
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``.


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 that way:

* 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 left
argument to the '%' operator).  Extensions must define their own
conversion behavior.


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


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 in front of the name, with leading underscores removed, and
a single underscore inserted in front of the class 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.


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.

With the exception of bytes literals, these all correspond to
immutable data types, and hence the object's identity is less
important than its value. Multiple evaluations of literals with the
same value (either the same occurrence in the program text or a
different occurrence) may obtain the same object or a different object
with the same value.


Parenthesized forms
-------------------

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

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

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.


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" in the enclosing scope.


List displays
-------------

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

   list_display ::= "[" [expression_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.


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 ::= "{" (expression_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.


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
   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 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.


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 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 the detail.


Yield expressions
-----------------

   yield_atom       ::= "(" yield_expression ")"
   yield_expression ::= "yield" [expression_list]

The ``yield`` expression is only used when defining a generator
function, and can only be used in the body of a function definition.
Using a ``yield`` expression in a function definition is sufficient to
cause that definition to create a generator function instead of a
normal function.

When a generator function is called, it returns an iterator known as a
generator.  That generator then controls the execution of a generator
function. The execution starts when one of the generator's methods is
called.  At that time, the execution proceeds to the first ``yield``
expression, where it is suspended again, returning the value of
**expression_list** to generator's caller.  By suspended we mean that
all local state is retained, including the current bindings of local
variables, the instruction pointer, and the internal evaluation stack.
When the execution is resumed by calling one of the generator's
methods, the function can proceed exactly as if the ``yield``
expression was just another external call.  The value of the ``yield``
expression after resuming depends on the method which resumed the
execution.

All of this makes generator functions quite similar to coroutines;
they yield multiple times, they have more than one entry point and
their execution can be suspended.  The only difference is that a
generator function cannot control where should the execution continue
after it yields; the control is always transfered to the generator's
caller.

The ``yield`` statement is allowed in the ``try`` clause of a ``try``
...  ``finally`` 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.

The following generator's methods can be used to control the execution
of a generator function:

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 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 raises
   ``StopIteration`` (by exiting normally, or due to already being
   closed) or ``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.

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, 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.

See also:

   **PEP 0255** - Simple Generators
      The proposal for adding generators and the ``yield`` statement
      to Python.

   **PEP 0342** - Coroutines via Enhanced Generators
      The proposal to enhance the API and syntax of generators, making
      them usable as simple coroutines.


Primaries
=========

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

   primary ::= atom | attributeref | subscription | slicing | call


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 (which 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.


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,
e.g. a list or dictionary.  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. If this value is negative, the length of the sequence is
added to it (so that, e.g., ``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).

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


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 must evaluate
to a mapping object, and it 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.


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 ["," keyword_arguments]
                       ["," "*" expression] ["," keyword_arguments]
                       ["," "**" expression]
                     | keyword_arguments ["," "*" expression]
                       ["," keyword_arguments] ["," "**" expression]
                     | "*" expression ["," keyword_arguments] ["," "**" expression]
                     | "**" expression
   positional_arguments ::= expression ("," expression)*
   keyword_arguments    ::= keyword_item ("," keyword_item)*
   keyword_item         ::= identifier "=" expression

A 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.

Note: An implementation may provide builtin 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 a sequence.  Elements from this
sequence are treated as if they were additional positional arguments;
if there are positional arguments *x1*,..., *xN*, and ``expression``
evaluates to a sequence *y1*, ..., *yM*, this is equivalent to a call
with M+N positional arguments *x1*, ..., *xN*, *y1*, ..., *yM*.

A consequence of this is that although the ``*expression`` syntax may
appear *after* some keyword arguments, it is processed *before* the
keyword arguments (and the ``**expression`` argument, if any -- 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 ?
   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.  In the case of a keyword
appearing in both ``expression`` and as an explicit keyword argument,
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.

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.


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 ::= 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``.)


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.


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 "//" 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 ``/`` (division) and ``//`` (floor division) operators yield the
quotient of their arguments.  The numeric arguments are first
converted to a common type. Integer division yields a float, while
floor division of integers results in an integer; the result is that
of mathematical division with the 'floor' function applied to the
result.  Division by zero raises the ``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 *Old String Formatting Operations*.

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 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.


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


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.


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).

The operators ``<``, ``>``, ``==``, ``>=``, ``<=``, and ``!=`` compare
the values of two objects.  The objects need not have the same type.
If both are numbers, they are converted to a common type.  Otherwise,
the ``==`` and ``!=`` operators *always* consider objects of different
types to be unequal, while the ``<``, ``>``, ``>=`` and ``<=``
operators raise a ``TypeError`` when comparing objects of different
types that do not implement these operators for the given pair of
types.  You can control comparison behavior of objects of non-builtin
types by defining rich comparison methods like ``__gt__()``, described
in section *Basic customization*.

Comparison of objects of the same type depends on the type:

* Numbers are compared arithmetically.

* The values ``float('NaN')`` and ``Decimal('NaN')`` are special. The
  are identical to themselves, ``x is x`` but are not equal to
  themselves, ``x != x``.  Additionally, comparing any value to a
  not-a-number value will return ``False``.  For example, both ``3 <
  float('NaN')`` and ``float('NaN') < 3`` will return ``False``.

* Bytes objects are compared lexicographically using the numeric
  values of their elements.

* Strings are compared lexicographically using the numeric equivalents
  (the result of the built-in function ``ord()``) of their characters.
  [3] String and bytes object can't be compared!

* Tuples and lists are compared lexicographically using comparison of
  corresponding elements.  This means that to compare equal, each
  element must compare equal and the two sequences must be of the same
  type and have the same length.

  If not equal, the sequences are ordered the same as their first
  differing elements.  For example, ``[1,2,x] <= [1,2,y]`` has the
  same value as ``x <= y``.  If the corresponding element does not
  exist, the shorter sequence is ordered first (for example, ``[1,2] <
  [1,2,3]``).

* Mappings (dictionaries) compare equal if and only if their sorted
  ``(key, value)`` lists compare equal. [4] Outcomes other than
  equality are resolved consistently, but are not otherwise defined.
  [5]

* Sets and frozensets define comparison operators to mean subset and
  superset tests.  Those relations do not define total orderings (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.

* Most other objects of builtin types compare unequal unless they are
  the same object; the choice whether one object is considered smaller
  or larger than another one is made arbitrarily but consistently
  within one execution of a program.

Comparison of objects of the differing types depends on whether either
of the types provide explicit support for the comparison.  Most
numeric types can be compared with one another, but comparisons of
``float`` and ``Decimal`` are not supported to avoid the inevitable
confusion arising from representation issues such as ``float('1.1')``
being inexactly represented and therefore not exactly equal to
``Decimal('1.1')`` which is.  When cross-type comparison is not
supported, the comparison method returns ``NotImplemented``.  This can
create the illusion of non-transitivity between supported cross-type
comparisons and unsupported comparisons.  For example, ``Decimal(2) ==
2`` and *2 == float(2)`* but ``Decimal(2) != float(2)``.

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 a 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 val
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`` is true if and only if ``y.__contains__(x)`` is true.

For user-defined classes which do not define ``__contains__()`` and do
define ``__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``.

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.  ``x is
not y`` yields the inverse truth value. [6]


Boolean operations
==================

Boolean operations have the lowest priority of all Python operations:

   expression             ::= conditional_expression | lambda_form
   expression_nocond      ::= or_test | lambda_form_nocond
   conditional_expression ::= or_test ["if" or_test "else" expression]
   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 if C else y`` first evaluates *C* (*not* *x*); if
*C* is true, *x* is evaluated and its value is returned; otherwise,
*y* is evaluated and its value is returned.

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
invent a value anyway, it does not bother to return a value of the
same type as its argument, so e.g., ``not 'foo'`` yields ``False``,
not ``''``.)


Lambdas
=======

   lambda_form        ::= "lambda" [parameter_list]: expression
   lambda_form_nocond ::= "lambda" [parameter_list]: expression_nocond

Lambda forms (lambda expressions) have the same syntactic position as
expressions.  They are a shorthand 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 forms cannot contain
statements or annotations.


Expression lists
================

   expression_list ::= expression ( "," expression )* [","]

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.

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: ``()``.)


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


Summary
=======

The following table summarizes the operator precedences in Python,
from lowest precedence (least binding) to highest precedence (most
binding).  Operators in the same box have the same precedence.  Unless
the syntax is explicitly given, operators are binary.  Operators in
the same box group left to right (except for comparisons, including
tests, which all have the same precedence and chain from left to right
--- see section *Comparisons* --- and exponentiation, which groups
from right to left).

+-------------------------------------------------+---------------------------------------+
| Operator                                        | Description                           |
+=================================================+=======================================+
| ``lambda``                                      | Lambda 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, division, remainder   |
+-------------------------------------------------+---------------------------------------+
| ``+x``, ``-x``, ``~x``                          | Positive, negative, bitwise NOT       |
+-------------------------------------------------+---------------------------------------+
| ``**``                                          | Exponentiation [7]                    |
+-------------------------------------------------+---------------------------------------+
| ``x[index]``, ``x[index:index]``,               | Subscription, slicing, call,          |
| ``x(arguments...)``, ``x.attribute``            | attribute reference                   |
+-------------------------------------------------+---------------------------------------+
| ``(expressions...)``, ``[expressions...]``,     | Binding or tuple display, list        |
| ``{key:datum...}``,                             | display, dictionary 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``.  Function
    ``fmod()`` in the ``math`` module 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] While comparisons between strings make sense at the byte level,
    they may be counter-intuitive to users.  For example, the strings
    ``"\u00C7"`` and ``"\u0327\u0043"`` compare differently, even
    though they both represent the same unicode character (LATIN
    CAPITAL LETTER C WITH CEDILLA).  To compare strings in a human
    recognizable way, compare using ``unicodedata.normalize()``.

[4] The implementation computes this efficiently, without constructing
    lists or sorting.

[5] Earlier versions of Python used lexicographic comparison of the
    sorted (key, value) lists, but this was very expensive for the
    common case of comparing for equality.  An even earlier version of
    Python compared dictionaries by identity only, but this caused
    surprises because people expected to be able to test a dictionary
    for emptiness by comparing it to ``{}``.

[6] 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.

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