Free Monoid

#### npm package:

$3

``js
const M = freeMonoid(operator);
`

$3

#### (M)(a) = (a) = (a)(M)

$3

#### ((a)(b))(c) = (a)(b)(c) = (a)((b)(c))

Installation

`sh
$ npm install free-monoid
`

Usage

`js
const freeMonoid = require("free-monoid");
`

Additive monoid derived from free-monoid

`js
const _M = () => freeMonoid(operator);
const operator = list => {
list.eval = () => list.val.reduce((a, b) => (a + b));
};
const M = _M();

const x = (M)(1);
const y = (M)(2);
const z = (M)(5);

console.log(x);
console.log(
(M)(x) // === (x) left identity
);
console.log(
(x)(M) // === (x) right identity
);

const xyz = (x)(y)(z);
console.log(xyz);
console.log(xyz.eval()); //lazy eval
`

`sh
8
`

List monad derived from free-monoid

#### monad laws validation

`js
const util = require("util");
const validate = a => b => util.inspect(a) === util.inspect(b)
? true : false;

const f = x => (M)(x + 7);
const g = x => (M)(x * 5);
const a = 9;
const m = (M)(3)(5)(7);

console.log(
validate(
(M)(a).bind(f)
)(
f(a)
)
);
console.log(
validate(
m.bind(M)
)(
m
)
);
console.log(
validate(
m.bind(f)
.bind(g)
)(
m.bind(x => f(x)
.bind(g))
)
);
`

`sh
true
true
true
`

Other derivatives from free-monoid`

$3