\chapter{Expressions\label{expressions}}

\index{expression}

This chapter explains the meaning of the elements of expressions in

Python.

\strong{Syntax Notes:} In this and the following chapters, extended

BNF\index{BNF} notation will be used to describe syntax, not lexical

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

\begin{productionlist}[*]

\production{name}{\token{othername}}

\end{productionlist}

and no semantics are given, the semantics of this form of \code{name}

are the same as for \code{othername}.

\index{syntax}

\section{Arithmetic conversions\label{conversions}}

\indexii{arithmetic}{conversion}

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 the end of

chapter \ref{datamodel}. If both arguments are standard numeric

types, the following coercions are applied:

\begin{itemize}

\item If either argument is a complex number, the other is converted

to complex;

\item otherwise, if either argument is a floating point number,

the other is converted to floating point;

\item otherwise, if either argument is a long integer,

the other is converted to long integer;

\item otherwise, both must be plain integers and no conversion

is necessary.

\end{itemize}

Some additional rules apply for certain operators (e.g., a string left

argument to the `\%' operator). Extensions can define their own

coercions.

\section{Atoms\label{atoms}}

\index{atom}

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:

\begin{productionlist}

\production{atom}

{\token{identifier} | \token{literal} | \token{enclosure}}

\production{enclosure}

{\token{parenth_form} | \token{list_display}}

\productioncont{| \token{dict_display} | \token{string_conversion}}

\end{productionlist}

\subsection{Identifiers (Names)\label{atom-identifiers}}

\index{name}

\index{identifier}

An identifier occurring as an atom is a name. See Section 4.1 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 \exception{NameError} exception.

\exindex{NameError}

\strong{Private name mangling:}%

\indexii{name}{mangling}%

\indexii{private}{names}%

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 \dfn{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 \code{__spam} occurring in a class named \code{Ham} will be

transformed to \code{_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.

\subsection{Literals\label{atom-literals}}

\index{literal}

Python supports string literals and various numeric literals:

\begin{productionlist}

\production{literal}

{\token{stringliteral} | \token{integer} | \token{longinteger}}

\productioncont{| \token{floatnumber} | \token{imagnumber}}

\end{productionlist}

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 \ref{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.

\indexiii{immutable}{data}{type}

\indexii{immutable}{object}

\subsection{Parenthesized forms\label{parenthesized}}

\index{parenthesized form}

A parenthesized form is an optional expression list enclosed in

parentheses:

\begin{productionlist}

\production{parenth_form}

{"(" [\token{expression_list}] ")"}

\end{productionlist}

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).

\indexii{empty}{tuple}

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 \emph{are} required --- allowing unparenthesized ``nothing''

in expressions would cause ambiguities and allow common typos to

pass uncaught.

\index{comma}

\indexii{tuple}{display}

\subsection{List displays\label{lists}}

\indexii{list}{display}

\indexii{list}{comprehensions}

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

square brackets:

\begin{productionlist}

\production{list_display}

{"[" [\token{listmaker}] "]"}

\production{listmaker}

{\token{expression} ( \token{list_for}

| ( "," \token{expression})* [","] )}

\production{list_iter}

{\token{list_for} | \token{list_if}}

\production{list_for}

{"for" \token{expression_list} "in" \token{testlist}

[\token{list_iter}]}

\production{list_if}

{"if" \token{test} [\token{list_iter}]}

\end{productionlist}

A list display yields a new list object. Its contents are specified

by providing either a list of expressions or a list comprehension.

\indexii{list}{comprehensions}

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 \keyword{for} clause and zero or

more \keyword{for} or \keyword{if} clauses. In this

case, the elements of the new list are those that would be produced

by considering each of the \keyword{for} or \keyword{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.

\obindex{list}

\indexii{empty}{list}

\subsection{Dictionary displays\label{dict}}

\indexii{dictionary}{display}

A dictionary display is a possibly empty series of key/datum pairs

enclosed in curly braces:

\index{key}

\index{datum}

\index{key/datum pair}

\begin{productionlist}

\production{dict_display}

{"\{" [\token{key_datum_list}] "\}"}

\production{key_datum_list}

{\token{key_datum} ("," \token{key_datum})* [","]}

\production{key_datum}

{\token{expression} ":" \token{expression}}

\end{productionlist}

A dictionary display yields a new dictionary object.

\obindex{dictionary}

The key/datum pairs 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.

Restrictions on the types of the key values are listed earlier in

section \ref{types}. (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.

\indexii{immutable}{object}

\subsection{String conversions\label{string-conversions}}

\indexii{string}{conversion}

\indexii{reverse}{quotes}

\indexii{backward}{quotes}

\index{back-quotes}

A string conversion is an expression list enclosed in reverse (a.k.a.

backward) quotes:

\begin{productionlist}

\production{string_conversion}

{"`" \token{expression_list} "`"}

\end{productionlist}

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, \code{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 \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 \samp{...} to

indicate a recursive reference, and the result cannot be passed to

\function{eval()} to get an equal value (\exception{SyntaxError} will

be raised instead).

\obindex{recursive}

The built-in function \function{repr()} performs exactly the same

conversion in its argument as enclosing it in parentheses and reverse

quotes does. The built-in function \function{str()} performs a

similar but more user-friendly conversion.

\bifuncindex{repr}

\bifuncindex{str}

\section{Primaries\label{primaries}}

\index{primary}

Primaries represent the most tightly bound operations of the language.

Their syntax is:

\begin{productionlist}

\production{primary}

{\token{atom} | \token{attributeref}

| \token{subscription} | \token{slicing} | \token{call}}

\end{productionlist}

\subsection{Attribute references\label{attribute-references}}

\indexii{attribute}{reference}

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

\begin{productionlist}

\production{attributeref}

{\token{primary} "." \token{identifier}}

\end{productionlist}

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

\exception{AttributeError}\exindex{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.

\obindex{module}

\obindex{list}

\subsection{Subscriptions\label{subscriptions}}

\index{subscription}

A subscription selects an item of a sequence (string, tuple or list)

or mapping (dictionary) object:

\obindex{sequence}

\obindex{mapping}

\obindex{string}

\obindex{tuple}

\obindex{list}

\obindex{dictionary}

\indexii{sequence}{item}

\begin{productionlist}

\production{subscription}

{\token{primary} "[" \token{expression_list} "]"}

\end{productionlist}

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., \code{x[-1]} selects the last item of

\code{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.

\index{character}

\indexii{string}{item}

\subsection{Slicings\label{slicings}}

\index{slicing}

\index{slice}

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:

\obindex{sequence}

\obindex{string}

\obindex{tuple}

\obindex{list}

\begin{productionlist}

\production{slicing}

{\token{simple_slicing} | \token{extended_slicing}}

\production{simple_slicing}

{\token{primary} "[" \token{short_slice} "]"}

\production{extended_slicing}

{\token{primary} "[" \token{slice_list} "]" }

\production{slice_list}

{\token{slice_item} ("," \token{slice_item})* [","]}

\production{slice_item}

{\token{expression} | \token{proper_slice} | \token{ellipsis}}

\production{proper_slice}

{\token{short_slice} | \token{long_slice}}

\production{short_slice}

{[\token{lower_bound}] ":" [\token{upper_bound}]}

\production{long_slice}

{\token{short_slice} ":" [\token{stride}]}

\production{lower_bound}

{\token{expression}}

\production{upper_bound}

{\token{expression}}

\production{stride}

{\token{expression}}

\production{ellipsis}

{"..."}

\end{productionlist}

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.\indexii{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

\code{sys.maxint}, respectively. If either bound is negative, the

sequence's length is added to it. The slicing now selects all items

with index \var{k} such that

\code{\var{i} <= \var{k} < \var{j}} where \var{i}

and \var{j} are the specified lower and upper bounds. This may be an

empty sequence. It is not an error if \var{i} or \var{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 \code{Ellipsis} object. The conversion of a

proper slice is a slice object (see section \ref{types}) whose

\member{start}, \member{stop} and \member{step} attributes are the

values of the expressions given as lower bound, upper bound and

stride, respectively, substituting \code{None} for missing

expressions.

\withsubitem{(slice object attribute)}{\ttindex{start}

\ttindex{stop}\ttindex{step}}

\subsection{Calls\label{calls}}

\index{call}

A call calls a callable object (e.g., a function) with a possibly empty

series of arguments:

\obindex{callable}

\begin{productionlist}

\production{call}

{\token{primary} "(" [\token{argument_list} [","]] ")"}

\production{argument_list}

{\token{positional_arguments} ["," \token{keyword_arguments}]}

\productioncont{ ["," "*" \token{expression}]}

\productioncont{ ["," "**" \token{expression}]}

\productioncont{| \token{keyword_arguments} ["," "*" \token{expression}]}

\productioncont{ ["," "**" \token{expression}]}

\productioncont{| "*" \token{expression} ["," "**" \token{expression}]}

\productioncont{| "**" \token{expression}}

\production{positional_arguments}

{\token{expression} ("," \token{expression})*}

\production{keyword_arguments}

{\token{keyword_item} ("," \token{keyword_item})*}

\production{keyword_item}

{\token{identifier} "=" \token{expression}}

\end{productionlist}

A trailing comma may be present after an argument list 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 \ref{function} 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 \exception{TypeError} exception is raised.

Otherwise, the value of the argument is placed in the slot, filling it

(even if the expression is \code{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 \exception{TypeError} exception is raised. Otherwise,

the list of filled slots is used as the argument list for the call.

If there are more positional arguments than there are formal parameter

slots, a \exception{TypeError} exception is raised, unless a formal

parameter using the syntax \samp{*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 \exception{TypeError} exception is raised, unless a formal

parameter using the syntax \samp{**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 \samp{*expression} appears in the function call,

\samp{expression} must evaluate to a sequence. Elements from this

sequence are treated as if they were additional positional arguments;

if there are postional arguments \var{x1},...,\var{xN} , and

\samp{expression} evaluates to a sequence \var{y1},...,\var{yM}, this

is equivalent to a call with M+N positional arguments

\var{x1},...,\var{xN},\var{y1},...,\var{yM}.

A consequence of this is that although the \samp{*expression} syntax

appears \emph{after} any keyword arguments, it is processed

\emph{before} the keyword arguments (and the

\samp{**expression} argument, if any -- see below). So:

\begin{verbatim}

>>> 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

\end{verbatim}

It is unusual for both keyword arguments and the

\samp{*expression} syntax to be used in the same call, so in practice

this confusion does not arise.

If the syntax \samp{**expression} appears in the function call,

\samp{expression} must evaluate to a (subclass of) dictionary, the

contents of which are treated as additional keyword arguments. In the

case of a keyword appearing in both \samp{expression} and as an

explicit keyword argument, a \exception{TypeError} exception is

raised.

Formal parameters using the syntax \samp{*identifier} or

\samp{**identifier} cannot be used as positional argument slots or

as keyword argument names. Formal parameters using the syntax

\samp{(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 \code{None}, unless it

raises an exception. How this value is computed depends on the type

of the callable object.

If it is---

\begin{description}

\item[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 \ref{function}. When the code block executes a

\keyword{return} statement, this specifies the return value of the

function call.

\indexii{function}{call}

\indexiii{user-defined}{function}{call}

\obindex{user-defined function}

\obindex{function}

\item[a built-in function or method:] The result is up to the

interpreter; see the \citetitle[../lib/built-in-funcs.html]{Python

Library Reference} for the descriptions of built-in functions and

methods.

\indexii{function}{call}

\indexii{built-in function}{call}

\indexii{method}{call}

\indexii{built-in method}{call}

\obindex{built-in method}

\obindex{built-in function}

\obindex{method}

\obindex{function}

\item[a class object:] A new instance of that class is returned.

\obindex{class}

\indexii{class object}{call}

\item[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.

\obindex{class instance}

\obindex{instance}

\indexii{class instance}{call}

\item[a class instance:] The class must define a \method{__call__()}

method; the effect is then the same as if that method was called.

\indexii{instance}{call}

\withsubitem{(object method)}{\ttindex{__call__()}}

\end{description}

\section{The power operator\label{power}}

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:

\begin{productionlist}

\production{power}

{\token{primary} ["**" \token{u_expr}]}

\end{productionlist}

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).

The power operator has the same semantics as the built-in

\function{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, \code{10**2} returns \code{100},

but \code{10**-2} returns \code{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 \code{0.0} to a negative power results in a

\exception{ZeroDivisionError}. Raising a negative number to a

fractional power results in a \exception{ValueError}.

\section{Unary arithmetic operations \label{unary}}

\indexiii{unary}{arithmetic}{operation}

\indexiii{unary}{bit-wise}{operation}

All unary arithmetic (and bit-wise) operations have the same priority:

\begin{productionlist}

\production{u_expr}

{\token{power} | "-" \token{u_expr}

| "+" \token{u_expr} | "{\~}" \token{u_expr}}

\end{productionlist}

The unary \code{-} (minus) operator yields the negation of its

numeric argument.

\index{negation}

\index{minus}

The unary \code{+} (plus) operator yields its numeric argument

unchanged.

\index{plus}

The unary \code{\~} (invert) operator yields the bit-wise inversion

of its plain or long integer argument. The bit-wise inversion of

\code{x} is defined as \code{-(x+1)}. It only applies to integral

numbers.

\index{inversion}

In all three cases, if the argument does not have the proper type,

a \exception{TypeError} exception is raised.

\exindex{TypeError}

\section{Binary arithmetic operations\label{binary}}

\indexiii{binary}{arithmetic}{operation}

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:

\begin{productionlist}

\production{m_expr}

{\token{u_expr} | \token{m_expr} "*" \token{u_expr}

| \token{m_expr} "//" \token{u_expr}

| \token{m_expr} "/" \token{u_expr}}

\productioncont{| \token{m_expr} "\%" \token{u_expr}}

\production{a_expr}

{\token{m_expr} | \token{a_expr} "+" \token{m_expr}

| \token{a_expr} "-" \token{m_expr}}

\end{productionlist}

The \code{*} (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.

\index{multiplication}

The \code{/} (division) and \code{//} (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

\exception{ZeroDivisionError} exception.

\exindex{ZeroDivisionError}

\index{division}

The \code{\%} (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 \exception{ZeroDivisionError} exception. The arguments may be floating

point numbers, e.g., \code{3.14\%0.7} equals \code{0.34} (since

\code{3.14} equals \code{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\footnote{

While \code{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 \code{-1e-100 \% 1e100}

have the same sign as \code{1e100}, the computed result is

\code{-1e-100 + 1e100}, which is numerically exactly equal

to \code{1e100}. Function \function{fmod()} in the \module{math}

module returns a result whose sign matches the sign of the

first argument instead, and so returns \code{-1e-100} in this case.

Which approach is more appropriate depends on the application.

}.

\index{modulo}

The integer division and modulo operators are connected by the

following identity: \code{x == (x/y)*y + (x\%y)}. Integer division and

modulo are also connected with the built-in function \function{divmod()}:

\code{divmod(x, y) == (x/y, x\%y)}. These identities don't hold for

floating point numbers; there similar identities hold

approximately where \code{x/y} is replaced by \code{floor(x/y)}) or

\code{floor(x/y) - 1}\footnote{

If x is very close to an exact integer multiple of y, it's

possible for \code{floor(x/y)} to be one larger than

\code{(x-x\%y)/y} due to rounding. In such cases, Python returns

the latter result, in order to preserve that \code{divmod(x,y)[0]

* y + x \%{} y} be very close to \code{x}.

}.

\deprecated{2.3}{The floor division operator, the modulo operator,

and the \function{divmod()} function are no longer defined for complex

numbers. Instead, convert to a floating point number using the

\function{abs()} function if appropriate.}

The \code{+} (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.

\index{addition}

The \code{-} (subtraction) operator yields the difference of its

arguments. The numeric arguments are first converted to a common

type.

\index{subtraction}

\section{Shifting operations\label{shifting}}

\indexii{shifting}{operation}

The shifting operations have lower priority than the arithmetic

operations:

\begin{productionlist}

\production{shift_expr}

{\token{a_expr}

| \token{shift_expr} ( "<<" | ">>" ) \token{a_expr}}

\end{productionlist}

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 \var{n} bits is defined as division by

\code{pow(2,\var{n})}. A left shift by \var{n} bits is defined as

multiplication with \code{pow(2,\var{n})}; for plain integers there is

no overflow check so in that case the operation drops bits and flips

the sign if the result is not less than \code{pow(2,31)} in absolute

value. Negative shift counts raise a \exception{ValueError}

exception.

\exindex{ValueError}

\section{Binary bit-wise operations\label{bitwise}}

\indexiii{binary}{bit-wise}{operation}

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

\begin{productionlist}

\production{and_expr}

{\token{shift_expr} | \token{and_expr} "\&" \token{shift_expr}}

\production{xor_expr}

{\token{and_expr} | \token{xor_expr} "\textasciicircum" \token{and_expr}}

\production{or_expr}

{\token{xor_expr} | \token{or_expr} "|" \token{xor_expr}}

\end{productionlist}

The \code{\&} operator yields the bitwise AND of its arguments, which

must be plain or long integers. The arguments are converted to a

common type.

\indexii{bit-wise}{and}

The \code{\^} 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.

\indexii{bit-wise}{xor}

\indexii{exclusive}{or}

The \code{|} operator yields the bitwise (inclusive) OR of its

arguments, which must be plain or long integers. The arguments are

converted to a common type.

\indexii{bit-wise}{or}

\indexii{inclusive}{or}

\section{Comparisons\label{comparisons}}

\index{comparison}

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 \code{a < b < c} have the

interpretation that is conventional in mathematics:

\indexii{C}{language}

\begin{productionlist}

\production{comparison}

{\token{or_expr} ( \token{comp_operator} \token{or_expr} )*}

\production{comp_operator}

{"<" | ">" | "==" | ">=" | "<=" | "<>" | "!="}

\productioncont{| "is" ["not"] | ["not"] "in"}

\end{productionlist}

Comparisons yield integer values: \code{1} for true, \code{0} for false.

Comparisons can be chained arbitrarily, e.g., \code{x < y <= z} is

equivalent to \code{x < y and y <= z}, except that \code{y} is

evaluated only once (but in both cases \code{z} is not evaluated at all

when \code{x < y} is found to be false).

\indexii{chaining}{comparisons}

Formally, if \var{a}, \var{b}, \var{c}, \ldots, \var{y}, \var{z} are

expressions and \var{opa}, \var{opb}, \ldots, \var{opy} are comparison

operators, then \var{a opa b opb c} \ldots \var{y opy z} is equivalent

to \var{a opa b} \keyword{and} \var{b opb c} \keyword{and} \ldots

\var{y opy z}, except that each expression is evaluated at most once.

Note that \var{a opa b opb c} doesn't imply any kind of comparison

between \var{a} and \var{c}, so that, e.g., \code{x < y > z} is

perfectly legal (though perhaps not pretty).

The forms \code{<>} and \code{!=} are equivalent; for consistency with

C, \code{!=} is preferred; where \code{!=} is mentioned below

\code{<>} is also accepted. The \code{<>} spelling is considered

obsolescent.

The operators \code{<}, \code{>}, \code{==}, \code{>=}, \code{<=}, and

\code{!=} 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,

objects of different types \emph{always} compare unequal, and are

ordered consistently but arbitrarily.

(This unusual definition of comparison was used to simplify the

definition of operations like sorting and the \keyword{in} and

\keyword{not in} operators. In the future, the comparison rules for

objects of different types are likely to change.)

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

\begin{itemize}

\item

Numbers are compared arithmetically.

\item

Strings are compared lexicographically using the numeric equivalents

(the result of the built-in function \function{ord()}) of their

characters. Unicode and 8-bit strings are fully interoperable in this

behavior.

\item

Tuples and lists are compared lexicographically using comparison of

corresponding items.

\item

Mappings (dictionaries) compare equal if and only if their sorted

(key, value) lists compare equal.\footnote{The implementation computes

this efficiently, without constructing lists or sorting.}

Outcomes other than equality are resolved consistently, but are not

otherwise defined.\footnote{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 \code{\{\}}.}

\item

Most other 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.

\end{itemize}

The operators \keyword{in} and \keyword{not in} test for set

membership. \code{\var{x} in \var{s}} evaluates to true if \var{x}

is a member of the set \var{s}, and false otherwise. \code{\var{x}

not in \var{s}} returns the negation of \code{\var{x} in \var{s}}.

The set membership test has traditionally been bound to sequences; an

object is a member of a set if the set is a sequence and contains an

element equal to that object. However, it is possible for an object

to support membership tests without being a sequence. In particular,

dictionaries support memership testing as a nicer way of spelling

\code{\var{key} in \var{dict}}; other mapping types may follow suit.

For the list and tuple types, \code{\var{x} in \var{y}} is true if and

only if there exists an index \var{i} such that

\code{\var{x} == \var{y}[\var{i}]} is true.

For the Unicode and string types, \code{\var{x} in \var{y}} is true if

and only if there exists an index \var{i} such that \code{\var{x} ==

\var{y}[\var{i}]} is true. If \code{\var{x}} is not a string or

Unicode object of length \code{1}, a \exception{TypeError} exception

is raised.

For user-defined classes which define the \method{__contains__()} method,

\code{\var{x} in \var{y}} is true if and only if

\code{\var{y}.__contains__(\var{x})} is true.

For user-defined classes which do not define \method{__contains__()} and

do define \method{__getitem__()}, \code{\var{x} in \var{y}} is true if

and only if there is a non-negative integer index \var{i} such that

\code{\var{x} == \var{y}[\var{i}]}, and all lower integer indices

do not raise \exception{IndexError} exception. (If any other exception

is raised, it is as if \keyword{in} raised that exception).

The operator \keyword{not in} is defined to have the inverse true value

of \keyword{in}.

\opindex{in}

\opindex{not in}

\indexii{membership}{test}

\obindex{sequence}

The operators \keyword{is} and \keyword{is not} test for object identity:

\code{\var{x} is \var{y}} is true if and only if \var{x} and \var{y}

are the same object. \code{\var{x} is not \var{y}} yields the inverse

truth value.

\opindex{is}

\opindex{is not}

\indexii{identity}{test}

\section{Boolean operations\label{Booleans}}

\indexii{Boolean}{operation}

Boolean operations have the lowest priority of all Python operations:

\begin{productionlist}

\production{expression}

{\token{or_test} | \token{lambda_form}}

\production{or_test}

{\token{and_test} | \token{or_test} "or" \token{and_test}}

\production{and_test}

{\token{not_test} | \token{and_test} "and" \token{not_test}}

\production{not_test}

{\token{comparison} | "not" \token{not_test}}

\production{lambda_form}

{"lambda" [\token{parameter_list}]: \token{expression}}

\end{productionlist}

In the context of Boolean operations, and also when expressions are

used by control flow statements, the following values are interpreted

as false: \code{None}, numeric zero of all types, empty sequences

(strings, tuples and lists), and empty mappings (dictionaries). All

other values are interpreted as true.

The operator \keyword{not} yields \code{1} if its argument is false,

\code{0} otherwise.

\opindex{not}

The expression \code{\var{x} and \var{y}} first evaluates \var{x}; if

\var{x} is false, its value is returned; otherwise, \var{y} is

evaluated and the resulting value is returned.

\opindex{and}

The expression \code{\var{x} or \var{y}} first evaluates \var{x}; if

\var{x} is true, its value is returned; otherwise, \var{y} is

evaluated and the resulting value is returned.

\opindex{or}

(Note that neither \keyword{and} nor \keyword{or} restrict the value

and type they return to \code{0} and \code{1}, but rather return the

last evaluated argument.

This is sometimes useful, e.g., if \code{s} is a string that should be

replaced by a default value if it is empty, the expression

\code{s or 'foo'} yields the desired value. Because \keyword{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., \code{not 'foo'} yields \code{0},

not \code{''}.)

\section{Lambdas\label{lambdas}}

\indexii{lambda}{expression}

\indexii{lambda}{form}

\indexii{anonmymous}{function}

Lambda forms (lambda expressions) have the same syntactic position as

expressions. They are a shorthand to create anonymous functions; the

expression \code{lambda \var{arguments}: \var{expression}}

yields a function object. The unnamed object behaves like a function

object defined with

\begin{verbatim}

def name(arguments):