Using itertools for recursive function application

Question

I need a Python function iterate(f, x) that creates an iterator returning the values x, f(x), f(f(x)), f(f(f(x))), etc (like, e.g., Clojure\'s iterate). First of a

Answer 1

You can use an anamorphism (or unfold) to simplify the definition of iterate, and to use only one starting value. Here's an implementation I once used, based on a quite well-known paper:

def ana(build, predicate):
    def h(x):
        if predicate(x):
            return
        else:
            a, b = build(x)
            yield a
            for i in h(b):
                yield i
            # with newer syntax: 
            # yield from h(b)
    return h

Implementing iterate with ana then looks like this:

def iterate(f, x):
    return ana(lambda x: (x, f(x)), lambda _: False)(x)

No itertools, though... And I agree that this isn't the most readable variant. In fact, it is rather cryptic.

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UPDATE: There's an easier version, which even looks quite nice. It's taken from here:

def unfold(f, x):
    while True:
        w, x = f(x)
        yield w

And that gives you:

def iterate(f, x):
    return unfold(lambda y: (y, f(y)), x)