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," the arguments
are coerced using the coercion rules listed at  Coercion rules.  If
both arguments are standard numeric types, the following coercions are
applied:

* 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, if either argument is a long integer, the other is
  converted to long integer;

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

Some additional rules apply for certain operators (e.g., a string left
argument to the '%' operator). Extensions can define their own
coercions.


Atoms
=====

Atoms are the most basic elements of expressions.  The simplest atoms
are identifiers or literals.  Forms enclosed in reverse quotes or 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
                 | generator_expression | dict_display | set_display
                 | string_conversion | 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, 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.


Literals
--------

Python supports string literals and various numeric literals:

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

Evaluation of a literal yields an object of the given type (string,
integer, long 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.


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.


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

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

   list_display        ::= "[" [expression_list | list_comprehension] "]"
   list_comprehension  ::= expression list_for
   list_for            ::= "for" target_list "in" old_expression_list [list_iter]
   old_expression_list ::= old_expression [("," old_expression)+ [","]]
   old_expression      ::= or_test | old_lambda_expr
   list_iter           ::= list_for | list_if
   list_if             ::= "if" old_expression [list_iter]

A list display yields a new list object.  Its contents are specified
by providing either a list of expressions or a list 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 list comprehension is supplied, it 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
list 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 a list element each time the innermost block
is reached [1].


Displays for sets and dictionaries
----------------------------------

For constructing 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.


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.


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.


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.


String conversions
------------------

A string conversion is an expression list enclosed in reverse (a.k.a.
backward) quotes:

   string_conversion ::= "`" expression_list "`"

A string conversion evaluates the contained expression list and
converts the resulting object into a string according to rules
specific to its type.

If the object is a string, a number, "None", or a tuple, list or
dictionary containing only objects whose type is one of these, the
resulting string is a valid Python expression which can be passed to
the built-in function "eval()" to yield an expression with the same
value (or an approximation, if floating point numbers are involved).

(In particular, converting a string adds quotes around it and converts
"funny" characters to escape sequences that are safe to print.)

Recursive objects (for example, lists or dictionaries that contain a
reference to themselves, directly or indirectly) use "..." to indicate
a recursive reference, and the result cannot be passed to "eval()" to
get an equal value ("SyntaxError" will be raised instead).

The built-in function "repr()" performs exactly the same conversion in
its argument as enclosing it in parentheses and reverse quotes does.
The built-in function "str()" performs a similar but more user-
friendly conversion.


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

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

New in version 2.5.

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 transferred to the generator's
caller.


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.

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 generator.next()
   Execution starts when 'next()' is called for the first time.
   1
   >>> print generator.next()
   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 342** - 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, e.g., a module, list, or an instance.  This
object is then asked to produce the attribute whose name is the
identifier.  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 of a sequence or mapping type.

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 a
plain 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          ::= simple_slicing | extended_slicing
   simple_slicing   ::= primary "[" short_slice "]"
   extended_slicing ::= primary "[" slice_list "]"
   slice_list       ::= slice_item ("," slice_item)* [","]
   slice_item       ::= expression | proper_slice | ellipsis
   proper_slice     ::= short_slice | long_slice
   short_slice      ::= [lower_bound] ":" [upper_bound]
   long_slice       ::= short_slice ":" [stride]
   lower_bound      ::= expression
   upper_bound      ::= expression
   stride           ::= expression
   ellipsis         ::= "..."

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 nor ellipses).  Similarly, when the slice
list has exactly one short slice and no trailing comma, the
interpretation as a simple slicing takes priority over that as an
extended slicing.

The semantics for a simple slicing are as follows.  The primary must
evaluate to a sequence object.  The lower and upper bound expressions,
if present, must evaluate to plain integers; defaults are zero and the
"sys.maxint", respectively.  If either bound is negative, the
sequence's length is added to it.  The slicing now selects all items
with index *k* such that "i <= k < j" where *i* and *j* are the
specified lower and upper bounds.  This may be an empty sequence.  It
is not an error if *i* or *j* lie outside the range of valid indexes
(such items don't exist so they aren't selected).

The semantics for an extended slicing are as follows.  The primary
must evaluate to a mapping object, and it is indexed 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 an ellipsis slice
item is the built-in "Ellipsis" object.  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 [","]
            | expression genexpr_for] ")"
   argument_list        ::= positional_arguments ["," keyword_arguments]
                       ["," "*" expression] ["," keyword_arguments]
                       ["," "**" expression]
                     | keyword_arguments ["," "*" expression]
                       ["," "**" 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 certain class instances
themselves are callable; extensions may define additional callable
object types).  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 this iterable 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 <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.  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.  Formal parameters using the syntax "(sublist)" cannot be used
as keyword argument names; the outermost sublist corresponds to a
single unnamed argument slot, and the argument value is assigned to
the sublist using the usual tuple assignment rules after all other
parameter processing is done.

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.  The result type is that of the
arguments after coercion.

With mixed operand types, the coercion rules for binary arithmetic
operators apply. For int and long int operands, the result has the
same type as the operands (after coercion) 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". (This last feature was added in Python 2.2.
In Python 2.1 and before, if both arguments were of integer types and
the second argument was negative, an exception was raised).

Raising "0.0" to a negative power results in a "ZeroDivisionError".
Raising a negative number to a fractional power results in 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
plain or long 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 (plain or long) 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. Plain or long integer division yields an
integer of the same type; 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 [2].

The integer division and modulo operators are connected by the
following identity: "x == (x/y)*y + (x%y)".  Integer division and
modulo are also connected with the built-in function "divmod()":
"divmod(x, y) == (x/y, x%y)".  These identities don't hold for
floating point numbers; there similar identities hold approximately
where "x/y" is replaced by "floor(x/y)" or "floor(x/y) - 1" [3].

In addition to performing the modulo operation on numbers, the "%"
operator is also overloaded by string and unicode objects to perform
string formatting (also known as interpolation). The syntax for string
formatting is described in the Python Library Reference, section
String Formatting Operations.

Deprecated since version 2.3: The floor division operator, the modulo
operator, and the "divmod()" function are no longer 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 plain or long integers as arguments.  The
arguments are converted to a common type.  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)".
Negative shift counts raise a "ValueError" exception.

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.


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 plain or long integers.  The arguments are converted to a common
type.

The "^" operator yields the bitwise XOR (exclusive OR) of its
arguments, which must be plain or long integers.  The arguments are
converted to a common type.

The "|" operator yields the bitwise (inclusive) OR of its arguments,
which must be plain or long integers.  The arguments are converted to
a common type.


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 forms "<>" and "!=" are equivalent; for consistency with C, "!="
is preferred; where "!=" is mentioned below "<>" is also accepted.
The "<>" spelling is considered obsolescent.


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.

Types can customize their comparison behavior by implementing a
"__cmp__()" method or *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").

The default order comparison ("<", ">", "<=", and ">=") gives a
consistent but arbitrary order.

(This unusual definition of comparison was used to simplify the
definition of operations like sorting and the "in" and "not in"
operators. In the future, the comparison rules for objects of
different types are likely to change.)

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,
  long, 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.

* Strings (instances of "str" or "unicode") compare
  lexicographically using the numeric equivalents (the result of the
  built-in function "ord()") of their characters. [4] When comparing
  an 8-bit string and a Unicode string, the 8-bit string is converted
  to Unicode.  If the conversion fails, the strings are considered
  unequal.

* Instances of "tuple" or "list" can be compared only within each of
  their types.  Equality comparison across these types results in
  unequality, and ordering comparison across these types gives an
  arbitrary order.

  These 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.

  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 are ordered the same as their first unequal elements
    (for example, "cmp([1,2,x], [1,2,y])" returns the same as
    "cmp(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.

  Outcomes other than equality are resolved consistently, but are not
  otherwise defined. [5]

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

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.


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".


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


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.  (See the "__nonzero__()" special method for a way to change
this.)

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 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 "''".)


Conditional Expressions
=======================

New in version 2.5.

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

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*
(*not* *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.


Lambdas
=======

   lambda_expr     ::= "lambda" [parameter_list]: expression
   old_lambda_expr ::= "lambda" [parameter_list]: old_expression

Lambda expressions (sometimes called lambda forms) 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 name(arguments):
       return expression

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


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


Operator precedence
===================

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                     |
+-------------------------------------------------+---------------------------------------+
| "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, division, remainder   |
|                                                 | [7]                                   |
+-------------------------------------------------+---------------------------------------+
| "+x", "-x", "~x"                                | Positive, negative, bitwise NOT       |
+-------------------------------------------------+---------------------------------------+
| "**"                                            | Exponentiation [8]                    |
+-------------------------------------------------+---------------------------------------+
| "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, string   |
|                                                 | conversion                            |
+-------------------------------------------------+---------------------------------------+

-[ Footnotes ]-

[1] In Python 2.3 and later releases, a list comprehension "leaks"
    the control variables of each "for" it contains into the
    containing scope.  However, this behavior is deprecated, and
    relying on it will not work in Python 3.

[2] 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.

[3] If x is very close to an exact integer multiple of y, it's
    possible for "floor(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".

[4] 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 unicode strings compare at the level
    of Unicode code points. This may be counter-intuitive to humans.
    For example, "u"\u00C7" == u"\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()".

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

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