gistfile1.txt

# A practical introduction to functional programming

Many functional programming articles teach abstract functional techniques.  That is, composition, pipelining, higher order functions.  This one is different.  It shows examples of imperative code that people write every day and translates them to a functional style.

The imperative examples are all loops.  The first section of the article takes short, data transforming loops and translates them into functional maps and reduces.  The second section takes longer loops, breaks them up into units and makes each unit functional.  The third section takes a loop that is a long series of successive data transformations and decomposes it into a functional pipeline.

The examples are in Python, because many people find Python easy to read.  A number of the examples eschew pythonicity in order to demonstrate functional techniques common to many languages: map, reduce, pipeline.

## A guide rope

When people talk about functional programming, they mention a dizzying number of "functional" characteristics.  They mention immutable data[1], first class functions[2] and tail call optimisation[3].  These are language features that aid functional programming.  They mention mapping, reducing, pipelining, recursing, currying[4] and the use of higher order functions.  These are programming techniques used to write functional code.  They mention parallelization[5], lazy evaluation[6] and determinism[7].  These are advantageous properties of functional programs.

Ignore all that.  Functional code is characterised by one thing: the absence of side effects.  It doesn't rely on data outside the current function, and it doesn't change the data that exists outside the current function.  Every other "functional" thing can be derived from this property.  Use it as a guide rope as you learn.

This is an unfunctional function:

    a = 0
    def increment1():
        global a
        a += 1

This is a functional function:

    def increment2(a):
        return a + 1

## Don't iterate.  Use map and reduce.

### Map

Map takes a function and a collection of items.  It makes a new collection, runs the function on each item in the original collection and inserts each return value into the new collection.  It returns the new collection.

This is a simple map that takes a list of names and returns a list of the lengths of those names:

    name_lengths = map(len, ["Mary", "Isla", "Sam"])

    print name_lengths
    # => [4, 4, 3]

This is a map that squares every number in the passed collection:

    squares = map(lambda x: x * x, [0, 1, 2, 3, 4])

    print squares
    # => [0, 1, 4, 9, 16]

The next map doesn't take a named function.  It takes an anonymous, inlined function defined with `lambda`.  The parameters of the lambda are defined to the left of the colon.  The function body is defined to the right of the colon.  The result of running the function body is (implicitly) returned.

The unfunctional code below takes a list of real names and replaces them with randomly assigned code names.

    import random

    names = ['Mary', 'Isla', 'Sam']
    code_names = ['Mr. Pink', 'Mr. Orange', 'Mr. Blonde']

    for i in range(len(names)):
        names[i] = random.choice(code_names)

    print names
    # => ['Mr. Blonde', 'Mr. Blonde', 'Mr. Blonde']

(As you can see, this algorithm can potentially assign the same secret code name to multiple secret agents.  Hopefully, this won't be a source of confusion during the secret mission.)

This can be rewritten as a map:

    import random

    names = ['Mary', 'Isla', 'Sam']

    secret_names = map(lambda x: random.choice(['Mr. Pink',
                                                'Mr. Orange',
                                                'Mr. Blonde']),
                       names)

Try rewriting the code below as a map.  It takes a list of real names and replaces them with code names produced using a more robust strategy.

    names = ['Mary', 'Isla', 'Sam']

    for i in range(len(names)):
        names[i] = hash(names[i])

    print names
    # => [6306819796133686941, 8135353348168144921, -1228887169324443034]

(Hopefully, the secret agents will have good memories and won't forget each other's secret code names during the secret mission.)

My solution:

    names = ['Mary', 'Isla', 'Sam']

    secret_names = map(hash, names)

### Reduce

Reduce takes a function and a collection of items.  It returns a value that is created by combining the items.

This is a simple reduce.  It returns the sum of all the items in the collection.

    sum = reduce(lambda a, x: a + x, [0, 1, 2, 3, 4])

    print sum
    # => 10

`a` is the accumulator.  It is the value returned by the execution of the lambda on the previous item.  `x` is the current item.  `reduce()` walks through the items.  For each one, it runs the lambda on the current `a` and `x` and returns the result as the `a` of the next iteration.

What is `a` in the first iteration? There is no previous iteration result for it to pass along.  `reduce()` uses the first item in the collection for `a` in the first iteration and starts iterating at the second item.  That is, the first `x` is the second item.

This code counts how often the word `'Sam'` appears in a list of strings:

    sentences = ['Mary read a story to Sam and Isla.',
                 'Isla cuddled Sam.',
                 'Sam chortled.']

    sam_count = 0
    for sentence in sentences:
        sam_count += sentence.count('Sam')

    print sam_count
    # => 3

This is the same code written as a reduce:

    sentences = ['Mary read a story to Sam and Isla.',
                 'Isla cuddled Sam.',
                 'Sam chortled.']

    sam_count = reduce(lambda a, x: a + x.count('Sam'),
                       sentences,
                       0)

How does this code come up with its initial `a`? The starting point for the number of incidences of `Sam` can not be `Mary read a story to Sam and Isla.`.  The initial accumulator is specified with the third argument to `reduce`.  This allows the use of a value of a different type from the items in the collection.

Why are map and reduce better?

First, they are often one-liners.

Second, the important parts of the iteration - the collection, the operation and the return value - are always in the same places in every map and reduce.

Third, the code in a loop may affect variables defined before it or code that runs after it.  By convention, maps and reduces do not affect their surroundings.

Fourth, map and reduce are elemental operations.  Every time a person reads a `for` loop, they have to work through the logic line by line.  There are few structural regularities they can use to create a scaffolding on which to hang their understanding of the code.  In contrast, map, reduce and their friends are at once building blocks that can be combined into complex algorithms, and elements that the code reader can instantly understand and abstract in their mind.  "Ah, this code is transforming the items in this collection.  It's throwing some of the transformations away.  It's combining the remainder into a single output."

Try rewriting the code below using map, reduce and filter.  Filter takes a function and a collection.  It returns a collection of every item for which the function returned `True`.

    people = [{'name': 'Mary', 'height': 160},
              {'name': 'Isla', 'height': 80},
              {'name': 'Sam'}]

    height_total = 0
    height_count = 0
    for person in people:
        if 'height' in person:
            height_total += person['height']
            height_count += 1

    if height_count > 0:
        average_height = height_total / height_count

        print average_height
        # => 120

If this seems tricky, try not thinking about the operations on the data.  Think of the states the data will go through, from the list of people dictionaries to the average height.  Don't try and bundle multiple transformations together.  Put each on a separate line and assign the result to a descriptively-named variable.  Once the code works, condense it.

This is my solution:

    people = [{'name': 'Mary', 'height': 160},
              {'name': 'Isla', 'height': 80},
              {'name': 'Sam'}]

    heights = map(lambda x: x['height'],
                  filter(lambda x: 'height' in x, people))

    if len(heights) > 0:
        from operator import add
        average_height = reduce(add, heights) / len(heights)

## Write declaratively, not imperatively

The program below runs a race between three cars.  At each time step, each car may move forwards or it may stall.  At each time step, the program prints out the paths of the cars so far.  After five time steps, the race is over.

This is some sample output:

    -
    --
    --

    --
    --
    ---

    ---
    --
    ---

    ----
    ---
    ----

    ----
    ----
    -----

This is the program:

    from random import random

    time = 5
    car_positions = [0, 0, 0]

    while time:
        # decrease time
        time -= 1

        print ''
        for i in range(len(car_positions)):
            # move car
            if random() > 0.3:
                car_positions[i] += 1

            # draw car
            print '-' * car_positions[i]

The code is written imperatively.  A functional version would be declarative.  It would describe what to do, rather than how to do it.

### Use functions

A program can be made more declarative by bundling pieces of the code into functions.

    from random import random

    def move_cars():
        for i, _ in enumerate(car_positions):
            if random() > 0.3:
                car_positions[i] += 1

    def draw_car(car_position):
        print '-' * car_position

    def run_step_of_race():
        global time
        time -= 1
        move_cars()

    def draw():
        print ''
        for car_position in car_positions:
            draw_car(car_position)

    time = 5
    car_positions = [1, 1, 1]

    while time:
        run_step_of_race()
        draw()

To understand this program, the reader just reads the main loop.  "If there is time left, run a step of the race and draw.  Check the time again."  If the reader wants to understand more about what it means to run a step of the race, or draw, they can read the code in those functions.

There are no comments any more.  The code describes itself.

Splitting code into functions is a great, low brain power way to make code more readable.

This technique uses functions, but it uses them as sub-routines. They are parcels of code.  The code is not functional in the sense of the guide rope.  The functions in the code use state that was not passed as arguments.  They affect the code around them by changing external variables, rather than by returning values.  To check what a function really does, the reader must read each line carefully.  If they find an external variable, they must find its origin.  They must see what changes the function makes to that variable.  They must see what other functions change that variable.

### Remove state

This is a functional version of the car race code:

    from random import random

    def move_cars(car_positions):
        return map(lambda x: x + 1 if random() > 0.3 else x,
                   car_positions)

    def output_car(car_position):
        return '-' * car_position

    def run_step_of_race(state):
        return {'time': state['time'] - 1,
                'car_positions': move_cars(state['car_positions'])}

    def draw(state):
        print ''
        print '\n'.join(map(output_car, state['car_positions']))

    def race(state):
        draw(state)
        if state['time']:
            race(run_step_of_race(state))

    race({'time': 5,
          'car_positions': [1, 1, 1]})

The code is still split into functions, but the functions are functional.  There are three signs of this.  First, there are no longer any shared variables.  `time` and `car_positions` get passed straight into `race()`.  Second, functions take parameters.  Third, no variables are instantiated inside functions.  All data changes are done with return values.  `race()` recurses[3] with the result of `run_step_of_race()`.  Each time a step generates a new state, it is passed immediately into the next step.

It is not trivial to avoid mutating data.  `move_cars()` would have side effects if it did its work with a loop, rather than a map:

    from random import random

    def move_cars(car_positions):
        for i, _ in enumerate(car_positions):
            if random() > 0.3:
                car_positions[i] += 1
        return car_positions

This version of `move_cars()` returns `car_positions`, but it also mutates the same instance it is passed.  If the function that calls `move_cars()` uses the passed in `car_positions` for some work after calling `move_cars()`, it will find its toes have been stepped on.

Now imagine a function called `rule_sequence()`.  It takes a data string and some rule functions.  It calls the first rule on the data.  Unless `None` is returned, it takes the return value and calls the second rule on it.  Unless `None` is returned, it takes the return value and calls the third rule on it.  And so forth.  If any rule returns `None`, `rule_sequence()` returns `None`.  Otherwise, it returns the return value of the last rule.

This is some sample input and output:

    print rule_sequence('abcd', [lambda x: x[1:],
                                 lambda x: x[1:],
                                 lambda x: x[1:]])
    # => d

This is the imperative, non-functional version of `rule_sequence()`:

    def rule_sequence(data, rules):
        for rule in rules:
            data = rule(data)
            if data == None:
                break

        return data

Try and rewrite it in a functional style.

Remember.  No shared variables.  Pass state via arguments and return values.  Use recursion for repeated operations.

This is my solution:

    def rule_sequence(data, rules):
        if not rules:
            return data

        rule_return = rules[0](data)
        if rule_return != None:
            return rule_sequence(rule_return, rules[1:])

## Use pipelines

In the previous section, some imperative loops were rewritten as recursions that called out to auxiliary functions.  In this section, a different type of imperative loop will be rewritten using a technique called a pipeline.

The loop below performs transformations on dictionaries that hold the name and active status of some bands.

    bands = [{'name': 'sunset rubdown', 'active': False},
             {'name': 'women', 'active': False},
             {'name': 'a silver mt. zion', 'active': True}]

    def format_bands(bands):
        for band in bands:
            band['country'] = 'Canada'

            for key in band:
                if isinstance(band[key], basestring):
                    band[key] = band[key].replace('.', '')

            band['name'] = ' '.join([word.capitalize()
                                     for word in band['name'].split()])

    format_bands(bands)

    print bands
    # => [{'name': 'Sunset Rubdown', 'active': False, 'country': 'Canada'},
    #     {'name': 'Women', 'active': False, 'country': 'Canada' },
    #     {'name': 'A Silver Mt Zion', 'active': True, 'country': 'Canada'}]

Worries are stirred by the name of the function.  "format" is very vague.  Upon closer inspection of the code, these worries begin to claw.  Three things happen in the same loop.  A `'country: 'Canada'` key/value pair gets added.  Punctuation is removed from dictionary values.  Band names get capitalized.  It is hard to tell what the code is intended to do and hard to tell if it does what it appears to do.  The code is hard to reuse, hard to test and hard to parallelize.

Compare it with this:

    print pipeline_each(bands, [insert_canada,
                                strip_punctuation,
                                uppercase_names])

This code is easy to understand.  It gives the impression that the auxiliary functions are functional because they seem to be chained together.  The output from the previous one comprises the input to the next.  If they are functional, they are easy to verify.  They are also easy to reuse, easy to test and easy to parallelize.

The job of `pipeline_each()` is to pass the bands, one at a time, to a transformation function.  After the transformation function has been applied to all the bands, it bundles up the transformed bands.  Then it passes each one to the next transformation function.

    def pipeline_each(data, fns):
        return reduce(lambda a, x: map(x, a),
                      fns,
                      data)

These are the auxiliary functions:

    def assoc(_d, key, value):
        from copy import deepcopy
        d = deepcopy(_d)
        d[key] = value
        return d

    def strip_punctuation(band):
        def strip_if_string(band, (k, v)):
            return assoc(band, k, v.replace('.', '')) if isinstance(v, str) else band
        return reduce(strip_if_string, band.items(), band)

    def uppercase_names(band):
        return assoc(band,
                     'name',
                     ' '.join([word.capitalize()
                               for word in band['name'].split()]))

    def insert_canada(band):
        return assoc(band, 'country', "Canada")

Note the presence of `deepcopy()` in `assoc()`.  The car code was able to use normal Python operations to make copies of data passed in arguments.  The auxiliary functions deal with dictionaries.  There is no easy way to modify a dictionary without mutating it.  `assoc()` solves this problem by using `deepcopy()` to produce a copy of the passed dictionary.  Each function makes its modification to the copy and returns it.

`uppercase_names()` and `insert_canada()` boil down to applying a transformation to a particular field on the passed band.  `call()` can be used to abstract that process.  It takes a function to apply and the key of the value to apply it to:

    print pipeline_each(bands, [call(lambda x: 'Canada', 'country'),
                                strip_punctuation,
                                call(lambda x: " ".join([y.capitalize()
                                                         for y in x.split()]),
                                     'name')])

The code for `call()`:

    def assoc(_d, key, value):
        from copy import deepcopy
        d = deepcopy(_d)
        d[key] = value
        return d

    def call(fn, key):
        def apply_fn(record):
            return assoc(record, key, fn(record.get(key)))
        return apply_fn

There is a lot going on here.  Let's take it piece by piece.

One.  `call()` is a higher order function.  A higher order function takes a function as an argument.  Or it returns a function.  Or, like `call()`, it does both.

Two.  `apply_fn()` looks very similar to `uppercase_names()` and `insert_canada()`.  It takes a record (a band).  It looks up the value at `record[key]`.  It calls `fn` on that value.  It assigns the result back to a copy of the record.  It returns the copy.

Three.  `call()` does not do any actual work.  `apply_fn()`, when called, will do the work.  In the example of using `pipeline_each()` above, one instance of `apply_fn()` will set `'country'` to 'Canada'` on each band.  Another instance will capitalize the names of each band.

Four.  When an `apply_fn()` instance is called, it will be out of the scope of the `call()` invocation that created it.  This seems to mean that it will not have access to `fn` and `key`.  But it will, because `apply_fn()` is a closure.  When a function is defined, Python saves references to the closed over variables: those that were defined in a scope outside the closure and that are used inside the closure.  When the closure is called and its code refers to a variable, Python determines if it was defined inside the closure.  If it wasn't, it will look in the saved references to closed over variables.  This is where it will find `fn` and `key`.

Five.  There is no mention of bands in the `call()` code.  That is because `call()` could be used to generate pipeline functions for any program, regardless of topic.  Functional programming is partly about building up a library of generic, reusable, composable functions.

Good job.  Closures, higher order functions and variable scope all covered in the space of a few paragraphs.  Have a nice lie down.

There is one more piece of band processing to do.  That is to remove everything but the name and country.  `extract_name_and_country()` can pull that information out:

    def extract_name_and_country(record):
        plucked_record = {}
        plucked_record['name'] = record['name']
        plucked_record['country'] = record['country']
        return plucked_record

    print pipeline_each(bands, [call(lambda x: 'Canada', 'country'),
                                strip_punctuation,
                                call(lambda x: " ".join([y.capitalize()
                                                         for y in x.split()]),
                                     'name'),
                                extract_name_and_country])

    # => [{'name': 'Sunset Rubdown', 'country': 'Canada'},
    #     {'name': 'Women', 'country': 'Canada'},
    #     {'name': 'A Silver Mt Zion', 'country': 'Canada'}]

`extract_name_and_country()` could have been written as a generic function called `pluck()`.  `pluck()` takes a list of keys to extract from each record.  Try and write it.  It will need to be a higher order function.

Here is my solution:

    def pluck(keys):
        def pluck_fn(record):
            plucked_record = {}
            for key in keys:
                plucked_record[key] = record[key]
            return plucked_record
        return pluck_fn

## What now?

A loop can be made into a map or a reduce.  Imperative code can be made into a recursion supported by functional functions.  A sequence of operations can be made into a pipeline.

The transformations in this article can be applied to any code base in any language.  Functional code co-exists very well with code written in other styles.

Try applying the transformations in this article to your own code.

------------

[1] An immutable piece of data is one that cannot be changed.  Some languages, like Clojure, make all values immutable by default.  Any "mutating" operations copy the value, change it and pass back the changed copy.  This eliminates bugs that arise from a programmer's incomplete model of the possible states their program may enter.

[2] Languages that support first class functions allow functions to be treated like any other value.  This means they can be created, passed to functions, returned from functions and stored inside data structures.

[3] Tail call optimisation is a programming language feature.  Each time a function recurses, a new stack frame is created.  A stack frame is used to store the arguments and local values for the current function invocation.  If a function recurses a large number of times, it is possible for the interpreter or compiler to run out of memory.  Languages with tail call optimisation reuse the same stack frame for their entire sequence of recursive calls.  Languages like Python that do not have tail call optimisation generally limit the number of times a function may recurse to some number in the thousands.  In the case of the `race()` function, there are only five time steps, so it is safe.

[4] Currying means decomposing a function that takes multiple arguments into a function that takes the first argument and returns a function that takes the next argument, and so forth for all the arguments.

[5] Parallelization means running the same code concurrently without synchronization.  These concurrent processes are often run on multiple processors.

[6] Lazy evaluation is a compiler technique that avoids running code until the result is needed.

[7] A process is deterministic if repetitions yield the same result every time.