Haskell Language Function composition Composition with binary function
Example
The regular composition works for unary functions. In the case of binary, we can define
(f .: g) x y = f (g x y) -- which is also
= f ((g x) y)
= (f . g x) y -- by definition of (.)
= (f .) (g x) y
= ((f .) . g) x y
Thus, (f .: g) = ((f .) . g) by eta-contraction, and furthermore,
(.:) f g = ((f .) . g)
= (.) (f .) g
= (.) ((.) f) g
= ((.) . (.)) f g
so (.:) = ((.) . (.)), a semi-famous definition.
Examples:
(map (+1) .: filter) even [1..5] -- [3,5]
(length .: filter) even [1..5] -- 2
