1 \chapter{Expressions
\label{expressions
}}
4 This chapter explains the meaning of the elements of expressions in
7 \strong{Syntax Notes:
} In this and the following chapters, extended
8 BNF
\index{BNF
} notation will be used to describe syntax, not lexical
9 analysis. When (one alternative of) a syntax rule has the form
11 \begin{productionlist
}[*
]
12 \production{name
}{\token{othername
}}
15 and no semantics are given, the semantics of this form of
\code{name
}
16 are the same as for
\code{othername
}.
20 \section{Arithmetic conversions
\label{conversions
}}
21 \indexii{arithmetic
}{conversion
}
23 When a description of an arithmetic operator below uses the phrase
24 ``the numeric arguments are converted to a common type,'' the
25 arguments are coerced using the coercion rules listed at the end of
26 chapter
\ref{datamodel
}. If both arguments are standard numeric
27 types, the following coercions are applied:
30 \item If either argument is a complex number, the other is converted
32 \item otherwise, if either argument is a floating point number,
33 the other is converted to floating point;
34 \item otherwise, if either argument is a long integer,
35 the other is converted to long integer;
36 \item otherwise, both must be plain integers and no conversion
40 Some additional rules apply for certain operators (e.g., a string left
41 argument to the `\%' operator). Extensions can define their own
45 \section{Atoms
\label{atoms
}}
48 Atoms are the most basic elements of expressions. The simplest atoms
49 are identifiers or literals. Forms enclosed in
50 reverse quotes or in parentheses, brackets or braces are also
51 categorized syntactically as atoms. The syntax for atoms is:
53 \begin{productionlist
}
55 {\token{identifier
} |
\token{literal
} |
\token{enclosure
}}
56 \production{enclosure
}
57 {\token{parenth_form
} |
\token{list_display
}}
58 \productioncont{|
\token{generator_expression
} |
\token{dict_display
}}
59 \productioncont{|
\token{string_conversion
}}
63 \subsection{Identifiers (Names)
\label{atom-identifiers
}}
67 An identifier occurring as an atom is a name. See
68 section~
\ref{naming
} for documentation of naming and binding.
70 When the name is bound to an object, evaluation of the atom yields
71 that object. When a name is not bound, an attempt to evaluate it
72 raises a
\exception{NameError
} exception.
75 \strong{Private name mangling:
}
76 \indexii{name
}{mangling
}%
77 \indexii{private
}{names
}%
78 When an identifier that textually occurs in a class definition begins
79 with two or more underscore characters and does not end in two or more
80 underscores, it is considered a
\dfn{private name
} of that class.
81 Private names are transformed to a longer form before code is
82 generated for them. The transformation inserts the class name in
83 front of the name, with leading underscores removed, and a single
84 underscore inserted in front of the class name. For example, the
85 identifier
\code{__spam
} occurring in a class named
\code{Ham
} will be
86 transformed to
\code{_Ham__spam
}. This transformation is independent
87 of the syntactical context in which the identifier is used. If the
88 transformed name is extremely long (longer than
255 characters),
89 implementation defined truncation may happen. If the class name
90 consists only of underscores, no transformation is done.
93 \subsection{Literals
\label{atom-literals
}}
96 Python supports string literals and various numeric literals:
98 \begin{productionlist
}
100 {\token{stringliteral
} |
\token{integer
} |
\token{longinteger
}}
101 \productioncont{|
\token{floatnumber
} |
\token{imagnumber
}}
104 Evaluation of a literal yields an object of the given type (string,
105 integer, long integer, floating point number, complex number) with the
106 given value. The value may be approximated in the case of floating
107 point and imaginary (complex) literals. See section
\ref{literals
}
110 All literals correspond to immutable data types, and hence the
111 object's identity is less important than its value. Multiple
112 evaluations of literals with the same value (either the same
113 occurrence in the program text or a different occurrence) may obtain
114 the same object or a different object with the same value.
115 \indexiii{immutable
}{data
}{type
}
116 \indexii{immutable
}{object
}
119 \subsection{Parenthesized forms
\label{parenthesized
}}
120 \index{parenthesized form
}
122 A parenthesized form is an optional expression list enclosed in
125 \begin{productionlist
}
126 \production{parenth_form
}
127 {"("
[\token{expression_list
}] ")"
}
130 A parenthesized expression list yields whatever that expression list
131 yields: if the list contains at least one comma, it yields a tuple;
132 otherwise, it yields the single expression that makes up the
135 An empty pair of parentheses yields an empty tuple object. Since
136 tuples are immutable, the rules for literals apply (i.e., two
137 occurrences of the empty tuple may or may not yield the same object).
138 \indexii{empty
}{tuple
}
140 Note that tuples are not formed by the parentheses, but rather by use
141 of the comma operator. The exception is the empty tuple, for which
142 parentheses
\emph{are
} required --- allowing unparenthesized ``nothing''
143 in expressions would cause ambiguities and allow common typos to
146 \indexii{tuple
}{display
}
149 \subsection{List displays
\label{lists
}}
150 \indexii{list
}{display
}
151 \indexii{list
}{comprehensions
}
153 A list display is a possibly empty series of expressions enclosed in
156 \begin{productionlist
}
158 {\token{and_test
} ( "or"
\token{and_test
} )*
159 |
\token{lambda_form
}}
160 \production{testlist
}
161 {\token{test
} ( ","
\token{test
} )*
[ ","
]}
162 \production{list_display
}
163 {"
["
[\token{listmaker
}] "
]"
}
164 \production{listmaker
}
165 {\token{expression
} (
\token{list_for
}
166 | ( ","
\token{expression
} )*
[","
] )
}
167 \production{list_iter
}
168 {\token{list_for
} |
\token{list_if
}}
169 \production{list_for
}
170 {"for"
\token{expression_list
} "in"
\token{testlist
}
173 {"if"
\token{test
} [\token{list_iter
}]}
176 A list display yields a new list object. Its contents are specified
177 by providing either a list of expressions or a list comprehension.
178 \indexii{list
}{comprehensions
}
179 When a comma-separated list of expressions is supplied, its elements are
180 evaluated from left to right and placed into the list object in that
181 order. When a list comprehension is supplied, it consists of a
182 single expression followed by at least one
\keyword{for
} clause and zero or
183 more
\keyword{for
} or
\keyword{if
} clauses. In this
184 case, the elements of the new list are those that would be produced
185 by considering each of the
\keyword{for
} or
\keyword{if
} clauses a block,
187 left to right, and evaluating the expression to produce a list element
188 each time the innermost block is reached
\footnote{In Python
2.3, a
189 list comprehension "leaks" the control variables of each
190 \samp{for
} it contains into the containing scope. However, this
191 behavior is deprecated, and relying on it will not work once this
192 bug is fixed in a future release
}.
194 \indexii{empty
}{list
}
197 \subsection{Generator expressions
\label{genexpr
}}
198 \indexii{generator
}{expression
}
200 A generator expression is a compact generator notation in parentheses:
202 \begin{productionlist
}
203 \production{generator_expression
}
204 {"("
\token{test
} \token{genexpr_for
} ")"
}
205 \production{genexpr_for
}
206 {"for"
\token{expression_list
} "in"
\token{test
}
207 [\token{genexpr_iter
}]}
208 \production{genexpr_iter
}
209 {\token{genexpr_for
} |
\token{genexpr_if
}}
210 \production{genexpr_if
}
211 {"if"
\token{test
} [\token{genexpr_iter
}]}
214 A generator expression yields a new generator object.
216 \obindex{generator expression
}
217 It consists of a single expression followed by at least one
218 \keyword{for
} clause and zero or more
\keyword{for
} or
\keyword{if
}
219 clauses. The iterating values of the new generator are those that
220 would be produced by considering each of the
\keyword{for
} or
221 \keyword{if
} clauses a block, nesting from left to right, and
222 evaluating the expression to yield a value that is reached the
223 innermost block for each iteration.
225 Variables used in the generator expression are evaluated lazily
226 when the
\method{next()
} method is called for generator object
227 (in the same fashion as normal generators). However, the leftmost
228 \keyword{for
} clause is immediately evaluated so that error produced
229 by it can be seen before any other possible error in the code that
230 handles the generator expression.
231 Subsequent
\keyword{for
} clauses cannot be evaluated immediately since
232 they may depend on the previous
\keyword{for
} loop.
233 For example:
\samp{(x*y for x in range(
10) for y in bar(x))
}.
235 The parentheses can be omitted on calls with only one argument.
236 See section
\ref{calls
} for the detail.
239 \subsection{Dictionary displays
\label{dict
}}
240 \indexii{dictionary
}{display
}
242 A dictionary display is a possibly empty series of key/datum pairs
243 enclosed in curly braces:
246 \index{key/datum pair
}
248 \begin{productionlist
}
249 \production{dict_display
}
250 {"\
{"
[\token{key_datum_list
}] "\
}"
}
251 \production{key_datum_list
}
252 {\token{key_datum
} (","
\token{key_datum
})*
[","
]}
253 \production{key_datum
}
254 {\token{expression
} ":"
\token{expression
}}
257 A dictionary display yields a new dictionary object.
260 The key/datum pairs are evaluated from left to right to define the
261 entries of the dictionary: each key object is used as a key into the
262 dictionary to store the corresponding datum.
264 Restrictions on the types of the key values are listed earlier in
265 section
\ref{types
}. (To summarize, the key type should be hashable,
266 which excludes all mutable objects.) Clashes between duplicate keys
267 are not detected; the last datum (textually rightmost in the display)
268 stored for a given key value prevails.
269 \indexii{immutable
}{object
}
272 \subsection{String conversions
\label{string-conversions
}}
273 \indexii{string
}{conversion
}
274 \indexii{reverse
}{quotes
}
275 \indexii{backward
}{quotes
}
278 A string conversion is an expression list enclosed in reverse (a.k.a.
281 \begin{productionlist
}
282 \production{string_conversion
}
283 {"`"
\token{expression_list
} "`"
}
286 A string conversion evaluates the contained expression list and
287 converts the resulting object into a string according to rules
288 specific to its type.
290 If the object is a string, a number,
\code{None
}, or a tuple, list or
291 dictionary containing only objects whose type is one of these, the
292 resulting string is a valid Python expression which can be passed to
293 the built-in function
\function{eval()
} to yield an expression with the
294 same value (or an approximation, if floating point numbers are
297 (In particular, converting a string adds quotes around it and converts
298 ``funny'' characters to escape sequences that are safe to print.)
300 Recursive objects (for example, lists or dictionaries that contain a
301 reference to themselves, directly or indirectly) use
\samp{...
} to
302 indicate a recursive reference, and the result cannot be passed to
303 \function{eval()
} to get an equal value (
\exception{SyntaxError
} will
307 The built-in function
\function{repr()
} performs exactly the same
308 conversion in its argument as enclosing it in parentheses and reverse
309 quotes does. The built-in function
\function{str()
} performs a
310 similar but more user-friendly conversion.
315 \section{Primaries
\label{primaries
}}
318 Primaries represent the most tightly bound operations of the language.
321 \begin{productionlist
}
323 {\token{atom
} |
\token{attributeref
}
324 |
\token{subscription
} |
\token{slicing
} |
\token{call
}}
328 \subsection{Attribute references
\label{attribute-references
}}
329 \indexii{attribute
}{reference
}
331 An attribute reference is a primary followed by a period and a name:
333 \begin{productionlist
}
334 \production{attributeref
}
335 {\token{primary
} "."
\token{identifier
}}
338 The primary must evaluate to an object of a type that supports
339 attribute references, e.g., a module, list, or an instance. This
340 object is then asked to produce the attribute whose name is the
341 identifier. If this attribute is not available, the exception
342 \exception{AttributeError
}\exindex{AttributeError
} is raised.
343 Otherwise, the type and value of the object produced is determined by
344 the object. Multiple evaluations of the same attribute reference may
345 yield different objects.
350 \subsection{Subscriptions
\label{subscriptions
}}
353 A subscription selects an item of a sequence (string, tuple or list)
354 or mapping (dictionary) object:
361 \indexii{sequence
}{item
}
363 \begin{productionlist
}
364 \production{subscription
}
365 {\token{primary
} "
["
\token{expression_list
} "
]"
}
368 The primary must evaluate to an object of a sequence or mapping type.
370 If the primary is a mapping, the expression list must evaluate to an
371 object whose value is one of the keys of the mapping, and the
372 subscription selects the value in the mapping that corresponds to that
373 key. (The expression list is a tuple except if it has exactly one
376 If the primary is a sequence, the expression (list) must evaluate to a
377 plain integer. If this value is negative, the length of the sequence
378 is added to it (so that, e.g.,
\code{x
[-
1]} selects the last item of
379 \code{x
}.) The resulting value must be a nonnegative integer less
380 than the number of items in the sequence, and the subscription selects
381 the item whose index is that value (counting from zero).
383 A string's items are characters. A character is not a separate data
384 type but a string of exactly one character.
386 \indexii{string
}{item
}
389 \subsection{Slicings
\label{slicings
}}
393 A slicing selects a range of items in a sequence object (e.g., a
394 string, tuple or list). Slicings may be used as expressions or as
395 targets in assignment or del statements. The syntax for a slicing:
401 \begin{productionlist
}
403 {\token{simple_slicing
} |
\token{extended_slicing
}}
404 \production{simple_slicing
}
405 {\token{primary
} "
["
\token{short_slice
} "
]"
}
406 \production{extended_slicing
}
407 {\token{primary
} "
["
\token{slice_list
} "
]"
}
408 \production{slice_list
}
409 {\token{slice_item
} (","
\token{slice_item
})*
[","
]}
410 \production{slice_item
}
411 {\token{expression
} |
\token{proper_slice
} |
\token{ellipsis
}}
412 \production{proper_slice
}
413 {\token{short_slice
} |
\token{long_slice
}}
414 \production{short_slice
}
415 {[\token{lower_bound
}] ":"
[\token{upper_bound
}]}
416 \production{long_slice
}
417 {\token{short_slice
} ":"
[\token{stride
}]}
418 \production{lower_bound
}
420 \production{upper_bound
}
424 \production{ellipsis
}
428 There is ambiguity in the formal syntax here: anything that looks like
429 an expression list also looks like a slice list, so any subscription
430 can be interpreted as a slicing. Rather than further complicating the
431 syntax, this is disambiguated by defining that in this case the
432 interpretation as a subscription takes priority over the
433 interpretation as a slicing (this is the case if the slice list
434 contains no proper slice nor ellipses). Similarly, when the slice
435 list has exactly one short slice and no trailing comma, the
436 interpretation as a simple slicing takes priority over that as an
437 extended slicing.
\indexii{extended
}{slicing
}
439 The semantics for a simple slicing are as follows. The primary must
440 evaluate to a sequence object. The lower and upper bound expressions,
441 if present, must evaluate to plain integers; defaults are zero and the
442 \code{sys.maxint
}, respectively. If either bound is negative, the
443 sequence's length is added to it. The slicing now selects all items
444 with index
\var{k
} such that
445 \code{\var{i
} <=
\var{k
} <
\var{j
}} where
\var{i
}
446 and
\var{j
} are the specified lower and upper bounds. This may be an
447 empty sequence. It is not an error if
\var{i
} or
\var{j
} lie outside the
448 range of valid indexes (such items don't exist so they aren't
451 The semantics for an extended slicing are as follows. The primary
452 must evaluate to a mapping object, and it is indexed with a key that
453 is constructed from the slice list, as follows. If the slice list
454 contains at least one comma, the key is a tuple containing the
455 conversion of the slice items; otherwise, the conversion of the lone
456 slice item is the key. The conversion of a slice item that is an
457 expression is that expression. The conversion of an ellipsis slice
458 item is the built-in
\code{Ellipsis
} object. The conversion of a
459 proper slice is a slice object (see section
\ref{types
}) whose
460 \member{start
},
\member{stop
} and
\member{step
} attributes are the
461 values of the expressions given as lower bound, upper bound and
462 stride, respectively, substituting
\code{None
} for missing
464 \withsubitem{(slice object attribute)
}{\ttindex{start
}
465 \ttindex{stop
}\ttindex{step
}}
468 \subsection{Calls
\label{calls
}}
471 A call calls a callable object (e.g., a function) with a possibly empty
475 \begin{productionlist
}
477 {\token{primary
} "("
[\token{argument_list
} [","
]] ")"
}
478 {\token{primary
} "("
[\token{argument_list
} [","
] |
479 \token{test
} \token{genexpr_for
} ] ")"
}
480 \production{argument_list
}
481 {\token{positional_arguments
} [","
\token{keyword_arguments
}]}
482 \productioncont{ ["," "*"
\token{expression
}]}
483 \productioncont{ ["," "**"
\token{expression
}]}
484 \productioncont{|
\token{keyword_arguments
} ["," "*"
\token{expression
}]}
485 \productioncont{ ["," "**"
\token{expression
}]}
486 \productioncont{| "*"
\token{expression
} ["," "**"
\token{expression
}]}
487 \productioncont{| "**"
\token{expression
}}
488 \production{positional_arguments
}
489 {\token{expression
} (","
\token{expression
})*
}
490 \production{keyword_arguments
}
491 {\token{keyword_item
} (","
\token{keyword_item
})*
}
492 \production{keyword_item
}
493 {\token{identifier
} "="
\token{expression
}}
496 A trailing comma may be present after the positional and keyword
497 arguments but does not affect the semantics.
499 The primary must evaluate to a callable object (user-defined
500 functions, built-in functions, methods of built-in objects, class
501 objects, methods of class instances, and certain class instances
502 themselves are callable; extensions may define additional callable
503 object types). All argument expressions are evaluated before the call
504 is attempted. Please refer to section
\ref{function
} for the syntax
505 of formal parameter lists.
507 If keyword arguments are present, they are first converted to
508 positional arguments, as follows. First, a list of unfilled slots is
509 created for the formal parameters. If there are N positional
510 arguments, they are placed in the first N slots. Next, for each
511 keyword argument, the identifier is used to determine the
512 corresponding slot (if the identifier is the same as the first formal
513 parameter name, the first slot is used, and so on). If the slot is
514 already filled, a
\exception{TypeError
} exception is raised.
515 Otherwise, the value of the argument is placed in the slot, filling it
516 (even if the expression is
\code{None
}, it fills the slot). When all
517 arguments have been processed, the slots that are still unfilled are
518 filled with the corresponding default value from the function
519 definition. (Default values are calculated, once, when the function
520 is defined; thus, a mutable object such as a list or dictionary used
521 as default value will be shared by all calls that don't specify an
522 argument value for the corresponding slot; this should usually be
523 avoided.) If there are any unfilled slots for which no default value
524 is specified, a
\exception{TypeError
} exception is raised. Otherwise,
525 the list of filled slots is used as the argument list for the call.
527 If there are more positional arguments than there are formal parameter
528 slots, a
\exception{TypeError
} exception is raised, unless a formal
529 parameter using the syntax
\samp{*identifier
} is present; in this
530 case, that formal parameter receives a tuple containing the excess
531 positional arguments (or an empty tuple if there were no excess
532 positional arguments).
534 If any keyword argument does not correspond to a formal parameter
535 name, a
\exception{TypeError
} exception is raised, unless a formal
536 parameter using the syntax
\samp{**identifier
} is present; in this
537 case, that formal parameter receives a dictionary containing the
538 excess keyword arguments (using the keywords as keys and the argument
539 values as corresponding values), or a (new) empty dictionary if there
540 were no excess keyword arguments.
542 If the syntax
\samp{*expression
} appears in the function call,
543 \samp{expression
} must evaluate to a sequence. Elements from this
544 sequence are treated as if they were additional positional arguments;
545 if there are postional arguments
\var{x1
},...,
\var{xN
} , and
546 \samp{expression
} evaluates to a sequence
\var{y1
},...,
\var{yM
}, this
547 is equivalent to a call with M+N positional arguments
548 \var{x1
},...,
\var{xN
},
\var{y1
},...,
\var{yM
}.
550 A consequence of this is that although the
\samp{*expression
} syntax
551 appears
\emph{after
} any keyword arguments, it is processed
552 \emph{before
} the keyword arguments (and the
553 \samp{**expression
} argument, if any -- see below). So:
562 Traceback (most recent call last):
563 File "<stdin>", line
1, in ?
564 TypeError: f() got multiple values for keyword argument 'a'
569 It is unusual for both keyword arguments and the
570 \samp{*expression
} syntax to be used in the same call, so in practice
571 this confusion does not arise.
573 If the syntax
\samp{**expression
} appears in the function call,
574 \samp{expression
} must evaluate to a (subclass of) dictionary, the
575 contents of which are treated as additional keyword arguments. In the
576 case of a keyword appearing in both
\samp{expression
} and as an
577 explicit keyword argument, a
\exception{TypeError
} exception is
580 Formal parameters using the syntax
\samp{*identifier
} or
581 \samp{**identifier
} cannot be used as positional argument slots or
582 as keyword argument names. Formal parameters using the syntax
583 \samp{(sublist)
} cannot be used as keyword argument names; the
584 outermost sublist corresponds to a single unnamed argument slot, and
585 the argument value is assigned to the sublist using the usual tuple
586 assignment rules after all other parameter processing is done.
588 A call always returns some value, possibly
\code{None
}, unless it
589 raises an exception. How this value is computed depends on the type
590 of the callable object.
596 \item[a user-defined function:
] The code block for the function is
597 executed, passing it the argument list. The first thing the code
598 block will do is bind the formal parameters to the arguments; this is
599 described in section
\ref{function
}. When the code block executes a
600 \keyword{return
} statement, this specifies the return value of the
602 \indexii{function
}{call
}
603 \indexiii{user-defined
}{function
}{call
}
604 \obindex{user-defined function
}
607 \item[a built-in function or method:
] The result is up to the
608 interpreter; see the
\citetitle[../lib/built-in-funcs.html
]{Python
609 Library Reference
} for the descriptions of built-in functions and
611 \indexii{function
}{call
}
612 \indexii{built-in function
}{call
}
613 \indexii{method
}{call
}
614 \indexii{built-in method
}{call
}
615 \obindex{built-in method
}
616 \obindex{built-in function
}
620 \item[a class object:
] A new instance of that class is returned.
622 \indexii{class object
}{call
}
624 \item[a class instance method:
] The corresponding user-defined
625 function is called, with an argument list that is one longer than the
626 argument list of the call: the instance becomes the first argument.
627 \obindex{class instance
}
629 \indexii{class instance
}{call
}
631 \item[a class instance:
] The class must define a
\method{__call__()
}
632 method; the effect is then the same as if that method was called.
633 \indexii{instance
}{call
}
634 \withsubitem{(object method)
}{\ttindex{__call__()
}}
639 \section{The power operator
\label{power
}}
641 The power operator binds more tightly than unary operators on its
642 left; it binds less tightly than unary operators on its right. The
645 \begin{productionlist
}
647 {\token{primary
} ["**"
\token{u_expr
}]}
650 Thus, in an unparenthesized sequence of power and unary operators, the
651 operators are evaluated from right to left (this does not constrain
652 the evaluation order for the operands).
654 The power operator has the same semantics as the built-in
655 \function{pow()
} function, when called with two arguments: it yields
656 its left argument raised to the power of its right argument. The
657 numeric arguments are first converted to a common type. The result
658 type is that of the arguments after coercion.
660 With mixed operand types, the coercion rules for binary arithmetic
661 operators apply. For int and long int operands, the result has the
662 same type as the operands (after coercion) unless the second argument
663 is negative; in that case, all arguments are converted to float and a
664 float result is delivered. For example,
\code{10**
2} returns
\code{100},
665 but
\code{10**-
2} returns
\code{0.01}. (This last feature was added in
666 Python
2.2. In Python
2.1 and before, if both arguments were of integer
667 types and the second argument was negative, an exception was raised).
669 Raising
\code{0.0} to a negative power results in a
670 \exception{ZeroDivisionError
}. Raising a negative number to a
671 fractional power results in a
\exception{ValueError
}.
674 \section{Unary arithmetic operations
\label{unary
}}
675 \indexiii{unary
}{arithmetic
}{operation
}
676 \indexiii{unary
}{bit-wise
}{operation
}
678 All unary arithmetic (and bit-wise) operations have the same priority:
680 \begin{productionlist
}
682 {\token{power
} | "-"
\token{u_expr
}
683 | "+"
\token{u_expr
} | "
{\~
}"
\token{u_expr
}}
686 The unary
\code{-
} (minus) operator yields the negation of its
691 The unary
\code{+
} (plus) operator yields its numeric argument
695 The unary
\code{\~
} (invert) operator yields the bit-wise inversion
696 of its plain or long integer argument. The bit-wise inversion of
697 \code{x
} is defined as
\code{-(x+
1)
}. It only applies to integral
701 In all three cases, if the argument does not have the proper type,
702 a
\exception{TypeError
} exception is raised.
706 \section{Binary arithmetic operations
\label{binary
}}
707 \indexiii{binary
}{arithmetic
}{operation
}
709 The binary arithmetic operations have the conventional priority
710 levels. Note that some of these operations also apply to certain
711 non-numeric types. Apart from the power operator, there are only two
712 levels, one for multiplicative operators and one for additive
715 \begin{productionlist
}
717 {\token{u_expr
} |
\token{m_expr
} "*"
\token{u_expr
}
718 |
\token{m_expr
} "//"
\token{u_expr
}
719 |
\token{m_expr
} "/"
\token{u_expr
}}
720 \productioncont{|
\token{m_expr
} "\%"
\token{u_expr
}}
722 {\token{m_expr
} |
\token{a_expr
} "+"
\token{m_expr
}
723 |
\token{a_expr
} "-"
\token{m_expr
}}
726 The
\code{*
} (multiplication) operator yields the product of its
727 arguments. The arguments must either both be numbers, or one argument
728 must be an integer (plain or long) and the other must be a sequence.
729 In the former case, the numbers are converted to a common type and
730 then multiplied together. In the latter case, sequence repetition is
731 performed; a negative repetition factor yields an empty sequence.
732 \index{multiplication
}
734 The
\code{/
} (division) and
\code{//
} (floor division) operators yield
735 the quotient of their arguments. The numeric arguments are first
736 converted to a common type. Plain or long integer division yields an
737 integer of the same type; the result is that of mathematical division
738 with the `floor' function applied to the result. Division by zero
740 \exception{ZeroDivisionError
} exception.
741 \exindex{ZeroDivisionError
}
744 The
\code{\%
} (modulo) operator yields the remainder from the
745 division of the first argument by the second. The numeric arguments
746 are first converted to a common type. A zero right argument raises
747 the
\exception{ZeroDivisionError
} exception. The arguments may be floating
748 point numbers, e.g.,
\code{3.14\%
0.7} equals
\code{0.34} (since
749 \code{3.14} equals
\code{4*
0.7 +
0.34}.) The modulo operator always
750 yields a result with the same sign as its second operand (or zero);
751 the absolute value of the result is strictly smaller than the absolute
752 value of the second operand
\footnote{
753 While
\code{abs(x\%y) < abs(y)
} is true mathematically, for
754 floats it may not be true numerically due to roundoff. For
755 example, and assuming a platform on which a Python float is an
756 IEEE
754 double-precision number, in order that
\code{-
1e-100 \%
1e100
}
757 have the same sign as
\code{1e100
}, the computed result is
758 \code{-
1e-100 +
1e100
}, which is numerically exactly equal
759 to
\code{1e100
}. Function
\function{fmod()
} in the
\module{math
}
760 module returns a result whose sign matches the sign of the
761 first argument instead, and so returns
\code{-
1e-100} in this case.
762 Which approach is more appropriate depends on the application.
766 The integer division and modulo operators are connected by the
767 following identity:
\code{x == (x/y)*y + (x\%y)
}. Integer division and
768 modulo are also connected with the built-in function
\function{divmod()
}:
769 \code{divmod(x, y) == (x/y, x\%y)
}. These identities don't hold for
770 floating point numbers; there similar identities hold
771 approximately where
\code{x/y
} is replaced by
\code{floor(x/y)
} or
772 \code{floor(x/y) -
1}\footnote{
773 If x is very close to an exact integer multiple of y, it's
774 possible for
\code{floor(x/y)
} to be one larger than
775 \code{(x-x\%y)/y
} due to rounding. In such cases, Python returns
776 the latter result, in order to preserve that
\code{divmod(x,y)
[0]
777 * y + x \%
{} y
} be very close to
\code{x
}.
780 In addition to performing the modulo operation on numbers, the
\code{\%
}
781 operator is also overloaded by string and unicode objects to perform
782 string formatting (also known as interpolation). The syntax for string
783 formatting is described in the
784 \citetitle[../lib/typesseq-strings.html
]{Python Library Reference
},
785 section ``Sequence Types''.
787 \deprecated{2.3}{The floor division operator, the modulo operator,
788 and the
\function{divmod()
} function are no longer defined for complex
789 numbers. Instead, convert to a floating point number using the
790 \function{abs()
} function if appropriate.
}
792 The
\code{+
} (addition) operator yields the sum of its arguments.
793 The arguments must either both be numbers or both sequences of the
794 same type. In the former case, the numbers are converted to a common
795 type and then added together. In the latter case, the sequences are
799 The
\code{-
} (subtraction) operator yields the difference of its
800 arguments. The numeric arguments are first converted to a common
805 \section{Shifting operations
\label{shifting
}}
806 \indexii{shifting
}{operation
}
808 The shifting operations have lower priority than the arithmetic
811 \begin{productionlist
}
812 % The empty groups below prevent conversion to guillemets.
813 \production{shift_expr
}
815 |
\token{shift_expr
} ( "<
{}<" | ">
{}>" )
\token{a_expr
}}
818 These operators accept plain or long integers as arguments. The
819 arguments are converted to a common type. They shift the first
820 argument to the left or right by the number of bits given by the
823 A right shift by
\var{n
} bits is defined as division by
824 \code{pow(
2,
\var{n
})
}. A left shift by
\var{n
} bits is defined as
825 multiplication with
\code{pow(
2,
\var{n
})
}; for plain integers there is
826 no overflow check so in that case the operation drops bits and flips
827 the sign if the result is not less than
\code{pow(
2,
31)
} in absolute
828 value. Negative shift counts raise a
\exception{ValueError
}
833 \section{Binary bit-wise operations
\label{bitwise
}}
834 \indexiii{binary
}{bit-wise
}{operation
}
836 Each of the three bitwise operations has a different priority level:
838 \begin{productionlist
}
839 \production{and_expr
}
840 {\token{shift_expr
} |
\token{and_expr
} "\&"
\token{shift_expr
}}
841 \production{xor_expr
}
842 {\token{and_expr
} |
\token{xor_expr
} "
\textasciicircum"
\token{and_expr
}}
844 {\token{xor_expr
} |
\token{or_expr
} "|"
\token{xor_expr
}}
847 The
\code{\&
} operator yields the bitwise AND of its arguments, which
848 must be plain or long integers. The arguments are converted to a
850 \indexii{bit-wise
}{and
}
852 The
\code{\^
} operator yields the bitwise XOR (exclusive OR) of its
853 arguments, which must be plain or long integers. The arguments are
854 converted to a common type.
855 \indexii{bit-wise
}{xor
}
856 \indexii{exclusive
}{or
}
858 The
\code{|
} operator yields the bitwise (inclusive) OR of its
859 arguments, which must be plain or long integers. The arguments are
860 converted to a common type.
861 \indexii{bit-wise
}{or
}
862 \indexii{inclusive
}{or
}
865 \section{Comparisons
\label{comparisons
}}
868 Unlike C, all comparison operations in Python have the same priority,
869 which is lower than that of any arithmetic, shifting or bitwise
870 operation. Also unlike C, expressions like
\code{a < b < c
} have the
871 interpretation that is conventional in mathematics:
872 \indexii{C
}{language
}
874 \begin{productionlist
}
875 \production{comparison
}
876 {\token{or_expr
} (
\token{comp_operator
} \token{or_expr
} )*
}
877 \production{comp_operator
}
878 {"<" | ">" | "==" | ">=" | "<=" | "<>" | "!="
}
879 \productioncont{| "is"
["not"
] |
["not"
] "in"
}
882 Comparisons yield boolean values:
\code{True
} or
\code{False
}.
884 Comparisons can be chained arbitrarily, e.g.,
\code{x < y <= z
} is
885 equivalent to
\code{x < y and y <= z
}, except that
\code{y
} is
886 evaluated only once (but in both cases
\code{z
} is not evaluated at all
887 when
\code{x < y
} is found to be false).
888 \indexii{chaining
}{comparisons
}
890 Formally, if
\var{a
},
\var{b
},
\var{c
},
\ldots,
\var{y
},
\var{z
} are
891 expressions and
\var{opa
},
\var{opb
},
\ldots,
\var{opy
} are comparison
892 operators, then
\var{a opa b opb c
} \ldots \var{y opy z
} is equivalent
893 to
\var{a opa b
} \keyword{and
} \var{b opb c
} \keyword{and
} \ldots
894 \var{y opy z
}, except that each expression is evaluated at most once.
896 Note that
\var{a opa b opb c
} doesn't imply any kind of comparison
897 between
\var{a
} and
\var{c
}, so that, e.g.,
\code{x < y > z
} is
898 perfectly legal (though perhaps not pretty).
900 The forms
\code{<>
} and
\code{!=
} are equivalent; for consistency with
901 C,
\code{!=
} is preferred; where
\code{!=
} is mentioned below
902 \code{<>
} is also accepted. The
\code{<>
} spelling is considered
905 The operators
\code{<
},
\code{>
},
\code{==
},
\code{>=
},
\code{<=
}, and
907 the values of two objects. The objects need not have the same type.
908 If both are numbers, they are converted to a common type. Otherwise,
909 objects of different types
\emph{always
} compare unequal, and are
910 ordered consistently but arbitrarily.
912 (This unusual definition of comparison was used to simplify the
913 definition of operations like sorting and the
\keyword{in
} and
914 \keyword{not in
} operators. In the future, the comparison rules for
915 objects of different types are likely to change.)
917 Comparison of objects of the same type depends on the type:
922 Numbers are compared arithmetically.
925 Strings are compared lexicographically using the numeric equivalents
926 (the result of the built-in function
\function{ord()
}) of their
927 characters. Unicode and
8-bit strings are fully interoperable in this
931 Tuples and lists are compared lexicographically using comparison of
932 corresponding elements. This means that to compare equal, each
933 element must compare equal and the two sequences must be of the same
934 type and have the same length.
936 If not equal, the sequences are ordered the same as their first
937 differing elements. For example,
\code{cmp(
[1,
2,x
],
[1,
2,y
])
} returns
938 the same as
\code{cmp(x,y)
}. If the corresponding element does not
939 exist, the shorter sequence is ordered first (for example,
940 \code{[1,
2] <
[1,
2,
3]}).
943 Mappings (dictionaries) compare equal if and only if their sorted
944 (key, value) lists compare equal.
\footnote{The implementation computes
945 this efficiently, without constructing lists or sorting.
}
946 Outcomes other than equality are resolved consistently, but are not
947 otherwise defined.
\footnote{Earlier versions of Python used
948 lexicographic comparison of the sorted (key, value) lists, but this
949 was very expensive for the common case of comparing for equality. An
950 even earlier version of Python compared dictionaries by identity only,
951 but this caused surprises because people expected to be able to test
952 a dictionary for emptiness by comparing it to
\code{\
{\
}}.
}
955 Most other types compare unequal unless they are the same object;
956 the choice whether one object is considered smaller or larger than
957 another one is made arbitrarily but consistently within one
958 execution of a program.
962 The operators
\keyword{in
} and
\keyword{not in
} test for set
963 membership.
\code{\var{x
} in
\var{s
}} evaluates to true if
\var{x
}
964 is a member of the set
\var{s
}, and false otherwise.
\code{\var{x
}
965 not in
\var{s
}} returns the negation of
\code{\var{x
} in
\var{s
}}.
966 The set membership test has traditionally been bound to sequences; an
967 object is a member of a set if the set is a sequence and contains an
968 element equal to that object. However, it is possible for an object
969 to support membership tests without being a sequence. In particular,
970 dictionaries support membership testing as a nicer way of spelling
971 \code{\var{key
} in
\var{dict
}}; other mapping types may follow suit.
973 For the list and tuple types,
\code{\var{x
} in
\var{y
}} is true if and
974 only if there exists an index
\var{i
} such that
975 \code{\var{x
} ==
\var{y
}[\var{i
}]} is true.
977 For the Unicode and string types,
\code{\var{x
} in
\var{y
}} is true if
978 and only if
\var{x
} is a substring of
\var{y
}. An equivalent test is
979 \code{y.find(x) != -
1}. Note,
\var{x
} and
\var{y
} need not be the
980 same type; consequently,
\code{u'ab' in 'abc'
} will return
\code{True
}.
981 Empty strings are always considered to be a substring of any other string,
982 so
\code{"" in "abc"
} will return
\code{True
}.
983 \versionchanged[Previously,
\var{x
} was required to be a string of
984 length
\code{1}]{2.3}
986 For user-defined classes which define the
\method{__contains__()
} method,
987 \code{\var{x
} in
\var{y
}} is true if and only if
988 \code{\var{y
}.__contains__(
\var{x
})
} is true.
990 For user-defined classes which do not define
\method{__contains__()
} and
991 do define
\method{__getitem__()
},
\code{\var{x
} in
\var{y
}} is true if
992 and only if there is a non-negative integer index
\var{i
} such that
993 \code{\var{x
} ==
\var{y
}[\var{i
}]}, and all lower integer indices
994 do not raise
\exception{IndexError
} exception. (If any other exception
995 is raised, it is as if
\keyword{in
} raised that exception).
997 The operator
\keyword{not in
} is defined to have the inverse true value
1001 \indexii{membership
}{test
}
1004 The operators
\keyword{is
} and
\keyword{is not
} test for object identity:
1005 \code{\var{x
} is
\var{y
}} is true if and only if
\var{x
} and
\var{y
}
1006 are the same object.
\code{\var{x
} is not
\var{y
}} yields the inverse
1010 \indexii{identity
}{test
}
1013 \section{Boolean operations
\label{Booleans
}}
1014 \indexii{Boolean
}{operation
}
1016 Boolean operations have the lowest priority of all Python operations:
1018 \begin{productionlist
}
1019 \production{expression
}
1020 {\token{or_test
} |
\token{lambda_form
}}
1021 \production{or_test
}
1022 {\token{and_test
} |
\token{or_test
} "or"
\token{and_test
}}
1023 \production{and_test
}
1024 {\token{not_test
} |
\token{and_test
} "and"
\token{not_test
}}
1025 \production{not_test
}
1026 {\token{comparison
} | "not"
\token{not_test
}}
1027 \end{productionlist
}
1029 In the context of Boolean operations, and also when expressions are
1030 used by control flow statements, the following values are interpreted
1031 as false:
\code{False
},
\code{None
}, numeric zero of all types, and empty
1032 strings and containers (including strings, tuples, lists, dictionaries,
1033 sets and frozensets). All other values are interpreted as true.
1035 The operator
\keyword{not
} yields
\code{True
} if its argument is false,
1036 \code{False
} otherwise.
1039 The expression
\code{\var{x
} and
\var{y
}} first evaluates
\var{x
}; if
1040 \var{x
} is false, its value is returned; otherwise,
\var{y
} is
1041 evaluated and the resulting value is returned.
1044 The expression
\code{\var{x
} or
\var{y
}} first evaluates
\var{x
}; if
1045 \var{x
} is true, its value is returned; otherwise,
\var{y
} is
1046 evaluated and the resulting value is returned.
1049 (Note that neither
\keyword{and
} nor
\keyword{or
} restrict the value
1050 and type they return to
\code{False
} and
\code{True
}, but rather return the
1051 last evaluated argument.
1052 This is sometimes useful, e.g., if
\code{s
} is a string that should be
1053 replaced by a default value if it is empty, the expression
1054 \code{s or 'foo'
} yields the desired value. Because
\keyword{not
} has to
1055 invent a value anyway, it does not bother to return a value of the
1056 same type as its argument, so e.g.,
\code{not 'foo'
} yields
\code{False
},
1059 \section{Lambdas
\label{lambdas
}}
1060 \indexii{lambda
}{expression
}
1061 \indexii{lambda
}{form
}
1062 \indexii{anonymous
}{function
}
1064 \begin{productionlist
}
1065 \production{lambda_form
}
1066 {"lambda"
[\token{parameter_list
}]:
\token{expression
}}
1067 \end{productionlist
}
1069 Lambda forms (lambda expressions) have the same syntactic position as
1070 expressions. They are a shorthand to create anonymous functions; the
1071 expression
\code{lambda
\var{arguments
}:
\var{expression
}}
1072 yields a function object. The unnamed object behaves like a function
1076 def name(arguments):
1080 See section
\ref{function
} for the syntax of parameter lists. Note
1081 that functions created with lambda forms cannot contain statements.
1084 \section{Expression lists
\label{exprlists
}}
1085 \indexii{expression
}{list
}
1087 \begin{productionlist
}
1088 \production{expression_list
}
1089 {\token{expression
} ( ","
\token{expression
} )*
[","
]}
1090 \end{productionlist
}
1092 An expression list containing at least one comma yields a
1093 tuple. The length of the tuple is the number of expressions in the
1094 list. The expressions are evaluated from left to right.
1097 The trailing comma is required only to create a single tuple (a.k.a. a
1098 \emph{singleton
}); it is optional in all other cases. A single
1099 expression without a trailing comma doesn't create a
1100 tuple, but rather yields the value of that expression.
1101 (To create an empty tuple, use an empty pair of parentheses:
1103 \indexii{trailing
}{comma
}
1105 \section{Evaluation order
\label{evalorder
}}
1106 \indexii{evaluation
}{order
}
1108 Python evaluates expressions from left to right. Notice that while
1109 evaluating an assignment, the right-hand side is evaluated before
1112 In the following lines, expressions will be evaluated in the
1113 arithmetic order of their suffixes:
1116 expr1, expr2, expr3, expr4
1117 (expr1, expr2, expr3, expr4)
1118 {expr1: expr2, expr3: expr4
}
1119 expr1 + expr2 * (expr3 - expr4)
1120 func(expr1, expr2, *expr3, **expr4)
1121 expr3, expr4 = expr1, expr2
1124 \section{Summary
\label{summary
}}
1126 The following table summarizes the operator
1127 precedences
\indexii{operator
}{precedence
} in Python, from lowest
1128 precedence (least binding) to highest precedence (most binding).
1129 Operators in the same box have the same precedence. Unless the syntax
1130 is explicitly given, operators are binary. Operators in the same box
1131 group left to right (except for comparisons, including tests, which all
1132 have the same precedence and chain from left to right --- see section
1133 \ref{comparisons
} -- and exponentiation, which groups from right to left).
1135 \begin{tableii
}{c|l
}{textrm
}{Operator
}{Description
}
1136 \lineii{\keyword{lambda
}} {Lambda expression
}
1138 \lineii{\keyword{or
}} {Boolean OR
}
1140 \lineii{\keyword{and
}} {Boolean AND
}
1142 \lineii{\keyword{not
} \var{x
}} {Boolean NOT
}
1144 \lineii{\keyword{in
},
\keyword{not
} \keyword{in
}}{Membership tests
}
1145 \lineii{\keyword{is
},
\keyword{is not
}}{Identity tests
}
1146 \lineii{\code{<
},
\code{<=
},
\code{>
},
\code{>=
},
1147 \code{<>
},
\code{!=
},
\code{==
}}
1150 \lineii{\code{|
}} {Bitwise OR
}
1152 \lineii{\code{\^
}} {Bitwise XOR
}
1154 \lineii{\code{\&
}} {Bitwise AND
}
1156 \lineii{\code{<
}\code{<
},
\code{>
}\code{>
}} {Shifts
}
1158 \lineii{\code{+
},
\code{-
}}{Addition and subtraction
}
1160 \lineii{\code{*
},
\code{/
},
\code{\%
}}
1161 {Multiplication, division, remainder
}
1163 \lineii{\code{+
\var{x
}},
\code{-
\var{x
}}} {Positive, negative
}
1164 \lineii{\code{\~
\var{x
}}} {Bitwise not
}
1166 \lineii{\code{**
}} {Exponentiation
}
1168 \lineii{\code{\var{x
}.
\var{attribute
}}} {Attribute reference
}
1169 \lineii{\code{\var{x
}[\var{index
}]}} {Subscription
}
1170 \lineii{\code{\var{x
}[\var{index
}:
\var{index
}]}} {Slicing
}
1171 \lineii{\code{\var{f
}(
\var{arguments
}...)
}} {Function call
}
1173 \lineii{\code{(
\var{expressions
}\ldots)
}} {Binding or tuple display
}
1174 \lineii{\code{[\var{expressions
}\ldots]}} {List display
}
1175 \lineii{\code{\
{\var{key
}:
\var{datum
}\ldots\
}}}{Dictionary display
}
1176 \lineii{\code{`
\var{expressions
}\ldots`
}} {String conversion
}