Explain the use of yields in this Game of Life implementation

Question

In this PyCon talk, Jack Diederich shows this "simple" implementation of Conway's Game of Life. I am not intimately familiar with either GoL or semi-advanced Python, but the code seems quite easy to grasp, if not for two things:

1. The use of yield. I have seen the use of yield to create generators before, but eight of them in a row is new... Does it return a list of eight generators, or how does this thing work?
2. set(itertools.chain(*map(neighbors, board))). The star unpacks the resulting list (?) from applying neighbours to board, and ... my mind just blew.

Could someone try to explain these two parts for a programmer that is used to hacking together some python code using map, filter and reduce, but that is not using Python on a daily basis? :-)

import itertools

def neighbors(point):
    x, y = point
    yield x + 1, y
    yield x - 1, y
    yield x, y + 1
    yield x, y - 1
    yield x + 1, y + 1
    yield x + 1, y - 1
    yield x - 1, y + 1
    yield x - 1, y - 1

def advance(board):
    newstate = set()
    recalc = board | set(itertools.chain(*map(neighbors, board)))
    for point in recalc:
        count = sum((neigh in board) for neigh in neighbors(point))
        if count == 3 or (count == 2 and point in board):
            newstate.add(point)
    return newstate

glider = set([(0,0), (1,0), (2, 0), (0,1), (1,2)])
for i in range(1000):
    glider = advance(glider)
    print glider

Answer 1

Generators operate on two principles: they produce a value each time a yield statement is encountered, and unless it is iterated over, their code is paused.

It doesn't matter how many yield statements are used in a generator, the code is still run in normal python ordering. In this case, there is no loop, just a series of yield statements, so each time the generator is advanced, python executes the next line, which is another yield statement.

What happens with the neighbors generator is this:

1. Generators always start paused, so calling neighbors(position) returns a generator that hasn't done anything yet.

2. When it is advanced (next() is called on it), the code is run until the first yield statement. First x, y = point is executed, then x + 1, y is calculated and yielded. The code pauses again.

3. When advanced again, the code runs until the next yield statement is encountered. It yields x - 1, y.

4. etc. until the function completes.

The set(itertools.chain(*map(neighbors, board))) line does:

1. map(neighbors, board) produces an iterator for each and every position in the board sequence. It simply loops over board, calls neighbors on each value, and returns a new sequence of the results. Each neighbors() function returns a generator.

2. The *parameter syntax expands the parameter sequence into a list of parameters, as if the function was called with each element in parameter as a separate positional parameter instead. param = [1, 2, 3]; foo(*param) would translate to foo(1, 2, 3).

   itertools.chain(*map(..)) takes each and every generator produced by the map, and applies that as a series of positional parameters to itertools.chain(). Looping over the output of chain means that each and every generator for each and every board position is iterated over once, in order.

3. All the generated positions are added to a set, essentially removing duplicates

You could expand the code to:

positions = set()
for board_position in board:
    for neighbor in neighbors(board):
        positions.add(neighbor)

In python 3, that line could be expressed a little more efficiently still by using itertools.chain.from_iterable() instead, because map() in Python 3 is a generator too; .from_iterable() doesn't force the map() to be expanded and will instead loop over the map() results one by one as needed.