Haskell function composition

Question

I am reading this tutorial on Haskell. They define function composition as the following:

(.)                     :: (b->c) -> (a->b) -> (a->c)
f . g                   = \ x -> f (g x)

No examples were provided, which I believe would enlighten me as to what is being defined here.

Can someone provide a simple example (with explanation) of how function composition is used?

Answer 1

Function composition is a way to "compose" two functions together into a single function. Here's an example:

Say you have these functions:

even :: Int -> Bool
not :: Bool -> Bool

and you want to define your own myOdd :: Int -> Bool function using the two above.

The obvious way to do this is the following:

myOdd :: Int -> Bool
myOdd x = not (even x)

But this can be done more succinctly using function composition:

myOdd :: Int -> Bool
myOdd = not . even

The myOdd functions behave exactly the same, but the second one is created by "glue-ing" two functions together.

A scenario where this is especially useful is to remove the need for an explicit lambda. E.g:

map (\x -> not (even x)) [1..9]

can be rewritten to:

map (not . even) [1..9]

A bit shorter, less room for errors.