List monad in JS

list-monad.js

const identity = x => x

// Monoid
Array.empty = () => []
Array.prototype.empty = Array.empty

// Monad
Array.prototype.chain = function (f) {
  return Function.prototype.apply.bind([].concat, []) (this.map(f))
}

// Applicative
Array.prototype.ap = function (other) {
  return this.chain(f => other.map(x => f(x)))
}

// Traversable
Array.prototype.traverse = function(of, f) {
  return this.reduce((ys, x) =>
    ys.map(x => y => x.concat([y])).ap(f(x)), of(this.empty))
}

Array.prototype.sequence = function(of) {
  return this.traverse(of, identity)
}

Array.prototype.foldMap = function(f, empty) {
  return empty != null
    ? this.reduce((acc, x, i) => acc.concat(f(x, i)), empty)
    : this.map(f).reduce((acc, x) => acc.concat(x))
}

Array.prototype.fold = function(empty) {
  return this.foldMap(identity, empty)
}
  

Array.of(1).map(double) // [[1, 1]]
Array.of(1).chain(double) // [1, 1)