The Coq mailing list

[Brian Aydemir <baydemir AT cis.upenn.edu>]

On Jul 6, 2008, at 01:49, Elnatan Reisner wrote:

> If I want to define a module type with parameters and definitions,  
> where the definitions depend on the parameters, is there a way to  
> do this without having to copy and paste the definitions in modules  
> which instantiate the module type? And beyond that, can I prove  
> things about a module type (without instantiating the parameters),  
> and then refer to those lemmas within a module where I *have*  
> instantiated the parameters?

I don't know about copying definitions, but here's one idea for  
"proving things about a module type": write a functor that abstracts  
over the module type and provides all the facts that you want.  The  
pattern is similar to what's found in the (Coq 8.1pl3) FSets  
library.  I haven't run the following code sketch through Coq, but  
hopefully it gives a flavor of the idea.

<<
Require Import List.

Module Type MY_SIG.
  Parameter aList : list nat.
  Inductive sublist : list nat -> Prop :=
     | sl : forall L n, In n L -> In n aList -> sublist L.
End MY_SIG.

Module MY_SIG_Facts (Import X : MY_SIG).
  (* Prove stuff any MY_SIG here. *)
End MY_SIG_Facts.

(* Instantiate MY_SIG_Facts as needed for each instance of MY_SIG. *)
>>

Cheers,
Brian