Introduction¶

This section explains the basic concept of functional programming; if you’re just interested in learning about Python language features, skip to the next section.

Programming languages support decomposing problems in several different ways:

• Most programming languages are procedural: programs are lists of instructions that tell the computer what to do with the program’s input. C, Pascal, and even Unix shells are procedural languages.

• In declarative languages, you write a specification that describes the problem to be solved, and the language implementation figures out how to perform the computation efficiently. SQL is the declarative language you’re most likely to be familiar with; a SQL query describes the data set you want to retrieve, and the SQL engine decides whether to scan tables or use indexes, which subclauses should be performed first, etc.

• Object-oriented programs manipulate collections of objects. Objects have internal state and support methods that query or modify this internal state in some way. Smalltalk and Java are object-oriented languages. C++ and Python are languages that support object-oriented programming, but don’t force the use of object-oriented features.

• Functional programming decomposes a problem into a set of functions. Ideally, functions only take inputs and produce outputs, and don’t have any internal state that affects the output produced for a given input. Well-known functional languages include the ML family (Standard ML, OCaml, and other variants) and Haskell.

The designers of some computer languages choose to emphasize one particular approach to programming. This often makes it difficult to write programs that use a different approach. Other languages are multi-paradigm languages that support several different approaches. Lisp, C++, and Python are multi-paradigm; you can write programs or libraries that are largely procedural, object-oriented, or functional in all of these languages. In a large program, different sections might be written using different approaches; the GUI might be object-oriented while the processing logic is procedural or functional, for example.

In a functional program, input flows through a set of functions. Each function operates on its input and produces some output. Functional style discourages functions with side effects that modify internal state or make other changes that aren’t visible in the function’s return value. Functions that have no side effects at all are called purely functional. Avoiding side effects means not using data structures that get updated as a program runs; every function’s output must only depend on its input.

Some languages are very strict about purity and don’t even have assignment statements such as a=3 or c = a + b, but it’s difficult to avoid all side effects. Printing to the screen or writing to a disk file are side effects, for example. For example, in Python a print statement or a time.sleep(1) both return no useful value; they’re only called for their side effects of sending some text to the screen or pausing execution for a second.

Python programs written in functional style usually won’t go to the extreme of avoiding all I/O or all assignments; instead, they’ll provide a functional-appearing interface but will use non-functional features internally. For example, the implementation of a function will still use assignments to local variables, but won’t modify global variables or have other side effects.

Functional programming can be considered the opposite of object-oriented programming. Objects are little capsules containing some internal state along with a collection of method calls that let you modify this state, and programs consist of making the right set of state changes. Functional programming wants to avoid state changes as much as possible and works with data flowing between functions. In Python you might combine the two approaches by writing functions that take and return instances representing objects in your application (e-mail messages, transactions, etc.).

Functional design may seem like an odd constraint to work under. Why should you avoid objects and side effects? There are theoretical and practical advantages to the functional style:

• Formal provability.

• Modularity.

• Composability.

• Ease of debugging and testing.

Iterators¶

I’ll start by looking at a Python language feature that’s an important foundation for writing functional-style programs: iterators.

An iterator is an object representing a stream of data; this object returns the data one element at a time. A Python iterator must support a method called next() that takes no arguments and always returns the next element of the stream. If there are no more elements in the stream, next() must raise the StopIteration exception. Iterators don’t have to be finite, though; it’s perfectly reasonable to write an iterator that produces an infinite stream of data.

The built-in iter() function takes an arbitrary object and tries to return an iterator that will return the object’s contents or elements, raising TypeError if the object doesn’t support iteration. Several of Python’s built-in data types support iteration, the most common being lists and dictionaries. An object is called an iterable object if you can get an iterator for it.

You can experiment with the iteration interface manually:

>>> L = [1,2,3]
>>> it = iter(L)
>>> print it
<...iterator object at ...>
>>> it.next()
1
>>> it.next()
2
>>> it.next()
3
>>> it.next()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
StopIteration
>>>

Python expects iterable objects in several different contexts, the most important being the for statement. In the statement for X in Y, Y must be an iterator or some object for which iter() can create an iterator. These two statements are equivalent:

for i in iter(obj):
    print i

for i in obj:
    print i

Iterators can be materialized as lists or tuples by using the list() or tuple() constructor functions:

>>> L = [1,2,3]
>>> iterator = iter(L)
>>> t = tuple(iterator)
>>> t
(1, 2, 3)

Sequence unpacking also supports iterators: if you know an iterator will return N elements, you can unpack them into an N-tuple:

>>> L = [1,2,3]
>>> iterator = iter(L)
>>> a,b,c = iterator
>>> a,b,c
(1, 2, 3)

Built-in functions such as max() and min() can take a single iterator argument and will return the largest or smallest element. The "in" and "not in" operators also support iterators: X in iterator is true if X is found in the stream returned by the iterator. You’ll run into obvious problems if the iterator is infinite; max(), min() will never return, and if the element X never appears in the stream, the "in" and "not in" operators won’t return either.

Note that you can only go forward in an iterator; there’s no way to get the previous element, reset the iterator, or make a copy of it. Iterator objects can optionally provide these additional capabilities, but the iterator protocol only specifies the next() method. Functions may therefore consume all of the iterator’s output, and if you need to do something different with the same stream, you’ll have to create a new iterator.

>>> m = {'Jan': 1, 'Feb': 2, 'Mar': 3, 'Apr': 4, 'May': 5, 'Jun': 6,
...      'Jul': 7, 'Aug': 8, 'Sep': 9, 'Oct': 10, 'Nov': 11, 'Dec': 12}
>>> for key in m:
...     print key, m[key]
Mar 3
Feb 2
Aug 8
Sep 9
Apr 4
Jun 6
Jul 7
Jan 1
May 5
Nov 11
Dec 12
Oct 10

>>> L = [('Italy', 'Rome'), ('France', 'Paris'), ('US', 'Washington DC')]
>>> dict(iter(L))
{'Italy': 'Rome', 'US': 'Washington DC', 'France': 'Paris'}

for line in file:
    # do something for each line
    ...

S = set((2, 3, 5, 7, 11, 13))
for i in S:
    print i

Generator expressions and list comprehensions¶

Two common operations on an iterator’s output are 1) performing some operation for every element, 2) selecting a subset of elements that meet some condition. For example, given a list of strings, you might want to strip off trailing whitespace from each line or extract all the strings containing a given substring.

List comprehensions and generator expressions (short form: “listcomps” and “genexps”) are a concise notation for such operations, borrowed from the functional programming language Haskell (https://www.haskell.org/). You can strip all the whitespace from a stream of strings with the following code:

line_list = ['  line 1\n', 'line 2  \n', ...]

# Generator expression -- returns iterator
stripped_iter = (line.strip() for line in line_list)

# List comprehension -- returns list
stripped_list = [line.strip() for line in line_list]

You can select only certain elements by adding an "if" condition:

stripped_list = [line.strip() for line in line_list
                 if line != ""]

With a list comprehension, you get back a Python list; stripped_list is a list containing the resulting lines, not an iterator. Generator expressions return an iterator that computes the values as necessary, not needing to materialize all the values at once. This means that list comprehensions aren’t useful if you’re working with iterators that return an infinite stream or a very large amount of data. Generator expressions are preferable in these situations.

Generator expressions are surrounded by parentheses (“()”) and list comprehensions are surrounded by square brackets (“[]”). Generator expressions have the form:

( expression for expr in sequence1
             if condition1
             for expr2 in sequence2
             if condition2
             for expr3 in sequence3 ...
             if condition3
             for exprN in sequenceN
             if conditionN )

Again, for a list comprehension only the outside brackets are different (square brackets instead of parentheses).

The elements of the generated output will be the successive values of expression. The if clauses are all optional; if present, expression is only evaluated and added to the result when condition is true.

Generator expressions always have to be written inside parentheses, but the parentheses signalling a function call also count. If you want to create an iterator that will be immediately passed to a function you can write:

obj_total = sum(obj.count for obj in list_all_objects())

The for...in clauses contain the sequences to be iterated over. The sequences do not have to be the same length, because they are iterated over from left to right, not in parallel. For each element in sequence1, sequence2 is looped over from the beginning. sequence3 is then looped over for each resulting pair of elements from sequence1 and sequence2.

To put it another way, a list comprehension or generator expression is equivalent to the following Python code:

for expr1 in sequence1:
    if not (condition1):
        continue   # Skip this element
    for expr2 in sequence2:
        if not (condition2):
            continue   # Skip this element
        ...
        for exprN in sequenceN:
            if not (conditionN):
                continue   # Skip this element

            # Output the value of
            # the expression.

This means that when there are multiple for...in clauses but no if clauses, the length of the resulting output will be equal to the product of the lengths of all the sequences. If you have two lists of length 3, the output list is 9 elements long:

>>> seq1 = 'abc'
>>> seq2 = (1,2,3)
>>> [(x,y) for x in seq1 for y in seq2]
[('a', 1), ('a', 2), ('a', 3),
 ('b', 1), ('b', 2), ('b', 3),
 ('c', 1), ('c', 2), ('c', 3)]

To avoid introducing an ambiguity into Python’s grammar, if expression is creating a tuple, it must be surrounded with parentheses. The first list comprehension below is a syntax error, while the second one is correct:

# Syntax error
[ x,y for x in seq1 for y in seq2]
# Correct
[ (x,y) for x in seq1 for y in seq2]

Generators¶

Generators are a special class of functions that simplify the task of writing iterators. Regular functions compute a value and return it, but generators return an iterator that returns a stream of values.

You’re doubtless familiar with how regular function calls work in Python or C. When you call a function, it gets a private namespace where its local variables are created. When the function reaches a return statement, the local variables are destroyed and the value is returned to the caller. A later call to the same function creates a new private namespace and a fresh set of local variables. But, what if the local variables weren’t thrown away on exiting a function? What if you could later resume the function where it left off? This is what generators provide; they can be thought of as resumable functions.

Here’s the simplest example of a generator function:

def generate_ints(N):
    for i in range(N):
        yield i

Any function containing a yield keyword is a generator function; this is detected by Python’s bytecode compiler which compiles the function specially as a result.

When you call a generator function, it doesn’t return a single value; instead it returns a generator object that supports the iterator protocol. On executing the yield expression, the generator outputs the value of i, similar to a return statement. The big difference between yield and a return statement is that on reaching a yield the generator’s state of execution is suspended and local variables are preserved. On the next call to the generator’s .next() method, the function will resume executing.

Here’s a sample usage of the generate_ints() generator:

>>> gen = generate_ints(3)
>>> gen
<generator object generate_ints at ...>
>>> gen.next()
0
>>> gen.next()
1
>>> gen.next()
2
>>> gen.next()
Traceback (most recent call last):
  File "stdin", line 1, in <module>
  File "stdin", line 2, in generate_ints
StopIteration

You could equally write for i in generate_ints(5), or a,b,c = generate_ints(3).

Inside a generator function, the return statement can only be used without a value, and signals the end of the procession of values; after executing a return the generator cannot return any further values. return with a value, such as return 5, is a syntax error inside a generator function. The end of the generator’s results can also be indicated by raising StopIteration manually, or by just letting the flow of execution fall off the bottom of the function.

You could achieve the effect of generators manually by writing your own class and storing all the local variables of the generator as instance variables. For example, returning a list of integers could be done by setting self.count to 0, and having the next() method increment self.count and return it. However, for a moderately complicated generator, writing a corresponding class can be much messier.

The test suite included with Python’s library, test_generators.py, contains a number of more interesting examples. Here’s one generator that implements an in-order traversal of a tree using generators recursively.

# A recursive generator that generates Tree leaves in in-order.
def inorder(t):
    if t:
        for x in inorder(t.left):
            yield x

        yield t.label

        for x in inorder(t.right):
            yield x

Two other examples in test_generators.py produce solutions for the N-Queens problem (placing N queens on an NxN chess board so that no queen threatens another) and the Knight’s Tour (finding a route that takes a knight to every square of an NxN chessboard without visiting any square twice).

val = (yield i)

def counter (maximum):
    i = 0
    while i < maximum:
        val = (yield i)
        # If value provided, change counter
        if val is not None:
            i = val
        else:
            i += 1

>>> it = counter(10)
>>> print it.next()
0
>>> print it.next()
1
>>> print it.send(8)
8
>>> print it.next()
9
>>> print it.next()
Traceback (most recent call last):
  File "t.py", line 15, in <module>
    print it.next()
StopIteration

Built-in functions¶

Let’s look in more detail at built-in functions often used with iterators.

Two of Python’s built-in functions, map() and filter(), are somewhat obsolete; they duplicate the features of list comprehensions but return actual lists instead of iterators.

map(f, iterA, iterB, ...) returns a list containing f(iterA[0], iterB[0]), f(iterA[1], iterB[1]), f(iterA[2], iterB[2]), ....

>>> def upper(s):
...     return s.upper()

>>> map(upper, ['sentence', 'fragment'])
['SENTENCE', 'FRAGMENT']

>>> [upper(s) for s in ['sentence', 'fragment']]
['SENTENCE', 'FRAGMENT']

As shown above, you can achieve the same effect with a list comprehension. The itertools.imap() function does the same thing but can handle infinite iterators; it’ll be discussed later, in the section on the itertools module.

filter(predicate, iter) returns a list that contains all the sequence elements that meet a certain condition, and is similarly duplicated by list comprehensions. A predicate is a function that returns the truth value of some condition; for use with filter(), the predicate must take a single value.

>>> def is_even(x):
...     return (x % 2) == 0

>>> filter(is_even, range(10))
[0, 2, 4, 6, 8]

This can also be written as a list comprehension:

>>> [x for x in range(10) if is_even(x)]
[0, 2, 4, 6, 8]

filter() also has a counterpart in the itertools module, itertools.ifilter(), that returns an iterator and can therefore handle infinite sequences just as itertools.imap() can.

reduce(func, iter, [initial_value]) doesn’t have a counterpart in the itertools module because it cumulatively performs an operation on all the iterable’s elements and therefore can’t be applied to infinite iterables. func must be a function that takes two elements and returns a single value. reduce() takes the first two elements A and B returned by the iterator and calculates func(A, B). It then requests the third element, C, calculates func(func(A, B), C), combines this result with the fourth element returned, and continues until the iterable is exhausted. If the iterable returns no values at all, a TypeError exception is raised. If the initial value is supplied, it’s used as a starting point and func(initial_value, A) is the first calculation.

>>> import operator
>>> reduce(operator.concat, ['A', 'BB', 'C'])
'ABBC'
>>> reduce(operator.concat, [])
Traceback (most recent call last):
  ...
TypeError: reduce() of empty sequence with no initial value
>>> reduce(operator.mul, [1,2,3], 1)
6
>>> reduce(operator.mul, [], 1)
1

If you use operator.add() with reduce(), you’ll add up all the elements of the iterable. This case is so common that there’s a special built-in called sum() to compute it:

>>> reduce(operator.add, [1,2,3,4], 0)
10
>>> sum([1,2,3,4])
10
>>> sum([])
0

For many uses of reduce(), though, it can be clearer to just write the obvious for loop:

# Instead of:
product = reduce(operator.mul, [1,2,3], 1)

# You can write:
product = 1
for i in [1,2,3]:
    product *= i

enumerate(iter) counts off the elements in the iterable, returning 2-tuples containing the count and each element.

>>> for item in enumerate(['subject', 'verb', 'object']):
...     print item
(0, 'subject')
(1, 'verb')
(2, 'object')

enumerate() is often used when looping through a list and recording the indexes at which certain conditions are met:

f = open('data.txt', 'r')
for i, line in enumerate(f):
    if line.strip() == '':
        print 'Blank line at line #%i' % i

sorted(iterable, [cmp=None], [key=None], [reverse=False]) collects all the elements of the iterable into a list, sorts the list, and returns the sorted result. The cmp, key, and reverse arguments are passed through to the constructed list’s .sort() method.

>>> import random
>>> # Generate 8 random numbers between [0, 10000)
>>> rand_list = random.sample(range(10000), 8)
>>> rand_list
[769, 7953, 9828, 6431, 8442, 9878, 6213, 2207]
>>> sorted(rand_list)
[769, 2207, 6213, 6431, 7953, 8442, 9828, 9878]
>>> sorted(rand_list, reverse=True)
[9878, 9828, 8442, 7953, 6431, 6213, 2207, 769]

(For a more detailed discussion of sorting, see the Sorting mini-HOWTO in the Python wiki at https://wiki.python.org/moin/HowTo/Sorting.)

The any(iter) and all(iter) built-ins look at the truth values of an iterable’s contents. any() returns True if any element in the iterable is a true value, and all() returns True if all of the elements are true values:

>>> any([0,1,0])
True
>>> any([0,0,0])
False
>>> any([1,1,1])
True
>>> all([0,1,0])
False
>>> all([0,0,0])
False
>>> all([1,1,1])
True

Small functions and the lambda expression¶

When writing functional-style programs, you’ll often need little functions that act as predicates or that combine elements in some way.

If there’s a Python built-in or a module function that’s suitable, you don’t need to define a new function at all:

stripped_lines = [line.strip() for line in lines]
existing_files = filter(os.path.exists, file_list)

If the function you need doesn’t exist, you need to write it. One way to write small functions is to use the lambda statement. lambda takes a number of parameters and an expression combining these parameters, and creates a small function that returns the value of the expression:

lowercase = lambda x: x.lower()

print_assign = lambda name, value: name + '=' + str(value)

adder = lambda x, y: x+y

An alternative is to just use the def statement and define a function in the usual way:

def lowercase(x):
    return x.lower()

def print_assign(name, value):
    return name + '=' + str(value)

def adder(x,y):
    return x + y

Which alternative is preferable? That’s a style question; my usual course is to avoid using lambda.

One reason for my preference is that lambda is quite limited in the functions it can define. The result has to be computable as a single expression, which means you can’t have multiway if... elif... else comparisons or try... except statements. If you try to do too much in a lambda statement, you’ll end up with an overly complicated expression that’s hard to read. Quick, what’s the following code doing?

total = reduce(lambda a, b: (0, a[1] + b[1]), items)[1]

You can figure it out, but it takes time to disentangle the expression to figure out what’s going on. Using a short nested def statements makes things a little bit better:

def combine (a, b):
    return 0, a[1] + b[1]

total = reduce(combine, items)[1]

But it would be best of all if I had simply used a for loop:

total = 0
for a, b in items:
    total += b

Or the sum() built-in and a generator expression:

total = sum(b for a,b in items)

Many uses of reduce() are clearer when written as for loops.

Fredrik Lundh once suggested the following set of rules for refactoring uses of lambda:

1. Write a lambda function.

2. Write a comment explaining what the heck that lambda does.

3. Study the comment for a while, and think of a name that captures the essence of the comment.

4. Convert the lambda to a def statement, using that name.

5. Remove the comment.

I really like these rules, but you’re free to disagree about whether this lambda-free style is better.

The itertools module¶

The itertools module contains a number of commonly-used iterators as well as functions for combining several iterators. This section will introduce the module’s contents by showing small examples.

The module’s functions fall into a few broad classes:

• Functions that create a new iterator based on an existing iterator.

• Functions for treating an iterator’s elements as function arguments.

• Functions for selecting portions of an iterator’s output.

• A function for grouping an iterator’s output.

itertools.count() =>
  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
itertools.count(10) =>
  10, 11, 12, 13, 14, 15, 16, 17, 18, 19, ...

itertools.cycle([1,2,3,4,5]) =>
  1, 2, 3, 4, 5, 1, 2, 3, 4, 5, ...

itertools.repeat('abc') =>
  abc, abc, abc, abc, abc, abc, abc, abc, abc, abc, ...
itertools.repeat('abc', 5) =>
  abc, abc, abc, abc, abc

itertools.chain(['a', 'b', 'c'], (1, 2, 3)) =>
  a, b, c, 1, 2, 3

itertools.izip(['a', 'b', 'c'], (1, 2, 3)) =>
  ('a', 1), ('b', 2), ('c', 3)

itertools.izip(['a', 'b'], (1, 2, 3)) =>
  ('a', 1), ('b', 2)

itertools.islice(range(10), 8) =>
  0, 1, 2, 3, 4, 5, 6, 7
itertools.islice(range(10), 2, 8) =>
  2, 3, 4, 5, 6, 7
itertools.islice(range(10), 2, 8, 2) =>
  2, 4, 6

itertools.tee( itertools.count() ) =>
   iterA, iterB

where iterA ->
   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...

and   iterB ->
   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...

itertools.imap(operator.add, [5, 6, 5], [1, 2, 3]) =>
  6, 8, 8

itertools.starmap(os.path.join,
                  [('/usr', 'bin', 'java'), ('/bin', 'python'),
                   ('/usr', 'bin', 'perl'),('/usr', 'bin', 'ruby')])
=>
  /usr/bin/java, /bin/python, /usr/bin/perl, /usr/bin/ruby

def is_even(x):
    return (x % 2) == 0

itertools.ifilter(is_even, itertools.count()) =>
  0, 2, 4, 6, 8, 10, 12, 14, ...

itertools.ifilterfalse(is_even, itertools.count()) =>
  1, 3, 5, 7, 9, 11, 13, 15, ...

def less_than_10(x):
    return (x < 10)

itertools.takewhile(less_than_10, itertools.count()) =>
  0, 1, 2, 3, 4, 5, 6, 7, 8, 9

itertools.takewhile(is_even, itertools.count()) =>
  0

itertools.dropwhile(less_than_10, itertools.count()) =>
  10, 11, 12, 13, 14, 15, 16, 17, 18, 19, ...

itertools.dropwhile(is_even, itertools.count()) =>
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...

city_list = [('Decatur', 'AL'), ('Huntsville', 'AL'), ('Selma', 'AL'),
             ('Anchorage', 'AK'), ('Nome', 'AK'),
             ('Flagstaff', 'AZ'), ('Phoenix', 'AZ'), ('Tucson', 'AZ'),
             ...
            ]

def get_state ((city, state)):
    return state

itertools.groupby(city_list, get_state) =>
  ('AL', iterator-1),
  ('AK', iterator-2),
  ('AZ', iterator-3), ...

where
iterator-1 =>
  ('Decatur', 'AL'), ('Huntsville', 'AL'), ('Selma', 'AL')
iterator-2 =>
  ('Anchorage', 'AK'), ('Nome', 'AK')
iterator-3 =>
  ('Flagstaff', 'AZ'), ('Phoenix', 'AZ'), ('Tucson', 'AZ')

The functools module¶

The functools module in Python 2.5 contains some higher-order functions. A higher-order function takes one or more functions as input and returns a new function. The most useful tool in this module is the functools.partial() function.

For programs written in a functional style, you’ll sometimes want to construct variants of existing functions that have some of the parameters filled in. Consider a Python function f(a, b, c); you may wish to create a new function g(b, c) that’s equivalent to f(1, b, c); you’re filling in a value for one of f()’s parameters. This is called “partial function application”.

The constructor for partial takes the arguments (function, arg1, arg2, ... kwarg1=value1, kwarg2=value2). The resulting object is callable, so you can just call it to invoke function with the filled-in arguments.

Here’s a small but realistic example:

import functools

def log (message, subsystem):
    "Write the contents of 'message' to the specified subsystem."
    print '%s: %s' % (subsystem, message)
    ...

server_log = functools.partial(log, subsystem='server')
server_log('Unable to open socket')

Revision History and Acknowledgements¶

The author would like to thank the following people for offering suggestions, corrections and assistance with various drafts of this article: Ian Bicking, Nick Coghlan, Nick Efford, Raymond Hettinger, Jim Jewett, Mike Krell, Leandro Lameiro, Jussi Salmela, Collin Winter, Blake Winton.

Version 0.1: posted June 30 2006.

Version 0.11: posted July 1 2006. Typo fixes.

Version 0.2: posted July 10 2006. Merged genexp and listcomp sections into one. Typo fixes.

Version 0.21: Added more references suggested on the tutor mailing list.

Version 0.30: Adds a section on the functional module written by Collin Winter; adds short section on the operator module; a few other edits.

References¶