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

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

**Syntax Notes:** 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

   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 type,” this means
that the operator implementation for built-in types works as follows:

* If either argument is a complex number, the other is converted to
  complex;

* otherwise, if either argument is a floating point number, the
  other is converted to floating point;

* otherwise, both must be integers and no conversion is necessary.

Some additional rules apply for certain operators (e.g., 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 identifiers or literals.  Forms enclosed in parentheses, brackets
or braces are also categorized syntactically as atoms.  The syntax for
atoms is:

   atom      ::= identifier | literal | enclosure
   enclosure ::= parenth_form | list_display | dict_display | set_display
                 | generator_expression | yield_atom


6.2.1. Identifiers (Names)
--------------------------

An identifier occurring as an atom is a name.  See section 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.

**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. Private names are transformed to a longer form
before code is generated for them.  The transformation inserts the
class name, with leading underscores removed and a single underscore
inserted, in front of the name.  For example, the identifier "__spam"
occurring in a class named "Ham" will be transformed to "_Ham__spam".
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.


6.2.2. Literals
---------------

Python supports string and bytes literals and various numeric
literals:

   literal ::= stringliteral | bytesliteral
               | integer | floatnumber | imagnumber

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 Literals for details.

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.


6.2.3. Parenthesized forms
--------------------------

A parenthesized form is an optional expression list enclosed in
parentheses:

   parenth_form ::= "(" [starred_expression] ")"

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.

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).

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 *are* required — allowing unparenthesized “nothing” in
expressions would cause ambiguities and allow common typos to pass
uncaught.


6.2.4. Displays for lists, sets and dictionaries
------------------------------------------------

For constructing a list, a set or a dictionary Python provides special
syntax called “displays”, each of them in two flavors:

* either the container contents are listed explicitly, or

* they are computed via a set of looping and filtering instructions,
  called a *comprehension*.

Common syntax elements for comprehensions are:

   comprehension ::= expression comp_for
   comp_for      ::= "for" target_list "in" or_test [comp_iter]
   comp_iter     ::= comp_for | comp_if
   comp_if       ::= "if" expression_nocond [comp_iter]

The comprehension consists of a single expression followed by at least
one "for" clause and zero or more "for" or "if" clauses. In this case,
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
each time the innermost block is reached.

Note that the comprehension is executed in a separate scope, so names
assigned to in the target list don’t “leak” into the enclosing scope.


6.2.5. List displays
--------------------

A list display is a possibly empty series of expressions enclosed in
square brackets:

   list_display ::= "[" [starred_list | comprehension] "]"

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.


6.2.6. Set displays
-------------------

A set display is denoted by curly braces and distinguishable from
dictionary displays by the lack of colons separating keys and values:

   set_display ::= "{" (starred_list | comprehension) "}"

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.

An empty set cannot be constructed with "{}"; this literal constructs
an empty dictionary.


6.2.7. Dictionary displays
--------------------------

A dictionary display is a possibly empty series of key/datum pairs
enclosed in curly braces:

   dict_display       ::= "{" [key_datum_list | dict_comprehension] "}"
   key_datum_list     ::= key_datum ("," key_datum)* [","]
   key_datum          ::= expression ":" expression | "**" or_expr
   dict_comprehension ::= expression ":" expression comp_for

A dictionary display yields a new dictionary object.

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.

A double asterisk "**" denotes *dictionary unpacking*. Its operand
must be a *mapping*.  Each mapping item is added to the new
dictionary.  Later values replace values already set by earlier
key/datum pairs and earlier dictionary unpackings.

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

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.

Restrictions on the types of the key values are listed earlier in
section The standard type hierarchy.  (To summarize, the key type
should be *hashable*, 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.


6.2.8. Generator expressions
----------------------------

A generator expression is a compact generator notation in parentheses:

   generator_expression ::= "(" expression comp_for ")"

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 leftmost "for"
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 "for" clauses cannot be evaluated
immediately since they may depend on the previous "for" loop. For
example: "(x*y for x in range(10) for y in bar(x))".

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


6.2.9. Yield expressions
------------------------

   yield_atom       ::= "(" yield_expression ")"
   yield_expression ::= "yield" [expression_list | "from" expression]

The yield expression is only used when defining a *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.

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
"expression_list" to the generator’s caller.  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, it treats the supplied expression as
a subiterator. All values produced by that subiterator 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 sub-iterator is a generator
(by returning a value from the sub-generator).

   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 sub-generators easy.


6.2.9.1. 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 "expression_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(type[, value[, traceback]])

   Raises an exception of type "type" 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.

generator.close()

   Raises a "GeneratorExit" at the point where the generator function
   was paused.  If the generator function then exits gracefully, is
   already closed, or raises "GeneratorExit" (by not catching the
   exception), close returns to its caller.  If the generator yields a
   value, a "RuntimeError" is raised.  If the generator raises any
   other exception, it is propagated to the caller.  "close()" does
   nothing if the generator has already exited due to an exception or
   normal exit.


6.2.9.2. 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.”


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

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

   primary ::= atom | attributeref | subscription | slicing | 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.  This
production can be customized by overriding the "__getattr__()" method.
If this attribute is not available, the exception "AttributeError" 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.


6.3.2. Subscriptions
--------------------

A subscription selects an item of a sequence (string, tuple or list)
or mapping (dictionary) object:

   subscription ::= primary "[" expression_list "]"

The primary must evaluate to an object that supports subscription
(lists or dictionaries for example).  User-defined objects can support
subscription by defining a "__getitem__()" method.

For built-in objects, there are two types of objects that support
subscription:

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.)

If the primary is a sequence, the expression (list) must evaluate to
an integer or a slice (as discussed in the following section).

The formal syntax makes no special provision for negative indices in
sequences; however, built-in sequences all provide a "__getitem__()"
method that interprets negative indices by adding the length of the
sequence to the index (so that "x[-1]" selects the last item of "x").
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 "__getitem__()"
method, subclasses overriding this method will need to explicitly add
that support.

A string’s items are characters.  A character is not a separate data
type but a string of exactly one character.


6.3.3. Slicings
---------------

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 "del" statements.  The syntax for a slicing:

   slicing      ::= primary "[" slice_list "]"
   slice_list   ::= slice_item ("," slice_item)* [","]
   slice_item   ::= expression | proper_slice
   proper_slice ::= [lower_bound] ":" [upper_bound] [ ":" [stride] ]
   lower_bound  ::= expression
   upper_bound  ::= expression
   stride       ::= expression

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).

The semantics for a slicing are as follows.  The primary is indexed
(using the same "__getitem__()" 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 The standard type hierarchy) whose "start",
"stop" and "step" attributes are the values of the expressions given
as lower bound, upper bound and stride, respectively, substituting
"None" for missing expressions.


6.3.4. 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 ::= ["*"] 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
value of 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
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 keyword is already
present (as an explicit keyword argument, or from another unpacking),
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.

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

New 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.  The 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".)


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 unary "+" (plus) operator yields its numeric argument unchanged.

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.

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

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

New 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 "%" (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 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 type
and then added together. In the latter case, the sequences are
concatenated.

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


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.

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)".

Note: In the current implementation, the right-hand operand is
  required to be at most "sys.maxsize".  If the right-hand operand is
  larger than "sys.maxsize" an "OverflowError" exception is raised.


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.

The "^" operator yields the bitwise XOR (exclusive OR) of its
arguments, which must be integers.

The "|" operator yields the bitwise (inclusive) OR of its arguments,
which must be integers.


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".

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('NaN')" are
  special.  They are identical to themselves ("x is x" is true) but
  are not equal to themselves ("x == x" is false).  Additionally,
  comparing any number to a not-a-number value will return "False".
  For example, both "3 < float('NaN')" and "float('NaN') < 3" will
  return "False".

* 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 unequality, and ordering comparison across
  these types raises "TypeError".

  Sequences compare lexicographically using comparison of
  corresponding elements, whereby reflexivity of the elements is
  enforced.

  In enforcing reflexivity of elements, the comparison of collections
  assumes that for a collection element "x", "x == x" is always true.
  Based on that assumption, element identity is compared first, and
  element comparison is performed only for distinct elements.  This
  approach yields the same result as a strict element comparison
  would, if the compared elements are reflexive.  For non-reflexive
  elements, the result is different than for strict element
  comparison, and may be surprising:  The non-reflexive not-a-number
  values for example result in the following comparison behavior when
  used in a list:

     >>> nan = float('NaN')
     >>> nan is nan
     True
     >>> nan == nan
     False                 <-- the defined non-reflexive behavior of NaN
     >>> [nan] == [nan]
     True                  <-- list enforces reflexivity and tests identity first

  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
  "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" with "x ==
z" 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 == y[i]", and all lower
integer indices do not raise "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 true value of
"in".


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

The operators "is" and "is not" test for object identity: "x is y" is
true if and only if *x* and *y* are the same object.  Object 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", 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 "__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. Conditional expressions
=============================

   conditional_expression ::= or_test ["if" or_test "else" expression]
   expression             ::= conditional_expression | lambda_expr
   expression_nocond      ::= or_test | lambda_expr_nocond

Conditional expressions (sometimes called a “ternary operator”) have
the lowest priority of all Python operations.

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.


6.13. Lambdas
=============

   lambda_expr        ::= "lambda" [parameter_list]: expression
   lambda_expr_nocond ::= "lambda" [parameter_list]: expression_nocond

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

   def <lambda>(arguments):
       return expression

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


6.14. Expression lists
======================

   expression_list    ::= expression ( "," expression )* [","]
   starred_list       ::= starred_item ( "," starred_item )* [","]
   starred_expression ::= expression | ( starred_item "," )* [starred_item]
   starred_item       ::= expression | "*" or_expr

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.

An asterisk "*" denotes *iterable unpacking*.  Its operand must be 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.

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

The trailing comma is required only to create a single tuple (a.k.a. a
*singleton*); 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. 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


6.16. Operator precedence
=========================

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

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

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