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Variance problem in higher-order Functors?
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Date: 2006-07-25 (20:45)
From: Jacques Carette <carette@m...>
Subject: How do I achiece this, was Re: [Caml-list] Variance problem in higher-order Functors?
My real question is (and should have been), how do I translate

module type DOMAIN = sig type kind end
type domain_is_field
type domain_is_ring
module Rational = struct type kind = domain_is_field end
module Integer = struct type kind = domain_is_ring end

module DivisionUpdate(D:DOMAIN with type kind = domain_is_field) = struct
  (* something only valid with D a field*)

module GeneralUpdate(D:DOMAIN) = struct
   (* something that always works, for rings and fields *)

The behaviour I want should be the same as the first-order applications
module A = DivisionUpdate(Rational)  (* OK *)
module B = GeneralUpdate(Rational)  (* OK *)
module C = DivisionUpdate(Integer)  (* ERROR *)
module D = GeneralUpdate(Integer)  (* OK *)
BUT I want to pass all these modules as parameters to a functor.  I 
don't see how to build the proper type that will work!
[I have read the manuals in depth, Googled around the caml.inria.fr web 
site, played around with the implementation, etc to no avail]

In other words, I want to be able to define
module type Trans = functor(U:UPDATE) ->  functor(D:DOMAIN) -> sig ... end
but none of my attempts have worked, even though the first-order code 
works fine.

I would be happy with a solution that uses polymorphic variants, or 
objects, or whatever work.  The only thing I can't do is "run-time" 
tests, as I have a dozen domains, with more functors and more 
constraints floating around, so I really want this to be a type-level 
solution.  If OCaml had conditional module application, I could use 
that, but "expanding" my definitions is not realistic.