Module `AltErgoLib.Ty`

Types

This module defines the representation of types.

Definition

type t =

| Tint
(*
Integer numbers
*)
| Treal
(*
Real numbers
*)
| Tbool
(*
Booleans
*)
| Tvar of tvar
(*
Type variables
*)
| Tbitv of int
(*
Bitvectors of a given length
*)
| Text of t list * Uid.ty_cst
(*
Abstract types applied to arguments. Text (args, s) is the application of the abstract type constructor s to arguments args.
*)
| Tfarray of t * t
(*
Functional arrays. TFarray (src,dst) maps values of type src to values of type dst.
*)
| Tadt of Uid.ty_cst * t list
(*
Application of algebraic data types. Tadt (a, params) denotes the application of the polymorphic datatype a to the types parameters params.
For instance the type of integer lists can be represented by the value Tadt (Hstring.make "list", [Tint] where the identifier list denotes a polymorphic ADT defined by the user with t_adt.
*)
| Trecord of trecord
(*
Record type.
*)

and tvar = {

v : int;
(*
Unique identifier
*)
mutable value : t option;
(*
Pointer to the current value of the type variable.
*)

}

Type variables. The value field is mutated during unification, hence distinct types should have disjoints sets of type variables (see function fresh).

and trecord = {

mutable args : t list;
(*
Arguments passed to the record constructor
*)
name : Uid.ty_cst;
(*
Name of the record type
*)
mutable lbs : (Uid.term_cst * t) list;
(*
List of fields of the record. Each field has a name, and an associated type.
*)
record_constr : Uid.term_cst;
(*
record constructor. Useful is case it's a specialization of an algeberaic datatype. Default value is "{__name"
*)

}

Record types.

type adt_constr = {

constr : Uid.term_cst;
(*
constructor of an ADT type
*)
destrs : (Uid.term_cst * t) list;
(*
the list of destructors associated with the constructor and their respective types
*)

}

type type_body = adt_constr list

Bodies of types definitions. Currently, bodies are inlined in the type t for records and enumerations. But, this is not possible for recursive ADTs

module Svty : Set.S with type elt = int

Sets of type variables, indexed by their identifier.

module Set : Set.S with type elt = t

Sets of types

val assoc_destrs : Uid.term_cst -> adt_constr list -> (Uid.term_cst * t) list

assoc_destrs cons cases returns the list of destructors associated with the constructor cons in the ADT defined by cases.

raises Not_found
if the constructor is not in the given list.

val type_body : Uid.ty_cst -> t list -> type_body

Type inspection

val hash : t -> int

Hash function

val equal : t -> t -> bool

Equality function

val compare : t -> t -> int

Comparison function

val pp_smtlib : Format.formatter -> t -> unit

Printing function for types in smtlib2 format.

val print : Format.formatter -> t -> unit

Printing function for types (does not print the type of each fields for records).

val print_list : Format.formatter -> t list -> unit

Print function for lists of types (does not print the type of each fields for records).

val print_full : Format.formatter -> t -> unit

Print function including the record fields.

val vty_of : t -> Svty.t

Returns the set of type variables that occur in a given type.

Building types

val tunit : t

The unit type.

val fresh_var : unit -> tvar

Generate a fresh type variable, guaranteed to be distinct from any other previously generated by this function.

val fresh_tvar : unit -> t

Wrap the fresh_var function to return a type.

val fresh_empty_text : unit -> t

Return a fesh abstract type.

val text : t list -> Uid.ty_cst -> t

Apply the abstract type constructor to the list of type arguments given.

val t_adt : 
  ?body:(Uid.term_cst * (Uid.term_cst * t) list) list option ->
  Uid.ty_cst ->
  t list ->
  t

Create an algebraic datatype. The body is a list of constructors, where each constructor is associated with the list of its destructors with their respective types. If body is none, then no definition will be registered for this type. The second argument is the name of the type. The third one provides its list of arguments.

val trecord : 
  ?sort_fields:bool ->
  record_constr:Uid.term_cst ->
  t list ->
  Uid.ty_cst ->
  (Uid.term_cst * t) list ->
  t

Create a record type. trecord args name lbs creates a record type with name name, arguments args and fields lbs.

If sort_fields is true, the record fields are sorted according to Hstring.compare. This is to preserve compatibility with the old typechecker behavior and should not be used in new code.

Substitutions

module M : Map.S with type key = int

Maps from type variables identifiers.

type subst = t M.t

The type of substitution, i.e. maps from type variables identifiers to types.

val compare_subst : subst -> subst -> int

Comparison of substitutions.

val equal_subst : subst -> subst -> bool

Equality of substitutions.

val print_subst : Format.formatter -> subst -> unit

Print function for substitutions.

val esubst : subst

The empty substitution, a.k.a. the identity.

val apply_subst : subst -> t -> t

Substitution application.

val union_subst : subst -> subst -> subst

union_subst u v applies v to u, resulting in u'. It then computes the union of u' and v, prioritizing bindings from u' in case of conflict.

Unification/Matching

exception TypeClash of t * t

Exception raised during matching or unification. TypeClash (u, v) is raised when u and v could not be matched or unified (u and v may be sub-types of the types being actually unified or matched).

val unify : t -> t -> unit

Destructive unification. Mutates the value fields of type variables.

raises TypeClash
when unification is impossible. In this case, the value fields of already mutated type variables are left modified, which may prevent future unifications.

val matching : subst -> t -> t -> subst

Matching of types (non-destructive). matching pat t returns a substitution subst such that apply_subst subst pat is equal to t.

val shorten : t -> t

Shorten paths in type variables values. Unification in particular can create chains where the value field of one type variable points to another and so on... This function short-circuits such chains so that the value of a type variable can be accessed directly.

Manipulations on types

val fresh : t -> subst -> t * subst

Apply the given substitution, all while generating fresh variables for the variables not already bound in the substitution. Returns a substitution containing bindings from old variable to their fresh counterpart.

val fresh_list : t list -> subst -> t list * subst

Same as fresh but on lists of types.

val instantiate : t list -> t list -> t -> t

instantiate vars args t builds the substitutions mapping each type variable in vars to the corresponding term in args, then apply that substitution to t.

raises Invalid_argument
if the lists vars and args do not have the same length

raises Assertion_failure
if one type in vars is not a type variable.

val monomorphize : t -> t

Return a monomorphized variant of the given type, where type variable without values have been replaced by abstract types.

type goal_sort =

| Cut
(*
Introduce a cut in a goal. Once the cut proved, it's added as a hypothesis.
*)
| Check
(*
Check if some intermediate assertion is prouvable
*)
| Thm
(*
The goal to be proved valid
*)
| Sat
(*
The goal to be proved satisfiable
*)

Goal sort. Used in typed declarations.

val fresh_hypothesis_name : goal_sort -> string

create a fresh hypothesis name given a goal sort.

val is_local_hyp : string -> bool

Assuming a name generated by fresh_hypothesis_name, answers whether the name design a local hypothesis ?

val is_global_hyp : string -> bool

Assuming a name generated by fresh_hypothesis_name, does the name design a global hypothesis ?

val print_goal_sort : Format.formatter -> goal_sort -> unit

Print a goal sort

val reinit_decls : unit -> unit

Empties the decls cache

Install

Dune Dependency

Authors

Maintainers

Sources

doc/alt-ergo-lib/AltErgoLib/Ty/index.html

Module `AltErgoLib.Ty`

Definition

Type inspection

Building types

Substitutions

Unification/Matching

Manipulations on types

package alt-ergo-lib

Install

Dune Dependency

Authors

Maintainers

Sources

doc/alt-ergo-lib/AltErgoLib/Ty/index.html

Module AltErgoLib.Ty

Definition

Type inspection

Building types

Substitutions

Unification/Matching

Manipulations on types

Module `AltErgoLib.Ty`