Functions under composition form a Monoid

functions_monoid.js

// These are our elements
const f = x => x + 1;
const g = x => x + 2;
const h = x => x + 3;

// This is our neutral element, a function which does nothing
const id = x => x;

// This is the composition
f(g(h(1))) // 7

// Which is associative by definition...
compose(f, compose(g,h)) === compose(compose(f,g),h)

// If we compose a function with "id", it's like calling the function directly
compose(f, id) === f
compose(id, f) === f