Chapter 12 Language extensions

7 Substituting inside a signature

• 7.1 Destructive substitutions
• 7.2 Local substitution declarations
• 7.3 Module type substitutions

7.1 Destructive substitutions

(Introduced in OCaml 3.12, generalized in 4.06)

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

7.2 Local substitution declarations

(Introduced in OCaml 4.08, module type substitution introduced in 4.13)

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.

7.3 Module type substitutions

(Introduced in OCaml 4.13)

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 :
  (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)