\chapter{Expressions and conditions}

\index{expression}

\index{condition}

{\bf Note:} In this and the following chapters, extended BNF notation

will be used to describe syntax, not lexical analysis.

\index{BNF}

This chapter explains the meaning of the elements of expressions and

conditions. Conditions are a superset of expressions, and a condition

may be used wherever an expression is required by enclosing it in

parentheses. The only places where expressions are used in the syntax

instead of conditions is in expression statements and on the

right-hand side of assignment statements; this catches some nasty bugs

like accidentally writing \verb@x == 1@ instead of \verb@x = 1@.

\indexii{assignment}{statement}

The comma plays several roles in Python's syntax. It is usually an

operator with a lower precedence than all others, but occasionally

serves other purposes as well; e.g. it separates function arguments,

is used in list and dictionary constructors, and has special semantics

in \verb@print@ statements.

\index{comma}

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

\begin{verbatim}

name: othername

\end{verbatim}

and no semantics are given, the semantics of this form of \verb@name@

are the same as for \verb@othername@.

\index{syntax}

\section{Arithmetic conversions}

\indexii{arithmetic}{conversion}

When a description of an arithmetic operator below uses the phrase

``the numeric arguments are converted to a common type'',

this both means that if either argument is not a number, a

\verb@TypeError@ exception is raised, and that otherwise

the following conversions are applied:

\exindex{TypeError}

\indexii{floating point}{number}

\indexii{long}{integer}

\indexii{plain}{integer}

\begin{itemize}

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

the other is converted to floating point;

\item else, 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}

\section{Atoms}

\index{atom}

Atoms are the most basic elements of expressions. Forms enclosed in

reverse quotes or in parentheses, brackets or braces are also

categorized syntactically as atoms. The syntax for atoms is:

\begin{verbatim}

atom: identifier | literal | enclosure

enclosure: parenth_form|list_display|dict_display|string_conversion

\end{verbatim}

\subsection{Identifiers (Names)}

\index{name}

\index{identifier}

An identifier occurring as an atom is a reference to a local, global

or built-in name binding. If a name is assigned to anywhere in a code

block (even in unreachable code), and is not mentioned in a

\verb@global@ statement in that code block, then it refers to a local

name throughout that code block. When it is not assigned to anywhere

in the block, or when it is assigned to but also explicitly listed in

a \verb@global@ statement, it refers to a global name if one exists,

else to a built-in name (and this binding may dynamically change).

\indexii{name}{binding}

\index{code block}

\stindex{global}

\indexii{built-in}{name}

\indexii{global}{name}

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 \verb@NameError@ exception.

\exindex{NameError}

\subsection{Literals}

\index{literal}

Python knows string and numeric literals:

\begin{verbatim}

literal: stringliteral | integer | longinteger | floatnumber

\end{verbatim}

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

integer, long integer, floating point number) with the given value.

The value may be approximated in the case of floating point 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}

(In the original implementation, all literals in the same code block

with the same type and value yield the same object.)

\subsection{Parenthesized forms}

\index{parenthesized form}

A parenthesized form is an optional condition list enclosed in

parentheses:

\begin{verbatim}

parenth_form: "(" [condition_list] ")"

\end{verbatim}

A parenthesized condition list yields whatever that condition list

yields.

An empty pair of parentheses yields an empty tuple object. Since

tuples are immutable, the rules for literals apply here.

\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 {\em 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}

\indexii{list}{display}

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

square brackets:

\begin{verbatim}

list_display: "[" [condition_list] "]"

\end{verbatim}

A list display yields a new list object.

\obindex{list}

If it has no condition list, the list object has no items. Otherwise,

the elements of the condition list are evaluated from left to right

and inserted in the list object in that order.

\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{verbatim}

dict_display: "{" [key_datum_list] "}"

key_datum_list: key_datum ("," key_datum)* [","]

key_datum: condition ":" condition

\end{verbatim}

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}.

Clashes between duplicate keys are not detected; the last

datum (textually rightmost in the display) stored for a given key

value prevails.

\exindex{TypeError}

\subsection{String conversions}

\indexii{string}{conversion}

\indexii{reverse}{quotes}

\indexii{backward}{quotes}

\index{back-quotes}

A string conversion is a condition list enclosed in reverse (or

backward) quotes:

\begin{verbatim}

string_conversion: "`" condition_list "`"

\end{verbatim}

A string conversion evaluates the contained condition list and

converts the resulting object into a string according to rules

specific to its type.

If the object is a string, a number, \verb@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 \verb@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.)

It is illegal to attempt to convert recursive objects (e.g. lists or

dictionaries that contain a reference to themselves, directly or

indirectly.)

\obindex{recursive}

The built-in function \verb@repr()@ performs exactly the same

conversion in its argument as enclosing it it reverse quotes does.

The built-in function \verb@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{verbatim}

primary: atom | attributeref | subscription | slicing | call

\end{verbatim}

\subsection{Attribute references}

\indexii{attribute}{reference}

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

\begin{verbatim}

attributeref: primary "." identifier

\end{verbatim}

The primary must evaluate to an object of a type that supports

attribute references, e.g. a module or a list. This object is then

asked to produce the attribute whose name is the identifier. If this

attribute is not available, the exception \verb@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}

\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{verbatim}

subscription: primary "[" condition "]"

\end{verbatim}

The primary must evaluate to an object of a sequence or mapping type.

If it is a mapping, the condition 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.

If it is a sequence, the condition must evaluate to a plain integer.

If this value is negative, the length of the sequence is added to it

(so that, e.g. \verb@x[-1]@ selects the last item of \verb@x@.)

The resulting value must be a nonnegative integer smaller 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}

\index{slicing}

\index{slice}

A slicing (or slice) selects a range of items in a sequence (string,

tuple or list) object:

\obindex{sequence}

\obindex{string}

\obindex{tuple}

\obindex{list}

\begin{verbatim}

slicing: primary "[" [condition] ":" [condition] "]"

\end{verbatim}

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 sequence's length, 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).

\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{verbatim}

call: primary "(" [condition_list] ")"

\end{verbatim}

The primary must evaluate to a callable object (user-defined

functions, built-in functions, methods of built-in objects, class

objects, and methods of class instances are callable). If it is a

class, the argument list must be empty; otherwise, the arguments are

evaluated.

A call always returns some value, possibly \verb@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

\verb@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 library reference manual 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{instance}{call}

\indexii{class instance}{call}

\end{description}

\section{Unary arithmetic operations}

\indexiii{unary}{arithmetic}{operation}

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

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

\begin{verbatim}

u_expr: primary | "-" u_expr | "+" u_expr | "~" u_expr

\end{verbatim}

The unary \verb@"-"@ (minus) operator yields the negation of its

numeric argument.

\index{negation}

\index{minus}

The unary \verb@"+"@ (plus) operator yields its numeric argument

unchanged.

\index{plus}

The unary \verb@"~"@ (invert) operator yields the bit-wise inversion

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

\verb@x@ is defined as \verb@-(x+1)@.

\index{inversion}

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

a \verb@TypeError@ exception is raised.

\exindex{TypeError}

\section{Binary arithmetic operations}

\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. There is no ``power'' operator, so there are only

two levels, one for multiplicative operators and one for additive

operators:

\begin{verbatim}

m_expr: u_expr | m_expr "*" u_expr

| m_expr "/" u_expr | m_expr "%" u_expr

a_expr: m_expr | aexpr "+" m_expr | aexpr "-" m_expr

\end{verbatim}

The \verb@"*"@ (multiplication) operator yields the product of its

arguments. The arguments must either both be numbers, or one argument

must be a plain integer and the other must be a sequence. In the

former case, the numbers are converted to a common type and then

multiplied together. In the latter case, sequence repetition is

performed; a negative repetition factor yields an empty sequence.

\index{multiplication}

The \verb@"/"@ (division) operator yields the quotient of its

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

\verb@ZeroDivisionError@ exception.

\exindex{ZeroDivisionError}

\index{division}

The \verb@"%"@ (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 \verb@ZeroDivisionError@ exception. The arguments may be floating

point numbers, e.g. \[email protected] % 0.7@ equals \[email protected]@. 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 second operand.

\index{modulo}

The integer division and modulo operators are connected by the

following identity: \verb@x == (x/y)*y + (x%y)@. Integer division and

modulo are also connected with the built-in function \verb@divmod()@:

\verb@divmod(x, y) == (x/y, x%y)@. These identities don't hold for

floating point numbers; there a similar identity holds where

\verb@x/y@ is replaced by \verb@floor(x/y)@).

The \verb@"+"@ (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 \verb@"-"@ (subtraction) operator yields the difference of its

arguments. The numeric arguments are first converted to a common

type.

\index{subtraction}

\section{Shifting operations}

\indexii{shifting}{operation}

The shifting operations have lower priority than the arithmetic

operations:

\begin{verbatim}

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

\end{verbatim}

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 this 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 \verb@ValueError@ exception.

\exindex{ValueError}

\section{Binary bit-wise operations}

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

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

\begin{verbatim}

and_expr: shift_expr | and_expr "&" shift_expr

xor_expr: and_expr | xor_expr "^" and_expr

or_expr: xor_expr | or_expr "|" xor_expr

\end{verbatim}

The \verb@"&"@ 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 \verb@"^"@ 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 \verb@"|"@ 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}

\index{comparison}

Contrary to C, all comparison operations in Python have the same

priority, which is lower than that of any arithmetic, shifting or

bitwise operation. Also contrary to C, expressions like

\verb@a < b < c@ have the interpretation that is conventional in

mathematics:

\index{C}

\begin{verbatim}

comparison: or_expr (comp_operator or_expr)*

comp_operator: "<"|">"|"=="|">="|"<="|"<>"|"!="|"is" ["not"]|["not"] "in"

\end{verbatim}

Comparisons yield integer values: 1 for true, 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} \code{and} \var{b opb c} \code{and} \ldots \code{and}

\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 \verb@<>@ and \verb@!=@ are equivalent; for consistency with

C, \verb@!=@ is preferred; where \verb@!=@ is mentioned below

\verb@<>@ is also implied.

The operators {\tt "<", ">", "==", ">=", "<="}, and {\tt "!="} compare

the values of two objects. The objects needn't have the same type.

If both are numbers, they are coverted to a common type. Otherwise,

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

ordered consistently but arbitrarily.

(This unusual definition of comparison is done to simplify the

definition of operations like sorting and the \verb@in@ and

\verb@not@ \verb@in@ operators.)

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 \verb@ord@) of their characters.

\item

Tuples and lists are compared lexicographically using comparison of

corresponding items.

\item

Mappings (dictionaries) are compared through lexicographic

comparison of their sorted (key, value) lists.%

\footnote{This is expensive since it requires sorting the keys first,

but about the only sensible definition. An 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 {\tt \{\}}.}

\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 \verb@in@ and \verb@not in@ test for sequence

membership: if \var{y} is a sequence, \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}]}.

\code{\var{x} not in \var{y}} yields the inverse truth value. The

exception \verb@TypeError@ is raised when \var{y} is not a sequence,

or when \var{y} is a string and \var{x} is not a string of length one.%

\footnote{The latter restriction is sometimes a nuisance.}

\opindex{in}

\opindex{not in}

\indexii{membership}{test}

\obindex{sequence}

The operators \verb@is@ and \verb@is not@ test for object identity:

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

are the same object. \var{x} \code{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{verbatim}

condition: or_test | lambda_form

or_test: and_test | or_test "or" and_test

and_test: not_test | and_test "and" not_test

not_test: comparison | "not" not_test

lambda_form: "lambda" [parameter_list]: condition

\end{verbatim}

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

used by control flow statements, the following values are interpreted

as false: \verb@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 \verb@not@ yields 1 if its argument is false, 0 otherwise.

\opindex{not}

The condition \var{x} \verb@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 condition \var{x} \verb@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 \verb@and@ and \verb@or@ do not restrict the value and type

they return to 0 and 1, but rather return the last evaluated argument.

This is sometimes useful, e.g. if \verb@s@ is a string that should be

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

\verb@s or 'foo'@ yields the desired value. Because \verb@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. \verb@not 'foo'@ yields \verb@0@,

not \verb@''@.)

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

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

expression {\em {\tt lambda} arguments{\tt :} condition}

yields a function object that behaves virtually identical to one

defined with

{\em {\tt def} name {\tt (}arguments{\tt ): return} condition}.

See section \ref{function} for the syntax of

parameter lists. Note that functions created with lambda forms cannot

contain statements.

\label{lambda}

\indexii{lambda}{expression}

\indexii{lambda}{form}

\indexii{anonmymous}{function}

\section{Expression lists and condition lists}

\indexii{expression}{list}

\indexii{condition}{list}

\begin{verbatim}

expr_list: or_expr ("," or_expr)* [","]

cond_list: condition ("," condition)* [","]

\end{verbatim}

The only difference between expression lists and condition lists is

the lowest priority of operators that can be used in them without

being enclosed in parentheses; condition lists allow all operators,

while expression lists don't allow comparisons and Boolean operators

(they do allow bitwise and shift operators though).

Expression lists are used in expression statements and assignments;

condition lists are used everywhere else where a list of

comma-separated values is required.

An expression (condition) list containing at least one comma yields a

tuple. The length of the tuple is the number of expressions

(conditions) in the list. The expressions (conditions) are evaluated

from left to right. (Condition lists are used syntactically is a few

places where no tuple is constructed but a list of values is needed

nevertheless.)

\obindex{tuple}

The trailing comma is required only to create a single tuple (a.k.a. a

{\em singleton}); it is optional in all other cases. A single

expression (condition) without a trailing comma doesn't create a

tuple, but rather yields the value of that expression (condition).

\indexii{trailing}{comma}

(To create an empty tuple, use an empty pair of parentheses:

\verb@()@.)

\section{Summary}

The following table summarizes the operator precedences in Python,

from lowest precedence (least binding) to highest precedence (most

binding). Operators in the same box have the same precedence. Unless

the syntax is explicitly given, operators are binary. Operators in

the same box group left to right (except for comparisons, which

chain from left to right --- see above).

\begin{center}

\begin{tabular}{|c|c|}

\hline

\code{or} & Boolean OR \\

\hline

\code{and} & Boolean AND \\

\hline

\code{not} \var{x} & Boolean NOT \\

\hline

\code{in}, \code{not} \code{in} & Membership tests \\

\code{is}, \code{is} \code{not} & Identity tests \\

\code{<}, \code{<=}, \code{>}, \code{>=}, \code{<>}, \code{!=}, \code{=} &

Comparisons \\

\hline

\code{|} & Bitwise OR \\

\hline

\code{\^} & Bitwise XOR \\

\hline

\code{\&} & Bitwise AND \\

\hline

\code{<<}, \code{>>} & Shifts \\

\hline

\code{+}, \code{-} & Addition and subtraction \\

\hline

\code{*}, \code{/}, \code{\%} & Multiplication, division, remainder \\

\hline

\code{+\var{x}}, \code{-\var{x}} & Positive, negative \\

\code{\~\var{x}} & Bitwise not \\

\hline

\code{\var{x}.\var{attribute}} & Attribute reference \\

\code{\var{x}[\var{index}]} & Subscription \\

\code{\var{x}[\var{index}:\var{index}]} & Slicing \\

\code{\var{f}(\var{arguments}...)} & Function call \\

\hline

\code{(\var{expressions}\ldots)} & Binding or tuple display \\

\code{[\var{expressions}\ldots]} & List display \\

\code{\{\var{key}:\var{datum}\ldots\}} & Dictionary display \\

\code{`\var{expression}\ldots`} & String conversion \\

\hline

\end{tabular}

\end{center}