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)

Answer 2

There doesn't seem to be something in itertools that does what you want, but itertools is a deep treasure chest, so I could have missed something.

Your generator code looks great. I don't know why you'd write it with accumulate unless you were playing an absurd game of code golf, or you were trying to impress Haskell snobs. Write your function so that it is readable, understandable, and maintainable. No need to be overly clever.