JavaScriptで(型無し)ラムダ計算

lambda_calc.js

const I = (x) => x;
const K = (x) => (y) => x;
const S = (x) => (y) => (z) => x (z) (y (z));

const SII = (x) => S (I) (I) (x);
const KSII = (x) => K (SII) (x);

const Y = (x) => S (KSII) (S (S (K (S)) (K)) (KSII)) (x);

const T = K;
const F = K (I);

const NOT = (x) => S (S (I) (K (F))) (K (T)) (x);

T ('then') ('else'); // 'then'
F ('then') ('else'); // 'else'

(NOT (F)) ('then') ('else'); // 'then'
(NOT (T)) ('then') ('else'); // 'else'

const OR = (x) => (y) => S (I) (K (T)) (x) (y);

(OR (F) (F)) ('then') ('else'); // 'else'
(OR (T) (F)) ('then') ('else'); // 'then'
(OR (F) (T)) ('then') ('else'); // 'then'
(OR (T) (T)) ('then') ('else'); // 'then'

const AND = (x) => (y) => S (S) (K (K (F))) (x) (y);

(AND (F) (F)) ('then') ('else'); // 'else'
(AND (T) (F)) ('then') ('else'); // 'else'
(AND (F) (T)) ('then') ('else'); // 'else'
(AND (T) (T)) ('then') ('else'); // 'then'

const Zero = (f) => (x) => x;
const Succ = (n) => (f) => (x) => f (n (f) (x));

const One   = Succ (Zero);
const Two   = Succ (One);
const Three = Succ (Two);

Zero  ((n) => n + 1) (0); // 0
One   ((n) => n + 1) (0); // 1
Two   ((n) => n + 1) (0); // 2
Three ((n) => n + 1) (0); // 3

const Add = (x) => (y) => (p) => (q) => x (p) (y (p) (q));

const Five = Add (Two) (Three);
Five ((n) => n + 1) (0); // 5

const Multiply = (x) => (y) => (z) => x (y (z));

const Four = Multiply (Two) (Two);
Four ((n) => n + 1) (0); // 4

const Exponentiation = (x) => (y) => y (x);

const Eight = Exponentiation (Two) (Three);
Eight ((n) => n + 1) (0); // 8

const Pred = (n) => (f) => (x) => n ((p) => (q) => q (p (f))) ((a) => x) (I);
 
const Seven = Pred (Eight);
Seven ((n) => n + 1) (0); // 7

const Subtract = (x) => (y) => y (Pred) (x);

const Six = Subtract (Eight) (Two);
Six ((n) => n + 1) (0); // 6