Functional Composition through functor map

functional-composition-with-functor-map.js

//  add :: Number -> Number -> Number
var add = function(left) { return function(right) { return left + right } };

//  multiply :: Number -> Number -> Number
var multiply = function(left) { return function(right) { return left * right } };

//  map :: (a -> b) -> Functor a -> Functor b
var map = function(fn, val) { return val.map(fn) };

//
// Functor: Identity
//
var Identity = function(val) {
  this.val = val;
};
Identity.of = function(x) {
  return new Identity(x);
};
Identity.prototype.map = function(fn) {
  return Identity.of(fn(this.val));
};

//
// Functor: Function
//
Function.prototype.map = function(fn2) {
  return function(val) {
    return fn2(this(val));
  }.bind(this);
};

//
// Function composition through functor map
//
var formula = map(multiply(2), add(1));     //=> (Number -> Number)
var result  = map(formula, Identity.of(3)); //=> Identity(8)