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 <div class="section" id="functional-programming-howto">
<h1>Functional Programming HOWTO<a class="headerlink" href="#functional-programming-howto" title="Permalink to this headline">¶</a></h1>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field"><th class="field-name">Author:</th><td class="field-body">A. M. Kuchling</td>
</tr>
<tr class="field"><th class="field-name">Release:</th><td class="field-body">0.31</td>
</tr>
</tbody>
</table>
(This is a first draft. Please send comments/error reports/suggestions to
<a class="reference external" href="mailto:amk&#37;&#52;&#48;amk&#46;ca">amk&#64;amk&#46;ca</a>.)
In this document, we&#8217;ll take a tour of Python&#8217;s features suitable for
implementing programs in a functional style. After an introduction to the
concepts of functional programming, we&#8217;ll look at language features such as
<a class="reference external" href="../glossary.html#term-iterator">iterator</a>s and <a class="reference external" href="../glossary.html#term-generator">generator</a>s and relevant library modules such as
<a title="Functions creating iterators for efficient looping." class="reference external" href="../library/itertools.html#module-itertools"><tt class="xref docutils literal">itertools</tt></a> and <a title="Higher order functions and operations on callable objects." class="reference external" href="../library/functools.html#module-functools"><tt class="xref docutils literal">functools</tt></a>.
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h2>
This section explains the basic concept of functional programming; if you&#8217;re
just interested in learning about Python language features, skip to the next
section.
Programming languages support decomposing problems in several different ways:
<ul class="simple">
<li>Most programming languages are procedural: programs are lists of
instructions that tell the computer what to do with the program&#8217;s input. C,
Pascal, and even Unix shells are procedural languages.</li>
<li>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&#8217;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.</li>
<li>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&#8217;t force the
use of object-oriented features.</li>
<li>Functional programming decomposes a problem into a set of functions.
Ideally, functions only take inputs and produce outputs, and don&#8217;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.</li>
</ul>
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&#8217;t visible in the function&#8217;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&#8217;s
output must only depend on its input.
Some languages are very strict about purity and don&#8217;t even have assignment
statements such as <tt class="docutils literal">a=3</tt> or <tt class="docutils literal">c = a + b</tt>, but it&#8217;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 <tt class="docutils literal">print</tt> statement or a
<tt class="docutils literal">time.sleep(1)</tt> both return no useful value; they&#8217;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&#8217;t go to the extreme of
avoiding all I/O or all assignments; instead, they&#8217;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&#8217;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:
<ul class="simple">
<li>Formal provability.</li>
<li>Modularity.</li>
<li>Composability.</li>
<li>Ease of debugging and testing.</li>
</ul>
<div class="section" id="formal-provability">
<h3>Formal provability<a class="headerlink" href="#formal-provability" title="Permalink to this headline">¶</a></h3>
A theoretical benefit is that it&#8217;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&#8217;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&#8217;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&#8217; and Y&#8217; 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&#8217;s output.
Functional programming&#8217;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&#8217;s an error in it, and you wrongly believe you&#8217;ve proved the
program correct.
</div>
<div class="section" id="modularity">
<h3>Modularity<a class="headerlink" href="#modularity" title="Permalink to this headline">¶</a></h3>
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&#8217;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.
</div>
<div class="section" id="ease-of-debugging-and-testing">
<h3>Ease of debugging and testing<a class="headerlink" href="#ease-of-debugging-and-testing" title="Permalink to this headline">¶</a></h3>
Testing and debugging a functional-style program is easier.
Debugging is simplified because functions are generally small and clearly
specified. When a program doesn&#8217;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&#8217;s responsible for a bug.
Testing is easier because each function is a potential subject for a unit test.
Functions don&#8217;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.
</div>
<div class="section" id="composability">
<h3>Composability<a class="headerlink" href="#composability" title="Permalink to this headline">¶</a></h3>
As you work on a functional-style program, you&#8217;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&#8217;ll form a personal library of utilities. Often you&#8217;ll assemble
new programs by arranging existing functions in a new configuration and writing
a few functions specialized for the current task.
</div>
</div>
<div class="section" id="iterators">
<h2>Iterators<a class="headerlink" href="#iterators" title="Permalink to this headline">¶</a></h2>
I&#8217;ll start by looking at a Python language feature that&#8217;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
<tt class="docutils literal">next()</tt> that takes no arguments and always returns the next element of the
stream. If there are no more elements in the stream, <tt class="docutils literal">next()</tt> must raise the
<tt class="docutils literal">StopIteration</tt> exception. Iterators don&#8217;t have to be finite, though; it&#8217;s
perfectly reasonable to write an iterator that produces an infinite stream of
data.
The built-in <a title="iter" class="reference external" href="../library/functions.html#iter"><tt class="xref docutils literal">iter()</tt></a> function takes an arbitrary object and tries to return
an iterator that will return the object&#8217;s contents or elements, raising
<a title="exceptions.TypeError" class="reference external" href="../library/exceptions.html#exceptions.TypeError"><tt class="xref docutils literal">TypeError</tt></a> if the object doesn&#8217;t support iteration. Several of Python&#8217;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:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; L = [1,2,3]
&gt;&gt;&gt; it = iter(L)
&gt;&gt;&gt; print it
&lt;...iterator object at ...&gt;
&gt;&gt;&gt; it.next()
1
&gt;&gt;&gt; it.next()
2
&gt;&gt;&gt; it.next()
3
&gt;&gt;&gt; it.next()
Traceback (most recent call last):
 File &quot;&lt;stdin&gt;&quot;, line 1, in ?
StopIteration
&gt;&gt;&gt;
</pre></div>
</div>
Python expects iterable objects in several different contexts, the most
important being the <tt class="docutils literal">for</tt> statement. In the statement <tt class="docutils literal">for X in Y</tt>, Y must
be an iterator or some object for which <tt class="docutils literal">iter()</tt> can create an iterator.
These two statements are equivalent:
<div class="highlight-python"><div class="highlight"><pre>for i in iter(obj):
 print i

for i in obj:
 print i
</pre></div>
</div>
Iterators can be materialized as lists or tuples by using the <a title="list" class="reference external" href="../library/functions.html#list"><tt class="xref docutils literal">list()</tt></a> or
<a title="tuple" class="reference external" href="../library/functions.html#tuple"><tt class="xref docutils literal">tuple()</tt></a> constructor functions:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; L = [1,2,3]
&gt;&gt;&gt; iterator = iter(L)
&gt;&gt;&gt; t = tuple(iterator)
&gt;&gt;&gt; t
(1, 2, 3)
</pre></div>
</div>
Sequence unpacking also supports iterators: if you know an iterator will return
N elements, you can unpack them into an N-tuple:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; L = [1,2,3]
&gt;&gt;&gt; iterator = iter(L)
&gt;&gt;&gt; a,b,c = iterator
&gt;&gt;&gt; a,b,c
(1, 2, 3)
</pre></div>
</div>
Built-in functions such as <a title="max" class="reference external" href="../library/functions.html#max"><tt class="xref docutils literal">max()</tt></a> and <a title="min" class="reference external" href="../library/functions.html#min"><tt class="xref docutils literal">min()</tt></a> can take a single
iterator argument and will return the largest or smallest element. The <tt class="docutils literal">&quot;in&quot;</tt>
and <tt class="docutils literal">&quot;not in&quot;</tt> operators also support iterators: <tt class="docutils literal">X in iterator</tt> is true if
X is found in the stream returned by the iterator. You&#8217;ll run into obvious
problems if the iterator is infinite; <tt class="docutils literal">max()</tt>, <tt class="docutils literal">min()</tt>, and <tt class="docutils literal">&quot;not in&quot;</tt>
will never return, and if the element X never appears in the stream, the
<tt class="docutils literal">&quot;in&quot;</tt> operator won&#8217;t return either.
Note that you can only go forward in an iterator; there&#8217;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 <tt class="docutils literal">next()</tt> method. Functions may therefore consume all of
the iterator&#8217;s output, and if you need to do something different with the same
stream, you&#8217;ll have to create a new iterator.
<div class="section" id="data-types-that-support-iterators">
<h3>Data Types That Support Iterators<a class="headerlink" href="#data-types-that-support-iterators" title="Permalink to this headline">¶</a></h3>
We&#8217;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 <a title="iter" class="reference external" href="../library/functions.html#iter"><tt class="xref docutils literal">iter()</tt></a> on a dictionary returns an iterator that will loop over the
dictionary&#8217;s keys:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; m = {&#39;Jan&#39;: 1, &#39;Feb&#39;: 2, &#39;Mar&#39;: 3, &#39;Apr&#39;: 4, &#39;May&#39;: 5, &#39;Jun&#39;: 6,
... &#39;Jul&#39;: 7, &#39;Aug&#39;: 8, &#39;Sep&#39;: 9, &#39;Oct&#39;: 10, &#39;Nov&#39;: 11, &#39;Dec&#39;: 12}
&gt;&gt;&gt; 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
</pre></div>
</div>
Note that the order is essentially random, because it&#8217;s based on the hash
ordering of the objects in the dictionary.
Applying <tt class="docutils literal">iter()</tt> to a dictionary always loops over the keys, but dictionaries
have methods that return other iterators. If you want to iterate over keys,
values, or key/value pairs, you can explicitly call the <tt class="docutils literal">iterkeys()</tt>,
<tt class="docutils literal">itervalues()</tt>, or <tt class="docutils literal">iteritems()</tt> methods to get an appropriate iterator.
The <a title="dict" class="reference external" href="../library/stdtypes.html#dict"><tt class="xref docutils literal">dict()</tt></a> constructor can accept an iterator that returns a finite stream
of <tt class="docutils literal">(key, value)</tt> tuples:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; L = [(&#39;Italy&#39;, &#39;Rome&#39;), (&#39;France&#39;, &#39;Paris&#39;), (&#39;US&#39;, &#39;Washington DC&#39;)]
&gt;&gt;&gt; dict(iter(L))
{&#39;Italy&#39;: &#39;Rome&#39;, &#39;US&#39;: &#39;Washington DC&#39;, &#39;France&#39;: &#39;Paris&#39;}
</pre></div>
</div>
Files also support iteration by calling the <tt class="docutils literal">readline()</tt> method until there
are no more lines in the file. This means you can read each line of a file like
this:
<div class="highlight-python"><div class="highlight"><pre>for line in file:
 # do something for each line
 ...
</pre></div>
</div>
Sets can take their contents from an iterable and let you iterate over the set&#8217;s
elements:
<div class="highlight-python"><div class="highlight"><pre>S = set((2, 3, 5, 7, 11, 13))
for i in S:
 print i
</pre></div>
</div>
</div>
</div>
<div class="section" id="generator-expressions-and-list-comprehensions">
<h2>Generator expressions and list comprehensions<a class="headerlink" href="#generator-expressions-and-list-comprehensions" title="Permalink to this headline">¶</a></h2>
Two common operations on an iterator&#8217;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: &#8220;listcomps&#8221; and
&#8220;genexps&#8221;) are a concise notation for such operations, borrowed from the
functional programming language Haskell (<a class="reference external" href="http://www.haskell.org/">http://www.haskell.org/</a>). You can strip
all the whitespace from a stream of strings with the following code:
<div class="highlight-python"><div class="highlight"><pre>line_list = [&#39; line 1\n&#39;, &#39;line 2 \n&#39;, ...]

# 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]
</pre></div>
</div>
You can select only certain elements by adding an <tt class="docutils literal">&quot;if&quot;</tt> condition:
<div class="highlight-python"><div class="highlight"><pre>stripped_list = [line.strip() for line in line_list
 if line != &quot;&quot;]
</pre></div>
</div>
With a list comprehension, you get back a Python list; <tt class="docutils literal">stripped_list</tt> 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&#8217;t
useful if you&#8217;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 (&#8220;()&#8221;) and list
comprehensions are surrounded by square brackets (&#8220;[]&#8221;). Generator expressions
have the form:
<div class="highlight-python"><pre>( 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 )</pre>
</div>
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
<tt class="docutils literal">expression</tt>. The <tt class="docutils literal">if</tt> clauses are all optional; if present, <tt class="docutils literal">expression</tt>
is only evaluated and added to the result when <tt class="docutils literal">condition</tt> 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:
<div class="highlight-python"><div class="highlight"><pre>obj_total = sum(obj.count for obj in list_all_objects())
</pre></div>
</div>
The <tt class="docutils literal">for...in</tt> 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 <tt class="docutils literal">sequence1</tt>,
<tt class="docutils literal">sequence2</tt> is looped over from the beginning. <tt class="docutils literal">sequence3</tt> is then looped
over for each resulting pair of elements from <tt class="docutils literal">sequence1</tt> and <tt class="docutils literal">sequence2</tt>.
To put it another way, a list comprehension or generator expression is
equivalent to the following Python code:
<div class="highlight-python"><div class="highlight"><pre>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.
</pre></div>
</div>
This means that when there are multiple <tt class="docutils literal">for...in</tt> clauses but no <tt class="docutils literal">if</tt>
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:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; seq1 = &#39;abc&#39;
&gt;&gt;&gt; seq2 = (1,2,3)
&gt;&gt;&gt; [(x,y) for x in seq1 for y in seq2]
[(&#39;a&#39;, 1), (&#39;a&#39;, 2), (&#39;a&#39;, 3),
 (&#39;b&#39;, 1), (&#39;b&#39;, 2), (&#39;b&#39;, 3),
 (&#39;c&#39;, 1), (&#39;c&#39;, 2), (&#39;c&#39;, 3)]
</pre></div>
</div>
To avoid introducing an ambiguity into Python&#8217;s grammar, if <tt class="docutils literal">expression</tt> 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:
<div class="highlight-python"><pre># Syntax error
[ x,y for x in seq1 for y in seq2]
# Correct
[ (x,y) for x in seq1 for y in seq2]</pre>
</div>
</div>
<div class="section" id="generators">
<h2>Generators<a class="headerlink" href="#generators" title="Permalink to this headline">¶</a></h2>
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&#8217;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 <tt class="docutils literal">return</tt> 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&#8217;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&#8217;s the simplest example of a generator function:
<div class="highlight-python"><div class="highlight"><pre>def generate_ints(N):
 for i in range(N):
 yield i
</pre></div>
</div>
Any function containing a <tt class="docutils literal">yield</tt> keyword is a generator function; this is
detected by Python&#8217;s <a class="reference external" href="../glossary.html#term-bytecode">bytecode</a> compiler which compiles the function
specially as a result.
When you call a generator function, it doesn&#8217;t return a single value; instead it
returns a generator object that supports the iterator protocol. On executing
the <tt class="docutils literal">yield</tt> expression, the generator outputs the value of <tt class="docutils literal">i</tt>, similar to a
<tt class="docutils literal">return</tt> statement. The big difference between <tt class="docutils literal">yield</tt> and a <tt class="docutils literal">return</tt>
statement is that on reaching a <tt class="docutils literal">yield</tt> the generator&#8217;s state of execution is
suspended and local variables are preserved. On the next call to the
generator&#8217;s <tt class="docutils literal">.next()</tt> method, the function will resume executing.
Here&#8217;s a sample usage of the <tt class="docutils literal">generate_ints()</tt> generator:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; gen = generate_ints(3)
&gt;&gt;&gt; gen
&lt;generator object generate_ints at ...&gt;
&gt;&gt;&gt; gen.next()
0
&gt;&gt;&gt; gen.next()
1
&gt;&gt;&gt; gen.next()
2
&gt;&gt;&gt; gen.next()
Traceback (most recent call last):
 File &quot;stdin&quot;, line 1, in ?
 File &quot;stdin&quot;, line 2, in generate_ints
StopIteration
</pre></div>
</div>
You could equally write <tt class="docutils literal">for i in generate_ints(5)</tt>, or <tt class="docutils literal">a,b,c =
generate_ints(3)</tt>.
Inside a generator function, the <tt class="docutils literal">return</tt> statement can only be used without a
value, and signals the end of the procession of values; after executing a
<tt class="docutils literal">return</tt> the generator cannot return any further values. <tt class="docutils literal">return</tt> with a
value, such as <tt class="docutils literal">return 5</tt>, is a syntax error inside a generator function. The
end of the generator&#8217;s results can also be indicated by raising
<tt class="docutils literal">StopIteration</tt> 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 <tt class="docutils literal">self.count</tt> to
0, and having the <tt class="docutils literal">next()</tt> method increment <tt class="docutils literal">self.count</tt> and return it.
However, for a moderately complicated generator, writing a corresponding class
can be much messier.
The test suite included with Python&#8217;s library, <tt class="docutils literal">test_generators.py</tt>, contains
a number of more interesting examples. Here&#8217;s one generator that implements an
in-order traversal of a tree using generators recursively.
<div class="highlight-python"><div class="highlight"><pre># 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
</pre></div>
</div>
Two other examples in <tt class="docutils literal">test_generators.py</tt> produce solutions for the N-Queens
problem (placing N queens on an NxN chess board so that no queen threatens
another) and the Knight&#8217;s Tour (finding a route that takes a knight to every
square of an NxN chessboard without visiting any square twice).
<div class="section" id="passing-values-into-a-generator">
<h3>Passing values into a generator<a class="headerlink" href="#passing-values-into-a-generator" title="Permalink to this headline">¶</a></h3>
In Python 2.4 and earlier, generators only produced output. Once a generator&#8217;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&#8217;s a simple way to pass values into a generator.
<a class="reference external" href="../reference/simple_stmts.html#yield"><tt class="xref docutils literal">yield</tt></a> became an expression, returning a value that can be assigned to
a variable or otherwise operated on:
<div class="highlight-python"><div class="highlight"><pre>val = (yield i)
</pre></div>
</div>
I recommend that you always put parentheses around a <tt class="docutils literal">yield</tt> expression
when you&#8217;re doing something with the returned value, as in the above example.
The parentheses aren&#8217;t always necessary, but it&#8217;s easier to always add them
instead of having to remember when they&#8217;re needed.
(PEP 342 explains the exact rules, which are that a <tt class="docutils literal">yield</tt>-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 <tt class="docutils literal">val = yield i</tt>
but have to use parentheses when there&#8217;s an operation, as in <tt class="docutils literal">val = (yield i)
+ 12</tt>.)
Values are sent into a generator by calling its <tt class="docutils literal">send(value)</tt> method. This
method resumes the generator&#8217;s code and the <tt class="docutils literal">yield</tt> expression returns the
specified value. If the regular <tt class="docutils literal">next()</tt> method is called, the <tt class="docutils literal">yield</tt>
returns <tt class="xref docutils literal">None</tt>.
Here&#8217;s a simple counter that increments by 1 and allows changing the value of
the internal counter.
<div class="highlight-python"><div class="highlight"><pre>def counter (maximum):
 i = 0
 while i &lt; maximum:
 val = (yield i)
 # If value provided, change counter
 if val is not None:
 i = val
 else:
 i += 1
</pre></div>
</div>
And here&#8217;s an example of changing the counter:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; it = counter(10)
&gt;&gt;&gt; print it.next()
0
&gt;&gt;&gt; print it.next()
1
&gt;&gt;&gt; print it.send(8)
8
&gt;&gt;&gt; print it.next()
9
&gt;&gt;&gt; print it.next()
Traceback (most recent call last):
 File &quot;t.py&quot;, line 15, in ?
 print it.next()
StopIteration
</pre></div>
</div>
Because <tt class="docutils literal">yield</tt> will often be returning <tt class="xref docutils literal">None</tt>, you should always check for
this case. Don&#8217;t just use its value in expressions unless you&#8217;re sure that the
<tt class="docutils literal">send()</tt> method will be the only method used resume your generator function.
In addition to <tt class="docutils literal">send()</tt>, there are two other new methods on generators:
<ul>
<li><tt class="docutils literal">throw(type, value=None, traceback=None)</tt> is used to raise an exception
inside the generator; the exception is raised by the <tt class="docutils literal">yield</tt> expression
where the generator&#8217;s execution is paused.
</li>
<li><tt class="docutils literal">close()</tt> raises a <a title="exceptions.GeneratorExit" class="reference external" href="../library/exceptions.html#exceptions.GeneratorExit"><tt class="xref docutils literal">GeneratorExit</tt></a> exception inside the generator to
terminate the iteration. On receiving this exception, the generator&#8217;s code
must either raise <a title="exceptions.GeneratorExit" class="reference external" href="../library/exceptions.html#exceptions.GeneratorExit"><tt class="xref docutils literal">GeneratorExit</tt></a> or <a title="exceptions.StopIteration" class="reference external" href="../library/exceptions.html#exceptions.StopIteration"><tt class="xref docutils literal">StopIteration</tt></a>; catching the
exception and doing anything else is illegal and will trigger a
<a title="exceptions.RuntimeError" class="reference external" href="../library/exceptions.html#exceptions.RuntimeError"><tt class="xref docutils literal">RuntimeError</tt></a>. <tt class="docutils literal">close()</tt> will also be called by Python&#8217;s garbage
collector when the generator is garbage-collected.
If you need to run cleanup code when a <a title="exceptions.GeneratorExit" class="reference external" href="../library/exceptions.html#exceptions.GeneratorExit"><tt class="xref docutils literal">GeneratorExit</tt></a> occurs, I suggest
using a <tt class="docutils literal">try: ... finally:</tt> suite instead of catching <a title="exceptions.GeneratorExit" class="reference external" href="../library/exceptions.html#exceptions.GeneratorExit"><tt class="xref docutils literal">GeneratorExit</tt></a>.
</li>
</ul>
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 <tt class="docutils literal">return</tt> statement), but coroutines can be entered, exited,
and resumed at many different points (the <tt class="docutils literal">yield</tt> statements).
</div>
</div>
<div class="section" id="built-in-functions">
<h2>Built-in functions<a class="headerlink" href="#built-in-functions" title="Permalink to this headline">¶</a></h2>
Let&#8217;s look in more detail at built-in functions often used with iterators.
Two of Python&#8217;s built-in functions, <a title="map" class="reference external" href="../library/functions.html#map"><tt class="xref docutils literal">map()</tt></a> and <a title="filter" class="reference external" href="../library/functions.html#filter"><tt class="xref docutils literal">filter()</tt></a>, are somewhat
obsolete; they duplicate the features of list comprehensions but return actual
lists instead of iterators.
<tt class="docutils literal">map(f, iterA, iterB, ...)</tt> returns a list containing <tt class="docutils literal">f(iterA[0], iterB[0]),
f(iterA[1], iterB[1]), f(iterA[2], iterB[2]), ...</tt>.
<blockquote>
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; def upper(s):
... return s.upper()
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; map(upper, [&#39;sentence&#39;, &#39;fragment&#39;])
[&#39;SENTENCE&#39;, &#39;FRAGMENT&#39;]
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; [upper(s) for s in [&#39;sentence&#39;, &#39;fragment&#39;]]
[&#39;SENTENCE&#39;, &#39;FRAGMENT&#39;]
</pre></div>
</div>
</blockquote>
As shown above, you can achieve the same effect with a list comprehension. The
<a title="itertools.imap" class="reference external" href="../library/itertools.html#itertools.imap"><tt class="xref docutils literal">itertools.imap()</tt></a> function does the same thing but can handle infinite
iterators; it&#8217;ll be discussed later, in the section on the <a title="Functions creating iterators for efficient looping." class="reference external" href="../library/itertools.html#module-itertools"><tt class="xref docutils literal">itertools</tt></a> module.
<tt class="docutils literal">filter(predicate, iter)</tt> 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 <a title="filter" class="reference external" href="../library/functions.html#filter"><tt class="xref docutils literal">filter()</tt></a>, the predicate must take a single
value.
<blockquote>
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; def is_even(x):
... return (x % 2) == 0
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; filter(is_even, range(10))
[0, 2, 4, 6, 8]
</pre></div>
</div>
</blockquote>
This can also be written as a list comprehension:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; [x for x in range(10) if is_even(x)]
[0, 2, 4, 6, 8]
</pre></div>
</div>
<a title="filter" class="reference external" href="../library/functions.html#filter"><tt class="xref docutils literal">filter()</tt></a> also has a counterpart in the <a title="Functions creating iterators for efficient looping." class="reference external" href="../library/itertools.html#module-itertools"><tt class="xref docutils literal">itertools</tt></a> module,
<a title="itertools.ifilter" class="reference external" href="../library/itertools.html#itertools.ifilter"><tt class="xref docutils literal">itertools.ifilter()</tt></a>, that returns an iterator and can therefore handle
infinite sequences just as <a title="itertools.imap" class="reference external" href="../library/itertools.html#itertools.imap"><tt class="xref docutils literal">itertools.imap()</tt></a> can.
<tt class="docutils literal">reduce(func, iter, [initial_value])</tt> doesn&#8217;t have a counterpart in the
<a title="Functions creating iterators for efficient looping." class="reference external" href="../library/itertools.html#module-itertools"><tt class="xref docutils literal">itertools</tt></a> module because it cumulatively performs an operation on all the
iterable&#8217;s elements and therefore can&#8217;t be applied to infinite iterables.
<tt class="docutils literal">func</tt> must be a function that takes two elements and returns a single value.
<a title="reduce" class="reference external" href="../library/functions.html#reduce"><tt class="xref docutils literal">reduce()</tt></a> takes the first two elements A and B returned by the iterator and
calculates <tt class="docutils literal">func(A, B)</tt>. It then requests the third element, C, calculates
<tt class="docutils literal">func(func(A, B), C)</tt>, combines this result with the fourth element returned,
and continues until the iterable is exhausted. If the iterable returns no
values at all, a <a title="exceptions.TypeError" class="reference external" href="../library/exceptions.html#exceptions.TypeError"><tt class="xref docutils literal">TypeError</tt></a> exception is raised. If the initial value is
supplied, it&#8217;s used as a starting point and <tt class="docutils literal">func(initial_value, A)</tt> is the
first calculation.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; import operator
&gt;&gt;&gt; reduce(operator.concat, [&#39;A&#39;, &#39;BB&#39;, &#39;C&#39;])
&#39;ABBC&#39;
&gt;&gt;&gt; reduce(operator.concat, [])
Traceback (most recent call last):
 ...
TypeError: reduce() of empty sequence with no initial value
&gt;&gt;&gt; reduce(operator.mul, [1,2,3], 1)
6
&gt;&gt;&gt; reduce(operator.mul, [], 1)
1
</pre></div>
</div>
If you use <a title="operator.add" class="reference external" href="../library/operator.html#operator.add"><tt class="xref docutils literal">operator.add()</tt></a> with <a title="reduce" class="reference external" href="../library/functions.html#reduce"><tt class="xref docutils literal">reduce()</tt></a>, you&#8217;ll add up all the
elements of the iterable. This case is so common that there&#8217;s a special
built-in called <a title="sum" class="reference external" href="../library/functions.html#sum"><tt class="xref docutils literal">sum()</tt></a> to compute it:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; reduce(operator.add, [1,2,3,4], 0)
10
&gt;&gt;&gt; sum([1,2,3,4])
10
&gt;&gt;&gt; sum([])
0
</pre></div>
</div>
For many uses of <a title="reduce" class="reference external" href="../library/functions.html#reduce"><tt class="xref docutils literal">reduce()</tt></a>, though, it can be clearer to just write the
obvious <a class="reference external" href="../reference/compound_stmts.html#for"><tt class="xref docutils literal">for</tt></a> loop:
<div class="highlight-python"><div class="highlight"><pre># Instead of:
product = reduce(operator.mul, [1,2,3], 1)

# You can write:
product = 1
for i in [1,2,3]:
 product *= i
</pre></div>
</div>
<tt class="docutils literal">enumerate(iter)</tt> counts off the elements in the iterable, returning 2-tuples
containing the count and each element.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; for item in enumerate([&#39;subject&#39;, &#39;verb&#39;, &#39;object&#39;]):
... print item
(0, &#39;subject&#39;)
(1, &#39;verb&#39;)
(2, &#39;object&#39;)
</pre></div>
</div>
<a title="enumerate" class="reference external" href="../library/functions.html#enumerate"><tt class="xref docutils literal">enumerate()</tt></a> is often used when looping through a list and recording the
indexes at which certain conditions are met:
<div class="highlight-python"><div class="highlight"><pre>f = open(&#39;data.txt&#39;, &#39;r&#39;)
for i, line in enumerate(f):
 if line.strip() == &#39;&#39;:
 print &#39;Blank line at line #%i&#39; % i
</pre></div>
</div>
<tt class="docutils literal">sorted(iterable, [cmp=None], [key=None], [reverse=False])</tt> collects all the
elements of the iterable into a list, sorts the list, and returns the sorted
result. The <tt class="docutils literal">cmp</tt>, <tt class="docutils literal">key</tt>, and <tt class="docutils literal">reverse</tt> arguments are passed through to
the constructed list&#8217;s <tt class="docutils literal">.sort()</tt> method.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; import random
&gt;&gt;&gt; # Generate 8 random numbers between [0, 10000)
&gt;&gt;&gt; rand_list = random.sample(range(10000), 8)
&gt;&gt;&gt; rand_list
[769, 7953, 9828, 6431, 8442, 9878, 6213, 2207]
&gt;&gt;&gt; sorted(rand_list)
[769, 2207, 6213, 6431, 7953, 8442, 9828, 9878]
&gt;&gt;&gt; sorted(rand_list, reverse=True)
[9878, 9828, 8442, 7953, 6431, 6213, 2207, 769]
</pre></div>
</div>
(For a more detailed discussion of sorting, see the Sorting mini-HOWTO in the
Python wiki at <a class="reference external" href="http://wiki.python.org/moin/HowTo/Sorting">http://wiki.python.org/moin/HowTo/Sorting</a>.)
The <tt class="docutils literal">any(iter)</tt> and <tt class="docutils literal">all(iter)</tt> built-ins look at the truth values of an
iterable&#8217;s contents. <a title="any" class="reference external" href="../library/functions.html#any"><tt class="xref docutils literal">any()</tt></a> returns True if any element in the iterable is
a true value, and <a title="all" class="reference external" href="../library/functions.html#all"><tt class="xref docutils literal">all()</tt></a> returns True if all of the elements are true
values:
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; any([0,1,0])
True
&gt;&gt;&gt; any([0,0,0])
False
&gt;&gt;&gt; any([1,1,1])
True
&gt;&gt;&gt; all([0,1,0])
False
&gt;&gt;&gt; all([0,0,0])
False
&gt;&gt;&gt; all([1,1,1])
True
</pre></div>
</div>
</div>
<div class="section" id="small-functions-and-the-lambda-expression">
<h2>Small functions and the lambda expression<a class="headerlink" href="#small-functions-and-the-lambda-expression" title="Permalink to this headline">¶</a></h2>
When writing functional-style programs, you&#8217;ll often need little functions that
act as predicates or that combine elements in some way.
If there&#8217;s a Python built-in or a module function that&#8217;s suitable, you don&#8217;t
need to define a new function at all:
<div class="highlight-python"><div class="highlight"><pre>stripped_lines = [line.strip() for line in lines]
existing_files = filter(os.path.exists, file_list)
</pre></div>
</div>
If the function you need doesn&#8217;t exist, you need to write it. One way to write
small functions is to use the <tt class="docutils literal">lambda</tt> statement. <tt class="docutils literal">lambda</tt> takes a number
of parameters and an expression combining these parameters, and creates a small
function that returns the value of the expression:
<div class="highlight-python"><div class="highlight"><pre>lowercase = lambda x: x.lower()

print_assign = lambda name, value: name + &#39;=&#39; + str(value)

adder = lambda x, y: x+y
</pre></div>
</div>
An alternative is to just use the <tt class="docutils literal">def</tt> statement and define a function in the
usual way:
<div class="highlight-python"><div class="highlight"><pre>def lowercase(x):
 return x.lower()

def print_assign(name, value):
 return name + &#39;=&#39; + str(value)

def adder(x,y):
 return x + y
</pre></div>
</div>
Which alternative is preferable? That&#8217;s a style question; my usual course is to
avoid using <tt class="docutils literal">lambda</tt>.
One reason for my preference is that <tt class="docutils literal">lambda</tt> is quite limited in the
functions it can define. The result has to be computable as a single
expression, which means you can&#8217;t have multiway <tt class="docutils literal">if... elif... else</tt>
comparisons or <tt class="docutils literal">try... except</tt> statements. If you try to do too much in a
<tt class="docutils literal">lambda</tt> statement, you&#8217;ll end up with an overly complicated expression that&#8217;s
hard to read. Quick, what&#8217;s the following code doing?
<div class="highlight-python"><div class="highlight"><pre>total = reduce(lambda a, b: (0, a[1] + b[1]), items)[1]
</pre></div>
</div>
You can figure it out, but it takes time to disentangle the expression to figure
out what&#8217;s going on. Using a short nested <tt class="docutils literal">def</tt> statements makes things a
little bit better:
<div class="highlight-python"><div class="highlight"><pre>def combine (a, b):
 return 0, a[1] + b[1]

total = reduce(combine, items)[1]
</pre></div>
</div>
But it would be best of all if I had simply used a <tt class="docutils literal">for</tt> loop:
<div class="highlight-python"><div class="highlight"><pre>total = 0
for a, b in items:
 total += b
</pre></div>
</div>
Or the <a title="sum" class="reference external" href="../library/functions.html#sum"><tt class="xref docutils literal">sum()</tt></a> built-in and a generator expression:
<div class="highlight-python"><div class="highlight"><pre>total = sum(b for a,b in items)
</pre></div>
</div>
Many uses of <a title="reduce" class="reference external" href="../library/functions.html#reduce"><tt class="xref docutils literal">reduce()</tt></a> are clearer when written as <tt class="docutils literal">for</tt> loops.
Fredrik Lundh once suggested the following set of rules for refactoring uses of
<tt class="docutils literal">lambda</tt>:
<ol class="arabic simple">
<li>Write a lambda function.</li>
<li>Write a comment explaining what the heck that lambda does.</li>
<li>Study the comment for a while, and think of a name that captures the essence
of the comment.</li>
<li>Convert the lambda to a def statement, using that name.</li>
<li>Remove the comment.</li>
</ol>
I really like these rules, but you&#8217;re free to disagree
about whether this lambda-free style is better.
</div>
<div class="section" id="the-itertools-module">
<h2>The itertools module<a class="headerlink" href="#the-itertools-module" title="Permalink to this headline">¶</a></h2>
The <a title="Functions creating iterators for efficient looping." class="reference external" href="../library/itertools.html#module-itertools"><tt class="xref docutils literal">itertools</tt></a> module contains a number of commonly-used iterators as well
as functions for combining several iterators. This section will introduce the
module&#8217;s contents by showing small examples.
The module&#8217;s functions fall into a few broad classes:
<ul class="simple">
<li>Functions that create a new iterator based on an existing iterator.</li>
<li>Functions for treating an iterator&#8217;s elements as function arguments.</li>
<li>Functions for selecting portions of an iterator&#8217;s output.</li>
<li>A function for grouping an iterator&#8217;s output.</li>
</ul>
<div class="section" id="creating-new-iterators">
<h3>Creating new iterators<a class="headerlink" href="#creating-new-iterators" title="Permalink to this headline">¶</a></h3>
<tt class="docutils literal">itertools.count(n)</tt> returns an infinite stream of integers, increasing by 1
each time. You can optionally supply the starting number, which defaults to 0:
<div class="highlight-python"><pre>itertools.count() =&gt;
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
itertools.count(10) =&gt;
 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, ...</pre>
</div>
<tt class="docutils literal">itertools.cycle(iter)</tt> 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.
<div class="highlight-python"><pre>itertools.cycle([1,2,3,4,5]) =&gt;
 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, ...</pre>
</div>
<tt class="docutils literal">itertools.repeat(elem, [n])</tt> returns the provided element <tt class="docutils literal">n</tt> times, or
returns the element endlessly if <tt class="docutils literal">n</tt> is not provided.
<div class="highlight-python"><pre>itertools.repeat('abc') =&gt;
 abc, abc, abc, abc, abc, abc, abc, abc, abc, abc, ...
itertools.repeat('abc', 5) =&gt;
 abc, abc, abc, abc, abc</pre>
</div>
<tt class="docutils literal">itertools.chain(iterA, iterB, ...)</tt> 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.
<div class="highlight-python"><pre>itertools.chain(['a', 'b', 'c'], (1, 2, 3)) =&gt;
 a, b, c, 1, 2, 3</pre>
</div>
<tt class="docutils literal">itertools.izip(iterA, iterB, ...)</tt> takes one element from each iterable and
returns them in a tuple:
<div class="highlight-python"><pre>itertools.izip(['a', 'b', 'c'], (1, 2, 3)) =&gt;
 ('a', 1), ('b', 2), ('c', 3)</pre>
</div>
It&#8217;s similar to the built-in <a title="zip" class="reference external" href="../library/functions.html#zip"><tt class="xref docutils literal">zip()</tt></a> function, but doesn&#8217;t construct an
in-memory list and exhaust all the input iterators before returning; instead
tuples are constructed and returned only if they&#8217;re requested. (The technical
term for this behaviour is <a class="reference external" href="http://en.wikipedia.org/wiki/Lazy_evaluation">lazy evaluation</a>.)
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.
<div class="highlight-python"><pre>itertools.izip(['a', 'b'], (1, 2, 3)) =&gt;
 ('a', 1), ('b', 2)</pre>
</div>
You should avoid doing this, though, because an element may be taken from the
longer iterators and discarded. This means you can&#8217;t go on to use the iterators
further because you risk skipping a discarded element.
<tt class="docutils literal">itertools.islice(iter, [start], stop, [step])</tt> returns a stream that&#8217;s a
slice of the iterator. With a single <tt class="docutils literal">stop</tt> argument, it will return the
first <tt class="docutils literal">stop</tt> elements. If you supply a starting index, you&#8217;ll get
<tt class="docutils literal">stop-start</tt> elements, and if you supply a value for <tt class="docutils literal">step</tt>, elements will
be skipped accordingly. Unlike Python&#8217;s string and list slicing, you can&#8217;t use
negative values for <tt class="docutils literal">start</tt>, <tt class="docutils literal">stop</tt>, or <tt class="docutils literal">step</tt>.
<div class="highlight-python"><pre>itertools.islice(range(10), 8) =&gt;
 0, 1, 2, 3, 4, 5, 6, 7
itertools.islice(range(10), 2, 8) =&gt;
 2, 3, 4, 5, 6, 7
itertools.islice(range(10), 2, 8, 2) =&gt;
 2, 4, 6</pre>
</div>
<tt class="docutils literal">itertools.tee(iter, [n])</tt> replicates an iterator; it returns <tt class="docutils literal">n</tt>
independent iterators that will all return the contents of the source iterator.
If you don&#8217;t supply a value for <tt class="docutils literal">n</tt>, 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.
<div class="highlight-python"><pre>itertools.tee( itertools.count() ) =&gt;
 iterA, iterB

where iterA -&gt;
   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...

and iterB -&gt;
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...</pre>
</div>
</div>
<div class="section" id="calling-functions-on-elements">
<h3>Calling functions on elements<a class="headerlink" href="#calling-functions-on-elements" title="Permalink to this headline">¶</a></h3>
Two functions are used for calling other functions on the contents of an
iterable.
<tt class="docutils literal">itertools.imap(f, iterA, iterB, ...)</tt> returns a stream containing
<tt class="docutils literal">f(iterA[0], iterB[0]), f(iterA[1], iterB[1]), f(iterA[2], iterB[2]), ...</tt>:
<div class="highlight-python"><pre>itertools.imap(operator.add, [5, 6, 5], [1, 2, 3]) =&gt;
 6, 8, 8</pre>
</div>
The <tt class="docutils literal">operator</tt> module contains a set of functions corresponding to Python&#8217;s
operators. Some examples are <tt class="docutils literal">operator.add(a, b)</tt> (adds two values),
<tt class="docutils literal">operator.ne(a, b)</tt> (same as <tt class="docutils literal">a!=b</tt>), and <tt class="docutils literal">operator.attrgetter('id')</tt>
(returns a callable that fetches the <tt class="docutils literal">&quot;id&quot;</tt> attribute).
<tt class="docutils literal">itertools.starmap(func, iter)</tt> assumes that the iterable will return a stream
of tuples, and calls <tt class="docutils literal">f()</tt> using these tuples as the arguments:
<div class="highlight-python"><pre>itertools.starmap(os.path.join,
 [('/usr', 'bin', 'java'), ('/bin', 'python'),
 ('/usr', 'bin', 'perl'),('/usr', 'bin', 'ruby')])
=&gt;
 /usr/bin/java, /bin/python, /usr/bin/perl, /usr/bin/ruby</pre>
</div>
</div>
<div class="section" id="selecting-elements">
<h3>Selecting elements<a class="headerlink" href="#selecting-elements" title="Permalink to this headline">¶</a></h3>
Another group of functions chooses a subset of an iterator&#8217;s elements based on a
predicate.
<tt class="docutils literal">itertools.ifilter(predicate, iter)</tt> returns all the elements for which the
predicate returns true:
<div class="highlight-python"><pre>def is_even(x):
 return (x % 2) == 0

itertools.ifilter(is_even, itertools.count()) =&gt;
 0, 2, 4, 6, 8, 10, 12, 14, ...</pre>
</div>
<tt class="docutils literal">itertools.ifilterfalse(predicate, iter)</tt> is the opposite, returning all
elements for which the predicate returns false:
<div class="highlight-python"><pre>itertools.ifilterfalse(is_even, itertools.count()) =&gt;
 1, 3, 5, 7, 9, 11, 13, 15, ...</pre>
</div>
<tt class="docutils literal">itertools.takewhile(predicate, iter)</tt> returns elements for as long as the
predicate returns true. Once the predicate returns false, the iterator will
signal the end of its results.
<div class="highlight-python"><pre>def less_than_10(x):
 return (x &lt; 10)

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

itertools.takewhile(is_even, itertools.count()) =&gt;
 0</pre>
</div>
<tt class="docutils literal">itertools.dropwhile(predicate, iter)</tt> discards elements while the predicate
returns true, and then returns the rest of the iterable&#8217;s results.
<div class="highlight-python"><pre>itertools.dropwhile(less_than_10, itertools.count()) =&gt;
 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, ...

itertools.dropwhile(is_even, itertools.count()) =&gt;
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...</pre>
</div>
</div>
<div class="section" id="grouping-elements">
<h3>Grouping elements<a class="headerlink" href="#grouping-elements" title="Permalink to this headline">¶</a></h3>
The last function I&#8217;ll discuss, <tt class="docutils literal">itertools.groupby(iter, key_func=None)</tt>, is
the most complicated. <tt class="docutils literal">key_func(elem)</tt> is a function that can compute a key
value for each element returned by the iterable. If you don&#8217;t supply a key
function, the key is simply each element itself.
<tt class="docutils literal">groupby()</tt> 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.
<div class="highlight-python"><pre>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) =&gt;
  ('AL', iterator-1),
  ('AK', iterator-2),
  ('AZ', iterator-3), ...

where
iterator-1 =&gt;
 ('Decatur', 'AL'), ('Huntsville', 'AL'), ('Selma', 'AL')
iterator-2 =&gt;
 ('Anchorage', 'AK'), ('Nome', 'AK')
iterator-3 =&gt;
 ('Flagstaff', 'AZ'), ('Phoenix', 'AZ'), ('Tucson', 'AZ')</pre>
</div>
<tt class="docutils literal">groupby()</tt> assumes that the underlying iterable&#8217;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.
</div>
</div>
<div class="section" id="the-functools-module">
<h2>The functools module<a class="headerlink" href="#the-functools-module" title="Permalink to this headline">¶</a></h2>
The <a title="Higher order functions and operations on callable objects." class="reference external" href="../library/functools.html#module-functools"><tt class="xref docutils literal">functools</tt></a> 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
<a title="functools.partial" class="reference external" href="../library/functools.html#functools.partial"><tt class="xref docutils literal">functools.partial()</tt></a> function.
For programs written in a functional style, you&#8217;ll sometimes want to construct
variants of existing functions that have some of the parameters filled in.
Consider a Python function <tt class="docutils literal">f(a, b, c)</tt>; you may wish to create a new function
<tt class="docutils literal">g(b, c)</tt> that&#8217;s equivalent to <tt class="docutils literal">f(1, b, c)</tt>; you&#8217;re filling in a value for
one of <tt class="docutils literal">f()</tt>&#8216;s parameters. This is called &#8220;partial function application&#8221;.
The constructor for <tt class="docutils literal">partial</tt> takes the arguments <tt class="docutils literal">(function, arg1, arg2,
... kwarg1=value1, kwarg2=value2)</tt>. The resulting object is callable, so you
can just call it to invoke <tt class="docutils literal">function</tt> with the filled-in arguments.
Here&#8217;s a small but realistic example:
<div class="highlight-python"><div class="highlight"><pre>import functools

def log (message, subsystem):
 &quot;Write the contents of &#39;message&#39; to the specified subsystem.&quot;
 print &#39;%s: %s&#39; % (subsystem, message)
 ...

server_log = functools.partial(log, subsystem=&#39;server&#39;)
server_log(&#39;Unable to open socket&#39;)
</pre></div>
</div>
<div class="section" id="the-operator-module">
<h3>The operator module<a class="headerlink" href="#the-operator-module" title="Permalink to this headline">¶</a></h3>
The <a title="Functions corresponding to the standard operators." class="reference external" href="../library/operator.html#module-operator"><tt class="xref docutils literal">operator</tt></a> module was mentioned earlier. It contains a set of
functions corresponding to Python&#8217;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:
<ul class="simple">
<li>Math operations: <tt class="docutils literal">add()</tt>, <tt class="docutils literal">sub()</tt>, <tt class="docutils literal">mul()</tt>, <tt class="docutils literal">div()</tt>, <tt class="docutils literal">floordiv()</tt>,
<tt class="docutils literal">abs()</tt>, ...</li>
<li>Logical operations: <tt class="docutils literal">not_()</tt>, <tt class="docutils literal">truth()</tt>.</li>
<li>Bitwise operations: <tt class="docutils literal">and_()</tt>, <tt class="docutils literal">or_()</tt>, <tt class="docutils literal">invert()</tt>.</li>
<li>Comparisons: <tt class="docutils literal">eq()</tt>, <tt class="docutils literal">ne()</tt>, <tt class="docutils literal">lt()</tt>, <tt class="docutils literal">le()</tt>, <tt class="docutils literal">gt()</tt>, and <tt class="docutils literal">ge()</tt>.</li>
<li>Object identity: <tt class="docutils literal">is_()</tt>, <tt class="docutils literal">is_not()</tt>.</li>
</ul>
Consult the operator module&#8217;s documentation for a complete list.
</div>
<div class="section" id="the-functional-module">
<h3>The functional module<a class="headerlink" href="#the-functional-module" title="Permalink to this headline">¶</a></h3>
Collin Winter&#8217;s <a class="reference external" href="http://oakwinter.com/code/functional/">functional module</a>
provides a number of more advanced tools for functional programming. It also
reimplements several Python built-ins, trying to make them more intuitive to
those used to functional programming in other languages.
This section contains an introduction to some of the most important functions in
<tt class="docutils literal">functional</tt>; full documentation can be found at <a class="reference external" href="http://oakwinter.com/code/functional/documentation/">the project&#8217;s website</a>.
<tt class="docutils literal">compose(outer, inner, unpack=False)</tt>
The <tt class="docutils literal">compose()</tt> function implements function composition. In other words, it
returns a wrapper around the <tt class="docutils literal">outer</tt> and <tt class="docutils literal">inner</tt> callables, such that the
return value from <tt class="docutils literal">inner</tt> is fed directly to <tt class="docutils literal">outer</tt>. That is,
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; def add(a, b):
... return a + b
...
&gt;&gt;&gt; def double(a):
... return 2 * a
...
&gt;&gt;&gt; compose(double, add)(5, 6)
22
</pre></div>
</div>
is equivalent to
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; double(add(5, 6))
22
</pre></div>
</div>
The <tt class="docutils literal">unpack</tt> keyword is provided to work around the fact that Python functions
are not always <a class="reference external" href="http://en.wikipedia.org/wiki/Currying">fully curried</a>. By
default, it is expected that the <tt class="docutils literal">inner</tt> function will return a single object
and that the <tt class="docutils literal">outer</tt> function will take a single argument. Setting the
<tt class="docutils literal">unpack</tt> argument causes <tt class="docutils literal">compose</tt> to expect a tuple from <tt class="docutils literal">inner</tt> which
will be expanded before being passed to <tt class="docutils literal">outer</tt>. Put simply,
<div class="highlight-python"><div class="highlight"><pre>compose(f, g)(5, 6)
</pre></div>
</div>
is equivalent to:
<div class="highlight-python"><div class="highlight"><pre>f(g(5, 6))
</pre></div>
</div>
while
<div class="highlight-python"><div class="highlight"><pre>compose(f, g, unpack=True)(5, 6)
</pre></div>
</div>
is equivalent to:
<div class="highlight-python"><div class="highlight"><pre>f(*g(5, 6))
</pre></div>
</div>
Even though <tt class="docutils literal">compose()</tt> only accepts two functions, it&#8217;s trivial to build up a
version that will compose any number of functions. We&#8217;ll use <tt class="docutils literal">reduce()</tt>,
<tt class="docutils literal">compose()</tt> and <tt class="docutils literal">partial()</tt> (the last of which is provided by both
<tt class="docutils literal">functional</tt> and <tt class="docutils literal">functools</tt>).
<div class="highlight-python"><div class="highlight"><pre>from functional import compose, partial

multi_compose = partial(reduce, compose)
</pre></div>
</div>
We can also use <tt class="docutils literal">map()</tt>, <tt class="docutils literal">compose()</tt> and <tt class="docutils literal">partial()</tt> to craft a version of
<tt class="docutils literal">&quot;&quot;.join(...)</tt> that converts its arguments to string:
<div class="highlight-python"><div class="highlight"><pre>from functional import compose, partial

join = compose(&quot;&quot;.join, partial(map, str))
</pre></div>
</div>
<tt class="docutils literal">flip(func)</tt>
<tt class="docutils literal">flip()</tt> wraps the callable in <tt class="docutils literal">func</tt> and causes it to receive its
non-keyword arguments in reverse order.
<div class="highlight-python"><div class="highlight"><pre>&gt;&gt;&gt; def triple(a, b, c):
... return (a, b, c)
...
&gt;&gt;&gt; triple(5, 6, 7)
(5, 6, 7)
&gt;&gt;&gt;
&gt;&gt;&gt; flipped_triple = flip(triple)
&gt;&gt;&gt; flipped_triple(5, 6, 7)
(7, 6, 5)
</pre></div>
</div>
<tt class="docutils literal">foldl(func, start, iterable)</tt>
<tt class="docutils literal">foldl()</tt> takes a binary function, a starting value (usually some kind of
&#8216;zero&#8217;), and an iterable. The function is applied to the starting value and the
first element of the list, then the result of that and the second element of the
list, then the result of that and the third element of the list, and so on.
This means that a call such as:
<div class="highlight-python"><div class="highlight"><pre>foldl(f, 0, [1, 2, 3])
</pre></div>
</div>
is equivalent to:
<div class="highlight-python"><div class="highlight"><pre>f(f(f(0, 1), 2), 3)
</pre></div>
</div>
<tt class="docutils literal">foldl()</tt> is roughly equivalent to the following recursive function:
<div class="highlight-python"><div class="highlight"><pre>def foldl(func, start, seq):
 if len(seq) == 0:
 return start

return foldl(func, func(start, seq[0]), seq[1:])
</pre></div>
</div>
Speaking of equivalence, the above <tt class="docutils literal">foldl</tt> call can be expressed in terms of
the built-in <tt class="docutils literal">reduce</tt> like so:
<div class="highlight-python"><div class="highlight"><pre>reduce(f, [1, 2, 3], 0)
</pre></div>
</div>
We can use <tt class="docutils literal">foldl()</tt>, <tt class="docutils literal">operator.concat()</tt> and <tt class="docutils literal">partial()</tt> to write a
cleaner, more aesthetically-pleasing version of Python&#8217;s <tt class="docutils literal">&quot;&quot;.join(...)</tt>
idiom:
<div class="highlight-python"><pre>from functional import foldl, partial from operator import concat

join = partial(foldl, concat, "")</pre>
</div>
</div>
</div>
<div class="section" id="revision-history-and-acknowledgements">
<h2>Revision History and Acknowledgements<a class="headerlink" href="#revision-history-and-acknowledgements" title="Permalink to this headline">¶</a></h2>
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 <tt class="docutils literal">functional</tt> module written by Collin
Winter; adds short section on the operator module; a few other edits.
</div>
<div class="section" id="references">
<h2>References<a class="headerlink" href="#references" title="Permalink to this headline">¶</a></h2>
<div class="section" id="general">
<h3>General<a class="headerlink" href="#general" title="Permalink to this headline">¶</a></h3>
Structure and Interpretation of Computer Programs, by Harold Abelson and
Gerald Jay Sussman with Julie Sussman. Full text at
<a class="reference external" href="http://mitpress.mit.edu/sicp/">http://mitpress.mit.edu/sicp/</a>. 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.
<a class="reference external" href="http://www.defmacro.org/ramblings/fp.html">http://www.defmacro.org/ramblings/fp.html</a>: A general introduction to functional
programming that uses Java examples and has a lengthy historical introduction.
<a class="reference external" href="http://en.wikipedia.org/wiki/Functional_programming">http://en.wikipedia.org/wiki/Functional_programming</a>: General Wikipedia entry
describing functional programming.
<a class="reference external" href="http://en.wikipedia.org/wiki/Coroutine">http://en.wikipedia.org/wiki/Coroutine</a>: Entry for coroutines.
<a class="reference external" href="http://en.wikipedia.org/wiki/Currying">http://en.wikipedia.org/wiki/Currying</a>: Entry for the concept of currying.
</div>
<div class="section" id="python-specific">
<h3>Python-specific<a class="headerlink" href="#python-specific" title="Permalink to this headline">¶</a></h3>
<a class="reference external" href="http://gnosis.cx/TPiP/">http://gnosis.cx/TPiP/</a>: The first chapter of David Mertz&#8217;s book
<cite>Text Processing in Python</cite> discusses functional programming
for text processing, in the section titled &#8220;Utilizing Higher-Order Functions in
Text Processing&#8221;.
Mertz also wrote a 3-part series of articles on functional programming
for IBM&#8217;s DeveloperWorks site; see
<a class="reference external" href="http://www-128.ibm.com/developerworks/library/l-prog.html">part 1</a>,
<a class="reference external" href="http://www-128.ibm.com/developerworks/library/l-prog2.html">part 2</a>, and
<a class="reference external" href="http://www-128.ibm.com/developerworks/linux/library/l-prog3.html">part 3</a>,
</div>
<div class="section" id="python-documentation">
<h3>Python documentation<a class="headerlink" href="#python-documentation" title="Permalink to this headline">¶</a></h3>
Documentation for the <a title="Functions creating iterators for efficient looping." class="reference external" href="../library/itertools.html#module-itertools"><tt class="xref docutils literal">itertools</tt></a> module.
Documentation for the <a title="Functions corresponding to the standard operators." class="reference external" href="../library/operator.html#module-operator"><tt class="xref docutils literal">operator</tt></a> module.
<a class="reference external" href="http://www.python.org/dev/peps/pep-0289">PEP 289</a>: &#8220;Generator Expressions&#8221;
<a class="reference external" href="http://www.python.org/dev/peps/pep-0342">PEP 342</a>: &#8220;Coroutines via Enhanced Generators&#8221; describes the new generator
features in Python 2.5.
</div>
</div>
</div>

</div>
 </div>
 </div>
 <div class="sphinxsidebar">
 <div class="sphinxsidebarwrapper">
 <h3><a href="../contents.html">Table Of Contents</a></h3>
 <ul>
<li><a class="reference external" href="#">Functional Programming HOWTO</a><ul>
<li><a class="reference external" href="#introduction">Introduction</a><ul>
<li><a class="reference external" href="#formal-provability">Formal provability</a></li>
<li><a class="reference external" href="#modularity">Modularity</a></li>
<li><a class="reference external" href="#ease-of-debugging-and-testing">Ease of debugging and testing</a></li>
<li><a class="reference external" href="#composability">Composability</a></li>
</ul>
</li>
<li><a class="reference external" href="#iterators">Iterators</a><ul>
<li><a class="reference external" href="#data-types-that-support-iterators">Data Types That Support Iterators</a></li>
</ul>
</li>
<li><a class="reference external" href="#generator-expressions-and-list-comprehensions">Generator expressions and list comprehensions</a></li>
<li><a class="reference external" href="#generators">Generators</a><ul>
<li><a class="reference external" href="#passing-values-into-a-generator">Passing values into a generator</a></li>
</ul>
</li>
<li><a class="reference external" href="#built-in-functions">Built-in functions</a></li>
<li><a class="reference external" href="#small-functions-and-the-lambda-expression">Small functions and the lambda expression</a></li>
<li><a class="reference external" href="#the-itertools-module">The itertools module</a><ul>
<li><a class="reference external" href="#creating-new-iterators">Creating new iterators</a></li>
<li><a class="reference external" href="#calling-functions-on-elements">Calling functions on elements</a></li>
<li><a class="reference external" href="#selecting-elements">Selecting elements</a></li>
<li><a class="reference external" href="#grouping-elements">Grouping elements</a></li>
</ul>
</li>
<li><a class="reference external" href="#the-functools-module">The functools module</a><ul>
<li><a class="reference external" href="#the-operator-module">The operator module</a></li>
<li><a class="reference external" href="#the-functional-module">The functional module</a></li>
</ul>
</li>
<li><a class="reference external" href="#revision-history-and-acknowledgements">Revision History and Acknowledgements</a></li>
<li><a class="reference external" href="#references">References</a><ul>
<li><a class="reference external" href="#general">General</a></li>
<li><a class="reference external" href="#python-specific">Python-specific</a></li>
<li><a class="reference external" href="#python-documentation">Python documentation</a></li>
</ul>
</li>
</ul>
</li>
</ul>

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