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  99. <li><a class="reference internal" href="#introduction">Introduction</a><ul>

  100. <li><a class="reference internal" href="#formal-provability">Formal provability</a></li>

  101. <li><a class="reference internal" href="#modularity">Modularity</a></li>

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  103. <li><a class="reference internal" href="#composability">Composability</a></li>

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  106. <li><a class="reference internal" href="#iterators">Iterators</a><ul>

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  117. <li><a class="reference internal" href="#creating-new-iterators">Creating new iterators</a></li>

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  119. <li><a class="reference internal" href="#selecting-elements">Selecting elements</a></li>

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  227.   <section id="functional-programming-howto">

  228. <h1>Functional Programming HOWTO<a class="headerlink" href="#functional-programming-howto" title="Link to this heading">¶</a></h1>

  229. <dl class="field-list simple">

  230. <dt class="field-odd">Author<span class="colon">:</span></dt>

  231. <dd class="field-odd"><p>A. M. Kuchling</p>

  232. </dd>

  233. <dt class="field-even">Release<span class="colon">:</span></dt>

  234. <dd class="field-even"><p>0.32</p>

  235. </dd>

  236. </dl>

  237. <p>In this document, we’ll take a tour of Python’s features suitable for

  238. implementing programs in a functional style.  After an introduction to the

  239. concepts of functional programming, we’ll look at language features such as

  240. <a class="reference internal" href="../glossary.html#term-iterator"><span class="xref std std-term">iterator</span></a>s and <a class="reference internal" href="../glossary.html#term-generator"><span class="xref std std-term">generator</span></a>s and relevant library modules such as

  241. <a class="reference internal" href="../library/itertools.html#module-itertools" title="itertools: Functions creating iterators for efficient looping."><code class="xref py py-mod docutils literal notranslate"><span class="pre">itertools</span></code></a> and <a class="reference internal" href="../library/functools.html#module-functools" title="functools: Higher-order functions and operations on callable objects."><code class="xref py py-mod docutils literal notranslate"><span class="pre">functools</span></code></a>.</p>

  242. <section id="introduction">

  243. <h2>Introduction<a class="headerlink" href="#introduction" title="Link to this heading">¶</a></h2>

  244. <p>This section explains the basic concept of functional programming; if

  245. you’re just interested in learning about Python language features,

  246. skip to the next section on <a class="reference internal" href="#functional-howto-iterators"><span class="std std-ref">Iterators</span></a>.</p>

  247. <p>Programming languages support decomposing problems in several different ways:</p>

  248. <ul class="simple">

  249. <li><p>Most programming languages are <strong>procedural</strong>: programs are lists of

  250. instructions that tell the computer what to do with the program’s input.  C,

  251. Pascal, and even Unix shells are procedural languages.</p></li>

  252. <li><p>In <strong>declarative</strong> languages, you write a specification that describes the

  253. problem to be solved, and the language implementation figures out how to

  254. perform the computation efficiently.  SQL is the declarative language you’re

  255. most likely to be familiar with; a SQL query describes the data set you want

  256. to retrieve, and the SQL engine decides whether to scan tables or use indexes,

  257. which subclauses should be performed first, etc.</p></li>

  258. <li><p><strong>Object-oriented</strong> programs manipulate collections of objects.  Objects have

  259. internal state and support methods that query or modify this internal state in

  260. some way. Smalltalk and Java are object-oriented languages.  C++ and Python

  261. are languages that support object-oriented programming, but don’t force the

  262. use of object-oriented features.</p></li>

  263. <li><p><strong>Functional</strong> programming decomposes a problem into a set of functions.

  264. Ideally, functions only take inputs and produce outputs, and don’t have any

  265. internal state that affects the output produced for a given input.  Well-known

  266. functional languages include the ML family (Standard ML, OCaml, and other

  267. variants) and Haskell.</p></li>

  268. </ul>

  269. <p>The designers of some computer languages choose to emphasize one

  270. particular approach to programming.  This often makes it difficult to

  271. write programs that use a different approach.  Other languages are

  272. multi-paradigm languages that support several different approaches.

  273. Lisp, C++, and Python are multi-paradigm; you can write programs or

  274. libraries that are largely procedural, object-oriented, or functional

  275. in all of these languages.  In a large program, different sections

  276. might be written using different approaches; the GUI might be

  277. object-oriented while the processing logic is procedural or

  278. functional, for example.</p>

  279. <p>In a functional program, input flows through a set of functions. Each function

  280. operates on its input and produces some output.  Functional style discourages

  281. functions with side effects that modify internal state or make other changes

  282. that aren’t visible in the function’s return value.  Functions that have no side

  283. effects at all are called <strong>purely functional</strong>.  Avoiding side effects means

  284. not using data structures that get updated as a program runs; every function’s

  285. output must only depend on its input.</p>

  286. <p>Some languages are very strict about purity and don’t even have assignment

  287. statements such as <code class="docutils literal notranslate"><span class="pre">a=3</span></code> or <code class="docutils literal notranslate"><span class="pre">c</span> <span class="pre">=</span> <span class="pre">a</span> <span class="pre">+</span> <span class="pre">b</span></code>, but it’s difficult to avoid all

  288. side effects, such as printing to the screen or writing to a disk file. Another

  289. example is a call to the <a class="reference internal" href="../library/functions.html#print" title="print"><code class="xref py py-func docutils literal notranslate"><span class="pre">print()</span></code></a> or <a class="reference internal" href="../library/time.html#time.sleep" title="time.sleep"><code class="xref py py-func docutils literal notranslate"><span class="pre">time.sleep()</span></code></a> function, neither

  290. of which returns a useful value. Both are called only for their side effects

  291. of sending some text to the screen or pausing execution for a second.</p>

  292. <p>Python programs written in functional style usually won’t go to the extreme of

  293. avoiding all I/O or all assignments; instead, they’ll provide a

  294. functional-appearing interface but will use non-functional features internally.

  295. For example, the implementation of a function will still use assignments to

  296. local variables, but won’t modify global variables or have other side effects.</p>

  297. <p>Functional programming can be considered the opposite of object-oriented

  298. programming.  Objects are little capsules containing some internal state along

  299. with a collection of method calls that let you modify this state, and programs

  300. consist of making the right set of state changes.  Functional programming wants

  301. to avoid state changes as much as possible and works with data flowing between

  302. functions.  In Python you might combine the two approaches by writing functions

  303. that take and return instances representing objects in your application (e-mail

  304. messages, transactions, etc.).</p>

  305. <p>Functional design may seem like an odd constraint to work under.  Why should you

  306. avoid objects and side effects?  There are theoretical and practical advantages

  307. to the functional style:</p>

  308. <ul class="simple">

  309. <li><p>Formal provability.</p></li>

  310. <li><p>Modularity.</p></li>

  311. <li><p>Composability.</p></li>

  312. <li><p>Ease of debugging and testing.</p></li>

  313. </ul>

  314. <section id="formal-provability">

  315. <h3>Formal provability<a class="headerlink" href="#formal-provability" title="Link to this heading">¶</a></h3>

  316. <p>A theoretical benefit is that it’s easier to construct a mathematical proof that

  317. a functional program is correct.</p>

  318. <p>For a long time researchers have been interested in finding ways to

  319. mathematically prove programs correct.  This is different from testing a program

  320. on numerous inputs and concluding that its output is usually correct, or reading

  321. a program’s source code and concluding that the code looks right; the goal is

  322. instead a rigorous proof that a program produces the right result for all

  323. possible inputs.</p>

  324. <p>The technique used to prove programs correct is to write down <strong>invariants</strong>,

  325. properties of the input data and of the program’s variables that are always

  326. true.  For each line of code, you then show that if invariants X and Y are true

  327. <strong>before</strong> the line is executed, the slightly different invariants X’ and Y’ are

  328. true <strong>after</strong> the line is executed.  This continues until you reach the end of

  329. the program, at which point the invariants should match the desired conditions

  330. on the program’s output.</p>

  331. <p>Functional programming’s avoidance of assignments arose because assignments are

  332. difficult to handle with this technique; assignments can break invariants that

  333. were true before the assignment without producing any new invariants that can be

  334. propagated onward.</p>

  335. <p>Unfortunately, proving programs correct is largely impractical and not relevant

  336. to Python software. Even trivial programs require proofs that are several pages

  337. long; the proof of correctness for a moderately complicated program would be

  338. enormous, and few or none of the programs you use daily (the Python interpreter,

  339. your XML parser, your web browser) could be proven correct.  Even if you wrote

  340. down or generated a proof, there would then be the question of verifying the

  341. proof; maybe there’s an error in it, and you wrongly believe you’ve proved the

  342. program correct.</p>

  343. </section>

  344. <section id="modularity">

  345. <h3>Modularity<a class="headerlink" href="#modularity" title="Link to this heading">¶</a></h3>

  346. <p>A more practical benefit of functional programming is that it forces you to

  347. break apart your problem into small pieces.  Programs are more modular as a

  348. result.  It’s easier to specify and write a small function that does one thing

  349. than a large function that performs a complicated transformation.  Small

  350. functions are also easier to read and to check for errors.</p>

  351. </section>

  352. <section id="ease-of-debugging-and-testing">

  353. <h3>Ease of debugging and testing<a class="headerlink" href="#ease-of-debugging-and-testing" title="Link to this heading">¶</a></h3>

  354. <p>Testing and debugging a functional-style program is easier.</p>

  355. <p>Debugging is simplified because functions are generally small and clearly

  356. specified.  When a program doesn’t work, each function is an interface point

  357. where you can check that the data are correct.  You can look at the intermediate

  358. inputs and outputs to quickly isolate the function that’s responsible for a bug.</p>

  359. <p>Testing is easier because each function is a potential subject for a unit test.

  360. Functions don’t depend on system state that needs to be replicated before

  361. running a test; instead you only have to synthesize the right input and then

  362. check that the output matches expectations.</p>

  363. </section>

  364. <section id="composability">

  365. <h3>Composability<a class="headerlink" href="#composability" title="Link to this heading">¶</a></h3>

  366. <p>As you work on a functional-style program, you’ll write a number of functions

  367. with varying inputs and outputs.  Some of these functions will be unavoidably

  368. specialized to a particular application, but others will be useful in a wide

  369. variety of programs.  For example, a function that takes a directory path and

  370. returns all the XML files in the directory, or a function that takes a filename

  371. and returns its contents, can be applied to many different situations.</p>

  372. <p>Over time you’ll form a personal library of utilities.  Often you’ll assemble

  373. new programs by arranging existing functions in a new configuration and writing

  374. a few functions specialized for the current task.</p>

  375. </section>

  376. </section>

  377. <section id="iterators">

  378. <span id="functional-howto-iterators"></span><h2>Iterators<a class="headerlink" href="#iterators" title="Link to this heading">¶</a></h2>

  379. <p>I’ll start by looking at a Python language feature that’s an important

  380. foundation for writing functional-style programs: iterators.</p>

  381. <p>An iterator is an object representing a stream of data; this object returns the

  382. data one element at a time.  A Python iterator must support a method called

  383. <a class="reference internal" href="../library/stdtypes.html#iterator.__next__" title="iterator.__next__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__next__()</span></code></a> that takes no arguments and always returns the next

  384. element of the stream.  If there are no more elements in the stream,

  385. <a class="reference internal" href="../library/stdtypes.html#iterator.__next__" title="iterator.__next__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__next__()</span></code></a> must raise the <a class="reference internal" href="../library/exceptions.html#StopIteration" title="StopIteration"><code class="xref py py-exc docutils literal notranslate"><span class="pre">StopIteration</span></code></a> exception.

  386. Iterators don’t have to be finite, though; it’s perfectly reasonable to write

  387. an iterator that produces an infinite stream of data.</p>

  388. <p>The built-in <a class="reference internal" href="../library/functions.html#iter" title="iter"><code class="xref py py-func docutils literal notranslate"><span class="pre">iter()</span></code></a> function takes an arbitrary object and tries to return

  389. an iterator that will return the object’s contents or elements, raising

  390. <a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">TypeError</span></code></a> if the object doesn’t support iteration.  Several of Python’s

  391. built-in data types support iteration, the most common being lists and

  392. dictionaries.  An object is called <a class="reference internal" href="../glossary.html#term-iterable"><span class="xref std std-term">iterable</span></a> if you can get an iterator

  393. for it.</p>

  394. <p>You can experiment with the iteration interface manually:</p>

  395. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">L</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>

  396. <span class="gp">&gt;&gt;&gt; </span><span class="n">it</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">L</span><span class="p">)</span>

  397. <span class="gp">&gt;&gt;&gt; </span><span class="n">it</span>  

  398. <span class="go">&lt;...iterator object at ...&gt;</span>

  399. <span class="gp">&gt;&gt;&gt; </span><span class="n">it</span><span class="o">.</span><span class="fm">__next__</span><span class="p">()</span>  <span class="c1"># same as next(it)</span>

  400. <span class="go">1</span>

  401. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>

  402. <span class="go">2</span>

  403. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>

  404. <span class="go">3</span>

  405. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>

  406. <span class="gt">Traceback (most recent call last):</span>

  407.   File <span class="nb">&quot;&lt;stdin&gt;&quot;</span>, line <span class="m">1</span>, in <span class="n">&lt;module&gt;</span>

  408. <span class="gr">StopIteration</span>

  409. <span class="gp">&gt;&gt;&gt;</span>

  410. </pre></div>

  411. </div>

  412. <p>Python expects iterable objects in several different contexts, the most

  413. important being the <a class="reference internal" href="../reference/compound_stmts.html#for"><code class="xref std std-keyword docutils literal notranslate"><span class="pre">for</span></code></a> statement.  In the statement <code class="docutils literal notranslate"><span class="pre">for</span> <span class="pre">X</span> <span class="pre">in</span> <span class="pre">Y</span></code>,

  414. Y must be an iterator or some object for which <a class="reference internal" href="../library/functions.html#iter" title="iter"><code class="xref py py-func docutils literal notranslate"><span class="pre">iter()</span></code></a> can create an

  415. iterator.  These two statements are equivalent:</p>

  416. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">iter</span><span class="p">(</span><span class="n">obj</span><span class="p">):</span>

  417.     <span class="nb">print</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>

  418. 

  419. <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">obj</span><span class="p">:</span>

  420.     <span class="nb">print</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>

  421. </pre></div>

  422. </div>

  423. <p>Iterators can be materialized as lists or tuples by using the <a class="reference internal" href="../library/stdtypes.html#list" title="list"><code class="xref py py-func docutils literal notranslate"><span class="pre">list()</span></code></a> or

  424. <a class="reference internal" href="../library/stdtypes.html#tuple" title="tuple"><code class="xref py py-func docutils literal notranslate"><span class="pre">tuple()</span></code></a> constructor functions:</p>

  425. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">L</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>

  426. <span class="gp">&gt;&gt;&gt; </span><span class="n">iterator</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">L</span><span class="p">)</span>

  427. <span class="gp">&gt;&gt;&gt; </span><span class="n">t</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterator</span><span class="p">)</span>

  428. <span class="gp">&gt;&gt;&gt; </span><span class="n">t</span>

  429. <span class="go">(1, 2, 3)</span>

  430. </pre></div>

  431. </div>

  432. <p>Sequence unpacking also supports iterators: if you know an iterator will return

  433. N elements, you can unpack them into an N-tuple:</p>

  434. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">L</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>

  435. <span class="gp">&gt;&gt;&gt; </span><span class="n">iterator</span> <span class="o">=</span> <span class="nb">iter</span><span class="p">(</span><span class="n">L</span><span class="p">)</span>

  436. <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span> <span class="o">=</span> <span class="n">iterator</span>

  437. <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span>

  438. <span class="go">(1, 2, 3)</span>

  439. </pre></div>

  440. </div>

  441. <p>Built-in functions such as <a class="reference internal" href="../library/functions.html#max" title="max"><code class="xref py py-func docutils literal notranslate"><span class="pre">max()</span></code></a> and <a class="reference internal" href="../library/functions.html#min" title="min"><code class="xref py py-func docutils literal notranslate"><span class="pre">min()</span></code></a> can take a single

  442. iterator argument and will return the largest or smallest element.  The <code class="docutils literal notranslate"><span class="pre">&quot;in&quot;</span></code>

  443. and <code class="docutils literal notranslate"><span class="pre">&quot;not</span> <span class="pre">in&quot;</span></code> operators also support iterators: <code class="docutils literal notranslate"><span class="pre">X</span> <span class="pre">in</span> <span class="pre">iterator</span></code> is true if

  444. X is found in the stream returned by the iterator.  You’ll run into obvious

  445. problems if the iterator is infinite; <a class="reference internal" href="../library/functions.html#max" title="max"><code class="xref py py-func docutils literal notranslate"><span class="pre">max()</span></code></a>, <a class="reference internal" href="../library/functions.html#min" title="min"><code class="xref py py-func docutils literal notranslate"><span class="pre">min()</span></code></a>

  446. will never return, and if the element X never appears in the stream, the

  447. <code class="docutils literal notranslate"><span class="pre">&quot;in&quot;</span></code> and <code class="docutils literal notranslate"><span class="pre">&quot;not</span> <span class="pre">in&quot;</span></code> operators won’t return either.</p>

  448. <p>Note that you can only go forward in an iterator; there’s no way to get the

  449. previous element, reset the iterator, or make a copy of it.  Iterator objects

  450. can optionally provide these additional capabilities, but the iterator protocol

  451. only specifies the <a class="reference internal" href="../library/stdtypes.html#iterator.__next__" title="iterator.__next__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__next__()</span></code></a> method.  Functions may therefore

  452. consume all of the iterator’s output, and if you need to do something different

  453. with the same stream, you’ll have to create a new iterator.</p>

  454. <section id="data-types-that-support-iterators">

  455. <h3>Data Types That Support Iterators<a class="headerlink" href="#data-types-that-support-iterators" title="Link to this heading">¶</a></h3>

  456. <p>We’ve already seen how lists and tuples support iterators.  In fact, any Python

  457. sequence type, such as strings, will automatically support creation of an

  458. iterator.</p>

  459. <p>Calling <a class="reference internal" href="../library/functions.html#iter" title="iter"><code class="xref py py-func docutils literal notranslate"><span class="pre">iter()</span></code></a> on a dictionary returns an iterator that will loop over the

  460. dictionary’s keys:</p>

  461. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">m</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;Jan&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s1">&#39;Feb&#39;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s1">&#39;Mar&#39;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="s1">&#39;Apr&#39;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="s1">&#39;May&#39;</span><span class="p">:</span> <span class="mi">5</span><span class="p">,</span> <span class="s1">&#39;Jun&#39;</span><span class="p">:</span> <span class="mi">6</span><span class="p">,</span>

  462. <span class="gp">... </span>     <span class="s1">&#39;Jul&#39;</span><span class="p">:</span> <span class="mi">7</span><span class="p">,</span> <span class="s1">&#39;Aug&#39;</span><span class="p">:</span> <span class="mi">8</span><span class="p">,</span> <span class="s1">&#39;Sep&#39;</span><span class="p">:</span> <span class="mi">9</span><span class="p">,</span> <span class="s1">&#39;Oct&#39;</span><span class="p">:</span> <span class="mi">10</span><span class="p">,</span> <span class="s1">&#39;Nov&#39;</span><span class="p">:</span> <span class="mi">11</span><span class="p">,</span> <span class="s1">&#39;Dec&#39;</span><span class="p">:</span> <span class="mi">12</span><span class="p">}</span>

  463. <span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">m</span><span class="p">:</span>

  464. <span class="gp">... </span>    <span class="nb">print</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">m</span><span class="p">[</span><span class="n">key</span><span class="p">])</span>

  465. <span class="go">Jan 1</span>

  466. <span class="go">Feb 2</span>

  467. <span class="go">Mar 3</span>

  468. <span class="go">Apr 4</span>

  469. <span class="go">May 5</span>

  470. <span class="go">Jun 6</span>

  471. <span class="go">Jul 7</span>

  472. <span class="go">Aug 8</span>

  473. <span class="go">Sep 9</span>

  474. <span class="go">Oct 10</span>

  475. <span class="go">Nov 11</span>

  476. <span class="go">Dec 12</span>

  477. </pre></div>

  478. </div>

  479. <p>Note that starting with Python 3.7, dictionary iteration order is guaranteed

  480. to be the same as the insertion order. In earlier versions, the behaviour was

  481. unspecified and could vary between implementations.</p>

  482. <p>Applying <a class="reference internal" href="../library/functions.html#iter" title="iter"><code class="xref py py-func docutils literal notranslate"><span class="pre">iter()</span></code></a> to a dictionary always loops over the keys, but

  483. dictionaries have methods that return other iterators.  If you want to iterate

  484. over values or key/value pairs, you can explicitly call the

  485. <a class="reference internal" href="../library/stdtypes.html#dict.values" title="dict.values"><code class="xref py py-meth docutils literal notranslate"><span class="pre">values()</span></code></a> or <a class="reference internal" href="../library/stdtypes.html#dict.items" title="dict.items"><code class="xref py py-meth docutils literal notranslate"><span class="pre">items()</span></code></a> methods to get an appropriate

  486. iterator.</p>

  487. <p>The <a class="reference internal" href="../library/stdtypes.html#dict" title="dict"><code class="xref py py-func docutils literal notranslate"><span class="pre">dict()</span></code></a> constructor can accept an iterator that returns a finite stream

  488. of <code class="docutils literal notranslate"><span class="pre">(key,</span> <span class="pre">value)</span></code> tuples:</p>

  489. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">L</span> <span class="o">=</span> <span class="p">[(</span><span class="s1">&#39;Italy&#39;</span><span class="p">,</span> <span class="s1">&#39;Rome&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;France&#39;</span><span class="p">,</span> <span class="s1">&#39;Paris&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;US&#39;</span><span class="p">,</span> <span class="s1">&#39;Washington DC&#39;</span><span class="p">)]</span>

  490. <span class="gp">&gt;&gt;&gt; </span><span class="nb">dict</span><span class="p">(</span><span class="nb">iter</span><span class="p">(</span><span class="n">L</span><span class="p">))</span>

  491. <span class="go">{&#39;Italy&#39;: &#39;Rome&#39;, &#39;France&#39;: &#39;Paris&#39;, &#39;US&#39;: &#39;Washington DC&#39;}</span>

  492. </pre></div>

  493. </div>

  494. <p>Files also support iteration by calling the <a class="reference internal" href="../library/io.html#io.TextIOBase.readline" title="io.TextIOBase.readline"><code class="xref py py-meth docutils literal notranslate"><span class="pre">readline()</span></code></a>

  495. method until there are no more lines in the file.  This means you can read each

  496. line of a file like this:</p>

  497. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">file</span><span class="p">:</span>

  498.     <span class="c1"># do something for each line</span>

  499.     <span class="o">...</span>

  500. </pre></div>

  501. </div>

  502. <p>Sets can take their contents from an iterable and let you iterate over the set’s

  503. elements:</p>

  504. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">S</span> <span class="o">=</span> <span class="p">{</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">13</span><span class="p">}</span>

  505. <span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">S</span><span class="p">:</span>

  506. <span class="gp">... </span>    <span class="nb">print</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>

  507. <span class="go">2</span>

  508. <span class="go">3</span>

  509. <span class="go">5</span>

  510. <span class="go">7</span>

  511. <span class="go">11</span>

  512. <span class="go">13</span>

  513. </pre></div>

  514. </div>

  515. </section>

  516. </section>

  517. <section id="generator-expressions-and-list-comprehensions">

  518. <h2>Generator expressions and list comprehensions<a class="headerlink" href="#generator-expressions-and-list-comprehensions" title="Link to this heading">¶</a></h2>

  519. <p>Two common operations on an iterator’s output are 1) performing some operation

  520. for every element, 2) selecting a subset of elements that meet some condition.

  521. For example, given a list of strings, you might want to strip off trailing

  522. whitespace from each line or extract all the strings containing a given

  523. substring.</p>

  524. <p>List comprehensions and generator expressions (short form: “listcomps” and

  525. “genexps”) are a concise notation for such operations, borrowed from the

  526. functional programming language Haskell (<a class="reference external" href="https://www.haskell.org/">https://www.haskell.org/</a>).  You can strip

  527. all the whitespace from a stream of strings with the following code:</p>

  528. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">line_list</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;  line 1</span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">,</span> <span class="s1">&#39;line 2  </span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">,</span> <span class="s1">&#39; </span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">,</span> <span class="s1">&#39;&#39;</span><span class="p">]</span>

  529. 

  530. <span class="gp">&gt;&gt;&gt; </span><span class="c1"># Generator expression -- returns iterator</span>

  531. <span class="gp">&gt;&gt;&gt; </span><span class="n">stripped_iter</span> <span class="o">=</span> <span class="p">(</span><span class="n">line</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">line_list</span><span class="p">)</span>

  532. 

  533. <span class="gp">&gt;&gt;&gt; </span><span class="c1"># List comprehension -- returns list</span>

  534. <span class="gp">&gt;&gt;&gt; </span><span class="n">stripped_list</span> <span class="o">=</span> <span class="p">[</span><span class="n">line</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">line_list</span><span class="p">]</span>

  535. </pre></div>

  536. </div>

  537. <p>You can select only certain elements by adding an <code class="docutils literal notranslate"><span class="pre">&quot;if&quot;</span></code> condition:</p>

  538. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">stripped_list</span> <span class="o">=</span> <span class="p">[</span><span class="n">line</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">line_list</span>

  539. <span class="gp">... </span>                 <span class="k">if</span> <span class="n">line</span> <span class="o">!=</span> <span class="s2">&quot;&quot;</span><span class="p">]</span>

  540. </pre></div>

  541. </div>

  542. <p>With a list comprehension, you get back a Python list; <code class="docutils literal notranslate"><span class="pre">stripped_list</span></code> is a

  543. list containing the resulting lines, not an iterator.  Generator expressions

  544. return an iterator that computes the values as necessary, not needing to

  545. materialize all the values at once.  This means that list comprehensions aren’t

  546. useful if you’re working with iterators that return an infinite stream or a very

  547. large amount of data.  Generator expressions are preferable in these situations.</p>

  548. <p>Generator expressions are surrounded by parentheses (“()”) and list

  549. comprehensions are surrounded by square brackets (“[]”).  Generator expressions

  550. have the form:</p>

  551. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="p">(</span> <span class="n">expression</span> <span class="k">for</span> <span class="n">expr</span> <span class="ow">in</span> <span class="n">sequence1</span>

  552.              <span class="k">if</span> <span class="n">condition1</span>

  553.              <span class="k">for</span> <span class="n">expr2</span> <span class="ow">in</span> <span class="n">sequence2</span>

  554.              <span class="k">if</span> <span class="n">condition2</span>

  555.              <span class="k">for</span> <span class="n">expr3</span> <span class="ow">in</span> <span class="n">sequence3</span>

  556.              <span class="o">...</span>

  557.              <span class="k">if</span> <span class="n">condition3</span>

  558.              <span class="k">for</span> <span class="n">exprN</span> <span class="ow">in</span> <span class="n">sequenceN</span>

  559.              <span class="k">if</span> <span class="n">conditionN</span> <span class="p">)</span>

  560. </pre></div>

  561. </div>

  562. <p>Again, for a list comprehension only the outside brackets are different (square

  563. brackets instead of parentheses).</p>

  564. <p>The elements of the generated output will be the successive values of

  565. <code class="docutils literal notranslate"><span class="pre">expression</span></code>.  The <code class="docutils literal notranslate"><span class="pre">if</span></code> clauses are all optional; if present, <code class="docutils literal notranslate"><span class="pre">expression</span></code>

  566. is only evaluated and added to the result when <code class="docutils literal notranslate"><span class="pre">condition</span></code> is true.</p>

  567. <p>Generator expressions always have to be written inside parentheses, but the

  568. parentheses signalling a function call also count.  If you want to create an

  569. iterator that will be immediately passed to a function you can write:</p>

  570. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">obj_total</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">obj</span><span class="o">.</span><span class="n">count</span> <span class="k">for</span> <span class="n">obj</span> <span class="ow">in</span> <span class="n">list_all_objects</span><span class="p">())</span>

  571. </pre></div>

  572. </div>

  573. <p>The <code class="docutils literal notranslate"><span class="pre">for...in</span></code> clauses contain the sequences to be iterated over.  The

  574. sequences do not have to be the same length, because they are iterated over from

  575. left to right, <strong>not</strong> in parallel.  For each element in <code class="docutils literal notranslate"><span class="pre">sequence1</span></code>,

  576. <code class="docutils literal notranslate"><span class="pre">sequence2</span></code> is looped over from the beginning.  <code class="docutils literal notranslate"><span class="pre">sequence3</span></code> is then looped

  577. over for each resulting pair of elements from <code class="docutils literal notranslate"><span class="pre">sequence1</span></code> and <code class="docutils literal notranslate"><span class="pre">sequence2</span></code>.</p>

  578. <p>To put it another way, a list comprehension or generator expression is

  579. equivalent to the following Python code:</p>

  580. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">expr1</span> <span class="ow">in</span> <span class="n">sequence1</span><span class="p">:</span>

  581.     <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">condition1</span><span class="p">):</span>

  582.         <span class="k">continue</span>   <span class="c1"># Skip this element</span>

  583.     <span class="k">for</span> <span class="n">expr2</span> <span class="ow">in</span> <span class="n">sequence2</span><span class="p">:</span>

  584.         <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">condition2</span><span class="p">):</span>

  585.             <span class="k">continue</span>   <span class="c1"># Skip this element</span>

  586.         <span class="o">...</span>

  587.         <span class="k">for</span> <span class="n">exprN</span> <span class="ow">in</span> <span class="n">sequenceN</span><span class="p">:</span>

  588.             <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">conditionN</span><span class="p">):</span>

  589.                 <span class="k">continue</span>   <span class="c1"># Skip this element</span>

  590. 

  591.             <span class="c1"># Output the value of</span>

  592.             <span class="c1"># the expression.</span>

  593. </pre></div>

  594. </div>

  595. <p>This means that when there are multiple <code class="docutils literal notranslate"><span class="pre">for...in</span></code> clauses but no <code class="docutils literal notranslate"><span class="pre">if</span></code>

  596. clauses, the length of the resulting output will be equal to the product of the

  597. lengths of all the sequences.  If you have two lists of length 3, the output

  598. list is 9 elements long:</p>

  599. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">seq1</span> <span class="o">=</span> <span class="s1">&#39;abc&#39;</span>

  600. <span class="gp">&gt;&gt;&gt; </span><span class="n">seq2</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>

  601. <span class="gp">&gt;&gt;&gt; </span><span class="p">[(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">seq1</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">seq2</span><span class="p">]</span>  

  602. <span class="go">[(&#39;a&#39;, 1), (&#39;a&#39;, 2), (&#39;a&#39;, 3),</span>

  603. <span class="go"> (&#39;b&#39;, 1), (&#39;b&#39;, 2), (&#39;b&#39;, 3),</span>

  604. <span class="go"> (&#39;c&#39;, 1), (&#39;c&#39;, 2), (&#39;c&#39;, 3)]</span>

  605. </pre></div>

  606. </div>

  607. <p>To avoid introducing an ambiguity into Python’s grammar, if <code class="docutils literal notranslate"><span class="pre">expression</span></code> is

  608. creating a tuple, it must be surrounded with parentheses.  The first list

  609. comprehension below is a syntax error, while the second one is correct:</p>

  610. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Syntax error</span>

  611. <span class="p">[</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">seq1</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">seq2</span><span class="p">]</span>

  612. <span class="c1"># Correct</span>

  613. <span class="p">[(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">seq1</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">seq2</span><span class="p">]</span>

  614. </pre></div>

  615. </div>

  616. </section>

  617. <section id="generators">

  618. <h2>Generators<a class="headerlink" href="#generators" title="Link to this heading">¶</a></h2>

  619. <p>Generators are a special class of functions that simplify the task of writing

  620. iterators.  Regular functions compute a value and return it, but generators

  621. return an iterator that returns a stream of values.</p>

  622. <p>You’re doubtless familiar with how regular function calls work in Python or C.

  623. When you call a function, it gets a private namespace where its local variables

  624. are created.  When the function reaches a <code class="docutils literal notranslate"><span class="pre">return</span></code> statement, the local

  625. variables are destroyed and the value is returned to the caller.  A later call

  626. to the same function creates a new private namespace and a fresh set of local

  627. variables. But, what if the local variables weren’t thrown away on exiting a

  628. function?  What if you could later resume the function where it left off?  This

  629. is what generators provide; they can be thought of as resumable functions.</p>

  630. <p>Here’s the simplest example of a generator function:</p>

  631. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">generate_ints</span><span class="p">(</span><span class="n">N</span><span class="p">):</span>

  632. <span class="gp">... </span>   <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">):</span>

  633. <span class="gp">... </span>       <span class="k">yield</span> <span class="n">i</span>

  634. </pre></div>

  635. </div>

  636. <p>Any function containing a <a class="reference internal" href="../reference/simple_stmts.html#yield"><code class="xref std std-keyword docutils literal notranslate"><span class="pre">yield</span></code></a> keyword is a generator function;

  637. this is detected by Python’s <a class="reference internal" href="../glossary.html#term-bytecode"><span class="xref std std-term">bytecode</span></a> compiler which compiles the

  638. function specially as a result.</p>

  639. <p>When you call a generator function, it doesn’t return a single value; instead it

  640. returns a generator object that supports the iterator protocol.  On executing

  641. the <code class="docutils literal notranslate"><span class="pre">yield</span></code> expression, the generator outputs the value of <code class="docutils literal notranslate"><span class="pre">i</span></code>, similar to a

  642. <code class="docutils literal notranslate"><span class="pre">return</span></code> statement.  The big difference between <code class="docutils literal notranslate"><span class="pre">yield</span></code> and a <code class="docutils literal notranslate"><span class="pre">return</span></code>

  643. statement is that on reaching a <code class="docutils literal notranslate"><span class="pre">yield</span></code> the generator’s state of execution is

  644. suspended and local variables are preserved.  On the next call to the

  645. generator’s <a class="reference internal" href="../reference/expressions.html#generator.__next__" title="generator.__next__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__next__()</span></code></a> method, the function will resume

  646. executing.</p>

  647. <p>Here’s a sample usage of the <code class="docutils literal notranslate"><span class="pre">generate_ints()</span></code> generator:</p>

  648. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">gen</span> <span class="o">=</span> <span class="n">generate_ints</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>

  649. <span class="gp">&gt;&gt;&gt; </span><span class="n">gen</span>  

  650. <span class="go">&lt;generator object generate_ints at ...&gt;</span>

  651. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">gen</span><span class="p">)</span>

  652. <span class="go">0</span>

  653. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">gen</span><span class="p">)</span>

  654. <span class="go">1</span>

  655. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">gen</span><span class="p">)</span>

  656. <span class="go">2</span>

  657. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">gen</span><span class="p">)</span>

  658. <span class="gt">Traceback (most recent call last):</span>

  659.   File <span class="nb">&quot;stdin&quot;</span>, line <span class="m">1</span>, in <span class="n">&lt;module&gt;</span>

  660.   File <span class="nb">&quot;stdin&quot;</span>, line <span class="m">2</span>, in <span class="n">generate_ints</span>

  661. <span class="gr">StopIteration</span>

  662. </pre></div>

  663. </div>

  664. <p>You could equally write <code class="docutils literal notranslate"><span class="pre">for</span> <span class="pre">i</span> <span class="pre">in</span> <span class="pre">generate_ints(5)</span></code>, or <code class="docutils literal notranslate"><span class="pre">a,</span> <span class="pre">b,</span> <span class="pre">c</span> <span class="pre">=</span>

  665. <span class="pre">generate_ints(3)</span></code>.</p>

  666. <p>Inside a generator function, <code class="docutils literal notranslate"><span class="pre">return</span> <span class="pre">value</span></code> causes <code class="docutils literal notranslate"><span class="pre">StopIteration(value)</span></code>

  667. to be raised from the <a class="reference internal" href="../reference/expressions.html#generator.__next__" title="generator.__next__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__next__()</span></code></a> method.  Once this happens, or

  668. the bottom of the function is reached, the procession of values ends and the

  669. generator cannot yield any further values.</p>

  670. <p>You could achieve the effect of generators manually by writing your own class

  671. and storing all the local variables of the generator as instance variables.  For

  672. example, returning a list of integers could be done by setting <code class="docutils literal notranslate"><span class="pre">self.count</span></code> to

  673. 0, and having the <a class="reference internal" href="../library/stdtypes.html#iterator.__next__" title="iterator.__next__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__next__()</span></code></a> method increment <code class="docutils literal notranslate"><span class="pre">self.count</span></code> and

  674. return it.

  675. However, for a moderately complicated generator, writing a corresponding class

  676. can be much messier.</p>

  677. <p>The test suite included with Python’s library,

  678. <a class="reference external" href="https://github.com/python/cpython/tree/3.12/Lib/test/test_generators.py">Lib/test/test_generators.py</a>, contains

  679. a number of more interesting examples.  Here’s one generator that implements an

  680. in-order traversal of a tree using generators recursively.</p>

  681. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># A recursive generator that generates Tree leaves in in-order.</span>

  682. <span class="k">def</span> <span class="nf">inorder</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>

  683.     <span class="k">if</span> <span class="n">t</span><span class="p">:</span>

  684.         <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">inorder</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">left</span><span class="p">):</span>

  685.             <span class="k">yield</span> <span class="n">x</span>

  686. 

  687.         <span class="k">yield</span> <span class="n">t</span><span class="o">.</span><span class="n">label</span>

  688. 

  689.         <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">inorder</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">right</span><span class="p">):</span>

  690.             <span class="k">yield</span> <span class="n">x</span>

  691. </pre></div>

  692. </div>

  693. <p>Two other examples in <code class="docutils literal notranslate"><span class="pre">test_generators.py</span></code> produce solutions for the N-Queens

  694. problem (placing N queens on an NxN chess board so that no queen threatens

  695. another) and the Knight’s Tour (finding a route that takes a knight to every

  696. square of an NxN chessboard without visiting any square twice).</p>

  697. <section id="passing-values-into-a-generator">

  698. <h3>Passing values into a generator<a class="headerlink" href="#passing-values-into-a-generator" title="Link to this heading">¶</a></h3>

  699. <p>In Python 2.4 and earlier, generators only produced output.  Once a generator’s

  700. code was invoked to create an iterator, there was no way to pass any new

  701. information into the function when its execution is resumed.  You could hack

  702. together this ability by making the generator look at a global variable or by

  703. passing in some mutable object that callers then modify, but these approaches

  704. are messy.</p>

  705. <p>In Python 2.5 there’s a simple way to pass values into a generator.

  706. <a class="reference internal" href="../reference/simple_stmts.html#yield"><code class="xref std std-keyword docutils literal notranslate"><span class="pre">yield</span></code></a> became an expression, returning a value that can be assigned to

  707. a variable or otherwise operated on:</p>

  708. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">val</span> <span class="o">=</span> <span class="p">(</span><span class="k">yield</span> <span class="n">i</span><span class="p">)</span>

  709. </pre></div>

  710. </div>

  711. <p>I recommend that you <strong>always</strong> put parentheses around a <code class="docutils literal notranslate"><span class="pre">yield</span></code> expression

  712. when you’re doing something with the returned value, as in the above example.

  713. The parentheses aren’t always necessary, but it’s easier to always add them

  714. instead of having to remember when they’re needed.</p>

  715. <p>(<span class="target" id="index-0"></span><a class="pep reference external" href="https://peps.python.org/pep-0342/"><strong>PEP 342</strong></a> explains the exact rules, which are that a <code class="docutils literal notranslate"><span class="pre">yield</span></code>-expression must

  716. always be parenthesized except when it occurs at the top-level expression on the

  717. right-hand side of an assignment.  This means you can write <code class="docutils literal notranslate"><span class="pre">val</span> <span class="pre">=</span> <span class="pre">yield</span> <span class="pre">i</span></code>

  718. but have to use parentheses when there’s an operation, as in <code class="docutils literal notranslate"><span class="pre">val</span> <span class="pre">=</span> <span class="pre">(yield</span> <span class="pre">i)</span>

  719. <span class="pre">+</span> <span class="pre">12</span></code>.)</p>

  720. <p>Values are sent into a generator by calling its <a class="reference internal" href="../reference/expressions.html#generator.send" title="generator.send"><code class="xref py py-meth docutils literal notranslate"><span class="pre">send(value)</span></code></a> method.  This method resumes the generator’s code and the

  721. <code class="docutils literal notranslate"><span class="pre">yield</span></code> expression returns the specified value.  If the regular

  722. <a class="reference internal" href="../reference/expressions.html#generator.__next__" title="generator.__next__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__next__()</span></code></a> method is called, the <code class="docutils literal notranslate"><span class="pre">yield</span></code> returns <code class="docutils literal notranslate"><span class="pre">None</span></code>.</p>

  723. <p>Here’s a simple counter that increments by 1 and allows changing the value of

  724. the internal counter.</p>

  725. <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">counter</span><span class="p">(</span><span class="n">maximum</span><span class="p">):</span>

  726.     <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>

  727.     <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">maximum</span><span class="p">:</span>

  728.         <span class="n">val</span> <span class="o">=</span> <span class="p">(</span><span class="k">yield</span> <span class="n">i</span><span class="p">)</span>

  729.         <span class="c1"># If value provided, change counter</span>

  730.         <span class="k">if</span> <span class="n">val</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>

  731.             <span class="n">i</span> <span class="o">=</span> <span class="n">val</span>

  732.         <span class="k">else</span><span class="p">:</span>

  733.             <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>

  734. </pre></div>

  735. </div>

  736. <p>And here’s an example of changing the counter:</p>

  737. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">it</span> <span class="o">=</span> <span class="n">counter</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>  

  738. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>  

  739. <span class="go">0</span>

  740. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>  

  741. <span class="go">1</span>

  742. <span class="gp">&gt;&gt;&gt; </span><span class="n">it</span><span class="o">.</span><span class="n">send</span><span class="p">(</span><span class="mi">8</span><span class="p">)</span>  

  743. <span class="go">8</span>

  744. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>  

  745. <span class="go">9</span>

  746. <span class="gp">&gt;&gt;&gt; </span><span class="nb">next</span><span class="p">(</span><span class="n">it</span><span class="p">)</span>  

  747. <span class="gt">Traceback (most recent call last):</span>

  748.   File <span class="nb">&quot;t.py&quot;</span>, line <span class="m">15</span>, in <span class="n">&lt;module&gt;</span>

  749. <span class="w">    </span><span class="n">it</span><span class="o">.</span><span class="n">next</span><span class="p">()</span>

  750. <span class="gr">StopIteration</span>

  751. </pre></div>

  752. </div>

  753. <p>Because <code class="docutils literal notranslate"><span class="pre">yield</span></code> will often be returning <code class="docutils literal notranslate"><span class="pre">None</span></code>, you should always check for

  754. this case.  Don’t just use its value in expressions unless you’re sure that the

  755. <a class="reference internal" href="../reference/expressions.html#generator.send" title="generator.send"><code class="xref py py-meth docutils literal notranslate"><span class="pre">send()</span></code></a> method will be the only method used to resume your

  756. generator function.</p>

  757. <p>In addition to <a class="reference internal" href="../reference/expressions.html#generator.send" title="generator.send"><code class="xref py py-meth docutils literal notranslate"><span class="pre">send()</span></code></a>, there are two other methods on

  758. generators:</p>

  759. <ul>

  760. <li><p><a class="reference internal" href="../reference/expressions.html#generator.throw" title="generator.throw"><code class="xref py py-meth docutils literal notranslate"><span class="pre">throw(value)</span></code></a> is used to

  761. raise an exception inside the generator; the exception is raised by the

  762. <code class="docutils literal notranslate"><span class="pre">yield</span></code> expression where the generator’s execution is paused.</p></li>

  763. <li><p><a class="reference internal" href="../reference/expressions.html#generator.close" title="generator.close"><code class="xref py py-meth docutils literal notranslate"><span class="pre">close()</span></code></a> raises a <a class="reference internal" href="../library/exceptions.html#GeneratorExit" title="GeneratorExit"><code class="xref py py-exc docutils literal notranslate"><span class="pre">GeneratorExit</span></code></a> exception inside the

  764. generator to terminate the iteration.  On receiving this exception, the

  765. generator’s code must either raise <a class="reference internal" href="../library/exceptions.html#GeneratorExit" title="GeneratorExit"><code class="xref py py-exc docutils literal notranslate"><span class="pre">GeneratorExit</span></code></a> or

  766. <a class="reference internal" href="../library/exceptions.html#StopIteration" title="StopIteration"><code class="xref py py-exc docutils literal notranslate"><span class="pre">StopIteration</span></code></a>; catching the exception and doing anything else is

  767. illegal and will trigger a <a class="reference internal" href="../library/exceptions.html#RuntimeError" title="RuntimeError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">RuntimeError</span></code></a>.  <a class="reference internal" href="../reference/expressions.html#generator.close" title="generator.close"><code class="xref py py-meth docutils literal notranslate"><span class="pre">close()</span></code></a>

  768. will also be called by Python’s garbage collector when the generator is

  769. garbage-collected.</p>

  770. <p>If you need to run cleanup code when a <a class="reference internal" href="../library/exceptions.html#GeneratorExit" title="GeneratorExit"><code class="xref py py-exc docutils literal notranslate"><span class="pre">GeneratorExit</span></code></a> occurs, I suggest

  771. using a <code class="docutils literal notranslate"><span class="pre">try:</span> <span class="pre">...</span> <span class="pre">finally:</span></code> suite instead of catching <a class="reference internal" href="../library/exceptions.html#GeneratorExit" title="GeneratorExit"><code class="xref py py-exc docutils literal notranslate"><span class="pre">GeneratorExit</span></code></a>.</p>

  772. </li>

  773. </ul>

  774. <p>The cumulative effect of these changes is to turn generators from one-way

  775. producers of information into both producers and consumers.</p>

  776. <p>Generators also become <strong>coroutines</strong>, a more generalized form of subroutines.

  777. Subroutines are entered at one point and exited at another point (the top of the

  778. function, and a <code class="docutils literal notranslate"><span class="pre">return</span></code> statement), but coroutines can be entered, exited,

  779. and resumed at many different points (the <code class="docutils literal notranslate"><span class="pre">yield</span></code> statements).</p>

  780. </section>

  781. </section>

  782. <section id="built-in-functions">

  783. <h2>Built-in functions<a class="headerlink" href="#built-in-functions" title="Link to this heading">¶</a></h2>

  784. <p>Let’s look in more detail at built-in functions often used with iterators.</p>

  785. <p>Two of Python’s built-in functions, <a class="reference internal" href="../library/functions.html#map" title="map"><code class="xref py py-func docutils literal notranslate"><span class="pre">map()</span></code></a> and <a class="reference internal" href="../library/functions.html#filter" title="filter"><code class="xref py py-func docutils literal notranslate"><span class="pre">filter()</span></code></a> duplicate the

  786. features of generator expressions:</p>

  787. <dl>

  788. <dt><a class="reference internal" href="../library/functions.html#map" title="map"><code class="xref py py-func docutils literal notranslate"><span class="pre">map(f,</span> <span class="pre">iterA,</span> <span class="pre">iterB,</span> <span class="pre">...)</span></code></a> returns an iterator over the sequence</dt><dd><p><code class="docutils literal notranslate"><span class="pre">f(iterA[0],</span> <span class="pre">iterB[0]),</span> <span class="pre">f(iterA[1],</span> <span class="pre">iterB[1]),</span> <span class="pre">f(iterA[2],</span> <span class="pre">iterB[2]),</span> <span class="pre">...</span></code>.</p>

  789. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">upper</span><span class="p">(</span><span class="n">s</span><span class="p">):</span>

  790. <span class="gp">... </span>    <span class="k">return</span> <span class="n">s</span><span class="o">.</span><span class="n">upper</span><span class="p">()</span>

  791. </pre></div>

  792. </div>

  793. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">upper</span><span class="p">,</span> <span class="p">[</span><span class="s1">&#39;sentence&#39;</span><span class="p">,</span> <span class="s1">&#39;fragment&#39;</span><span class="p">]))</span>

  794. <span class="go">[&#39;SENTENCE&#39;, &#39;FRAGMENT&#39;]</span>

  795. <span class="gp">&gt;&gt;&gt; </span><span class="p">[</span><span class="n">upper</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="p">[</span><span class="s1">&#39;sentence&#39;</span><span class="p">,</span> <span class="s1">&#39;fragment&#39;</span><span class="p">]]</span>

  796. <span class="go">[&#39;SENTENCE&#39;, &#39;FRAGMENT&#39;]</span>

  797. </pre></div>

  798. </div>

  799. </dd>

  800. </dl>

  801. <p>You can of course achieve the same effect with a list comprehension.</p>

  802. <p><a class="reference internal" href="../library/functions.html#filter" title="filter"><code class="xref py py-func docutils literal notranslate"><span class="pre">filter(predicate,</span> <span class="pre">iter)</span></code></a> returns an iterator over all the

  803. sequence elements that meet a certain condition, and is similarly duplicated by

  804. list comprehensions.  A <strong>predicate</strong> is a function that returns the truth

  805. value of some condition; for use with <a class="reference internal" href="../library/functions.html#filter" title="filter"><code class="xref py py-func docutils literal notranslate"><span class="pre">filter()</span></code></a>, the predicate must take a

  806. single value.</p>

  807. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">is_even</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>

  808. <span class="gp">... </span>    <span class="k">return</span> <span class="p">(</span><span class="n">x</span> <span class="o">%</span> <span class="mi">2</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>

  809. </pre></div>

  810. </div>

  811. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="n">is_even</span><span class="p">,</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)))</span>

  812. <span class="go">[0, 2, 4, 6, 8]</span>

  813. </pre></div>

  814. </div>

  815. <p>This can also be written as a list comprehension:</p>

  816. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nb">list</span><span class="p">(</span><span class="n">x</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="k">if</span> <span class="n">is_even</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>

  817. <span class="go">[0, 2, 4, 6, 8]</span>

  818. </pre></div>

  819. </div>

  820. <p><a class="reference internal" href="../library/functions.html#enumerate" title="enumerate"><code class="xref py py-func docutils literal notranslate"><span class="pre">enumerate(iter,</span> <span class="pre">start=0)</span></code></a> counts off the elements in the

  821. iterable returning 2-tuples containing the count (from <em>start</em>) and

  822. each element.</p>

  823. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">([</span><span class="s1">&#39;subject&#39;</span><span class="p">,</span> <span class="s1">&#39;verb&#39;</span><span class="p">,</span> <span class="s1">&#39;object&#39;</span><span class="p">]):</span>

  824. <span class="gp">... </span>    <span class="nb">print</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>

  825. <span class="go">(0, &#39;subject&#39;)</span>

  826. <span class="go">(1, &#39;verb&#39;)</span>

  827. <span class="go">(2, &#39;object&#39;)</span>

  828. </pre></div>

  829. </div>

  830. <p><a class="reference internal" href="../library/functions.html#enumerate" title="enumerate"><code class="xref py py-func docutils literal notranslate"><span class="pre">enumerate()</span></code></a> is often used when looping through a list and recording the

  831. indexes at which certain conditions are met:</p>

  832. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">f</span> <span class="o">=</span> <span class="nb">open</span><span class="p">(</span><span class="s1">&#39;data.txt&#39;</span><span class="p">,</span> <span class="s1">&#39;r&#39;</span><span class="p">)</span>

  833. <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">line</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>

  834.     <span class="k">if</span> <span class="n">line</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="o">==</span> <span class="s1">&#39;&#39;</span><span class="p">:</span>

  835.         <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Blank line at line #</span><span class="si">%i</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">i</span><span class="p">)</span>

  836. </pre></div>

  837. </div>

  838. <p><a class="reference internal" href="../library/functions.html#sorted" title="sorted"><code class="xref py py-func docutils literal notranslate"><span class="pre">sorted(iterable,</span> <span class="pre">key=None,</span> <span class="pre">reverse=False)</span></code></a> collects all the

  839. elements of the iterable into a list, sorts the list, and returns the sorted

  840. result.  The <em>key</em> and <em>reverse</em> arguments are passed through to the

  841. constructed list’s <a class="reference internal" href="../library/stdtypes.html#list.sort" title="list.sort"><code class="xref py py-meth docutils literal notranslate"><span class="pre">sort()</span></code></a> method.</p>

  842. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">random</span>

  843. <span class="gp">&gt;&gt;&gt; </span><span class="c1"># Generate 8 random numbers between [0, 10000)</span>

  844. <span class="gp">&gt;&gt;&gt; </span><span class="n">rand_list</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">10000</span><span class="p">),</span> <span class="mi">8</span><span class="p">)</span>

  845. <span class="gp">&gt;&gt;&gt; </span><span class="n">rand_list</span>  

  846. <span class="go">[769, 7953, 9828, 6431, 8442, 9878, 6213, 2207]</span>

  847. <span class="gp">&gt;&gt;&gt; </span><span class="nb">sorted</span><span class="p">(</span><span class="n">rand_list</span><span class="p">)</span>  

  848. <span class="go">[769, 2207, 6213, 6431, 7953, 8442, 9828, 9878]</span>

  849. <span class="gp">&gt;&gt;&gt; </span><span class="nb">sorted</span><span class="p">(</span><span class="n">rand_list</span><span class="p">,</span> <span class="n">reverse</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  

  850. <span class="go">[9878, 9828, 8442, 7953, 6431, 6213, 2207, 769]</span>

  851. </pre></div>

  852. </div>

  853. <p>(For a more detailed discussion of sorting, see the <a class="reference internal" href="sorting.html#sortinghowto"><span class="std std-ref">Sorting Techniques</span></a>.)</p>

  854. <p>The <a class="reference internal" href="../library/functions.html#any" title="any"><code class="xref py py-func docutils literal notranslate"><span class="pre">any(iter)</span></code></a> and <a class="reference internal" href="../library/functions.html#all" title="all"><code class="xref py py-func docutils literal notranslate"><span class="pre">all(iter)</span></code></a> built-ins look at the

  855. truth values of an iterable’s contents.  <a class="reference internal" href="../library/functions.html#any" title="any"><code class="xref py py-func docutils literal notranslate"><span class="pre">any()</span></code></a> returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if any element

  856. in the iterable is a true value, and <a class="reference internal" href="../library/functions.html#all" title="all"><code class="xref py py-func docutils literal notranslate"><span class="pre">all()</span></code></a> returns <code class="docutils literal notranslate"><span class="pre">True</span></code> if all of the

  857. elements are true values:</p>

  858. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="nb">any</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>

  859. <span class="go">True</span>

  860. <span class="gp">&gt;&gt;&gt; </span><span class="nb">any</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>

  861. <span class="go">False</span>

  862. <span class="gp">&gt;&gt;&gt; </span><span class="nb">any</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>

  863. <span class="go">True</span>

  864. <span class="gp">&gt;&gt;&gt; </span><span class="nb">all</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>

  865. <span class="go">False</span>

  866. <span class="gp">&gt;&gt;&gt; </span><span class="nb">all</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>

  867. <span class="go">False</span>

  868. <span class="gp">&gt;&gt;&gt; </span><span class="nb">all</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>

  869. <span class="go">True</span>

  870. </pre></div>

  871. </div>

  872. <p><a class="reference internal" href="../library/functions.html#zip" title="zip"><code class="xref py py-func docutils literal notranslate"><span class="pre">zip(iterA,</span> <span class="pre">iterB,</span> <span class="pre">...)</span></code></a> takes one element from each iterable and

  873. returns them in a tuple:</p>

  874. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="nb">zip</span><span class="p">([</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;c&#39;</span><span class="p">],</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <span class="o">=&gt;</span>

  875.   <span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;c&#39;</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>

  876. </pre></div>

  877. </div>

  878. <p>It doesn’t construct an in-memory list and exhaust all the input iterators

  879. before returning; instead tuples are constructed and returned only if they’re

  880. requested.  (The technical term for this behaviour is <a class="reference external" href="https://en.wikipedia.org/wiki/Lazy_evaluation">lazy evaluation</a>.)</p>

  881. <p>This iterator is intended to be used with iterables that are all of the same

  882. length.  If the iterables are of different lengths, the resulting stream will be

  883. the same length as the shortest iterable.</p>

  884. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="nb">zip</span><span class="p">([</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">],</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <span class="o">=&gt;</span>

  885.   <span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>

  886. </pre></div>

  887. </div>

  888. <p>You should avoid doing this, though, because an element may be taken from the

  889. longer iterators and discarded.  This means you can’t go on to use the iterators

  890. further because you risk skipping a discarded element.</p>

  891. </section>

  892. <section id="the-itertools-module">

  893. <h2>The itertools module<a class="headerlink" href="#the-itertools-module" title="Link to this heading">¶</a></h2>

  894. <p>The <a class="reference internal" href="../library/itertools.html#module-itertools" title="itertools: Functions creating iterators for efficient looping."><code class="xref py py-mod docutils literal notranslate"><span class="pre">itertools</span></code></a> module contains a number of commonly used iterators as well

  895. as functions for combining several iterators.  This section will introduce the

  896. module’s contents by showing small examples.</p>

  897. <p>The module’s functions fall into a few broad classes:</p>

  898. <ul class="simple">

  899. <li><p>Functions that create a new iterator based on an existing iterator.</p></li>

  900. <li><p>Functions for treating an iterator’s elements as function arguments.</p></li>

  901. <li><p>Functions for selecting portions of an iterator’s output.</p></li>

  902. <li><p>A function for grouping an iterator’s output.</p></li>

  903. </ul>

  904. <section id="creating-new-iterators">

  905. <h3>Creating new iterators<a class="headerlink" href="#creating-new-iterators" title="Link to this heading">¶</a></h3>

  906. <p><a class="reference internal" href="../library/itertools.html#itertools.count" title="itertools.count"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.count(start,</span> <span class="pre">step)</span></code></a> returns an infinite

  907. stream of evenly spaced values.  You can optionally supply the starting number,

  908. which defaults to 0, and the interval between numbers, which defaults to 1:</p>

  909. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">count</span><span class="p">()</span> <span class="o">=&gt;</span>

  910.   <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="o">...</span>

  911. <span class="n">itertools</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="o">=&gt;</span>

  912.   <span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="mi">13</span><span class="p">,</span> <span class="mi">14</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">17</span><span class="p">,</span> <span class="mi">18</span><span class="p">,</span> <span class="mi">19</span><span class="p">,</span> <span class="o">...</span>

  913. <span class="n">itertools</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span> <span class="o">=&gt;</span>

  914.   <span class="mi">10</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="mi">35</span><span class="p">,</span> <span class="mi">40</span><span class="p">,</span> <span class="mi">45</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">55</span><span class="p">,</span> <span class="o">...</span>

  915. </pre></div>

  916. </div>

  917. <p><a class="reference internal" href="../library/itertools.html#itertools.cycle" title="itertools.cycle"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.cycle(iter)</span></code></a> saves a copy of the contents of

  918. a provided iterable and returns a new iterator that returns its elements from

  919. first to last.  The new iterator will repeat these elements infinitely.</p>

  920. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">cycle</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> <span class="o">=&gt;</span>

  921.   <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="o">...</span>

  922. </pre></div>

  923. </div>

  924. <p><a class="reference internal" href="../library/itertools.html#itertools.repeat" title="itertools.repeat"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.repeat(elem,</span> <span class="pre">[n])</span></code></a> returns the provided

  925. element <em>n</em> times, or returns the element endlessly if <em>n</em> is not provided.</p>

  926. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="s1">&#39;abc&#39;</span><span class="p">)</span> <span class="o">=&gt;</span>

  927.   <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="o">...</span>

  928. <span class="n">itertools</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="s1">&#39;abc&#39;</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span> <span class="o">=&gt;</span>

  929.   <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span><span class="p">,</span> <span class="n">abc</span>

  930. </pre></div>

  931. </div>

  932. <p><a class="reference internal" href="../library/itertools.html#itertools.chain" title="itertools.chain"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.chain(iterA,</span> <span class="pre">iterB,</span> <span class="pre">...)</span></code></a> takes an arbitrary

  933. number of iterables as input, and returns all the elements of the first

  934. iterator, then all the elements of the second, and so on, until all of the

  935. iterables have been exhausted.</p>

  936. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">chain</span><span class="p">([</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;c&#39;</span><span class="p">],</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <span class="o">=&gt;</span>

  937.   <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span>

  938. </pre></div>

  939. </div>

  940. <p><a class="reference internal" href="../library/itertools.html#itertools.islice" title="itertools.islice"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.islice(iter,</span> <span class="pre">[start],</span> <span class="pre">stop,</span> <span class="pre">[step])</span></code></a> returns

  941. a stream that’s a slice of the iterator.  With a single <em>stop</em> argument, it

  942. will return the first <em>stop</em> elements.  If you supply a starting index, you’ll

  943. get <em>stop-start</em> elements, and if you supply a value for <em>step</em>, elements

  944. will be skipped accordingly.  Unlike Python’s string and list slicing, you can’t

  945. use negative values for <em>start</em>, <em>stop</em>, or <em>step</em>.</p>

  946. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">islice</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">),</span> <span class="mi">8</span><span class="p">)</span> <span class="o">=&gt;</span>

  947.   <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span>

  948. <span class="n">itertools</span><span class="o">.</span><span class="n">islice</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">),</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span> <span class="o">=&gt;</span>

  949.   <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span>

  950. <span class="n">itertools</span><span class="o">.</span><span class="n">islice</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">),</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">=&gt;</span>

  951.   <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">6</span>

  952. </pre></div>

  953. </div>

  954. <p><a class="reference internal" href="../library/itertools.html#itertools.tee" title="itertools.tee"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.tee(iter,</span> <span class="pre">[n])</span></code></a> replicates an iterator; it

  955. returns <em>n</em> independent iterators that will all return the contents of the

  956. source iterator.

  957. If you don’t supply a value for <em>n</em>, the default is 2.  Replicating iterators

  958. requires saving some of the contents of the source iterator, so this can consume

  959. significant memory if the iterator is large and one of the new iterators is

  960. consumed more than the others.</p>

  961. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">tee</span><span class="p">(</span> <span class="n">itertools</span><span class="o">.</span><span class="n">count</span><span class="p">()</span> <span class="p">)</span> <span class="o">=&gt;</span>

  962.    <span class="n">iterA</span><span class="p">,</span> <span class="n">iterB</span>

  963. 

  964. <span class="n">where</span> <span class="n">iterA</span> <span class="o">-&gt;</span>

  965.    <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="o">...</span>

  966. 

  967. <span class="ow">and</span>   <span class="n">iterB</span> <span class="o">-&gt;</span>

  968.    <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="o">...</span>

  969. </pre></div>

  970. </div>

  971. </section>

  972. <section id="calling-functions-on-elements">

  973. <h3>Calling functions on elements<a class="headerlink" href="#calling-functions-on-elements" title="Link to this heading">¶</a></h3>

  974. <p>The <a class="reference internal" href="../library/operator.html#module-operator" title="operator: Functions corresponding to the standard operators."><code class="xref py py-mod docutils literal notranslate"><span class="pre">operator</span></code></a> module contains a set of functions corresponding to Python’s

  975. operators.  Some examples are <a class="reference internal" href="../library/operator.html#operator.add" title="operator.add"><code class="xref py py-func docutils literal notranslate"><span class="pre">operator.add(a,</span> <span class="pre">b)</span></code></a> (adds

  976. two values), <a class="reference internal" href="../library/operator.html#operator.ne" title="operator.ne"><code class="xref py py-func docutils literal notranslate"><span class="pre">operator.ne(a,</span> <span class="pre">b)</span></code></a> (same as <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">!=</span> <span class="pre">b</span></code>), and

  977. <a class="reference internal" href="../library/operator.html#operator.attrgetter" title="operator.attrgetter"><code class="xref py py-func docutils literal notranslate"><span class="pre">operator.attrgetter('id')</span></code></a>

  978. (returns a callable that fetches the <code class="docutils literal notranslate"><span class="pre">.id</span></code> attribute).</p>

  979. <p><a class="reference internal" href="../library/itertools.html#itertools.starmap" title="itertools.starmap"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.starmap(func,</span> <span class="pre">iter)</span></code></a> assumes that the

  980. iterable will return a stream of tuples, and calls <em>func</em> using these tuples as

  981. the arguments:</p>

  982. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">starmap</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">,</span>

  983.                   <span class="p">[(</span><span class="s1">&#39;/bin&#39;</span><span class="p">,</span> <span class="s1">&#39;python&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;/usr&#39;</span><span class="p">,</span> <span class="s1">&#39;bin&#39;</span><span class="p">,</span> <span class="s1">&#39;java&#39;</span><span class="p">),</span>

  984.                    <span class="p">(</span><span class="s1">&#39;/usr&#39;</span><span class="p">,</span> <span class="s1">&#39;bin&#39;</span><span class="p">,</span> <span class="s1">&#39;perl&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;/usr&#39;</span><span class="p">,</span> <span class="s1">&#39;bin&#39;</span><span class="p">,</span> <span class="s1">&#39;ruby&#39;</span><span class="p">)])</span>

  985. <span class="o">=&gt;</span>

  986.   <span class="o">/</span><span class="nb">bin</span><span class="o">/</span><span class="n">python</span><span class="p">,</span> <span class="o">/</span><span class="n">usr</span><span class="o">/</span><span class="nb">bin</span><span class="o">/</span><span class="n">java</span><span class="p">,</span> <span class="o">/</span><span class="n">usr</span><span class="o">/</span><span class="nb">bin</span><span class="o">/</span><span class="n">perl</span><span class="p">,</span> <span class="o">/</span><span class="n">usr</span><span class="o">/</span><span class="nb">bin</span><span class="o">/</span><span class="n">ruby</span>

  987. </pre></div>

  988. </div>

  989. </section>

  990. <section id="selecting-elements">

  991. <h3>Selecting elements<a class="headerlink" href="#selecting-elements" title="Link to this heading">¶</a></h3>

  992. <p>Another group of functions chooses a subset of an iterator’s elements based on a

  993. predicate.</p>

  994. <p><a class="reference internal" href="../library/itertools.html#itertools.filterfalse" title="itertools.filterfalse"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.filterfalse(predicate,</span> <span class="pre">iter)</span></code></a> is the

  995. opposite of <a class="reference internal" href="../library/functions.html#filter" title="filter"><code class="xref py py-func docutils literal notranslate"><span class="pre">filter()</span></code></a>, returning all elements for which the predicate

  996. returns false:</p>

  997. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">filterfalse</span><span class="p">(</span><span class="n">is_even</span><span class="p">,</span> <span class="n">itertools</span><span class="o">.</span><span class="n">count</span><span class="p">())</span> <span class="o">=&gt;</span>

  998.   <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">13</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="o">...</span>

  999. </pre></div>

  1000. </div>

  1001. <p><a class="reference internal" href="../library/itertools.html#itertools.takewhile" title="itertools.takewhile"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.takewhile(predicate,</span> <span class="pre">iter)</span></code></a> returns

  1002. elements for as long as the predicate returns true.  Once the predicate returns

  1003. false, the iterator will signal the end of its results.</p>

  1004. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">less_than_10</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>

  1005.     <span class="k">return</span> <span class="n">x</span> <span class="o">&lt;</span> <span class="mi">10</span>

  1006. 

  1007. <span class="n">itertools</span><span class="o">.</span><span class="n">takewhile</span><span class="p">(</span><span class="n">less_than_10</span><span class="p">,</span> <span class="n">itertools</span><span class="o">.</span><span class="n">count</span><span class="p">())</span> <span class="o">=&gt;</span>

  1008.   <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span>

  1009. 

  1010. <span class="n">itertools</span><span class="o">.</span><span class="n">takewhile</span><span class="p">(</span><span class="n">is_even</span><span class="p">,</span> <span class="n">itertools</span><span class="o">.</span><span class="n">count</span><span class="p">())</span> <span class="o">=&gt;</span>

  1011.   <span class="mi">0</span>

  1012. </pre></div>

  1013. </div>

  1014. <p><a class="reference internal" href="../library/itertools.html#itertools.dropwhile" title="itertools.dropwhile"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.dropwhile(predicate,</span> <span class="pre">iter)</span></code></a> discards

  1015. elements while the predicate returns true, and then returns the rest of the

  1016. iterable’s results.</p>

  1017. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">dropwhile</span><span class="p">(</span><span class="n">less_than_10</span><span class="p">,</span> <span class="n">itertools</span><span class="o">.</span><span class="n">count</span><span class="p">())</span> <span class="o">=&gt;</span>

  1018.   <span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="mi">13</span><span class="p">,</span> <span class="mi">14</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">17</span><span class="p">,</span> <span class="mi">18</span><span class="p">,</span> <span class="mi">19</span><span class="p">,</span> <span class="o">...</span>

  1019. 

  1020. <span class="n">itertools</span><span class="o">.</span><span class="n">dropwhile</span><span class="p">(</span><span class="n">is_even</span><span class="p">,</span> <span class="n">itertools</span><span class="o">.</span><span class="n">count</span><span class="p">())</span> <span class="o">=&gt;</span>

  1021.   <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="o">...</span>

  1022. </pre></div>

  1023. </div>

  1024. <p><a class="reference internal" href="../library/itertools.html#itertools.compress" title="itertools.compress"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.compress(data,</span> <span class="pre">selectors)</span></code></a> takes two

  1025. iterators and returns only those elements of <em>data</em> for which the corresponding

  1026. element of <em>selectors</em> is true, stopping whenever either one is exhausted:</p>

  1027. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">compress</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">])</span> <span class="o">=&gt;</span>

  1028.    <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span>

  1029. </pre></div>

  1030. </div>

  1031. </section>

  1032. <section id="combinatoric-functions">

  1033. <h3>Combinatoric functions<a class="headerlink" href="#combinatoric-functions" title="Link to this heading">¶</a></h3>

  1034. <p>The <a class="reference internal" href="../library/itertools.html#itertools.combinations" title="itertools.combinations"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.combinations(iterable,</span> <span class="pre">r)</span></code></a>

  1035. returns an iterator giving all possible <em>r</em>-tuple combinations of the

  1036. elements contained in <em>iterable</em>.</p>

  1037. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">combinations</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="mi">2</span><span class="p">)</span> <span class="o">=&gt;</span>

  1038.   <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1039.   <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1040.   <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1041.   <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>

  1042. 

  1043. <span class="n">itertools</span><span class="o">.</span><span class="n">combinations</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="mi">3</span><span class="p">)</span> <span class="o">=&gt;</span>

  1044.   <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1045.   <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1046.   <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>

  1047. </pre></div>

  1048. </div>

  1049. <p>The elements within each tuple remain in the same order as

  1050. <em>iterable</em> returned them.  For example, the number 1 is always before

  1051. 2, 3, 4, or 5 in the examples above.  A similar function,

  1052. <a class="reference internal" href="../library/itertools.html#itertools.permutations" title="itertools.permutations"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.permutations(iterable,</span> <span class="pre">r=None)</span></code></a>,

  1053. removes this constraint on the order, returning all possible

  1054. arrangements of length <em>r</em>:</p>

  1055. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">permutations</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="mi">2</span><span class="p">)</span> <span class="o">=&gt;</span>

  1056.   <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1057.   <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1058.   <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1059.   <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1060.   <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>

  1061. 

  1062. <span class="n">itertools</span><span class="o">.</span><span class="n">permutations</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> <span class="o">=&gt;</span>

  1063.   <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1064.   <span class="o">...</span>

  1065.   <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>

  1066. </pre></div>

  1067. </div>

  1068. <p>If you don’t supply a value for <em>r</em> the length of the iterable is used,

  1069. meaning that all the elements are permuted.</p>

  1070. <p>Note that these functions produce all of the possible combinations by

  1071. position and don’t require that the contents of <em>iterable</em> are unique:</p>

  1072. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">permutations</span><span class="p">(</span><span class="s1">&#39;aba&#39;</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span> <span class="o">=&gt;</span>

  1073.   <span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">),</span>

  1074.   <span class="p">(</span><span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">)</span>

  1075. </pre></div>

  1076. </div>

  1077. <p>The identical tuple <code class="docutils literal notranslate"><span class="pre">('a',</span> <span class="pre">'a',</span> <span class="pre">'b')</span></code> occurs twice, but the two ‘a’

  1078. strings came from different positions.</p>

  1079. <p>The <a class="reference internal" href="../library/itertools.html#itertools.combinations_with_replacement" title="itertools.combinations_with_replacement"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.combinations_with_replacement(iterable,</span> <span class="pre">r)</span></code></a>

  1080. function relaxes a different constraint: elements can be repeated

  1081. within a single tuple.  Conceptually an element is selected for the

  1082. first position of each tuple and then is replaced before the second

  1083. element is selected.</p>

  1084. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">combinations_with_replacement</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="mi">2</span><span class="p">)</span> <span class="o">=&gt;</span>

  1085.   <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1086.   <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1087.   <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1088.   <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>

  1089.   <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>

  1090. </pre></div>

  1091. </div>

  1092. </section>

  1093. <section id="grouping-elements">

  1094. <h3>Grouping elements<a class="headerlink" href="#grouping-elements" title="Link to this heading">¶</a></h3>

  1095. <p>The last function I’ll discuss, <a class="reference internal" href="../library/itertools.html#itertools.groupby" title="itertools.groupby"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.groupby(iter,</span> <span class="pre">key_func=None)</span></code></a>, is the most complicated.  <code class="docutils literal notranslate"><span class="pre">key_func(elem)</span></code> is a function

  1096. that can compute a key value for each element returned by the iterable.  If you

  1097. don’t supply a key function, the key is simply each element itself.</p>

  1098. <p><a class="reference internal" href="../library/itertools.html#itertools.groupby" title="itertools.groupby"><code class="xref py py-func docutils literal notranslate"><span class="pre">groupby()</span></code></a> collects all the consecutive elements from the

  1099. underlying iterable that have the same key value, and returns a stream of

  1100. 2-tuples containing a key value and an iterator for the elements with that key.</p>

  1101. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">city_list</span> <span class="o">=</span> <span class="p">[(</span><span class="s1">&#39;Decatur&#39;</span><span class="p">,</span> <span class="s1">&#39;AL&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Huntsville&#39;</span><span class="p">,</span> <span class="s1">&#39;AL&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Selma&#39;</span><span class="p">,</span> <span class="s1">&#39;AL&#39;</span><span class="p">),</span>

  1102.              <span class="p">(</span><span class="s1">&#39;Anchorage&#39;</span><span class="p">,</span> <span class="s1">&#39;AK&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Nome&#39;</span><span class="p">,</span> <span class="s1">&#39;AK&#39;</span><span class="p">),</span>

  1103.              <span class="p">(</span><span class="s1">&#39;Flagstaff&#39;</span><span class="p">,</span> <span class="s1">&#39;AZ&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Phoenix&#39;</span><span class="p">,</span> <span class="s1">&#39;AZ&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Tucson&#39;</span><span class="p">,</span> <span class="s1">&#39;AZ&#39;</span><span class="p">),</span>

  1104.              <span class="o">...</span>

  1105.             <span class="p">]</span>

  1106. 

  1107. <span class="k">def</span> <span class="nf">get_state</span><span class="p">(</span><span class="n">city_state</span><span class="p">):</span>

  1108.     <span class="k">return</span> <span class="n">city_state</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>

  1109. 

  1110. <span class="n">itertools</span><span class="o">.</span><span class="n">groupby</span><span class="p">(</span><span class="n">city_list</span><span class="p">,</span> <span class="n">get_state</span><span class="p">)</span> <span class="o">=&gt;</span>

  1111.   <span class="p">(</span><span class="s1">&#39;AL&#39;</span><span class="p">,</span> <span class="n">iterator</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span>

  1112.   <span class="p">(</span><span class="s1">&#39;AK&#39;</span><span class="p">,</span> <span class="n">iterator</span><span class="o">-</span><span class="mi">2</span><span class="p">),</span>

  1113.   <span class="p">(</span><span class="s1">&#39;AZ&#39;</span><span class="p">,</span> <span class="n">iterator</span><span class="o">-</span><span class="mi">3</span><span class="p">),</span> <span class="o">...</span>

  1114. 

  1115. <span class="n">where</span>

  1116. <span class="n">iterator</span><span class="o">-</span><span class="mi">1</span> <span class="o">=&gt;</span>

  1117.   <span class="p">(</span><span class="s1">&#39;Decatur&#39;</span><span class="p">,</span> <span class="s1">&#39;AL&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Huntsville&#39;</span><span class="p">,</span> <span class="s1">&#39;AL&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Selma&#39;</span><span class="p">,</span> <span class="s1">&#39;AL&#39;</span><span class="p">)</span>

  1118. <span class="n">iterator</span><span class="o">-</span><span class="mi">2</span> <span class="o">=&gt;</span>

  1119.   <span class="p">(</span><span class="s1">&#39;Anchorage&#39;</span><span class="p">,</span> <span class="s1">&#39;AK&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Nome&#39;</span><span class="p">,</span> <span class="s1">&#39;AK&#39;</span><span class="p">)</span>

  1120. <span class="n">iterator</span><span class="o">-</span><span class="mi">3</span> <span class="o">=&gt;</span>

  1121.   <span class="p">(</span><span class="s1">&#39;Flagstaff&#39;</span><span class="p">,</span> <span class="s1">&#39;AZ&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Phoenix&#39;</span><span class="p">,</span> <span class="s1">&#39;AZ&#39;</span><span class="p">),</span> <span class="p">(</span><span class="s1">&#39;Tucson&#39;</span><span class="p">,</span> <span class="s1">&#39;AZ&#39;</span><span class="p">)</span>

  1122. </pre></div>

  1123. </div>

  1124. <p><a class="reference internal" href="../library/itertools.html#itertools.groupby" title="itertools.groupby"><code class="xref py py-func docutils literal notranslate"><span class="pre">groupby()</span></code></a> assumes that the underlying iterable’s contents will

  1125. already be sorted based on the key.  Note that the returned iterators also use

  1126. the underlying iterable, so you have to consume the results of iterator-1 before

  1127. requesting iterator-2 and its corresponding key.</p>

  1128. </section>

  1129. </section>

  1130. <section id="the-functools-module">

  1131. <h2>The functools module<a class="headerlink" href="#the-functools-module" title="Link to this heading">¶</a></h2>

  1132. <p>The <a class="reference internal" href="../library/functools.html#module-functools" title="functools: Higher-order functions and operations on callable objects."><code class="xref py py-mod docutils literal notranslate"><span class="pre">functools</span></code></a> module contains some higher-order functions.

  1133. A <strong>higher-order function</strong> takes one or more functions as input and returns a

  1134. new function.  The most useful tool in this module is the

  1135. <a class="reference internal" href="../library/functools.html#functools.partial" title="functools.partial"><code class="xref py py-func docutils literal notranslate"><span class="pre">functools.partial()</span></code></a> function.</p>

  1136. <p>For programs written in a functional style, you’ll sometimes want to construct

  1137. variants of existing functions that have some of the parameters filled in.

  1138. Consider a Python function <code class="docutils literal notranslate"><span class="pre">f(a,</span> <span class="pre">b,</span> <span class="pre">c)</span></code>; you may wish to create a new function

  1139. <code class="docutils literal notranslate"><span class="pre">g(b,</span> <span class="pre">c)</span></code> that’s equivalent to <code class="docutils literal notranslate"><span class="pre">f(1,</span> <span class="pre">b,</span> <span class="pre">c)</span></code>; you’re filling in a value for

  1140. one of <code class="docutils literal notranslate"><span class="pre">f()</span></code>’s parameters.  This is called “partial function application”.</p>

  1141. <p>The constructor for <a class="reference internal" href="../library/functools.html#functools.partial" title="functools.partial"><code class="xref py py-func docutils literal notranslate"><span class="pre">partial()</span></code></a> takes the arguments

  1142. <code class="docutils literal notranslate"><span class="pre">(function,</span> <span class="pre">arg1,</span> <span class="pre">arg2,</span> <span class="pre">...,</span> <span class="pre">kwarg1=value1,</span> <span class="pre">kwarg2=value2)</span></code>.  The resulting

  1143. object is callable, so you can just call it to invoke <code class="docutils literal notranslate"><span class="pre">function</span></code> with the

  1144. filled-in arguments.</p>

  1145. <p>Here’s a small but realistic example:</p>

  1146. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">functools</span>

  1147. 

  1148. <span class="k">def</span> <span class="nf">log</span><span class="p">(</span><span class="n">message</span><span class="p">,</span> <span class="n">subsystem</span><span class="p">):</span>

  1149. <span class="w">    </span><span class="sd">&quot;&quot;&quot;Write the contents of &#39;message&#39; to the specified subsystem.&quot;&quot;&quot;</span>

  1150.     <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">%s</span><span class="s1">: </span><span class="si">%s</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">subsystem</span><span class="p">,</span> <span class="n">message</span><span class="p">))</span>

  1151.     <span class="o">...</span>

  1152. 

  1153. <span class="n">server_log</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">partial</span><span class="p">(</span><span class="n">log</span><span class="p">,</span> <span class="n">subsystem</span><span class="o">=</span><span class="s1">&#39;server&#39;</span><span class="p">)</span>

  1154. <span class="n">server_log</span><span class="p">(</span><span class="s1">&#39;Unable to open socket&#39;</span><span class="p">)</span>

  1155. </pre></div>

  1156. </div>

  1157. <p><a class="reference internal" href="../library/functools.html#functools.reduce" title="functools.reduce"><code class="xref py py-func docutils literal notranslate"><span class="pre">functools.reduce(func,</span> <span class="pre">iter,</span> <span class="pre">[initial_value])</span></code></a>

  1158. cumulatively performs an operation on all the iterable’s elements and,

  1159. therefore, can’t be applied to infinite iterables. <em>func</em> must be a function

  1160. that takes two elements and returns a single value.  <a class="reference internal" href="../library/functools.html#functools.reduce" title="functools.reduce"><code class="xref py py-func docutils literal notranslate"><span class="pre">functools.reduce()</span></code></a>

  1161. takes the first two elements A and B returned by the iterator and calculates

  1162. <code class="docutils literal notranslate"><span class="pre">func(A,</span> <span class="pre">B)</span></code>.  It then requests the third element, C, calculates

  1163. <code class="docutils literal notranslate"><span class="pre">func(func(A,</span> <span class="pre">B),</span> <span class="pre">C)</span></code>, combines this result with the fourth element returned,

  1164. and continues until the iterable is exhausted.  If the iterable returns no

  1165. values at all, a <a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">TypeError</span></code></a> exception is raised.  If the initial value is

  1166. supplied, it’s used as a starting point and <code class="docutils literal notranslate"><span class="pre">func(initial_value,</span> <span class="pre">A)</span></code> is the

  1167. first calculation.</p>

  1168. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">operator</span><span class="o">,</span> <span class="nn">functools</span>

  1169. <span class="gp">&gt;&gt;&gt; </span><span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">concat</span><span class="p">,</span> <span class="p">[</span><span class="s1">&#39;A&#39;</span><span class="p">,</span> <span class="s1">&#39;BB&#39;</span><span class="p">,</span> <span class="s1">&#39;C&#39;</span><span class="p">])</span>

  1170. <span class="go">&#39;ABBC&#39;</span>

  1171. <span class="gp">&gt;&gt;&gt; </span><span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">concat</span><span class="p">,</span> <span class="p">[])</span>

  1172. <span class="gt">Traceback (most recent call last):</span>

  1173. <span class="w">  </span><span class="c">...</span>

  1174. <span class="gr">TypeError</span>: <span class="n">reduce() of empty sequence with no initial value</span>

  1175. <span class="gp">&gt;&gt;&gt; </span><span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">mul</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="mi">1</span><span class="p">)</span>

  1176. <span class="go">6</span>

  1177. <span class="gp">&gt;&gt;&gt; </span><span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">mul</span><span class="p">,</span> <span class="p">[],</span> <span class="mi">1</span><span class="p">)</span>

  1178. <span class="go">1</span>

  1179. </pre></div>

  1180. </div>

  1181. <p>If you use <a class="reference internal" href="../library/operator.html#operator.add" title="operator.add"><code class="xref py py-func docutils literal notranslate"><span class="pre">operator.add()</span></code></a> with <a class="reference internal" href="../library/functools.html#functools.reduce" title="functools.reduce"><code class="xref py py-func docutils literal notranslate"><span class="pre">functools.reduce()</span></code></a>, you’ll add up all the

  1182. elements of the iterable.  This case is so common that there’s a special

  1183. built-in called <a class="reference internal" href="../library/functions.html#sum" title="sum"><code class="xref py py-func docutils literal notranslate"><span class="pre">sum()</span></code></a> to compute it:</p>

  1184. <div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">functools</span><span class="o">,</span> <span class="nn">operator</span>

  1185. <span class="gp">&gt;&gt;&gt; </span><span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span>

  1186. <span class="go">10</span>

  1187. <span class="gp">&gt;&gt;&gt; </span><span class="nb">sum</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>

  1188. <span class="go">10</span>

  1189. <span class="gp">&gt;&gt;&gt; </span><span class="nb">sum</span><span class="p">([])</span>

  1190. <span class="go">0</span>

  1191. </pre></div>

  1192. </div>

  1193. <p>For many uses of <a class="reference internal" href="../library/functools.html#functools.reduce" title="functools.reduce"><code class="xref py py-func docutils literal notranslate"><span class="pre">functools.reduce()</span></code></a>, though, it can be clearer to just

  1194. write the obvious <a class="reference internal" href="../reference/compound_stmts.html#for"><code class="xref std std-keyword docutils literal notranslate"><span class="pre">for</span></code></a> loop:</p>

  1195. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">functools</span>

  1196. <span class="c1"># Instead of:</span>

  1197. <span class="n">product</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">mul</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="mi">1</span><span class="p">)</span>

  1198. 

  1199. <span class="c1"># You can write:</span>

  1200. <span class="n">product</span> <span class="o">=</span> <span class="mi">1</span>

  1201. <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]:</span>

  1202.     <span class="n">product</span> <span class="o">*=</span> <span class="n">i</span>

  1203. </pre></div>

  1204. </div>

  1205. <p>A related function is <a class="reference internal" href="../library/itertools.html#itertools.accumulate" title="itertools.accumulate"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.accumulate(iterable,</span> <span class="pre">func=operator.add)</span></code></a>.  It performs the same calculation, but instead of

  1206. returning only the final result, <a class="reference internal" href="../library/itertools.html#itertools.accumulate" title="itertools.accumulate"><code class="xref py py-func docutils literal notranslate"><span class="pre">accumulate()</span></code></a> returns an iterator

  1207. that also yields each partial result:</p>

  1208. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">itertools</span><span class="o">.</span><span class="n">accumulate</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> <span class="o">=&gt;</span>

  1209.   <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">15</span>

  1210. 

  1211. <span class="n">itertools</span><span class="o">.</span><span class="n">accumulate</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="n">operator</span><span class="o">.</span><span class="n">mul</span><span class="p">)</span> <span class="o">=&gt;</span>

  1212.   <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">24</span><span class="p">,</span> <span class="mi">120</span>

  1213. </pre></div>

  1214. </div>

  1215. <section id="the-operator-module">

  1216. <h3>The operator module<a class="headerlink" href="#the-operator-module" title="Link to this heading">¶</a></h3>

  1217. <p>The <a class="reference internal" href="../library/operator.html#module-operator" title="operator: Functions corresponding to the standard operators."><code class="xref py py-mod docutils literal notranslate"><span class="pre">operator</span></code></a> module was mentioned earlier.  It contains a set of

  1218. functions corresponding to Python’s operators.  These functions are often useful

  1219. in functional-style code because they save you from writing trivial functions

  1220. that perform a single operation.</p>

  1221. <p>Some of the functions in this module are:</p>

  1222. <ul class="simple">

  1223. <li><p>Math operations: <code class="docutils literal notranslate"><span class="pre">add()</span></code>, <code class="docutils literal notranslate"><span class="pre">sub()</span></code>, <code class="docutils literal notranslate"><span class="pre">mul()</span></code>, <code class="docutils literal notranslate"><span class="pre">floordiv()</span></code>, <code class="docutils literal notranslate"><span class="pre">abs()</span></code>, …</p></li>

  1224. <li><p>Logical operations: <code class="docutils literal notranslate"><span class="pre">not_()</span></code>, <code class="docutils literal notranslate"><span class="pre">truth()</span></code>.</p></li>

  1225. <li><p>Bitwise operations: <code class="docutils literal notranslate"><span class="pre">and_()</span></code>, <code class="docutils literal notranslate"><span class="pre">or_()</span></code>, <code class="docutils literal notranslate"><span class="pre">invert()</span></code>.</p></li>

  1226. <li><p>Comparisons: <code class="docutils literal notranslate"><span class="pre">eq()</span></code>, <code class="docutils literal notranslate"><span class="pre">ne()</span></code>, <code class="docutils literal notranslate"><span class="pre">lt()</span></code>, <code class="docutils literal notranslate"><span class="pre">le()</span></code>, <code class="docutils literal notranslate"><span class="pre">gt()</span></code>, and <code class="docutils literal notranslate"><span class="pre">ge()</span></code>.</p></li>

  1227. <li><p>Object identity: <code class="docutils literal notranslate"><span class="pre">is_()</span></code>, <code class="docutils literal notranslate"><span class="pre">is_not()</span></code>.</p></li>

  1228. </ul>

  1229. <p>Consult the operator module’s documentation for a complete list.</p>

  1230. </section>

  1231. </section>

  1232. <section id="small-functions-and-the-lambda-expression">

  1233. <h2>Small functions and the lambda expression<a class="headerlink" href="#small-functions-and-the-lambda-expression" title="Link to this heading">¶</a></h2>

  1234. <p>When writing functional-style programs, you’ll often need little functions that

  1235. act as predicates or that combine elements in some way.</p>

  1236. <p>If there’s a Python built-in or a module function that’s suitable, you don’t

  1237. need to define a new function at all:</p>

  1238. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">stripped_lines</span> <span class="o">=</span> <span class="p">[</span><span class="n">line</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span> <span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">lines</span><span class="p">]</span>

  1239. <span class="n">existing_files</span> <span class="o">=</span> <span class="nb">filter</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">,</span> <span class="n">file_list</span><span class="p">)</span>

  1240. </pre></div>

  1241. </div>

  1242. <p>If the function you need doesn’t exist, you need to write it.  One way to write

  1243. small functions is to use the <a class="reference internal" href="../reference/expressions.html#lambda"><code class="xref std std-keyword docutils literal notranslate"><span class="pre">lambda</span></code></a> expression.  <code class="docutils literal notranslate"><span class="pre">lambda</span></code> takes a

  1244. number of parameters and an expression combining these parameters, and creates

  1245. an anonymous function that returns the value of the expression:</p>

  1246. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">adder</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">x</span><span class="o">+</span><span class="n">y</span>

  1247. 

  1248. <span class="n">print_assign</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="p">:</span> <span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;=&#39;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>

  1249. </pre></div>

  1250. </div>

  1251. <p>An alternative is to just use the <code class="docutils literal notranslate"><span class="pre">def</span></code> statement and define a function in the

  1252. usual way:</p>

  1253. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">adder</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>

  1254.     <span class="k">return</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span>

  1255. 

  1256. <span class="k">def</span> <span class="nf">print_assign</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>

  1257.     <span class="k">return</span> <span class="n">name</span> <span class="o">+</span> <span class="s1">&#39;=&#39;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>

  1258. </pre></div>

  1259. </div>

  1260. <p>Which alternative is preferable?  That’s a style question; my usual course is to

  1261. avoid using <code class="docutils literal notranslate"><span class="pre">lambda</span></code>.</p>

  1262. <p>One reason for my preference is that <code class="docutils literal notranslate"><span class="pre">lambda</span></code> is quite limited in the

  1263. functions it can define.  The result has to be computable as a single

  1264. expression, which means you can’t have multiway <code class="docutils literal notranslate"><span class="pre">if...</span> <span class="pre">elif...</span> <span class="pre">else</span></code>

  1265. comparisons or <code class="docutils literal notranslate"><span class="pre">try...</span> <span class="pre">except</span></code> statements.  If you try to do too much in a

  1266. <code class="docutils literal notranslate"><span class="pre">lambda</span></code> statement, you’ll end up with an overly complicated expression that’s

  1267. hard to read.  Quick, what’s the following code doing?</p>

  1268. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">functools</span>

  1269. <span class="n">total</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="k">lambda</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">:</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">items</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>

  1270. </pre></div>

  1271. </div>

  1272. <p>You can figure it out, but it takes time to disentangle the expression to figure

  1273. out what’s going on.  Using a short nested <code class="docutils literal notranslate"><span class="pre">def</span></code> statements makes things a

  1274. little bit better:</p>

  1275. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">functools</span>

  1276. <span class="k">def</span> <span class="nf">combine</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>

  1277.     <span class="k">return</span> <span class="mi">0</span><span class="p">,</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>

  1278. 

  1279. <span class="n">total</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">combine</span><span class="p">,</span> <span class="n">items</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>

  1280. </pre></div>

  1281. </div>

  1282. <p>But it would be best of all if I had simply used a <code class="docutils literal notranslate"><span class="pre">for</span></code> loop:</p>

  1283. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">total</span> <span class="o">=</span> <span class="mi">0</span>

  1284. <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">items</span><span class="p">:</span>

  1285.     <span class="n">total</span> <span class="o">+=</span> <span class="n">b</span>

  1286. </pre></div>

  1287. </div>

  1288. <p>Or the <a class="reference internal" href="../library/functions.html#sum" title="sum"><code class="xref py py-func docutils literal notranslate"><span class="pre">sum()</span></code></a> built-in and a generator expression:</p>

  1289. <div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">total</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">b</span> <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">items</span><span class="p">)</span>

  1290. </pre></div>

  1291. </div>

  1292. <p>Many uses of <a class="reference internal" href="../library/functools.html#functools.reduce" title="functools.reduce"><code class="xref py py-func docutils literal notranslate"><span class="pre">functools.reduce()</span></code></a> are clearer when written as <code class="docutils literal notranslate"><span class="pre">for</span></code> loops.</p>

  1293. <p>Fredrik Lundh once suggested the following set of rules for refactoring uses of

  1294. <code class="docutils literal notranslate"><span class="pre">lambda</span></code>:</p>

  1295. <ol class="arabic simple">

  1296. <li><p>Write a lambda function.</p></li>

  1297. <li><p>Write a comment explaining what the heck that lambda does.</p></li>

  1298. <li><p>Study the comment for a while, and think of a name that captures the essence

  1299. of the comment.</p></li>

  1300. <li><p>Convert the lambda to a def statement, using that name.</p></li>

  1301. <li><p>Remove the comment.</p></li>

  1302. </ol>

  1303. <p>I really like these rules, but you’re free to disagree

  1304. about whether this lambda-free style is better.</p>

  1305. </section>

  1306. <section id="revision-history-and-acknowledgements">

  1307. <h2>Revision History and Acknowledgements<a class="headerlink" href="#revision-history-and-acknowledgements" title="Link to this heading">¶</a></h2>

  1308. <p>The author would like to thank the following people for offering suggestions,

  1309. corrections and assistance with various drafts of this article: Ian Bicking,

  1310. Nick Coghlan, Nick Efford, Raymond Hettinger, Jim Jewett, Mike Krell, Leandro

  1311. Lameiro, Jussi Salmela, Collin Winter, Blake Winton.</p>

  1312. <p>Version 0.1: posted June 30 2006.</p>

  1313. <p>Version 0.11: posted July 1 2006.  Typo fixes.</p>

  1314. <p>Version 0.2: posted July 10 2006.  Merged genexp and listcomp sections into one.

  1315. Typo fixes.</p>

  1316. <p>Version 0.21: Added more references suggested on the tutor mailing list.</p>

  1317. <p>Version 0.30: Adds a section on the <code class="docutils literal notranslate"><span class="pre">functional</span></code> module written by Collin

  1318. Winter; adds short section on the operator module; a few other edits.</p>

  1319. </section>

  1320. <section id="references">

  1321. <h2>References<a class="headerlink" href="#references" title="Link to this heading">¶</a></h2>

  1322. <section id="general">

  1323. <h3>General<a class="headerlink" href="#general" title="Link to this heading">¶</a></h3>

  1324. <p><strong>Structure and Interpretation of Computer Programs</strong>, by Harold Abelson and

  1325. Gerald Jay Sussman with Julie Sussman.  The book can be found at

  1326. <a class="reference external" href="https://mitpress.mit.edu/sicp">https://mitpress.mit.edu/sicp</a>.  In this classic textbook of computer science,

  1327. chapters 2 and 3 discuss the use of sequences and streams to organize the data

  1328. flow inside a program.  The book uses Scheme for its examples, but many of the

  1329. design approaches described in these chapters are applicable to functional-style

  1330. Python code.</p>

  1331. <p><a class="reference external" href="https://www.defmacro.org/ramblings/fp.html">https://www.defmacro.org/ramblings/fp.html</a>: A general introduction to functional

  1332. programming that uses Java examples and has a lengthy historical introduction.</p>

  1333. <p><a class="reference external" href="https://en.wikipedia.org/wiki/Functional_programming">https://en.wikipedia.org/wiki/Functional_programming</a>: General Wikipedia entry

  1334. describing functional programming.</p>

  1335. <p><a class="reference external" href="https://en.wikipedia.org/wiki/Coroutine">https://en.wikipedia.org/wiki/Coroutine</a>: Entry for coroutines.</p>

  1336. <p><a class="reference external" href="https://en.wikipedia.org/wiki/Partial_application">https://en.wikipedia.org/wiki/Partial_application</a>: Entry for the concept of partial function application.</p>

  1337. <p><a class="reference external" href="https://en.wikipedia.org/wiki/Currying">https://en.wikipedia.org/wiki/Currying</a>: Entry for the concept of currying.</p>

  1338. </section>

  1339. <section id="python-specific">

  1340. <h3>Python-specific<a class="headerlink" href="#python-specific" title="Link to this heading">¶</a></h3>

  1341. <p><a class="reference external" href="https://gnosis.cx/TPiP/">https://gnosis.cx/TPiP/</a>: The first chapter of David Mertz’s book

  1342. <cite>Text Processing in Python</cite> discusses functional programming

  1343. for text processing, in the section titled “Utilizing Higher-Order Functions in

  1344. Text Processing”.</p>

  1345. <p>Mertz also wrote a 3-part series of articles on functional programming

  1346. for IBM’s DeveloperWorks site; see

  1347. <a class="reference external" href="https://developer.ibm.com/articles/l-prog/">part 1</a>,

  1348. <a class="reference external" href="https://developer.ibm.com/tutorials/l-prog2/">part 2</a>, and

  1349. <a class="reference external" href="https://developer.ibm.com/tutorials/l-prog3/">part 3</a>,</p>

  1350. </section>

  1351. <section id="python-documentation">

  1352. <h3>Python documentation<a class="headerlink" href="#python-documentation" title="Link to this heading">¶</a></h3>

  1353. <p>Documentation for the <a class="reference internal" href="../library/itertools.html#module-itertools" title="itertools: Functions creating iterators for efficient looping."><code class="xref py py-mod docutils literal notranslate"><span class="pre">itertools</span></code></a> module.</p>

  1354. <p>Documentation for the <a class="reference internal" href="../library/functools.html#module-functools" title="functools: Higher-order functions and operations on callable objects."><code class="xref py py-mod docutils literal notranslate"><span class="pre">functools</span></code></a> module.</p>

  1355. <p>Documentation for the <a class="reference internal" href="../library/operator.html#module-operator" title="operator: Functions corresponding to the standard operators."><code class="xref py py-mod docutils literal notranslate"><span class="pre">operator</span></code></a> module.</p>

  1356. <p><span class="target" id="index-1"></span><a class="pep reference external" href="https://peps.python.org/pep-0289/"><strong>PEP 289</strong></a>: “Generator Expressions”</p>

  1357. <p><span class="target" id="index-2"></span><a class="pep reference external" href="https://peps.python.org/pep-0342/"><strong>PEP 342</strong></a>: “Coroutines via Enhanced Generators” describes the new generator

  1358. features in Python 2.5.</p>

  1359. </section>

  1360. </section>

  1361. </section>

  1362. 

  1363. 

  1364.             <div class="clearer"></div>

  1365.           </div>

  1366.         </div>

  1367.       </div>

  1368.       <div class="sphinxsidebar" role="navigation" aria-label="main navigation">

  1369.         <div class="sphinxsidebarwrapper">

  1370.   <div>

  1371.     <h3><a href="../contents.html">Table of Contents</a></h3>

  1372.     <ul>

  1373. <li><a class="reference internal" href="#">Functional Programming HOWTO</a><ul>

  1374. <li><a class="reference internal" href="#introduction">Introduction</a><ul>

  1375. <li><a class="reference internal" href="#formal-provability">Formal provability</a></li>

  1376. <li><a class="reference internal" href="#modularity">Modularity</a></li>

  1377. <li><a class="reference internal" href="#ease-of-debugging-and-testing">Ease of debugging and testing</a></li>

  1378. <li><a class="reference internal" href="#composability">Composability</a></li>

  1379. </ul>

  1380. </li>

  1381. <li><a class="reference internal" href="#iterators">Iterators</a><ul>

  1382. <li><a class="reference internal" href="#data-types-that-support-iterators">Data Types That Support Iterators</a></li>

  1383. </ul>

  1384. </li>

  1385. <li><a class="reference internal" href="#generator-expressions-and-list-comprehensions">Generator expressions and list comprehensions</a></li>

  1386. <li><a class="reference internal" href="#generators">Generators</a><ul>

  1387. <li><a class="reference internal" href="#passing-values-into-a-generator">Passing values into a generator</a></li>

  1388. </ul>

  1389. </li>

  1390. <li><a class="reference internal" href="#built-in-functions">Built-in functions</a></li>

  1391. <li><a class="reference internal" href="#the-itertools-module">The itertools module</a><ul>

  1392. <li><a class="reference internal" href="#creating-new-iterators">Creating new iterators</a></li>

  1393. <li><a class="reference internal" href="#calling-functions-on-elements">Calling functions on elements</a></li>

  1394. <li><a class="reference internal" href="#selecting-elements">Selecting elements</a></li>

  1395. <li><a class="reference internal" href="#combinatoric-functions">Combinatoric functions</a></li>

  1396. <li><a class="reference internal" href="#grouping-elements">Grouping elements</a></li>

  1397. </ul>

  1398. </li>

  1399. <li><a class="reference internal" href="#the-functools-module">The functools module</a><ul>

  1400. <li><a class="reference internal" href="#the-operator-module">The operator module</a></li>

  1401. </ul>

  1402. </li>

  1403. <li><a class="reference internal" href="#small-functions-and-the-lambda-expression">Small functions and the lambda expression</a></li>

  1404. <li><a class="reference internal" href="#revision-history-and-acknowledgements">Revision History and Acknowledgements</a></li>

  1405. <li><a class="reference internal" href="#references">References</a><ul>

  1406. <li><a class="reference internal" href="#general">General</a></li>

  1407. <li><a class="reference internal" href="#python-specific">Python-specific</a></li>

  1408. <li><a class="reference internal" href="#python-documentation">Python documentation</a></li>

  1409. </ul>

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