Question

Hi I am new to functional programming. What i did is

>>> g=lambda x:x*2
>>> f=g
>>> g=lambda x:f(f(x))
>>> g(9)
36

Now, it is not creating g as a nonterminating recursive function – g(x) is transformed to a new function which gives the result g(g(x)).

>>> f=g
>>> g=lambda x:f(f(x))
>>> f(8)
RuntimeError: maximum recursion depth exceeded

I expected g to be transformed into a function which gives the result g(g(g(x))), according to the first definition of g(x). Why does it not? Is it possible to make a new function which results in g(g(g(...(g(x))....))) for a certain number of iterations in this way?

Answer 1

When you do f = g for the second time, f becomes lambda x: f(x). Closures are created by name, not by value.

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This becomes easy with a helper function:

def compose(f, g):
    return lambda x: f(g(x))

square = lambda x:x*2
g = square
for i in xrange(4):
    g = compose(g, square)