[Haskell-cafe] Re: Pointfree composition for higher arity

[oleg at okmij.org]

Sean Leather wrote:
> (...) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
> (...) f g x y = f (g x y)

> Does anybody else care about this? What are some alternative
> solutions?

Here is a different solution:

http://okmij.org/ftp/Haskell/polyvariadic.html#polyvar-comp

         f:: a1->a2-> .... ->cp  (where cp is not a function type)
         g:: cp->d
         f `mcomp` g:: a1->a2-> .... ->d

Now that we know how to generically decide if a type is not a
functional type, mcomp can be defined fully generically, for any type
cp that is not a function. If there is interest, I can write that
code.

One particular application of the mcomp combinator is the prod combinator:
Given two functions,
   f:: a1->a2->...->an->c   |c,d non-exponential types
   g:: b1->b2->...->bn->d
their product f `prod` g:: a1->a2->...->an->b1->b2->...->bn->(c,d)
The number of as and bs is arbitrary.

The definition of prod is very simple:

> prod = (. ((. (,)) . mcomp)) . mcomp

The web page
	http://okmij.org/ftp/Haskell/polyvariadic.html#categorical-max3
gives a few explanations and further examples.