Common combinators in JavaScript

combinators.js

const I = x => x;
const K = x => y => x;
const A = f => x => f(x);
const T = x => f => f(x);
const W = f => x => f(x)(x);
const C = f => y => x => f(x)(y);
const B = f => g => x => f(g(x));
const S = f => g => x => f(x)(g(x));
const P = f => g => x => y => f(g(x))(g(y));
const Y = f => (g => g(g))(g => f(x => g(g)(x)));

combinators.md

Name	#	Birds	Haskell	Ramda	Sanctuary	Signature
identity	I	Idiot	id	identity	I	a → a
constant	K	Kestrel	const	always	K	a → b → a
apply	A		($)	call	A	(a → b) → a → b
thrush	T	Thrush	(&)	applyTo	T	a → (a → b) → b
duplication	W	Warble	join²	unnest²	join²	(a → a → b) → a → b
flip	C	Cardinal	flip	flip	flip	(a → b → c) → b → a → c
compose	B	Bluebird	(.), fmap²	map²	compose, map²	(b → c) → (a → b) → a → c
substitution	S	Starling	ap²	ap²	ap²	(a → b → c) → (a → b) → a → c
psi	P		on		on	(b → b → c) → (a → b) → a → a → c
fix-point¹	Y		fix			(a → a) → a

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¹) In JavaScript and other non-lazy languages, it is impossible to implement the Y-combinator. Instead a variant known as the applicative or strict fix-point combinator is implemented. This variant is sometimes rererred to as the Z-combinator.

²) Algebras like ap have different implementations for different types. They work like Function combinators only for Function inputs.

references.md

Note that when I use the word "combinator" in this context, it implies "function combinator in the untyped lambda calculus".

• To Mock a Mocking Bird (book of combinatory puzzles and examples)
• Combinator Birds (summary of all combinators named by the book)
• CombinatorsJS (implementation of all the same combinators in JavaScripts)
• Fantasy Combinators (implementation of common combinators in JavaScript)
• Collected Lambdas (collection of noteworthy combinators)
• Programming With Nothing (talk)
• Church Encoding (wikipedia)
• Fixed-point combinator (wikipedia)
• Lambda calculus (wikipedia)
• SKI combinator calculus (wikipedia)
• BCKW combinator calculus (wikipedia)