Re: [Caml-list] What is an applicative functor?

[Gerd Stolpmann <info@gerd-stolpmann.de>]

Am Donnerstag, den 07.04.2011, 23:12 +0200 schrieb Dawid Toton:
> What does it mean that a functor is applicative?

Roughly: If you apply a functor twice with the same input modules, the
opaque types in the output remain compatible. For instance:

module S1 = Set.Make(String)
module S2 = Set.Make(String)

Now, S1.t and S2.t are type-compatible, although this type is opaque.
(E.g. you can do S1.empty = S2.empty.)

Compare this with:

module Make(X : sig end) = struct type t = Variant end
module M1 = Make(struct end)
module M2 = Make(struct end)

Now, M1.t and M2.t are incompatible - for nominal types like variants
the functors aren't applicative, and each instance is a thing of its
own:

# M1.Variant = M2.Variant;;
Error: This expression has type M2.t but an expression was expected of
type M1.t

Gerd


> Is there any analogy between applicative functors in OCaml and the 
> Applicative type class of Haskell?
> Dawid
> 


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