Improve Your Python: 'yield' and Generators Explained

Prior to beginning tutoring sessions, I ask new students to fill out a briefself-assessment where they rate their understanding of various Python concepts. Some topics ("control flow with if/else" or "defining and using functions") are understood by a majority of students before ever beginning tutoring. There are ahandful of topics, however, that almost all students report having noknowledge orvery limited understanding of. Of these, "generators and theyield keyword" is one of the biggest culprits. I'm guessing this is the case formostnovice Python programmers.

Many report having difficulty understanding generators and the yield keyword even after making a concerted effort to teach themselves the topic.I want to change that. In this post, I'll explainwhat the yield keyword does, why it's useful, and how to use it.

Note: In recent years, generators have grown more powerful as features have been added through PEPs. In my next post, I'll explore the true power ofyield with respect to coroutines, cooperative multitasking and asynchronous I/O (especially their use in the"tulip" prototype implementation GvR has been working on). Before we get there, however, we need a solid understanding of how theyield keyword and generators work.

Coroutines and Subroutines

When we call a normal Python function, execution starts at function's first lineand continues until areturn statement, exception, or the end of thefunction (which is seen as an implicitreturn None) is encountered.Once a function returns control to its caller, that's it. Any work done by thefunction and stored in local variables is lost. A new call to the functioncreates everything from scratch.

This is all very standard when discussing functions (more generally referred to assubroutines) incomputer programming. There are times, though, when it's beneficial to havethe ability to create a "function" which, instead of simply returning a singlevalue, is able to yield a series of values. To do so, such a function would needto be able to "save its work," so to speak.

I said, "yield a series of values" because our hypothetical function doesn't "return" in the normal sense.return implies that the function is returning control of execution to the point where the function was called. "Yield," however, implies thatthe transfer of control is temporary and voluntary, and our function expects to regain it in the future.

In Python, "functions" with these capabilities are called generators, and they're incredibly useful.generators (and the yield statement) were initially introduced to give programmers a more straightforward way to write code responsible for producing a series ofvalues. Previously, creating something like a random number generator requireda class or module that both generated values and kept track of state between calls. With the introduction ofgenerators, this became much simpler.

To better understand the problem generators solve, let's take a look at an example. Throughout the example, keep in mind the core problem being solved:generating a series of values.

Note: Outside of Python, all but the simplest generators would be referred to ascoroutines. I'll use the latter term later in the post. The important thing to remember is, in Python, everything described here as acoroutine is still a generator. Python formally defines the termgenerator; coroutine is used in discussion but has no formal definition in the language.

Example: Fun With Prime Numbers

Suppose our boss asks us to write a function that takes a list ofints and returns some Iterable containing the elements which are prime¹ numbers.

Remember, an Iterable is just an object capable of returning its members one at a time.

"Simple," we say, and we write the following:

def get_primes(input_list):    result_list = list()    for element in input_list:        if is_prime(element):            result_list.append()    return result_list# or better yet...def get_primes(input_list):    return (element for element in input_list if is_prime(element))# not germane to the example, but here's a possible implementation of# is_prime...def is_prime(number):    if number > 1:        if number == 2:            return True        if number % 2 == 0:            return False        for current in range(3, int(math.sqrt(number) + 1), 2):            if number % current == 0:                 return False        return True    return False

Either get_primes implementation above fulfills the requirements, so we tell our boss we're done. She reports our function works and is exactly what she wanted.

Dealing With Infinite Sequences

Well, not quite exactly. A few days later, our boss comes back and tells us she's run into a small problem: she wants to use ourget_primes function on avery large list of numbers. In fact, the list is so large that merely creating it would consume all of the system's memory. To work around this, she wants to be able to callget_primes with a start value and get all the primes larger thanstart (perhaps she's solving Project Euler problem 10).

Once we think about this new requirement, it becomes clear that it requires more than a simple change toget_primes. Clearly, we can't return a list of all the prime numbers fromstart to infinity (operating on infinite sequences, though, has a wide range of useful applications). The chances of solving this problem using a normal function seem bleak.

Before we give up, let's determine the core obstacle preventing us from writing a function that satisfies our boss's new requirements.Thinking about it, we arrive at the following:functions only get one chance to return results, and thus must return all results at once.It seems pointless to make such an obvious statement; "functions justwork that way," we think. The real value lies in asking, "but what if theydidn't?"

Imagine what we could do if get_primes could simply return the next valueinstead of all the values at once. It wouldn't need to createa list at all. No list, no memory issues. Since our boss told us she's just iterating over the results, she wouldn't know the difference.

Unfortunately, this doesn't seem possible. Even if we had a magical function that allowed us to iterate fromn to infinity, we'd get stuck after returning the first value:

def get_primes(start):    for element in magical_infinite_range(start):        if is_prime(element):            return element

Imagine get_primes is called like so:

def solve_number_10():    # She *is* working on Project Euler #10, I knew it!    total = 2    for next_prime in get_primes(3):        if next_prime < 2000000:            total += next_prime        else:            print(total)            return

Clearly, in get_primes, we would immediately hit the case where number = 3 and return at line 4.Instead of return, we need a way to generate a value and, when asked for the next one, pick up where we left off.

Functions, though, can't do this. When they return, they'redone for good. Even if we could guarantee a function would be called again, wehave no way of saying, "OK, now, instead of starting at the first line likewe normally do, start up where we left off at line 4." Functions have a single entrypoint: the first line.

Enter the Generator

This sort of problem is so common that a new construct was added to Pythonto solve it: thegenerator. A generator "generates" values. Creatinggenerators was made as straightforward as possible through the concept ofgenerator functions, introduced simultaneously.

A generator function is defined like a normal function, but whenever it needs to generate avalue, it does so with theyield keyword rather than return. If the body of a def contains yield, the function automatically becomes a generator function (even if italso contains a return statement). There's nothing else we need to do to create one.

generator functions create generator iterators. That's the last time you'll see the termgenerator iterator, though, since they're almostalways referred to as "generators". Just remember that ageneratoris a special type of iterator. To be considered aniterator, generators must define a few methods, one of which is__next__(). To get the next value from a generator, we use the same built-in function asforiterators: next().

This point bears repeating: to get the next value from a generator, we use the same built-in function as foriterators: next().

(next() takes care of calling the generator's __next__() method). Since agenerator is a type ofiterator, it can be used in a for loop.

So whenever next() is called on a generator, the generator is responsiblefor passing back a value to whomever called next(). It does so by calling yieldalong with the value to be passed back (e.g.yield 7). The easiest way to rememberwhat yield does is to think of it asreturn (plus a little magic) for generator functions.**

Again, this bears repeating: yield is just return (plus a little magic) forgenerator functions.

Here's a simple generator function:

>>> def simple_generator_function():>>>    yield 1>>>    yield 2>>>    yield 3

And here are two simple ways to use it:

>>> for value in simple_generator_function():>>>     print(value)123>>> our_generator = simple_generator_function()>>> next(our_generator)1>>> next(our_generator)2>>> next(our_generator)3

Magic?

What's the magic part? Glad you asked! When a generator function callsyield, the "state" of the generator function is frozen; the values of all variables are saved and the next line of code to be executed is recorded untilnext() is calledagain. Once it is, the generator function simply resumes where it left off.Ifnext() is never called again, the state recorded during the yield call is (eventually) discarded.

Let's rewrite get_primes as a generator function. Notice that we no longer need themagical_infinite_range function. Using a simple while loop, we can create our own infinite sequence:

def get_primes(number):    while True:        if is_prime(number):            yield number        number += 1

If a generator function calls return or reaches the end its definition, aStopIteration exception is raised. This signals to whoever was callingnext()that the generator is exhausted (this is normal iterator behavior). It is also the reason the while True: loop is present inget_primes. If it weren't, the first time next() was called we would check if the number is prime and possibly yield it. Ifnext() were called again, we would uselessly add 1 to number and hit the end of thegenerator function (causing StopIteration to be raised). Once a generator has been exhausted, calling next() on it will result in an error, so you can only consume all the values of agenerator once. The following will not work:

>>> our_generator = simple_generator_function()>>> for value in our_generator:>>>     print(value)>>> # our_generator has been exhausted...>>> print(next(our_generator))Traceback (most recent call last):  File "<ipython-input-13-7e48a609051a>", line 1, in <module>    next(our_generator)StopIteration>>> # however, we can always create a new generator>>> # by calling the generator function again...>>> new_generator = simple_generator_function()>>> print(next(new_generator)) # perfectly valid1

Thus, the while loop is there to make sure we never reach the end ofget_primes. It allows us to generate a value for as long asnext() is calledon the generator. This is a common idiom when dealing with infinite series (andgenerators in general).

Visualizing the flow

Let's go back to the code that was calling get_primes: solve_number_10.

def solve_number_10():    # She *is* working on Project Euler #10, I knew it!    total = 2    for next_prime in get_primes(3):        if next_prime < 2000000:            total += next_prime        else:            print(total)            return

It's helpful to visualize how the first few elements are created when we callget_primes insolve_number_10's for loop. When the for loop requests the first value fromget_primes, we enter get_primes as we would in a normal function.

1. We enter the while loop on line 3
2. The if condition holds (3 is prime)
3. We yield the value 3 and control to solve_number_10.

Then, back in solve_number_10:

1. The value 3 is passed back to the for loop
2. The for loop assigns next_prime to this value
3. next_prime is added to total
4. The for loop requests the next element from get_primes

This time, though, instead of entering get_primes back at the top, we resume at line5, where we left off.

def get_primes(number):    while True:        if is_prime(number):            yield number        number += 1 # <<<<<<<<<<

Most importantly, number still has the same value it did when we calledyield(i.e. 3). Remember, yield both passes a value to whoever callednext(),and saves the "state" of the generator function. Clearly, then,number is incremented to 4, we hit the top of the while loop, and keep incrementing number until we hit the next prime number (5). Again weyield the value of number to the for loop insolve_number_10. This cycle continues until the for loop stops (at the first prime greater than2,000,000).

Moar Power

In PEP 342, support was added for passing valuesinto generators. PEP 342 gave generators the power to yield a value (as before), receive avalue, or both yield a value and receive a (possibly different) value in a single statement.

To illustrate how values are sent to a generator, let's return to our prime number example. This time, instead of simply printing every prime number greater thannumber, we'll find the smallest prime number greater than successive powers of a number (i.e. for 10, we wantthe smallest prime greater than 10, then 100, then 1000, etc.). We start in the same way asget_primes:

def print_successive_primes(iterations, base=10):    # like normal functions, a generator function    # can be assigned to a variable    prime_generator = get_primes(base)    # missing code...    for power in range(iterations):        # missing code...def get_primes(number):    while True:        if is_prime(number):        # ... what goes here?

The next line of get_primes takes a bit of explanation. While yield number would yield thevalue of number, a statement of the formother = yield foo means, "yield foo and,when a value is sent to me, setother to that value." You can "send" values toa generator using the generator'ssend method.

def get_primes(number):    while True:        if is_prime(number):            number = yield number        number += 1

In this way, we can set number to a different value each time the generatoryields. We can now fill in the missing code inprint_successive_primes:

def print_successive_primes(iterations, base=10):    prime_generator = get_primes(base)    prime_generator.send(None)    for power in range(iterations):        print(prime_generator.send(base ** power))

Two things to note here: First, we're printing the result of generator.send,which is possible becausesend both sends a value to the generator andreturns the value yielded by the generator (mirroring howyield works fromwithin the generator function).

Second, notice the prime_generator.send(None) line. When you're using send to "start" a generator (that is, execute the code from the first line of the generator function up tothe firstyield statement), you must send None. This makes sense, since by definitionthe generator hasn't gotten to the firstyield statement yet, so if we sent areal value there would be nothing to "receive" it. Once the generator is started, wecan send values as we do above.

Round-up

In the second half of this series, we'll discuss the various ways in whichgenerators have been enhanced and the power they gained as a result.yield hasbecome one of the most powerful keywords in Python. Now that we've built a solidunderstanding of howyield works, we have the knowledge necessaryto understand some of the more "mind-bending" things thatyield can be used for.

Believe it or not, we've barely scratched the surface of the power of yield.For example, whilesend does work as described above, it's almost neverused when generating simple sequences like our example. Below, I've pasteda small demonstration of one common waysend is used. I'll not say any moreabout it as figuring out how and why it works will be a good warm-up for parttwo.

import randomdef get_data():    """Return 3 random integers between 0 and 9"""    return random.sample(range(10), 3)def consume():    """Displays a running average across lists of integers sent to it"""    running_sum = 0    data_items_seen = 0    while True:        data = yield        data_items_seen += len(data)        running_sum += sum(data)        print('The running average is {}'.format(running_sum / float(data_items_seen)))def produce(consumer):    """Produces a set of values and forwards them to the pre-defined consumer    function"""    while True:        data = get_data()        print('Produced {}'.format(data))        consumer.send(data)        yieldif __name__ == '__main__':    consumer = consume()    consumer.send(None)    producer = produce(consumer)    for _ in range(10):        print('Producing...')        next(producer)

Remember...

There are a few key ideas I hope you take away from thisdiscussion:

• generators are used to generate a series of values
• yield is like the return of generator functions
• The only other thing yield does is save the "state" of a generator function
• A generator is just a special type of iterator
• Like iterators, we can get the next value from a generator usingnext()
  • for gets values by calling next() implicitly

I hope this post was helpful. If you had never heard of generators, I hope you now understand what they are,why they're useful, and how to use them. If you were somewhat familiar withgenerators, I hope any confusion is now cleared up.

As always, if any section is unclear (or, more importantly, contains errors), byall means let me know. You can leave a comment below, email me [e-mail], or hit me up on Twitter@jeffknupp.

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Quick refresher: a prime number is a positive integer greater than 1that has no divisors other than 1 and itself. 3 is prime because there are nonumbers that evenly divide it other than 1 and 3 itself.