meus churchezinhos

lambdazinhs.js

/* 
ChUrChEsZiNhUs

baseado na palestra : https://www.youtube.com/watch?v=VpzhH9CXOy0
*/

const ID = x => x

const TRUE = x => y => x
TRUE("0")("1") // 0
const FALSE = x => y => y
FALSE("0")("1") // 1

const IF_THEN_ELSE = p => x => y => p(x)(y)
const toBool = b => IF_THEN_ELSE(b)(true)(false)

const AND = x => y => x(y)(FALSE)
const OR = x => y => x(TRUE)(y)
const NOT = x => x(FALSE)(TRUE)

toBool(AND(TRUE)(TRUE)),    // true
toBool(AND(FALSE)(TRUE)),   // false
toBool(AND(TRUE)(FALSE)),   // false
toBool(AND(FALSE)(FALSE))   // false

toBool(OR(TRUE)(TRUE)),    // true
toBool(OR(FALSE)(TRUE)),   // true
toBool(OR(TRUE)(FALSE)),   // true
toBool(OR(FALSE)(FALSE))   // false

toBool(NOT(TRUE)),   // false
toBool(NOT(FALSE))   // true

const ZERO = f => x => x
const ONE = f => x => f(x)
const TWO = f => x => f(f(x))
const THREE = f => x => f(f(f(x)))
const FOUR = f => x => f(f(f(f(x))))

// recursao
const Y = f => (x => x(x))(y => f(x => y(y)(x)));

const SUCC = n => f => x => f(n(f)(x))
const PRED = n => n(p => z => z(SUCC(p(TRUE)))(p(TRUE)))(z => z(ZERO)(ZERO))(FALSE)
const SUCC_PAIR = p => PAIR(SECOND(p))(SUCC(SECOND(p)))
const PRED = n => FIRST(n(SUCC_PAIR)(PAIR(ZERO)(ZERO)))
const FOUR2 = SUCC(THREE)

const ADD = n => m => m(SUCC)(n)
const SUB = n => m => m(PRED)(n)
const MULT = n => m => m(ADD(n))(ZERO)
const EXP = n => m => m(n)
const FIVE = ADD(TWO)(THREE)

const IZ = n => (x => FALSE)(TRUE)
const LEQ = m => n => IZ(SUB(m)(n))

// const FIB = Y(r => n => IF(LEQ(n)(ONE)))

const toInt = n => n(x => x + 1)(0)

https://github.com/terremoth/js-church-encoding