fac.js

//Lambda Calc JS
const TRUE = x => y => x;
const FALSE = x => y => y;

const ZERO = x => y => y;
const ONE = x => y => x(y);

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

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

const PAIR = x => y => f => f(x)(y);
const CAR = p => p(x => y => x);
const CDR = p => p(x => y => y);

const PHI = p => PAIR(CDR(p))(SUCC(CDR(p)));
const PRED = n => CAR(n(PHI)(PAIR(ZERO)(ZERO)));
const SUB = x => y => y(PRED)(x);

const IS_ZERO = n => n(x => FALSE)(TRUE);
const LEQ = x => y => IS_ZERO(SUB(x)(y));

const Z = f => (x => f(y => x(x)(y)))(x => f(y => x(x)(y)));

const FAC = Z(f => n => LEQ(ONE)(n)(x => MULT(n)(f(PRED(n)))(x))(ONE));

// 5! = 120
print(FAC(to_cn(5)));

// --- JS helpers. not strict lambda calc below

function print(n) {
  console.log(n(x => x + 1)(0));
}

function to_cn(x) {
  return Z(f => x => (x === 0 ? ZERO : y => SUCC(f(x - 1))(y)))(x);
}

fac_expanded.js

console.log(
  (x =>
    (n => n(x => x + 1)(0))(
      (x => (y => x(z => y(y)(z)))(y => x(z => y(y)(z))))(x => y =>
        (x => y =>
          (x => x(x => x => y => y)(x => y => x))(
            (x => y =>
              y(x =>
                (x => x(x => y => x))(
                  x(x =>
                    (x => y => z => z(x)(y))((x => x(x => y => y))(x))(
                      (x => y => z => y(x(y)(z)))((x => x(x => y => y))(x))
                    )
                  )((x => y => z => z(x)(y))(x => y => y)(x => y => y))
                )
              )(x))(x)(y)
          ))(x => y => x(y))(y)(z =>
          (x => y => z => x(y(z)))(y)(
            x(
              (x =>
                (x => x(x => y => x))(
                  x(x =>
                    (x => y => z => z(x)(y))((x => x(x => y => y))(x))(
                      (x => y => z => y(x(y)(z)))((x => x(x => y => y))(x))
                    )
                  )((x => y => z => z(x)(y))(x => y => y)(x => y => y))
                ))(y)
            )
          )(z)
        )(x => y => x(y))
      )(
        (x =>
          (x => (y => x(z => y(y)(z)))(y => x(z => y(y)(z))))(x => y =>
            y === 0
              ? x => y => y
              : z => (x => y => z => y(x(y)(z)))(x(y - 1))(z)
          )(x))(x)
      )
    ))(5)
);

/* minified:
FAC = x=>(n=>n(x=>x+1)(0))((x=>(y=>x(z=>y(y)(z)))(y=>x(z=>y(y)(z))))(x=>y=>(x=>y=>(x=>x(x=>x=>y=>y)(x=>y=>x))((x=>y=>y(x=>(x=>x(x=>y=>x))(x(x=>(x=>y=>z=>z(x)(y))((x=>x(x=>y=>y))(x))((x=>y=>z=>y(x(y)(z)))((x=>x(x=>y=>y))(x))))((x=>y=>z=>z(x)(y))(x=>y=>y)(x=>y=>y))))(x))(x)(y)))(x=>y=>x(y))(y)(z=>(x=>y=>z=>x(y(z)))(y)(x((x=>(x=>x(x=>y=>x))(x(x=>(x=>y=>z=>z(x)(y))((x=>x(x=>y=>y))(x))((x=>y=>z=>y(x(y)(z)))((x=>x(x=>y=>y))(x))))((x=>y=>z=>z(x)(y))(x=>y=>y)(x=>y=>y))))(y)))(z))(x=>y=>x(y)))((x=>(x=>(y=>x(z=>y(y)(z)))(y=>x(z=>y(y)(z))))(x=>y=>y===0?x=>y=>y:z=>(x=>y=>z=>y(x(y)(z)))(x(y-1))(z))(x))(x)))
*/

lambda.js

//Lambda Calc JS

const I = x => x;

const TRUE = x => y => x;
const FALSE = x => y => y;

const ZERO = x => y => y;
const ONE = x => y => x(y);
const TWO = x => y => x(x(y));

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

const THREE = SUCC(TWO);
const FOUR = SUCC(SUCC(TWO));

const ADD = x => y => x(SUCC)(y);

const FIVE = ADD(TWO)(THREE);
const TEN = ADD(FIVE)(FIVE);

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

const ONE_HUNDRED = MULT(TEN)(TEN);

const IS_ZERO = n => n(x => FALSE)(TRUE);

const PAIR = x => y => f => f(x)(y);

const CAR = p => p(x => y => x);
const CDR = p => p(x => y => y);

const PHI = p => PAIR(CDR(p))(SUCC(CDR(p)));

const PRED = n => CAR(n(PHI)(PAIR(ZERO)(ZERO)));

const NINE = PRED(TEN);

const SUB = x => y => y(PRED)(x);

const SIX = SUB(TEN)(FOUR);

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

const LEQ = x => y => IS_ZERO(SUB(x)(y));
const GEQ = x => y => IS_ZERO(SUB(y)(x));
const GT = x => y => NOT(LEQ(x)(y));
const LT = x => y => NOT(GEQ(x)(y));
const EQ = x => y => AND(LEQ(x)(y))(LEQ(y)(x));

const Z = f => (x => f(y => x(x)(y)))(x => f(y => x(x)(y)));

const FAC = Z(f => n => GT(n)(ONE)(x => MULT(n)(f(SUB(n)(ONE)))(x))(ONE));
printNum(FAC(FIVE));

// js helpers

function print(f) {
  console.log(f);
}

function printNum(n) {
  print(n(x => x + 1)(0));
}

module.exports = {
  TRUE,
  FALSE,
  ZERO,
  ONE,
  SUCC,
  ADD,
  MULT,
  PAIR,
  CAR,
  CDR,
  PHI,
  PRED,
  SUB,
  NOT,
  AND,
  OR,
  LE,
  GE,
  GT,
  LT,
  EQ,
  Z,
};