1
ZERO = lambda f:lambda x:x
2
SUC = lambda church:lambda f:lambda x:church(f)(f(x))
3

4
to_int = lambda n:n(lambda x:x+1)(0)
5
to_church = lambda n:ZERO if n==0 else SUC(to_church(n-1))
6

7
ONE = to_church(1)
8
TWO = to_church(2)
9
THREE = to_church(3)
10
FOUR = to_church(4)
11
FIVE = to_church(5)
12
SIX = to_church(6)
13
SEVEN = to_church(7
14

15
ADD = lambda m:lambda n:lambda f:lambda x:m(f)(n(f)(x))
16
ADD_1 = lambda m:lambda n:m(SUC)(n)
17
MUL = lambda m:lambda n:lambda f:lambda x:m(lambda x1:n(f)(x1))(x)
18
POW = lambda m:lambda n:n(MUL(m))(ONE) #POW(m)(n) = m^n
19

20
PAIR = lambda x:lambda y:lambda f:f(x)(y)
21
FST = lambda p: p(lambda x: lambda y: x)
22
LST = lambda p: p(lambda x: lambda y: y)
23
PHI = lambda p: PAIR(LST(p))(SUC(LST(p)))
24
PRED = lambda n:FST(n(PHI)(PAIR(ZERO)(ZERO)))
25
SUB = lambda m: lambda n: n(PRED)(m)
26

27
PAIR = lambda x:lambda y:lambda f:f(x)(y)
28
FST = lambda p: p(lambda x: lambda y: x)
29
LST = lambda p: p(lambda x: lambda y: y)
30
PHI = lambda p: PAIR(LST(p))(SUC(LST(p)))
31
PRED = lambda n:FST(n(PHI)(PAIR(ZERO)(ZERO)))
32
SUB = lambda m: lambda n: n(PRED)(m)
33

34
IS_ZERO = lambda n:n(lambda x:FALSE)(TRUE)
35
LTE = lambda m:lambda n:IS_ZERO(SUB(m)(n))
36
GT = lambda m:lambda n:NOT(LTE(m)(n))
37
EQ = lambda m:lambda n:AND(LTE(m)(n))(LTE(n)(m))
38
GTE = lambda m:lambda n:OR(GT(m)(n))(EQ(m)(n))
39
LT = lambda m:lambda n:NOT(GTE(m)(n))
40

41
I = lambda x:x
42
W = lambda f:lambda x:f(x)(x)
43
Y = lambda f:f