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

[rossberg@mpi-sws.org]

> On 04/08/2011 10:20 AM, Jacques Garrigue wrote:
>> Applicative functors have other advantages, like the fact you can refer to
>> a
>> type produced by a functor without having really applied it.

I agree with Jacques. My primary argument for applicative functors is
diamond import in libraries. Assume you have a set functor in a library A
(e.g. the stdlib). Then there are two seperate libraries B and C, perhaps
from different sources. Both need to use sets. And you want to use B and C
and pass sets from one to the other.

Without applicative functors, there are 3 possibilities:

1. Both B and C instantiate the Set functor separately and export the result
-- then you have to convert between the incompatible set types all the time.

2. Both B and C functorize all their modules over a Set instance -- I think
it's obvious that this doesn't scale.

3. A mixture of (1) and (2).

Basically, this is the higher-order functor example in disguise, but dressed
up in a more "real world" fashion.

I believe avoiding this kind of road block is important for modularity. In
ML, we don't really make that much use of functors, mainly because they are
relatively heavyweight syntactically. But if you look at other languages,
e.g. Haskell or C++, then their libraries heavily rely on type classes, resp
templates, being "applicative" (with fairly bogus semantics in the latter
case). So if we claim that ML modules are superior, I think we need
applicative functors (besides generative ones).

/Andreas