Install (other package managers are available):
npm i -S combinators-js
Import (other module systems are available):
import { B, B1, B2, B3, C, C_, C__, D, D1, D2, E, F, F_, F__ G, H, I, I_, I__, J, K, L, M, M2, O, Q, Q1, Q2, Q3, Q4, R, R_, R__, S, T, U, V, V_, V__, W, W_, W__, W1, Y, } from 'combinators-js'
Here are the included combinators with their definitions:
const B = a => b => c => a(b(c)) const B1 = a => b => c => d => a(b(c)(d)) const B2 = a => b => c => d => e => a(b(c)(d)(e)) const B3 = a => b => c => d => a(b(c(d))) const C = a => b => c => a(c)(b) const C_ = a => b => c => d => a(b)(d)(c) const C__ = a => b => c => d => e => a(b)(c)(e)(d) const D = a => b => c => d => a(b)(c(d)) const D1 = a => b => c => d => e => a(b)(c)(d(e)) const D2 = a => b => c => d => e => a(b(c))(d(e)) const E = a => b => c => d => e => a(b)(c(d)(e)) const F = a => b => c => c(b)(a) const F_ = a => b => c => d => a(d)(c)(b) const F__ = a => b => c => d => e => a(b)(e)(d)(c) const G = a => b => c => d => a(d)(b(c)) const H = a => b => c => a(b)(c)(b) const I = a => a const I_ = a => b => a(b) const I__ = a => b => c => a(b)(c) const J = a => b => c => d => a(b)(a(d)(c)) const K = a => b => a const L = a => b => a(b(b)) const M = a => a(a) const M2 = a => b => a(b)(a(b)) const O = a => b => b(a(b)) const Q = a => b => c => b(a(c)) const Q1 = a => b => c => a(c(b)) const Q2 = a => b => c => b(c(a)) const Q3 = a => b => c => c(a(b)) const Q4 = a => b => c => c(b(a)) const R = a => b => c => b(c)(a) const R_ = a => b => c => d => a(c)(d)(b) const R__ = a => b => c => d => e => a(b)(d)(e)(c) const S = a => b => c => a(c)(b(c)) const T = a => b => b(a) const U = a => b => b(a(a)(b)) const V = a => b => c => c(a)(b) const V_ = a => b => c => d => a(c)(b)(d) const V__ = a => b => c => d => e => a(b)(e)(c)(d) const W = a => b => a(b)(b) const W_ = a => b => c => a(b)(c)(c) const W__ = a => b => c => d => a(b)(c)(d)(d) const W1 = a => b => b(a)(a) const Y = a => (b => b(b))(b => a(c => b(b)(c)))
test('B')(S(K(S))(K)) test('B1')(S(K(S(K(S))(K)))(S(K(S))(K))) test('B2')(S(K(S(K(S(K(S))(K)))(S(K(S))(K))))(S(K(S))(K))) test('C')(S(S(K(S(K(S))(K)))(S))(K(K))) test('C_')(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))) test('C__')(S(K(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))))) test('D')(S(K(S(K(S))(K)))) test('D1')(S(K(S(K(S(K(S))(K)))))) test('D2')(S(K(S(K(S))(K)))(S(K(S(K(S))(K))))) test('E')(S(K(S(K(S(K(S))(K)))(S(K(S))(K))))) test('F')(S(K(S(S(K)(K))(K(S(K(S(S(K)(K))))(K)))))(S(K(S(K(S(K(S))(K)))(S(K(S))(K))))(S(K(S(S(K)(K))))(K)))) test('F_')(S(K(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))))(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))))) test('F__')(S(K(S(K(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))))(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))))))) test('G')(S(K(S(K(S))(K)))(S(S(K(S(K(S))(K)))(S))(K(K)))) test('H')(S(K(S(K(S(S(K(S(S(K)(K))(S(K)(K))))(S(K(S(K(S))(K)))(S(K(S(S(K)(K))))(K))))))(K)))(S(K(S(S(K(S(K(S))(K)))(S))(K(K)))))) test('I')(S(K)(K)) test('I_')(S(S(K))) test('J')(S(K(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))))(S(S(K(S(S(K)(K))(S(K)(K))))(S(K(S(K(S))(K)))(S(K(S(S(K)(K))))(K))))(K(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S(K(S(K(S))(K)))(S(K(S))(K))))))))) test('K')(K) test('L')(S(S(K(S))(K))(K(S(S(K)(K))(S(K)(K))))) test('M')(S(S(K)(K))(S(K)(K))) test('M2')(S(K(S(S(K)(K))(S(K)(K))))) test('O')(S(S(K)(K))) test('Q')(S(K(S(S(K(S))(K))))(K)) test('Q1')(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S))(K))) test('Q2')(S(K(S(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S))(K)))))(K)) test('Q3')(S(K(S(K(S(S(K)(K))))(K)))) test('Q4')(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S))(K)))))(K))) test('R')(S(K(S(K(S))(K)))(S(K(S(S(K)(K))))(K))) test('R_')(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S(S(K(S(K(S))(K)))(S))(K(K)))))) test('R__')(S(K(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S(S(K(S(K(S))(K)))(S))(K(K)))))))) test('S')(S) test('T')(S(K(S(S(K)(K))))(K)) test('U')(S(K(S(S(K)(K))))(S(S(K)(K))(S(K)(K)))) test('V')(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S(S(K)(K))))(K))) test('V_')(S(K(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))))(S(K(S(S(K(S(K(S))(K)))(S))(K(K))))(S(K(S(S(K(S(K(S))(K)))(S))(K(K)))))))))) test('W')(S(K(S(S(K(S(S(K)(K))(S(K)(K))))(S(K(S(K(S))(K)))(S(K(S(S(K)(K))))(K))))))(K)) test('W_')(S(K(S(K(S(S(K(S(S(K)(K))(S(K)(K))))(S(K(S(K(S))(K)))(S(K(S(S(K)(K))))(K))))))(K)))) test('W__')(S(K(S(K(S(K(S(S(K(S(S(K)(K))(S(K)(K))))(S(K(S(K(S))(K)))(S(K(S(S(K)(K))))(K))))))(K)))))) test('W1')(S(K(S(S(K(S(S(K(S(S(K)(K))(S(K)(K))))(S(K(S(K(S))(K)))(S(K(S(S(K)(K))))(K))))))(K))))(K))
// LISP data structures const KI = K(I) const cons = (a, b) => V(a)(b) // manual uncurry const car = T(K) const cdr = T(KI) console.log(car(cons(0, 1))) // => 0 console.log(cdr(cons(0, 1))) // => 1 const nil = () => {} const list = (...args) => args.reduce((l, arg) => V(arg)(l), nil) const reverse = (l, m = nil) => l === nil ? m : reverse(l(KI), V(l(K))(m)) const reduce = f => l => m => l(KI) === undefined ? m : f(reduce(f)(l(KI))(m))(l(K)) const map = f => l => reduce(acc => val => V(f(val))(acc))(l)(nil) const length = l => reduce(acc => val => 1 + acc)(l)(0) const filter = f => l => reduce(acc => val => f(val) ? V(val)(acc) : acc)(l)(nil) const arbitraryList = list(0, 1, 2, 3, 4, 5) console.log(length(arbitraryList)) // => 6 const reduced = reduce(acc => val => V(val)(acc))(arbitraryList)(nil) const filtered = filter(x => x > 2)(reduced) const mapped = map(x => x ** 2)(filtered) const reversed = reverse(mapped) console.log(length(reversed)) // => 3 map(::console.log)(reversed) // => 25 16 9
// recursion of anonymous functions Y(recur => x => x === 1 ? 1 : x * recur(x - 1))(5) // => 120 // TCO'd recursion of anonymous functions using a modified Y // taking a variadic non-combinator function const Y_ = a => (b => a((...c) => b(b)(...c)))(b => a((...c) => b(b)(...c))) Y_(recur => (x, y = 1) => x === 1 ? y : recur(x - 1, x * y))(5) // => 120
// omega bird (mock a mockingbird) M(M)
̄\_(ツ)_/ ̄
I built a Church encoding library too.