TRUE/FALSE/AND/OR/NOT/数値の定理をJSのlambda式で書いてみた

code:javascript

// Debug用

const FN = (x) => x + 1;

const TRUE = 1;

const FALSE = 0;

// 0 := λf x. x

const _0 = (f) => (x) => x

// SUCC := λn f x. f (n f x)

const SUCC = (n) => (f) => (x) => f(n(f)(x));

// 1 := λf x. f x

const _1 = SUCC(_0);

// 2 := λf x. f (f x)

const _2 = SUCC(_1);

const _3 = SUCC(_2);

const _4 = SUCC(_3);

// PLUS := λm n f x. m f (n f x)

const PLUS = (m) => (n) => (f) => (x) => m(f)(n(f)(x));

// T := λx y. x

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

// F := λx y. y

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

// NOT := λp. p F T

const NOT = (p) => p(F)(T);

// OR := λp q. p T q

const OR = (p) => (q) => p(T)(q);

// AND := λp q. p q F

const AND = (p) => (q) => p(q)(F);

console.log(NOT(T)(TRUE)(FALSE)); // -> 0

console.log(NOT(F)(TRUE)(FALSE)); // -> 1

console.log(OR(T)(T)(TRUE)(FALSE)); // -> 1

console.log(OR(T)(F)(TRUE)(FALSE)); // -> 1

console.log(OR(F)(T)(TRUE)(FALSE)); // -> 1

console.log(OR(F)(F)(TRUE)(FALSE)); // -> 0

console.log(AND(T)(T)(TRUE)(FALSE)); // -> 1

console.log(AND(F)(T)(TRUE)(FALSE)); // -> 0

console.log(AND(T)(F)(TRUE)(FALSE)); // -> 0

console.log(AND(F)(F)(TRUE)(FALSE)); // -> 0

console.log(_0(FN)(0)); // -> 0

console.log(_1(FN)(0)); // -> 1

console.log(_2(FN)(0)); // -> 1

console.log(_3(FN)(0)); // -> 1

console.log(_4(FN)(0)); // -> 4

console.log(SUCC(_1)(FN)(0)); // -> 2

console.log(PLUS(_1)(_2)(FN)(0)); // -> 3

省略版

code:javascript

// Debug用

const FN = (x) => x + '1';

const TRUE = 1;

const FALSE = 2;

// 0 := λf x. x

const _0 = (f, x) => x

// 1 := λf x. f x

const _1 = (f, x) => f(x);

// 2 := λf x. f (f x)

const _2 = (f, x) => f(f(x));

// SUCC := λn f x. f (n f x)

const SUCC = (n) => (f, x) => f(n(f, x));

// PLUS := λm n f x. m f (n f x)

const PLUS = (m, n) => (f, x) => m(f, n(f, x));

// PLUS := λm n. m SUCC n

const PLUS_VER2 = (m, n) => m(SUCC, n);

const T = (x, y) => x;

const F = (x, y) => y;

// NOT := λp. p FALSE TRUE

const NOT = (p) => p(F, T);

// OR := λp q. p TRUE q

const OR = (p, q) => p(T, q);

// AND := λp q. p q FALSE

const AND = (p, q) => p(q, F);

console.log(NOT(T)(TRUE, FALSE)); // -> 1

console.log(NOT(F)(TRUE, FALSE)); // -> 2

console.log(OR(T, T)(TRUE, FALSE)); // -> 1

console.log(OR(T, F)(TRUE, FALSE)); // -> 1

console.log(OR(F, T)(TRUE, FALSE)); // -> 1

console.log(OR(F, F)(TRUE, FALSE)); // -> 2

console.log(AND(T, T)(TRUE, FALSE)); // -> 1

console.log(AND(F, T)(TRUE, FALSE)); // -> 2

console.log(AND(T, F)(TRUE, FALSE)); // -> 2

console.log(AND(F, F)(TRUE, FALSE)); // -> 2

console.log(SUCC(_1)(FN, '')); // -> 11

console.log(PLUS(_1, _2)(FN, '')); // -> 111

console.log(PLUS_VER2(_1, _2)(FN, '')); // -> 111

code:ruby

FN = (-> (x) {x + 1})

T = (-> (x, y) { x }).curry

F = (-> (x, y) { y }).curry

_0 = (-> (f, x) {x}).curry

# MULT := λm n. m (PLUS n) 0

# PRED := λn f x. n (λg h. h (g f)) (λu. x) (λu. u)

PRED = (-> (n, f, x) {n})

# PRED := λn. n (λg k. (g 1) (λu. PLUS (g k) 1) k) (λv. 0) 0