Or operator as a monoid

or_monoid.js

'use strict';

// Or (||) operator as a monoid

function Or(v) {
  return {
    value: v
  };
}

function binary(v1, v2) {
  return v1 || v2;
}

function empty() {
  return Or(false);
}

function append(m1, m2) {
  return Or(binary(m1.value, m2.value));
}

function concat(ms) {
  return ms.reduce(append, empty());
}


function assertSameValue(m1, m2) {
  if(m1.value !== m2.value) {
    throw new Error('Expected ' + JSON.stringify(m1) + ' to have the same value as ' + JSON.stringify(m2));
  }
}

// `empty` must act as the identity with respect to `append`

var appendEmptyLeft = append(empty(), Or(true));

assertSameValue(appendEmptyLeft, Or(true));

var appendEmptyRight = append(Or(false), empty());

assertSameValue(appendEmptyRight, Or(false));


// `append` must be associative

var generalAppend = append(Or(false), Or(true));

assertSameValue(
  append(generalAppend, Or(false)),
  append(Or(false), generalAppend)
);


// `concat` can take a list of monoid values and reduce them to a single value

var ors = [false, false, true].map(Or);

assertSameValue(concat(ors), Or(true));