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

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

On Apr 8, 2011, at 18:43, Till Varoquaux wrote:
> I tend to consider using Impure functors as very poor coding hygiene..
> I am sure there are compelling use cases but I've yet to come across
> one. Providing safer types for impure functors does not seem
> compelling enough to justify having several kind of functors.

Alain gave a good example. An even simpler one is a generator for a  
type of abstract names. There are a number of others, e.g. modules  
accessing external resources. Even more uses potentially arise with  
first-class modules, which can take the role of powerful (probably  
stateful) objects, with functors being their constructors.

> I am not really sure I want applicative functors (based upon my
> experience they are pretty hard to explain and rarely buy me anything)
> but I balk at the idea of having both applicative and generative
> functors..

It doesn't have to be complicated, especially not for the user.  
Admittedly, previous approaches providing both made it much more  
complicated than necessary, with duplicated syntax and all -- all you  
really need is to have the type system track whether a module is pure.  
We have a relatively elegant formulation of such a system in our F-ing  
Modules framework (I just have to find the time to write that paper).

I don't think that pure functors are incredibly hard to explain either  
-- after all, even C++ programmers find them natural. Of course,  
terminology like "applicative" or "generative" is less helpful then it  
has to be.

/Andreas