Tail recursion in Python

Tail recursion in Python(chrispenner.ca)

193 points by zweedeend 8 years ago | 80 comments

shakna 8 years ago |

Someone recently pointed out to me you can bypass the recursion limit with an inbuilt decorator, because it's basically a memoiser.

lru_cache, from the functools library.

The example given in the docs [0] is:

    import functools

    @functools.lru_cache(maxsize=None)
    def fib(n):
        if n < 2:
            return n
        return fib(n-1) + fib(n-2)

[0] https://docs.python.org/3/library/functools.html#functools.l...

kqr 8 years ago | |

This only works in specific cases (namely those where dynamic programming algorithms suffice), and does not avoid the recursion limit in general.

abhirag 8 years ago | | |

Don't dismiss one of my favorite higher order functions so soon :)

"Recursion + memoization provides most of the benefits of dynamic programming, including usually the same running time." -- Steven Skiena

lru_cache decorator is great for people who are happy to let the language handle the caching of results for them, and often leads to code which is much more concise than the dynamic programming approach. The limitation you are referring to is that the decorator uses a dictionary to cache results and that dictionary uses the arguments as keys so the arguments need to be hashable. That limitation can be avoided by using immutable data structures (Clojure also has a higher order function called memoize which does the same thing and has no limitations because the core data structures in Clojure are immutable) and although Python not having structural sharing can mean that this approach can hurt memory and GC efficiency a bit, but that trade-off is at least worth considering :)

Still have to keep the stack depth less than sys.getrecursionlimit() so no substitute for tail recursion but surely a substitute for dynamic programming in a lot of cases.

e12e 8 years ago | | |

It's worth pointing out that python expands the datatype of numbers as needed (ending up at BigInt or similar, I belive). So any stack rewriting would have to accommodate an accumulator that starts as an integer and expands to arbitrarily many bits. It might be easily handled as I guess all arguments are references to python objects, and the regular code for expanding numbers could switch out the reference - but the point remains that proper tail call optimization in python needs to deal with objects as arguments.

d0mine 8 years ago | |

It won't help unless you call it in a specific order e.g., fib(10_000) may produce RecursionError unless you run for n in range(10_000): fib(n)

shakna 8 years ago | | |

Right, it's a memoiser.

You side-step some recursion through previously stored results. It works well for some class of algorithms, which coincides with quite a large subsection of problems where TCO would help formulate algorithms.

There are still a bunch of limits, because you're caching results, not eliminating call frames.

The first obvious drawback is performance and memory use: All results get stored in a dictionary.

naveen99 8 years ago | |

Is that really tail recursion though ? Seems like you are making two recursive calls to fib(). I thought tail recursion requires a single final call to recursive function.

Your memorization helps, but seems you will still run out of stack space if you call it with a big number without a warm up.

kahnjw 8 years ago | | |

I don’t think op is claiming that method is tail recursive, just pointing out you can get away with using recursion and LRU cache.

bjoli 8 years ago |

The hackyness/speed issues aside:

When compiling/transpiling/whatever between languages, I have found that relying on regular procedure calls and TCO is generally a lot simpler than having to force the looping facility of one language into the semantics of another language.

The only one I can actually imagine porting other loops to is the common lisp loop macro, but that is probably the most flexible looping facility known to man.

Edit: and oh, cool thing: racket and guile has expanding stacks and doesn't have a recursion limit other than the whole memory of the computer. This is pretty handy when implementing something like map, since you can write a non-tail-recursive procedure so that you don't have to reverse the list at the end.

leowoo91 8 years ago |

This can also be done using trampolines without using try/catch method: https://github.com/0x65/trampoline

jwilk 8 years ago |

Code snippets you won't see if you have JS disabled:

https://gist.github.com/ChrisPenner/c0b3f4feb054daa2f6370d2e...

https://gist.github.com/ChrisPenner/c958afbf6e7a763c188d8b83...

roryhughes 8 years ago | |

JS fully disabled in this day and age?

_jal 8 years ago | | |

I've noticed a shift over the last while how privacy-protective people are becoming "out-group" and a little weird.

I mean, I personally don't care; I've always been a little weird. But it is funny to see technical preferences as a signaling mechanism.

Funny, that is, until it hits a certain point... http://www.wired.co.uk/article/chinese-government-social-cre...

smoe 8 years ago | | |

I have started using a "Quick Javascript Switcher" extension some years ago to easily opt-in for certain pages but have js disabled by default.

This was one of the best quality of life decision in terms of web browsing I have ever made.

The vast majority of pages that I randomly access (e.g. from hacker news) are text based and usually work just fine without js. But the time until I can start reading is much faster (less jumping around of content) and I don't get the growth hackers modals shoven down my throat two paragraphs in. The pages I use regularly are usually white listed

pjmlp 8 years ago | | |

Yep, a cheap way to minimize ads, tracking and browser exploits.

Also avoiding downloading JS libraries bigger than Quake while on the go.

abstractbeliefs 8 years ago | | |

It's more common than you think.

bru 8 years ago |

> def tail_factorial(n, accumulator=1):

> if n == 0: return 1

> else: return tail_factorial(n-1, accumulator * n)

The second line should be "if n == 0: return accumulator"

rahimnathwani 8 years ago | |

0! == 1

EDIT: Oops. As pointed out below, the code is indeed incorrect, and my comment is irrelevant.

kelnage 8 years ago | | |

True, but irrelevant. For all values of n > 1, that function will return 1, which is clearly not what the author intended.

stunt 8 years ago |

Your code is still allocating a new stack frame anyway. So no optimization is happening. You are simply avoiding a stack overflow which is not the purpose of tail-call optimization.

I'm not sure if there is any advantage when language/compiler does not provide a proper tail recursive optimization.

quietbritishjim 8 years ago | |

It's a gross exaggeration to say there's no advantage. Who decided that stack frame re-use is "the purpose" of tail-call optimization, while not blowing the stack is not? It seems to me that being able to run the function at all is more important than whether it runs quickly.

a-nikolaev 8 years ago |

> It turns out that most recursive functions can be reworked into the tail-call form.

This statement in the beginning is not entirely correct. A more accurate statement would be that all recursive programs that are _iterative_ (if they are loops in disguise), can be rewritten in a tail-call form. That is, there must be a single chain of function calls.

The inherently recursive procedures cannot be converted into a tail-call form.

__s 8 years ago |

A patch that implements TCO in Python with explicit syntax like 'return from f(x)' could likely get accepted, ending these hacks

shakna 8 years ago | |

Would it? My impression is that Guido is fairly against any such thing occurring [0].

> So let me defend my position (which is that I don't want TRE in the language). If you want a short answer, it's simply unpythonic.

[0] http://neopythonic.blogspot.com.au/2009/04/tail-recursion-el...

__s 8 years ago | | |

His primary concern is with implicit tail recursion

I tried making such a patch in the past, got stuck in the much of trying to update the grammar file in a way that wouldn't complain about ambiguity

Main thing to get from tail calls vs loops is the case of mutually recursive functions

nullp0tr 8 years ago | |

It's actually not likely at ALL. Guido van Rossum said[0] on multiple occasions that it's un-pythonic and it won't happen.

Edit: I didn't see shakna's comment.

[0] http://neopythonic.blogspot.de/2009/04/tail-recursion-elimin...

iainmerrick 8 years ago | |

That would be great, especially as it doubles as an annotation/assertion that TCO is both expected and required at that specific point in the code.

orf 8 years ago |

I experimented with something similar to this way back[1], but took a slightly different approach - you can replace the reference to the function itself inside the function with a new function[2], one that returns a 'Recurse' object. That way it looks like it's calling the original method but really it's doing your own thing.

1. https://tomforb.es/adding-tail-call-optimization-to-python/

2. https://gist.github.com/orf/41746c53b8eda5b988c5#file-tail_c...

Vosporos 8 years ago |

I'm not a pythonista, but this code seems to get rid of the recursion limitation of the interpreter. Does it actually "optimize" things and make the function take a constant space as it is calling itself?

ericfrederich 8 years ago | |

It takes a constant space since it is not even recursive. The decorator makes it a non-recursive function with a loop.

It'll effectively side-steps the recursion limit in Python. For runs under the limit anyway, it'd be interesting to see whether it's any faster. It trades function call overhead for exception handling overhead.

By the way, the first example where it has `return 1` is wrong. It shoudl `return accumulator`. Clicking the GitHub link someone suggested this in December.

Bogdanp 8 years ago |

You can also do this by rewriting functions with a decorator.

https://github.com/Bogdanp/tcopy

Bromskloss 8 years ago |

  def tail_factorial(n, accumulator=1):
    if n == 0: return 1
    else: return tail_factorial(n-1, accumulator * n)

This just returns 1 every time.

msuvakov 8 years ago | |

It should be:

  def tail_factorial(n, accumulator=1):
    if n == 0: return accumulator
    else: return tail_factorial(n-1, accumulator * n)

quietbritishjim 8 years ago |

This article and the other comments here are interesting, but some are trying to be a bit too clever. The original article isn't too bad, but one of the other comments suggests re-writing the contents of the function at run time, which I really don't think is a practical suggestion (think about debugging such a thing).

If I wanted to do this in practice, I'd just write the trampoline out explicitly, unless I wanted to do it a huge number of times. Doing it this way only takes a couple of extra lines of code but I think that's worth it for the improvement in explicitness, which is a big help for future maintainers (possibly me!).

    from functools import partial

    def _tail_factorial(n, accumulator):
        if n == 0: 
            return accumulator
        else: 
            return partial(_tail_factorial, n - 1, accumulator * n)

    def factorial(n):
        result = partial(_tail_factorial, n, 1)
        while isinstance(result, partial):
            result = result()
        return result

Animats 8 years ago |

Tail recursion is a programming idea left over from the LISP era. It's from when iteration constructs were "while" and "for", and there were no "do this to all that stuff" primitives. Python doesn't really need it.

lispm 8 years ago | |

Tail recursion is unrelated to WHILE and FOR.

Scheme also did not just introduce tail recursion, but full tail call optimization.

Python sure does not need it, it already has a more complex iteration stuff like generators.

yorwba 8 years ago | |

Tail calls aren't always just used for some simple iteration. For example, you could have several mutually recursive functions calling each other in tail position. If you wanted to turn that into a loop, you'd have to roll all those functions into a single loop body, which would be made even less elegant due to the lack of goto statement. (TCO essentially turns a call into a goto whenever possible.)

viraptor 8 years ago | | |

Lots of languages can express it better though - even without gotos. For example in python you can do:

    while some_condition:
        x = one_generator(y)
        y = other_generator(x)

where the generators yield values. No need for goto, no TCO, no magic.

Even in languages like C, a nicer way to express it may be via two explicit state machines rather than going full Duff's device at this problem.

tu7001 8 years ago |

I used it to play with some functional programming in Python https://github.com/lion137/Functional---Python

e12e 8 years ago |

> def tail_factorial(n, accumulator=1):

> if n == 0: return 1

> else: return tail_factorial(n-1, accumulator * n)

Does this ever return the accumulator?

[ed: ah, no. I see the first comment on the article is about this bug; it should return accumulator, not 1]

chapill 8 years ago |

Tail recursion is a bad idea in multicore land. You end up with a one sided tree structure that can't be parallel processed.

rahimnathwani 8 years ago |

Interesting use of exceptions.

harryf 8 years ago | |

Indeed although generally it's usually a bad idea to misappropriate the exception throwing / handling mechanism for other purposes, as it's probably be less well optimised, performance-wise, than other parts of a VM.

throwaway110116 8 years ago | | |

not in python. exceptions for flow control are not looked down upon unless it’s gratuitous usage. many frameworks do exactly this.

cup-of-tea 8 years ago |

This is the same as recur in Clojure. It's not general TCO, though, which is much more powerful.

I do think it's a shame that Python doesn't have general TCO. It's said to be unpythonic because it means there will be two ways to do things. But some things are so easily expressed as a recursion but require considerable thought to be turned into a loop.

jvandonsel 8 years ago | |

The nice thing about recur in Clojure is that it won't even compile if the call isn't in the tail position. I've inadvertently made a code change that moved the recur call out of the tail position and the error became immediately obvious. With TCO you might not even notice until your stack blows up on a deep nesting.

e12e 8 years ago | |

> But some things are so easily expressed as a recursion but require considerable thought to be turned into a loop.

Do you have some examples of problem+solutions where tco works fine (in a language with tco) - but the manual translation is hard(ish)?

I wonder in part after reading the Julia thread on tco - and difficulties with providing guarantees in the general case with tco:

https://github.com/JuliaLang/julia/issues/4964

lysium 8 years ago | | |

Usually, I implement state machines with mutually tail recursive functions. Each function represents one state.

dragonwriter 8 years ago | |

> I do think it's a shame that Python doesn't have general TCO. It's said to be unpythonic because it means there will be two ways to do things.

The usual complaint I hear is about stack traces, not “two ways to do things”, which Python rather often provides anyway.