lambda-in-js.js

// Lambda calculus functions in JavaScript. #untyped

// @ts-nocheck

/** identity */
const I = (x) => x

/** compose unary */
const B = (f) => (g) => (x) => f(g(x))

/** compose binary */
const B1 = (f) => (g) => (a) => (b) => f(g(a)(b))

/** kestrel */
const K = (k) => (_) => k

const T = (x) => (y) => x
const F = (x) => (y) => y

const not = (x) => x(F)(T)
const and = (x) => (y) => x(y)(F)
const or = (x) => (y) => x(T)(y)

const pair = (a) => (b) => (f) => f(a)(b)
const fst = (p) => p(T)
const snd = (p) => p(F)
const phi = (p) => pair(snd(p))(succ(snd(p)))

const succ = (n) => (s) => B(s)(n(s))
const prev = (n) => fst(n(phi)(pair(n0)(n0)))
const n0 = (s) => (z) => z
const n1 = succ(n0)
const n2 = succ(n1)
const n3 = succ(n2)
const n4 = succ(n3)
const n5 = succ(n4)

const jsnum = (n) => n((x) => x + 1)(0)
const lcnum = (n) => (n ? succ(lcnum(n - 1)) : n0)
const add = (a) => (b) => a(succ)(b)
const sub = (a) => (b) => a(prev)(b)
const mult = B
const pow = (x) => (y) => y(x)
const isZero = (n) => n(K(F))(T)

const leq = (x) => (y) => isZero(sub(x)(y))
const eq = (x) => (y) => and(leq(x)(y))(leq(y)(x))
const gt = B1(not)(leq)

export {}