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<div class="section" id="expressions">
<span id="id1"></span><h1>5. Expressions<a class="headerlink" href="#expressions" title="Permalink to this headline">¶</a></h1>
<p id="index-0">This chapter explains the meaning of the elements of expressions in Python.</p>
<p><strong>Syntax Notes:</strong> In this and the following chapters, extended BNF notation will
be used to describe syntax, not lexical analysis. When (one alternative of) a
syntax rule has the form</p>
<pre>
<strong id="grammar-token-name">name</strong> ::= <tt class="xref docutils literal"><span class="pre">othername</span></tt>
</pre>
<p>and no semantics are given, the semantics of this form of <tt class="docutils literal"><span class="pre">name</span></tt> are the same
as for <tt class="docutils literal"><span class="pre">othername</span></tt>.</p>
<div class="section" id="arithmetic-conversions">
<span id="conversions"></span><h2>5.1. Arithmetic conversions<a class="headerlink" href="#arithmetic-conversions" title="Permalink to this headline">¶</a></h2>
<p id="index-1">When a description of an arithmetic operator below uses the phrase “the numeric
arguments are converted to a common type,” this means that the operator
implementation for built-in types works that way:</p>
<ul class="simple">
<li>If either argument is a complex number, the other is converted to complex;</li>
<li>otherwise, if either argument is a floating point number, the other is
converted to floating point;</li>
<li>otherwise, both must be integers and no conversion is necessary.</li>
</ul>
<p>Some additional rules apply for certain operators (e.g., a string left argument
to the ‘%’ operator). Extensions must define their own conversion behavior.</p>
</div>
<div class="section" id="atoms">
<span id="id2"></span><h2>5.2. Atoms<a class="headerlink" href="#atoms" title="Permalink to this headline">¶</a></h2>
<p id="index-2">Atoms are the most basic elements of expressions. The simplest atoms are
identifiers or literals. Forms enclosed in parentheses, brackets or braces are
also categorized syntactically as atoms. The syntax for atoms is:</p>
<pre>
<strong id="grammar-token-atom">atom </strong> ::= <a class="reference internal" href="lexical_analysis.html#grammar-token-identifier"><tt class="xref docutils literal"><span class="pre">identifier</span></tt></a> | <a class="reference internal" href="#grammar-token-literal"><tt class="xref docutils literal"><span class="pre">literal</span></tt></a> | <a class="reference internal" href="#grammar-token-enclosure"><tt class="xref docutils literal"><span class="pre">enclosure</span></tt></a>
<strong id="grammar-token-enclosure">enclosure</strong> ::= <a class="reference internal" href="#grammar-token-parenth_form"><tt class="xref docutils literal"><span class="pre">parenth_form</span></tt></a> | <a class="reference internal" href="#grammar-token-list_display"><tt class="xref docutils literal"><span class="pre">list_display</span></tt></a> | <a class="reference internal" href="#grammar-token-dict_display"><tt class="xref docutils literal"><span class="pre">dict_display</span></tt></a> | <a class="reference internal" href="#grammar-token-set_display"><tt class="xref docutils literal"><span class="pre">set_display</span></tt></a>
| <a class="reference internal" href="#grammar-token-generator_expression"><tt class="xref docutils literal"><span class="pre">generator_expression</span></tt></a> | <a class="reference internal" href="#grammar-token-yield_atom"><tt class="xref docutils literal"><span class="pre">yield_atom</span></tt></a>
</pre>
<div class="section" id="atom-identifiers">
<span id="identifiers-names"></span><h3>5.2.1. Identifiers (Names)<a class="headerlink" href="#atom-identifiers" title="Permalink to this headline">¶</a></h3>
<p id="index-3">An identifier occurring as an atom is a name. See section <a class="reference internal" href="lexical_analysis.html#identifiers"><em>Identifiers and keywords</em></a>
for lexical definition and section <a class="reference internal" href="executionmodel.html#naming"><em>Naming and binding</em></a> for documentation of naming and
binding.</p>
<p id="index-4">When the name is bound to an object, evaluation of the atom yields that object.
When a name is not bound, an attempt to evaluate it raises a <a class="reference internal" href="../library/exceptions.html#NameError" title="NameError"><tt class="xref py py-exc docutils literal"><span class="pre">NameError</span></tt></a>
exception.</p>
<p id="index-5"><strong>Private name mangling:</strong> When an identifier that textually occurs in a class
definition begins with two or more underscore characters and does not end in two
or more underscores, it is considered a <em class="dfn">private name</em> of that class.
Private names are transformed to a longer form before code is generated for
them. The transformation inserts the class name in front of the name, with
leading underscores removed, and a single underscore inserted in front of the
class name. For example, the identifier <tt class="docutils literal"><span class="pre">__spam</span></tt> occurring in a class named
<tt class="docutils literal"><span class="pre">Ham</span></tt> will be transformed to <tt class="docutils literal"><span class="pre">_Ham__spam</span></tt>. This transformation is
independent of the syntactical context in which the identifier is used. If the
transformed name is extremely long (longer than 255 characters), implementation
defined truncation may happen. If the class name consists only of underscores,
no transformation is done.</p>
</div>
<div class="section" id="literals">
<span id="atom-literals"></span><h3>5.2.2. Literals<a class="headerlink" href="#literals" title="Permalink to this headline">¶</a></h3>
<p id="index-6">Python supports string and bytes literals and various numeric literals:</p>
<pre>
<strong id="grammar-token-literal">literal</strong> ::= <a class="reference internal" href="lexical_analysis.html#grammar-token-stringliteral"><tt class="xref docutils literal"><span class="pre">stringliteral</span></tt></a> | <a class="reference internal" href="lexical_analysis.html#grammar-token-bytesliteral"><tt class="xref docutils literal"><span class="pre">bytesliteral</span></tt></a>
| <a class="reference internal" href="lexical_analysis.html#grammar-token-integer"><tt class="xref docutils literal"><span class="pre">integer</span></tt></a> | <a class="reference internal" href="lexical_analysis.html#grammar-token-floatnumber"><tt class="xref docutils literal"><span class="pre">floatnumber</span></tt></a> | <a class="reference internal" href="lexical_analysis.html#grammar-token-imagnumber"><tt class="xref docutils literal"><span class="pre">imagnumber</span></tt></a>
</pre>
<p>Evaluation of a literal yields an object of the given type (string, bytes,
integer, floating point number, complex number) with the given value. The value
may be approximated in the case of floating point and imaginary (complex)
literals. See section <a class="reference internal" href="lexical_analysis.html#literals"><em>Literals</em></a> for details.</p>
<p id="index-7">With the exception of bytes literals, these all correspond to immutable data
types, and hence the object’s identity is less important than its value.
Multiple evaluations of literals with the same value (either the same occurrence
in the program text or a different occurrence) may obtain the same object or a
different object with the same value.</p>
</div>
<div class="section" id="parenthesized-forms">
<span id="parenthesized"></span><h3>5.2.3. Parenthesized forms<a class="headerlink" href="#parenthesized-forms" title="Permalink to this headline">¶</a></h3>
<p id="index-8">A parenthesized form is an optional expression list enclosed in parentheses:</p>
<pre>
<strong id="grammar-token-parenth_form">parenth_form</strong> ::= "(" [<a class="reference internal" href="#grammar-token-expression_list"><tt class="xref docutils literal"><span class="pre">expression_list</span></tt></a>] ")"
</pre>
<p>A parenthesized expression list yields whatever that expression list yields: if
the list contains at least one comma, it yields a tuple; otherwise, it yields
the single expression that makes up the expression list.</p>
<p id="index-9">An empty pair of parentheses yields an empty tuple object. Since tuples are
immutable, the rules for literals apply (i.e., two occurrences of the empty
tuple may or may not yield the same object).</p>
<p id="index-10">Note that tuples are not formed by the parentheses, but rather by use of the
comma operator. The exception is the empty tuple, for which parentheses <em>are</em>
required — allowing unparenthesized “nothing” in expressions would cause
ambiguities and allow common typos to pass uncaught.</p>
</div>
<div class="section" id="displays-for-lists-sets-and-dictionaries">
<span id="comprehensions"></span><h3>5.2.4. Displays for lists, sets and dictionaries<a class="headerlink" href="#displays-for-lists-sets-and-dictionaries" title="Permalink to this headline">¶</a></h3>
<p>For constructing a list, a set or a dictionary Python provides special syntax
called “displays”, each of them in two flavors:</p>
<ul class="simple">
<li>either the container contents are listed explicitly, or</li>
<li>they are computed via a set of looping and filtering instructions, called a
<em class="dfn">comprehension</em>.</li>
</ul>
<p>Common syntax elements for comprehensions are:</p>
<pre>
<strong id="grammar-token-comprehension">comprehension</strong> ::= <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> <a class="reference internal" href="#grammar-token-comp_for"><tt class="xref docutils literal"><span class="pre">comp_for</span></tt></a>
<strong id="grammar-token-comp_for">comp_for </strong> ::= "for" <a class="reference internal" href="simple_stmts.html#grammar-token-target_list"><tt class="xref docutils literal"><span class="pre">target_list</span></tt></a> "in" <a class="reference internal" href="#grammar-token-or_test"><tt class="xref docutils literal"><span class="pre">or_test</span></tt></a> [<a class="reference internal" href="#grammar-token-comp_iter"><tt class="xref docutils literal"><span class="pre">comp_iter</span></tt></a>]
<strong id="grammar-token-comp_iter">comp_iter </strong> ::= <a class="reference internal" href="#grammar-token-comp_for"><tt class="xref docutils literal"><span class="pre">comp_for</span></tt></a> | <a class="reference internal" href="#grammar-token-comp_if"><tt class="xref docutils literal"><span class="pre">comp_if</span></tt></a>
<strong id="grammar-token-comp_if">comp_if </strong> ::= "if" <a class="reference internal" href="#grammar-token-expression_nocond"><tt class="xref docutils literal"><span class="pre">expression_nocond</span></tt></a> [<a class="reference internal" href="#grammar-token-comp_iter"><tt class="xref docutils literal"><span class="pre">comp_iter</span></tt></a>]
</pre>
<p>The comprehension consists of a single expression followed by at least one
<a class="reference internal" href="compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> clause and zero or more <a class="reference internal" href="compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> or <a class="reference internal" href="compound_stmts.html#if"><tt class="xref std std-keyword docutils literal"><span class="pre">if</span></tt></a> clauses.
In this case, the elements of the new container are those that would be produced
by considering each of the <a class="reference internal" href="compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> or <a class="reference internal" href="compound_stmts.html#if"><tt class="xref std std-keyword docutils literal"><span class="pre">if</span></tt></a> clauses a block,
nesting from left to right, and evaluating the expression to produce an element
each time the innermost block is reached.</p>
<p>Note that the comprehension is executed in a separate scope, so names assigned
to in the target list don’t “leak” in the enclosing scope.</p>
</div>
<div class="section" id="list-displays">
<span id="lists"></span><h3>5.2.5. List displays<a class="headerlink" href="#list-displays" title="Permalink to this headline">¶</a></h3>
<p id="index-11">A list display is a possibly empty series of expressions enclosed in square
brackets:</p>
<pre>
<strong id="grammar-token-list_display">list_display</strong> ::= "[" [<a class="reference internal" href="#grammar-token-expression_list"><tt class="xref docutils literal"><span class="pre">expression_list</span></tt></a> | <a class="reference internal" href="#grammar-token-comprehension"><tt class="xref docutils literal"><span class="pre">comprehension</span></tt></a>] "]"
</pre>
<p>A list display yields a new list object, the contents being specified by either
a list of expressions or a comprehension. When a comma-separated list of
expressions is supplied, its elements are evaluated from left to right and
placed into the list object in that order. When a comprehension is supplied,
the list is constructed from the elements resulting from the comprehension.</p>
</div>
<div class="section" id="set-displays">
<span id="set"></span><h3>5.2.6. Set displays<a class="headerlink" href="#set-displays" title="Permalink to this headline">¶</a></h3>
<p id="index-12">A set display is denoted by curly braces and distinguishable from dictionary
displays by the lack of colons separating keys and values:</p>
<pre>
<strong id="grammar-token-set_display">set_display</strong> ::= "{" (<a class="reference internal" href="#grammar-token-expression_list"><tt class="xref docutils literal"><span class="pre">expression_list</span></tt></a> | <a class="reference internal" href="#grammar-token-comprehension"><tt class="xref docutils literal"><span class="pre">comprehension</span></tt></a>) "}"
</pre>
<p>A set display yields a new mutable set object, the contents being specified by
either a sequence of expressions or a comprehension. When a comma-separated
list of expressions is supplied, its elements are evaluated from left to right
and added to the set object. When a comprehension is supplied, the set is
constructed from the elements resulting from the comprehension.</p>
<p>An empty set cannot be constructed with <tt class="docutils literal"><span class="pre">{}</span></tt>; this literal constructs an empty
dictionary.</p>
</div>
<div class="section" id="dictionary-displays">
<span id="dict"></span><h3>5.2.7. Dictionary displays<a class="headerlink" href="#dictionary-displays" title="Permalink to this headline">¶</a></h3>
<p id="index-13">A dictionary display is a possibly empty series of key/datum pairs enclosed in
curly braces:</p>
<pre>
<strong id="grammar-token-dict_display">dict_display </strong> ::= "{" [<a class="reference internal" href="#grammar-token-key_datum_list"><tt class="xref docutils literal"><span class="pre">key_datum_list</span></tt></a> | <a class="reference internal" href="#grammar-token-dict_comprehension"><tt class="xref docutils literal"><span class="pre">dict_comprehension</span></tt></a>] "}"
<strong id="grammar-token-key_datum_list">key_datum_list </strong> ::= <a class="reference internal" href="#grammar-token-key_datum"><tt class="xref docutils literal"><span class="pre">key_datum</span></tt></a> ("," <a class="reference internal" href="#grammar-token-key_datum"><tt class="xref docutils literal"><span class="pre">key_datum</span></tt></a>)* [","]
<strong id="grammar-token-key_datum">key_datum </strong> ::= <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> ":" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>
<strong id="grammar-token-dict_comprehension">dict_comprehension</strong> ::= <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> ":" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> <a class="reference internal" href="#grammar-token-comp_for"><tt class="xref docutils literal"><span class="pre">comp_for</span></tt></a>
</pre>
<p>A dictionary display yields a new dictionary object.</p>
<p>If a comma-separated sequence of key/datum pairs is given, they are evaluated
from left to right to define the entries of the dictionary: each key object is
used as a key into the dictionary to store the corresponding datum. This means
that you can specify the same key multiple times in the key/datum list, and the
final dictionary’s value for that key will be the last one given.</p>
<p>A dict comprehension, in contrast to list and set comprehensions, needs two
expressions separated with a colon followed by the usual “for” and “if” clauses.
When the comprehension is run, the resulting key and value elements are inserted
in the new dictionary in the order they are produced.</p>
<p id="index-14">Restrictions on the types of the key values are listed earlier in section
<a class="reference internal" href="datamodel.html#types"><em>The standard type hierarchy</em></a>. (To summarize, the key type should be <a class="reference internal" href="../glossary.html#term-hashable"><em class="xref std std-term">hashable</em></a>, which excludes
all mutable objects.) Clashes between duplicate keys are not detected; the last
datum (textually rightmost in the display) stored for a given key value
prevails.</p>
</div>
<div class="section" id="generator-expressions">
<span id="genexpr"></span><h3>5.2.8. Generator expressions<a class="headerlink" href="#generator-expressions" title="Permalink to this headline">¶</a></h3>
<p id="index-15">A generator expression is a compact generator notation in parentheses:</p>
<pre>
<strong id="grammar-token-generator_expression">generator_expression</strong> ::= "(" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> <a class="reference internal" href="#grammar-token-comp_for"><tt class="xref docutils literal"><span class="pre">comp_for</span></tt></a> ")"
</pre>
<p>A generator expression yields a new generator object. Its syntax is the same as
for comprehensions, except that it is enclosed in parentheses instead of
brackets or curly braces.</p>
<p>Variables used in the generator expression are evaluated lazily when the
<tt class="xref py py-meth docutils literal"><span class="pre">__next__()</span></tt> method is called for generator object (in the same fashion as
normal generators). However, the leftmost <a class="reference internal" href="compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> clause is immediately
evaluated, so that an error produced by it can be seen before any other possible
error in the code that handles the generator expression. Subsequent
<a class="reference internal" href="compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> clauses cannot be evaluated immediately since they may depend on
the previous <a class="reference internal" href="compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> loop. For example: <tt class="docutils literal"><span class="pre">(x*y</span> <span class="pre">for</span> <span class="pre">x</span> <span class="pre">in</span> <span class="pre">range(10)</span> <span class="pre">for</span> <span class="pre">y</span>
<span class="pre">in</span> <span class="pre">bar(x))</span></tt>.</p>
<p>The parentheses can be omitted on calls with only one argument. See section
<a class="reference internal" href="#calls"><em>Calls</em></a> for the detail.</p>
</div>
<div class="section" id="yield-expressions">
<span id="yieldexpr"></span><h3>5.2.9. Yield expressions<a class="headerlink" href="#yield-expressions" title="Permalink to this headline">¶</a></h3>
<pre id="index-16">
<strong id="grammar-token-yield_atom">yield_atom </strong> ::= "(" <a class="reference internal" href="#grammar-token-yield_expression"><tt class="xref docutils literal"><span class="pre">yield_expression</span></tt></a> ")"
<strong id="grammar-token-yield_expression">yield_expression</strong> ::= "yield" [<a class="reference internal" href="#grammar-token-expression_list"><tt class="xref docutils literal"><span class="pre">expression_list</span></tt></a>]
</pre>
<p>The <a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> expression is only used when defining a generator function,
and can only be used in the body of a function definition. Using a
<a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> expression in a function definition is sufficient to cause that
definition to create a generator function instead of a normal function.</p>
<p>When a generator function is called, it returns an iterator known as a
generator. That generator then controls the execution of a generator function.
The execution starts when one of the generator’s methods is called. At that
time, the execution proceeds to the first <a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> expression, where it
is suspended again, returning the value of <a class="reference internal" href="#grammar-token-expression_list"><tt class="xref std std-token docutils literal"><span class="pre">expression_list</span></tt></a> to
generator’s caller. By suspended we mean that all local state is retained,
including the current bindings of local variables, the instruction pointer, and
the internal evaluation stack. When the execution is resumed by calling one of
the generator’s methods, the function can proceed exactly as if the
<a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> expression was just another external call. The value of the
<a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> expression after resuming depends on the method which resumed
the execution.</p>
<p id="index-17">All of this makes generator functions quite similar to coroutines; they yield
multiple times, they have more than one entry point and their execution can be
suspended. The only difference is that a generator function cannot control
where should the execution continue after it yields; the control is always
transferred to the generator’s caller.</p>
<p>The <a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> statement is allowed in the <a class="reference internal" href="compound_stmts.html#try"><tt class="xref std std-keyword docutils literal"><span class="pre">try</span></tt></a> clause of a
<a class="reference internal" href="compound_stmts.html#try"><tt class="xref std std-keyword docutils literal"><span class="pre">try</span></tt></a> ... <a class="reference internal" href="compound_stmts.html#finally"><tt class="xref std std-keyword docutils literal"><span class="pre">finally</span></tt></a> construct. If the generator is not
resumed before it is finalized (by reaching a zero reference count or by being
garbage collected), the generator-iterator’s <tt class="xref py py-meth docutils literal"><span class="pre">close()</span></tt> method will be
called, allowing any pending <a class="reference internal" href="compound_stmts.html#finally"><tt class="xref std std-keyword docutils literal"><span class="pre">finally</span></tt></a> clauses to execute.</p>
<p id="index-18">The following generator’s methods can be used to control the execution of a
generator function:</p>
<span class="target" id="index-19"></span><dl class="method">
<dt id="generator.__next__">
<tt class="descclassname">generator.</tt><tt class="descname">__next__</tt><big>(</big><big>)</big><a class="headerlink" href="#generator.__next__" title="Permalink to this definition">¶</a></dt>
<dd><p>Starts the execution of a generator function or resumes it at the last
executed <a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> expression. When a generator function is resumed
with a <a class="reference internal" href="#generator.__next__" title="generator.__next__"><tt class="xref py py-meth docutils literal"><span class="pre">__next__()</span></tt></a> method, the current <a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> expression
always evaluates to <a class="reference internal" href="../library/constants.html#None" title="None"><tt class="xref py py-const xref docutils literal"><span class="pre">None</span></tt></a>. The execution then continues to the next
<a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> expression, where the generator is suspended again, and the
value of the <a class="reference internal" href="#grammar-token-expression_list"><tt class="xref std std-token docutils literal"><span class="pre">expression_list</span></tt></a> is returned to <a class="reference internal" href="../library/functions.html#next" title="next"><tt class="xref py py-meth docutils literal"><span class="pre">next()</span></tt></a>‘s caller.
If the generator exits without yielding another value, a <a class="reference internal" href="../library/exceptions.html#StopIteration" title="StopIteration"><tt class="xref py py-exc docutils literal"><span class="pre">StopIteration</span></tt></a>
exception is raised.</p>
<p>This method is normally called implicitly, e.g. by a <a class="reference internal" href="compound_stmts.html#for"><tt class="xref std std-keyword docutils literal"><span class="pre">for</span></tt></a> loop, or
by the built-in <a class="reference internal" href="../library/functions.html#next" title="next"><tt class="xref py py-func docutils literal"><span class="pre">next()</span></tt></a> function.</p>
</dd></dl>
<dl class="method">
<dt id="generator.send">
<tt class="descclassname">generator.</tt><tt class="descname">send</tt><big>(</big><em>value</em><big>)</big><a class="headerlink" href="#generator.send" title="Permalink to this definition">¶</a></dt>
<dd><p>Resumes the execution and “sends” a value into the generator function. The
<tt class="docutils literal"><span class="pre">value</span></tt> argument becomes the result of the current <a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a>
expression. The <a class="reference internal" href="#generator.send" title="generator.send"><tt class="xref py py-meth docutils literal"><span class="pre">send()</span></tt></a> method returns the next value yielded by the
generator, or raises <a class="reference internal" href="../library/exceptions.html#StopIteration" title="StopIteration"><tt class="xref py py-exc docutils literal"><span class="pre">StopIteration</span></tt></a> if the generator exits without
yielding another value. When <a class="reference internal" href="#generator.send" title="generator.send"><tt class="xref py py-meth docutils literal"><span class="pre">send()</span></tt></a> is called to start the generator,
it must be called with <a class="reference internal" href="../library/constants.html#None" title="None"><tt class="xref py py-const xref docutils literal"><span class="pre">None</span></tt></a> as the argument, because there is no
<a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> expression that could receive the value.</p>
</dd></dl>
<dl class="method">
<dt id="generator.throw">
<tt class="descclassname">generator.</tt><tt class="descname">throw</tt><big>(</big><em>type</em><span class="optional">[</span>, <em>value</em><span class="optional">[</span>, <em>traceback</em><span class="optional">]</span><span class="optional">]</span><big>)</big><a class="headerlink" href="#generator.throw" title="Permalink to this definition">¶</a></dt>
<dd><p>Raises an exception of type <tt class="docutils literal"><span class="pre">type</span></tt> at the point where generator was paused,
and returns the next value yielded by the generator function. If the generator
exits without yielding another value, a <a class="reference internal" href="../library/exceptions.html#StopIteration" title="StopIteration"><tt class="xref py py-exc docutils literal"><span class="pre">StopIteration</span></tt></a> exception is
raised. If the generator function does not catch the passed-in exception, or
raises a different exception, then that exception propagates to the caller.</p>
</dd></dl>
<span class="target" id="index-20"></span><dl class="method">
<dt id="generator.close">
<tt class="descclassname">generator.</tt><tt class="descname">close</tt><big>(</big><big>)</big><a class="headerlink" href="#generator.close" title="Permalink to this definition">¶</a></dt>
<dd><p>Raises a <a class="reference internal" href="../library/exceptions.html#GeneratorExit" title="GeneratorExit"><tt class="xref py py-exc docutils literal"><span class="pre">GeneratorExit</span></tt></a> at the point where the generator function was
paused. If the generator function then raises <a class="reference internal" href="../library/exceptions.html#StopIteration" title="StopIteration"><tt class="xref py py-exc docutils literal"><span class="pre">StopIteration</span></tt></a> (by
exiting normally, or due to already being closed) or <a class="reference internal" href="../library/exceptions.html#GeneratorExit" title="GeneratorExit"><tt class="xref py py-exc docutils literal"><span class="pre">GeneratorExit</span></tt></a> (by
not catching the exception), close returns to its caller. If the generator
yields a value, a <a class="reference internal" href="../library/exceptions.html#RuntimeError" title="RuntimeError"><tt class="xref py py-exc docutils literal"><span class="pre">RuntimeError</span></tt></a> is raised. If the generator raises any
other exception, it is propagated to the caller. <a class="reference internal" href="#generator.close" title="generator.close"><tt class="xref py py-meth docutils literal"><span class="pre">close()</span></tt></a> does nothing
if the generator has already exited due to an exception or normal exit.</p>
</dd></dl>
<p>Here is a simple example that demonstrates the behavior of generators and
generator functions:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">def</span> <span class="nf">echo</span><span class="p">(</span><span class="n">value</span><span class="o">=</span><span class="k">None</span><span class="p">):</span>
<span class="gp">... </span> <span class="nb">print</span><span class="p">(</span><span class="s">"Execution starts when 'next()' is called for the first time."</span><span class="p">)</span>
<span class="gp">... </span> <span class="k">try</span><span class="p">:</span>
<span class="gp">... </span> <span class="k">while</span> <span class="k">True</span><span class="p">:</span>
<span class="gp">... </span> <span class="k">try</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">value</span> <span class="o">=</span> <span class="p">(</span><span class="k">yield</span> <span class="n">value</span><span class="p">)</span>
<span class="gp">... </span> <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">value</span> <span class="o">=</span> <span class="n">e</span>
<span class="gp">... </span> <span class="k">finally</span><span class="p">:</span>
<span class="gp">... </span> <span class="nb">print</span><span class="p">(</span><span class="s">"Don't forget to clean up when 'close()' is called."</span><span class="p">)</span>
<span class="gp">...</span>
<span class="gp">>>> </span><span class="n">generator</span> <span class="o">=</span> <span class="n">echo</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">generator</span><span class="p">))</span>
<span class="go">Execution starts when 'next()' is called for the first time.</span>
<span class="go">1</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="nb">next</span><span class="p">(</span><span class="n">generator</span><span class="p">))</span>
<span class="go">None</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">generator</span><span class="o">.</span><span class="n">send</span><span class="p">(</span><span class="mi">2</span><span class="p">))</span>
<span class="go">2</span>
<span class="gp">>>> </span><span class="n">generator</span><span class="o">.</span><span class="n">throw</span><span class="p">(</span><span class="ne">TypeError</span><span class="p">,</span> <span class="s">"spam"</span><span class="p">)</span>
<span class="go">TypeError('spam',)</span>
<span class="gp">>>> </span><span class="n">generator</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
<span class="go">Don't forget to clean up when 'close()' is called.</span>
</pre></div>
</div>
<div class="admonition-see-also admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><span class="target" id="index-21"></span><a class="pep reference external" href="http://www.python.org/dev/peps/pep-0255"><strong>PEP 0255</strong></a> - Simple Generators</dt>
<dd>The proposal for adding generators and the <a class="reference internal" href="simple_stmts.html#yield"><tt class="xref std std-keyword docutils literal"><span class="pre">yield</span></tt></a> statement to Python.</dd>
<dt><span class="target" id="index-22"></span><a class="pep reference external" href="http://www.python.org/dev/peps/pep-0342"><strong>PEP 0342</strong></a> - Coroutines via Enhanced Generators</dt>
<dd>The proposal to enhance the API and syntax of generators, making them
usable as simple coroutines.</dd>
</dl>
</div>
</div>
</div>
<div class="section" id="primaries">
<span id="id3"></span><h2>5.3. Primaries<a class="headerlink" href="#primaries" title="Permalink to this headline">¶</a></h2>
<p id="index-23">Primaries represent the most tightly bound operations of the language. Their
syntax is:</p>
<pre>
<strong id="grammar-token-primary">primary</strong> ::= <a class="reference internal" href="#grammar-token-atom"><tt class="xref docutils literal"><span class="pre">atom</span></tt></a> | <a class="reference internal" href="#grammar-token-attributeref"><tt class="xref docutils literal"><span class="pre">attributeref</span></tt></a> | <a class="reference internal" href="#grammar-token-subscription"><tt class="xref docutils literal"><span class="pre">subscription</span></tt></a> | <a class="reference internal" href="#grammar-token-slicing"><tt class="xref docutils literal"><span class="pre">slicing</span></tt></a> | <a class="reference internal" href="#grammar-token-call"><tt class="xref docutils literal"><span class="pre">call</span></tt></a>
</pre>
<div class="section" id="attribute-references">
<span id="id4"></span><h3>5.3.1. Attribute references<a class="headerlink" href="#attribute-references" title="Permalink to this headline">¶</a></h3>
<p id="index-24">An attribute reference is a primary followed by a period and a name:</p>
<pre>
<strong id="grammar-token-attributeref">attributeref</strong> ::= <a class="reference internal" href="#grammar-token-primary"><tt class="xref docutils literal"><span class="pre">primary</span></tt></a> "." <a class="reference internal" href="lexical_analysis.html#grammar-token-identifier"><tt class="xref docutils literal"><span class="pre">identifier</span></tt></a>
</pre>
<p id="index-25">The primary must evaluate to an object of a type that supports attribute
references, which most objects do. This object is then asked to produce the
attribute whose name is the identifier (which can be customized by overriding
the <a class="reference internal" href="datamodel.html#object.__getattr__" title="object.__getattr__"><tt class="xref py py-meth docutils literal"><span class="pre">__getattr__()</span></tt></a> method). If this attribute is not available, the
exception <a class="reference internal" href="../library/exceptions.html#AttributeError" title="AttributeError"><tt class="xref py py-exc docutils literal"><span class="pre">AttributeError</span></tt></a> is raised. Otherwise, the type and value of the
object produced is determined by the object. Multiple evaluations of the same
attribute reference may yield different objects.</p>
</div>
<div class="section" id="subscriptions">
<span id="id5"></span><h3>5.3.2. Subscriptions<a class="headerlink" href="#subscriptions" title="Permalink to this headline">¶</a></h3>
<span class="target" id="index-26"></span><p id="index-27">A subscription selects an item of a sequence (string, tuple or list) or mapping
(dictionary) object:</p>
<pre>
<strong id="grammar-token-subscription">subscription</strong> ::= <a class="reference internal" href="#grammar-token-primary"><tt class="xref docutils literal"><span class="pre">primary</span></tt></a> "[" <a class="reference internal" href="#grammar-token-expression_list"><tt class="xref docutils literal"><span class="pre">expression_list</span></tt></a> "]"
</pre>
<p>The primary must evaluate to an object that supports subscription, e.g. a list
or dictionary. User-defined objects can support subscription by defining a
<a class="reference internal" href="datamodel.html#object.__getitem__" title="object.__getitem__"><tt class="xref py py-meth docutils literal"><span class="pre">__getitem__()</span></tt></a> method.</p>
<p>For built-in objects, there are two types of objects that support subscription:</p>
<p>If the primary is a mapping, the expression list must evaluate to an object
whose value is one of the keys of the mapping, and the subscription selects the
value in the mapping that corresponds to that key. (The expression list is a
tuple except if it has exactly one item.)</p>
<p>If the primary is a sequence, the expression (list) must evaluate to an integer
or a slice (as discussed in the following section).</p>
<p>The formal syntax makes no special provision for negative indices in
sequences; however, built-in sequences all provide a <a class="reference internal" href="datamodel.html#object.__getitem__" title="object.__getitem__"><tt class="xref py py-meth docutils literal"><span class="pre">__getitem__()</span></tt></a>
method that interprets negative indices by adding the length of the sequence
to the index (so that <tt class="docutils literal"><span class="pre">x[-1]</span></tt> selects the last item of <tt class="docutils literal"><span class="pre">x</span></tt>). The
resulting value must be a nonnegative integer less than the number of items in
the sequence, and the subscription selects the item whose index is that value
(counting from zero). Since the support for negative indices and slicing
occurs in the object’s <a class="reference internal" href="datamodel.html#object.__getitem__" title="object.__getitem__"><tt class="xref py py-meth docutils literal"><span class="pre">__getitem__()</span></tt></a> method, subclasses overriding
this method will need to explicitly add that support.</p>
<p id="index-28">A string’s items are characters. A character is not a separate data type but a
string of exactly one character.</p>
</div>
<div class="section" id="slicings">
<span id="id6"></span><h3>5.3.3. Slicings<a class="headerlink" href="#slicings" title="Permalink to this headline">¶</a></h3>
<span class="target" id="index-29"></span><p id="index-30">A slicing selects a range of items in a sequence object (e.g., a string, tuple
or list). Slicings may be used as expressions or as targets in assignment or
<a class="reference internal" href="simple_stmts.html#del"><tt class="xref std std-keyword docutils literal"><span class="pre">del</span></tt></a> statements. The syntax for a slicing:</p>
<pre>
<strong id="grammar-token-slicing">slicing </strong> ::= <a class="reference internal" href="#grammar-token-primary"><tt class="xref docutils literal"><span class="pre">primary</span></tt></a> "[" <a class="reference internal" href="#grammar-token-slice_list"><tt class="xref docutils literal"><span class="pre">slice_list</span></tt></a> "]"
<strong id="grammar-token-slice_list">slice_list </strong> ::= <a class="reference internal" href="#grammar-token-slice_item"><tt class="xref docutils literal"><span class="pre">slice_item</span></tt></a> ("," <a class="reference internal" href="#grammar-token-slice_item"><tt class="xref docutils literal"><span class="pre">slice_item</span></tt></a>)* [","]
<strong id="grammar-token-slice_item">slice_item </strong> ::= <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> | <a class="reference internal" href="#grammar-token-proper_slice"><tt class="xref docutils literal"><span class="pre">proper_slice</span></tt></a>
<strong id="grammar-token-proper_slice">proper_slice</strong> ::= [<a class="reference internal" href="#grammar-token-lower_bound"><tt class="xref docutils literal"><span class="pre">lower_bound</span></tt></a>] ":" [<a class="reference internal" href="#grammar-token-upper_bound"><tt class="xref docutils literal"><span class="pre">upper_bound</span></tt></a>] [ ":" [<a class="reference internal" href="#grammar-token-stride"><tt class="xref docutils literal"><span class="pre">stride</span></tt></a>] ]
<strong id="grammar-token-lower_bound">lower_bound </strong> ::= <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>
<strong id="grammar-token-upper_bound">upper_bound </strong> ::= <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>
<strong id="grammar-token-stride">stride </strong> ::= <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>
</pre>
<p>There is ambiguity in the formal syntax here: anything that looks like an
expression list also looks like a slice list, so any subscription can be
interpreted as a slicing. Rather than further complicating the syntax, this is
disambiguated by defining that in this case the interpretation as a subscription
takes priority over the interpretation as a slicing (this is the case if the
slice list contains no proper slice).</p>
<p id="index-31">The semantics for a slicing are as follows. The primary must evaluate to a
mapping object, and it is indexed (using the same <a class="reference internal" href="datamodel.html#object.__getitem__" title="object.__getitem__"><tt class="xref py py-meth docutils literal"><span class="pre">__getitem__()</span></tt></a> method as
normal subscription) with a key that is constructed from the slice list, as
follows. If the slice list contains at least one comma, the key is a tuple
containing the conversion of the slice items; otherwise, the conversion of the
lone slice item is the key. The conversion of a slice item that is an
expression is that expression. The conversion of a proper slice is a slice
object (see section <a class="reference internal" href="datamodel.html#types"><em>The standard type hierarchy</em></a>) whose <tt class="xref py py-attr docutils literal"><span class="pre">start</span></tt>, <tt class="xref py py-attr docutils literal"><span class="pre">stop</span></tt> and
<tt class="xref py py-attr docutils literal"><span class="pre">step</span></tt> attributes are the values of the expressions given as lower bound,
upper bound and stride, respectively, substituting <tt class="xref docutils literal"><span class="pre">None</span></tt> for missing
expressions.</p>
</div>
<div class="section" id="calls">
<span id="id7"></span><h3>5.3.4. Calls<a class="headerlink" href="#calls" title="Permalink to this headline">¶</a></h3>
<span class="target" id="index-32"></span><p id="index-33">A call calls a callable object (e.g., a function) with a possibly empty series
of arguments:</p>
<pre>
<strong id="grammar-token-call">call </strong> ::= <a class="reference internal" href="#grammar-token-primary"><tt class="xref docutils literal"><span class="pre">primary</span></tt></a> "(" [<a class="reference internal" href="#grammar-token-argument_list"><tt class="xref docutils literal"><span class="pre">argument_list</span></tt></a> [","] | <a class="reference internal" href="#grammar-token-comprehension"><tt class="xref docutils literal"><span class="pre">comprehension</span></tt></a>] ")"
<strong id="grammar-token-argument_list">argument_list </strong> ::= <a class="reference internal" href="#grammar-token-positional_arguments"><tt class="xref docutils literal"><span class="pre">positional_arguments</span></tt></a> ["," <a class="reference internal" href="#grammar-token-keyword_arguments"><tt class="xref docutils literal"><span class="pre">keyword_arguments</span></tt></a>]
["," "*" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>] ["," <a class="reference internal" href="#grammar-token-keyword_arguments"><tt class="xref docutils literal"><span class="pre">keyword_arguments</span></tt></a>]
["," "**" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>]
| <a class="reference internal" href="#grammar-token-keyword_arguments"><tt class="xref docutils literal"><span class="pre">keyword_arguments</span></tt></a> ["," "*" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>]
["," <a class="reference internal" href="#grammar-token-keyword_arguments"><tt class="xref docutils literal"><span class="pre">keyword_arguments</span></tt></a>] ["," "**" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>]
| "*" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> ["," <a class="reference internal" href="#grammar-token-keyword_arguments"><tt class="xref docutils literal"><span class="pre">keyword_arguments</span></tt></a>] ["," "**" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>]
| "**" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>
<strong id="grammar-token-positional_arguments">positional_arguments</strong> ::= <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> ("," <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>)*
<strong id="grammar-token-keyword_arguments">keyword_arguments </strong> ::= <a class="reference internal" href="#grammar-token-keyword_item"><tt class="xref docutils literal"><span class="pre">keyword_item</span></tt></a> ("," <a class="reference internal" href="#grammar-token-keyword_item"><tt class="xref docutils literal"><span class="pre">keyword_item</span></tt></a>)*
<strong id="grammar-token-keyword_item">keyword_item </strong> ::= <a class="reference internal" href="lexical_analysis.html#grammar-token-identifier"><tt class="xref docutils literal"><span class="pre">identifier</span></tt></a> "=" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>
</pre>
<p>A trailing comma may be present after the positional and keyword arguments but
does not affect the semantics.</p>
<p>The primary must evaluate to a callable object (user-defined functions, built-in
functions, methods of built-in objects, class objects, methods of class
instances, and all objects having a <a class="reference internal" href="datamodel.html#object.__call__" title="object.__call__"><tt class="xref py py-meth docutils literal"><span class="pre">__call__()</span></tt></a> method are callable). All
argument expressions are evaluated before the call is attempted. Please refer
to section <a class="reference internal" href="compound_stmts.html#function"><em>Function definitions</em></a> for the syntax of formal parameter lists.</p>
<p>If keyword arguments are present, they are first converted to positional
arguments, as follows. First, a list of unfilled slots is created for the
formal parameters. If there are N positional arguments, they are placed in the
first N slots. Next, for each keyword argument, the identifier is used to
determine the corresponding slot (if the identifier is the same as the first
formal parameter name, the first slot is used, and so on). If the slot is
already filled, a <a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> exception is raised. Otherwise, the value of
the argument is placed in the slot, filling it (even if the expression is
<tt class="xref docutils literal"><span class="pre">None</span></tt>, it fills the slot). When all arguments have been processed, the slots
that are still unfilled are filled with the corresponding default value from the
function definition. (Default values are calculated, once, when the function is
defined; thus, a mutable object such as a list or dictionary used as default
value will be shared by all calls that don’t specify an argument value for the
corresponding slot; this should usually be avoided.) If there are any unfilled
slots for which no default value is specified, a <a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> exception is
raised. Otherwise, the list of filled slots is used as the argument list for
the call.</p>
<div class="impl-detail compound">
<p><strong>CPython implementation detail:</strong> An implementation may provide built-in functions whose positional parameters
do not have names, even if they are ‘named’ for the purpose of documentation,
and which therefore cannot be supplied by keyword. In CPython, this is the
case for functions implemented in C that use <a class="reference internal" href="../c-api/arg.html#PyArg_ParseTuple" title="PyArg_ParseTuple"><tt class="xref c c-func docutils literal"><span class="pre">PyArg_ParseTuple()</span></tt></a> to
parse their arguments.</p>
</div>
<p>If there are more positional arguments than there are formal parameter slots, a
<a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> exception is raised, unless a formal parameter using the syntax
<tt class="docutils literal"><span class="pre">*identifier</span></tt> is present; in this case, that formal parameter receives a tuple
containing the excess positional arguments (or an empty tuple if there were no
excess positional arguments).</p>
<p>If any keyword argument does not correspond to a formal parameter name, a
<a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> exception is raised, unless a formal parameter using the syntax
<tt class="docutils literal"><span class="pre">**identifier</span></tt> is present; in this case, that formal parameter receives a
dictionary containing the excess keyword arguments (using the keywords as keys
and the argument values as corresponding values), or a (new) empty dictionary if
there were no excess keyword arguments.</p>
<p id="index-34">If the syntax <tt class="docutils literal"><span class="pre">*expression</span></tt> appears in the function call, <tt class="docutils literal"><span class="pre">expression</span></tt> must
evaluate to an iterable. Elements from this iterable are treated as if they
were additional positional arguments; if there are positional arguments
<em>x1</em>, ..., <em>xN</em>, and <tt class="docutils literal"><span class="pre">expression</span></tt> evaluates to a sequence <em>y1</em>, ..., <em>yM</em>,
this is equivalent to a call with M+N positional arguments <em>x1</em>, ..., <em>xN</em>,
<em>y1</em>, ..., <em>yM</em>.</p>
<p>A consequence of this is that although the <tt class="docutils literal"><span class="pre">*expression</span></tt> syntax may appear
<em>after</em> some keyword arguments, it is processed <em>before</em> the keyword arguments
(and the <tt class="docutils literal"><span class="pre">**expression</span></tt> argument, if any – see below). So:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="gp">>>> </span><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
<span class="gp">... </span> <span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="gp">...</span>
<span class="gp">>>> </span><span class="n">f</span><span class="p">(</span><span class="n">b</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="o">*</span><span class="p">(</span><span class="mi">2</span><span class="p">,))</span>
<span class="go">2 1</span>
<span class="gp">>>> </span><span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="o">*</span><span class="p">(</span><span class="mi">2</span><span class="p">,))</span>
<span class="gt">Traceback (most recent call last):</span>
File <span class="nb">"<stdin>"</span>, line <span class="m">1</span>, in <span class="n-Identifier">?</span>
<span class="nc">TypeError</span>: <span class="n-Identifier">f() got multiple values for keyword argument 'a'</span>
<span class="gp">>>> </span><span class="n">f</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">*</span><span class="p">(</span><span class="mi">2</span><span class="p">,))</span>
<span class="go">1 2</span>
</pre></div>
</div>
<p>It is unusual for both keyword arguments and the <tt class="docutils literal"><span class="pre">*expression</span></tt> syntax to be
used in the same call, so in practice this confusion does not arise.</p>
<p id="index-35">If the syntax <tt class="docutils literal"><span class="pre">**expression</span></tt> appears in the function call, <tt class="docutils literal"><span class="pre">expression</span></tt> must
evaluate to a mapping, the contents of which are treated as additional keyword
arguments. In the case of a keyword appearing in both <tt class="docutils literal"><span class="pre">expression</span></tt> and as an
explicit keyword argument, a <a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> exception is raised.</p>
<p>Formal parameters using the syntax <tt class="docutils literal"><span class="pre">*identifier</span></tt> or <tt class="docutils literal"><span class="pre">**identifier</span></tt> cannot be
used as positional argument slots or as keyword argument names.</p>
<p>A call always returns some value, possibly <tt class="xref docutils literal"><span class="pre">None</span></tt>, unless it raises an
exception. How this value is computed depends on the type of the callable
object.</p>
<p>If it is—</p>
<dl class="docutils">
<dt>a user-defined function:</dt>
<dd><p class="first last" id="index-36">The code block for the function is executed, passing it the argument list. The
first thing the code block will do is bind the formal parameters to the
arguments; this is described in section <a class="reference internal" href="compound_stmts.html#function"><em>Function definitions</em></a>. When the code block
executes a <a class="reference internal" href="simple_stmts.html#return"><tt class="xref std std-keyword docutils literal"><span class="pre">return</span></tt></a> statement, this specifies the return value of the
function call.</p>
</dd>
<dt>a built-in function or method:</dt>
<dd><p class="first last" id="index-37">The result is up to the interpreter; see <a class="reference internal" href="../library/functions.html#built-in-funcs"><em>Built-in Functions</em></a> for the
descriptions of built-in functions and methods.</p>
</dd>
<dt>a class object:</dt>
<dd><p class="first last" id="index-38">A new instance of that class is returned.</p>
</dd>
<dt>a class instance method:</dt>
<dd><p class="first last" id="index-39">The corresponding user-defined function is called, with an argument list that is
one longer than the argument list of the call: the instance becomes the first
argument.</p>
</dd>
<dt>a class instance:</dt>
<dd><p class="first last" id="index-40">The class must define a <a class="reference internal" href="datamodel.html#object.__call__" title="object.__call__"><tt class="xref py py-meth docutils literal"><span class="pre">__call__()</span></tt></a> method; the effect is then the same as
if that method was called.</p>
</dd>
</dl>
</div>
</div>
<div class="section" id="the-power-operator">
<span id="power"></span><h2>5.4. The power operator<a class="headerlink" href="#the-power-operator" title="Permalink to this headline">¶</a></h2>
<p>The power operator binds more tightly than unary operators on its left; it binds
less tightly than unary operators on its right. The syntax is:</p>
<pre>
<strong id="grammar-token-power">power</strong> ::= <a class="reference internal" href="#grammar-token-primary"><tt class="xref docutils literal"><span class="pre">primary</span></tt></a> ["**" <a class="reference internal" href="#grammar-token-u_expr"><tt class="xref docutils literal"><span class="pre">u_expr</span></tt></a>]
</pre>
<p>Thus, in an unparenthesized sequence of power and unary operators, the operators
are evaluated from right to left (this does not constrain the evaluation order
for the operands): <tt class="docutils literal"><span class="pre">-1**2</span></tt> results in <tt class="docutils literal"><span class="pre">-1</span></tt>.</p>
<p>The power operator has the same semantics as the built-in <a class="reference internal" href="../library/functions.html#pow" title="pow"><tt class="xref py py-func docutils literal"><span class="pre">pow()</span></tt></a> function,
when called with two arguments: it yields its left argument raised to the power
of its right argument. The numeric arguments are first converted to a common
type, and the result is of that type.</p>
<p>For int operands, the result has the same type as the operands unless the second
argument is negative; in that case, all arguments are converted to float and a
float result is delivered. For example, <tt class="docutils literal"><span class="pre">10**2</span></tt> returns <tt class="docutils literal"><span class="pre">100</span></tt>, but
<tt class="docutils literal"><span class="pre">10**-2</span></tt> returns <tt class="docutils literal"><span class="pre">0.01</span></tt>.</p>
<p>Raising <tt class="docutils literal"><span class="pre">0.0</span></tt> to a negative power results in a <a class="reference internal" href="../library/exceptions.html#ZeroDivisionError" title="ZeroDivisionError"><tt class="xref py py-exc docutils literal"><span class="pre">ZeroDivisionError</span></tt></a>.
Raising a negative number to a fractional power results in a <a class="reference internal" href="../library/functions.html#complex" title="complex"><tt class="xref py py-class docutils literal"><span class="pre">complex</span></tt></a>
number. (In earlier versions it raised a <a class="reference internal" href="../library/exceptions.html#ValueError" title="ValueError"><tt class="xref py py-exc docutils literal"><span class="pre">ValueError</span></tt></a>.)</p>
</div>
<div class="section" id="unary-arithmetic-and-bitwise-operations">
<span id="unary"></span><h2>5.5. Unary arithmetic and bitwise operations<a class="headerlink" href="#unary-arithmetic-and-bitwise-operations" title="Permalink to this headline">¶</a></h2>
<p id="index-41">All unary arithmetic and bitwise operations have the same priority:</p>
<pre>
<strong id="grammar-token-u_expr">u_expr</strong> ::= <a class="reference internal" href="#grammar-token-power"><tt class="xref docutils literal"><span class="pre">power</span></tt></a> | "-" <a class="reference internal" href="#grammar-token-u_expr"><tt class="xref docutils literal"><span class="pre">u_expr</span></tt></a> | "+" <a class="reference internal" href="#grammar-token-u_expr"><tt class="xref docutils literal"><span class="pre">u_expr</span></tt></a> | "~" <a class="reference internal" href="#grammar-token-u_expr"><tt class="xref docutils literal"><span class="pre">u_expr</span></tt></a>
</pre>
<p id="index-42">The unary <tt class="docutils literal"><span class="pre">-</span></tt> (minus) operator yields the negation of its numeric argument.</p>
<p id="index-43">The unary <tt class="docutils literal"><span class="pre">+</span></tt> (plus) operator yields its numeric argument unchanged.</p>
<p id="index-44">The unary <tt class="docutils literal"><span class="pre">~</span></tt> (invert) operator yields the bitwise inversion of its integer
argument. The bitwise inversion of <tt class="docutils literal"><span class="pre">x</span></tt> is defined as <tt class="docutils literal"><span class="pre">-(x+1)</span></tt>. It only
applies to integral numbers.</p>
<p id="index-45">In all three cases, if the argument does not have the proper type, a
<a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> exception is raised.</p>
</div>
<div class="section" id="binary-arithmetic-operations">
<span id="binary"></span><h2>5.6. Binary arithmetic operations<a class="headerlink" href="#binary-arithmetic-operations" title="Permalink to this headline">¶</a></h2>
<p id="index-46">The binary arithmetic operations have the conventional priority levels. Note
that some of these operations also apply to certain non-numeric types. Apart
from the power operator, there are only two levels, one for multiplicative
operators and one for additive operators:</p>
<pre>
<strong id="grammar-token-m_expr">m_expr</strong> ::= <a class="reference internal" href="#grammar-token-u_expr"><tt class="xref docutils literal"><span class="pre">u_expr</span></tt></a> | <a class="reference internal" href="#grammar-token-m_expr"><tt class="xref docutils literal"><span class="pre">m_expr</span></tt></a> "*" <a class="reference internal" href="#grammar-token-u_expr"><tt class="xref docutils literal"><span class="pre">u_expr</span></tt></a> | <a class="reference internal" href="#grammar-token-m_expr"><tt class="xref docutils literal"><span class="pre">m_expr</span></tt></a> "//" <a class="reference internal" href="#grammar-token-u_expr"><tt class="xref docutils literal"><span class="pre">u_expr</span></tt></a> | <a class="reference internal" href="#grammar-token-m_expr"><tt class="xref docutils literal"><span class="pre">m_expr</span></tt></a> "/" <a class="reference internal" href="#grammar-token-u_expr"><tt class="xref docutils literal"><span class="pre">u_expr</span></tt></a>
| <a class="reference internal" href="#grammar-token-m_expr"><tt class="xref docutils literal"><span class="pre">m_expr</span></tt></a> "%" <a class="reference internal" href="#grammar-token-u_expr"><tt class="xref docutils literal"><span class="pre">u_expr</span></tt></a>
<strong id="grammar-token-a_expr">a_expr</strong> ::= <a class="reference internal" href="#grammar-token-m_expr"><tt class="xref docutils literal"><span class="pre">m_expr</span></tt></a> | <a class="reference internal" href="#grammar-token-a_expr"><tt class="xref docutils literal"><span class="pre">a_expr</span></tt></a> "+" <a class="reference internal" href="#grammar-token-m_expr"><tt class="xref docutils literal"><span class="pre">m_expr</span></tt></a> | <a class="reference internal" href="#grammar-token-a_expr"><tt class="xref docutils literal"><span class="pre">a_expr</span></tt></a> "-" <a class="reference internal" href="#grammar-token-m_expr"><tt class="xref docutils literal"><span class="pre">m_expr</span></tt></a>
</pre>
<p id="index-47">The <tt class="docutils literal"><span class="pre">*</span></tt> (multiplication) operator yields the product of its arguments. The
arguments must either both be numbers, or one argument must be an integer and
the other must be a sequence. In the former case, the numbers are converted to a
common type and then multiplied together. In the latter case, sequence
repetition is performed; a negative repetition factor yields an empty sequence.</p>
<p id="index-48">The <tt class="docutils literal"><span class="pre">/</span></tt> (division) and <tt class="docutils literal"><span class="pre">//</span></tt> (floor division) operators yield the quotient of
their arguments. The numeric arguments are first converted to a common type.
Integer division yields a float, while floor division of integers results in an
integer; the result is that of mathematical division with the ‘floor’ function
applied to the result. Division by zero raises the <a class="reference internal" href="../library/exceptions.html#ZeroDivisionError" title="ZeroDivisionError"><tt class="xref py py-exc docutils literal"><span class="pre">ZeroDivisionError</span></tt></a>
exception.</p>
<p id="index-49">The <tt class="docutils literal"><span class="pre">%</span></tt> (modulo) operator yields the remainder from the division of the first
argument by the second. The numeric arguments are first converted to a common
type. A zero right argument raises the <a class="reference internal" href="../library/exceptions.html#ZeroDivisionError" title="ZeroDivisionError"><tt class="xref py py-exc docutils literal"><span class="pre">ZeroDivisionError</span></tt></a> exception. The
arguments may be floating point numbers, e.g., <tt class="docutils literal"><span class="pre">3.14%0.7</span></tt> equals <tt class="docutils literal"><span class="pre">0.34</span></tt>
(since <tt class="docutils literal"><span class="pre">3.14</span></tt> equals <tt class="docutils literal"><span class="pre">4*0.7</span> <span class="pre">+</span> <span class="pre">0.34</span></tt>.) The modulo operator always yields a
result with the same sign as its second operand (or zero); the absolute value of
the result is strictly smaller than the absolute value of the second operand
<a class="footnote-reference" href="#id16" id="id8">[1]</a>.</p>
<p>The floor division and modulo operators are connected by the following
identity: <tt class="docutils literal"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">(x//y)*y</span> <span class="pre">+</span> <span class="pre">(x%y)</span></tt>. Floor division and modulo are also
connected with the built-in function <a class="reference internal" href="../library/functions.html#divmod" title="divmod"><tt class="xref py py-func docutils literal"><span class="pre">divmod()</span></tt></a>: <tt class="docutils literal"><span class="pre">divmod(x,</span> <span class="pre">y)</span> <span class="pre">==</span> <span class="pre">(x//y,</span>
<span class="pre">x%y)</span></tt>. <a class="footnote-reference" href="#id17" id="id9">[2]</a>.</p>
<p>In addition to performing the modulo operation on numbers, the <tt class="docutils literal"><span class="pre">%</span></tt> operator is
also overloaded by string objects to perform old-style string formatting (also
known as interpolation). The syntax for string formatting is described in the
Python Library Reference, section <a class="reference internal" href="../library/stdtypes.html#old-string-formatting"><em>Old String Formatting Operations</em></a>.</p>
<p>The floor division operator, the modulo operator, and the <a class="reference internal" href="../library/functions.html#divmod" title="divmod"><tt class="xref py py-func docutils literal"><span class="pre">divmod()</span></tt></a>
function are not defined for complex numbers. Instead, convert to a floating
point number using the <a class="reference internal" href="../library/functions.html#abs" title="abs"><tt class="xref py py-func docutils literal"><span class="pre">abs()</span></tt></a> function if appropriate.</p>
<p id="index-50">The <tt class="docutils literal"><span class="pre">+</span></tt> (addition) operator yields the sum of its arguments. The arguments
must either both be numbers or both sequences of the same type. In the former
case, the numbers are converted to a common type and then added together. In
the latter case, the sequences are concatenated.</p>
<p id="index-51">The <tt class="docutils literal"><span class="pre">-</span></tt> (subtraction) operator yields the difference of its arguments. The
numeric arguments are first converted to a common type.</p>
</div>
<div class="section" id="shifting-operations">
<span id="shifting"></span><h2>5.7. Shifting operations<a class="headerlink" href="#shifting-operations" title="Permalink to this headline">¶</a></h2>
<p id="index-52">The shifting operations have lower priority than the arithmetic operations:</p>
<pre>
<strong id="grammar-token-shift_expr">shift_expr</strong> ::= <a class="reference internal" href="#grammar-token-a_expr"><tt class="xref docutils literal"><span class="pre">a_expr</span></tt></a> | <a class="reference internal" href="#grammar-token-shift_expr"><tt class="xref docutils literal"><span class="pre">shift_expr</span></tt></a> ( "<<" | ">>" ) <a class="reference internal" href="#grammar-token-a_expr"><tt class="xref docutils literal"><span class="pre">a_expr</span></tt></a>
</pre>
<p>These operators accept integers as arguments. They shift the first argument to
the left or right by the number of bits given by the second argument.</p>
<p id="index-53">A right shift by <em>n</em> bits is defined as division by <tt class="docutils literal"><span class="pre">pow(2,n)</span></tt>. A left shift
by <em>n</em> bits is defined as multiplication with <tt class="docutils literal"><span class="pre">pow(2,n)</span></tt>.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">In the current implementation, the right-hand operand is required
to be at most <a class="reference internal" href="../library/sys.html#sys.maxsize" title="sys.maxsize"><tt class="xref py py-attr docutils literal"><span class="pre">sys.maxsize</span></tt></a>. If the right-hand operand is larger than
<a class="reference internal" href="../library/sys.html#sys.maxsize" title="sys.maxsize"><tt class="xref py py-attr docutils literal"><span class="pre">sys.maxsize</span></tt></a> an <a class="reference internal" href="../library/exceptions.html#OverflowError" title="OverflowError"><tt class="xref py py-exc docutils literal"><span class="pre">OverflowError</span></tt></a> exception is raised.</p>
</div>
</div>
<div class="section" id="binary-bitwise-operations">
<span id="bitwise"></span><h2>5.8. Binary bitwise operations<a class="headerlink" href="#binary-bitwise-operations" title="Permalink to this headline">¶</a></h2>
<p id="index-54">Each of the three bitwise operations has a different priority level:</p>
<pre>
<strong id="grammar-token-and_expr">and_expr</strong> ::= <a class="reference internal" href="#grammar-token-shift_expr"><tt class="xref docutils literal"><span class="pre">shift_expr</span></tt></a> | <a class="reference internal" href="#grammar-token-and_expr"><tt class="xref docutils literal"><span class="pre">and_expr</span></tt></a> "&" <a class="reference internal" href="#grammar-token-shift_expr"><tt class="xref docutils literal"><span class="pre">shift_expr</span></tt></a>
<strong id="grammar-token-xor_expr">xor_expr</strong> ::= <a class="reference internal" href="#grammar-token-and_expr"><tt class="xref docutils literal"><span class="pre">and_expr</span></tt></a> | <a class="reference internal" href="#grammar-token-xor_expr"><tt class="xref docutils literal"><span class="pre">xor_expr</span></tt></a> "^" <a class="reference internal" href="#grammar-token-and_expr"><tt class="xref docutils literal"><span class="pre">and_expr</span></tt></a>
<strong id="grammar-token-or_expr">or_expr </strong> ::= <a class="reference internal" href="#grammar-token-xor_expr"><tt class="xref docutils literal"><span class="pre">xor_expr</span></tt></a> | <a class="reference internal" href="#grammar-token-or_expr"><tt class="xref docutils literal"><span class="pre">or_expr</span></tt></a> "|" <a class="reference internal" href="#grammar-token-xor_expr"><tt class="xref docutils literal"><span class="pre">xor_expr</span></tt></a>
</pre>
<p id="index-55">The <tt class="docutils literal"><span class="pre">&</span></tt> operator yields the bitwise AND of its arguments, which must be
integers.</p>
<p id="index-56">The <tt class="docutils literal"><span class="pre">^</span></tt> operator yields the bitwise XOR (exclusive OR) of its arguments, which
must be integers.</p>
<p id="index-57">The <tt class="docutils literal"><span class="pre">|</span></tt> operator yields the bitwise (inclusive) OR of its arguments, which
must be integers.</p>
</div>
<div class="section" id="not-in">
<span id="in"></span><span id="is-not"></span><span id="is"></span><span id="comparisons"></span><span id="id10"></span><h2>5.9. Comparisons<a class="headerlink" href="#not-in" title="Permalink to this headline">¶</a></h2>
<span class="target" id="index-58"></span><p id="index-59">Unlike C, all comparison operations in Python have the same priority, which is
lower than that of any arithmetic, shifting or bitwise operation. Also unlike
C, expressions like <tt class="docutils literal"><span class="pre">a</span> <span class="pre"><</span> <span class="pre">b</span> <span class="pre"><</span> <span class="pre">c</span></tt> have the interpretation that is conventional
in mathematics:</p>
<pre>
<strong id="grammar-token-comparison">comparison </strong> ::= <a class="reference internal" href="#grammar-token-or_expr"><tt class="xref docutils literal"><span class="pre">or_expr</span></tt></a> ( <a class="reference internal" href="#grammar-token-comp_operator"><tt class="xref docutils literal"><span class="pre">comp_operator</span></tt></a> <a class="reference internal" href="#grammar-token-or_expr"><tt class="xref docutils literal"><span class="pre">or_expr</span></tt></a> )*
<strong id="grammar-token-comp_operator">comp_operator</strong> ::= "<" | ">" | "==" | ">=" | "<=" | "!="
| "is" ["not"] | ["not"] "in"
</pre>
<p>Comparisons yield boolean values: <tt class="xref docutils literal"><span class="pre">True</span></tt> or <tt class="xref docutils literal"><span class="pre">False</span></tt>.</p>
<p id="index-60">Comparisons can be chained arbitrarily, e.g., <tt class="docutils literal"><span class="pre">x</span> <span class="pre"><</span> <span class="pre">y</span> <span class="pre"><=</span> <span class="pre">z</span></tt> is equivalent to
<tt class="docutils literal"><span class="pre">x</span> <span class="pre"><</span> <span class="pre">y</span> <span class="pre">and</span> <span class="pre">y</span> <span class="pre"><=</span> <span class="pre">z</span></tt>, except that <tt class="docutils literal"><span class="pre">y</span></tt> is evaluated only once (but in both
cases <tt class="docutils literal"><span class="pre">z</span></tt> is not evaluated at all when <tt class="docutils literal"><span class="pre">x</span> <span class="pre"><</span> <span class="pre">y</span></tt> is found to be false).</p>
<p>Formally, if <em>a</em>, <em>b</em>, <em>c</em>, ..., <em>y</em>, <em>z</em> are expressions and <em>op1</em>, <em>op2</em>, ...,
<em>opN</em> are comparison operators, then <tt class="docutils literal"><span class="pre">a</span> <span class="pre">op1</span> <span class="pre">b</span> <span class="pre">op2</span> <span class="pre">c</span> <span class="pre">...</span> <span class="pre">y</span> <span class="pre">opN</span> <span class="pre">z</span></tt> is equivalent
to <tt class="docutils literal"><span class="pre">a</span> <span class="pre">op1</span> <span class="pre">b</span> <span class="pre">and</span> <span class="pre">b</span> <span class="pre">op2</span> <span class="pre">c</span> <span class="pre">and</span> <span class="pre">...</span> <span class="pre">y</span> <span class="pre">opN</span> <span class="pre">z</span></tt>, except that each expression is
evaluated at most once.</p>
<p>Note that <tt class="docutils literal"><span class="pre">a</span> <span class="pre">op1</span> <span class="pre">b</span> <span class="pre">op2</span> <span class="pre">c</span></tt> doesn’t imply any kind of comparison between <em>a</em> and
<em>c</em>, so that, e.g., <tt class="docutils literal"><span class="pre">x</span> <span class="pre"><</span> <span class="pre">y</span> <span class="pre">></span> <span class="pre">z</span></tt> is perfectly legal (though perhaps not
pretty).</p>
<p>The operators <tt class="docutils literal"><span class="pre"><</span></tt>, <tt class="docutils literal"><span class="pre">></span></tt>, <tt class="docutils literal"><span class="pre">==</span></tt>, <tt class="docutils literal"><span class="pre">>=</span></tt>, <tt class="docutils literal"><span class="pre"><=</span></tt>, and <tt class="docutils literal"><span class="pre">!=</span></tt> compare the
values of two objects. The objects need not have the same type. If both are
numbers, they are converted to a common type. Otherwise, the <tt class="docutils literal"><span class="pre">==</span></tt> and <tt class="docutils literal"><span class="pre">!=</span></tt>
operators <em>always</em> consider objects of different types to be unequal, while the
<tt class="docutils literal"><span class="pre"><</span></tt>, <tt class="docutils literal"><span class="pre">></span></tt>, <tt class="docutils literal"><span class="pre">>=</span></tt> and <tt class="docutils literal"><span class="pre"><=</span></tt> operators raise a <a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a> when
comparing objects of different types that do not implement these operators for
the given pair of types. You can control comparison behavior of objects of
non-built-in types by defining rich comparison methods like <a class="reference internal" href="datamodel.html#object.__gt__" title="object.__gt__"><tt class="xref py py-meth docutils literal"><span class="pre">__gt__()</span></tt></a>,
described in section <a class="reference internal" href="datamodel.html#customization"><em>Basic customization</em></a>.</p>
<p>Comparison of objects of the same type depends on the type:</p>
<ul>
<li><p class="first">Numbers are compared arithmetically.</p>
</li>
<li><p class="first">The values <tt class="xref py py-const docutils literal"><span class="pre">float('NaN')</span></tt> and <tt class="xref py py-const docutils literal"><span class="pre">Decimal('NaN')</span></tt> are special.
The are identical to themselves, <tt class="docutils literal"><span class="pre">x</span> <span class="pre">is</span> <span class="pre">x</span></tt> but are not equal to themselves,
<tt class="docutils literal"><span class="pre">x</span> <span class="pre">!=</span> <span class="pre">x</span></tt>. Additionally, comparing any value to a not-a-number value
will return <tt class="xref docutils literal"><span class="pre">False</span></tt>. For example, both <tt class="docutils literal"><span class="pre">3</span> <span class="pre"><</span> <span class="pre">float('NaN')</span></tt> and
<tt class="docutils literal"><span class="pre">float('NaN')</span> <span class="pre"><</span> <span class="pre">3</span></tt> will return <tt class="xref docutils literal"><span class="pre">False</span></tt>.</p>
</li>
<li><p class="first">Bytes objects are compared lexicographically using the numeric values of their
elements.</p>
</li>
<li><p class="first">Strings are compared lexicographically using the numeric equivalents (the
result of the built-in function <a class="reference internal" href="../library/functions.html#ord" title="ord"><tt class="xref py py-func docutils literal"><span class="pre">ord()</span></tt></a>) of their characters. <a class="footnote-reference" href="#id18" id="id11">[3]</a> String
and bytes object can’t be compared!</p>
</li>
<li><p class="first">Tuples and lists are compared lexicographically using comparison of
corresponding elements. This means that to compare equal, each element must
compare equal and the two sequences must be of the same type and have the same
length.</p>
<p>If not equal, the sequences are ordered the same as their first differing
elements. For example, <tt class="docutils literal"><span class="pre">[1,2,x]</span> <span class="pre"><=</span> <span class="pre">[1,2,y]</span></tt> has the same value as
<tt class="docutils literal"><span class="pre">x</span> <span class="pre"><=</span> <span class="pre">y</span></tt>. If the corresponding element does not exist, the shorter
sequence is ordered first (for example, <tt class="docutils literal"><span class="pre">[1,2]</span> <span class="pre"><</span> <span class="pre">[1,2,3]</span></tt>).</p>
</li>
<li><p class="first">Mappings (dictionaries) compare equal if and only if they have the same
<tt class="docutils literal"><span class="pre">(key,</span> <span class="pre">value)</span></tt> pairs. Order comparisons <tt class="docutils literal"><span class="pre">('<',</span> <span class="pre">'<=',</span> <span class="pre">'>=',</span> <span class="pre">'>')</span></tt>
raise <a class="reference internal" href="../library/exceptions.html#TypeError" title="TypeError"><tt class="xref py py-exc docutils literal"><span class="pre">TypeError</span></tt></a>.</p>
</li>
<li><p class="first">Sets and frozensets define comparison operators to mean subset and superset
tests. Those relations do not define total orderings (the two sets <tt class="docutils literal"><span class="pre">{1,2}</span></tt>
and {2,3} are not equal, nor subsets of one another, nor supersets of one
another). Accordingly, sets are not appropriate arguments for functions
which depend on total ordering. For example, <a class="reference internal" href="../library/functions.html#min" title="min"><tt class="xref py py-func docutils literal"><span class="pre">min()</span></tt></a>, <a class="reference internal" href="../library/functions.html#max" title="max"><tt class="xref py py-func docutils literal"><span class="pre">max()</span></tt></a>, and
<a class="reference internal" href="../library/functions.html#sorted" title="sorted"><tt class="xref py py-func docutils literal"><span class="pre">sorted()</span></tt></a> produce undefined results given a list of sets as inputs.</p>
</li>
<li><p class="first">Most other objects of built-in types compare unequal unless they are the same
object; the choice whether one object is considered smaller or larger than
another one is made arbitrarily but consistently within one execution of a
program.</p>
</li>
</ul>
<p>Comparison of objects of the differing types depends on whether either
of the types provide explicit support for the comparison. Most numeric types
can be compared with one another, but comparisons of <a class="reference internal" href="../library/functions.html#float" title="float"><tt class="xref py py-class docutils literal"><span class="pre">float</span></tt></a> and
<tt class="xref py py-class docutils literal"><span class="pre">Decimal</span></tt> are not supported to avoid the inevitable confusion arising
from representation issues such as <tt class="docutils literal"><span class="pre">float('1.1')</span></tt> being inexactly represented
and therefore not exactly equal to <tt class="docutils literal"><span class="pre">Decimal('1.1')</span></tt> which is. When
cross-type comparison is not supported, the comparison method returns
<tt class="docutils literal"><span class="pre">NotImplemented</span></tt>. This can create the illusion of non-transitivity between
supported cross-type comparisons and unsupported comparisons. For example,
<tt class="docutils literal"><span class="pre">Decimal(2)</span> <span class="pre">==</span> <span class="pre">2</span></tt> and <tt class="docutils literal"><span class="pre">2</span> <span class="pre">==</span> <span class="pre">float(2)</span></tt> but <tt class="docutils literal"><span class="pre">Decimal(2)</span> <span class="pre">!=</span> <span class="pre">float(2)</span></tt>.</p>
<p id="membership-test-details">The operators <a class="reference internal" href="#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a> and <a class="reference internal" href="#not-in"><tt class="xref std std-keyword docutils literal"><span class="pre">not</span> <span class="pre">in</span></tt></a> test for membership. <tt class="docutils literal"><span class="pre">x</span> <span class="pre">in</span>
<span class="pre">s</span></tt> evaluates to true if <em>x</em> is a member of <em>s</em>, and false otherwise. <tt class="docutils literal"><span class="pre">x</span> <span class="pre">not</span>
<span class="pre">in</span> <span class="pre">s</span></tt> returns the negation of <tt class="docutils literal"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">s</span></tt>. All built-in sequences and set types
support this as well as dictionary, for which <a class="reference internal" href="#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a> tests whether a the
dictionary has a given key. For container types such as list, tuple, set,
frozenset, dict, or collections.deque, the expression <tt class="docutils literal"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">y</span></tt> is equivalent
to <tt class="docutils literal"><span class="pre">any(x</span> <span class="pre">is</span> <span class="pre">e</span> <span class="pre">or</span> <span class="pre">x</span> <span class="pre">==</span> <span class="pre">e</span> <span class="pre">for</span> <span class="pre">e</span> <span class="pre">in</span> <span class="pre">y)</span></tt>.</p>
<p>For the string and bytes types, <tt class="docutils literal"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">y</span></tt> is true if and only if <em>x</em> is a
substring of <em>y</em>. An equivalent test is <tt class="docutils literal"><span class="pre">y.find(x)</span> <span class="pre">!=</span> <span class="pre">-1</span></tt>. Empty strings are
always considered to be a substring of any other string, so <tt class="docutils literal"><span class="pre">""</span> <span class="pre">in</span> <span class="pre">"abc"</span></tt> will
return <tt class="xref docutils literal"><span class="pre">True</span></tt>.</p>
<p>For user-defined classes which define the <a class="reference internal" href="datamodel.html#object.__contains__" title="object.__contains__"><tt class="xref py py-meth docutils literal"><span class="pre">__contains__()</span></tt></a> method, <tt class="docutils literal"><span class="pre">x</span> <span class="pre">in</span>
<span class="pre">y</span></tt> is true if and only if <tt class="docutils literal"><span class="pre">y.__contains__(x)</span></tt> is true.</p>
<p>For user-defined classes which do not define <a class="reference internal" href="datamodel.html#object.__contains__" title="object.__contains__"><tt class="xref py py-meth docutils literal"><span class="pre">__contains__()</span></tt></a> but do define
<a class="reference internal" href="datamodel.html#object.__iter__" title="object.__iter__"><tt class="xref py py-meth docutils literal"><span class="pre">__iter__()</span></tt></a>, <tt class="docutils literal"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">y</span></tt> is true if some value <tt class="docutils literal"><span class="pre">z</span></tt> with <tt class="docutils literal"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">z</span></tt> is
produced while iterating over <tt class="docutils literal"><span class="pre">y</span></tt>. If an exception is raised during the
iteration, it is as if <a class="reference internal" href="#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a> raised that exception.</p>
<p>Lastly, the old-style iteration protocol is tried: if a class defines
<a class="reference internal" href="datamodel.html#object.__getitem__" title="object.__getitem__"><tt class="xref py py-meth docutils literal"><span class="pre">__getitem__()</span></tt></a>, <tt class="docutils literal"><span class="pre">x</span> <span class="pre">in</span> <span class="pre">y</span></tt> is true if and only if there is a non-negative
integer index <em>i</em> such that <tt class="docutils literal"><span class="pre">x</span> <span class="pre">==</span> <span class="pre">y[i]</span></tt>, and all lower integer indices do not
raise <a class="reference internal" href="../library/exceptions.html#IndexError" title="IndexError"><tt class="xref py py-exc docutils literal"><span class="pre">IndexError</span></tt></a> exception. (If any other exception is raised, it is as
if <a class="reference internal" href="#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a> raised that exception).</p>
<p id="index-61">The operator <a class="reference internal" href="#not-in"><tt class="xref std std-keyword docutils literal"><span class="pre">not</span> <span class="pre">in</span></tt></a> is defined to have the inverse true value of
<a class="reference internal" href="#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a>.</p>
<p id="index-62">The operators <a class="reference internal" href="#is"><tt class="xref std std-keyword docutils literal"><span class="pre">is</span></tt></a> and <a class="reference internal" href="#is-not"><tt class="xref std std-keyword docutils literal"><span class="pre">is</span> <span class="pre">not</span></tt></a> test for object identity: <tt class="docutils literal"><span class="pre">x</span>
<span class="pre">is</span> <span class="pre">y</span></tt> is true if and only if <em>x</em> and <em>y</em> are the same object. <tt class="docutils literal"><span class="pre">x</span> <span class="pre">is</span> <span class="pre">not</span> <span class="pre">y</span></tt>
yields the inverse truth value. <a class="footnote-reference" href="#id19" id="id12">[4]</a></p>
</div>
<div class="section" id="boolean-operations">
<span id="not"></span><span id="or"></span><span id="and"></span><span id="booleans"></span><h2>5.10. Boolean operations<a class="headerlink" href="#boolean-operations" title="Permalink to this headline">¶</a></h2>
<pre id="index-63">
<strong id="grammar-token-or_test">or_test </strong> ::= <a class="reference internal" href="#grammar-token-and_test"><tt class="xref docutils literal"><span class="pre">and_test</span></tt></a> | <a class="reference internal" href="#grammar-token-or_test"><tt class="xref docutils literal"><span class="pre">or_test</span></tt></a> "or" <a class="reference internal" href="#grammar-token-and_test"><tt class="xref docutils literal"><span class="pre">and_test</span></tt></a>
<strong id="grammar-token-and_test">and_test</strong> ::= <a class="reference internal" href="#grammar-token-not_test"><tt class="xref docutils literal"><span class="pre">not_test</span></tt></a> | <a class="reference internal" href="#grammar-token-and_test"><tt class="xref docutils literal"><span class="pre">and_test</span></tt></a> "and" <a class="reference internal" href="#grammar-token-not_test"><tt class="xref docutils literal"><span class="pre">not_test</span></tt></a>
<strong id="grammar-token-not_test">not_test</strong> ::= <a class="reference internal" href="#grammar-token-comparison"><tt class="xref docutils literal"><span class="pre">comparison</span></tt></a> | "not" <a class="reference internal" href="#grammar-token-not_test"><tt class="xref docutils literal"><span class="pre">not_test</span></tt></a>
</pre>
<p>In the context of Boolean operations, and also when expressions are used by
control flow statements, the following values are interpreted as false:
<tt class="xref docutils literal"><span class="pre">False</span></tt>, <tt class="xref docutils literal"><span class="pre">None</span></tt>, numeric zero of all types, and empty strings and containers
(including strings, tuples, lists, dictionaries, sets and frozensets). All
other values are interpreted as true. User-defined objects can customize their
truth value by providing a <a class="reference internal" href="datamodel.html#object.__bool__" title="object.__bool__"><tt class="xref py py-meth docutils literal"><span class="pre">__bool__()</span></tt></a> method.</p>
<p id="index-64">The operator <a class="reference internal" href="#not"><tt class="xref std std-keyword docutils literal"><span class="pre">not</span></tt></a> yields <tt class="xref docutils literal"><span class="pre">True</span></tt> if its argument is false, <tt class="xref docutils literal"><span class="pre">False</span></tt>
otherwise.</p>
<p id="index-65">The expression <tt class="docutils literal"><span class="pre">x</span> <span class="pre">and</span> <span class="pre">y</span></tt> first evaluates <em>x</em>; if <em>x</em> is false, its value is
returned; otherwise, <em>y</em> is evaluated and the resulting value is returned.</p>
<p id="index-66">The expression <tt class="docutils literal"><span class="pre">x</span> <span class="pre">or</span> <span class="pre">y</span></tt> first evaluates <em>x</em>; if <em>x</em> is true, its value is
returned; otherwise, <em>y</em> is evaluated and the resulting value is returned.</p>
<p>(Note that neither <a class="reference internal" href="#and"><tt class="xref std std-keyword docutils literal"><span class="pre">and</span></tt></a> nor <a class="reference internal" href="#or"><tt class="xref std std-keyword docutils literal"><span class="pre">or</span></tt></a> restrict the value and type
they return to <tt class="xref docutils literal"><span class="pre">False</span></tt> and <tt class="xref docutils literal"><span class="pre">True</span></tt>, but rather return the last evaluated
argument. This is sometimes useful, e.g., if <tt class="docutils literal"><span class="pre">s</span></tt> is a string that should be
replaced by a default value if it is empty, the expression <tt class="docutils literal"><span class="pre">s</span> <span class="pre">or</span> <span class="pre">'foo'</span></tt> yields
the desired value. Because <a class="reference internal" href="#not"><tt class="xref std std-keyword docutils literal"><span class="pre">not</span></tt></a> has to invent a value anyway, it does
not bother to return a value of the same type as its argument, so e.g., <tt class="docutils literal"><span class="pre">not</span>
<span class="pre">'foo'</span></tt> yields <tt class="xref docutils literal"><span class="pre">False</span></tt>, not <tt class="docutils literal"><span class="pre">''</span></tt>.)</p>
</div>
<div class="section" id="conditional-expressions">
<h2>5.11. Conditional expressions<a class="headerlink" href="#conditional-expressions" title="Permalink to this headline">¶</a></h2>
<pre id="index-67">
<strong id="grammar-token-conditional_expression">conditional_expression</strong> ::= <a class="reference internal" href="#grammar-token-or_test"><tt class="xref docutils literal"><span class="pre">or_test</span></tt></a> ["if" <a class="reference internal" href="#grammar-token-or_test"><tt class="xref docutils literal"><span class="pre">or_test</span></tt></a> "else" <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>]
<strong id="grammar-token-expression">expression </strong> ::= <a class="reference internal" href="#grammar-token-conditional_expression"><tt class="xref docutils literal"><span class="pre">conditional_expression</span></tt></a> | <a class="reference internal" href="#grammar-token-lambda_form"><tt class="xref docutils literal"><span class="pre">lambda_form</span></tt></a>
<strong id="grammar-token-expression_nocond">expression_nocond </strong> ::= <a class="reference internal" href="#grammar-token-or_test"><tt class="xref docutils literal"><span class="pre">or_test</span></tt></a> | <a class="reference internal" href="#grammar-token-lambda_form_nocond"><tt class="xref docutils literal"><span class="pre">lambda_form_nocond</span></tt></a>
</pre>
<p>Conditional expressions (sometimes called a “ternary operator”) have the lowest
priority of all Python operations.</p>
<p>The expression <tt class="docutils literal"><span class="pre">x</span> <span class="pre">if</span> <span class="pre">C</span> <span class="pre">else</span> <span class="pre">y</span></tt> first evaluates the condition, <em>C</em> (<em>not</em> <em>x</em>);
if <em>C</em> is true, <em>x</em> is evaluated and its value is returned; otherwise, <em>y</em> is
evaluated and its value is returned.</p>
<p>See <span class="target" id="index-68"></span><a class="pep reference external" href="http://www.python.org/dev/peps/pep-0308"><strong>PEP 308</strong></a> for more details about conditional expressions.</p>
</div>
<div class="section" id="lambda">
<span id="lambdas"></span><span id="id13"></span><h2>5.12. Lambdas<a class="headerlink" href="#lambda" title="Permalink to this headline">¶</a></h2>
<pre id="index-69">
<strong id="grammar-token-lambda_form">lambda_form </strong> ::= "lambda" [<a class="reference internal" href="compound_stmts.html#grammar-token-parameter_list"><tt class="xref docutils literal"><span class="pre">parameter_list</span></tt></a>]: <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a>
<strong id="grammar-token-lambda_form_nocond">lambda_form_nocond</strong> ::= "lambda" [<a class="reference internal" href="compound_stmts.html#grammar-token-parameter_list"><tt class="xref docutils literal"><span class="pre">parameter_list</span></tt></a>]: <a class="reference internal" href="#grammar-token-expression_nocond"><tt class="xref docutils literal"><span class="pre">expression_nocond</span></tt></a>
</pre>
<p>Lambda forms (lambda expressions) have the same syntactic position as
expressions. They are a shorthand to create anonymous functions; the expression
<tt class="docutils literal"><span class="pre">lambda</span> <span class="pre">arguments:</span> <span class="pre">expression</span></tt> yields a function object. The unnamed object
behaves like a function object defined with</p>
<div class="highlight-python3"><pre>def <lambda>(arguments):
return expression</pre>
</div>
<p>See section <a class="reference internal" href="compound_stmts.html#function"><em>Function definitions</em></a> for the syntax of parameter lists. Note that
functions created with lambda forms cannot contain statements or annotations.</p>
</div>
<div class="section" id="expression-lists">
<span id="exprlists"></span><h2>5.13. Expression lists<a class="headerlink" href="#expression-lists" title="Permalink to this headline">¶</a></h2>
<pre id="index-70">
<strong id="grammar-token-expression_list">expression_list</strong> ::= <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> ( "," <a class="reference internal" href="#grammar-token-expression"><tt class="xref docutils literal"><span class="pre">expression</span></tt></a> )* [","]
</pre>
<p id="index-71">An expression list containing at least one comma yields a tuple. The length of
the tuple is the number of expressions in the list. The expressions are
evaluated from left to right.</p>
<p id="index-72">The trailing comma is required only to create a single tuple (a.k.a. a
<em>singleton</em>); it is optional in all other cases. A single expression without a
trailing comma doesn’t create a tuple, but rather yields the value of that
expression. (To create an empty tuple, use an empty pair of parentheses:
<tt class="docutils literal"><span class="pre">()</span></tt>.)</p>
</div>
<div class="section" id="evaluation-order">
<span id="evalorder"></span><h2>5.14. Evaluation order<a class="headerlink" href="#evaluation-order" title="Permalink to this headline">¶</a></h2>
<p id="index-73">Python evaluates expressions from left to right. Notice that while evaluating
an assignment, the right-hand side is evaluated before the left-hand side.</p>
<p>In the following lines, expressions will be evaluated in the arithmetic order of
their suffixes:</p>
<div class="highlight-python3"><div class="highlight"><pre><span class="n">expr1</span><span class="p">,</span> <span class="n">expr2</span><span class="p">,</span> <span class="n">expr3</span><span class="p">,</span> <span class="n">expr4</span>
<span class="p">(</span><span class="n">expr1</span><span class="p">,</span> <span class="n">expr2</span><span class="p">,</span> <span class="n">expr3</span><span class="p">,</span> <span class="n">expr4</span><span class="p">)</span>
<span class="p">{</span><span class="n">expr1</span><span class="p">:</span> <span class="n">expr2</span><span class="p">,</span> <span class="n">expr3</span><span class="p">:</span> <span class="n">expr4</span><span class="p">}</span>
<span class="n">expr1</span> <span class="o">+</span> <span class="n">expr2</span> <span class="o">*</span> <span class="p">(</span><span class="n">expr3</span> <span class="o">-</span> <span class="n">expr4</span><span class="p">)</span>
<span class="n">expr1</span><span class="p">(</span><span class="n">expr2</span><span class="p">,</span> <span class="n">expr3</span><span class="p">,</span> <span class="o">*</span><span class="n">expr4</span><span class="p">,</span> <span class="o">**</span><span class="n">expr5</span><span class="p">)</span>
<span class="n">expr3</span><span class="p">,</span> <span class="n">expr4</span> <span class="o">=</span> <span class="n">expr1</span><span class="p">,</span> <span class="n">expr2</span>
</pre></div>
</div>
</div>
<div class="section" id="summary">
<span id="operator-summary"></span><h2>5.15. Summary<a class="headerlink" href="#summary" title="Permalink to this headline">¶</a></h2>
<p id="index-74">The following table summarizes the operator precedences in Python, from lowest
precedence (least binding) to highest precedence (most binding). Operators in
the same box have the same precedence. Unless the syntax is explicitly given,
operators are binary. Operators in the same box group left to right (except for
comparisons, including tests, which all have the same precedence and chain from
left to right — see section <a class="reference internal" href="#comparisons"><em>Comparisons</em></a> — and exponentiation, which
groups from right to left).</p>
<table border="1" class="docutils">
<colgroup>
<col width="56%" />
<col width="44%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head">Operator</th>
<th class="head">Description</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><a class="reference internal" href="#lambda"><tt class="xref std std-keyword docutils literal"><span class="pre">lambda</span></tt></a></td>
<td>Lambda expression</td>
</tr>
<tr><td><a class="reference internal" href="compound_stmts.html#if"><tt class="xref std std-keyword docutils literal"><span class="pre">if</span></tt></a> – <a class="reference internal" href="compound_stmts.html#else"><tt class="xref std std-keyword docutils literal"><span class="pre">else</span></tt></a></td>
<td>Conditional expression</td>
</tr>
<tr><td><a class="reference internal" href="#or"><tt class="xref std std-keyword docutils literal"><span class="pre">or</span></tt></a></td>
<td>Boolean OR</td>
</tr>
<tr><td><a class="reference internal" href="#and"><tt class="xref std std-keyword docutils literal"><span class="pre">and</span></tt></a></td>
<td>Boolean AND</td>
</tr>
<tr><td><a class="reference internal" href="#not"><tt class="xref std std-keyword docutils literal"><span class="pre">not</span></tt></a> <em>x</em></td>
<td>Boolean NOT</td>
</tr>
<tr><td><a class="reference internal" href="#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a>, <a class="reference internal" href="#not"><tt class="xref std std-keyword docutils literal"><span class="pre">not</span></tt></a> <a class="reference internal" href="#in"><tt class="xref std std-keyword docutils literal"><span class="pre">in</span></tt></a>,
<a class="reference internal" href="#is"><tt class="xref std std-keyword docutils literal"><span class="pre">is</span></tt></a>, <a class="reference internal" href="#is-not"><tt class="xref std std-keyword docutils literal"><span class="pre">is</span> <span class="pre">not</span></tt></a>, <tt class="docutils literal"><span class="pre"><</span></tt>,
<tt class="docutils literal"><span class="pre"><=</span></tt>, <tt class="docutils literal"><span class="pre">></span></tt>, <tt class="docutils literal"><span class="pre">>=</span></tt>, <tt class="docutils literal"><span class="pre">!=</span></tt>, <tt class="docutils literal"><span class="pre">==</span></tt></td>
<td>Comparisons, including membership
tests and identity tests,</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">|</span></tt></td>
<td>Bitwise OR</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">^</span></tt></td>
<td>Bitwise XOR</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">&</span></tt></td>
<td>Bitwise AND</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre"><<</span></tt>, <tt class="docutils literal"><span class="pre">>></span></tt></td>
<td>Shifts</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">+</span></tt>, <tt class="docutils literal"><span class="pre">-</span></tt></td>
<td>Addition and subtraction</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">*</span></tt>, <tt class="docutils literal"><span class="pre">/</span></tt>, <tt class="docutils literal"><span class="pre">//</span></tt>, <tt class="docutils literal"><span class="pre">%</span></tt></td>
<td>Multiplication, division, remainder
<a class="footnote-reference" href="#id20" id="id14">[5]</a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">+x</span></tt>, <tt class="docutils literal"><span class="pre">-x</span></tt>, <tt class="docutils literal"><span class="pre">~x</span></tt></td>
<td>Positive, negative, bitwise NOT</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">**</span></tt></td>
<td>Exponentiation <a class="footnote-reference" href="#id21" id="id15">[6]</a></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">x[index]</span></tt>, <tt class="docutils literal"><span class="pre">x[index:index]</span></tt>,
<tt class="docutils literal"><span class="pre">x(arguments...)</span></tt>, <tt class="docutils literal"><span class="pre">x.attribute</span></tt></td>
<td>Subscription, slicing,
call, attribute reference</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">(expressions...)</span></tt>,
<tt class="docutils literal"><span class="pre">[expressions...]</span></tt>,
<tt class="docutils literal"><span class="pre">{key:datum...}</span></tt>,
<tt class="docutils literal"><span class="pre">{expressions...}</span></tt></td>
<td>Binding or tuple display,
list display,
dictionary display,
set display</td>
</tr>
</tbody>
</table>
<p class="rubric">Footnotes</p>
<table class="docutils footnote" frame="void" id="id16" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id8">[1]</a></td><td>While <tt class="docutils literal"><span class="pre">abs(x%y)</span> <span class="pre"><</span> <span class="pre">abs(y)</span></tt> is true mathematically, for floats it may not be
true numerically due to roundoff. For example, and assuming a platform on which
a Python float is an IEEE 754 double-precision number, in order that <tt class="docutils literal"><span class="pre">-1e-100</span> <span class="pre">%</span>
<span class="pre">1e100</span></tt> have the same sign as <tt class="docutils literal"><span class="pre">1e100</span></tt>, the computed result is <tt class="docutils literal"><span class="pre">-1e-100</span> <span class="pre">+</span>
<span class="pre">1e100</span></tt>, which is numerically exactly equal to <tt class="docutils literal"><span class="pre">1e100</span></tt>. The function
<a class="reference internal" href="../library/math.html#math.fmod" title="math.fmod"><tt class="xref py py-func docutils literal"><span class="pre">math.fmod()</span></tt></a> returns a result whose sign matches the sign of the
first argument instead, and so returns <tt class="docutils literal"><span class="pre">-1e-100</span></tt> in this case. Which approach
is more appropriate depends on the application.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id17" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id9">[2]</a></td><td>If x is very close to an exact integer multiple of y, it’s possible for
<tt class="docutils literal"><span class="pre">x//y</span></tt> to be one larger than <tt class="docutils literal"><span class="pre">(x-x%y)//y</span></tt> due to rounding. In such
cases, Python returns the latter result, in order to preserve that
<tt class="docutils literal"><span class="pre">divmod(x,y)[0]</span> <span class="pre">*</span> <span class="pre">y</span> <span class="pre">+</span> <span class="pre">x</span> <span class="pre">%</span> <span class="pre">y</span></tt> be very close to <tt class="docutils literal"><span class="pre">x</span></tt>.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id18" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id11">[3]</a></td><td>While comparisons between strings make sense at the byte level, they may
be counter-intuitive to users. For example, the strings <tt class="docutils literal"><span class="pre">"\u00C7"</span></tt> and
<tt class="docutils literal"><span class="pre">"\u0327\u0043"</span></tt> compare differently, even though they both represent the
same unicode character (LATIN CAPITAL LETTER C WITH CEDILLA). To compare
strings in a human recognizable way, compare using
<a class="reference internal" href="../library/unicodedata.html#unicodedata.normalize" title="unicodedata.normalize"><tt class="xref py py-func docutils literal"><span class="pre">unicodedata.normalize()</span></tt></a>.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id19" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id12">[4]</a></td><td>Due to automatic garbage-collection, free lists, and the dynamic nature of
descriptors, you may notice seemingly unusual behaviour in certain uses of
the <a class="reference internal" href="#is"><tt class="xref std std-keyword docutils literal"><span class="pre">is</span></tt></a> operator, like those involving comparisons between instance
methods, or constants. Check their documentation for more info.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id20" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id14">[5]</a></td><td>The <tt class="docutils literal"><span class="pre">%</span></tt> operator is also used for string formatting; the same
precedence applies.</td></tr>
</tbody>
</table>
<table class="docutils footnote" frame="void" id="id21" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id15">[6]</a></td><td>The power operator <tt class="docutils literal"><span class="pre">**</span></tt> binds less tightly than an arithmetic or
bitwise unary operator on its right, that is, <tt class="docutils literal"><span class="pre">2**-1</span></tt> is <tt class="docutils literal"><span class="pre">0.5</span></tt>.</td></tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<div class="sphinxsidebar">
<div class="sphinxsidebarwrapper">
<h3><a href="../contents.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">5. Expressions</a><ul>
<li><a class="reference internal" href="#arithmetic-conversions">5.1. Arithmetic conversions</a></li>
<li><a class="reference internal" href="#atoms">5.2. Atoms</a><ul>
<li><a class="reference internal" href="#atom-identifiers">5.2.1. Identifiers (Names)</a></li>
<li><a class="reference internal" href="#literals">5.2.2. Literals</a></li>
<li><a class="reference internal" href="#parenthesized-forms">5.2.3. Parenthesized forms</a></li>
<li><a class="reference internal" href="#displays-for-lists-sets-and-dictionaries">5.2.4. Displays for lists, sets and dictionaries</a></li>
<li><a class="reference internal" href="#list-displays">5.2.5. List displays</a></li>
<li><a class="reference internal" href="#set-displays">5.2.6. Set displays</a></li>
<li><a class="reference internal" href="#dictionary-displays">5.2.7. Dictionary displays</a></li>
<li><a class="reference internal" href="#generator-expressions">5.2.8. Generator expressions</a></li>
<li><a class="reference internal" href="#yield-expressions">5.2.9. Yield expressions</a></li>
</ul>
</li>
<li><a class="reference internal" href="#primaries">5.3. Primaries</a><ul>
<li><a class="reference internal" href="#attribute-references">5.3.1. Attribute references</a></li>
<li><a class="reference internal" href="#subscriptions">5.3.2. Subscriptions</a></li>
<li><a class="reference internal" href="#slicings">5.3.3. Slicings</a></li>
<li><a class="reference internal" href="#calls">5.3.4. Calls</a></li>
</ul>
</li>
<li><a class="reference internal" href="#the-power-operator">5.4. The power operator</a></li>
<li><a class="reference internal" href="#unary-arithmetic-and-bitwise-operations">5.5. Unary arithmetic and bitwise operations</a></li>
<li><a class="reference internal" href="#binary-arithmetic-operations">5.6. Binary arithmetic operations</a></li>
<li><a class="reference internal" href="#shifting-operations">5.7. Shifting operations</a></li>
<li><a class="reference internal" href="#binary-bitwise-operations">5.8. Binary bitwise operations</a></li>
<li><a class="reference internal" href="#not-in">5.9. Comparisons</a></li>
<li><a class="reference internal" href="#boolean-operations">5.10. Boolean operations</a></li>
<li><a class="reference internal" href="#conditional-expressions">5.11. Conditional expressions</a></li>
<li><a class="reference internal" href="#lambda">5.12. Lambdas</a></li>
<li><a class="reference internal" href="#expression-lists">5.13. Expression lists</a></li>
<li><a class="reference internal" href="#evaluation-order">5.14. Evaluation order</a></li>
<li><a class="reference internal" href="#summary">5.15. Summary</a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
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title="next chapter">6. Simple statements</a></p>
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