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Church numerals in Python
#! /usr/bin/python
#
# Church numerals in Python.
# See http://en.wikipedia.org/wiki/Church_encoding
#
# Vivek Haldar <vh@vivekhaldar.com>
#
# https://gist.github.com/2438498
zero = lambda f: lambda x: x
# Compute the successor of a Church numeral, n.
# Apply function one more time.
succ = (lambda n: lambda f: lambda x:
f(n(f)(x)))
one = succ(zero)
# Add two Church numerals, n, m.
add = (lambda m: lambda n: lambda f: lambda x:
n(f)(m(f)(x)))
# Multiply two Church numerals, n, m.
mult = (lambda m: lambda n:
lambda f: lambda x: n(m(f))(x))
# Exponentiation: n^m
exp = lambda m: lambda n: n(m)
# Convert a Church numeral into a concrete integer.
# n = 0, f = (add 1 to a number)
plus1 = lambda x: x + 1
church2int = lambda n: n(plus1)(0)
# Convert a concrete integer into a church numeral.
def int2church(i):
if i == 0:
return zero
else:
return succ(int2church(i - 1))
# Eval and print a string
def peval(s):
print s, ' = ', eval(s)
peval('church2int(zero)')
peval('church2int(succ(zero))')
peval('church2int(one)')
peval('church2int(succ(one))')
peval('church2int(succ(succ(one)))')
peval('church2int(succ(succ(succ(one))))')
peval('church2int(add(one)(succ(one)))')
peval('church2int(add(succ(one))(succ(one)))')
peval('church2int(mult(succ(one))(succ(one)))')
peval('church2int(exp(succ(one))(succ(one)))')
peval('church2int(int2church(0))')
peval('church2int(int2church(1))')
peval('church2int(int2church(111))')
c232 = int2church(232)
c421 = int2church(421)
peval('church2int(mult(c232)(c421))')
print '232 * 421 = ', 232 * 421
c2 = int2church(2)
c10 = int2church(10)
peval('church2int(exp(c2)(c10))')
print '2 ** 10 = ', 2 ** 10
@brianharvey

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brianharvey commented Jul 7, 2014

subtraction?

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ghost commented Jan 13, 2015

# Kleene's predecessor
pred = lambda n: lambda f: lambda x: n (lambda g: lambda h: h (g (f))) (lambda y: x) (lambda x: x)

# Subtraction of Church numerals
minus = lambda n: lambda m: m (pred) (n)
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