Functional composition with multi-valued functions in haskell?

Question

I was wondering if it was possible to do functional composition with functions that take more than one argument. I want to be able to do something like this

x = (+3).(*)

setting x equal to a function that adds three to the product of two numbers.

Answer 1

There are multiple ways to do it, but they're all somewhat awkward.

((+3).) . (*)
≡ fmap (+3) . (*)
≡ curry $ (+3) . uncurry (*)
≡ \l r -> l*r + 3

Oh, wait, this was the signature where there's also a compact definition, guess what it's called...

((.).(.)) (+3) (*)

I'd argue that the lambda solution, being most explicit, is rather the best here.

What helps, and is often done just locally as a one(or two)-liner, is to define this composition as a custom infix:

(.:) :: (c->d) -> (a->b->c) -> a->b->d
f .: i = \l r -> f $ i l r

Which allows you to write simply (+3) .: (*).

BTW, for the similar (b->b->c) -> (a->b) -> a->a->c (precompose the right function to both arguments of the infix) there exists a widely-used standard implementation.