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	#	Haskell	Ramda	Sanctuary	Signature
identity	I	id	identity	I	a → a
constant	K	const	always	K	a → b → a
apply	A	($)	call	A	(a → b) → a → b
thrush	T	(&)		T	a → (a → b) → b
duplication	W	join²	unnest²	join²	(a → a → b) → a → b
flip	C	flip	flip	flip	(a → b → c) → b → a → c
compose	B	(.)	map²	compose, map²	(b → c) → (a → b) → a → c
substitution	S	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

• Combinator Birds
• CombinatorsJS
• Collected Lambdas
• To Mock a Mocking Bird
• Fantasy Combinators
• Fixed-point combinator
• Lambda calculus
• SKI combinator calculus
• BCKW combinator calculus
• Programming With Nothing