6. Expressions
**************

This chapter explains the meaning of the elements of expressions in
Python.

**Syntax Notes:** In this and the following chapters, grammar notation
will be used to describe syntax, not lexical analysis.

When (one alternative of) a syntax rule has the form:

   name: othername

and no semantics are given, the semantics of this form of "name" are
the same as for "othername".


6.1. Arithmetic conversions
===========================

When a description of an arithmetic operator below uses the phrase
"the numeric arguments are converted to a common real type", this
means that the operator implementation for built-in numeric types
works as described in the Numeric Types section of the standard
library documentation.

Some additional rules apply for certain operators and non-numeric
operands (for example, a string as a left argument to the "%"
operator). Extensions must define their own conversion behavior.


6.2. Atoms
==========

Atoms are the most basic elements of expressions. The simplest atoms
are builtin constants, names and literals. More complex atoms are
enclosed in paired delimiters:

* "()" (parentheses): groups, tuple displays, yield atoms, and
  generator expressions;

* "[]" (square brackets): list displays;

* "{}" (curly braces): dictionary and set displays.

Formally, the syntax for atoms is:

   atom:
      | builtin_constant
      | identifier
      | literal
      | parenthesized_enclosure
      | bracketed_enclosure
      | braced_enclosure
   parenthesized_enclosure:
      | group
      | tuple
      | yield_atom
      | generator_expression
   bracketed_enclosure:
      | listcomp
      | list
   braced_enclosure:
      | dictcomp
      | dict
      | setcomp
      | set


6.2.1. Built-in constants
-------------------------

The keywords "True", "False", and "None" name built-in constants. The
token "..." names the "Ellipsis" constant.

Evaluation of these atoms yields the corresponding value.

Note:

  Several more built-in constants are available as global variables,
  but only the ones mentioned here are keywords. In particular, these
  names cannot be reassigned or used as attributes:

     >>> False = 123
       File "<input>", line 1
        False = 123
        ^^^^^
     SyntaxError: cannot assign to False

Formally, the syntax for built-in constants is:

   builtin_constant: 'True' | 'False' | 'None' | '...'


6.2.2. Identifiers (Names)
--------------------------

An identifier occurring as an atom is a name.  See section Names
(identifiers and keywords) for lexical definition and section Naming
and binding for documentation of naming and binding.

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 "NameError" exception.


6.2.2.1. Private name mangling
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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 *private name* of that class.

See also: The class specifications.

More precisely, private names are transformed to a longer form before
code is generated for them.  If the transformed name is longer than
255 characters, implementation-defined truncation may happen.

The transformation is independent of the syntactical context in which
the identifier is used but only the following private identifiers are
mangled:

* Any name used as the name of a variable that is assigned or read or
  any name of an attribute being accessed.

  The "__name__" attribute of nested functions, classes, and type
  aliases is however not mangled.

* The name of imported modules, e.g., "__spam" in "import __spam". If
  the module is part of a package (i.e., its name contains a dot), the
  name is *not* mangled, e.g., the "__foo" in "import __foo.bar" is
  not mangled.

* The name of an imported member, e.g., "__f" in "from spam import
  __f".

The transformation rule is defined as follows:

* The class name, with leading underscores removed and a single
  leading underscore inserted, is inserted in front of the identifier,
  e.g., the identifier "__spam" occurring in a class named "Foo",
  "_Foo" or "__Foo" is transformed to "_Foo__spam".

* If the class name consists only of underscores, the transformation
  is the identity, e.g., the identifier "__spam" occurring in a class
  named "_" or "__" is left as is.


6.2.3. Literals
---------------

A *literal* is a textual representation of a value. Python supports
numeric, string and bytes literals. Format strings and template
strings are treated as string literals.

Numeric literals consist of a single "NUMBER" token, which names an
integer, floating-point number, or an imaginary number. See the
Numeric literals section in Lexical analysis documentation for
details.

String and bytes literals may consist of several tokens. See section
String literal concatenation for details.

Note that negative and complex numbers, like "-3" or "3+4.2j", are
syntactically not literals, but unary or binary arithmetic operations
involving the "-" or "+" operator.

Evaluation of a literal yields an object of the given type ("int",
"float", "complex", "str", "bytes", or "Template") with the given
value. The value may be approximated in the case of floating-point and
imaginary literals.

The formal grammar for literals is:

   literal: strings | NUMBER


6.2.3.1. Literals and object identity
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

All literals 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.

CPython implementation detail: For example, in CPython, *small*
integers with the same value evaluate to the same object:

   >>> x = 7
   >>> y = 7
   >>> x is y
   True

However, large integers evaluate to different objects:

   >>> x = 123456789
   >>> y = 123456789
   >>> x is y
   False

This behavior may change in future versions of CPython. In particular,
the boundary between "small" and "large" integers has already changed
in the past.CPython will emit a "SyntaxWarning" when you compare
literals using "is":

   >>> x = 7
   >>> x is 7
   <input>:1: SyntaxWarning: "is" with 'int' literal. Did you mean "=="?
   True

See When can I rely on identity tests with the is operator? for more
information.

Template strings are immutable but may reference mutable objects as
"Interpolation" values. For the purposes of this section, two
t-strings have the "same value" if both their structure and the
*identity* of the values match.

**CPython implementation detail:** Currently, each evaluation of a
template string results in a different object.


6.2.3.2. String literal concatenation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiple adjacent string or bytes literals, possibly using different
quoting conventions, are allowed, and their meaning is the same as
their concatenation:

   >>> "hello" 'world'
   "helloworld"

This feature is defined at the syntactical level, so it only works
with literals. To concatenate string expressions at run time, the '+'
operator may be used:

   >>> greeting = "Hello"
   >>> space = " "
   >>> name = "Blaise"
   >>> print(greeting + space + name)   # not: print(greeting space name)
   Hello Blaise

Literal concatenation can freely mix raw strings, triple-quoted
strings, and formatted string literals. For example:

   >>> "Hello" r', ' f"{name}!"
   "Hello, Blaise!"

This feature can be used to reduce the number of backslashes needed,
to split long strings conveniently across long lines, or even to add
comments to parts of strings. For example:

   re.compile("[A-Za-z_]"       # letter or underscore
              "[A-Za-z0-9_]*"   # letter, digit or underscore
             )

However, bytes literals may only be combined with other byte literals;
not with string literals of any kind. Also, template string literals
may only be combined with other template string literals:

   >>> t"Hello" t"{name}!"
   Template(strings=('Hello', '!'), interpolations=(...))

Formally:

   strings: (STRING | fstring)+ | tstring+


6.2.4. Parenthesized groups
---------------------------

A *parenthesized group* is an expression enclosed in parentheses. The
group evaluates to the same value as the expression inside.

Groups are used to override or clarify operator precedence, in the
same way as in math notation. For example:

   >>> 3 << 2 | 4
   12
   >>> 3 << (2 | 4)   # Override precedence of the | (bitwise OR)
   192
   >>> (3 << 2) | 4   # Same as without parentheses (but more clear)
   12

Note that not everything in parentheses is a *group*. Specifically, a
parenthesized group must include exactly one expression, and cannot
end with a comma. See tuple displays and generator expressions for
other parenthesized forms.

Formally, the syntax for groups is:

   group: '(' assignment_expression ')'


6.2.5. Container displays
-------------------------

For constructing builtin containers (lists, sets, tuples or
dictionaries), Python provides special syntax called *displays*. There
are subtle differences between the four kinds of displays, detailed in
the following sections. All displays, however, consist of comma-
separated items enclosed in paired delimiters.

For example, a *list display* is a series of expressions enclosed in
square brackets:

   >>> ["one", "two", "three"]
   ['one', 'two', 'three']
   >>> [1 + 2, 2 + 3]
   [3, 5]

In list, tuple and dictionary (but not set) displays, the series may
be empty:

   >>> []  # empty list
   []
   >>> ()  # empty tuple
   ()
   >>> {}  # empty dictionary
   {}

If the series is not empty, the items may be followed by an additional
comma, which has no effect:

   >>> ["one", "two", "three",]  # note comma after "three"
   ['one', 'two', 'three']

Note:

  The trailing comma is often used for displays that span multiple
  lines (using implicit line joining), so when a future programmer
  adds a new entry at the end, they do not need to modify an existing
  line:

     >>> [
     ...     'one',
     ...     'two',
     ...     'three',
     ... ]
     ['one', 'two', 'three']

At runtime, when a display is evaluated, the listed items are
evaluated from left to right and placed into a new container of the
appropriate type.

For tuple, list and set (but not dict) displays, any item in the
display may be prefixed with an asterisk ("*"). This denotes iterable
unpacking. At runtime, the asterisk-prefixed expression must evaluate
to an iterable, whose contents are inserted into the container at the
location of the unpacking. For example:

   >>> numbers = (1, 2)
   >>> [*numbers, 'word', *numbers]
   [1, 2, 'word', 1, 2]

Dictionary displays use a similar mechanism called *dictionary
unpacking*, denoted with a double asterisk ("**"). See Dictionary
displays for details.

A more advanced form of displays are *comprehensions*, where items are
computed via a set of looping and filtering instructions. See the
Comprehensions section for details.

Added in version 3.5: Iterable and dictionary unpacking in displays,
originally proposed by **PEP 448**.


6.2.5.1. List displays
~~~~~~~~~~~~~~~~~~~~~~

A *list display* is a possibly empty series of expressions enclosed in
square brackets. For example:

   >>> ["one", "two", "three"]
   ['one', 'two', 'three']
   >>> ["one"]  # One-element list
   ['one']
   >>> []       # empty list
   []

See Container displays for general information on displays.

The formal grammar for list displays is:

   list: '[' [flexible_expression_list] ']'


6.2.5.2. Set displays
~~~~~~~~~~~~~~~~~~~~~

A *set display* is a *non-empty* series of expressions enclosed in
curly braces. For example:

   >>> {"one", "two", "three"}
   {'one', 'three', 'two'}
   >>> {"one"}  # One-element set
   {'one'}

See Container displays for general information on displays.

There is no special syntax for the empty set. The "{}" literal is a
dictionary display that constructs an empty dictionary. Call "set()"
with no arguments to get an empty set.

The formal grammar for set displays is:

   set: '{' flexible_expression_list '}'


6.2.5.3. Tuple displays
~~~~~~~~~~~~~~~~~~~~~~~

A *tuple display* is a series of expressions enclosed in parentheses.
For example:

   >>> (1, 2)
   (1, 2)
   >>> ()  # an empty tuple
   ()

See Container displays for general information on displays.

To avoid ambiguity, if a tuple display has exactly one element, it
requires a trailing comma. Without it, you get a parenthesized group:

   >>> ('single',)  # single-element tuple
   ('single',)
   >>> ('single')   # no comma: single string
   'single'

To put it in other words, a tuple display is a parenthesized list of
either:

* two or more comma-separated expressions, or

* zero or more expressions, each followed by a comma.

Since tuples are immutable, object identity rules for literals also
apply to tuples: at runtime, two occurrences of tuples with the same
values may or may not yield the same object.

Note:

  Python's syntax also includes expression lists, where a comma-
  separated list of expressions is *not* enclosed in parentheses but
  evaluates to tuple.In other words, when it comes to tuple syntax,
  the comma is more important that the use of parentheses. Only the
  empty tuple is spelled without a comma.

The formal grammar for tuple displays is:

   tuple:
      | '(' flexible_expression (',' flexible_expression)+ [','] ')'
      | '(' flexible_expression ',' ')'
      | '(' ')'


6.2.5.4. Dictionary displays
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A *dictionary display* is a possibly empty series of *dict items*
enclosed in curly braces. Each dict item is a colon-separated pair of
expressions: the *key* and its associated *value*. For example:

   >>> {1: 'one', 2: 'two'}
   {1: 'one', 2: 'two'}

At runtime, when a dictionary comprehension is evaluated, the
expressions are evaluated from left to right. Each key object is used
as a key into the dictionary to store the corresponding value. This
means that you can specify the same key multiple times in the
comprehension, and the final dictionary's value for a given key will
be the last one given. For example:

   >>> {
   ...     1: 'this will be overridden',
   ...     2: 'two',
   ...     1: 'also overridden',
   ...     1: 'one',
   ... }
   {1: 'one', 2: 'two'}

Instead of a key-value pair, a dict item may be an expression prefixed
by a double asterisk "**". This denotes *dictionary unpacking*. At
runtime, the expression must evaluate to a *mapping*; each item of the
mapping is added to the new dictionary. As with key-value pairs, later
values replace values already set by earlier items and unpackings.
This may be used to override a set of defaults:

   >>> defaults = {'color': 'blue', 'count': 8}
   >>> overrides = {'color': 'yellow'}
   >>> {**defaults, **overrides}
   {'color': 'yellow', 'count': 8}

Added in version 3.5: Unpacking into dictionary displays, originally
proposed by **PEP 448**.

The formal grammar for dict displays is:

   dict:                   '{' [double_starred_kvpairs] '}'
   double_starred_kvpairs: ','.double_starred_kvpair+ [',']
   double_starred_kvpair:  '**' or_expr | kvpair
   kvpair:                 expression ':' expression


6.2.6. Comprehensions
---------------------

List, set and dictionary *comprehensions* are a form of container
displays where items are computed via a set of looping and filtering
instructions rather than listed explicitly.

In its simplest form, a comprehension consists of a single expression
followed by a "for" clause. The "for" clause has the same syntax as
the header of a for statement, without a trailing colon.

For example, a list of the first ten squares is:

   >>> [x**2 for x in range(10)]
   [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

At run time, a list comprehension creates a new list. The expression
after "in" must evaluate to an *iterable*. For each element of this
iterable, the element is bound to the "for" clause's target as in a
"for" statement, then the expression before "for" is evaluated with
the target in scope and the result is added to the new list. Thus, the
example above is roughly equivalent to defining and calling the
following function:

   def make_list_of_squares(iterable):
       result = []
       for x in iterable:
           result.append(x**2)
       return result

   make_list_of_squares(range(10))

Set comprehensions work similarly. For example, here is a set of
lowercase letters:

   >>> {x.lower() for x in ['a', 'A', 'b', 'C']}
   {'c', 'a', 'b'}

At run time, this corresponds roughly to calling this function:

   def make_lowercase_set(iterable):
       result = set(iterable)
       for x in iterable:
           result.append(x.lower())
       return result

   make_lowercase_set(['a', 'A', 'b', 'C'])

Dictionary comprehensions start with a colon-separated key-value pair
instead of an expression. For example:

   >>> {func.__name__: func for func in [print, hex, any]}
   {'print': <built-in function print>,
    'hex': <built-in function hex>,
    'any': <built-in function any>}

At run time, this corresponds roughly to:

   def make_dict_mapping_names_to_functions(iterable):
       result = {}
       for func in iterable:
           result[func.__name__] = func
       return result

   iterable([print, hex, any])

As in other kinds of dictionary displays, the same key may be
specified multiple times. Earlier values are overwritten by ones that
are evaluated later.

There are no *tuple comprehensions*. A similar syntax is instead used
for generator expressions, from which you can construct a tuple like
this:

   >>> tuple(x**2 for x in range(10))
   (0, 1, 4, 9, 16, 25, 36, 49, 64, 81)

Changed in version 3.8: Prior to Python 3.8, in dict comprehensions,
the evaluation order of key and value was not well-defined.  In
CPython, the value was evaluated before the key.  Starting with 3.8,
the key is evaluated before the value, as proposed by **PEP 572**.


6.2.6.1. Filtering in comprehensions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The "for" clause may be followed by an "if" clause with an expression.

For example, a list of names from the "math" module that start with
"f" is:

   >>> [name for name in vars(math) if name.startswith('f')]
   ['fabs', 'factorial', 'floor', 'fma', 'fmod', 'frexp', 'fsum']

At run time, the expression after "if" is evaluated before each
element is added to the resulting container, and if it is false, the
element is skipped. Thus, the above example roughly corresponds to
defining and calling the following function:

   def get_math_f_names(iterable):
       result = []
       for name in iterable:
           if name.startswith('f'):
              result.append(name)
       return result

   get_math_f_names(vars(math))

Filtering is a special case of more complex comprehensions. See the
next section for a more formal description.


6.2.6.2. Complex comprehensions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Generally, a comprehension's initial "for" clause may be followed by
zero or more additional "for" or "if" clauses. For example, here is a
list of names exposed by two Python modules, filtered to only include
names that start with "a":

   >>> import array
   >>> import math
   >>> [
   ...     name
   ...     for module in [array, math]
   ...     for name in vars(module)
   ...     if name.startswith('a')
   ... ]
   ['array', 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh']

At run time, this roughly corresponds to defining and calling:

   def get_a_names(iterable):
       result = []
       for module in iterable:
           for name in vars(module):
               if name.startswith('a'):
                   result.append(name)
       return result

   get_a_names([array, math])

The elements of the new container are those that would be produced by
considering each of the "for" or "if" clauses a block, nesting from
left to right, and evaluating the expression to produce an element (or
dictionary entry) each time the innermost block is reached.

Aside from the iterable expression in the leftmost "for" clause, the
comprehension is executed in a separate implicitly nested scope. This
ensures that names assigned to in the target list don't "leak" into
the enclosing scope. For example:

   >>> x = 'old value'
   >>> [x**2 for x in range(10)]  # this `x` is local to the comprehension
   >>> x
   'old value'

The iterable expression in the leftmost "for" clause is evaluated
directly in the enclosing scope and then passed as an argument to the
implicitly nested scope.

Subsequent "for" clauses and any filter condition in the leftmost
"for" clause cannot be evaluated in the enclosing scope as they may
depend on the values obtained from the leftmost iterable.

To ensure the comprehension always results in a container of the
appropriate type, "yield" and "yield from" expressions are prohibited
in the implicitly nested scope.

Assignment expressions are not allowed inside comprehension iterable
expressions (that is, the expressions after the "in" keyword), nor
anywhere within comprehensions that appear directly in a class
definition.

Changed in version 3.8: "yield" and "yield from" prohibited in the
implicitly nested scope.


6.2.6.3. Unpacking in comprehensions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If the expression of a list or set comprehension is starred, the
result will be unpacked to produce zero or more elements.

This is often used for "flattening" lists, for example:

   >>> students = ['Petr', 'Blaise', 'Jarka']
   >>> teachers = ['Salim', 'Bartosz']
   >>> lists_of_people = [students, teachers]
   >>> [*people for people in lists_of_people]
   ['Petr', 'Blaise', 'Jarka', 'Salim', 'Bartosz']

At run time, this comprehension roughly corresponds to:

   def flatten_names(lists_of_people):
       result = []
       for people in lists_of_people:
           result.extend(people)
       return result

In dict comprehensions, a double-starred expression will be evaluated
and then unpacked using dictionary unpacking, inserting zero or more
key/value pairs into the new dictionary. As in other kinds of
dictionary displays, if the same key is specified multiple times, the
associated value in the resulting dictionary will be the last one
specified.

For example:

   >>> system_defaults = {'color': 'blue', 'count': 8}
   >>> user_defaults = {'color': 'yellow'}
   >>> overrides = {'count': 5}

   >>> configuration_sets = [system_defaults, user_defaults, overrides]

   >>> {**d for d in configuration_sets}
   {'color': 'yellow', 'count': 5}

Added in version 3.15: Unpacking in comprehensions using the "*" and
"**" operators was introduced in **PEP 798**.


6.2.6.4. Asynchronous comprehensions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In an "async def" function, an "async for" clause may be used to
iterate over a *asynchronous iterator*. A comprehension in an "async
def" function may consist of either a "for" or "async for" clause
following the leading expression, may contain additional "for" or
"async for" clauses, and may also use "await" expressions.

If a comprehension contains "async for" clauses, or if it contains
"await" expressions or other asynchronous comprehensions anywhere
except the iterable expression in the leftmost "for" clause, it is
called an *asynchronous comprehension*. An asynchronous comprehension
may suspend the execution of the coroutine function in which it
appears.

Added in version 3.6: Asynchronous comprehensions were introduced in
**PEP 530**.

Changed in version 3.11: Asynchronous comprehensions are now allowed
inside comprehensions in asynchronous functions. Outer comprehensions
implicitly become asynchronous.


6.2.6.5. Formal grammar for comprehensions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The formal grammar for comprehensions is:

   listcomp:      '[' comprehension ']'
   setcomp:       '{' comprehension '}'
   comprehension: flexible_expression for_if_clause+

   dictcomp:
       | '{' kvpair for_if_clause+ '}'
       | '{' '**' expression for_if_clause+ '}'

   for_if_clause:
       | ['async'] 'for' target_list 'in' or_test ('if' or_test)*


6.2.7. Generator expressions
----------------------------

A generator expression is a compact generator notation in parentheses:

   generator_expression: "(" comprehension ")"

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.

Variables used in the generator expression are evaluated lazily when
the "__next__()" method is called for the generator object (in the
same fashion as normal generators).  However, the iterable expression
in the leftmost "for" clause is immediately evaluated, and the
*iterator* is immediately created for that iterable, so that an error
produced while creating the iterator will be emitted at the point
where the generator expression is defined, rather than at the point
where the first value is retrieved. Subsequent "for" clauses and any
filter condition in the leftmost "for" clause cannot be evaluated in
the enclosing scope as they may depend on the values obtained from the
leftmost iterable. For example: "(x*y for x in range(10) for y in
range(x, x+10))".

The parentheses can be omitted on calls with only one argument.  See
section Calls for details.

To avoid interfering with the expected operation of the generator
expression itself, "yield" and "yield from" expressions are prohibited
in the implicitly defined generator.

If a generator expression contains either "async for" clauses or
"await" expressions it is called an *asynchronous generator
expression*.  An asynchronous generator expression returns a new
asynchronous generator object, which is an asynchronous iterator (see
Asynchronous Iterators).

Added in version 3.6: Asynchronous generator expressions were
introduced.

Changed in version 3.7: Prior to Python 3.7, asynchronous generator
expressions could only appear in "async def" coroutines.  Starting
with 3.7, any function can use asynchronous generator expressions.

Changed in version 3.8: "yield" and "yield from" prohibited in the
implicitly nested scope.


6.2.8. Yield expressions
------------------------

   yield_atom:       "(" yield_expression ")"
   yield_from:       "yield" "from" expression
   yield_expression: "yield" yield_list | yield_from

The yield expression is used when defining a *generator* function or
an *asynchronous generator* function and thus can only be used in the
body of a function definition.  Using a yield expression in a
function's body causes that function to be a generator function, and
using it in an "async def" function's body causes that coroutine
function to be an asynchronous generator function. For example:

   def gen():  # defines a generator function
       yield 123

   async def agen(): # defines an asynchronous generator function
       yield 123

Due to their side effects on the containing scope, "yield" expressions
are not permitted as part of the implicitly defined scopes used to
implement comprehensions and generator expressions.

Changed in version 3.8: Yield expressions prohibited in the implicitly
nested scopes used to implement comprehensions and generator
expressions.

Generator functions are described below, while asynchronous generator
functions are described separately in section Asynchronous generator
functions.

When a generator function is called, it returns an iterator known as a
generator.  That generator then controls the execution of the
generator function.  The execution starts when one of the generator's
methods is called. At that time, the execution proceeds to the first
yield expression, where it is suspended again, returning the value of
"yield_list" to the generator's caller, or "None" if "yield_list" is
omitted. By suspended, we mean that all local state is retained,
including the current bindings of local variables, the instruction
pointer, the internal evaluation stack, and the state of any exception
handling. When the execution is resumed by calling one of the
generator's methods, the function can proceed exactly as if the yield
expression were just another external call.  The value of the yield
expression after resuming depends on the method which resumed the
execution.  If "__next__()" is used (typically via either a "for" or
the "next()" builtin) then the result is "None".  Otherwise, if
"send()" is used, then the result will be the value passed in to that
method.

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 the execution should continue
after it yields; the control is always transferred to the generator's
caller.

Yield expressions are allowed anywhere in a "try" 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 "close()" method will be called, allowing any pending
"finally" clauses to execute.

When "yield from <expr>" is used, the supplied expression must be an
iterable. The values produced by iterating that iterable are passed
directly to the caller of the current generator's methods. Any values
passed in with "send()" and any exceptions passed in with "throw()"
are passed to the underlying iterator if it has the appropriate
methods.  If this is not the case, then "send()" will raise
"AttributeError" or "TypeError", while "throw()" will just raise the
passed in exception immediately.

When the underlying iterator is complete, the "value" attribute of the
raised "StopIteration" instance becomes the value of the yield
expression. It can be either set explicitly when raising
"StopIteration", or automatically when the subiterator is a generator
(by returning a value from the subgenerator).

Changed in version 3.3: Added "yield from <expr>" to delegate control
flow to a subiterator.

The parentheses may be omitted when the yield expression is the sole
expression on the right hand side of an assignment statement.

See also:

  **PEP 255** - Simple Generators
     The proposal for adding generators and the "yield" statement to
     Python.

  **PEP 342** - Coroutines via Enhanced Generators
     The proposal to enhance the API and syntax of generators, making
     them usable as simple coroutines.

  **PEP 380** - Syntax for Delegating to a Subgenerator
     The proposal to introduce the "yield_from" syntax, making
     delegation to subgenerators easy.

  **PEP 525** - Asynchronous Generators
     The proposal that expanded on **PEP 492** by adding generator
     capabilities to coroutine functions.


6.2.8.1. Generator-iterator methods
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This subsection describes the methods of a generator iterator.  They
can be used to control the execution of a generator function.

Note that calling any of the generator methods below when the
generator is already executing raises a "ValueError" exception.

generator.__next__()

   Starts the execution of a generator function or resumes it at the
   last executed yield expression.  When a generator function is
   resumed with a "__next__()" method, the current yield expression
   always evaluates to "None".  The execution then continues to the
   next yield expression, where the generator is suspended again, and
   the value of the "yield_list" is returned to "__next__()"'s caller.
   If the generator exits without yielding another value, a
   "StopIteration" exception is raised.

   This method is normally called implicitly, e.g. by a "for" loop, or
   by the built-in "next()" function.

generator.send(value)

   Resumes the execution and "sends" a value into the generator
   function.  The *value* argument becomes the result of the current
   yield expression.  The "send()" method returns the next value
   yielded by the generator, or raises "StopIteration" if the
   generator exits without yielding another value.  When "send()" is
   called to start the generator, it must be called with "None" as the
   argument, because there is no yield expression that could receive
   the value.

generator.throw(value)
generator.throw(type[, value[, traceback]])

   Raises an exception at the point where the generator was paused,
   and returns the next value yielded by the generator function.  If
   the generator exits without yielding another value, a
   "StopIteration" 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.

   In typical use, this is called with a single exception instance
   similar to the way the "raise" keyword is used.

   For backwards compatibility, however, the second signature is
   supported, following a convention from older versions of Python.
   The *type* argument should be an exception class, and *value*
   should be an exception instance. If the *value* is not provided,
   the *type* constructor is called to get an instance. If *traceback*
   is provided, it is set on the exception, otherwise any existing
   "__traceback__" attribute stored in *value* may be cleared.

   Changed in version 3.12: The second signature (type[, value[,
   traceback]]) is deprecated and may be removed in a future version
   of Python.

generator.close()

   Raises a "GeneratorExit" exception at the point where the generator
   function was paused (equivalent to calling "throw(GeneratorExit)").
   The exception is raised by the yield expression where the generator
   was paused. If the generator function catches the exception and
   returns a value, this value is returned from "close()".  If the
   generator function is already closed, or raises "GeneratorExit" (by
   not catching the exception), "close()" returns "None".  If the
   generator yields a value, a "RuntimeError" is raised.  If the
   generator raises any other exception, it is propagated to the
   caller.  If the generator has already exited due to an exception or
   normal exit, "close()" returns "None" and has no other effect.

   Changed in version 3.13: If a generator returns a value upon being
   closed, the value is returned by "close()".


6.2.8.2. Examples
~~~~~~~~~~~~~~~~~

Here is a simple example that demonstrates the behavior of generators
and generator functions:

   >>> def echo(value=None):
   ...     print("Execution starts when 'next()' is called for the first time.")
   ...     try:
   ...         while True:
   ...             try:
   ...                 value = (yield value)
   ...             except Exception as e:
   ...                 value = e
   ...     finally:
   ...         print("Don't forget to clean up when 'close()' is called.")
   ...
   >>> generator = echo(1)
   >>> print(next(generator))
   Execution starts when 'next()' is called for the first time.
   1
   >>> print(next(generator))
   None
   >>> print(generator.send(2))
   2
   >>> generator.throw(TypeError, "spam")
   TypeError('spam',)
   >>> generator.close()
   Don't forget to clean up when 'close()' is called.

For examples using "yield from", see PEP 380: Syntax for Delegating to
a Subgenerator in "What's New in Python."


6.2.8.3. Asynchronous generator functions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The presence of a yield expression in a function or method defined
using "async def" further defines the function as an *asynchronous
generator* function.

When an asynchronous generator function is called, it returns an
asynchronous iterator known as an asynchronous generator object. That
object then controls the execution of the generator function. An
asynchronous generator object is typically used in an "async for"
statement in a coroutine function analogously to how a generator
object would be used in a "for" statement.

Calling one of the asynchronous generator's methods returns an
*awaitable* object, and the execution starts when this object is
awaited on. At that time, the execution proceeds to the first yield
expression, where it is suspended again, returning the value of
"yield_list" to the awaiting coroutine. As with a generator,
suspension means that all local state is retained, including the
current bindings of local variables, the instruction pointer, the
internal evaluation stack, and the state of any exception handling.
When the execution is resumed by awaiting on the next object returned
by the asynchronous generator's methods, the function can proceed
exactly as if the yield expression were just another external call.
The value of the yield expression after resuming depends on the method
which resumed the execution.  If "__anext__()" is used then the result
is "None". Otherwise, if "asend()" is used, then the result will be
the value passed in to that method.

If an asynchronous generator happens to exit early by "break", the
caller task being cancelled, or other exceptions, the generator's
async cleanup code will run and possibly raise exceptions or access
context variables in an unexpected context--perhaps after the lifetime
of tasks it depends, or during the event loop shutdown when the async-
generator garbage collection hook is called. To prevent this, the
caller must explicitly close the async generator by calling "aclose()"
method to finalize the generator and ultimately detach it from the
event loop.

In an asynchronous generator function, yield expressions are allowed
anywhere in a "try" construct. However, if an asynchronous generator
is not resumed before it is finalized (by reaching a zero reference
count or by being garbage collected), then a yield expression within a
"try" construct could result in a failure to execute pending "finally"
clauses.  In this case, it is the responsibility of the event loop or
scheduler running the asynchronous generator to call the asynchronous
generator-iterator's "aclose()" method and run the resulting coroutine
object, thus allowing any pending "finally" clauses to execute.

To take care of finalization upon event loop termination, an event
loop should define a *finalizer* function which takes an asynchronous
generator-iterator and presumably calls "aclose()" and executes the
coroutine. This  *finalizer* may be registered by calling
"sys.set_asyncgen_hooks()". When first iterated over, an asynchronous
generator-iterator will store the registered *finalizer* to be called
upon finalization. For a reference example of a *finalizer* method see
the implementation of "asyncio.Loop.shutdown_asyncgens" in
Lib/asyncio/base_events.py.

The expression "yield from <expr>" is a syntax error when used in an
asynchronous generator function.


6.2.8.4. Asynchronous generator-iterator methods
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This subsection describes the methods of an asynchronous generator
iterator, which are used to control the execution of a generator
function.

async agen.__anext__()

   Returns an awaitable which when run starts to execute the
   asynchronous generator or resumes it at the last executed yield
   expression.  When an asynchronous generator function is resumed
   with an "__anext__()" method, the current yield expression always
   evaluates to "None" in the returned awaitable, which when run will
   continue to the next yield expression. The value of the
   "yield_list" of the yield expression is the value of the
   "StopIteration" exception raised by the completing coroutine.  If
   the asynchronous generator exits without yielding another value,
   the awaitable instead raises a "StopAsyncIteration" exception,
   signalling that the asynchronous iteration has completed.

   This method is normally called implicitly by a "async for" loop.

async agen.asend(value)

   Returns an awaitable which when run resumes the execution of the
   asynchronous generator. As with the "send()" method for a
   generator, this "sends" a value into the asynchronous generator
   function, and the *value* argument becomes the result of the
   current yield expression. The awaitable returned by the "asend()"
   method will return the next value yielded by the generator as the
   value of the raised "StopIteration", or raises "StopAsyncIteration"
   if the asynchronous generator exits without yielding another value.
   When "asend()" is called to start the asynchronous generator, it
   must be called with "None" as the argument, because there is no
   yield expression that could receive the value.

async agen.athrow(value)
async agen.athrow(type[, value[, traceback]])

   Returns an awaitable that raises an exception of type "type" at the
   point where the asynchronous generator was paused, and returns the
   next value yielded by the generator function as the value of the
   raised "StopIteration" exception.  If the asynchronous generator
   exits without yielding another value, a "StopAsyncIteration"
   exception is raised by the awaitable. If the generator function
   does not catch the passed-in exception, or raises a different
   exception, then when the awaitable is run that exception propagates
   to the caller of the awaitable.

   Changed in version 3.12: The second signature (type[, value[,
   traceback]]) is deprecated and may be removed in a future version
   of Python.

async agen.aclose()

   Returns an awaitable that when run will throw a "GeneratorExit"
   into the asynchronous generator function at the point where it was
   paused. If the asynchronous generator function then exits
   gracefully, is already closed, or raises "GeneratorExit" (by not
   catching the exception), then the returned awaitable will raise a
   "StopIteration" exception. Any further awaitables returned by
   subsequent calls to the asynchronous generator will raise a
   "StopAsyncIteration" exception.  If the asynchronous generator
   yields a value, a "RuntimeError" is raised by the awaitable.  If
   the asynchronous generator raises any other exception, it is
   propagated to the caller of the awaitable.  If the asynchronous
   generator has already exited due to an exception or normal exit,
   then further calls to "aclose()" will return an awaitable that does
   nothing.


6.3. Primaries
==============

Primaries represent the most tightly bound operations of the language.
Their syntax is:

   primary: atom | attributeref | subscription | call


6.3.1. Attribute references
---------------------------

An attribute reference is a primary followed by a period and a name:

   attributeref: primary "." identifier

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. The type
and value produced is determined by the object.  Multiple evaluations
of the same attribute reference may yield different objects.

This production can be customized by overriding the
"__getattribute__()" method or the "__getattr__()" method.  The
"__getattribute__()" method is called first and either returns a value
or raises "AttributeError" if the attribute is not available.

If an "AttributeError" is raised and the object has a "__getattr__()"
method, that method is called as a fallback.


6.3.2. Subscriptions and slicings
---------------------------------

The *subscription* syntax is usually used for selecting an element
from a container -- for example, to get a value from a "dict":

   >>> digits_by_name = {'one': 1, 'two': 2}
   >>> digits_by_name['two']  # Subscripting a dictionary using the key 'two'
   2

In the subscription syntax, the object being subscribed -- a primary
-- is followed by a *subscript* in square brackets. In the simplest
case, the subscript is a single expression.

Depending on the type of the object being subscribed, the subscript is
sometimes called a *key* (for mappings), *index* (for sequences), or
*type argument* (for *generic types*). Syntactically, these are all
equivalent:

   >>> colors = ['red', 'blue', 'green', 'black']
   >>> colors[3]  # Subscripting a list using the index 3
   'black'

   >>> list[str]  # Parameterizing the list type using the type argument str
   list[str]

At runtime, the interpreter will evaluate the primary and the
subscript, and call the primary's "__getitem__()" or
"__class_getitem__()" *special method* with the subscript as argument.
For more details on which of these methods is called, see
__class_getitem__ versus __getitem__.

To show how subscription works, we can define a custom object that
implements "__getitem__()" and prints out the value of the subscript:

   >>> class SubscriptionDemo:
   ...     def __getitem__(self, key):
   ...         print(f'subscripted with: {key!r}')
   ...
   >>> demo = SubscriptionDemo()
   >>> demo[1]
   subscripted with: 1
   >>> demo['a' * 3]
   subscripted with: 'aaa'

See "__getitem__()" documentation for how built-in types handle
subscription.

Subscriptions may also be used as targets in assignment or deletion
statements. In these cases, the interpreter will call the subscripted
object's "__setitem__()" or "__delitem__()" *special method*,
respectively, instead of "__getitem__()".

   >>> colors = ['red', 'blue', 'green', 'black']
   >>> colors[3] = 'white'  # Setting item at index
   >>> colors
   ['red', 'blue', 'green', 'white']
   >>> del colors[3]  # Deleting item at index 3
   >>> colors
   ['red', 'blue', 'green']

All advanced forms of *subscript* documented in the following sections
are also usable for assignment and deletion.


6.3.2.1. Slicings
~~~~~~~~~~~~~~~~~

A more advanced form of subscription, *slicing*, is commonly used to
extract a portion of a sequence. In this form, the subscript is a
*slice*: up to three expressions separated by colons. Any of the
expressions may be omitted, but a slice must contain at least one
colon:

   >>> number_names = ['zero', 'one', 'two', 'three', 'four', 'five']
   >>> number_names[1:3]
   ['one', 'two']
   >>> number_names[1:]
   ['one', 'two', 'three', 'four', 'five']
   >>> number_names[:3]
   ['zero', 'one', 'two']
   >>> number_names[:]
   ['zero', 'one', 'two', 'three', 'four', 'five']
   >>> number_names[::2]
   ['zero', 'two', 'four']
   >>> number_names[:-3]
   ['zero', 'one', 'two']
   >>> del number_names[4:]
   >>> number_names
   ['zero', 'one', 'two', 'three']

When a slice is evaluated, the interpreter constructs a "slice" object
whose "start", "stop" and "step" attributes, respectively, are the
results of the expressions between the colons. Any missing expression
evaluates to "None". This "slice" object is then passed to the
"__getitem__()" or "__class_getitem__()" *special method*, as above.

   # continuing with the SubscriptionDemo instance defined above:
   >>> demo[2:3]
   subscripted with: slice(2, 3, None)
   >>> demo[::'spam']
   subscripted with: slice(None, None, 'spam')


6.3.2.2. Comma-separated subscripts
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The subscript can also be given as two or more comma-separated
expressions or slices:

   # continuing with the SubscriptionDemo instance defined above:
   >>> demo[1, 2, 3]
   subscripted with: (1, 2, 3)
   >>> demo[1:2, 3]
   subscripted with: (slice(1, 2, None), 3)

This form is commonly used with numerical libraries for slicing multi-
dimensional data. In this case, the interpreter constructs a "tuple"
of the results of the expressions or slices, and passes this tuple to
the "__getitem__()" or "__class_getitem__()" *special method*, as
above.

The subscript may also be given as a single expression or slice
followed by a comma, to specify a one-element tuple:

   >>> demo['spam',]
   subscripted with: ('spam',)


6.3.2.3. "Starred" subscriptions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Added in version 3.11: Expressions in *tuple_slices* may be starred.
See **PEP 646**.

The subscript can also contain a starred expression. In this case, the
interpreter unpacks the result into a tuple, and passes this tuple to
"__getitem__()" or "__class_getitem__()":

   # continuing with the SubscriptionDemo instance defined above:
   >>> demo[*range(10)]
   subscripted with: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

Starred expressions may be combined with comma-separated expressions
and slices:

   >>> demo['a', 'b', *range(3), 'c']
   subscripted with: ('a', 'b', 0, 1, 2, 'c')


6.3.2.4. Formal subscription grammar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

   subscription:     primary '[' subscript ']'
   subscript:        single_subscript | tuple_subscript
   single_subscript: proper_slice | assignment_expression
   proper_slice:     [expression] ":" [expression] [ ":" [expression] ]
   tuple_subscript:  ','.(single_subscript | starred_expression)+ [',']

Recall that the "|" operator denotes ordered choice. Specifically, in
"subscript", if both alternatives would match, the first
("single_subscript") has priority.


6.3.3. Calls
------------

A call calls a callable object (e.g., a *function*) with a possibly
empty series of *arguments*:

   call:                 primary "(" [argument_list [","] | comprehension] ")"
   argument_list:        positional_arguments ["," starred_and_keywords]
                           ["," keywords_arguments]
                         | starred_and_keywords ["," keywords_arguments]
                         | keywords_arguments
   positional_arguments: positional_item ("," positional_item)*
   positional_item:      assignment_expression | "*" expression
   starred_and_keywords: ("*" expression | keyword_item)
                         ("," "*" expression | "," keyword_item)*
   keywords_arguments:   (keyword_item | "**" expression)
                         ("," keyword_item | "," "**" expression)*
   keyword_item:         identifier "=" expression

An optional trailing comma may be present after the positional and
keyword arguments but does not affect the semantics.

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
"__call__()" method are callable).  All argument expressions are
evaluated before the call is attempted.  Please refer to section
Function definitions for the syntax of formal *parameter* lists.

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 "TypeError" exception is raised. Otherwise, the
argument is placed in the slot, filling it (even if the expression is
"None", 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 "TypeError" exception
is raised.  Otherwise, the list of filled slots is used as the
argument list for the call.

**CPython implementation detail:** 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 "PyArg_ParseTuple()" to parse
their arguments.

If there are more positional arguments than there are formal parameter
slots, a "TypeError" exception is raised, unless a formal parameter
using the syntax "*identifier" 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).

If any keyword argument does not correspond to a formal parameter
name, a "TypeError" exception is raised, unless a formal parameter
using the syntax "**identifier" 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.

If the syntax "*expression" appears in the function call, "expression"
must evaluate to an *iterable*.  Elements from these iterables are
treated as if they were additional positional arguments.  For the call
"f(x1, x2, *y, x3, x4)", if *y* evaluates to a sequence *y1*, ...,
*yM*, this is equivalent to a call with M+4 positional arguments *x1*,
*x2*, *y1*, ..., *yM*, *x3*, *x4*.

A consequence of this is that although the "*expression" syntax may
appear *after* explicit keyword arguments, it is processed *before*
the keyword arguments (and any "**expression" arguments -- see below).
So:

   >>> def f(a, b):
   ...     print(a, b)
   ...
   >>> f(b=1, *(2,))
   2 1
   >>> f(a=1, *(2,))
   Traceback (most recent call last):
     File "<stdin>", line 1, in <module>
   TypeError: f() got multiple values for keyword argument 'a'
   >>> f(1, *(2,))
   1 2

It is unusual for both keyword arguments and the "*expression" syntax
to be used in the same call, so in practice this confusion does not
often arise.

If the syntax "**expression" appears in the function call,
"expression" must evaluate to a *mapping*, the contents of which are
treated as additional keyword arguments. If a parameter matching a key
has already been given a value (by an explicit keyword argument, or
from another unpacking), a "TypeError" exception is raised.

When "**expression" is used, each key in this mapping must be a
string. Each value from the mapping is assigned to the first formal
parameter eligible for keyword assignment whose name is equal to the
key. A key need not be a Python identifier (e.g. ""max-temp °F"" is
acceptable, although it will not match any formal parameter that could
be declared). If there is no match to a formal parameter the key-value
pair is collected by the "**" parameter, if there is one, or if there
is not, a "TypeError" exception is raised.

Formal parameters using the syntax "*identifier" or "**identifier"
cannot be used as positional argument slots or as keyword argument
names.

Changed in version 3.5: Function calls accept any number of "*" and
"**" unpackings, positional arguments may follow iterable unpackings
("*"), and keyword arguments may follow dictionary unpackings ("**").
Originally proposed by **PEP 448**.

A call always returns some value, possibly "None", unless it raises an
exception.  How this value is computed depends on the type of the
callable object.

If it is---

a user-defined function:
   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
   Function definitions.  When the code block executes a "return"
   statement, this specifies the return value of the function call.
   If execution reaches the end of the code block without executing a
   "return" statement, the return value is "None".

a built-in function or method:
   The result is up to the interpreter; see Built-in Functions for the
   descriptions of built-in functions and methods.

a class object:
   A new instance of that class is returned.

a class instance method:
   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.

a class instance:
   The class must define a "__call__()" method; the effect is then the
   same as if that method was called.


6.4. Await expression
=====================

Suspend the execution of *coroutine* on an *awaitable* object. Can
only be used inside a *coroutine function*.

   await_expr: "await" primary

Added in version 3.5.


6.5. The power operator
=======================

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:

   power: (await_expr | primary) ["**" u_expr]

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): "-1**2" results in "-1".

The power operator has the same semantics as the built-in "pow()"
function, when called with two arguments: it yields its left argument
raised to the power of its right argument. Numeric arguments are first
converted to a common type, and the result is of that type.

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,
"10**2" returns "100", but "10**-2" returns "0.01".

Raising "0.0" to a negative power results in a "ZeroDivisionError".
Raising a negative number to a fractional power results in a "complex"
number. (In earlier versions it raised a "ValueError".)

This operation can be customized using the special "__pow__()" and
"__rpow__()" methods.


6.6. Unary arithmetic and bitwise operations
============================================

All unary arithmetic and bitwise operations have the same priority:

   u_expr: power | "-" u_expr | "+" u_expr | "~" u_expr

The unary "-" (minus) operator yields the negation of its numeric
argument; the operation can be overridden with the "__neg__()" special
method.

The unary "+" (plus) operator yields its numeric argument unchanged;
the operation can be overridden with the "__pos__()" special method.

The unary "~" (invert) operator yields the bitwise inversion of its
integer argument.  The bitwise inversion of "x" is defined as
"-(x+1)".  It only applies to integral numbers or to custom objects
that override the "__invert__()" special method.

In all three cases, if the argument does not have the proper type, a
"TypeError" exception is raised.


6.7. Binary arithmetic operations
=================================

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:

   m_expr: u_expr | m_expr "*" u_expr | m_expr "@" m_expr |
           m_expr "//" u_expr | m_expr "/" u_expr |
           m_expr "%" u_expr
   a_expr: m_expr | a_expr "+" m_expr | a_expr "-" m_expr

The "*" (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 real type and then multiplied
together.  In the latter case, sequence repetition is performed; a
negative repetition factor yields an empty sequence.

This operation can be customized using the special "__mul__()" and
"__rmul__()" methods.

Changed in version 3.14: If only one operand is a complex number, the
other operand is converted to a floating-point number.

The "@" (at) operator is intended to be used for matrix
multiplication.  No builtin Python types implement this operator.

This operation can be customized using the special "__matmul__()" and
"__rmatmul__()" methods.

Added in version 3.5.

The "/" (division) and "//" (floor division) operators yield the
quotient of their arguments.  The numeric arguments are first
converted to a common type. Division of integers 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 "ZeroDivisionError" exception.

The division operation can be customized using the special
"__truediv__()" and "__rtruediv__()" methods. The floor division
operation can be customized using the special "__floordiv__()" and
"__rfloordiv__()" methods.

The "%" (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
"ZeroDivisionError" exception.  The arguments may be floating-point
numbers, e.g., "3.14%0.7" equals "0.34" (since "3.14" equals "4*0.7 +
0.34".)  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 [1].

The floor division and modulo operators are connected by the following
identity: "x == (x//y)*y + (x%y)".  Floor division and modulo are also
connected with the built-in function "divmod()": "divmod(x, y) ==
(x//y, x%y)". [2].

In addition to performing the modulo operation on numbers, the "%"
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 printf-style String Formatting.

The *modulo* operation can be customized using the special "__mod__()"
and "__rmod__()" methods.

The floor division operator, the modulo operator, and the "divmod()"
function are not defined for complex numbers.  Instead, convert to a
floating-point number using the "abs()" function if appropriate.

The "+" (addition) operator yields the sum of its arguments.  The
arguments must either both be numbers or both be sequences of the same
type.  In the former case, the numbers are converted to a common real
type and then added together. In the latter case, the sequences are
concatenated.

This operation can be customized using the special "__add__()" and
"__radd__()" methods.

Changed in version 3.14: If only one operand is a complex number, the
other operand is converted to a floating-point number.

The "-" (subtraction) operator yields the difference of its arguments.
The numeric arguments are first converted to a common real type.

This operation can be customized using the special "__sub__()" and
"__rsub__()" methods.

Changed in version 3.14: If only one operand is a complex number, the
other operand is converted to a floating-point number.


6.8. Shifting operations
========================

The shifting operations have lower priority than the arithmetic
operations:

   shift_expr: a_expr | shift_expr ("<<" | ">>") a_expr

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.

The left shift operation can be customized using the special
"__lshift__()" and "__rlshift__()" methods. The right shift operation
can be customized using the special "__rshift__()" and "__rrshift__()"
methods.

A right shift by *n* bits is defined as floor division by "pow(2,n)".
A left shift by *n* bits is defined as multiplication with "pow(2,n)".


6.9. Binary bitwise operations
==============================

Each of the three bitwise operations has a different priority level:

   and_expr: shift_expr | and_expr "&" shift_expr
   xor_expr: and_expr | xor_expr "^" and_expr
   or_expr:  xor_expr | or_expr "|" xor_expr

The "&" operator yields the bitwise AND of its arguments, which must
be integers or one of them must be a custom object overriding
"__and__()" or "__rand__()" special methods.

The "^" operator yields the bitwise XOR (exclusive OR) of its
arguments, which must be integers or one of them must be a custom
object overriding "__xor__()" or "__rxor__()" special methods.

The "|" operator yields the bitwise (inclusive) OR of its arguments,
which must be integers or one of them must be a custom object
overriding "__or__()" or "__ror__()" special methods.


6.10. Comparisons
=================

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 "a < b < c" have the
interpretation that is conventional in mathematics:

   comparison:    or_expr (comp_operator or_expr)*
   comp_operator: "<" | ">" | "==" | ">=" | "<=" | "!="
                  | "is" ["not"] | ["not"] "in"

Comparisons yield boolean values: "True" or "False". Custom *rich
comparison methods* may return non-boolean values. In this case Python
will call "bool()" on such value in boolean contexts.

Comparisons can be chained arbitrarily, e.g., "x < y <= z" is
equivalent to "x < y and y <= z", except that "y" is evaluated only
once (but in both cases "z" is not evaluated at all when "x < y" is
found to be false).

Formally, if *a*, *b*, *c*, ..., *y*, *z* are expressions and *op1*,
*op2*, ..., *opN* are comparison operators, then "a op1 b op2 c ... y
opN z" is equivalent to "a op1 b and b op2 c and ... y opN z", except
that each expression is evaluated at most once.

Note that "a op1 b op2 c" doesn't imply any kind of comparison between
*a* and *c*, so that, e.g., "x < y > z" is perfectly legal (though
perhaps not pretty).


6.10.1. Value comparisons
-------------------------

The operators "<", ">", "==", ">=", "<=", and "!=" compare the values
of two objects.  The objects do not need to have the same type.

Chapter Objects, values and types states that objects have a value (in
addition to type and identity).  The value of an object is a rather
abstract notion in Python: For example, there is no canonical access
method for an object's value.  Also, there is no requirement that the
value of an object should be constructed in a particular way, e.g.
comprised of all its data attributes. Comparison operators implement a
particular notion of what the value of an object is.  One can think of
them as defining the value of an object indirectly, by means of their
comparison implementation.

Because all types are (direct or indirect) subtypes of "object", they
inherit the default comparison behavior from "object".  Types can
customize their comparison behavior by implementing *rich comparison
methods* like "__lt__()", described in Basic customization.

The default behavior for equality comparison ("==" and "!=") is based
on the identity of the objects.  Hence, equality comparison of
instances with the same identity results in equality, and equality
comparison of instances with different identities results in
inequality.  A motivation for this default behavior is the desire that
all objects should be reflexive (i.e. "x is y" implies "x == y").

A default order comparison ("<", ">", "<=", and ">=") is not provided;
an attempt raises "TypeError".  A motivation for this default behavior
is the lack of a similar invariant as for equality.

The behavior of the default equality comparison, that instances with
different identities are always unequal, may be in contrast to what
types will need that have a sensible definition of object value and
value-based equality.  Such types will need to customize their
comparison behavior, and in fact, a number of built-in types have done
that.

The following list describes the comparison behavior of the most
important built-in types.

* Numbers of built-in numeric types (Numeric Types --- int, float,
  complex) and of the standard library types "fractions.Fraction" and
  "decimal.Decimal" can be compared within and across their types,
  with the restriction that complex numbers do not support order
  comparison.  Within the limits of the types involved, they compare
  mathematically (algorithmically) correct without loss of precision.

  The not-a-number values "float('NaN')" and "decimal.Decimal('NaN')"
  are special.  Any ordered comparison of a number to a not-a-number
  value is false. A counter-intuitive implication is that not-a-number
  values are not equal to themselves.  For example, if "x =
  float('NaN')", "3 < x", "x < 3" and "x == x" are all false, while "x
  != x" is true.  This behavior is compliant with IEEE 754.

* "None" and "NotImplemented" are singletons.  **PEP 8** advises that
  comparisons for singletons should always be done with "is" or "is
  not", never the equality operators.

* Binary sequences (instances of "bytes" or "bytearray") can be
  compared within and across their types.  They compare
  lexicographically using the numeric values of their elements.

* Strings (instances of "str") compare lexicographically using the
  numerical Unicode code points (the result of the built-in function
  "ord()") of their characters. [3]

  Strings and binary sequences cannot be directly compared.

* Sequences (instances of "tuple", "list", or "range") can be compared
  only within each of their types, with the restriction that ranges do
  not support order comparison.  Equality comparison across these
  types results in inequality, and ordering comparison across these
  types raises "TypeError".

  Sequences compare lexicographically using comparison of
  corresponding elements.  The built-in containers typically assume
  identical objects are equal to themselves.  That lets them bypass
  equality tests for identical objects to improve performance and to
  maintain their internal invariants.

  Lexicographical comparison between built-in collections works as
  follows:

  * For two collections to compare equal, they must be of the same
    type, have the same length, and each pair of corresponding
    elements must compare equal (for example, "[1,2] == (1,2)" is
    false because the type is not the same).

  * Collections that support order comparison are ordered the same as
    their first unequal elements (for example, "[1,2,x] <= [1,2,y]"
    has the same value as "x <= y").  If a corresponding element does
    not exist, the shorter collection is ordered first (for example,
    "[1,2] < [1,2,3]" is true).

* Mappings (instances of "dict") compare equal if and only if they
  have equal "(key, value)" pairs. Equality comparison of the keys and
  values enforces reflexivity.

  Order comparisons ("<", ">", "<=", and ">=") raise "TypeError".

* Sets (instances of "set" or "frozenset") can be compared within and
  across their types.

  They define order comparison operators to mean subset and superset
  tests.  Those relations do not define total orderings (for example,
  the two sets "{1,2}" 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, "min()", "max()", and "sorted()" produce undefined
  results given a list of sets as inputs).

  Comparison of sets enforces reflexivity of its elements.

* Most other built-in types have no comparison methods implemented, so
  they inherit the default comparison behavior.

User-defined classes that customize their comparison behavior should
follow some consistency rules, if possible:

* Equality comparison should be reflexive. In other words, identical
  objects should compare equal:

     "x is y" implies "x == y"

* Comparison should be symmetric. In other words, the following
  expressions should have the same result:

     "x == y" and "y == x"

     "x != y" and "y != x"

     "x < y" and "y > x"

     "x <= y" and "y >= x"

* Comparison should be transitive. The following (non-exhaustive)
  examples illustrate that:

     "x > y and y > z" implies "x > z"

     "x < y and y <= z" implies "x < z"

* Inverse comparison should result in the boolean negation. In other
  words, the following expressions should have the same result:

     "x == y" and "not x != y"

     "x < y" and "not x >= y" (for total ordering)

     "x > y" and "not x <= y" (for total ordering)

  The last two expressions apply to totally ordered collections (e.g.
  to sequences, but not to sets or mappings). See also the
  "@~functools.total_ordering" decorator.

* The "hash()" result should be consistent with equality. Objects that
  are equal should either have the same hash value, or be marked as
  unhashable.

Python does not enforce these consistency rules. In fact, the
not-a-number values are an example for not following these rules.


6.10.2. Membership test operations
----------------------------------

The operators "in" and "not in" test for membership.  "x in s"
evaluates to "True" if *x* is a member of *s*, and "False" otherwise.
"x not in s" returns the negation of "x in s".  All built-in sequences
and set types support this as well as dictionary, for which "in" tests
whether the dictionary has a given key. For container types such as
list, tuple, set, frozenset, dict, or collections.deque, the
expression "x in y" is equivalent to "any(x is e or x == e for e in
y)".

For the string and bytes types, "x in y" is "True" if and only if *x*
is a substring of *y*.  An equivalent test is "y.find(x) != -1".
Empty strings are always considered to be a substring of any other
string, so """ in "abc"" will return "True".

For user-defined classes which define the "__contains__()" method, "x
in y" returns "True" if "y.__contains__(x)" returns a true value, and
"False" otherwise.

For user-defined classes which do not define "__contains__()" but do
define "__iter__()", "x in y" is "True" if some value "z", for which
the expression "x is z or x == z" is true, is produced while iterating
over "y". If an exception is raised during the iteration, it is as if
"in" raised that exception.

Lastly, the old-style iteration protocol is tried: if a class defines
"__getitem__()", "x in y" is "True" if and only if there is a non-
negative integer index *i* such that "x is y[i] or x == y[i]", and no
lower integer index raises the "IndexError" exception.  (If any other
exception is raised, it is as if "in" raised that exception).

The operator "not in" is defined to have the inverse truth value of
"in".


6.10.3. Identity comparisons
----------------------------

The operators "is" and "is not" test for an object's identity: "x is
y" is true if and only if *x* and *y* are the same object.  An
Object's identity is determined using the "id()" function.  "x is not
y" yields the inverse truth value. [4]


6.11. Boolean operations
========================

   or_test:  and_test | or_test "or" and_test
   and_test: not_test | and_test "and" not_test
   not_test: comparison | "not" not_test

In the context of Boolean operations, and also when expressions are
used by control flow statements, the following values are interpreted
as false: "False", "None", zero of any numeric type, 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
"__bool__()" method.

The operator "not" yields "True" if its argument is false, "False"
otherwise.

The expression "x and y" first evaluates *x*; if *x* is false, its
value is returned; otherwise, *y* is evaluated and the resulting value
is returned.

The expression "x or y" first evaluates *x*; if *x* is true, its value
is returned; otherwise, *y* is evaluated and the resulting value is
returned.

Note that neither "and" nor "or" restrict the value and type they
return to "False" and "True", but rather return the last evaluated
argument.  This is sometimes useful, e.g., if "s" is a string that
should be replaced by a default value if it is empty, the expression
"s or 'foo'" yields the desired value.  Because "not" has to create a
new value, it returns a boolean value regardless of the type of its
argument (for example, "not 'foo'" produces "False" rather than "''".)


6.12. Assignment expressions
============================

   assignment_expression: [identifier ":="] expression

An assignment expression (sometimes also called a "named expression"
or "walrus") assigns an "expression" to an "identifier", while also
returning the value of the "expression".

One common use case is when handling matched regular expressions:

   if matching := pattern.search(data):
       do_something(matching)

Or, when processing a file stream in chunks:

   while chunk := file.read(9000):
       process(chunk)

Assignment expressions must be surrounded by parentheses when used as
expression statements and when used as sub-expressions in slicing,
conditional, lambda, keyword-argument, and comprehension-if
expressions and in "assert", "with", and "assignment" statements. In
all other places where they can be used, parentheses are not required,
including in "if" and "while" statements.

Added in version 3.8: See **PEP 572** for more details about
assignment expressions.


6.13. Conditional expressions
=============================

   conditional_expression: or_test ["if" or_test "else" expression]
   expression:             conditional_expression | lambda_expr

A conditional expression (sometimes called a "ternary operator") is an
alternative to the if-else statement. As it is an expression, it
returns a value and can appear as a sub-expression.

The expression "x if C else y" first evaluates the condition, *C*
rather than *x*. If *C* is true, *x* is evaluated and its value is
returned; otherwise, *y* is evaluated and its value is returned.

See **PEP 308** for more details about conditional expressions.


6.14. Lambdas
=============

   lambda_expr: "lambda" [parameter_list] ":" expression

Lambda expressions (sometimes called lambda forms) are used to create
anonymous functions. The expression "lambda parameters: expression"
yields a function object.  The unnamed object behaves like a function
object defined with:

   def <lambda>(parameters):
       return expression

See section Function definitions for the syntax of parameter lists.
Note that functions created with lambda expressions cannot contain
statements or annotations.


6.15. Expression lists
======================

   starred_expression:       "*" or_expr | expression
   flexible_expression:      assignment_expression | starred_expression
   flexible_expression_list: flexible_expression ("," flexible_expression)* [","]
   starred_expression_list:  starred_expression ("," starred_expression)* [","]
   expression_list:          expression ("," expression)* [","]
   yield_list:               expression_list | starred_expression "," [starred_expression_list]

Except when part of a list or set display, 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.

A trailing comma is required only to create a one-item tuple, such as
"1,"; 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: "()".)


6.15.1. Iterable unpacking
--------------------------

In an expression list or tuple, list or set display, any expression
may be prefixed with an asterisk ("*"). This denotes *iterable
unpacking*.

At runtime, the asterisk-prefixed expression must evaluate to an
*iterable*. The iterable is expanded into a sequence of items, which
are included in the new tuple, list, or set, at the site of the
unpacking.

Added in version 3.5: Iterable unpacking in expression lists,
originally proposed by **PEP 448**.

Added in version 3.11: Any item in an expression list may be starred.
See **PEP 646**.


6.16. Evaluation order
======================

Python evaluates expressions from left to right.  Notice that while
evaluating an assignment, the right-hand side is evaluated before the
left-hand side.

In the following lines, expressions will be evaluated in the
arithmetic order of their suffixes:

   expr1, expr2, expr3, expr4
   (expr1, expr2, expr3, expr4)
   {expr1: expr2, expr3: expr4}
   expr1 + expr2 * (expr3 - expr4)
   expr1(expr2, expr3, *expr4, **expr5)
   expr3, expr4 = expr1, expr2


6.17. Operator precedence
=========================

The following table summarizes the operator precedence in Python, from
highest precedence (most binding) to lowest precedence (least
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 exponentiation and
conditional expressions, which group from right to left).

Note that comparisons, membership tests, and identity tests, all have
the same precedence and have a left-to-right chaining feature as
described in the Comparisons section.

+-------------------------------------------------+---------------------------------------+
| Operator                                        | Description                           |
|=================================================|=======================================|
| "(expressions...)",  "[expressions...]", "{key: | Binding or parenthesized expression,  |
| value...}", "{expressions...}"                  | list display, dictionary display, set |
|                                                 | display                               |
+-------------------------------------------------+---------------------------------------+
| "x[index]", "x[index:index]" "x(arguments...)", | Subscription (including slicing),     |
| "x.attribute"                                   | call, attribute reference             |
+-------------------------------------------------+---------------------------------------+
| "await x"                                       | Await expression                      |
+-------------------------------------------------+---------------------------------------+
| "**"                                            | Exponentiation [5]                    |
+-------------------------------------------------+---------------------------------------+
| "+x", "-x", "~x"                                | Positive, negative, bitwise NOT       |
+-------------------------------------------------+---------------------------------------+
| "*", "@", "/", "//", "%"                        | Multiplication, matrix                |
|                                                 | multiplication, division, floor       |
|                                                 | division, remainder [6]               |
+-------------------------------------------------+---------------------------------------+
| "+", "-"                                        | Addition and subtraction              |
+-------------------------------------------------+---------------------------------------+
| "<<", ">>"                                      | Shifts                                |
+-------------------------------------------------+---------------------------------------+
| "&"                                             | Bitwise AND                           |
+-------------------------------------------------+---------------------------------------+
| "^"                                             | Bitwise XOR                           |
+-------------------------------------------------+---------------------------------------+
| "|"                                             | Bitwise OR                            |
+-------------------------------------------------+---------------------------------------+
| "in", "not in", "is", "is not", "<", "<=", ">", | Comparisons, including membership     |
| ">=", "!=", "=="                                | tests and identity tests              |
+-------------------------------------------------+---------------------------------------+
| "not x"                                         | Boolean NOT                           |
+-------------------------------------------------+---------------------------------------+
| "and"                                           | Boolean AND                           |
+-------------------------------------------------+---------------------------------------+
| "or"                                            | Boolean OR                            |
+-------------------------------------------------+---------------------------------------+
| "if" -- "else"                                  | Conditional expression                |
+-------------------------------------------------+---------------------------------------+
| "lambda"                                        | Lambda expression                     |
+-------------------------------------------------+---------------------------------------+
| ":="                                            | Assignment expression                 |
+-------------------------------------------------+---------------------------------------+

-[ Footnotes ]-

[1] While "abs(x%y) < abs(y)" 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 "-1e-100 % 1e100" have the same
    sign as "1e100", the computed result is "-1e-100 + 1e100", which
    is numerically exactly equal to "1e100".  The function
    "math.fmod()" returns a result whose sign matches the sign of the
    first argument instead, and so returns "-1e-100" in this case.
    Which approach is more appropriate depends on the application.

[2] If x is very close to an exact integer multiple of y, it's
    possible for "x//y" to be one larger than "(x-x%y)//y" due to
    rounding.  In such cases, Python returns the latter result, in
    order to preserve that "divmod(x,y)[0] * y + x % y" be very close
    to "x".

[3] The Unicode standard distinguishes between *code points* (e.g.
    U+0041) and *abstract characters* (e.g. "LATIN CAPITAL LETTER A").
    While most abstract characters in Unicode are only represented
    using one code point, there is a number of abstract characters
    that can in addition be represented using a sequence of more than
    one code point.  For example, the abstract character "LATIN
    CAPITAL LETTER C WITH CEDILLA" can be represented as a single
    *precomposed character* at code position U+00C7, or as a sequence
    of a *base character* at code position U+0043 (LATIN CAPITAL
    LETTER C), followed by a *combining character* at code position
    U+0327 (COMBINING CEDILLA).

    The comparison operators on strings compare at the level of
    Unicode code points. This may be counter-intuitive to humans.  For
    example, ""\u00C7" == "\u0043\u0327"" is "False", even though both
    strings represent the same abstract character "LATIN CAPITAL
    LETTER C WITH CEDILLA".

    To compare strings at the level of abstract characters (that is,
    in a way intuitive to humans), use "unicodedata.normalize()".

[4] Due to automatic garbage-collection, free lists, and the dynamic
    nature of descriptors, you may notice seemingly unusual behaviour
    in certain uses of the "is" operator, like those involving
    comparisons between instance methods, or constants.  Check their
    documentation for more info.

[5] The power operator "**" binds less tightly than an arithmetic or
    bitwise unary operator on its right, that is, "2**-1" is "0.5".

[6] The "%" operator is also used for string formatting; the same
    precedence applies.
