# Good with Computers

The Sixty North Blog

# Software Process Dynamics

At the Software Architect 2015 conference in London I presented What if? Supporting decisions with software dynamics simulations.1 This talk introduces the idea of performing numerical simulations of software development teams and the products they build. The value in such simulations is to inform policy decisions and guide deliberate perturbations to the software development process, such as whether and when to add or remove personnel from a project. Simulations should not be used to make hard predications about, for example, when a particular project will be finished.

# Event-Sourced Domain Models in Python at PyCon UK

At PyCon UK 2015 I led a very well attended workshop with the goal of introducing Python developers to the tried-and-tested techniques and patterns of Domain Driven Design (DDD), in particular when used as part of an event-sourced architecture.

The two-and-a-half hour workshop was comprised of excerpts from our training course DDD Patterns in Python. Although the workshop material was heavily edited and compressed from the course – I’m confident that the majority of attendees grasped the main principles.

Several attendees have since asked for the introductory slides, which preceded the exercises. Here they are:

# Event Processing with Transducers

In the previous article in this series on transducers we looked at lazily evaluating transducers. This time we’ll look not at pulling output through a transducer chain from downstream, but at pushing input items into the chain from upstream.

All of the uses of transducers we’ve demonstrated in Python so far are probably better handled by existing and well established Python programming techniques, such as generator expressions and generator functions. At this point in the series, we move definitely beyond that into new territory where transducers bring completely new capabilities to Python.

One the key selling points of transducers is that they abstract the essence of a transformation away from the details of the data series that is being transformed. We’ll show this in Python by using transducers to transform a series of events modelled using Python coroutines.

# Coroutines in Python

Coroutines in Python are little-used, and their workings are not widely known, so their implementation bears repeating here. If you’re familiar with the notion of coroutines in general, and the specifics of how they’re implemented in Python, you can skim over this section.

Coroutines are like generator functions insofar as they are resumable functions. In fact, coroutines in Python are generator functions which use yield as an expression rather than a statement. What this means in practice is that generator function objects sport a send() method which allows the client of the generator function to transmit information to a running generator and for the generator to receive this data as the value of the yield expression. As usual, an example will serve to make things clearer.

We’ll start by defining a generator function which enters an infinite loop, waits at the yield expression for a value to be received, and then prints this value to the console.

>>> def event_receiver():
...     while True:
...         message = (yield)
...         print("Message:", message)
...
>>>


We create a generator object just the same as we would with any other generator:

>>> r = event_receiver()
>>> r


Now we’ll try to send it a message, using the send() method of the generator object:

>>> r.send("message")
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: can't send non-None value to a just-started generator
>>>


This actually fails, because the generator code has not yet been executed at all. We need to prime the pump, so to speak, by advancing execution to the first occurrence of yield. We can do this by passing the generator to the next() built-in:

>>> next(r)


We’ll fix this pump-priming annoyance of generator based coroutines shortly.

Now we can send messages:

>>> r.send("message")
Message: message
>>> r.send("another message")
Message: another message


When we’re done, we terminate the coroutine by calling the close() method. (This actually raises a GeneratorExit exception at the site of the yield expression, which allows control flow to exit the otherwise infinite loop; this special exception is intercepted by the Python runtime system, so it isn’t seen by us at the console).

>>> r.close()
>>>


Any further attempts to send() messages into the generator function cause StopIteration to be raised. This, of course, is the normal means of indicating that a generator is exhausted:

>>> r.send("message")
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
StopIteration
>>>


## Priming generator-based coroutines

Now to address the awkwardness of having to prime coroutine generator functions by initially passing them to next(). We can improve this with a function decorator which creates the generator object and calls next on our behalf. We’ll call the decorator @coroutine:

def coroutine(func):
def start(*args, **kwargs):
g = func(*args, **kwargs)
next(g)
return g
return start


We’ll use our new decorator to assist in defining a slightly more sophisticated coroutine for printing, called rprint():

import sys

@coroutine
def rprint(sep='\n', end=''):
"""A coroutine sink which prints received items to stdout

Args:
sep: Optional separator to be printed between received items.
end: Optional terminator to be printed after the last item.
"""
try:
first_item = (yield)
sys.stdout.write(str(first_item))
sys.stdout.flush()
while True:
item = (yield)
sys.stdout.write(sep)
sys.stdout.write(str((item)))
sys.stdout.flush()
except GeneratorExit:
sys.stdout.write(end)
sys.stdout.flush()


In this implementation, we intercept GeneratorExit explicitly to give us the opportunity to print a terminator. We also regularly flush the stream so we get immediate feedback for our following experiments.

## Event sources

The opposite of a sink is a source. Until now, we’ve been sourcing ‘events’ ourself by sending them from the REPL, but to make this a little more interesting, we’ll cook up a function – just a plain old function, not a generator – which takes values from an iterable series and intermittently sends them, after a delay, to anything with a send() method such as our coroutine generators. For fun, the random delay has a so-called Poisson distribution which mimics a radioactive source; imagine a device with a geiger counter which sends the next item from an iterable series each time an atom decays:

def poisson_source(rate, iterable, target):
"""Send events at random times with uniform probability.

Args:
rate: The average number of events to send per second.

iterable: A series of items which will be sent to the target
one by one.

target: The target coroutine or sink.

Returns:
The completed value, or None if iterable was exhausted
and the target was closed.
"""
for item in iterable:
duration = random.expovariate(rate)
sleep(duration)
try:
target.send(item)
except StopIteration as e:
return e.value
target.close()
return None


When either the iterable series is exhausted or the target signals it has terminated (by raising StopIteration) we call close() on the target. Note that by supplying an infinite iterable series we could make the source send events forever.

Let’s hook our source and sink together at the REPL:

>>> printer = rprint(sep=', ', end='\nDONE!\n')
>>> count_to_nine = range(10)
>>> poisson_source(rate=0.5, iterable=count_to_nine, target=printer)
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
DONE!
>>>


## Combined event sources and event sinks

Of course, we can build functions which act as both sinks and sources, transforming the messages they receive in some way and forwarding the processed results onwards to another sink. Here’s a combined source and sink function, which simply doubles the values it receives:

@coroutine
def doubler(target):
while True:
item = (yield)
doubled_item = item * 2
try:
target.send(doubled_item)
except StopIteration as e:
return e.value


To use, doubler() we chain the components of the pipeline together

>>> printer = rprint(sep=', ', end='\nDONE!\n')
>>> count_to_nine = range(10)
>>> poisson_source(rate=0.5,
...                iterable=count_to_nine,
...                target=doubler(target=printer))
0, 2, 4, 6, 8, 10, 12, 14, 16, 18
DONE!


From doubler() it’s but a short hop to a more general mapper() which accepts an arbitrary transforming function:

@coroutine
def mapper(transform, target):
while True:
item = (yield)
transformed_item = transform(item)
try:
target.send(transformed_item)
except StopIteration as e:
return e.value


Used like so,

>>> printer = rprint(sep=', ', end='\nDONE!\n')
>>> count_to_nine = range(10)
>>> poisson_source(rate=0.5,
iterable=count_to_nine,
target=mapper(transform=square,
target=printer))
0, 1, 4, 9, 16, 25, 36, 49, 64, 81
DONE!


From here, you can see how we could also implement equivalents of filter(), reduce() and so on to operate on the ‘push’ event stream modelled by Python coroutines.

The point here is that we can’t just re-use any existing functions which process ‘pull’ data series – such as the functions in itertools – with ‘push’ data series. Each and every function needs to be reimplemented to accept values pushed from upstream, and send processed results downstream.

## Transducing events

Transducers provide a way out of this quandary. We’ve demonstrated earlier in this series that ‘reduce’ is a fundamental operation, and by reimagining reduce() into a more general transduce() we were able to use the same transducers to operate on both eager and lazy data series. We can do the same with coroutine-based push events, by implementing a version of transduce() which allows us to use any transducer to process a stream of such events.

Our reactive_transduce() is a coroutine which accepts two arguments: a transducer and a target sink to which the transduced results will be sent:

@coroutine
def reactive_transduce(transducer, target=None):
reducer = transducer(sending())
accumulator = target if (target is not None) else reducer.initial()
try:
while True:
item = (yield)
accumulator = reducer.step(accumulator, item)
if isinstance(accumulator, Reduced):
accumulator = accumulator.value
break
except GeneratorExit:
pass
return reducer.complete(accumulator)


The reactive_transduce() function connects to the upstream end of a transducer chain, adapting from the coroutine protocol to the reducer interface. At the downstream end of the transducer chain, we need to adapt the other way, from the reducer interface to the coroutine protocol. To do this we use a reducer called Sending, which we hard-wire as the ‘bottom’ reducer on the first line of reactive_transduce(). The Sending reducer looks like this:

class Sending:

def initial(self):
return null_sink()

def step(self, result, item):
try:
result.send(item)
except StopIteration:
return Reduced(result)
else:
return result

def complete(result):
result.close()
return result


The step() method literally sends the next item to the result – which must therefore be a legitimate event sink. Should the sink indicate that it can’t accept a further item, by raising StopIteration we return the result wrapped in the Reduced sentinel. The initial() method provides a legitimate sink – just a simple do-nothing sink defined as:

@coroutine
def null_sink():
while True:
_ = (yield)


Going back to reactive_transduce() the main loop continues to iterate, receiving new values via a yield expression, until such time as GeneratorExit is signalled by the client or the reducer signals termination by returning Reduced.

When the main loop is exited by whatever means, we give the reducer opportunity to complete(), and the Sending.complete() method ensures that close() is called on the target.

With these pieces in place, let’s look at how to use reactive_transduce(). We’ll reproduce our previous example where we squared the output from poisson_source(), but this time using the mapping() transducer to do the work:

>>> poisson_source(rate=0.5,
...                iterable=range(10),
...                target=transduce(transducer=mapping(square),
...                                 target=printer))
...
0, 1, 4, 9, 16, 25, 36, 49, 64, 81
DONE!


The key point here is that we can now take an arbitrary transducer and reuse it with eager collections, lazy iterables, and push-events! In fact, simply by devising an appropriate transduce function we can use re-use our transducers in an arbitrary data-series processing context.

This is the true power of transducers: Data processing components completely abstracted away from how the input data arrives, or to where the output results are sent.

# Lazy Transducer Evaluation

In the previous article in this series on transducers we looked at transducers which push more items downstream through the reducer chain than they receive from upstream. We promised that this would make lazy evaluation of transducer chains quite interesting.

When used with our transduce() function, our mapping and filtering transducers are in some ways less flexible than the map() and filter() functions built into Python 3 because our transduce() eagerly evaluates the reduction operation, whereas the built-in map() and filter() are lazy.1

The eagerness of our mapping and filtering transducers is not inherent in their implementation though. The eagerness is a result of the for-loop in transduce() which must run to completion before returning. Thankfully, due to the clear separation of concerns between the reduction algorithm embodied in the transducers and the transducer “driver”, we can design an alternative transducible process which is lazy.

Here’s a reminder of our non-lazy transduce() function:

UNSET = object()

def transduce(transducer, reducer, iterable, init=UNSET):
r = transducer(reducer)
accumulator = init if (init is not UNSET) else reducer.initial()
for item in iterable:
accumulator = r.step(accumulator, item)
if isinstance(accumulator, Reduced):
accumulator = accumulator.value
break
return r.complete(accumulator)


Recall that our non-lazy transduce() function accepts, in addition to the transducer, a separate reducer argument which is used to collect the results of applying the transducer into, say, a list. Our lazy transduction function will be implemented as a Python generator function which yields each result as it becomes available, returning control to the caller, and then resumes execution when the next value is requested.

In order to handle early terminating transducers such as First, stateful transducers which emit left-over state such as Batching, and transducers which emit more elements than they consume such as Repeating, the lazy_transduce() function is necessarily quite complex:

from collections import deque

def lazy_transduce(transducer, iterable):
"""Lazy application of a transducer to an iterable."""
r = transducer(Appending())
accumulator = deque()
reduced = False
for item in iterable:
accumulator = r.step(accumulator, item)
if isinstance(accumulator, Reduced):
accumulator = accumulator.value
reduced = True

yield from all_pending_items_in(accumulator)

if reduced:
break

left_overs = r.complete(accumulator)
assert left_overs is accumulator

yield from all_pending_item_in(left_overs)

def all_pending_items_in(queue):
while queue:
yield queue.popleft()


Our function accepts only a transducer and the iterable series of source items. There’s no need to provide a reducer, because this function hardwires it’s own on the first line, where we provide an Appending reducer. Notice that unlike the eager transduce() we never call the Appending.initial() method to retrieve the seed value for the reduction, so we must provide a legitimate mutable sequence type. For reasons that will become clear shortly, we provide a deque from the Python Standard Library collections module2 – a double-ended queue, which supports append() to push items into the right-hand end.

We also set a flag reduced so we know when we’re finished.

The first part of the body of the for-loop is the same as for eager transduce(): we step the transducer, accumulating each item, looking for the sentinel Reduced value as we go. If we encounter Reduced we un-box its contents and set the reduced flag to signal that we’re (nearly) done.

The next part of the for-loop body is where things really diverge from the eager transduce() version. Bearing in mind that the call to step() may have appended multiple items to the accumulator, we now need to yield them one by-one to the client. We do this using the yield from statement which delegates to another generator function all_items_pending_in() which simply keeps yielding items from the queue until it is empty.

At the end of the for-loop, we check the reduced flag, and break out of the loop if we’re done.

After the loop, with all the input items dealt with, we make the necessary call to complete(), bearing in mind that this may append further results to the accumulator queue. After a sanity check that the return value from complete() is indeed the queue (which we know it should be, because Appending.complete() simply returns its argument) we use the yield from all_pending_items_in(left_overs) statement one last time to yield any lingering results to the client.

In order to demonstrate the laziness in action, we’ll create a little wrapper around the built-in range() sequence that logs the yielded integers to the console:

def logging_range(n):
for i in range(n):
print("i =", i)
yield i


Here it in in action, demonstrating it’s laziness:

>>> primes_repeating = compose(filtering(is_prime), repeating(3))
>>> repeated_primes = lazy_transduce(primes_repeating, logging_range(100))
>>> repeated_primes
<generator object lazy_transduce at 0x103027708>
>>> next(repeated_primes)
i = 0
i = 1
i = 2
2
>>> next(repeated_primes)
2
>>> next(repeated_primes)
2
>>> next(repeated_primes)
i = 3
3
>>> next(repeated_primes)
3
>>> next(repeated_primes)
3
>>> next(repeated_primes)
i = 4
i = 5
5
>>> next(repeated_primes)
5
>>> next(repeated_primes)
5
>>> next(repeated_primes)
i = 6
i = 7
7
>>> next(repeated_primes)
7
>>> next(repeated_primes)
7
>>> next(repeated_primes)
i = 8
i = 9
i = 10
i = 11
11
>>> next(repeated_primes)
11
>>> next(repeated_primes)
11
>>> next(repeated_primes)
i = 12
i = 13
13


So we see that transducers allow orthogonal specification of the reducing operation, the result collection and whether to evaluate eagerly or lazily. Neat!

In a future article we’ll look at using transducers to process ‘push’ events modelled by Python coroutines.

1. Back in Python 2 map() and filter() were eager.

2. The documentation for the Python collections.deque double-ended queue.

# Item Injecting Transducers

In the previous article in our series on understanding transducers through Python we showed how to support early termination of a reduction operation. This time, we’ll demonstrate how transducers can produce more items than they consume. Although this may seem obvious, it leads to some important consequences for implementing lazy evaluation of transducers, which is what we’ll look at next time.

Consider a transducer Repeating which repeats each source item multiple times into the output:

class Repeating:

def __init__(self, reducer, num_times):
self._reducer = reducer
self._num_times = num_times

def initial(self):
return self._reducer.initial()

def step(self, result, item):
for _ in range(self._num_times):
result = self._reducer.step(result, item)
return result

def complete(self, result):
return self._reducer.complete(result)

def repeating(num_times):

if num_times < 0:
raise ValueError("num_times cannot be negative")

def repeating_transducer(reducer):
return Repeating(reducer, num_times)

return repeating_transducer
&#91;/pyg&#93;

The key point to notice here, is that each call to <code>Repeating.step()</code> results in multiple calls to the underlying reducer's <code>self._reducer.step()</code>, thereby injecting more items into the output series than are received in the input series.

By composing it with our filtering primality checking predicate, we can use it to repeat each prime number three times:

[pyg lang="python" style="default" linenumbers=""]
>>> primes_repeating = compose(filtering(is_prime), repeating(3))
>>> transduce(primes_repeating, Appending(), range(100))
[2, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7, 7, 11, 11, 11, 13, 13, 13, 17, 17, 17,
19, 19, 19, 23, 23, 23, 29, 29, 29, 31, 31, 31, 37, 37, 37, 41, 41, 41,
43, 43, 43, 47, 47, 47, 53, 53, 53, 59, 59, 59, 61, 61, 61, 67, 67, 67,
71, 71, 71, 73, 73, 73, 79, 79, 79, 83, 83, 83, 89, 89, 89, 97, 97, 97]


In the next article, we’ll see that although seemingly fairly innocuous, support for item injecting transducers such as Repeating complicates lazy evaluation quite a bit!

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