Carry's fixed-point fonction for transformations of functions

carry_fixed_point.py

# Fixed-point function without explicit recursion:
def fix(f):
    def self_applied(self_applied):
        return f(wrap_selfappl(self_applied))
    return wrap_selfappl(self_applied)

# Auxiliary function:
def wrap_selfappl(f):
    def w(*args, **kwargs):
        return f(f)(*args, **kwargs)
    return w

# Fixed-point function with explicit recursion:
# XXX: cheating!
def fix_rec(f):
    def a(*args, **kwargs):
        return f(a)(*args, **kwargs)
    return a

# ----
# Test
# ----
if __name__ == "__main__":
    def rec_factorial_maker(f0):
        def f(n):
            if n == 0:
                return 1
            return n*f0(n - 1)
        return f

    fact = fix(rec_factorial_maker)
    assert (fact(0), fact(1), fact(2), fact(3), fact(6)) == (1, 1, 2, 6, 720)

    fact = fix_rec(rec_factorial_maker)
    assert (fact(0), fact(1), fact(2), fact(3), fact(6)) == (1, 1, 2, 6, 720)