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

[Andreas Rossberg <rossberg@mpi-sws.org>]

On Apr 7, 2011, at 23:49, Gerd Stolpmann wrote:
> 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:

Nitpick: the Make functor is still applicative. All functors in OCaml  
are applicative. The fact that you get different results above is  
caused by the way you apply the functor, not by the way it is defined.

"Applicative" distinguishes functor semantics in OCaml from that in  
SML, where functors are "generative", i.e. you always get new types  
when you apply them.

Aside: In general, you really want to have both: functors with impure  
bodies better be generative, while functors with pure bodies should be  
applicative. The absence of generative functors in OCaml also is the  
reason that you cannot unpack a first-class module in a functor body  
(non-locally), because that is unsound with applicative semantics.

/Andreas