Re: [Caml-list] concept style using first-class module

[Jacques Garrigue <garrigue@math.nagoya-u.ac.jp>]

On 2011/04/13, at 13:28, Satoshi Ogasawara wrote:
> Recently I learned concept style generic programming like Haskell type-class.
> I'd like to emulate that style in OCaml using first-class modules.
> 
> e.g.
> 
> module type Monad = sig
>  type 'a t
>  val return : 'a -> 'a t
>  val bind : 'a t -> ('a -> 'b t) -> 'b t
> end
> 
> module type MonadPlus = sig
>  type 'a t
>  include Monad with type 'a t := 'a t
>  val zero : 'a t
>  val plus : 'a t -> 'a t -> 'a t
> end
> 
> let foo (module M:MonadPlus) m = M.bind m (fun x -> M.return x)
> 
> But above code makes an error at the last line.
> 
>  Error: This `let module' expression has type 'a M.t -> 'a M.t
>  In this type, the locally bound module name M escapes its scope
> 
> I have tried to add a (type s) parameter and specialize module
> types but It's not work.
> 
> How can I make this code typable? Is it impossible without higher
> order type operator?

Unfortunately, you gave yourself the answer: one would need higher
kinded type variables to do that (they have them in Haskell).
Namely, in order to use M.t in the result, you need to bind it somewhere,
but a first-class module type cannot bind a type, and (type s) only works
with parameterless types.

Note that the extension allowing parameterized types in first-class
module with clauses does not help either, since it doesn't bind the
type constructor either, just allows to pass it around.

So you have to use a real functor here:

module Foo(M:MonadPlus) = struct
  let foo m = M.bind m (fun x -> M.return x)
end

You can also wrap this functor in a first-class module, but I don't see
how it would help.

Sorry,

	Jacques