A composition in functional programming is a function that has been ‘composed’ from two functions.

More formally a composition is when we have a function f that takes an argument of type A and returns B (A → B) and another function g that takes an argument of type B and returns C (B → C). Then we can create a function out of f and g that takes an argument of type A and returns C (A → C).

This type of function composition can be denoted as f ∘ g.

Below is an implementation of a compose function in JavaScript (note! the functions are applied in a left to right order).

Composing multiple functions

In practice a more useful compose function would allow you to compose a variadic amount of functions at the same time.

When composing multiple functions it’s good to realise that function composition is always associative. Which means that f ∘ (g ∘ h) gives the same result as (f ∘ g) ∘ h.

Below is an implementation in JavaScript that composes together a variadic amount of functions.