Changes copied from the FrameMaker version, and some new stuff

(complex numbers, power operator).
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Guido van Rossum 1998-07-23 21:57:42 +00:00
parent 5420f3321d
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@ -1,28 +1,12 @@
\chapter{Expressions and conditions} \chapter{Expressions}
\index{expression} \index{expression}
\index{condition}
\strong{Note:} In this and the following chapters, extended BNF This chapter explains the meaning of the elements of expressions in
notation will be used to describe syntax, not lexical analysis. Python.
\index{BNF}
This chapter explains the meaning of the elements of expressions and \strong{Syntax Notes:} In this and the following chapters, extended
conditions. Conditions are a superset of expressions, and a condition BNF\index{BNF} notation will be used to describe syntax, not lexical
may be used wherever an expression is required by enclosing it in analysis. When (one alternative of) a syntax rule has the form
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 \code{x == 1} instead of \code{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 \keyword{print} statements.
\index{comma}
When (one alternative of) a syntax rule has the form
\begin{verbatim} \begin{verbatim}
name: othername name: othername
@ -36,28 +20,30 @@ are the same as for \code{othername}.
\indexii{arithmetic}{conversion} \indexii{arithmetic}{conversion}
When a description of an arithmetic operator below uses the phrase When a description of an arithmetic operator below uses the phrase
``the numeric arguments are converted to a common type'', ``the numeric arguments are converted to a common type,'' the
this both means that if either argument is not a number, a arguments are coerced using the coercion rules listed at the end of
\exception{TypeError} exception is raised, and that otherwise chapter 3. If both arguments are standard numeric types, the
the following conversions are applied: following coercions are applied:
\exindex{TypeError}
\indexii{floating point}{number}
\indexii{long}{integer}
\indexii{plain}{integer}
\begin{itemize} \begin{itemize}
\item first, if either argument is a floating point number, \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; the other is converted to floating point;
\item else, if either argument is a long integer, \item otherwise, if either argument is a long integer,
the other is converted to long integer; the other is converted to long integer;
\item otherwise, both must be plain integers and no conversion \item otherwise, both must be plain integers and no conversion
is necessary. is necessary.
\end{itemize} \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} \section{Atoms}
\index{atom} \index{atom}
Atoms are the most basic elements of expressions. Forms enclosed in 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 reverse quotes or in parentheses, brackets or braces are also
categorized syntactically as atoms. The syntax for atoms is: categorized syntactically as atoms. The syntax for atoms is:
@ -89,19 +75,37 @@ that object. When a name is not bound, an attempt to evaluate it
raises a \exception{NameError} exception. raises a \exception{NameError} exception.
\exindex{NameError} \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 ``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} \subsection{Literals}
\index{literal} \index{literal}
Python knows string and numeric literals: Python supports string literals and various numeric literals:
\begin{verbatim} \begin{verbatim}
literal: stringliteral | integer | longinteger | floatnumber literal: stringliteral | integer | longinteger | floatnumber | imagnumber
\end{verbatim} \end{verbatim}
Evaluation of a literal yields an object of the given type (string, Evaluation of a literal yields an object of the given type (string,
integer, long integer, floating point number) with the given value. integer, long integer, floating point number, complex number) with the
The value may be approximated in the case of floating point literals. given value. The value may be approximated in the case of floating
See section \ref{literals} for details. point and imaginary (complex) literals. See section \ref{literals}
for details.
All literals correspond to immutable data types, and hence the All literals correspond to immutable data types, and hence the
object's identity is less important than its value. Multiple object's identity is less important than its value. Multiple
@ -109,51 +113,51 @@ evaluations of literals with the same value (either the same
occurrence in the program text or a different occurrence) may obtain occurrence in the program text or a different occurrence) may obtain
the same object or a different object with the same value. the same object or a different object with the same value.
\indexiii{immutable}{data}{type} \indexiii{immutable}{data}{type}
\indexii{immutable}{objects}
(In the original implementation, all literals in the same code block
with the same type and value yield the same object.)
\subsection{Parenthesized forms} \subsection{Parenthesized forms}
\index{parenthesized form} \index{parenthesized form}
A parenthesized form is an optional condition list enclosed in A parenthesized form is an optional expression list enclosed in
parentheses: parentheses:
\begin{verbatim} \begin{verbatim}
parenth_form: "(" [condition_list] ")" parenth_form: "(" [expression_list] ")"
\end{verbatim} \end{verbatim}
A parenthesized condition list yields whatever that condition list A parenthesized expression list yields whatever that expression list
yields. 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 An empty pair of parentheses yields an empty tuple object. Since
tuples are immutable, the rules for literals apply here. 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} \indexii{empty}{tuple}
(Note that tuples are not formed by the parentheses, but rather by use 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 of the comma operator. The exception is the empty tuple, for which
parentheses {\em are} required --- allowing unparenthesized ``nothing'' parentheses {\em are} required --- allowing unparenthesized ``nothing''
in expressions would cause ambiguities and allow common typos to in expressions would cause ambiguities and allow common typos to
pass uncaught.) pass uncaught.
\index{comma} \index{comma}
\indexii{tuple}{display} \indexii{tuple}{display}
\subsection{List displays} \subsection{List displays}
\indexii{list}{display} \indexii{list}{display}
A list display is a possibly empty series of conditions enclosed in A list display is a possibly empty series of expressions enclosed in
square brackets: square brackets:
\begin{verbatim} \begin{verbatim}
list_display: "[" [condition_list] "]" list_display: "[" [expression_list] "]"
\end{verbatim} \end{verbatim}
A list display yields a new list object. A list display yields a new list object. If it has no expression
list, the list object has no items. Otherwise, the elements of the
expression list are evaluated from left to right and inserted in the
list object in that order.
\obindex{list} \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} \indexii{empty}{list}
\subsection{Dictionary displays} \label{dict} \subsection{Dictionary displays} \label{dict}
@ -168,7 +172,7 @@ enclosed in curly braces:
\begin{verbatim} \begin{verbatim}
dict_display: "{" [key_datum_list] "}" dict_display: "{" [key_datum_list] "}"
key_datum_list: key_datum ("," key_datum)* [","] key_datum_list: key_datum ("," key_datum)* [","]
key_datum: condition ":" condition key_datum: expression ":" expression
\end{verbatim} \end{verbatim}
A dictionary display yields a new dictionary object. A dictionary display yields a new dictionary object.
@ -179,11 +183,11 @@ entries of the dictionary: each key object is used as a key into the
dictionary to store the corresponding datum. dictionary to store the corresponding datum.
Restrictions on the types of the key values are listed earlier in Restrictions on the types of the key values are listed earlier in
section \ref{types}. section \ref{types}. (To summarize,the key type should be hashable,
Clashes between duplicate keys are not detected; the last which excludes all mutable objects.) Clashes between duplicate keys
datum (textually rightmost in the display) stored for a given key are not detected; the last datum (textually rightmost in the display)
value prevails. stored for a given key value prevails.
\exindex{TypeError} \indexii{immutable}{objects}
\subsection{String conversions} \subsection{String conversions}
\indexii{string}{conversion} \indexii{string}{conversion}
@ -191,14 +195,14 @@ value prevails.
\indexii{backward}{quotes} \indexii{backward}{quotes}
\index{back-quotes} \index{back-quotes}
A string conversion is a condition list enclosed in reverse (or A string conversion is an expression list enclosed in reverse (a.k.a.
backward) quotes: backward) quotes:
\begin{verbatim} \begin{verbatim}
string_conversion: "`" condition_list "`" string_conversion: "`" expression_list "`"
\end{verbatim} \end{verbatim}
A string conversion evaluates the contained condition list and A string conversion evaluates the contained expression list and
converts the resulting object into a string according to rules converts the resulting object into a string according to rules
specific to its type. specific to its type.
@ -218,9 +222,9 @@ indirectly.)
\obindex{recursive} \obindex{recursive}
The built-in function \function{repr()} performs exactly the same The built-in function \function{repr()} performs exactly the same
conversion in its argument as enclosing it it reverse quotes does. conversion in its argument as enclosing it in parentheses and reverse
The built-in function \function{str()} performs a similar but more quotes does. The built-in function \function{str()} performs a
user-friendly conversion. similar but more user-friendly conversion.
\bifuncindex{repr} \bifuncindex{repr}
\bifuncindex{str} \bifuncindex{str}
@ -268,21 +272,23 @@ or mapping (dictionary) object:
\indexii{sequence}{item} \indexii{sequence}{item}
\begin{verbatim} \begin{verbatim}
subscription: primary "[" condition "]" subscription: primary "[" expression_list "]"
\end{verbatim} \end{verbatim}
The primary must evaluate to an object of a sequence or mapping type. 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 If the primary is a mapping, the expression list must evaluate to an
value is one of the keys of the mapping, and the subscription selects object whose value is one of the keys of the mapping, and the
the value in the mapping that corresponds to that key. 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 it is a sequence, the condition must evaluate to a plain integer. If the primary is a sequence, the expression (list) must evaluate to a
If this value is negative, the length of the sequence is added to it plain integer. If this value is negative, the length of the sequence
(so that, e.g. \code{x[-1]} selects the last item of \code{x}.) is added to it (so that, e.g., \code{x[-1]} selects the last item of
The resulting value must be a nonnegative integer smaller than the \code{x}.) The resulting value must be a nonnegative integer less
number of items in the sequence, and the subscription selects the item than the number of items in the sequence, and the subscription selects
whose index is that value (counting from zero). the item whose index is that value (counting from zero).
A string's items are characters. A character is not a separate data A string's items are characters. A character is not a separate data
type but a string of exactly one character. type but a string of exactly one character.
@ -293,53 +299,144 @@ type but a string of exactly one character.
\index{slicing} \index{slicing}
\index{slice} \index{slice}
A slicing (or slice) selects a range of items in a sequence (string, A slicing selects a range of items in a sequence object (e.g., a
tuple or list) object: 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{sequence}
\obindex{string} \obindex{string}
\obindex{tuple} \obindex{tuple}
\obindex{list} \obindex{list}
\begin{verbatim} \begin{verbatim}
slicing: primary "[" [condition] ":" [condition] "]" 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: "..."
\end{verbatim} \end{verbatim}
The primary must evaluate to a sequence object. The lower and upper There is ambiguity in the formal syntax here: anything that looks like
bound expressions, if present, must evaluate to plain integers; an expression list also looks like a slice list, so any subscription
defaults are zero and the sequence's length, respectively. If either can be interpreted as a slicing. Rather than further complicating the
bound is negative, the sequence's length is added to it. The slicing syntax, this is disambiguated by defining that in this case the
now selects all items with index \var{k} such that 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
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} \code{\var{i} <= \var{k} < \var{j}} where \var{i}
and \var{j} are the specified lower and upper bounds. This may be an 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 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 range of valid indexes (such items don't exist so they aren't
selected). 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
\code{start}, \code{stop} and \code{step} attributes are the values of
the expressions given as lower bound, upper bound and stride,
respectively, substituting \code{None} for missing expressions.
\subsection{Calls} \label{calls} \subsection{Calls} \label{calls}
\index{call} \index{call}
A call calls a callable object (e.g. a function) with a possibly empty A call calls a callable object (e.g. a function) with a possibly empty
series of arguments:\footnote{The new syntax for keyword arguments is series of arguments:
not yet documented in this manual. See chapter 12 of the Tutorial.}
\obindex{callable} \obindex{callable}
\begin{verbatim} \begin{verbatim}
call: primary "(" [condition_list] ")" call: primary "(" [argument_list [","]] ")"
argument_list: positional_arguments ["," keyword_arguments]
| keyword_arguments
positional_arguments: expression ("," expression)*
keyword_arguments: keyword_item ("," keyword_item)*
keyword_item: identifier "=" expression
\end{verbatim} \end{verbatim}
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 The primary must evaluate to a callable object (user-defined
functions, built-in functions, methods of built-in objects, class functions, built-in functions, methods of built-in objects, class
objects, and methods of class instances are callable). If it is a objects, methods of class instances, and certain class instances
class, the argument list must be empty; otherwise, the arguments are themselves are callable; extensions may define additional callable
evaluated. 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 ``\code{*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 ``\code{**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.
Formal parameters using the syntax ``\code{*identifier}'' or
``\code{**identifier}'' cannot be used as positional argument slots or
as keyword argument names. Formal parameters using the syntax
``\code{(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 A call always returns some value, possibly \code{None}, unless it
raises an exception. How this value is computed depends on the type raises an exception. How this value is computed depends on the type
of the callable object. If it is: of the callable object.
If it is---
\begin{description} \begin{description}
\item[a user-defined function:] the code block for the function is \item[a user-defined function:] The code block for the function is
executed, passing it the argument list. The first thing the code executed, passing it the argument list. The first thing the code
block will do is bind the formal parameters to the arguments; this is block will do is bind the formal parameters to the arguments; this is
described in section \ref{function}. When the code block executes a described in section \ref{function}. When the code block executes a
@ -350,7 +447,7 @@ function call.
\obindex{user-defined function} \obindex{user-defined function}
\obindex{function} \obindex{function}
\item[a built-in function or method:] the result is up to the \item[a built-in function or method:] The result is up to the
interpreter; see the library reference manual for the descriptions of interpreter; see the library reference manual for the descriptions of
built-in functions and methods. built-in functions and methods.
\indexii{function}{call} \indexii{function}{call}
@ -362,20 +459,49 @@ built-in functions and methods.
\obindex{method} \obindex{method}
\obindex{function} \obindex{function}
\item[a class object:] a new instance of that class is returned. \item[a class object:] A new instance of that class is returned.
\obindex{class} \obindex{class}
\indexii{class object}{call} \indexii{class object}{call}
\item[a class instance method:] the corresponding user-defined \item[a class instance method:] The corresponding user-defined
function is called, with an argument list that is one longer than the function is called, with an argument list that is one longer than the
argument list of the call: the instance becomes the first argument. argument list of the call: the instance becomes the first argument.
\obindex{class instance} \obindex{class instance}
\obindex{instance} \obindex{instance}
\indexii{instance}{call}
\indexii{class instance}{call} \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}
\ttindex{__call__}
\end{description} \end{description}
\section{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:
\begin{verbatim}
power: primary ["**" u_expr]
\end{verbatim}
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; if the result is not
expressible in that type (as in raising an integer to a negative
power, or a negative floating point number to a broken power), a
\exception{TypeError} exception is raised.
\section{Unary arithmetic operations} \section{Unary arithmetic operations}
\indexiii{unary}{arithmetic}{operation} \indexiii{unary}{arithmetic}{operation}
\indexiii{unary}{bit-wise}{operation} \indexiii{unary}{bit-wise}{operation}
@ -383,7 +509,7 @@ argument list of the call: the instance becomes the first argument.
All unary arithmetic (and bit-wise) operations have the same priority: All unary arithmetic (and bit-wise) operations have the same priority:
\begin{verbatim} \begin{verbatim}
u_expr: primary | "-" u_expr | "+" u_expr | "~" u_expr u_expr: power | "-" u_expr | "+" u_expr | "~" u_expr
\end{verbatim} \end{verbatim}
The unary \code{-} (minus) operator yields the negation of its The unary \code{-} (minus) operator yields the negation of its
@ -397,7 +523,8 @@ unchanged.
The unary \code{~} (invert) operator yields the bit-wise inversion The unary \code{~} (invert) operator yields the bit-wise inversion
of its plain or long integer argument. The bit-wise inversion of of its plain or long integer argument. The bit-wise inversion of
\code{x} is defined as \code{-(x+1)}. \code{x} is defined as \code{-(x+1)}. It only applies to integral
numbers.
\index{inversion} \index{inversion}
In all three cases, if the argument does not have the proper type, In all three cases, if the argument does not have the proper type,
@ -409,8 +536,8 @@ a \exception{TypeError} exception is raised.
The binary arithmetic operations have the conventional priority The binary arithmetic operations have the conventional priority
levels. Note that some of these operations also apply to certain levels. Note that some of these operations also apply to certain
non-numeric types. There is no ``power'' operator, so there are only non-numeric types. Apart from the power operator, there are only two
two levels, one for multiplicative operators and one for additive levels, one for multiplicative operators and one for additive
operators: operators:
\begin{verbatim} \begin{verbatim}
@ -440,21 +567,23 @@ The \code{\%} (modulo) operator yields the remainder from the
division of the first argument by the second. The numeric arguments division of the first argument by the second. The numeric arguments
are first converted to a common type. A zero right argument raises are first converted to a common type. A zero right argument raises
the \exception{ZeroDivisionError} exception. The arguments may be floating the \exception{ZeroDivisionError} exception. The arguments may be floating
point numbers, e.g. \code{3.14 \% 0.7} equals \code{0.34}. The modulo point numbers, e.g. \code{3.14\%0.7} equals \code{0.34} (since
operator always yields a result with the same sign as its second \code{3.14} equals \code{4*0.7 + 0.34}.) The modulo operator always
operand (or zero); the absolute value of the result is strictly yields a result with the same sign as its second operand (or zero);
smaller than the second operand. the absolute value of the result is strictly smaller than the second
operand.
\index{modulo} \index{modulo}
The integer division and modulo operators are connected by the The integer division and modulo operators are connected by the
following identity: \code{x == (x/y)*y + (x\%y)}. Integer division and following identity: \code{x == (x/y)*y + (x\%y)}. Integer division and
modulo are also connected with the built-in function \function{divmod()}: 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 \code{divmod(x, y) == (x/y, x\%y)}. These identities don't hold for
floating point numbers; there a similar identity holds where floating point and complex numbers; there a similar identity holds where
\code{x/y} is replaced by \code{floor(x/y)}). \code{x/y} is replaced by \code{floor(x/y)}) or
\code{floor((x/y).real)}, respectively.
The \code{+} (addition) operator yields the sum of its arguments. The \code{+} (addition) operator yields the sum of its arguments.
The arguments must either both be numbers, or both sequences of the 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 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 type and then added together. In the latter case, the sequences are
concatenated. concatenated.
@ -483,10 +612,10 @@ second argument.
A right shift by \var{n} bits is defined as division by 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 \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 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 no overflow check so in that case the operation drops bits and flips
is not less than \code{pow(2,31)} in absolute value. the sign if the result is not less than \code{pow(2,31)} in absolute
value. Negative shift counts raise a \exception{ValueError}
Negative shift counts raise a \exception{ValueError} exception. exception.
\exindex{ValueError} \exindex{ValueError}
\section{Binary bit-wise operations} \section{Binary bit-wise operations}
@ -543,16 +672,17 @@ when \code{x < y} is found to be false).
Formally, if \var{a}, \var{b}, \var{c}, \ldots, \var{y}, \var{z} are 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 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 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 \keyword{and} 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. \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 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 between \var{a} and \var{c}, so that, e.g., \code{x < y > z} is
perfectly legal (though perhaps not pretty). perfectly legal (though perhaps not pretty).
The forms \code{<>} and \code{!=} are equivalent; for consistency with The forms \code{<>} and \code{!=} are equivalent; for consistency with
C, \code{!=} is preferred; where \code{!=} is mentioned below C, \code{!=} is preferred; where \code{!=} is mentioned below
\code{<>} is also implied. \code{<>} is also acceptable. At some point in the (far) future,
\code{<>} may become obsolete.
The operators {\tt "<", ">", "==", ">=", "<="}, and {\tt "!="} compare The operators {\tt "<", ">", "==", ">=", "<="}, and {\tt "!="} compare
the values of two objects. The objects needn't have the same type. the values of two objects. The objects needn't have the same type.
@ -560,9 +690,10 @@ If both are numbers, they are coverted to a common type. Otherwise,
objects of different types {\em always} compare unequal, and are objects of different types {\em always} compare unequal, and are
ordered consistently but arbitrarily. ordered consistently but arbitrarily.
(This unusual definition of comparison is done to simplify the (This unusual definition of comparison was used to simplify the
definition of operations like sorting and the \keyword{in} and definition of operations like sorting and the \keyword{in} and
\keyword{not in} operators.) \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: Comparison of objects of the same type depends on the type:
@ -584,10 +715,10 @@ corresponding items.
Mappings (dictionaries) are compared through lexicographic Mappings (dictionaries) are compared through lexicographic
comparison of their sorted (key, value) lists.% comparison of their sorted (key, value) lists.%
\footnote{This is expensive since it requires sorting the keys first, \footnote{This is expensive since it requires sorting the keys first,
but about the only sensible definition. An earlier version of Python but it is about the only sensible definition. An earlier version of
compared dictionaries by identity only, but this caused surprises Python compared dictionaries by identity only, but this caused
because people expected to be able to test a dictionary for emptiness surprises because people expected to be able to test a dictionary for
by comparing it to \code{\{\}}.} emptiness by comparing it to \code{\{\}}.}
\item \item
Most other types compare unequal unless they are the same object; Most other types compare unequal unless they are the same object;
@ -624,14 +755,14 @@ truth value.
Boolean operations have the lowest priority of all Python operations: Boolean operations have the lowest priority of all Python operations:
\begin{verbatim} \begin{verbatim}
condition: or_test | lambda_form expression: or_test | lambda_form
or_test: and_test | or_test "or" and_test or_test: and_test | or_test "or" and_test
and_test: not_test | and_test "and" not_test and_test: not_test | and_test "and" not_test
not_test: comparison | "not" not_test not_test: comparison | "not" not_test
lambda_form: "lambda" [parameter_list]: condition lambda_form: "lambda" [parameter_list]: expression
\end{verbatim} \end{verbatim}
In the context of Boolean operations, and also when conditions are In the context of Boolean operations, and also when expressions are
used by control flow statements, the following values are interpreted used by control flow statements, the following values are interpreted
as false: \code{None}, numeric zero of all types, empty sequences as false: \code{None}, numeric zero of all types, empty sequences
(strings, tuples and lists), and empty mappings (dictionaries). All (strings, tuples and lists), and empty mappings (dictionaries). All
@ -641,20 +772,20 @@ The operator \keyword{not} yields \code{1} if its argument is false,
\code{0} otherwise. \code{0} otherwise.
\opindex{not} \opindex{not}
The condition \code{\var{x} and \var{y}} first evaluates \var{x}; if 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 \var{x} is false, its value is returned; otherwise, \var{y} is
evaluated and the resulting value is returned. evaluated and the resulting value is returned.
\opindex{and} \opindex{and}
The condition \code{\var{x} or \var{y}} first evaluates \var{x}; if 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 \var{x} is true, its value is returned; otherwise, \var{y} is
evaluated and the resulting value is returned. evaluated and the resulting value is returned.
\opindex{or} \opindex{or}
(Note that \keyword{and} and \keyword{or} do not restrict the value (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 and type they return to \code{0} and \code{1}, but rather return the
last evaluated argument. last evaluated argument.
This is sometimes useful, e.g.\ if \code{s} is a string that should be 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 replaced by a default value if it is empty, the expression
\code{s or 'foo'} yields the desired value. Because \keyword{not} has to \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 invent a value anyway, it does not bother to return a value of the
@ -662,54 +793,53 @@ same type as its argument, so e.g. \code{not 'foo'} yields \code{0},
not \code{''}.) not \code{''}.)
Lambda forms (lambda expressions) have the same syntactic position as Lambda forms (lambda expressions) have the same syntactic position as
conditions. They are a shorthand to create anonymous functions; the expressions. They are a shorthand to create anonymous functions; the
expression \code{lambda \var{arguments}: \var{condition}} expression \code{lambda \var{arguments}: \var{expression}}
yields a function object that behaves virtually identical to one yields a function object that behaves virtually identical to one
defined with defined with
\code{def \var{name}(\var{arguments}): return \var{condition}}.
See section \ref{function} for the syntax of \begin{verbatim}
parameter lists. Note that functions created with lambda forms cannot def name(arguments):
contain statements. return expression
\end{verbatim}
See section \ref{function} for the syntax of parameter lists. Note
that functions created with lambda forms cannot contain statements.
\label{lambda} \label{lambda}
\indexii{lambda}{expression} \indexii{lambda}{expression}
\indexii{lambda}{form} \indexii{lambda}{form}
\indexii{anonmymous}{function} \indexii{anonmymous}{function}
\section{Expression lists and condition lists} \strong{Programmer's note:} a lambda form defined inside a function
\indexii{expression}{list} has no access to names defined in the function's namespace. This is
\indexii{condition}{list} because Python has only two scopes: local and global. A common
work-around is to use default argument values to pass selected
variables into the lambda's namespace, e.g.:
\begin{verbatim} \begin{verbatim}
expression_list: or_expr ("," or_expr)* [","] def make_incrementor(increment):
condintion_list: condition ("," condition)* [","] return lambda x, n=increment: x+n
\end{verbatim} \end{verbatim}
The only difference between expression lists and condition lists is \section{Expression lists and expression lists}
the lowest priority of operators that can be used in them without \indexii{expression}{list}
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; \begin{verbatim}
condition lists are used everywhere else where a list of expression_list: expression ("," expression)* [","]
comma-separated values is required. \end{verbatim}
An expression (condition) list containing at least one comma yields a An expression (expression) list containing at least one comma yields a
tuple. The length of the tuple is the number of expressions tuple. The length of the tuple is the number of expressions in the
(conditions) in the list. The expressions (conditions) are evaluated list. The expressions are evaluated from left to right.
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} \obindex{tuple}
The trailing comma is required only to create a single tuple (a.k.a. a 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 {\em singleton}); it is optional in all other cases. A single
expression (condition) without a trailing comma doesn't create a expression (expression) without a trailing comma doesn't create a
tuple, but rather yields the value of that expression (condition). tuple, but rather yields the value of that expression (expression).
\indexii{trailing}{comma}
(To create an empty tuple, use an empty pair of parentheses: (To create an empty tuple, use an empty pair of parentheses:
\code{()}.) \code{()}.)
\indexii{trailing}{comma}
\section{Summary} \section{Summary}
@ -746,6 +876,8 @@ chain from left to right --- see above).
\hline \hline
\code{*}, \code{/}, \code{\%} & Multiplication, division, remainder \\ \code{*}, \code{/}, \code{\%} & Multiplication, division, remainder \\
\hline \hline
\code{**} & Power \\
\hline
\code{+\var{x}}, \code{-\var{x}} & Positive, negative \\ \code{+\var{x}}, \code{-\var{x}} & Positive, negative \\
\code{\~\var{x}} & Bitwise not \\ \code{\~\var{x}} & Bitwise not \\
\hline \hline
@ -757,7 +889,7 @@ chain from left to right --- see above).
\code{(\var{expressions}\ldots)} & Binding or tuple display \\ \code{(\var{expressions}\ldots)} & Binding or tuple display \\
\code{[\var{expressions}\ldots]} & List display \\ \code{[\var{expressions}\ldots]} & List display \\
\code{\{\var{key}:\var{datum}\ldots\}} & Dictionary display \\ \code{\{\var{key}:\var{datum}\ldots\}} & Dictionary display \\
\code{`\var{expression}\ldots`} & String conversion \\ \code{`\var{expressions}\ldots`} & String conversion \\
\hline \hline
\end{tabular} \end{tabular}
\end{center} \end{center}