Proposal discussion summary: Adding on

[Cale Gibbard]

On 08/11/06, Ashley Yakeley <ashley at semantic.org> wrote:
> Nils Anders Danielsson wrote:
> > The deadline for discussion is tomorrow, but in case anyone complains
> > I thought I'd summarise the previous discussion already today.
> >
> > * Consensus was reached that a module containing on plus some
> >   functions from the prelude should be added.
>
> That's S of SKI, isn't it? Looks good, as we already have "const" and "id".
>
> > * The module name Control.Function was not well received. A bunch of
> >   other names were suggested, and almost everyone accepted
> >   Data.Function.
>
> If we're creating Data.Function, can we add an "instance Functor ((->)
> a)" to it? I seem to remember it's currently in an odd place. Or maybe
> we should create a Data.Functor module.
>
> --
> Ashley Yakeley

Actually, the Functor and Monad instances for ((->) a) are somewhat
fundamental and I'd personally like to have them available from the
Prelude, but I suppose Data.Function would be fine.

One interesting thing which we noticed on the IRC channel the other
day is that if one is willing to permit a little more polymorphism
than at first comfortable, it's possible not only to unify {map, fmap,
liftM, liftA}, but function composition as well!

We could have
class Functor f where
   (.) :: (a -> b) -> (f a -> f b)

The instance for ((->) a) taking care of the ordinary composition
case. This would also allow things like
square . [1,2,3,4,5] = [1,4,9,16,25]
which is somewhat friendly to the view that (fully defined) lists are
like functions on the domain of their indices.

Function composition, and functor application both hold such a high
place in functional programming that it seems a bit strange to unify
them at first, but it's certainly nice to know that one could do so.

I'll admit that this notation starts getting bizarre when one starts
writing down the laws which must be satisfied...
(.) (f . g) = (.) f . (.) g
or perhaps even more frightening:
((f . g) .) = (f .) . (g .)

I believe I even scared xerox with that one. :)

 - Cale