lambda.py

#! /usr/bin/env python3

identity = lambda x: x

b_true = lambda x: lambda y: x
b_false = lambda x: lambda y: y
b_not = lambda b: b(b_false)(b_true)
b_and = lambda x: lambda y: x(y)(x)
b_or = lambda x: lambda y: x(x)(y)
b_xor = lambda x: lambda y: x(b_not(y))(y)
b_nor = lambda x: lambda y: x(b_false)(b_not(y))
b_nand = lambda x: lambda y: x(b_not(y))(b_true)
b_if = lambda b: lambda if_t: lambda if_f: b(if_t)(if_f)(identity)

pair = lambda x: lambda y: lambda z: z(x)(y)
p_first = lambda p: p(lambda x: lambda y: x)
p_second = lambda p: p(lambda x: lambda y: y)

n_iszero = lambda x: p_first(x)
n_zero = pair(b_true)(identity)
n_succ = lambda x: pair(b_false)(x)
n_pred = lambda x: p_second(x)
n_equal = lambda x: lambda y: b_if(
		n_iszero(x)
	)(
		lambda a: n_iszero(y)
	)(
		lambda a: b_if(
			n_iszero(y)
		)(
			lambda b: b_false
		)(
			lambda b: n_equal(n_pred(x))(n_pred(y))
		)
	)
n_add = lambda x: lambda y: b_if(
		n_iszero(x)
	)(
		lambda a: y
	)(
		lambda a: b_if (
			n_iszero(y)
		)(
			lambda b: x
		)(
			lambda b: n_add(n_pred(x))(n_succ(y))
		)
	)
n_difference = lambda x: lambda y: b_if(
		n_iszero(x)
	)(
		lambda a: y
	)(
		lambda a: b_if(
			n_iszero(y)
		)(
			lambda b: x
		)(
			lambda b: n_difference(n_pred(x))(n_pred(y))
		)
	)


################################################################################

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

def to_lambda(x):
	if x == None:
		return identity
	if type(x) == bool:
		if (x):
			return b_true
		return b_false
	if (type(x) == int):
		if (x >= 0):
			output = n_zero
			while x != 0:
				output = n_succ(output)
				x-=1
			return output
		raise TypeError()
	if (type(x) == tuple):
		if (len(x) == 2):
			return pair(to_lambda(x[0]))(to_lambda(x[1]))
		raise TypeError()
	raise TypeError()

def to_int(x):
	output = 0
	while not to_bool(n_iszero(x)):
		output += 1
		x = n_pred(x)
	return output