λ演算

lambda.js

ZERO = f => x => x
ONE = f => x => f(x)
TWO = f => x => f(f(x))
THREE = f => x => f(f(f(x)))
FOUR = f => x => f(f(f(f(x))))
FIVE = f => x => f(f(f(f(f(x)))))
SIX = f => x => f(f(f(f(f(f(x))))))
SEVEN = f => x => f(f(f(f(f(f(f(x)))))))
EIGHT = f => x => f(f(f(f(f(f(f(f(x))))))))
NINE = f => x => f(f(f(f(f(f(f(f(f(x)))))))))
TEN = f => x => f(f(f(f(f(f(f(f(f(f(x))))))))))
TRUE = x => y => x // 选第一个
FALSE = x => y => y // 选第二个
IF = bool => value1 => value2 => bool(value1)(value2)
// IF = bool => bool
IS_ZERO = n => n(() => FALSE)(TRUE)
UP = n => f => x => f(n(f)(x))
PAIR = x => y => f => f(x)(y)
FIRST = p => p(x => y => x)
SECOND = p => p(x => y => y)

SLIDE = p => PAIR(SECOND(p))(UP(SECOND(p)))
DOWN = n => FIRST( n(SLIDE)(PAIR(ZERO)(ZERO)) )

ADD = m => n => n(UP)(m) // m + n = m +1 +1 +1
SUB = m => n => n(DOWN)(m) // m - n = m -1 -1 -1
MUL = m => n => n(ADD(m))(ZERO) // m * n = 0 +m +m +m
POW = m => n => n(MUL(m))(ONE) // m ** n = 1 *m *m *m


// ------------------------------
toNumber = n => n(x => x + 1)(0)
toScratches = n => n(x => x + "|")("")
toBool = b => b(true)(false)


// p = PAIR(FOUR)(TWO) // [4, 2]
// f = FIRST(p)
// s = SECOND(p)
// console.log(toNumber(DOWN(TEN)))
// console.log(toNumber(f))
// console.log(toNumber(s))

// console.log(toBool(IS_ZERO(ZERO))) // true
// console.log(toBool(IS_ZERO(ONE))) // false
// console.log(toBool(IS_ZERO(TEN))) // false
















// console.log(IF(TRUE)("yes")("no")) // yes
// console.log(IF(FALSE)("yes")("no")) // no
// console.log(toBool(TRUE)) // true
// console.log(toBool(FALSE)) // false
// console.log(toNumber(ONE)) // 1
// console.log(toNumber(ZERO)) // 0
// console.log(toNumber(TEN)) // 10
// console.log(toScratches(ONE)) // 1
// console.log(toScratches(ZERO)) // 0
// console.log(toScratches(TEN)) // 10