g33k57
6/14/2019 - 8:15 PM

Common combinators in JavaScript

Common combinators in JavaScript

combinators.js
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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
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Name#HaskellRamdaSanctuarySignature
identityIididentityIa → a
constantKconstalwaysKa → b → a
apply¹A($)call(a → b) → a → b
thrushT(&)applyToTa → (a → b) → b
duplicationWjoin²unnest²join²(a → a → b) → a → b
flipCflipflipflip(a → b → c) → b → a → c
composeB(.), fmap²map²compose, map²(b → c) → (a → b) → a → c
substitutionSap²ap²ap²(a → b → c) → (a → b) → a → c
psiPonon(b → b → c) → (a → b) → a → a → c
fix-point³Yfix(a → a) → a

¹) The A-combinator can be implemented as an alias of the I-combinator. Its implementation in Haskell exists because the infix nature gives it some utility. Its implementation in Ramda exists because it is overloaded with additional functionality.

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

³) 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.

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