Finally figured out how to write fizzbuzz in python

LambdaFizzBuzz.py

ADD = lambda a: lambda b: \
    lambda f: lambda x: b(f)(a(f)(x))
MULT = lambda a: lambda b: \
    lambda f: lambda x: a(b(f))(x)

ZERO = lambda f: lambda x: x
ONE  = lambda f: lambda x: f(x)
TWO = ADD(ONE)(ONE)
THREE = ADD(ONE)(TWO)
FOUR = ADD(TWO)(TWO)
FIVE = ADD(TWO)(THREE)
FIFTEEN = MULT(THREE)(FIVE)
TEN = MULT(TWO)(FIVE)
HUNDRED = MULT(TEN)(TEN)

INC = ADD(ONE)
DEC = lambda n: \
    lambda f: \
      lambda x: n(lambda g: lambda h: h(g(f))) \
        (lambda y: x)(lambda y: y)
SUB = lambda m: lambda n: n(DEC)(m)

TRUE  = lambda t: lambda f: t
FALSE = lambda t: lambda f: f

IF = lambda b: b

IS_ZERO = lambda n: n(lambda _: FALSE)(TRUE)
IS_LTE = lambda m: lambda n: IS_ZERO(SUB(m)(n))

Z = lambda f: (lambda x: f(lambda y: x(x)(y) ) ) (lambda x: f(lambda y: x(x)(y)) )

MOD = Z(lambda f: lambda m: lambda n: \
    IF (IS_LTE(n)(m))
        (lambda x: f(SUB(m)(n))(n)(x))
        (m))

PAIR  = lambda x: lambda y: lambda f: f(x)(y)
LEFT  = lambda p: p(TRUE)
RIGHT = lambda p: p(FALSE)

NIL = PAIR(TRUE)(TRUE)
IS_EMPTY = LEFT
FIRST = lambda xs: LEFT(RIGHT(xs))
REST = lambda xs: RIGHT(RIGHT(xs))
CONS = lambda xs: lambda x: PAIR(FALSE)(PAIR(x)(xs))

RANGE = Z(lambda f: lambda m: lambda n: \
          IF (IS_LTE(m)(n)) (
                  lambda x: CONS(f(INC(m))(n))(m)(x)
          )(NIL))

FOLD = Z(lambda f: lambda xs: lambda x: lambda g: \
         IF (IS_EMPTY(xs))
           (x)
           (lambda y:
            g (f(REST(xs))(x)(g)) (FIRST(xs)) (y)
           ))

MAP = lambda f: lambda k: FOLD(k)(NIL)(
    lambda xs: lambda x: CONS(xs)(f(x))
  )

FLIP = lambda f: lambda a: lambda b: f(b)(a)

FOR = FLIP(MAP)

B   = TEN
F   = INC(B)
I   = INC(F)
U   = INC(I)
ZED = INC(U)

CONCAT = lambda a: lambda b: FOLD(a)(b)(CONS)

FIZZ     = CONS(CONS(CONS(CONS(NIL)(ZED))(ZED))(I))(F)
BUZZ     = CONS(CONS(CONS(CONS(NIL)(ZED))(ZED))(U))(B)
FIZZBUZZ = CONCAT(FIZZ)(BUZZ)

DIV = Z(lambda f: lambda m: lambda n:
        IF (IS_LTE(n)(m)) (lambda x: INC(f(SUB(m)(n))(n))(x))(ZERO))

SNOC = lambda xs: lambda x: FOLD(xs)(CONS(NIL)(x))(CONS)

TO_DIGITS = Z(lambda f: lambda n: SNOC(
      IF (IS_LTE (n) (DEC(TEN)))
        (NIL)
        (lambda x: f(DIV(n)(TEN))(x))
    )
    (MOD(n)(TEN)))

fb = (FOR (RANGE (ONE) (HUNDRED))
      (lambda n:
       IF (IS_ZERO(MOD (n) (FIFTEEN)))
         (FIZZBUZZ)
         (IF (IS_ZERO(MOD (n) (THREE)))
           (FIZZ)
           (IF (IS_ZERO(MOD (n) (FIVE)))
             (BUZZ)
             (TO_DIGITS(n))))))

def main():
    list(map(print, to_str_list(fb)))

def to_digits(N):
    return to_str(TO_DIGITS(N))

def to_char(C):
    return "0123456789BFiuz"[to_int(C)]

def to_str(S):
    return "".join(to_list_with(to_char)(S))

def to_list(XS):
    result = []
    while not to_bool(IS_EMPTY(XS)):
        result.append(FIRST(XS))
        XS = REST(XS)
    return result

def to_list_with(f):
    return lambda XS: list(map(f, to_list(XS)))

def to_bool(B):
    return B(True)(False)

def to_int(N):
    return N(lambda x: x + 1)(0)

to_int_list = to_list_with(to_int)
to_str_list = to_list_with(to_str)

if __name__ == "__main__":
    main()