package core_kernel

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package core_kernel
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This module extends Base.Type_equal.

include module type of struct include Base.Type_equal end with module Id := Base.Type_equal.Id
type ('a, 'b) t = ('a, 'b) Base.Type_equal.t =
  1. | T : ('a, 'a) t
val sexp_of_t : ('a -> Base.Sexp.t) -> ('b -> Base.Sexp.t) -> ('a, 'b) t -> Base.Sexp.t
type ('a, 'b) equal = ('a, 'b) t

just an alias, needed when t gets shadowed below

refl, sym, and trans construct proofs that type equality is reflexive, symmetric, and transitive.

val refl : ('a, 'a) t
val sym : ('a, 'b) t -> ('b, 'a) t
val trans : ('a, 'b) t -> ('b, 'c) t -> ('a, 'c) t
val conv : ('a, 'b) t -> 'a -> 'b

conv t x uses the type equality t : (a, b) t as evidence to safely cast x from type a to type b. conv is semantically just the identity function.

In a program that has t : (a, b) t where one has a value of type a that one wants to treat as a value of type b, it is often sufficient to pattern match on Type_equal.T rather than use conv. However, there are situations where OCaml's type checker will not use the type equality a = b, and one must use conv. For example:

module F (M1 : sig type t end) (M2 : sig type t end) : sig
  val f : (M1.t, M2.t) equal -> M1.t -> M2.t
end = struct
  let f equal (m1 : M1.t) = conv equal m1
end

If one wrote the body of F using pattern matching on T:

let f (T : (M1.t, M2.t) equal) (m1 : M1.t) = (m1 : M2.t)

this would give a type error.

It is always safe to conclude that if type a equals b, then for any type 'a t, type a t equals b t. The OCaml type checker uses this fact when it can. However, sometimes, e.g., when using conv, one needs to explicitly use this fact to construct an appropriate Type_equal.t. The Lift* functors do this.

module Lift = Base.Type_equal.Lift
module Lift2 = Base.Type_equal.Lift2
module Lift3 = Base.Type_equal.Lift3

tuple2 and detuple2 convert between equality on a 2-tuple and its components.

val detuple2 : ('a1 * 'a2, 'b1 * 'b2) t -> ('a1, 'b1) t * ('a2, 'b2) t
val tuple2 : ('a1, 'b1) t -> ('a2, 'b2) t -> ('a1 * 'a2, 'b1 * 'b2) t
module type Injective = Type_equal.Injective

Injective is an interface that states that a type is injective, where the type is viewed as a function from types to other types. The typical usage is:

module type Injective2 = Type_equal.Injective2

Injective2 is for a binary type that is injective in both type arguments.

module Composition_preserves_injectivity = Base.Type_equal.Composition_preserves_injectivity

Composition_preserves_injectivity is a functor that proves that composition of injective types is injective.

module Id : sig ... end