package logtk

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Type Inference

This module is used for two things that overlap:

  • inferring the types of symbols that have not been declared (e.g. in "fof" or "cnf" TPTP statements) so as to enrich a Signature
  • converting untyped terms or formulas into typed formulas, by inferring the exact type of each subterm (and possibly inferring type parameters).

In this context, generalizing type variables means that if some ID.t whose type was unknown and its type still contains variables after the type inference, those variables are quantified instead of being bound to a default type (typically .Type.i).

For instance: say f is not declared and occurs in the term f(f(nil)) with the declared constructor nil : list(A). The inferred type for f should be something like list(B) -> list(B).

  • If we generalize, we declare that f : list(A) -> list(A) (for all A).
  • If we don't, we declare that f : list($i) -> list($i).

Here we use a single scope when we unify and substitute type variables, the scope 0.

Many functions will use an Error monad to make errors explicit. The error type is or_error. The module CCError in containers can be used to deal with errors (including monadic operators).

type 'a or_error = ('a, string) CCResult.t
type type_ = TypedSTerm.t
type untyped = STerm.t

untyped term

type typed = TypedSTerm.t

typed term

type loc = ParseLocation.t
exception Error of string
val section : Util.Section.t

Types for Builtins

module TyBuiltin : sig ... end

Typing context

This module provides a typing context, with an applicative interface. The context is used to map terms to types locally during type inference. It also keeps and updates a signature when symbols' types are inferred.

This module is quite low-level, and shouldn't be used in simple cases (see the following modules)

module Ctx : sig ... end
val unify : ?loc:loc -> type_ -> type_ -> unit

Hindley-Milner Type Inference

This module, abstract in the exact kind of term it types, takes as input a signature and an untyped term, and updates the typing context so that the untyped term can be converted into a typed term.

val infer_ty_exn : Ctx.t -> untyped -> type_

Type conversion from untyped.

val infer_ty : Ctx.t -> untyped -> type_ or_error

Type conversion from untyped.

val infer_exn : Ctx.t -> untyped -> typed

Infer the type of this term under the given signature. This updates the context's typing environment!

  • parameter ctx

    the context

  • parameter untyped

    the untyped term whose type must be inferred

  • raises Error

    if the types are inconsistent

val infer : Ctx.t -> untyped -> typed or_error

Safe version of infer_exn. It returns `Error s rather than raising Error if the typechecking fails.

val infer_prop_exn : Ctx.t -> untyped -> typed

Same as infer_exn but forces the type of its result to be TypedSTerm.prop

val infer_clause_exn : Ctx.t -> untyped list -> typed list

Convert a clause. Free variables in each of the list's elements are shared

Constraining types

This section is mostly useful for inferring a signature without converting untyped_terms into typed_terms.

val constrain_term_term_exn : ?loc:loc -> Ctx.t -> untyped -> untyped -> unit

Force the two terms to have the same type in this context

  • raises Error

    if an inconsistency is detected

val constrain_term_type_exn : ?loc:loc -> Ctx.t -> untyped -> type_ -> unit

Force the term's type and the given type to be the same.

  • raises Error

    if an inconsistency is detected

val constrain_term_term : ?loc:loc -> Ctx.t -> untyped -> untyped -> unit or_error

Safe version of constrain_term_term_exn

val constrain_term_type : ?loc:loc -> Ctx.t -> untyped -> type_ -> unit or_error

Safe version of constrain_term_type_exn


type typed_statement = (typed, typed, type_) Statement.t
val infer_statement_exn : ?file:string -> Ctx.t -> UntypedAST.statement -> typed_statement * typed_statement list

infer_statement ctx ~f st checks and convert st into a typed statements, and a list of auxiliary type declarations for symbols that were inferred implicitly.

val infer_statements_exn : ?def_as_rewrite:bool -> ?on_var:[ `Infer | `Default ] -> ?on_undef:[ `Warn | `Fail | `Guess ] -> ?on_shadow:[ `Warn | `Ignore ] -> ?ctx:Ctx.t -> ?file:string -> implicit_ty_args:bool -> UntypedAST.statement Iter.t -> typed_statement CCVector.ro_vector

Infer all statements

  • parameter def_as_rewrite

    if true, definitions becomes rewrite rules

val infer_statements : ?def_as_rewrite:bool -> ?on_var:[ `Infer | `Default ] -> ?on_undef:[ `Warn | `Fail | `Guess ] -> ?on_shadow:[ `Warn | `Ignore ] -> ?ctx:Ctx.t -> ?file:string -> implicit_ty_args:bool -> UntypedAST.statement Iter.t -> typed_statement CCVector.ro_vector or_error