Basic example of S, K, and I in fantasy-combinators using mocha with JSVerify

test.js

const {constant, identity/*, substitution*/} = require('fantasy-combinators');
const substitution = f => g => x => f(x)(g(x));

const K = constant;
const I = identity;
const S = substitution;

const expect = require('expect.js');
const jsc = require('jsverify');

describe('verify jsverify is set up right', () => {
  jsc.property('boolean function applied thrice', jsc.fn(jsc.bool), jsc.bool,
    (f, b) => f(f(f(b))) === f(b)
  );
  
  jsc.property('(b && b) === b', jsc.bool,
    b => (b && b) === b
  );
});

describe('K', () => {
  jsc.property('K x y === x', jsc.bool, jsc.bool,
    (x, y) => K(x)(y) === x
  );

  jsc.property('K x y === x', jsc.string, jsc.number,
    (x, y) => K(x)(y) === x
  );
});

describe('I', () => {
  jsc.property('I x === x', jsc.int32,
    x => I(x) === x
  );
});

describe('S', () => {
  const add = x => y => x + y;
  const inc = add(1);

  jsc.property('S f g x = f x (g y)', jsc.number,
    x => S(add)(inc)(x) === add(x)(inc(x))
  );

  jsc.property('SKK = I', jsc.fn(jsc.number, jsc.number), jsc.fn(jsc.number), jsc.number,
    (f, g, x) => S(K)(K)(x) === I(x)
  );

  jsc.property('SKS = I', jsc.fn(jsc.number, jsc.number), jsc.fn(jsc.number), jsc.number,
    (f, g, x) => S(K)(S)(x) === I(x)
  );
});

describe('Booleans', () => {
  jsc.property('True = K True False',
    () => K(true)(false) === true
  ),
  jsc.property('False = SK True False',
    () => S(K)(() => true)(false) === false
  )
});