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.