Coq to Ocaml extraction functor using the Coq extraction engine

I have a function PolyInterpretation( http://color.inria.fr/doc/CoLoR.PolyInt.APolyInt.html )

Definition PolyInterpretation := forall f : Sig, poly (arity f).

and module signature TPolyInt( http://color.inria.fr/doc/CoLoR.PolyInt.APolyInt_MA.html )

Module Type TPolyInt.
  Parameter sig : Signature.
  Parameter trsInt : PolyInterpretation sig.
  Parameter trsInt_wm : PolyWeakMonotone trsInt.
End TPolyInt.

Module PolyInt (Export PI : TPolyInt).

Then in my file rainbow.vI define a module TPolyInt_impto use the functionPolyInt

Module TPolyInt_imp.
 Variable arity : symbol -> nat.
 Variable l : list {g : symbol & poly (arity f).
 Definition sig := Sig arity.
 Definition trsInt f := fun_of_pairs_list f l.
 ...
End TPolyInt_imp.

Where fun_of_pairs_listhas the type:forall f: Cpf0.symbol, list {g : symbol & poly (arity g)} -> poly (arity f)

Then I define the module P:

Module Export P := PolyInt TPolyInt_imp.

The review assistant Coqaccepted the definition Pabove.

Then I used the extract to extract it in Ocaml.

I am writing it in another file: extraction.v

Extraction Language Ocaml.
Set Extraction Optimize.
Set Extraction AccessOpaque.
Separate Extraction rainbow.P.

It works great.

Here is the code after retrieving

module TPolyInt_imp = 
 struct 
  (** val arity : symbol -> int **)

  let arity =
    failwith "AXIOM TO BE REALIZED"

  (** val l : (symbol, poly) sigT list **)

  let l =
    failwith "AXIOM TO BE REALIZED"

  (** val coq_sig : coq_Signature **)

  let coq_sig =
    coq_Sig arity

  (** val trsInt : symbol -> poly **)

  let trsInt f =
    fun_of_pairs_list arity f l
 end

module P = PolyInt(TPolyInt_imp)

TPolyInt_imp Variable failwith AXIOM, , .

Module Type Arity.
 Variable arity : symbol -> nat.
 Variable l : list {g : symbol & poly (arity g)}.
End Arity.

, (Arity) . TPolyInt_imp (, TPolyInt_imp ).

Module S (Import A: Arity).

  Module TPolyInt_imp.
    Definition sig := Sig arity.
    Definition trsInt f := fun_of_pairs_list f l.
    ...
  End TPolyInt_imp.

  Module P := PolyInt TPolyInt_imp.

End S.

, Ocaml.

Extraction Language Ocaml.
Set Extraction Optimize.
Set Extraction AccessOpaque.
Separate Extraction S.

:

Error: Signature mismatch:
       ...
       Values do not match:
         val trsInt : Cpf0.symbol -> Polynom.poly
       is not included in
         val trsInt : APolyInt.coq_PolyInterpretation
       File "rainbow.ml", line 534, characters 8-14: Actual declaration

:

module type Arity = 
 sig 
  val arity : symbol -> int
  val l : (symbol, poly) sigT list
 end

module S = 
 functor (A:Arity) ->
 struct 
  module TPolyInt_imp = 
   struct 
    (** val coq_sig : coq_Signature **)

    let coq_sig =
      coq_Sig A.arity

    (** val trsInt : symbol -> poly **)

    let trsInt f =
      fun_of_pairs_list A.arity f A.l
   end

  module P = PolyInt(TPolyInt_imp)

? ? , ?

, Arity.

, . .