Y-COMBINATOR-JS

derive the y combinator using pure javascript

The Y combinator discovered by Haskell B. Curry is an implementation of the fixed-point combinator in lambda calculus.It defined as:

• call by value: λf.(λx.f(λn.x x n))(λx.f(λn.x x n))
• call by name: λf.(λx.f(x x))(λx.f(x x))

so in ecmascript 2015, It can be implement by one line

f => (x => f(n => x(x)(n)))(x => f(n => x(x)(n)));

Installation

using npm

npm install y-combinator-js

Usage

it won't decrease the computation complexity, so don't use it in production enviroment,unless you know what you do.

import Y from 'y-combinator-js';

then enjoy it:

• factorial

  const FACT10 = 3628800;
  const fact = Y(f => (n => n === 0 ? 1 : n * f(n - 1)));
  fact(10).should.equal(FACT10);

• fibonacci

  const FIB = [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144];
  const fibonacci = Y(fib => (n => (n <= 2 ? 1 : fib(n - 1) + fib(n - 2))));
  fibonacci(5).should.equal(FIB[5]);
  fibonacci(10).should.equal(FIB[10]);

License

MIT