Functional Programming HOWTO

Functional Programming HOWTO¶
- Author:
A. M. Kuchling
- Release:
0.32
In this document, we’ll take a tour of Python’s features suitable for
implementing programs in a functional style. After an introduction to the
concepts of functional programming, we’ll look at language features such as
iterators and generators and relevant library modules such as
itertools
and functools
.
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 on Iterators.
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, such as printing to the screen or writing to a disk file. Another
example is a call to the print()
or time.sleep()
function, neither
of which returns a useful value. Both are called only 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.
Formal provability¶
A theoretical benefit is that it’s easier to construct a mathematical proof that a functional program is correct.
For a long time researchers have been interested in finding ways to mathematically prove programs correct. This is different from testing a program on numerous inputs and concluding that its output is usually correct, or reading a program’s source code and concluding that the code looks right; the goal is instead a rigorous proof that a program produces the right result for all possible inputs.
The technique used to prove programs correct is to write down invariants, properties of the input data and of the program’s variables that are always true. For each line of code, you then show that if invariants X and Y are true before the line is executed, the slightly different invariants X’ and Y’ are true after the line is executed. This continues until you reach the end of the program, at which point the invariants should match the desired conditions on the program’s output.
Functional programming’s avoidance of assignments arose because assignments are difficult to handle with this technique; assignments can break invariants that were true before the assignment without producing any new invariants that can be propagated onward.
Unfortunately, proving programs correct is largely impractical and not relevant to Python software. Even trivial programs require proofs that are several pages long; the proof of correctness for a moderately complicated program would be enormous, and few or none of the programs you use daily (the Python interpreter, your XML parser, your web browser) could be proven correct. Even if you wrote down or generated a proof, there would then be the question of verifying the proof; maybe there’s an error in it, and you wrongly believe you’ve proved the program correct.
Modularity¶
A more practical benefit of functional programming is that it forces you to break apart your problem into small pieces. Programs are more modular as a result. It’s easier to specify and write a small function that does one thing than a large function that performs a complicated transformation. Small functions are also easier to read and to check for errors.
Ease of debugging and testing¶
Testing and debugging a functional-style program is easier.
Debugging is simplified because functions are generally small and clearly specified. When a program doesn’t work, each function is an interface point where you can check that the data are correct. You can look at the intermediate inputs and outputs to quickly isolate the function that’s responsible for a bug.
Testing is easier because each function is a potential subject for a unit test. Functions don’t depend on system state that needs to be replicated before running a test; instead you only have to synthesize the right input and then check that the output matches expectations.
Composability¶
As you work on a functional-style program, you’ll write a number of functions with varying inputs and outputs. Some of these functions will be unavoidably specialized to a particular application, but others will be useful in a wide variety of programs. For example, a function that takes a directory path and returns all the XML files in the directory, or a function that takes a filename and returns its contents, can be applied to many different situations.
Over time you’ll form a personal library of utilities. Often you’ll assemble new programs by arranging existing functions in a new configuration and writing a few functions specialized for the current task.
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 iterable if you can get an iterator
for it.
You can experiment with the iteration interface manually:
>>> L = [1, 2, 3]
>>> it = iter(L)
>>> it
<...iterator object at ...>
>>> it.__next__() # same as next(it)
1
>>> next(it)
2
>>> next(it)
3
>>> next(it)
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.
Data Types That Support Iterators¶
We’ve already seen how lists and tuples support iterators. In fact, any Python sequence type, such as strings, will automatically support creation of an iterator.
Calling iter()
on a dictionary returns an iterator that will loop over the
dictionary’s keys:
>>> 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])
Jan 1
Feb 2
Mar 3
Apr 4
May 5
Jun 6
Jul 7
Aug 8
Sep 9
Oct 10
Nov 11
Dec 12
Note that starting with Python 3.7, dictionary iteration order is guaranteed to be the same as the insertion order. In earlier versions, the behaviour was unspecified and could vary between implementations.
Applying iter()
to a dictionary always loops over the keys, but
dictionaries have methods that return other iterators. If you want to iterate
over values or key/value pairs, you can explicitly call the
values()
or items()
methods to get an appropriate
iterator.
The dict()
constructor can accept an iterator that returns a finite stream
of (key, value)
tuples:
>>> L = [('Italy', 'Rome'), ('France', 'Paris'), ('US', 'Washington DC')]
>>> dict(iter(L))
{'Italy': 'Rome', 'France': 'Paris', 'US': 'Washington DC'}
Files also support iteration by calling the readline()
method until there are no more lines in the file. This means you can read each
line of a file like this:
for line in file:
# do something for each line
...
Sets can take their contents from an iterable and let you iterate over the set’s elements:
>>> S = {2, 3, 5, 7, 11, 13}
>>> for i in S:
... print(i)
2
3
5
7
11
13
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', ' \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 ...>
>>> next(gen)
0
>>> next(gen)
1
>>> next(gen)
2
>>> next(gen)
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, return value
causes StopIteration(value)
to be raised from the __next__()
method. Once this happens, or
the bottom of the function is reached, the procession of values ends and the
generator cannot yield any further values.
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, Lib/test/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).
Passing values into a generator¶
In Python 2.4 and earlier, generators only produced output. Once a generator’s code was invoked to create an iterator, there was no way to pass any new information into the function when its execution is resumed. You could hack together this ability by making the generator look at a global variable or by passing in some mutable object that callers then modify, but these approaches are messy.
In Python 2.5 there’s a simple way to pass values into a generator.
yield
became an expression, returning a value that can be assigned to
a variable or otherwise operated on:
val = (yield i)
I recommend that you always put parentheses around a yield
expression
when you’re doing something with the returned value, as in the above example.
The parentheses aren’t always necessary, but it’s easier to always add them
instead of having to remember when they’re needed.
(PEP 342 explains the exact rules, which are that a yield
-expression must
always be parenthesized except when it occurs at the top-level expression on the
right-hand side of an assignment. This means you can write val = yield i
but have to use parentheses when there’s an operation, as in val = (yield i)
+ 12
.)
Values are sent into a generator by calling its send(value)
method. This method resumes the generator’s code and the
yield
expression returns the specified value. If the regular
__next__()
method is called, the yield
returns None
.
Here’s a simple counter that increments by 1 and allows changing the value of the internal counter.
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
And here’s an example of changing the counter:
>>> it = counter(10)
>>> next(it)
0
>>> next(it)
1
>>> it.send(8)
8
>>> next(it)
9
>>> next(it)
Traceback (most recent call last):
File "t.py", line 15, in <module>
it.next()
StopIteration
Because yield
will often be returning None
, you should always check for
this case. Don’t just use its value in expressions unless you’re sure that the
send()
method will be the only method used to resume your
generator function.
In addition to send()
, there are two other methods on
generators:
throw(value)
is used to raise an exception inside the generator; the exception is raised by theyield
expression where the generator’s execution is paused.close()
sends aGeneratorExit
exception to the generator to terminate the iteration. On receiving this exception, the generator’s code must either raiseGeneratorExit
orStopIteration
; catching the exception and doing anything else is illegal and will trigger aRuntimeError
.close()
will also be called by Python’s garbage collector when the generator is garbage-collected.If you need to run cleanup code when a
GeneratorExit
occurs, I suggest using atry: ... finally:
suite instead of catchingGeneratorExit
.
The cumulative effect of these changes is to turn generators from one-way producers of information into both producers and consumers.
Generators also become coroutines, a more generalized form of subroutines.
Subroutines are entered at one point and exited at another point (the top of the
function, and a return
statement), but coroutines can be entered, exited,
and resumed at many different points (the yield
statements).
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()
duplicate the
features of generator expressions:
map(f, iterA, iterB, ...)
returns an iterator over the sequencef(iterA[0], iterB[0]), f(iterA[1], iterB[1]), f(iterA[2], iterB[2]), ...
.>>> def upper(s): ... return s.upper()
>>> list(map(upper, ['sentence', 'fragment'])) ['SENTENCE', 'FRAGMENT'] >>> [upper(s) for s in ['sentence', 'fragment']] ['SENTENCE', 'FRAGMENT']
You can of course achieve the same effect with a list comprehension.
filter(predicate, iter)
returns an iterator over 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
>>> list(filter(is_even, range(10)))
[0, 2, 4, 6, 8]
This can also be written as a list comprehension:
>>> list(x for x in range(10) if is_even(x))
[0, 2, 4, 6, 8]
enumerate(iter, start=0)
counts off the elements in the
iterable returning 2-tuples containing the count (from start) 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, key=None, reverse=False)
collects all the
elements of the iterable into a list, sorts the list, and returns the sorted
result. The 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 Techniques.)
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
zip(iterA, iterB, ...)
takes one element from each iterable and
returns them in a tuple:
zip(['a', 'b', 'c'], (1, 2, 3)) =>
('a', 1), ('b', 2), ('c', 3)
It doesn’t construct an in-memory list and exhaust all the input iterators before returning; instead tuples are constructed and returned only if they’re requested. (The technical term for this behaviour is lazy evaluation.)
This iterator is intended to be used with iterables that are all of the same length. If the iterables are of different lengths, the resulting stream will be the same length as the shortest iterable.
zip(['a', 'b'], (1, 2, 3)) =>
('a', 1), ('b', 2)
You should avoid doing this, though, because an element may be taken from the longer iterators and discarded. This means you can’t go on to use the iterators further because you risk skipping a discarded element.
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.
Creating new iterators¶
itertools.count(start, step)
returns an infinite
stream of evenly spaced values. You can optionally supply the starting number,
which defaults to 0, and the interval between numbers, which defaults to 1:
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.count(10, 5) =>
10, 15, 20, 25, 30, 35, 40, 45, 50, 55, ...
itertools.cycle(iter)
saves a copy of the contents of
a provided iterable and returns a new iterator that returns its elements from
first to last. The new iterator will repeat these elements infinitely.
itertools.cycle([1, 2, 3, 4, 5]) =>
1, 2, 3, 4, 5, 1, 2, 3, 4, 5, ...
itertools.repeat(elem, [n])
returns the provided
element n times, or returns the element endlessly if n is not provided.
itertools.repeat('abc') =>
abc, abc, abc, abc, abc, abc, abc, abc, abc, abc, ...
itertools.repeat('abc', 5) =>
abc, abc, abc, abc, abc
itertools.chain(iterA, iterB, ...)
takes an arbitrary
number of iterables as input, and returns all the elements of the first
iterator, then all the elements of the second, and so on, until all of the
iterables have been exhausted.
itertools.chain(['a', 'b', 'c'], (1, 2, 3)) =>
a, b, c, 1, 2, 3
itertools.islice(iter, [start], stop, [step])
returns
a stream that’s a slice of the iterator. With a single stop argument, it
will return the first stop elements. If you supply a starting index, you’ll
get stop-start elements, and if you supply a value for step, elements
will be skipped accordingly. Unlike Python’s string and list slicing, you can’t
use negative values for start, stop, or step.
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(iter, [n])
replicates an iterator; it
returns n independent iterators that will all return the contents of the
source iterator.
If you don’t supply a value for n, the default is 2. Replicating iterators
requires saving some of the contents of the source iterator, so this can consume
significant memory if the iterator is large and one of the new iterators is
consumed more than the others.
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, ...
Calling functions on elements¶
The operator
module contains a set of functions corresponding to Python’s
operators. Some examples are operator.add(a, b)
(adds
two values), operator.ne(a, b)
(same as a != b
), and
operator.attrgetter('id')
(returns a callable that fetches the .id
attribute).
itertools.starmap(func, iter)
assumes that the
iterable will return a stream of tuples, and calls func using these tuples as
the arguments:
itertools.starmap(os.path.join,
[('/bin', 'python'), ('/usr', 'bin', 'java'),
('/usr', 'bin', 'perl'), ('/usr', 'bin', 'ruby')])
=>
/bin/python, /usr/bin/java, /usr/bin/perl, /usr/bin/ruby
Selecting elements¶
Another group of functions chooses a subset of an iterator’s elements based on a predicate.
itertools.filterfalse(predicate, iter)
is the
opposite of filter()
, returning all elements for which the predicate
returns false:
itertools.filterfalse(is_even, itertools.count()) =>
1, 3, 5, 7, 9, 11, 13, 15, ...
itertools.takewhile(predicate, iter)
returns
elements for as long as the predicate returns true. Once the predicate returns
false, the iterator will signal the end of its results.
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(predicate, iter)
discards
elements while the predicate returns true, and then returns the rest of the
iterable’s results.
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, ...
itertools.compress(data, selectors)
takes two
iterators and returns only those elements of data for which the corresponding
element of selectors is true, stopping whenever either one is exhausted:
itertools.compress([1, 2, 3, 4, 5], [True, True, False, False, True]) =>
1, 2, 5
Combinatoric functions¶
The itertools.combinations(iterable, r)
returns an iterator giving all possible r-tuple combinations of the
elements contained in iterable.
itertools.combinations([1, 2, 3, 4, 5], 2) =>
(1, 2), (1, 3), (1, 4), (1, 5),
(2, 3), (2, 4), (2, 5),
(3, 4), (3, 5),
(4, 5)
itertools.combinations([1, 2, 3, 4, 5], 3) =>
(1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5), (1, 4, 5),
(2, 3, 4), (2, 3, 5), (2, 4, 5),
(3, 4, 5)
The elements within each tuple remain in the same order as
iterable returned them. For example, the number 1 is always before
2, 3, 4, or 5 in the examples above. A similar function,
itertools.permutations(iterable, r=None)
,
removes this constraint on the order, returning all possible
arrangements of length r:
itertools.permutations([1, 2, 3, 4, 5], 2) =>
(1, 2), (1, 3), (1, 4), (1, 5),
(2, 1), (2, 3), (2, 4), (2, 5),
(3, 1), (3, 2), (3, 4), (3, 5),
(4, 1), (4, 2), (4, 3), (4, 5),
(5, 1), (5, 2), (5, 3), (5, 4)
itertools.permutations([1, 2, 3, 4, 5]) =>
(1, 2, 3, 4, 5), (1, 2, 3, 5, 4), (1, 2, 4, 3, 5),
...
(5, 4, 3, 2, 1)
If you don’t supply a value for r the length of the iterable is used, meaning that all the elements are permuted.
Note that these functions produce all of the possible combinations by position and don’t require that the contents of iterable are unique:
itertools.permutations('aba', 3) =>
('a', 'b', 'a'), ('a', 'a', 'b'), ('b', 'a', 'a'),
('b', 'a', 'a'), ('a', 'a', 'b'), ('a', 'b', 'a')
The identical tuple ('a', 'a', 'b')
occurs twice, but the two ‘a’
strings came from different positions.
The itertools.combinations_with_replacement(iterable, r)
function relaxes a different constraint: elements can be repeated
within a single tuple. Conceptually an element is selected for the
first position of each tuple and then is replaced before the second
element is selected.
itertools.combinations_with_replacement([1, 2, 3, 4, 5], 2) =>
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5),
(2, 2), (2, 3), (2, 4), (2, 5),
(3, 3), (3, 4), (3, 5),
(4, 4), (4, 5),
(5, 5)
Grouping elements¶
The last function I’ll discuss, itertools.groupby(iter, key_func=None)
, is the most complicated. key_func(elem)
is a function
that can compute a key value for each element returned by the iterable. If you
don’t supply a key function, the key is simply each element itself.
groupby()
collects all the consecutive elements from the
underlying iterable that have the same key value, and returns a stream of
2-tuples containing a key value and an iterator for the elements with that key.
city_list = [('Decatur', 'AL'), ('Huntsville', 'AL'), ('Selma', 'AL'),
('Anchorage', 'AK'), ('Nome', 'AK'),
('Flagstaff', 'AZ'), ('Phoenix', 'AZ'), ('Tucson', 'AZ'),
...
]
def get_state(city_state):
return city_state[1]
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')
groupby()
assumes that the underlying iterable’s contents will
already be sorted based on the key. Note that the returned iterators also use
the underlying iterable, so you have to consume the results of iterator-1 before
requesting iterator-2 and its corresponding key.
The functools module¶
The functools
module 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')
functools.reduce(func, iter, [initial_value])
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. functools.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, functools
>>> functools.reduce(operator.concat, ['A', 'BB', 'C'])
'ABBC'
>>> functools.reduce(operator.concat, [])
Traceback (most recent call last):
...
TypeError: reduce() of empty sequence with no initial value
>>> functools.reduce(operator.mul, [1, 2, 3], 1)
6
>>> functools.reduce(operator.mul, [], 1)
1
If you use operator.add()
with functools.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:
>>> import functools, operator
>>> functools.reduce(operator.add, [1, 2, 3, 4], 0)
10
>>> sum([1, 2, 3, 4])
10
>>> sum([])
0
For many uses of functools.reduce()
, though, it can be clearer to just
write the obvious for
loop:
import functools
# Instead of:
product = functools.reduce(operator.mul, [1, 2, 3], 1)
# You can write:
product = 1
for i in [1, 2, 3]:
product *= i
A related function is itertools.accumulate(iterable, func=operator.add)
. It performs the same calculation, but instead of
returning only the final result, accumulate()
returns an iterator
that also yields each partial result:
itertools.accumulate([1, 2, 3, 4, 5]) =>
1, 3, 6, 10, 15
itertools.accumulate([1, 2, 3, 4, 5], operator.mul) =>
1, 2, 6, 24, 120
The operator module¶
The operator
module was mentioned earlier. It contains a set of
functions corresponding to Python’s operators. These functions are often useful
in functional-style code because they save you from writing trivial functions
that perform a single operation.
Some of the functions in this module are:
Math operations:
add()
,sub()
,mul()
,floordiv()
,abs()
, …Logical operations:
not_()
,truth()
.Bitwise operations:
and_()
,or_()
,invert()
.Comparisons:
eq()
,ne()
,lt()
,le()
,gt()
, andge()
.Object identity:
is_()
,is_not()
.
Consult the operator module’s documentation for a complete list.
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
expression. lambda
takes a
number of parameters and an expression combining these parameters, and creates
an anonymous function that returns the value of the expression:
adder = lambda x, y: x+y
print_assign = lambda name, value: name + '=' + str(value)
An alternative is to just use the def
statement and define a function in the
usual way:
def adder(x, y):
return x + y
def print_assign(name, value):
return name + '=' + str(value)
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?
import functools
total = functools.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:
import functools
def combine(a, b):
return 0, a[1] + b[1]
total = functools.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 functools.reduce()
are clearer when written as for
loops.
Fredrik Lundh once suggested the following set of rules for refactoring uses of
lambda
:
Write a lambda function.
Write a comment explaining what the heck that lambda does.
Study the comment for a while, and think of a name that captures the essence of the comment.
Convert the lambda to a def statement, using that name.
Remove the comment.
I really like these rules, but you’re free to disagree about whether this lambda-free style is better.
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¶
General¶
Structure and Interpretation of Computer Programs, by Harold Abelson and Gerald Jay Sussman with Julie Sussman. The book can be found at https://mitpress.mit.edu/sicp. In this classic textbook of computer science, chapters 2 and 3 discuss the use of sequences and streams to organize the data flow inside a program. The book uses Scheme for its examples, but many of the design approaches described in these chapters are applicable to functional-style Python code.
https://defmacro.org/2006/06/19/fp.html: A general introduction to functional programming that uses Java examples and has a lengthy historical introduction.
https://en.wikipedia.org/wiki/Functional_programming: General Wikipedia entry describing functional programming.
https://en.wikipedia.org/wiki/Coroutine: Entry for coroutines.
https://en.wikipedia.org/wiki/Partial_application: Entry for the concept of partial function application.
https://en.wikipedia.org/wiki/Currying: Entry for the concept of currying.
Python-specific¶
https://gnosis.cx/TPiP/: The first chapter of David Mertz’s book Text Processing in Python discusses functional programming for text processing, in the section titled “Utilizing Higher-Order Functions in Text Processing”.
Mertz also wrote a 3-part series of articles on functional programming for IBM’s DeveloperWorks site; see part 1, part 2, and part 3,
Python documentation¶
Documentation for the itertools
module.
Documentation for the functools
module.
Documentation for the operator
module.
PEP 289: “Generator Expressions”
PEP 342: “Coroutines via Enhanced Generators” describes the new generator features in Python 2.5.


— Resource usage information

resource
— Resource usage information¶
This module provides basic mechanisms for measuring and controlling system resources utilized by a program.
Availability: Unix, not WASI.
Symbolic constants are used to specify particular system resources and to request usage information about either the current process or its children.
An OSError
is raised on syscall failure.
Resource Limits¶
Resources usage can be limited using the setrlimit()
function described
below. Each resource is controlled by a pair of limits: a soft limit and a hard
limit. The soft limit is the current limit, and may be lowered or raised by a
process over time. The soft limit can never exceed the hard limit. The hard
limit can be lowered to any value greater than the soft limit, but not raised.
(Only processes with the effective UID of the super-user can raise a hard
limit.)
The specific resources that can be limited are system dependent. They are described in the getrlimit(2) man page. The resources listed below are supported when the underlying operating system supports them; resources which cannot be checked or controlled by the operating system are not defined in this module for those platforms.
- resource.RLIM_INFINITY¶
Constant used to represent the limit for an unlimited resource.
- resource.getrlimit(resource)¶
Returns a tuple
(soft, hard)
with the current soft and hard limits of resource. RaisesValueError
if an invalid resource is specified, orerror
if the underlying system call fails unexpectedly.
- resource.setrlimit(resource, limits)¶
Sets new limits of consumption of resource. The limits argument must be a tuple
(soft, hard)
of two integers describing the new limits. A value ofRLIM_INFINITY
can be used to request a limit that is unlimited.Raises
ValueError
if an invalid resource is specified, if the new soft limit exceeds the hard limit, or if a process tries to raise its hard limit. Specifying a limit ofRLIM_INFINITY
when the hard or system limit for that resource is not unlimited will result in aValueError
. A process with the effective UID of super-user can request any valid limit value, including unlimited, butValueError
will still be raised if the requested limit exceeds the system imposed limit.setrlimit
may also raiseerror
if the underlying system call fails.VxWorks only supports setting
RLIMIT_NOFILE
.Raises an auditing event
resource.setrlimit
with argumentsresource
,limits
.
- resource.prlimit(pid, resource[, limits])¶
Combines
setrlimit()
andgetrlimit()
in one function and supports to get and set the resources limits of an arbitrary process. If pid is 0, then the call applies to the current process. resource and limits have the same meaning as insetrlimit()
, except that limits is optional.When limits is not given the function returns the resource limit of the process pid. When limits is given the resource limit of the process is set and the former resource limit is returned.
Raises
ProcessLookupError
when pid can’t be found andPermissionError
when the user doesn’t haveCAP_SYS_RESOURCE
for the process.Raises an auditing event
resource.prlimit
with argumentspid
,resource
,limits
.Availability: Linux >= 2.6.36 with glibc >= 2.13.
Added in version 3.4.
These symbols define resources whose consumption can be controlled using the
setrlimit()
and getrlimit()
functions described below. The values of
these symbols are exactly the constants used by C programs.
The Unix man page for getrlimit(2) lists the available resources. Note that not all systems use the same symbol or same value to denote the same resource. This module does not attempt to mask platform differences — symbols not defined for a platform will not be available from this module on that platform.
- resource.RLIMIT_CORE¶
The maximum size (in bytes) of a core file that the current process can create. This may result in the creation of a partial core file if a larger core would be required to contain the entire process image.
- resource.RLIMIT_CPU¶
The maximum amount of processor time (in seconds) that a process can use. If this limit is exceeded, a
SIGXCPU
signal is sent to the process. (See thesignal
module documentation for information about how to catch this signal and do something useful, e.g. flush open files to disk.)
- resource.RLIMIT_FSIZE¶
The maximum size of a file which the process may create.
- resource.RLIMIT_DATA¶
The maximum size (in bytes) of the process’s heap.
- resource.RLIMIT_STACK¶
The maximum size (in bytes) of the call stack for the current process. This only affects the stack of the main thread in a multi-threaded process.
- resource.RLIMIT_RSS¶
The maximum resident set size that should be made available to the process.
- resource.RLIMIT_NPROC¶
The maximum number of processes the current process may create.
- resource.RLIMIT_NOFILE¶
The maximum number of open file descriptors for the current process.
- resource.RLIMIT_OFILE¶
The BSD name for
RLIMIT_NOFILE
.
- resource.RLIMIT_MEMLOCK¶
The maximum address space which may be locked in memory.
- resource.RLIMIT_VMEM¶
The largest area of mapped memory which the process may occupy. Usually an alias of
RLIMIT_AS
.Availability: Solaris, FreeBSD, NetBSD.
- resource.RLIMIT_AS¶
The maximum area (in bytes) of address space which may be taken by the process.
- resource.RLIMIT_MSGQUEUE¶
The number of bytes that can be allocated for POSIX message queues.
Availability: Linux >= 2.6.8.
Added in version 3.4.
- resource.RLIMIT_NICE¶
The ceiling for the process’s nice level (calculated as 20 - rlim_cur).
Availability: Linux >= 2.6.12.
Added in version 3.4.
- resource.RLIMIT_RTPRIO¶
The ceiling of the real-time priority.
Availability: Linux >= 2.6.12.
Added in version 3.4.
- resource.RLIMIT_RTTIME¶
The time limit (in microseconds) on CPU time that a process can spend under real-time scheduling without making a blocking syscall.
Availability: Linux >= 2.6.25.
Added in version 3.4.
- resource.RLIMIT_SIGPENDING¶
The number of signals which the process may queue.
Availability: Linux >= 2.6.8.
Added in version 3.4.
- resource.RLIMIT_SBSIZE¶
The maximum size (in bytes) of socket buffer usage for this user. This limits the amount of network memory, and hence the amount of mbufs, that this user may hold at any time.
Availability: FreeBSD, NetBSD.
Added in version 3.4.
- resource.RLIMIT_SWAP¶
The maximum size (in bytes) of the swap space that may be reserved or used by all of this user id’s processes. This limit is enforced only if bit 1 of the vm.overcommit sysctl is set. Please see tuning(7) for a complete description of this sysctl.
Availability: FreeBSD >= 8.
Added in version 3.4.
- resource.RLIMIT_NPTS¶
The maximum number of pseudo-terminals created by this user id.
Availability: FreeBSD >= 8.
Added in version 3.4.
- resource.RLIMIT_KQUEUES¶
The maximum number of kqueues this user id is allowed to create.
Availability: FreeBSD >= 11.
Added in version 3.10.
Resource Usage¶
These functions are used to retrieve resource usage information:
- resource.getrusage(who)¶
This function returns an object that describes the resources consumed by either the current process or its children, as specified by the who parameter. The who parameter should be specified using one of the
RUSAGE_*
constants described below.A simple example:
from resource import * import time # a non CPU-bound task time.sleep(3) print(getrusage(RUSAGE_SELF)) # a CPU-bound task for i in range(10 ** 8): _ = 1 + 1 print(getrusage(RUSAGE_SELF))
The fields of the return value each describe how a particular system resource has been used, e.g. amount of time spent running in user mode or number of times the process was swapped out of main memory. Some values are dependent on the clock tick interval, e.g. the amount of memory the process is using.
For backward compatibility, the return value is also accessible as a tuple of 16 elements.
The fields
ru_utime
andru_stime
of the return value are floating-point values representing the amount of time spent executing in user mode and the amount of time spent executing in system mode, respectively. The remaining values are integers. Consult the getrusage(2) man page for detailed information about these values. A brief summary is presented here:Index
Field
Resource
0
ru_utime
time in user mode (float seconds)
1
ru_stime
time in system mode (float seconds)
2
ru_maxrss
maximum resident set size
3
ru_ixrss
shared memory size
4
ru_idrss
unshared memory size
5
ru_isrss
unshared stack size
6
ru_minflt
page faults not requiring I/O
7
ru_majflt
page faults requiring I/O
8
ru_nswap
number of swap outs
9
ru_inblock
block input operations
10
ru_oublock
block output operations
11
ru_msgsnd
messages sent
12
ru_msgrcv
messages received
13
ru_nsignals
signals received
14
ru_nvcsw
voluntary context switches
15
ru_nivcsw
involuntary context switches
This function will raise a
ValueError
if an invalid who parameter is specified. It may also raiseerror
exception in unusual circumstances.
- resource.getpagesize()¶
Returns the number of bytes in a system page. (This need not be the same as the hardware page size.)
The following RUSAGE_*
symbols are passed to the getrusage()
function to specify which processes information should be provided for.
- resource.RUSAGE_SELF¶
Pass to
getrusage()
to request resources consumed by the calling process, which is the sum of resources used by all threads in the process.
- resource.RUSAGE_CHILDREN¶
Pass to
getrusage()
to request resources consumed by child processes of the calling process which have been terminated and waited for.
- resource.RUSAGE_BOTH¶
Pass to
getrusage()
to request resources consumed by both the current process and child processes. May not be available on all systems.
- resource.RUSAGE_THREAD¶
Pass to
getrusage()
to request resources consumed by the current thread. May not be available on all systems.Added in version 3.2.


High-level API Index

High-level API Index¶
This page lists all high-level async/await enabled asyncio APIs.
Tasks¶
Utilities to run asyncio programs, create Tasks, and await on multiple things with timeouts.
Create event loop, run a coroutine, close the loop. |
|
A context manager that simplifies multiple async function calls. |
|
Task object. |
|
A context manager that holds a group of tasks. Provides a convenient and reliable way to wait for all tasks in the group to finish. |
|
Start an asyncio Task, then returns it. |
|
Return the current Task. |
|
Return all tasks that are not yet finished for an event loop. |
|
|
Sleep for a number of seconds. |
|
Schedule and wait for things concurrently. |
|
Run with a timeout. |
|
Shield from cancellation. |
|
Monitor for completion. |
Run with a timeout. Useful in cases when |
|
Asynchronously run a function in a separate OS thread. |
|
Schedule a coroutine from another OS thread. |
|
|
Monitor for completion with a |
Examples
Queues¶
Queues should be used to distribute work amongst multiple asyncio Tasks, implement connection pools, and pub/sub patterns.
A FIFO queue. |
|
A priority queue. |
|
A LIFO queue. |
Examples
Subprocesses¶
Utilities to spawn subprocesses and run shell commands.
|
Create a subprocess. |
Run a shell command. |
Examples
See also the subprocess APIs documentation.
Streams¶
High-level APIs to work with network IO.
|
Establish a TCP connection. |
|
Establish a Unix socket connection. |
|
Start a TCP server. |
|
Start a Unix socket server. |
High-level async/await object to receive network data. |
|
High-level async/await object to send network data. |
Examples
See also the streams APIs documentation.
Synchronization¶
Threading-like synchronization primitives that can be used in Tasks.
A mutex lock. |
|
An event object. |
|
A condition object. |
|
A semaphore. |
|
A bounded semaphore. |
|
A barrier object. |
Examples
See also the documentation of asyncio synchronization primitives.
Exceptions¶
Raised when a Task is cancelled. See also |
|
Raised when a Barrier is broken. See also |
Examples
Handling CancelledError to run code on cancellation request.
See also the full list of asyncio-specific exceptions.