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

Compose two functions. f .: g is similar to f . g except that g will be fed two arguments instead of one before handing its result to f. This function is defined as
(f .: g) x y = f (g x y)
Example usage:
concatMap :: (a -> [b]) -> [a] -> [b]
concatMap = concat .: map
Notice how two arguments (the function and the list) will be given to map before the result is passed to concat. This is equivalent to:
concatMap f xs = concat (map f xs)
Equivalent to .: The pattern of appending asterisks is straightforward to extend to similar functions: (compose2 = .*, compose3 = .**, etc). However, .: has been commonly adopted amongst Haskellers, and the need for compose3 and beyond is rare in practice.
Compose composed with compose operator.
(f ... g) x y === f (g x y)
Compose functions with one argument with function with two arguments. f .: g = \x y -> f (g x y).
Binary composition: pass two args to the right argument before composing.
(f .: g) x y = f (g x y)
f .: g = curry (f . uncurry g)
This is the same as the common idiom (f .) . g but more easily extended to multiple uses, due to the fixity declaration.
Multivariant composition.
f .: g ≡ (f .) . g ≡ \c d -> f (g c d)
Wrap the result of a function applied to 2 arguments.