Shortcut to Grokking yield

When you see a function with yield statements, apply this easy trick to understand what will happen:

1. Insert a line result = [] at the start of the function.
2. Replace each yield expr with result.append(expr).
3. Insert a line return result at the bottom of the function.
4. Yay - no more yield statements! Read and figure out code.
5. Compare function to original definition.

This trick may give you an idea of the logic behind the function, but what actually happens with yieldis significantly different that what happens in the list based approach. In many cases the yield approach will be a lot more memory efficient and faster too. In other cases this trick will get you stuck in an infinite loop, even though the original function works just fine. Read on to learn more...

Don't confuse your Iterables, Iterators and Generators

First, the iterator protocol - when you write

for x in mylist:
    ...loop body...

Python performs the following two steps:

1. Gets an iterator for mylist:

   Call iter(mylist) -> this returns an object with a next() method (or __next__() in Python 3).

   [This is the step most people forget to tell you about]

2. Uses the iterator to loop over items:

   Keep calling the next() method on the iterator returned from step 1. The return value from next() is assigned to x and the loop body is executed. If an exception StopIteration is raised from within next(), it means there are no more values in the iterator and the loop is exited.

The truth is Python performs the above two steps anytime it wants to loop over the contents of an object - so it could be a for loop, but it could also be code like otherlist.extend(mylist) (where otherlist is a Python list).

Here mylist is an iterable because it implements the iterator protocol. In a user defined class, you can implement the __iter__() method to make instances of your class iterable. This method should return an iterator. An iterator is an object with a next() method. It is possible to implement both __iter__() and next() on the same class, and have __iter__() return self. This will work for simple cases, but not when you want two iterators looping over the same object at the same time.

So that's the iterator protocol, many objects implement this protocol:

1. Built-in lists, dictionaries, tuples, sets, files.
2. User defined classes that implement __iter__().
3. Generators.

Note that a for loop doesn't know what kind of object it's dealing with - it just follows the iterator protocol, and is happy to get item after item as it calls next(). Built-in lists return their items one by one, dictionaries return the keys one by one, files return the lines one by one, etc. And generators return... well that's where yield comes in:

def f123():
    yield 1
    yield 2
    yield 3

for item in f123():
    print item

Instead of yield statements, if you had three return statements in f123() only the first would get executed, and the function would exit. But f123() is no ordinary function. When f123() is called, itdoes not return any of the values in the yield statements! It returns a generator object. Also, the function does not really exit - it goes into a suspended state. When the for loop tries to loop over the generator object, the function resumes from its suspended state, runs until the next yield statement and returns that as the next item. This happens until the function exits, at which point the generator raises StopIteration, and the loop exits.

So the generator object is sort of like an adapter - at one end it exhibits the iterator protocol, by exposing __iter__() and next() methods to keep the for loop happy. At the other end however, it runs the function just enough to get the next value out of it, and puts it back in suspended mode.

Why Use Generators?

Usually you can write code that doesn't use generators but implements the same logic. One option is to use the temporary list 'trick' I mentioned before. That will not work in all cases, for e.g. if you have infinite loops, or it may make inefficient use of memory when you have a really long list. The other approach is to implement a new iterable class SomethingIter that keeps state in instance members and performs the next logical step in it's next() (or __next__() in Python 3) method. Depending on the logic, the code inside the next() method may end up looking very complex and be prone to bugs. Here generators provide a clean and easy solution.

Think of it this way:

An iterator is just a fancy sounding term for an object that has a next() method. So a yield-ed function ends up being something like this:

Original version:

def some_function():
    for i in xrange(4):
        yield i

for i in some_function():
    print i

This is basically what the python interpreter does with the above code:

class it:
    def __init__(self):
        #start at -1 so that we get 0 when we add 1 below.
        self.count = -1
    #the __iter__ method will be called once by the for loop.
    #the rest of the magic happens on the object returned by this method.
    #in this case it is the object itself.
    def __iter__(self):
        return self
    #the next method will be called repeatedly by the for loop
    #until it raises StopIteration.
    def next(self):
        self.count += 1
        if self.count < 4:
            return self.count
        else:
            #a StopIteration exception is raised
            #to signal that the iterator is done.
            #This is caught implicitly by the for loop.
            raise StopIteration 

def some_func():
    return it()

for i in some_func():
    print i

For more insight as to what's happening behind the scenes, the for loop can be rewritten to this:

iterator = some_func()
try:
    while 1:
        print iterator.next()
except StopIteration:
    pass

Does that make more sense or just confuse you more? :)

EDIT: I should note that this IS an oversimplification for illustrative purposes. :)

EDIT 2: Forgot to throw the StopIteration exception

The yield keyword is reduced to two simple facts:

1. If the compiler detects the yield keyword anywhere inside a function, that function no longer returns via the return statement. Instead, it immediately returns a lazy "pending list" objectcalled a generator
2. A generator is iterable. What is an iterable? It's anything like a list or set or range or dict-view, with a built-in protocol for visiting each element in a certain order.

In a nutshell: a generator is a lazy, incrementally-pending list, and yield statements allow you to use function notation to program the list values the generator should incrementally spit out.

generator = myYieldingFunction(...)
x = list(generator)

   generator
       v
[x[0], ..., ???]

         generator
             v
[x[0], x[1], ..., ???]

               generator
                   v
[x[0], x[1], x[2], ..., ???]

                       StopIteration exception
[x[0], x[1], x[2]]     done

list==[x[0], x[1], x[2]]

Example

Let's define a function makeRange that's just like Python's range. Calling makeRange(n) RETURNS A GENERATOR:

def makeRange(n):
    # return 0,1,2,...,n-1
    i = 0
    while i < n:
        yield i
        i += 1

>>> makeRange(5)
<generator object makeRange at 0x19e4aa0>

To force the generator to immediately return its pending values, you can pass it into list() (just like you could any iterable):

>>> list(makeRange(5))
[0, 1, 2, 3, 4]

Comparing example to "just returning a list"

The above example can be thought of as merely creating a list which you append to and return:

# list-version                   #  # generator-version
def makeRange(n):                #  def makeRange(n):
    """return [0,1,2,...,n-1]""" #~     """return 0,1,2,...,n-1"""
    TO_RETURN = []               #>
    i = 0                        #      i = 0
    while i < n:                 #      while i < n:
        TO_RETURN += [i]         #~         yield i
        i += 1                   #      i += 1
    return TO_RETURN             #>

>>> makeRange(5)
[0, 1, 2, 3, 4]

There is one major difference though; see the last section.

How you might use generators

An iterable is the last part of a list comprehension, and all generators are iterable, so they're often used like so:

#                   _ITERABLE_
>>> [x+10 for x in makeRange(5)]
[10, 11, 12, 13, 14]

To get a better feel for generators, you can play around with the itertools module (be sure to use chain.from_iterable rather than chain when warranted). For example, you might even use generators to implement infinitely-long lazy lists like itertools.count(). You could implement your own def enumerate(iterable): zip(count(), iterable), or alternatively do so with the yieldkeyword in a while-loop.

Please note: generators can actually be used for many more things, such as implementing coroutinesor non-deterministic programming or other elegant things. However, the "lazy lists" viewpoint I present here is the most common use you will find.

Behind the scenes

This is how the "Python iteration protocol" works. That is, what is going on when you do list(makeRange(5)). This is what I describe earlier as a "lazy, incremental list".

>>> x=iter(range(5))
>>> next(x)
0
>>> next(x)
1
>>> next(x)
2
>>> next(x)
3
>>> next(x)
4
>>> next(x)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
StopIteration

The built-in function next() just calls the objects .next() function, which is a part of the "iteration protocol" and is found on all iterators. You can manually use the next() function (and other parts of the iteration protocol) to implement fancy things, usually at the expense of readability, so try to avoid doing that...

Minutiae

Normally, most people would not care about the following distinctions and probably want to stop reading here.

In Python-speak, an iterable is any object which "understands the concept of a for-loop" like a list [1,2,3], and an iterator is a specific instance of the requested for-loop like [1,2,3].__iter__(). Agenerator is exactly the same as any iterator, except for the way it was written (with function syntax).

When you request an iterator from a list, it creates a new iterator. However, when you request an iterator from an iterator (which you would rarely do), it just gives you a copy of itself.

Thus, in the unlikely event that you are failing to do something like this...

> x = myRange(5)
> list(x)
[0, 1, 2, 3, 4]
> list(x)
[]

... then remember that a generator is an iterator; that is, it is one-time-use. If you want to reuse it, you should call myRange(...) again. Those who absolutely need to clone a generator (for example, who are doing terrifyingly hackish metaprogramming) can use itertools.tee if absolutely necessary, since the copyable iterator Python PEP standards proposal has been deferred.

I feel like I post a link to this presentation every day: David M. Beazly's Generator Tricks for Systems Programmers. If you're a Python programmer and you're not extremely familiar with generators, you should read this. It's a very clear explanation of what generators are, how they work, what the yield statement does, and it answers the question "Do you really want to mess around with this obscure language feature?"

SPOILER ALERT. The answer is: Yes. Yes, you do.

There's one extra thing to mention: a function that yields doesn't actually have to terminate. I've written code like this:

def fib():
    last, cur = 0, 1
    while True: 
        yield cur
        last, cur = cur, last + cur

Then I can use it in other code like this:

for f in fib():
    if some_condition: break
    coolfuncs(f);

It really helps simplify some problems, and makes some things easier to work with.

yield is just like return. It returns whatever you tell it to. The only difference is that the next time you call the function, execution starts from the last call to the yield statement.

In the case of your code, the function get_child_candidates is acting like an iterator so that when you extend your list, it adds one element at a time to the new list.

list.extend calls an iterator until it's exhausted. In the case of the code sample you posted, it would be much clearer to just return a tuple and append that to the list.

Yield gives you a generator.

def get_odd_numbers(i):
    return range(1, i, 2)
def yield_odd_numbers(i):
    for x in range(1, i, 2):
       yield x
foo = get_odd_numbers(10)
bar = yield_odd_numbers(10)
foo
[1, 3, 5, 7, 9]
bar
<generator object yield_odd_numbers at 0x1029c6f50>
bar.next()
1
bar.next()
3
bar.next()
5

As you can see, in the first case foo holds the entire list in memory at once. It's not a big deal for a list with 5 elements, but what if you want a list of 5 million? Not only is this a huge memory eater, it also costs a lot of time to build at the time that the function is called. In the second case, bar just gives you a generator. A generator is an iterable--which means you can use it in a for loop, etc, but each value can only be accessed once. All the values are also not stored in memory at the same time; the generator object "remembers" where it was in the looping the last time you called it--this way, if you're using an iterable to (say) count to 50 billion, you don't have to count to 50 billion all at once and store the 50 billion numbers to count through. Again, this is a pretty contrived example, you probably would use itertools if you really wanted to count to 50 billion. :)

This is the most simple use case of generators. As you said, it can be used to write efficient permutations, using yield to push things up through the call stack instead of using some sort of stack variable. Generators can also be used for specialized tree traversal, and all manner of other things.

For those who prefer a minimal working example, meditate on this interactive Python session:

>>> def f():
...   yield 1
...   yield 2
...   yield 3
... 
>>> g = f()
>>> for i in g:
...   print i
... 
1
2
3
>>> for i in g:
...   print i
... 
>>> # Note that this time nothing was printed

It's returning a generator. I'm not particularly familiar with Python, but I believe it's the same kind of thing as C#'s iterator blocks if you're familiar with those.

There's an IBM article which explains it reasonably well (for Python) as far as I can see.

The key idea is that the compiler/interpreter/whatever does some trickery so that as far as the caller is concerned, they can keep calling next() and it will keep returning values - as if the generator method was paused. Now obviously you can't really "pause" a method, so the compiler builds a state machine for you to remember where you currently are and what the local variables etc look like. This is much easier than writing an iterator yourself.

An example in plain language. I will provide a correspondence between high-level human concepts to low-level python concepts.

I want to operate on a sequence of numbers, but I don't want to bother my self with the creation of that sequence, I want only to focus on the operation I want to do. So, I do the following:

• I call you and tell you that I want a sequence of numbers which is produced in a specific way, and I let you know what the algorithm is.
  This step corresponds to defining the generator function, i.e. the function containing a yield.
• Sometime later, I tell you, "ok, get ready to tell me the sequence of numbers".
  This step corresponds to calling the generator function which returns a generator object.Note that you don't tell me any numbers yet, you just grab your paper and pencil.
• I ask you, "tell me the next number", and you tell me the first number; after that, you wait for me to ask you for the next number. It's your job to remember where you were, what numbers you have already said, what is the next number. I don't care about the details.
  This step corresponds to calling .next() on the generator object.
• … repeat previous step, until…
• eventually, you might come to an end. You don't tell me a number, you just shout, "hold your horses! I'm done! No more numbers!"
  This step corresponds to the generator object ending its job, and raising a StopIterationexception The generator function does not need to raise the exception, it's raised automatically when the function ends or issues a return.

This is what a generator does (a function that contains a yield); it starts executing, pauses whenever it does a yield, and when asked for a .next() value it continues from the point it was last. It fits perfectly by design with the iterator protocol of python, which describes how to sequentially request for values.

The most famous user of the iterator protocol is the for command in python. So, whenever you do a:

for item in sequence:

it doesn't matter if sequence is a list, a string, a dictionary or a generator object like described above; the result is the same: you read items off a sequence one by one.

Note that defining a function which contains a yield keyword is not the only way to create a generator; it's just the easiest way to create one.

For more accurate information, read about iterator types, the yield statement and generators in the Python documentation.

There is one type of answer that I don't feel has been given yet, among the many great answers that describe how to use generators. Here is the PL theory answer:

The yield statement in python returns a generator. A generator in python is a function that returnscontinuations (and specifically a type of coroutine, but continuations represent the more general mechanism to understand what is going on).

Continuations in programming languages theory are a much more fundamental kind of computation, but they are not often used because they are extremely hard to reason about and also very difficult to implement. But the idea of what a continuation is, is straightforward: it is the state of a computation that has not yet finished. In this state are saved the current values of variables and the operations that have yet to be performed, and so on. Then at some point later in the program the continuation can be invoked, such that the program's variables are reset to that state and the operations that were saved are carried out.

Continuations, in this more general form, can be implemented in two ways. In the call/cc way, the program's stack is literally saved and then when the continuation is invoked, the stack is restored.

In continuation passing style (CPS), continuations are just normal functions (only in languages where functions are first class) which the programmer explicitly manages and passes around to subroutines. In this style, program state is represented by closures (and the variables that happen to be encoded in them) rather than variables that reside somewhere on the stack. Functions that manage control flow accept continuation as arguments (in some variations of CPS, functions may accept multiple continuations) and manipulate control flow by invoking them by simply calling them and returning afterwards. A very simple example of continuation passing style is as follows:

def save_file(filename):
  def write_file_continuation():
    write_stuff_to_file(filename)

  check_if_file_exists_and_user_wants_to_overwrite( write_file_continuation )

In this (very simplistic) example, the programmer saves the operation of actually writing the file into a continuation (which can potentially be a very complex operation with many details to write out), and then passes that continuation (i.e, as a first-class closure) to another operator which does some more processing, and then calls it if necessary. (I use this design pattern a lot in actual GUI programming, either because it saves me lines of code or, more importantly, to wait for GUI events and then execute saved continuations repeatedly)

The rest of this post will, without loss of generality, conceptualize continuations as CPS, because it is a hell of a lot easier to understand and read.

Now let's talk about generators in python. Generators are a specific subtype of continuation. Whereascontinuations are able in general to save the state of a computation (i.e., the program's call stack), generators are only able to save the state of iteration over an iterator. Although, this definition is slightly misleading for certain use cases of generators. For instance:

def f():
  while True:
    yield 4

This is clearly a reasonable iterable whose behavior is well defined -- each time the generator iterates over it, it returns 4 (and does so forever). But it isn't probably the prototypical type of iterable that comes to mind when thinking of iterators (i.e., for x in collection: do_something(x)). This example illustrates the power of generators: if anything is an iterator, a generator can save the state of its iteration.

To reiterate: Continuations can save the state of a program's stack and generators can save the state of iteration. This means that continuations are more a lot powerful than generators, but also that generators are a lot, lot easier. They are easier for the language designer to implement, and they are easier for the programmer to use (if you have some time to burn, try to read and understand this page about continuations and call/cc).

But you could easily implement (and conceptualize) generators as a simple, specific case of continuation passing style:

Whenever yield is called, it tells the function to return a continuation. When the function is called again, it starts from wherever it left off. So, in pseudo-pseudocode (i.e., not pseudocode but not code) the generator's next method is basically as follows:

class Generator():
  def __init__(self,iterable,generatorfun):
    self.next_continuation = lambda:generatorfun(iterable)

  def next(self):
    value, next_continuation = self.next_continuation()
    self.next_continuation = next_continuation
    return value

where yield keyword is actually syntactic sugar for the real generator function, basically something like:

def generatorfun(iterable):
  if len(iterable) == 0:
    raise StopIteration
  else:
    return (iterable[0], lambda:generatorfun(iterable[1:]))

Remember that this is just pseudocode and the actual implementation of generators in python is more complex. But as an exercise to understand what is going on, try to use continuation passing style to implement generator objects without use of the yield keyword.

Here are some Python examples of how to actually implement generators as if Python did not provide syntactic sugar for them (or in a language without native syntax, like JavaScript). Snippets from that link is below.

As a Python generator:

from itertools import islice

def fib_gen():
    a, b = 1, 1
    while True:
        yield a
        a, b = b, a + b

assert [1, 1, 2, 3, 5] == list(islice(fib_gen(), 5))

Using lexical closures instead of generators

def ftake(fnext, last):
    return [fnext() for _ in xrange(last)]

def fib_gen2():
    #funky scope due to python2.x workaround
    #for python 3.x use nonlocal
    def _():
        _.a, _.b = _.b, _.a + _.b
        return _.a
    _.a, _.b = 0, 1
    return _

assert [1,1,2,3,5] == ftake(fib_gen2(), 5)

Using object closures instead of generators (because ClosuresAndObjectsAreEquivalent)

class fib_gen3:
    def __init__(self):
        self.a, self.b = 1, 1

    def __call__(self):
        r = self.a
        self.a, self.b = self.b, self.a + self.b
        return r

assert [1,1,2,3,5] == ftake(fib_gen3(), 5)

While a lot of answers show why you'd use a yield to create a generator, there are more uses for yield. It's quite easy to make a coroutine, which enables the passing of information between two blocks of code. I won't repeat any of the fine examples that have already been given about using yield to create a generator.

To help understand what a yield does in the following code, you can use your finger to trace the cycle through any code that has a yield. Every time your finger hits the yield, you have to wait for a next or a send to be entered. When a next is called, you trace through the code until you hit the yield… the code on the right of the yield is evaluated and returned to the caller… then you wait. When next is called again, you perform another loop through the code. However, you'll note that in a coroutine, yield can also be used with a send… which will send a value from the caller into the yielding function. If a send is given, then yield receives the value sent, and spits it out the left hand side… then the trace through the code progresses until you hit the yield again (returning the value at the end, as if next was called).

For example:

>>> def coroutine():
...     i = -1
...     while True:
...         i += 1
...         val = (yield i)
...         print("Received %s" % val)
...
>>> sequence = coroutine()
>>> sequence.next()
0
>>> sequence.next()
Received None
1
>>> sequence.send('hello')
Received hello
2
>>> sequence.close()

I was going to post "read page 19 of Beazley's 'Python: Essential Reference' for a quick description of generators", but so many others have posted good descriptions already.

Also, note that yield can be used in coroutines as the dual of their use in generator functions. Although it isn't the same use as your code snippet, (yield) can be used as an expression in a function. When a caller sends a value to the method using the send() method, then the coroutine will execute until the next (yield) statement is encountered.

Generators and coroutines are a cool way to set up data-flow type applications. I thought it would be worthwhile knowing about the other use of the yield statement in functions.

there is another yield use and meaning (since python 3.3):

yield from <expr>

http://legacy.python.org/dev/peps/pep-0380/

A syntax is proposed for a generator to delegate part of its operations to another generator. This allows a section of code containing 'yield' to be factored out and placed in another generator. Additionally, the subgenerator is allowed to return with a value, and the value is made available to the delegating generator.

The new syntax also opens up some opportunities for optimisation when one generator re-yields values produced by another.

Here is a mental image of what yield does.

I like to think of a thread as having a stack (even if it's not implemented that way).

When a normal function is called, it puts its local variables on the stack, does some computation, returns and clears the stack. The values of its local variables are never seen again.

With a yield function, when it's called first, it similarly adds its local variables to the stack, but then takes its local variables to a special hideaway instead of clearing them, when it returns via yield. A possible place to put them would be somewhere in the heap.

Note that it's not the function any more, it's a kind of an imprint or ghost of the function that the forloop is hanging onto.

When it is called again, it retrieves its local variables from its special hideaway and puts them back on the stack and computes, then hides them again in the same way.

here is simple example with result:

def isPrimeNumber(n):
        print "isPrimeNumber({}) call".format(n)
        if n==1:
            return False
        for x in range(2,n):
            if n % x == 0:
                return False
        return True


def primes (n=1):
        while(True):
            print "loop step ---------------- {}".format(n)
            if isPrimeNumber(n): yield n
            n += 1

for n in primes():
        if n> 10:break
        print "wiriting result {}".format(n)   

output :

loop step ---------------- 1
isPrimeNumber(1) call
loop step ---------------- 2
isPrimeNumber(2) call
loop step ---------------- 3
isPrimeNumber(3) call
wiriting result 3
loop step ---------------- 4
isPrimeNumber(4) call
loop step ---------------- 5
isPrimeNumber(5) call
wiriting result 5
loop step ---------------- 6
isPrimeNumber(6) call
loop step ---------------- 7
isPrimeNumber(7) call
wiriting result 7
loop step ---------------- 8
isPrimeNumber(8) call
loop step ---------------- 9
isPrimeNumber(9) call
loop step ---------------- 10
isPrimeNumber(10) call
loop step ---------------- 11
isPrimeNumber(11) call

I am not an python developer but it looks to me "yield" holds the position of program flow and next time loop start from "yield" position. Seems like waiting at that position and just before that returning value outside and next time continue to work.

Seems to me interesting and nice ability :D

From a programming viewpoint, the iterators are implemented as thunks

http://en.wikipedia.org/wiki/Thunk_(functional_programming)

To implement thunks (also called anonymous functions), one uses messages sent to a closure object, which has a dispatcher, and the dispatcher answers to "messages".

http://en.wikipedia.org/wiki/Message_passing

"next" is a message sent to a closure, created by "iter" call.