Function composition

Function composition is a well-known operator from mathematics, written as ∘, that combines two functions into a new one.

Basic function composition

Consider the following anonymous function:

\l -> show (length l)

This function returns the length of a list rendered as a string. It is not in the right shape to apply eta reduction to because, in its current form, we cannot identify one function that is applied to l.

The function composition operator captures this particular pattern in a general way:

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

This higher-order operator takes two functions and returns a new function that applies the first to the output of the second. We can use this to replace our preceding example with the following:

show . length

This can be read as "show composed with length" or, better, "show after length".

Pipelines

The function composition...