#!/usr/bin/python

# Truth testing
TRUE = lambda x: lambda y: x
FALSE = lambda x: lambda y: y
IF = lambda b: lambda t: lambda f: b(t)(f)
print "IF(TRUE)('yes')('no')", IF(TRUE)('yes')('no')
print "IF(FALSE)('yes')('no')", IF(FALSE)('yes')('no')

# def TRUE(x)(y): x
# def FALSE(x)(y): y
# def IF(b)(t)(f): b(t)(f)

# Pairs
PAIR = lambda x: lambda y: lambda b: b(x)(y)
FIRST = lambda p: p(TRUE)
REST = lambda p: p(FALSE)

# def PAIR(x)(y)(b): b(x)(y)
# def FIRST(p): p(TRUE)
# def REST(p): p(FALSE)

print "FIRST(PAIR('p')('q'))", FIRST(PAIR('p')('q'))
print "REST(PAIR('p')('q'))", REST(PAIR('p')('q'))

# Numbers!

ZERO = PAIR(TRUE)(TRUE)
SUCC = lambda n: PAIR(FALSE)(n)

ONE = SUCC(ZERO)
TWO = SUCC(ONE)
THREE = SUCC(TWO)
FOUR = SUCC(THREE)
FIVE = SUCC(FOUR)

# Tests etc.

print "IF(FIRST(ZERO))('yes')('no')", IF(FIRST(ZERO))('yes')('no')
print "IF(FIRST(ONE))('yes')('no')", IF(FIRST(ONE))('yes')('no')

YM = lambda f: (lambda x: (lambda y: f(x(x))))(lambda x: (lambda y: f(x(x))))
FORCE = lambda x: x
R = lambda g: (lambda m: lambda n: ( IF(FIRST(m)) 
                (lambda q: n)
                (lambda q: g(FORCE)(REST(m))(SUCC(n)))
            ) (FORCE)
        )
ADD = YM(R)(FORCE)

def INTIZE(n): 
   i = 0
   while 1: 
      if IF(FIRST(n))(1)(0): break
      i += 1
      n = REST(n)
   return i

print "INTIZE(ADD(ONE)(ONE))", INTIZE(ADD(ONE)(ONE))
print "INTIZE(ADD(ONE)(TWO))", INTIZE(ADD(ONE)(TWO))
print "INTIZE(ADD(THREE)(TWO))", INTIZE(ADD(THREE)(TWO))
print "INTIZE(ADD(THREE)(SUCC(TWO)))", INTIZE(ADD(THREE)(SUCC(TWO)))

# # ZERO = lambda f: lambda x: x
# ZERO = FALSE
# # ZERO = PAIR(TRUE)(TRUE) = lambda b: b(TRUE)(TRUE)
# SUCC = lambda n: lambda f: lambda x: f(n(f)(x))
# # SUCC = lambda n: PAIR(FALSE)(n)

# ADD = %mn.%f.%x.(m f) (n f x)
# def SUCC(n)(f)(x): f(n(f)(x))
# def ADD(m)(n)(f)(x): m(f)(n(f)(x))

# 
# N0 = ZERO
# N1 = SUCC(N0)
# N2 = SUCC(N1)
# N3 = SUCC(N2)
# N4 = SUCC(N3)

# IS_ZERO = lambda n: n(lambda k: FALSE)(TRUE)
# # IS_ZERO = lambda n: FIRST(n)
# print "IF(IS_ZERO(N0))('yes')('no')", IF(IS_ZERO(N0))('yes')('no')
# print "IF(IS_ZERO(N1))('yes')('no')", IF(IS_ZERO(N1))('yes')('no')

# ADD = lambda m, n: lambda f: lambda x: (m(f))(n(f)(x))
# INTIZE = lambda n: n(lambda x:x+1)(0)
# INTIZE(N3)

# print "INTIZE(ADD(N1, N1))", INTIZE(ADD(N1, N1))
# print "INTIZE(ADD(N1, N2))", INTIZE(ADD(N1, N2))
# print "INTIZE(ADD(N3, N2))", INTIZE(ADD(N3, N2))
# print "INTIZE(ADD(N3, SUCC(N2)))", INTIZE(ADD(N3, SUCC(N2)))