a module with multiple signatures

[Keiko Nakata <keiko@kurims.kyoto-u.ac.jp>]

Hello, 

I tried to give a module different signatures through an use of functors.
Then I faced a situation for which I do not understand the reason.

This is the simplified version of my situation.

module M = struct type s = S type t = T1 | T2 of s end

module F1 = functor (X : sig type t end) -> struct type t = X.t end

module F2 = functor (X : sig type s type t end) -> 
                 struct type s = X.s type t = X.t  end

module M1 = F1(M)

module M2 = F2(M)

let f x = match x with  M1.T1 -> 1 | M1.T2 x -> 2;;
(* This is not type checked *)
(* I got the error "Unbound constructor M1.T1" *)

(* This is type checked *)
let g (x : M1.t) = match x with  M.T1 -> 1 | M.T2 x -> 2;;

Why M1.T1 should not be bound?

Anyway,
there may be a nicer way to give a module multiple signatures
while avoiding duplicate type declarations as possible?
(In the above setting, I want to make the type s in M abstract in some 
context, but transparent in another context.)

Regards,
NAKATA Keiko