.26 - input_lexbuf, 30.3 - input_line, 28.2, 29.26 - input_lines, 29.26 - input_name, 30.3 - input_phrase_buffer, 30.3 - input_value, 28.2 - int, 28.1, 29.5, 29.46, 29.46, 33.1 - int_elt, 29.5 - int_in_range, 29.46, 29.46 - int_of_char, 28.2 - int_of_float, 28.2 - int_of_string, 28.2 - int_of_string_opt, 28.2 - int_size, 29.56 - int16_signed, 29.5 - int16_signed_elt, 29.5 - int16_unsigned, 29.5 - int16_unsigned_elt, 29.5 - int32, 28.1, 29.5, 29.46, 29.46 - int32_elt, 29.5 - int32_in_range, 29.46, 29.46 - int64, 28.1, 29.5, 29.46, 29.46 - int64_elt, 29.5 - int64_in_range, 29.46, 29.46 - int8_signed, 29.5 - int8_signed_elt, 29.5 - int8_unsigned, 29.5 - int8_unsigned_elt, 29.5 - inter, 29.36, 29.50 - interactive, 29.56 - interface, 30.5 - interleave, 29.49 - ints, 29.49 - inv, 29.12 - invalid_arg, 28.2 - is_binary_mode, 29.26, 29.41 - is_buffered, 29.41 - is_char, 29.58 - is_directory, 29.56 - is_empty, 29.16, 29.32, 29.33, 29.34, 29.36, 29.36, 29.45, 29.49, 29.50, 29.52 - is_error, 29.47 - is_finite, 29.21 - is_implicit, 29.20 - is_infinite, 29.21 - is_inline, 29.43 - is_integer, 29.21 - is_left, 29.18 - is_main_domain, 29.14 - is_nan, 29.21 - is_native, 35.1 - is_none, 29.40, 30.3 - is_ok, 29.47 - is_raise, 29.43 - is_randomized, 29.25, 29.36 - is_regular_file, 29.56 - is_relative, 29.20 - is_right, 29.18 - is_some, 29.40 - is_val, 29.30 - is_valid, 29.58 - is_valid_utf_16be, 29.8, 29.9, 29.54, 29.55 - is_valid_utf_16le, 29.8, 29.9, 29.54, 29.55 - is_valid_utf_8, 29.8, 29.9, 29.54, 29.55 - isatty, 29.26, 29.41 - iter, 29.2, 29.3, 29.8, 29.9, 29.16, 29.18, 29.21, 29.21, 29.25, 29.25, 29.25, 29.32, 29.33, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.40, 29.45, 29.47, 29.49, 29.50, 29.52, 29.54, 29.55, 29.60 - iter_error, 29.47 - iter2, 29.2, 29.3, 29.21, 29.21, 29.32, 29.33, 29.49 - iterate, 29.49 - iteri, 29.2, 29.3, 29.8, 29.9, 29.16, 29.21, 29.21, 29.32, 29.33, 29.49, 29.54, 29.55 - join, 29.14, 29.40, 29.47, 34.1 - K1, 29.19 - K2, 29.19 - Kn, 29.19 - kasprintf, 29.22 - kbprintf, 29.44 - kdprintf, 29.22 - key, 29.1, 29.14, 29.19, 29.19, 29.25, 29.25, 29.34, 29.36, 29.36, 29.36 - kfprintf, 29.22, 29.44 - kind, 29.5, 29.5, 29.5, 29.5, 29.5, 29.5 - kind_size_in_bytes, 29.5 - kprintf, 29.44 - kscanf, 29.48 - ksprintf, 29.22, 29.44 - ksscanf, 29.48 - LargeFile, 28.2 - Lazy, 28.2, 29.30 - Lazy (module), 11.6 - Lexing, 28.2, 29.31 - List, 28.2, 29.32, 29.53 - ListLabels, 28.2, 29.33 - Location, 30.3 - Longident, 30.4 - label, 30.2 - label_declaration, 30.6 - last, 30.4 - last_chars, 32.1 - layout, 29.5, 29.5, 29.5, 29.5, 29.5, 29.5 - lazy_t, 28.1 - ldexp, 28.2, 29.21 - left, 29.18 - length, 29.2, 29.3, 29.7, 29.8, 29.9, 29.16, 29.19, 29.19, 29.19, 29.19, 29.19, 29.21, 29.21, 29.25, 29.25, 29.25, 29.26, 29.32, 29.33, 29.36, 29.36, 29.36, 29.41, 29.45, 29.49, 29.52, 29.54, 29.55, 29.60 - letop, 30.6 - lexbuf, 29.31 - lexeme, 29.31 - lexeme_char, 29.31 - lexeme_end, 29.31 - lexeme_end_p, 29.31 - lexeme_start, 29.31 - lexeme_start_p, 29.31 - lifecycle, 33.1 - lifecycle_name, 33.1 - linking_error, 35.1 - list, 28.1 - lnot, 28.2 - loadfile, 35.1 - loadfile_private, 35.1 - loc, 30.2, 30.3 - location, 29.43, 29.43 - location_stack, 30.6 - lock, 29.37 - log, 28.2, 29.12, 29.21 - log10, 28.2, 29.21 - log1p, 28.2, 29.21 - log2, 29.21 - logand, 29.27, 29.28, 29.29, 29.38 - lognot, 29.27, 29.28, 29.29, 29.38 - logor, 29.27, 29.28, 29.29, 29.38 - logxor, 29.27, 29.28, 29.29, 29.38 - longident, 30.5, 30.7 - lowercase_ascii, 29.8, 29.9, 29.11, 29.54, 29.55 - Make, 29.19, 29.19, 29.19, 29.25, 29.34, 29.36, 29.36, 29.36, 29.50, 29.56, 29.60 - MakeSeeded, 29.19, 29.19, 29.19, 29.25, 29.36 - Map, 28.2, 29.34, 29.36 - Marshal, 28.2, 29.35 - Match_failure, 28.2 - Match_failure, 11.7.2, 11.7.2, 11.7.3, 28.1 - MD5, 29.15 - Memprof, 29.24 - MoreLabels, 28.2, 29.36 - Mutex, 28.2, 29.37 - main_program_units, 35.1 - major, 29.24 - major_slice, 29.24 - make, 29.2, 29.3, 29.4, 29.8, 29.9, 29.16, 29.19, 29.19, 29.19, 29.19, 29.19, 29.19, 29.21, 29.21, 29.46, 29.51, 29.51, 29.54, 29.55, 29.57 - make_contended, 29.4 - make_formatter, 29.22 - make_matrix, 29.2, 29.3, 29.21, 29.21 - make_self_init, 29.46 - make_symbolic_output_buffer, 29.22 - make_synchronized_formatter, 29.22 - map, 29.2, 29.3, 29.8, 29.9, 29.16, 29.18, 29.21, 29.21, 29.30, 29.32, 29.33, 29.34, 29.36, 29.36, 29.40, 29.47, 29.49, 29.50, 29.54, 29.55 - map_error, 29.47 - map_from_array, 29.21, 29.21 - map_inplace, 29.2, 29.3, 29.21, 29.21 - map_left, 29.18 - map_opt, 30.1 - map_product, 29.49 - map_right, 29.18 - map_to_array, 29.21, 29.21 - map_val, 29.30 - map2, 29.2, 29.3, 29.21, 29.21, 29.32, 29.33, 29.49 - mapi, 29.2, 29.3, 29.8, 29.9, 29.16, 29.21, 29.21, 29.32, 29.33, 29.34, 29.36, 29.49, 29.54, 29.55 - mapi_inplace, 29.2, 29.3, 29.21, 29.21 - mapper, 30.1 - match_beginning, 32.1 - match_end, 32.1 - match_with, 29.17 - matched_group, 32.1 - matched_string, 32.1 - max, 28.2, 29.21, 29.27, 29.28, 29.29, 29.38, 29.58 - max_array_length, 29.56 - max_binding, 29.34, 29.36 - max_binding_opt, 29.34, 29.36 - max_elt, 29.36, 29.50 - max_elt_opt, 29.36, 29.50 - max_float, 28.2, 29.21 - max_floatarray_length, 29.56 - max_int, 28.2, 29.27, 29.28, 29.29, 29.38 - max_num, 29.21 - max_string_length, 29.56 - mem, 29.2, 29.3, 29.19, 29.19, 29.21, 29.21, 29.25, 29.25, 29.25, 29.32, 29.33, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.50, 29.60 - mem_assoc, 29.32, 29.33 - mem_assq, 29.32, 29.33 - mem_ieee, 29.21, 29.21 - memoize, 29.49 - memq, 29.2, 29.3, 29.32, 29.33 - merge, 29.32, 29.33, 29.34, 29.36, 29.60 - min, 28.2, 29.21, 29.27, 29.28, 29.29, 29.38, 29.58 - min_binding, 29.34, 29.36 - min_binding_opt, 29.34, 29.36 - min_elt, 29.36, 29.50 - min_elt_opt, 29.36, 29.50 - min_float, 28.2, 29.21 - min_int, 28.2, 29.27, 29.28, 29.29, 29.38 - min_max, 29.21 - min_max_num, 29.21 - min_num, 29.21 - minor, 29.24 - minor_words, 29.24 - minus_one, 29.21, 29.27, 29.28, 29.29, 29.38 - mkdir, 29.56 - mkloc, 30.3 - mknoloc, 30.3 - mod_float, 28.2 - modf, 28.2, 29.21 - module_binding, 30.6 - module_declaration, 30.6 - module_expr, 30.5, 30.6, 30.7 - module_expr_desc, 30.6 - module_substitution, 30.6 - module_type, 30.5, 30.6, 30.7 - module_type_declaration, 30.6 - module_type_desc, 30.6 - msg, 30.3, 30.3 - mul, 29.12, 29.21, 29.27, 29.28, 29.29, 29.38 - mutable_flag, 30.2 - Nativeint, 28.2, 29.38 - Non_immediate, 29.56 - Not_found, 28.2 - Not_found, 28.1 - name, 29.43, 33.1 - name_of_input, 29.48 - nan, 28.2, 29.21 - nativebits, 29.46, 29.46 - nativeint, 28.1, 29.5, 29.46, 29.46 - nativeint_elt, 29.5 - nativeint_in_range, 29.46, 29.46 - neg, 29.12, 29.21, 29.27, 29.28, 29.29, 29.38 - neg_infinity, 28.2, 29.21 - negate, 29.23 - new_channel, 34.2 - new_key, 29.14 - new_line, 29.31 - next_after, 29.21 - node, 29.49 - none, 29.40, 30.3 - norm, 29.12 - norm2, 29.12 - not, 28.2, 29.6 - nth, 29.7, 29.32, 29.33 - nth_dim, 29.5 - nth_opt, 29.32, 29.33 - null, 29.20 - null_tracker, 29.24 - num_dims, 29.5 - Obj, 28.2 - Ocaml_operators, 29.61 - Oo, 28.2, 29.39 - Option, 28.2, 29.40 - OrderedType, 29.34, 29.36, 29.36, 29.50 - Out_channel, 28.2, 29.41 - Out_of_memory, 28.2 - Out_of_memory, 28.1 - object_field, 30.6 - object_field_desc, 30.6 - ocaml_release, 29.56 - ocaml_release_info, 29.56 - ocaml_version, 29.56 - of_array, 29.5, 29.5, 29.5, 29.16 - of_binary_string, 29.46 - of_bytes, 29.54, 29.55 - of_char, 29.58 - of_dispenser, 29.49 - of_float, 29.27, 29.28, 29.29, 29.38 - of_hex, 29.15, 29.15 - of_int, 29.21, 29.28, 29.29, 29.38, 29.58 - of_int32, 29.29, 29.38 - of_list, 29.2, 29.3, 29.16, 29.21, 29.21, 29.34, 29.36, 29.36, 29.50 - of_nativeint, 29.29 - of_seq, 29.2, 29.3, 29.7, 29.8, 29.9, 29.16, 29.19, 29.19, 29.21, 29.21, 29.25, 29.25, 29.25, 29.32, 29.33, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.45, 29.50, 29.52, 29.54, 29.55 - of_string, 29.8, 29.9, 29.21, 29.28, 29.29, 29.38 - of_string_opt, 29.21, 29.28, 29.29, 29.38 - of_value, 29.5 - ok, 29.47 - once, 29.49 - one, 29.12, 29.21, 29.27, 29.28, 29.29, 29.38 - opaque_identity, 29.56 - open_bin, 29.26, 29.41 - open_box, 29.22 - open_declaration, 30.6 - open_description, 30.6 - open_flag, 28.2, 29.26, 29.41 - open_gen, 29.26, 29.41 - open_hbox, 29.22 - open_hovbox, 29.22 - open_hvbox, 29.22 - open_in, 28.2, 29.48 - open_in_bin, 28.2, 29.48 - open_in_gen, 28.2 - open_infos, 30.6 - open_out, 28.2 - open_out_bin, 28.2 - open_out_gen, 28.2 - open_stag, 29.22 - open_tbox, 29.22 - open_temp_file, 29.20 - open_text, 29.26, 29.41 - open_vbox, 29.22 - option, 28.1 - os_type, 29.56 - out_channel, 28.2 - out_channel_length, 28.2, 28.2 - output, 28.2, 29.15, 29.15, 29.41 - output_bigarray, 29.41 - output_binary_int, 28.2 - output_buffer, 29.7 - output_byte, 28.2, 29.41 - output_bytes, 28.2, 29.41 - output_char, 28.2, 29.41 - output_string, 28.2, 29.41 - output_substring, 28.2, 29.41 - output_value, 28.2 - over_max_boxes, 29.22 - override_flag, 30.2 - Parse, 30.5 - Parse_error, 29.42 - Parsetree, 30.6 - Parsing, 28.2, 29.42 - Pprintast, 30.7 - Printexc, 28.2, 29.43 - Printf, 28.2, 29.44 - package_type, 30.6 - parent_dir_name, 29.20 - parse, 29.1, 30.4 - parse_and_expand_argv_dynamic, 29.1 - parse_argv, 29.1 - parse_argv_dynamic, 29.1 - parse_dynamic, 29.1 - parse_expand, 29.1 - partition, 29.32, 29.33, 29.34, 29.36, 29.36, 29.49, 29.50 - partition_map, 29.32, 29.33, 29.49 - pattern, 30.5, 30.6, 30.7 - pattern_desc, 30.6 - pause, 33.1 - payload, 30.6, 30.7 - peek, 29.45 - peek_opt, 29.45 - perform, 29.17 - pi, 29.21 - polar, 29.12 - poll, 34.2 - pop, 29.45, 29.52 - pop_last, 29.16 - pop_last_opt, 29.16 - pop_opt, 29.52 - pos, 29.26, 29.41 - pos_in, 28.2, 28.2 - pos_out, 28.2, 28.2 - position, 29.31 - pow, 29.12, 29.21 - pp_close_box, 29.22 - pp_close_stag, 29.22 - pp_close_tbox, 29.22 - pp_force_newline, 29.22 - pp_get_ellipsis_text, 29.22 - pp_get_formatter_out_functions, 29.22 - pp_get_formatter_output_functions, 29.22 - pp_get_formatter_stag_functions, 29.22 - pp_get_geometry, 29.22 - pp_get_margin, 29.22 - pp_get_mark_tags, 29.22 - pp_get_max_boxes, 29.22 - pp_get_max_indent, 29.22 - pp_get_print_tags, 29.22 - pp_infinity, 29.22 - pp_open_box, 29.22 - pp_open_hbox, 29.22 - pp_open_hovbox, 29.22 - pp_open_hvbox, 29.22 - pp_open_stag, 29.22 - pp_open_tbox, 29.22 - pp_open_vbox, 29.22 - pp_over_max_boxes, 29.22 - pp_print_array, 29.22 - pp_print_as, 29.22 - pp_print_bool, 29.22 - pp_print_break, 29.22 - pp_print_bytes, 29.22 - pp_print_char, 29.22 - pp_print_custom_break, 29.22 - pp_print_cut, 29.22 - pp_print_either, 29.22 - pp_print_float, 29.22 - pp_print_flush, 29.22 - pp_print_if_newline, 29.22 - pp_print_int, 29.22 - pp_print_iter, 29.22 - pp_print_list, 29.22 - pp_print_newline, 29.22 - pp_print_nothing, 29.22 - pp_print_option, 29.22 - pp_print_result, 29.22 - pp_print_seq, 29.22 - pp_print_space, 29.22 - pp_print_string, 29.22 - pp_print_tab, 29.22 - pp_print_tbreak, 29.22 - pp_print_text, 29.22 - pp_safe_set_geometry, 29.22 - pp_set_ellipsis_text, 29.22 - pp_set_formatter_out_channel, 29.22 - pp_set_formatter_out_functions, 29.22 - pp_set_formatter_output_functions, 29.22 - pp_set_formatter_stag_functions, 29.22 - pp_set_geometry, 29.22 - pp_set_margin, 29.22 - pp_set_mark_tags, 29.22 - pp_set_max_boxes, 29.22 - pp_set_max_indent, 29.22 - pp_set_print_tags, 29.22 - pp_set_tab, 29.22 - pp_set_tags, 29.22 - pp_update_geometry, 29.22 - pred, 28.2, 29.21, 29.27, 29.28, 29.29, 29.38, 29.58 - prerr_alert, 30.3 - prerr_bytes, 28.2 - prerr_char, 28.2 - prerr_endline, 28.2 - prerr_float, 28.2 - prerr_int, 28.2 - prerr_newline, 28.2 - prerr_string, 28.2 - prerr_warning, 30.3 - print, 29.43 - print_alert, 30.3 - print_as, 29.22 - print_backtrace, 29.43 - print_bool, 29.22 - print_break, 29.22 - print_bytes, 28.2, 29.22 - print_char, 28.2, 29.22 - print_cut, 29.22 - print_endline, 28.2 - print_filename, 30.3 - print_float, 28.2, 29.22 - print_flush, 29.22 - print_if_newline, 29.22 - print_int, 28.2, 29.22 - print_loc, 30.3 - print_locs, 30.3 - print_newline, 28.2, 29.22 - print_raw_backtrace, 29.43 - print_report, 30.3 - print_space, 29.22 - print_stat, 29.24 - print_string, 28.2, 29.22 - print_tab, 29.22 - print_tbreak, 29.22 - print_warning, 30.3 - printf, 29.22, 29.44 - private_flag, 30.2 - product, 29.49 - prohibit, 35.1 - protect, 29.23, 29.37 - provably_equal, 29.57 - public_dynamically_loaded_units, 35.1 - push, 29.45, 29.52 - Queue, 28.2, 29.45 - query, 29.19, 29.19, 29.19 - quick_stat, 29.24 - quiet_nan, 29.21 - quote, 29.20, 32.1 - quote_command, 29.20 - Random, 28.2, 29.46 - Result, 28.2, 29.47 - Runtime_events, 33.1 - raise, 28.2 - raise_errorf, 30.3 - raise_notrace, 28.2 - raise_with_backtrace, 29.43 - randomize, 29.25, 29.36 - raw_backtrace, 29.43 - raw_backtrace_entries, 29.43 - raw_backtrace_entry, 29.43 - raw_backtrace_length, 29.43 - raw_backtrace_slot, 29.43 - raw_backtrace_to_string, 29.43 - rcontains_from, 29.8, 29.9, 29.54, 29.55 - read_arg, 29.1 - read_arg0, 29.1 - read_float, 28.2 - read_float_opt, 28.2 - read_int, 28.2 - read_int_opt, 28.2 - read_line, 28.2 - read_poll, 33.1 - readdir, 29.56 - really_input, 28.2, 29.26 - really_input_bigarray, 29.26 - really_input_string, 28.2, 29.26 - rebuild, 29.25, 29.36 - rec_flag, 30.2 - receive, 34.2 - recommended_domain_count, 29.14 - record_backtrace, 29.43 - ref, 28.2, 28.2 - regexp, 32.1, 32.1 - regexp_case_fold, 32.1 - regexp_string, 32.1 - regexp_string_case_fold, 32.1 - register, 29.10, 30.1, 33.1, 33.1 - register_error_of_exn, 30.3 - register_exception, 29.10 - register_function, 30.1 - register_printer, 29.43 - release, 29.51, 29.51 - rem, 29.21, 29.27, 29.28, 29.29, 29.38 - remove, 29.19, 29.19, 29.19, 29.19, 29.19, 29.25, 29.25, 29.25, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.50, 29.56, 29.60 - remove_assoc, 29.32, 29.33 - remove_assq, 29.32, 29.33 - remove_extension, 29.20 - remove_last, 29.16 - rename, 29.56 - rep, 29.58 - repeat, 29.49 - replace, 29.19, 29.19, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36 - replace_first, 32.1 - replace_matched, 32.1 - replace_seq, 29.19, 29.19, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36 - report, 30.3 - report_alert, 30.3 - report_exception, 30.3 - report_kind, 30.3 - report_printer, 30.3, 30.3 - report_warning, 30.3 - repr, 29.56, 29.56 - reset, 29.7, 29.16, 29.19, 29.19, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36, 30.3 - reshape, 29.5 - reshape_0, 29.5 - reshape_1, 29.5 - reshape_2, 29.5 - reshape_3, 29.5 - result, 28.2 - resume, 33.1 - return, 29.49 - rev, 29.32, 29.33 - rev_append, 29.32, 29.33 - rev_map, 29.32, 29.33 - rev_map2, 29.32, 29.33 - rewrite_absolute_path, 30.3 - rewrite_find_all_existing_dirs, 30.3 - rewrite_find_first_existing, 30.3 - rhs_end, 29.42 - rhs_end_pos, 29.42 - rhs_interval, 30.3 - rhs_loc, 30.3 - rhs_start, 29.42 - rhs_start_pos, 29.42 - right, 29.18 - rindex, 29.8, 29.9, 29.54, 29.55 - rindex_from, 29.8, 29.9, 29.54, 29.55 - rindex_from_opt, 29.8, 29.9, 29.54, 29.55 - rindex_opt, 29.8, 29.9, 29.54, 29.55 - rmdir, 29.56 - round, 29.21 - row_field, 30.6 - row_field_desc, 30.6 - run_main, 30.1 - runtime_counter, 33.1 - runtime_counter_name, 33.1 - runtime_parameters, 29.56 - runtime_phase, 33.1 - runtime_phase_name, 33.1 - runtime_variant, 29.56 - runtime_warnings_enabled, 29.56 - S, 29.15, 29.19, 29.25, 29.34, 29.36, 29.36, 29.36, 29.50, 29.60 - Scan_failure, 29.48 - Scanf, 28.2, 29.48 - Scanning, 29.48 - SeededHashedType, 29.25, 29.36 - SeededS, 29.19, 29.25, 29.36 - Semaphore, 28.2, 29.51 - Seq, 28.2, 29.49 - Set, 28.2, 29.36, 29.50 - Shallow, 29.17 - Slot, 29.43 - Stack, 28.2, 29.52 - Stack_overflow, 28.2 - Stack_overflow, 28.1 - State, 29.46 - StdLabels, 28.2, 29.53 - Stdlib, 28.2 - Str, 32.1 - String, 28.2, 29.53, 29.54 - StringLabels, 28.2, 29.55 - Sys, 28.2, 29.56 - Sys_blocked_io, 28.2 - Sys_error, 28.2 - Sys_blocked_io, 28.1 - Sys_error, 28.1 - safe_set_geometry, 29.22 - scan, 29.49 - scanbuf, 29.48 - scanf, 29.48 - scanf_opt, 29.48 - scanner, 29.48 - scanner_opt, 29.48 - search_backward, 32.1 - search_forward, 32.1 - seeded_hash, 29.6, 29.11, 29.21, 29.25, 29.25, 29.27, 29.28, 29.29, 29.36, 29.36, 29.38, 29.54, 29.55 - seeded_hash_param, 29.25, 29.36 - seek, 29.26, 29.41 - seek_in, 28.2, 28.2 - seek_out, 28.2, 28.2 - select, 34.1, 34.2 - self, 29.14, 34.1 - self_init, 29.46 - send, 34.2 - separate_new_message, 30.3 - set, 29.2, 29.3, 29.4, 29.5, 29.5, 29.5, 29.5, 29.5, 29.8, 29.9, 29.14, 29.16, 29.21, 29.21, 29.24, 29.60 - set_allowed_units, 35.1 - set_binary_mode, 29.26, 29.41 - set_binary_mode_in, 28.2 - set_binary_mode_out, 28.2 - set_buffered, 29.41 - set_capacity, 29.16 - set_cookie, 30.1 - set_ellipsis_text, 29.22 - set_filename, 29.31 - set_formatter_out_channel, 29.22 - set_formatter_out_functions, 29.22 - set_formatter_output_functions, 29.22 - set_formatter_stag_functions, 29.22 - set_geometry, 29.22 - set_int16_be, 29.8, 29.9 - set_int16_le, 29.8, 29.9 - set_int16_ne, 29.8, 29.9 - set_int32_be, 29.8, 29.9 - set_int32_le, 29.8, 29.9 - set_int32_ne, 29.8, 29.9 - set_int64_be, 29.8, 29.9 - set_int64_le, 29.8, 29.9 - set_int64_ne, 29.8, 29.9 - set_int8, 29.8, 29.9 - set_margin, 29.22 - set_mark_tags, 29.22 - set_max_boxes, 29.22 - set_max_indent, 29.22 - set_position, 29.31 - set_print_tags, 29.22 - set_signal, 29.56 - set_state, 29.46 - set_tab, 29.22 - set_tags, 29.22 - set_temp_dir_name, 29.20 - set_trace, 29.42 - set_uint16_be, 29.8, 29.9 - set_uint16_le, 29.8, 29.9 - set_uint16_ne, 29.8, 29.9 - set_uint8, 29.8, 29.9 - set_uncaught_exception_handler, 29.43, 34.1 - set_utf_16be_uchar, 29.8, 29.9 - set_utf_16le_uchar, 29.8, 29.9 - set_utf_8_uchar, 29.8, 29.9 - shift_left, 29.27, 29.28, 29.29, 29.38 - shift_right, 29.27, 29.28, 29.29, 29.38 - shift_right_logical, 29.27, 29.28, 29.29, 29.38 - show_filename, 30.3 - shuffle, 29.2, 29.3, 29.21, 29.21 - sigabrt, 29.56 - sigalrm, 29.56 - sigbus, 29.56 - sigchld, 29.56 - sigcont, 29.56 - sigfpe, 29.56 - sighup, 29.56 - sigill, 29.56 - sigint, 29.56 - sigkill, 29.56 - sigmask, 34.1 - sign_bit, 29.21 - signal, 29.13, 29.56 - signal_behavior, 29.56 - signaling_nan, 29.21 - signature, 30.6, 30.7 - signature_item, 30.6, 30.7 - signature_item_desc, 30.6 - sigpipe, 29.56 - sigpoll, 29.56 - sigprof, 29.56 - sigquit, 29.56 - sigsegv, 29.56 - sigstop, 29.56 - sigsys, 29.56 - sigterm, 29.56 - sigtrap, 29.56 - sigtstp, 29.56 - sigttin, 29.56 - sigttou, 29.56 - sigurg, 29.56 - sigusr1, 29.56 - sigusr2, 29.56 - sigvtalrm, 29.56 - sigxcpu, 29.56 - sigxfsz, 29.56 - simple_module_path, 30.5 - sin, 28.2, 29.21 - singleton, 29.34, 29.36, 29.36, 29.50 - sinh, 28.2, 29.21 - size, 29.38 - size_in_bytes, 29.5, 29.5, 29.5, 29.5, 29.5 - slice, 29.5 - slice_left, 29.5, 29.5 - slice_left_1, 29.5 - slice_left_2, 29.5 - slice_right, 29.5, 29.5 - slice_right_1, 29.5 - slice_right_2, 29.5 - snd, 28.2 - some, 29.40 - sort, 29.2, 29.3, 29.21, 29.21, 29.32, 29.33 - sort_uniq, 29.32, 29.33 - sorted_merge, 29.49 - space_formatter, 30.7 - span, 33.1, 33.1 - spawn, 29.14 - spec, 29.1 - split, 29.2, 29.3, 29.32, 29.33, 29.34, 29.36, 29.36, 29.46, 29.46, 29.49, 29.50, 32.1 - split_delim, 32.1 - split_on_char, 29.8, 29.9, 29.54, 29.55 - split_result, 32.1 - sprintf, 29.22, 29.44 - sqrt, 28.2, 29.12, 29.21 - sscanf, 29.48 - sscanf_format, 29.48 - sscanf_opt, 29.48 - stable_sort, 29.2, 29.3, 29.21, 29.21, 29.32, 29.33 - stag, 29.22 - start, 29.24, 33.1 - starts_with, 29.8, 29.9, 29.54, 29.55 - stat, 29.24, 29.24 - statistics, 29.25, 29.36 - stats, 29.19, 29.19, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36, 29.60 - stats_alive, 29.19, 29.19 - std_formatter, 29.22 - stdbuf, 29.22 - stderr, 28.2, 29.41 - stdin, 28.2, 29.26, 29.48 - stdout, 28.2, 29.41 - stop, 29.24 - str_formatter, 29.22 - string, 28.1, 29.15, 29.15 - string_after, 32.1 - string_before, 32.1 - string_match, 32.1 - string_of_bool, 28.2 - string_of_expression, 30.7 - string_of_float, 28.2 - string_of_format, 28.2 - string_of_int, 28.2 - string_of_structure, 30.7 - string_partial_match, 32.1 - structure, 30.6, 30.7 - structure_item, 30.6, 30.7 - structure_item_desc, 30.6 - sub, 29.2, 29.3, 29.5, 29.7, 29.8, 29.9, 29.12, 29.21, 29.21, 29.21, 29.27, 29.28, 29.29, 29.38, 29.54, 29.55 - sub_left, 29.5, 29.5, 29.5 - sub_right, 29.5, 29.5, 29.5 - sub_string, 29.8, 29.9 - subbytes, 29.15, 29.15 - subset, 29.36, 29.50 - substitute_first, 32.1 - substring, 29.15, 29.15 - succ, 28.2, 29.21, 29.27, 29.28, 29.29, 29.38, 29.58 - symbol_end, 29.42 - symbol_end_pos, 29.42 - symbol_gloc, 30.3 - symbol_rloc, 30.3 - symbol_start, 29.42 - symbol_start_pos, 29.42 - symbolic_output_buffer, 29.22 - symbolic_output_item, 29.22 - sync, 34.2 - synchronized_formatter_of_out_channel, 29.22 - Thread, 34.1 - Timestamp, 33.1 - Type, 28.2, 29.57, 33.1 - t, 29.2, 29.3, 29.4, 29.5, 29.5, 29.5, 29.5, 29.5, 29.6, 29.7, 29.8, 29.9, 29.11, 29.12, 29.13, 29.14, 29.15, 29.15, 29.16, 29.17, 29.18, 29.19, 29.19, 29.19, 29.19, 29.19, 29.19, 29.19, 29.19, 29.21, 29.21, 29.21, 29.24, 29.25, 29.25, 29.25, 29.25, 29.25, 29.26, 29.27, 29.28, 29.29, 29.30, 29.32, 29.33, 29.34, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.36, 29.36, 29.36, 29.36, 29.37, 29.38, 29.40, 29.41, 29.43, 29.43, 29.45, 29.46, 29.47, 29.49, 29.50, 29.50, 29.51, 29.51, 29.52, 29.54, 29.55, 29.56, 29.56, 29.56, 29.57, 29.58, 29.59, 29.60, 29.60, 30.3, 30.4, 33.1, 33.1, 33.1, 33.1, 34.1 - tag, 29.22, 33.1, 33.1 - take, 29.45, 29.49 - take_opt, 29.45 - take_while, 29.49 - tan, 28.2, 29.21 - tanh, 28.2, 29.21 - temp_dir, 29.20 - temp_file, 29.20 - terminfo_toplevel_printer, 30.3 - time, 29.56 - tl, 29.32, 29.33 - to_array, 29.16 - to_binary_string, 29.46 - to_buffer, 29.35 - to_bytes, 29.7, 29.35, 29.54, 29.55 - to_channel, 29.35 - to_char, 29.58 - to_dispenser, 29.49 - to_float, 29.6, 29.27, 29.28, 29.29, 29.38 - to_hex, 29.15, 29.15 - to_int, 29.6, 29.21, 29.28, 29.29, 29.38, 29.58 - to_int32, 29.29, 29.38 - to_int64, 33.1 - to_list, 29.2, 29.3, 29.16, 29.21, 29.21, 29.34, 29.36, 29.36, 29.40, 29.47, 29.50 - to_nativeint, 29.29 - to_option, 29.47 - to_result, 29.40 - to_rev_seq, 29.34, 29.36, 29.36, 29.50 - to_seq, 29.2, 29.3, 29.7, 29.8, 29.9, 29.16, 29.21, 29.21, 29.25, 29.25, 29.25, 29.32, 29.33, 29.34, 29.36, 29.36, 29.36, 29.36, 29.36, 29.40, 29.45, 29.47, 29.50, 29.52, 29.54, 29.55 - to_seq_from, 29.34, 29.36, 29.36, 29.50 - to_seq_keys, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36 - to_seq_reentrant, 29.16 - to_seq_rev, 29.16 - to_seq_rev_reentrant, 29.16 - to_seq_values, 29.25, 29.25, 29.25, 29.36, 29.36, 29.36 - to_seqi, 29.2, 29.3, 29.7, 29.8, 29.9, 29.21, 29.21, 29.54, 29.55 - to_string, 29.6, 29.8, 29.9, 29.21, 29.27, 29.28, 29.29, 29.35, 29.38, 29.43, 29.59 - to_string_default, 29.43 - tool_name, 30.1 - top, 29.45, 29.52 - top_opt, 29.52 - top_phrase, 30.7 - toplevel_directive, 30.6 - toplevel_phrase, 30.5, 30.6, 30.7 - total_size, 29.35 - tracker, 29.24 - transfer, 29.45 - transpose, 29.49 - trim, 29.8, 29.9, 29.54, 29.55 - trunc, 29.21 - truncate, 28.2, 29.7, 29.16 - try_acquire, 29.51, 29.51 - try_lock, 29.37 - try_with, 29.17 - type_constraint, 30.6 - type_declaration, 30.6 - type_exception, 30.6 - type_extension, 30.6 - type_ident, 30.5 - type_kind, 30.6 - tyvar, 30.7 - tyvar_of_name, 30.7 - Uchar, 28.2, 29.58 - Undefined, 29.30 - Undefined_recursive_module, 28.2 - Undefined_recursive_module, 28.1 - Unhandled, 29.17 - Unit, 28.2, 29.59 - User, 33.1 - uid, 29.57 - uncapitalize_ascii, 29.8, 29.9, 29.54, 29.55 - uncons, 29.49 - unescaped, 29.48 - unflatten, 30.4 - unfold, 29.49 - union, 29.34, 29.36, 29.36, 29.50 - unit, 28.1, 33.1 - unix, 29.56 - unlock, 29.37 - unsafe_get, 29.5, 29.5, 29.5 - unsafe_of_string, 29.8, 29.9 - unsafe_set, 29.5, 29.5, 29.5 - unsafe_to_string, 29.8, 29.9 - unsigned_compare, 29.28, 29.29, 29.38 - unsigned_div, 29.28, 29.29, 29.38 - unsigned_rem, 29.28, 29.29, 29.38 - unsigned_to_int, 29.28, 29.29, 29.38 - unzip, 29.49 - update, 29.34, 29.36 - update_geometry, 29.22 - uppercase_ascii, 29.8, 29.9, 29.11, 29.54, 29.55 - usage, 29.1 - usage_msg, 29.1 - usage_string, 29.1 - use_file, 30.5 - use_printers, 29.43 - utf_16_byte_length, 29.58 - utf_8_byte_length, 29.58 - utf_decode, 29.58, 29.58 - utf_decode_invalid, 29.58 - utf_decode_is_valid, 29.58 - utf_decode_length, 29.58 - utf_decode_uchar, 29.58 - val_ident, 30.5 - value, 29.40, 29.47 - value_binding, 30.6 - value_constraint, 30.6 - value_description, 30.6 - variance, 30.2 - virtual_flag, 30.2 - Weak, 28.2, 29.60 - wait, 29.13 - wait_pid, 34.1 - wait_signal, 34.1 - wait_timed_read, 34.1 - wait_timed_write, 34.1 - warning_reporter, 30.3 - win32, 29.56 - with_constraint, 30.6 - with_open_bin, 29.26, 29.41 - with_open_gen, 29.26, 29.41 - with_open_text, 29.26, 29.41 - with_positions, 29.31 - word_size, 29.56 - wrap, 34.2 - wrap_abort, 34.2 - write, 33.1 - write_arg, 29.1 - write_arg0, 29.1 - yield, 34.1 - zero, 29.12, 29.21, 29.27, 29.28, 29.29, 29.38 - zip, 29.49 Chapter 38  Index of keywords ********************************* - and, 11.7, 11.8.1, 11.9.2, 11.9.3, 11.9.4, 11.9.5, 11.10, 11.11, 12.2, 12.5 - as, 11.4, 11.4, 11.4, 11.6, 11.6, 11.6, 11.9.2, 11.9.2 - asr, 11.3, 11.7.1, 11.7.5, 11.7.5 - assert, 11.7.8 - begin, 11.5, 11.7, 11.7.2 - class, 11.9.3, 11.9.4, 11.9.5, 11.10, 11.10.2, 11.10.2, 11.11, 11.11.2, 11.11.2 - constraint, 11.8.1, 11.8.1, 11.9.1, 11.9.1, 11.9.2, 11.9.2 - do, see while, for - done, see while, for - downto, see for - else, see if - end, 11.5, 11.7, 11.7.2, 11.9.1, 11.9.2, 11.10, 11.10.2, 11.11, 11.11.2 - exception, 11.8.2, 11.10, 11.10.2, 11.11, 11.11.2 - external, 11.10, 11.10.2, 11.11, 11.11.2 - false, 11.5 - for, 11.7, 11.7.3 - fun, 11.7, 11.7.1, 11.7.2, 11.9.2, 12.4 - function, 11.7, 11.7.1, 11.7.2 - functor, 11.10, 11.10.3, 11.11, 11.11.3 - if, 11.7, 11.7.1, 11.7.3 - in, see let - include, 11.10, 11.10.2, 11.11, 11.11.2, 12.6 - inherit, 11.9.1, 11.9.1, 11.9.2, 11.9.2 - initializer, 11.9.2, 11.9.2 - land, 11.3, 11.7.1, 11.7.5, 11.7.5 - lazy, 11.6, 11.7, 11.7.8 - let, 11.7, 11.7.1, 11.7.2, 11.7.8, 11.7.8, 11.9.2, 11.11, 11.11.2 - lor, 11.3, 11.7.1, 11.7.5, 11.7.5 - lsl, 11.3, 11.7.1, 11.7.5, 11.7.5 - lsr, 11.3, 11.7.1, 11.7.5, 11.7.5 - lxor, 11.3, 11.7.1, 11.7.5, 11.7.5 - match, 11.7, 11.7.1, 11.7.3, 12.10 - method, 11.9.1, 11.9.1, 11.9.1, 11.9.2, 11.9.2, 11.9.2 - mod, 11.3, 11.7.1, 11.7.5, 11.7.5 - module, 11.7.8, 11.10, 11.10.2, 11.10.2, 11.11, 11.11.2, 11.11.2, 12.2, 12.5, 12.6, 12.7, 12.8 - open, 11.7.8 - mutable, 11.8.1, 11.8.1, 11.9.1, 11.9.1, 11.9.2, 11.9.2, 11.9.2 - new, 11.7, 11.7.6 - nonrec, 11.8.1 - object, 11.7, 11.7.6, 11.9.1, 11.9.2 - of, 11.4, 11.8.1, 12.6 - open, 11.6, 11.10, 11.10.2, 11.11, 11.11.2 - open!, 12.9 - or, 11.7, 11.7.1, 11.7.3 - private, 11.9.1, 11.9.1, 11.9.1, 11.9.2, 11.9.2, 11.9.2, 12.3, 12.3.3 - rec, see let, module - sig, 11.10, 11.10.2 - struct, 11.11, 11.11.2 - then, see if - to, see for - true, 11.5 - try, 11.7, 11.7.1, 11.7.3 - type, 11.8.1, 11.9.5, 11.10, 11.10.2, 11.10.2, 11.10.2, 11.11, 11.11.2, 11.11.2, 11.11.2, 12.4, 12.6, 12.7, 12.10 - val, 11.9.1, 11.9.1, 11.9.2, 11.9.2, 11.9.2, 11.10, 11.10.2, 12.5 - virtual, see val, method, class - when, 11.7, 11.7.2, 12.12 - while, 11.7.3 - with, 11.7, 11.10, 11.10.4, 12.5, 12.7 ------------------------------------------------------------------------------ This document was translated from LaTeX by HeVeA (1). --------------------------------------- (1) http://hevea.inria.fr/index.html