Haskell function composition operator of type (c→d) → (a→b→c) → (a→b→d)

Question

Ordinary function composition is of the type

(.) :: (b -> c) -> (a -> b) -> a -> c

I figure this should generalize to types

Answer 1

I don't know of a standard library function that does this, but the point-free pattern that accomplishes it is to compose the composition function:

(.) . (.) :: (b -> c) -> (a -> a1 -> b) -> a -> a1 -> c