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 extensions to the core language (labeled arguments and polymorphic variants), and chapter 6 gives some advanced examples.
For this overview of OCaml, we use the interactive system, which is started by running ocaml from the Unix shell, or by launching the OCamlwin.exe application under Windows. 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).
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.
Recursive functions are defined with the let rec binding:
In addition to integers and floating-point numbers, OCaml offers the usual basic data types:
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.
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:
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.
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.
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:
Even function composition is definable:
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:
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.
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.
Record fields can also be accessed through pattern-matching:
Since there is only one case in this pattern matching, it is safe to expand directly the argument r in a record pattern:
Unneeded fields can be omitted:
Optionally, missing fields can be made explicit by ending the list of fields with a trailing wildcard _::
When both sides of the = sign are the same, it is possible to avoid repeating the field name by eliding the =field part:
This short notation for fields also works when constructing records:
At last, it is possible to update few fields of a record at once:
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):
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:
To define arithmetic operations for the number type, we use pattern-matching on the two numbers involved:
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:
This type is particularly useful when defining function that can fail in common situations, for instance
The most common usage of variant types is to describe recursive data structures. Consider for example the type of binary trees:
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):
( 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
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:
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:
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:
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:
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.
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.
Record fields can also be modified by assignment, provided they are declared mutable in the definition of the record type:
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:
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:
Again, there is nothing magical with references: they are implemented as a single-field mutable record, as follows.
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.
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.
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:
Exceptions can be trapped with the try…with construct:
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:
Also, finalization can be performed by trapping all exceptions, performing the finalization, then re-raising the exception:
An alternative to try…with is to catch the exception while pattern matching:
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,
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
the function f cannot raise a Done exception, which removes an entire class of misbehaving functions.
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.
We added print_endline "lazy_two evaluation" to see when the lazy expression is being evaluated.
The value of lazy_two is displayed as <lazy>, 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.
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 <lazy> anymore but as 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.
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.
We can also use lazy patterns in pattern matching.
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.
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:
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.
Now for a real symbolic processing, we define the derivative of an expression with respect to a variable dv:
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.
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 interspered with specifiers (for instance %d, %f). Next, the specifiers are substituted by the following arguments in their order of apparition in the format string:
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:
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 printer (for custom types). For instance, we can create a printing template that converts an integer argument to signed decimal:
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:
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:
Due to the way that format string are build, storing a format string requires an explicit type annotation:
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 $ ./fib 7 11 1
More complex standalone OCaml programs are typically composed of multiple source files, and can link with precompiled libraries. Chapters 9 and 12 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 the ocamlbuild compilation manager.