Z = lambda worker: (lambda x: worker(lambda *args: x(x)(*args)))(lambda x: worker(lambda *args: x(x)(*args)))
fact = lambda f: lambda x: 1 if x == 0 else x * f(x-1)

def fix1(worker):
    return (lambda x: worker(lambda *args: x(x)(*args)))(lambda x: worker(lambda *args: x(x)(*args)))

def fix2(worker):
    def left(x):
        return worker(lambda *args: x(x)(*args))
    def right(x):
        return worker(lambda *args: x(x)(*args))
    return left(right)

def fix3(worker):
    def step(x):
        return worker(lambda *args: x(x)(*args))
    return step(step)

def fix4(worker):
    def step():
        def recursor(*args):
            return step()(*args)
        return worker(recursor)
    return step()



def defact(recursor):
    def worker(x):
        return 1 if x == 0 else x * recursor(x-1)
    return worker

print '!', fix4(defact)(5)

#for fp_combinator in reversed((Z, fix1, fix2, fix3, fix4)):
#    print fp_combinator.__name__, fp_combinator(defact)(5) == 120