Re: [Caml-list] Question on functors (again...)

[Leo White <lpw25@cam.ac.uk>]

Jocelyn Sérot <Jocelyn.SEROT@univ-bpclermont.fr> writes:

> I was expecting that the constraints in the definition of the Make functor (".. with type elt=E.t and module Elt =E")
> would automatically  enforce the type equality "elt = Elt.t" for all modules defined by  applying Make (such as S1 and
> S2). This is obviously not the case. I  just can't see how to enforce this..

The compiler doesn't know that your `S1` and `S2` arguments have been
made with the `Make` functor so it cannot assume those constraints. You
should add the constraints to the `SET` module type itself:

    module type SET = sig
      type t
      type elt
      module Elt : sig type t = elt end
      val choose : t -> elt
      val singleton : elt -> t
    end

You've simplified your example, so there may be important complexity
that you've left out, but your code seems to be unnecessarily
complicated. You can probably simplify it to something that looks more
like the code below.

Regards,

Leo

    module type ELT = sig type t end
   
    module type SET = sig
      type t
      type elt
      val choose: t -> elt
      val singleton: elt -> t
    end
   
    module Make (E : ELT) : SET with type elt = E.t = struct
      type elt = E.t
      type t = elt list
      module Elt = E
      let choose s = List.hd s
      let singleton e = [e]
    end
   
    module MakePair (E1: ELT) (E2: ELT) : sig
      include ELT with type t = E1.t * E2.t
      val product : E1.t -> E2.t -> t
    end = struct
      type t = E1.t * E2.t
      let product x y = x,y
    end
   
    module MakeProduct (S1: SET) (S2: SET) : sig 
      include SET with type elt = S1.elt * S2.elt
      val product : S1.t -> S2.t -> t
    end = struct
      module P = MakePair(struct type t = S1.elt end)(struct type t = S2.elt end)
      module S = Make(P)
      include S
      let product s1 s2 = S.singleton (P.product (S1.choose s1) (S2.choose s2))
    end