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

[Josh Berdine <josh@berdine.net>]

On Tue, Jan 21 2014, SEROT Jocelyn wrote:
> Leo White <lpw25@cam.ac.uk> a écrit :
>>
>> 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
>
> Unfortunately, this is not possible since the ELT signature is  
> actually more complex than just 'sig type t end'.
> To illustrate this, without showing the original code (which, as you  
> guessed it, has some extra and maybe unrelated complexity), i've tried  
> to reuse your example, by simply changing
>
> module type ELT = sig type t end
>
> by
>
> module type ELT = sig type t val string_of: t -> string end

Shouldn't Elt.t and elt in SET be equal?  The following typechecks,
though maybe not what you want:

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

module type SET = sig
   type t
   module Elt : ELT
   type elt = Elt.t
   val choose: t -> elt
   val singleton: elt -> t
   val string_of: t -> string
end

> module Make (E : ELT) : SET with module Elt = E and 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]
>    let string_of s = "{" ^ E.string_of (choose s) ^ "}"
> 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
>    let string_of (x,y) = "(" ^ E1.string_of x ^ "," ^ E2.string_of 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(S1.Elt)(S2.Elt)
>    module S = Make(P)
>    include S
>    let product s1 s2 = S.singleton (P.product (S1.choose s1) (S2.choose s2))
> end

module MakeProduct (S1: SET) (S2: SET) : sig
   include SET with type Elt.t = S1.elt * S2.elt
   val product : S1.t -> S2.t -> t
end = struct
   module P = MakePair(S1.Elt)(S2.Elt)
   module S = Make(P)
   include S
   let product s1 s2 = S.singleton (P.product (S1.choose s1) (S2.choose s2))
end


Cheers, Josh