Compositions

gistfile1.py

#!/usr/bin/python3
from functools import partial,reduce

T = 1
F = 0

def CheckArgs(*args):
	for entry in args:
		if type(entry) is not Elem:
			raise Exception("Wrong arguments! Type: %s"%type(entry))

class Elem:
	_k = 0
	_v = 0
	def __init__(self, k = 0, v = 0):
		if type(k) is not int:
			raise Exception("Can not make elem of key %d", k)
		if type(v) is not int:
			raise Exception("Can not make elem of value %d", v)
		self._k = k
		self._v = v
	def __str__(self):
		return "Key: %d,Value: %d"%(self._k, self._v)

	def GetValue(self):
		return self._v

	def GetName(self):
		return self._k

def toLogic(a):
	if a > 0:
		return T
	else:
		return F

#1. Get name of variable
def GetName(*args):
	CheckArgs(*args)
	k1 = args[0].GetName()
	kn = args[-1].GetName()
	return Elem(kn,k1)

#2. Create veriable with name
def PutName(*args):
	CheckArgs(*args)
	v1 = args[0].GetValue()
	vn = args[-1].GetValue()
	return Elem(vn,v1)

#3. Zero Value
def Zero(*args):
	CheckArgs(*args)
	k1 = args[0].GetName()
	return Elem(k1,0)

#4. Increment
def Increment(*args):
	CheckArgs(*args)
	k1 = args[0].GetName()
	v1 = args[0].GetValue()
	return Elem(k1,v1+1)

#5. Summa
def Summa(*args):
	CheckArgs(*args)
	v = 0
	for entry in args:
		v = v + entry.GetValue()
	k1 = args[0].GetName()
	return Elem(k1,v)

#6. Equality
def Equals(*args):
	CheckArgs(*args)
	for i in range(0, len(args)-1):
		if args[i].GetValue() != args[i+1].GetValue():
			return F
	return T

#7. Selector
def Im(m, *args):
	return args[m]

def I(m):
	return partial(Im, m)

#8. Negation
def Neg(*args):
	if type(args[0]) != int:
		raise Exception("Wrong arguments! Type: %s"%type(args[0]))
	if args[0] == T:
		return F
	else:
		return T

#9. And
def And(*args):
	a = reduce(lambda x, y: x and y, args)
	if a:
		return T
	else:
		return F

#Composition Superposition
def S(function, *args):
	return lambda *x: function(*tuple(map(lambda y: y(*x), args)))

#Composition IF
def If(pred, true_value, false_value):
	return lambda *x: true_value(*x) if pred(*x) else false_value(*x)

#Composition FOR
def For(pred, *args):
	def func(*a):
		if len(a) != len(args):
			raise Exception("Argument count mismatch")
		while pred(*a):
			a = tuple(map(lambda y: y(*a), args))
		return a[0]
	return func

if __name__ == "__main__":
	#a = 7; b = 2; a - b
	#c = For(S(And, S(Neg, S(Equals, I(1), I(3))), S(Neg, S(Equals, I(2), I(3)))), Increment, I(1), I(2), S(Increment, I(3)))
	subtract = If(
		S(
			Equals,
			For(
				S(And, 
					S(Neg, S(Equals, I(1), I(3))),
					S(Neg, S(Equals, I(0), S(Summa, I(1), I(2))))
				),
				Increment, 
				I(1), 
				I(2), 
				S(Increment, I(3))
			),
			S(Summa, I(1), I(2))
		),
		Zero,
		For(
			S(And, 
				S(Neg, S(Equals, I(1), I(3))),
				S(Neg, S(Equals, I(0), S(Summa, I(1), I(2))))
			),
			Increment, 
			I(1), 
			I(2), 
			S(Increment, I(3))
		)
	)
	zero = Elem(1,0)
	a = Elem(2,6)
	b = Elem(3,1)
	print(c(zero, a, b, b))