Simple example of pointfree-fantasy composition and mapping

category.js

#!/usr/bin/env node
"use strict";
// tested with io.js 1.5.1 which supports ES6 'const'
// there are no mutable variables in the entire gist
const assert   = require('assert');
const util     = require('util');
const P        = require('pointfree-fantasy');
const map      = P.map;
const compose  = P.compose;
const Maybe    = require('pointfree-fantasy/instances/maybe');
const Identity = require('pointfree-fantasy/instances/identity').Identity;

const inspect = function(x) {return util.inspect(x,{showHidden:true,depth:null});};

console.log("======================================");
console.log("CATEGORIES");
console.log("======================================");

// ordinary functions that do something
const f  = function(x) {return x * 2;};
const g  = function(x) {return x / 3;};
const h  = function(x) {return x + 1;};

// ordinary identity function
const id = function(x) {return x;};

console.log("Ordinary Functions:");
// ==========================================
// associativity
// ==========================================
// X = (f . g) . h
const a1 = compose(h,compose(g,f));
const a2 = compose(compose(h,g),f);
assert.equal(a1(1),a2(1),"associativity");
console.log('    associativity OK');
// ==========================================
// identity
// ==========================================
// f.id === id.f
const i1 = compose(f,id);
const i2 = compose(id,f);
assert.equal(i1(1),i2(1),"identity");
console.log('    identity OK');

console.log("======================================");
console.log("create Functors");
// ==========================================
// promote ordinary functions to Functors
// ==========================================
const mf  = map(f);
const mg  = map(g);
const mh  = map(h);
// ==========================================
// create compositions for associativity
// ==========================================
const m1 = compose(mh,compose(mg,mf));
const m2 = compose(compose(mh,mg),mf);
// ==========================================
// create compositions for identity
// ==========================================
// map(f) . id == id . map(f)
const mid = map(id);
const mi1 = compose(mf,mid);
const mi2 = compose(mid,mf);
// ==========================================
// create compositions for distributivity
// ==========================================
const m5 = compose(mf,mg);
const m6 = map(compose(f,g));
console.log("======================================");

// ==========================================
// Functors
// ==========================================
console.log("Functors:");
const one = Identity(1);
// ===============================================
// associativity
// ===============================================
assert.deepEqual(m1(one),m2(one),"associativity");
console.log('    associativity OK');
// ==========================================
// identity
// ==========================================
assert.deepEqual(mi1(one),mi2(one),"identity");
console.log('    identity OK');
// ==========================================
// map(f).map(g) === map(f.g)
// ==========================================
assert.deepEqual(m5(one),m6(one),"distributive");
console.log('    distributivity OK');
console.log("======================================");

// ==========================================
// Arrays
// ==========================================
console.log("Arrays:");
const A = [1,2,3];
// ==========================================
// associativity
// ==========================================
assert.deepEqual(m1(A),m2(A),"associativity");
console.log('    associativity OK');
// ==========================================
// identity
// ==========================================
// map(f) . id == id . map(f)
assert.deepEqual(mi1(A),mi2(A),"identity");
console.log('    identity OK');
// ==========================================
// map(f).map(g) === map(f.g)
// ==========================================
assert.deepEqual(m5(A),m6(A),"distributive");
console.log('    distributivity OK');

console.log("======================================");