1 

     2 .. _expressions:

     3 

     4 ***********

     5 Expressions

     6 ***********

     7 

     8 .. index:: single: expression

     9 

    10 This chapter explains the meaning of the elements of expressions in Python.

    11 

    12 .. index:: single: BNF

    13 

    14 **Syntax Notes:** In this and the following chapters, extended BNF notation will

    15 be used to describe syntax, not lexical analysis.  When (one alternative of) a

    16 syntax rule has the form

    17 

    18 .. productionlist:: *

    19    name: `othername`

    20 

    21 .. index:: single: syntax

    22 

    23 and no semantics are given, the semantics of this form of ``name`` are the same

    24 as for ``othername``.

    25 

    26 

    27 .. _conversions:

    28 

    29 Arithmetic conversions

    30 ======================

    31 

    32 .. index:: pair: arithmetic; conversion

    33 

    34 When a description of an arithmetic operator below uses the phrase "the numeric

    35 arguments are converted to a common type," the arguments are coerced using the

    36 coercion rules listed at  :ref:`coercion-rules`.  If both arguments are standard

    37 numeric types, the following coercions are applied:

    38 

    39 * If either argument is a complex number, the other is converted to complex;

    40 

    41 * otherwise, if either argument is a floating point number, the other is

    42   converted to floating point;

    43 

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

    45   long integer;

    46 

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

    48 

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

    50 to the '%' operator). Extensions can define their own coercions.

    51 

    52 

    53 .. _atoms:

    54 

    55 Atoms

    56 =====

    57 

    58 .. index:: single: atom

    59 

    60 Atoms are the most basic elements of expressions.  The simplest atoms are

    61 identifiers or literals.  Forms enclosed in reverse quotes or in parentheses,

    62 brackets or braces are also categorized syntactically as atoms.  The syntax for

    63 atoms is:

    64 

    65 .. productionlist::

    66    atom: `identifier` | `literal` | `enclosure`

    67    enclosure: `parenth_form` | `list_display`

    68             : | `generator_expression` | `dict_display`

    69             : | `string_conversion` | `yield_atom`

    70 

    71 

    72 .. _atom-identifiers:

    73 

    74 Identifiers (Names)

    75 -------------------

    76 

    77 .. index::

    78    single: name

    79    single: identifier

    80 

    81 An identifier occurring as an atom is a name.  See section :ref:`identifiers`

    82 for lexical definition and section :ref:`naming` for documentation of naming and

    83 binding.

    84 

    85 .. index:: exception: NameError

    86 

    87 When the name is bound to an object, evaluation of the atom yields that object.

    88 When a name is not bound, an attempt to evaluate it raises a :exc:`NameError`

    89 exception.

    90 

    91 .. index::

    92    pair: name; mangling

    93    pair: private; names

    94 

    95 **Private name mangling:** When an identifier that textually occurs in a class

    96 definition begins with two or more underscore characters and does not end in two

    97 or more underscores, it is considered a :dfn:`private name` of that class.

    98 Private names are transformed to a longer form before code is generated for

    99 them.  The transformation inserts the class name in front of the name, with

   100 leading underscores removed, and a single underscore inserted in front of the

   101 class name.  For example, the identifier ``__spam`` occurring in a class named

   102 ``Ham`` will be transformed to ``_Ham__spam``.  This transformation is

   103 independent of the syntactical context in which the identifier is used.  If the

   104 transformed name is extremely long (longer than 255 characters), implementation

   105 defined truncation may happen.  If the class name consists only of underscores,

   106 no transformation is done.

   107 

   108 

   109 

   110 .. _atom-literals:

   111 

   112 Literals

   113 --------

   114 

   115 .. index:: single: literal

   116 

   117 Python supports string literals and various numeric literals:

   118 

   119 .. productionlist::

   120    literal: `stringliteral` | `integer` | `longinteger`

   121           : | `floatnumber` | `imagnumber`

   122 

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

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

   125 value may be approximated in the case of floating point and imaginary (complex)

   126 literals.  See section :ref:`literals` for details.

   127 

   128 .. index::

   129    triple: immutable; data; type

   130    pair: immutable; object

   131 

   132 All literals correspond to immutable data types, and hence the object's identity

   133 is less important than its value.  Multiple evaluations of literals with the

   134 same value (either the same occurrence in the program text or a different

   135 occurrence) may obtain the same object or a different object with the same

   136 value.

   137 

   138 

   139 .. _parenthesized:

   140 

   141 Parenthesized forms

   142 -------------------

   143 

   144 .. index:: single: parenthesized form

   145 

   146 A parenthesized form is an optional expression list enclosed in parentheses:

   147 

   148 .. productionlist::

   149    parenth_form: "(" [`expression_list`] ")"

   150 

   151 A parenthesized expression list yields whatever that expression list yields: if

   152 the list contains at least one comma, it yields a tuple; otherwise, it yields

   153 the single expression that makes up the expression list.

   154 

   155 .. index:: pair: empty; tuple

   156 

   157 An empty pair of parentheses yields an empty tuple object.  Since tuples are

   158 immutable, the rules for literals apply (i.e., two occurrences of the empty

   159 tuple may or may not yield the same object).

   160 

   161 .. index::

   162    single: comma

   163    pair: tuple; display

   164 

   165 Note that tuples are not formed by the parentheses, but rather by use of the

   166 comma operator.  The exception is the empty tuple, for which parentheses *are*

   167 required --- allowing unparenthesized "nothing" in expressions would cause

   168 ambiguities and allow common typos to pass uncaught.

   169 

   170 

   171 .. _lists:

   172 

   173 List displays

   174 -------------

   175 

   176 .. index::

   177    pair: list; display

   178    pair: list; comprehensions

   179 

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

   181 brackets:

   182 

   183 .. productionlist::

   184    list_display: "[" [`expression_list` | `list_comprehension`] "]"

   185    list_comprehension: `expression` `list_for`

   186    list_for: "for" `target_list` "in" `old_expression_list` [`list_iter`]

   187    old_expression_list: `old_expression` [("," `old_expression`)+ [","]]

   188    list_iter: `list_for` | `list_if`

   189    list_if: "if" `old_expression` [`list_iter`]

   190 

   191 .. index::

   192    pair: list; comprehensions

   193    object: list

   194    pair: empty; list

   195 

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

   197 providing either a list of expressions or a list comprehension.  When a

   198 comma-separated list of expressions is supplied, its elements are evaluated from

   199 left to right and placed into the list object in that order.  When a list

   200 comprehension is supplied, it consists of a single expression followed by at

   201 least one :keyword:`for` clause and zero or more :keyword:`for` or :keyword:`if`

   202 clauses.  In this case, the elements of the new list are those that would be

   203 produced by considering each of the :keyword:`for` or :keyword:`if` clauses a

   204 block, nesting from left to right, and evaluating the expression to produce a

   205 list element each time the innermost block is reached [#]_.

   206 

   207 

   208 .. _genexpr:

   209 

   210 Generator expressions

   211 ---------------------

   212 

   213 .. index:: pair: generator; expression

   214 

   215 A generator expression is a compact generator notation in parentheses:

   216 

   217 .. productionlist::

   218    generator_expression: "(" `expression` `genexpr_for` ")"

   219    genexpr_for: "for" `target_list` "in" `or_test` [`genexpr_iter`]

   220    genexpr_iter: `genexpr_for` | `genexpr_if`

   221    genexpr_if: "if" `old_expression` [`genexpr_iter`]

   222 

   223 .. index:: object: generator

   224 

   225 A generator expression yields a new generator object.  It consists of a single

   226 expression followed by at least one :keyword:`for` clause and zero or more

   227 :keyword:`for` or :keyword:`if` clauses.  The iterating values of the new

   228 generator are those that would be produced by considering each of the

   229 :keyword:`for` or :keyword:`if` clauses a block, nesting from left to right, and

   230 evaluating the expression to yield a value that is reached the innermost block

   231 for each iteration.

   232 

   233 Variables used in the generator expression are evaluated lazily in a separate

   234 scope when the :meth:`next` method is called for the generator object (in the

   235 same fashion as for normal generators).  However, the :keyword:`in` expression

   236 of the leftmost :keyword:`for` clause is immediately evaluated in the current

   237 scope so that an error produced by it can be seen before any other possible

   238 error in the code that handles the generator expression.  Subsequent

   239 :keyword:`for` and :keyword:`if` clauses cannot be evaluated immediately since

   240 they may depend on the previous :keyword:`for` loop.  For example:

   241 ``(x*y for x in range(10) for y in bar(x))``.

   242 

   243 The parentheses can be omitted on calls with only one argument. See section

   244 :ref:`calls` for the detail.

   245 

   246 

   247 .. _dict:

   248 

   249 Dictionary displays

   250 -------------------

   251 

   252 .. index:: pair: dictionary; display

   253 

   254 .. index::

   255    single: key

   256    single: datum

   257    single: key/datum pair

   258 

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

   260 curly braces:

   261 

   262 .. productionlist::

   263    dict_display: "{" [`key_datum_list`] "}"

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

   265    key_datum: `expression` ":" `expression`

   266 

   267 .. index:: object: dictionary

   268 

   269 A dictionary display yields a new dictionary object.

   270 

   271 The key/datum pairs are evaluated from left to right to define the entries of

   272 the dictionary: each key object is used as a key into the dictionary to store

   273 the corresponding datum.

   274 

   275 .. index:: pair: immutable; object

   276 

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

   278 :ref:`types`.  (To summarize, the key type should be :term:`hashable`, which excludes

   279 all mutable objects.)  Clashes between duplicate keys are not detected; the last

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

   281 prevails.

   282 

   283 

   284 .. _string-conversions:

   285 

   286 String conversions

   287 ------------------

   288 

   289 .. index::

   290    pair: string; conversion

   291    pair: reverse; quotes

   292    pair: backward; quotes

   293    single: back-quotes

   294 

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

   296 quotes:

   297 

   298 .. productionlist::

   299    string_conversion: "'" `expression_list` "'"

   300 

   301 A string conversion evaluates the contained expression list and converts the

   302 resulting object into a string according to rules specific to its type.

   303 

   304 If the object is a string, a number, ``None``, or a tuple, list or dictionary

   305 containing only objects whose type is one of these, the resulting string is a

   306 valid Python expression which can be passed to the built-in function

   307 :func:`eval` to yield an expression with the same value (or an approximation, if

   308 floating point numbers are involved).

   309 

   310 (In particular, converting a string adds quotes around it and converts "funny"

   311 characters to escape sequences that are safe to print.)

   312 

   313 .. index:: object: recursive

   314 

   315 Recursive objects (for example, lists or dictionaries that contain a reference

   316 to themselves, directly or indirectly) use ``...`` to indicate a recursive

   317 reference, and the result cannot be passed to :func:`eval` to get an equal value

   318 (:exc:`SyntaxError` will be raised instead).

   319 

   320 .. index::

   321    builtin: repr

   322    builtin: str

   323 

   324 The built-in function :func:`repr` performs exactly the same conversion in its

   325 argument as enclosing it in parentheses and reverse quotes does.  The built-in

   326 function :func:`str` performs a similar but more user-friendly conversion.

   327 

   328 

   329 .. _yieldexpr:

   330 

   331 Yield expressions

   332 -----------------

   333 

   334 .. index::

   335    keyword: yield

   336    pair: yield; expression

   337    pair: generator; function

   338 

   339 .. productionlist::

   340    yield_atom: "(" `yield_expression` ")"

   341    yield_expression: "yield" [`expression_list`]

   342 

   343 .. versionadded:: 2.5

   344 

   345 The :keyword:`yield` expression is only used when defining a generator function,

   346 and can only be used in the body of a function definition. Using a

   347 :keyword:`yield` expression in a function definition is sufficient to cause that

   348 definition to create a generator function instead of a normal function.

   349 

   350 When a generator function is called, it returns an iterator known as a

   351 generator.  That generator then controls the execution of a generator function.

   352 The execution starts when one of the generator's methods is called.  At that

   353 time, the execution proceeds to the first :keyword:`yield` expression, where it

   354 is suspended again, returning the value of :token:`expression_list` to

   355 generator's caller.  By suspended we mean that all local state is retained,

   356 including the current bindings of local variables, the instruction pointer, and

   357 the internal evaluation stack.  When the execution is resumed by calling one of

   358 the generator's methods, the function can proceed exactly as if the

   359 :keyword:`yield` expression was just another external call. The value of the

   360 :keyword:`yield` expression after resuming depends on the method which resumed

   361 the execution.

   362 

   363 .. index:: single: coroutine

   364 

   365 All of this makes generator functions quite similar to coroutines; they yield

   366 multiple times, they have more than one entry point and their execution can be

   367 suspended.  The only difference is that a generator function cannot control

   368 where should the execution continue after it yields; the control is always

   369 transfered to the generator's caller.

   370 

   371 .. index:: object: generator

   372 

   373 The following generator's methods can be used to control the execution of a

   374 generator function:

   375 

   376 .. index:: exception: StopIteration

   377 

   378 

   379 .. method:: generator.next()

   380 

   381    Starts the execution of a generator function or resumes it at the last executed

   382    :keyword:`yield` expression.  When a generator function is resumed with a

   383    :meth:`next` method, the current :keyword:`yield` expression always evaluates to

   384    :const:`None`.  The execution then continues to the next :keyword:`yield`

   385    expression, where the generator is suspended again, and the value of the

   386    :token:`expression_list` is returned to :meth:`next`'s caller. If the generator

   387    exits without yielding another value, a :exc:`StopIteration` exception is

   388    raised.

   389 

   390 

   391 .. method:: generator.send(value)

   392 

   393    Resumes the execution and "sends" a value into the generator function.  The

   394    ``value`` argument becomes the result of the current :keyword:`yield`

   395    expression.  The :meth:`send` method returns the next value yielded by the

   396    generator, or raises :exc:`StopIteration` if the generator exits without

   397    yielding another value. When :meth:`send` is called to start the generator, it

   398    must be called with :const:`None` as the argument, because there is no

   399    :keyword:`yield` expression that could receive the value.

   400 

   401 

   402 .. method:: generator.throw(type[, value[, traceback]])

   403 

   404    Raises an exception of type ``type`` at the point where generator was paused,

   405    and returns the next value yielded by the generator function.  If the generator

   406    exits without yielding another value, a :exc:`StopIteration` exception is

   407    raised.  If the generator function does not catch the passed-in exception, or

   408    raises a different exception, then that exception propagates to the caller.

   409 

   410 .. index:: exception: GeneratorExit

   411 

   412 

   413 .. method:: generator.close()

   414 

   415    Raises a :exc:`GeneratorExit` at the point where the generator function was

   416    paused.  If the generator function then raises :exc:`StopIteration` (by exiting

   417    normally, or due to already being closed) or :exc:`GeneratorExit` (by not

   418    catching the exception), close returns to its caller.  If the generator yields a

   419    value, a :exc:`RuntimeError` is raised.  If the generator raises any other

   420    exception, it is propagated to the caller.  :meth:`close` does nothing if the

   421    generator has already exited due to an exception or normal exit.

   422 

   423 Here is a simple example that demonstrates the behavior of generators and

   424 generator functions::

   425 

   426    >>> def echo(value=None):

   427    ...     print "Execution starts when 'next()' is called for the first time."

   428    ...     try:

   429    ...         while True:

   430    ...             try:

   431    ...                 value = (yield value)

   432    ...             except Exception, e:

   433    ...                 value = e

   434    ...     finally:

   435    ...         print "Don't forget to clean up when 'close()' is called."

   436    ...

   437    >>> generator = echo(1)

   438    >>> print generator.next()

   439    Execution starts when 'next()' is called for the first time.

   440    1

   441    >>> print generator.next()

   442    None

   443    >>> print generator.send(2)

   444    2

   445    >>> generator.throw(TypeError, "spam")

   446    TypeError('spam',)

   447    >>> generator.close()

   448    Don't forget to clean up when 'close()' is called.

   449 

   450 

   451 .. seealso::

   452 

   453    :pep:`0342` - Coroutines via Enhanced Generators

   454       The proposal to enhance the API and syntax of generators, making them usable as

   455       simple coroutines.

   456 

   457 

   458 .. _primaries:

   459 

   460 Primaries

   461 =========

   462 

   463 .. index:: single: primary

   464 

   465 Primaries represent the most tightly bound operations of the language. Their

   466 syntax is:

   467 

   468 .. productionlist::

   469    primary: `atom` | `attributeref` | `subscription` | `slicing` | `call`

   470 

   471 

   472 .. _attribute-references:

   473 

   474 Attribute references

   475 --------------------

   476 

   477 .. index:: pair: attribute; reference

   478 

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

   480 

   481 .. productionlist::

   482    attributeref: `primary` "." `identifier`

   483 

   484 .. index::

   485    exception: AttributeError

   486    object: module

   487    object: list

   488 

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

   490 references, e.g., a module, list, or an instance.  This object is then asked to

   491 produce the attribute whose name is the identifier.  If this attribute is not

   492 available, the exception :exc:`AttributeError` is raised. Otherwise, the type

   493 and value of the object produced is determined by the object.  Multiple

   494 evaluations of the same attribute reference may yield different objects.

   495 

   496 

   497 .. _subscriptions:

   498 

   499 Subscriptions

   500 -------------

   501 

   502 .. index:: single: subscription

   503 

   504 .. index::

   505    object: sequence

   506    object: mapping

   507    object: string

   508    object: tuple

   509    object: list

   510    object: dictionary

   511    pair: sequence; item

   512 

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

   514 (dictionary) object:

   515 

   516 .. productionlist::

   517    subscription: `primary` "[" `expression_list` "]"

   518 

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

   520 

   521 If the primary is a mapping, the expression list must evaluate to an object

   522 whose value is one of the keys of the mapping, and the subscription selects the

   523 value in the mapping that corresponds to that key.  (The expression list is a

   524 tuple except if it has exactly one item.)

   525 

   526 If the primary is a sequence, the expression (list) must evaluate to a plain

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

   528 (so that, e.g., ``x[-1]`` selects the last item of ``x``.)  The resulting value

   529 must be a nonnegative integer less than the number of items in the sequence, and

   530 the subscription selects the item whose index is that value (counting from

   531 zero).

   532 

   533 .. index::

   534    single: character

   535    pair: string; item

   536 

   537 A string's items are characters.  A character is not a separate data type but a

   538 string of exactly one character.

   539 

   540 

   541 .. _slicings:

   542 

   543 Slicings

   544 --------

   545 

   546 .. index::

   547    single: slicing

   548    single: slice

   549 

   550 .. index::

   551    object: sequence

   552    object: string

   553    object: tuple

   554    object: list

   555 

   556 A slicing selects a range of items in a sequence object (e.g., a string, tuple

   557 or list).  Slicings may be used as expressions or as targets in assignment or

   558 :keyword:`del` statements.  The syntax for a slicing:

   559 

   560 .. productionlist::

   561    slicing: `simple_slicing` | `extended_slicing`

   562    simple_slicing: `primary` "[" `short_slice` "]"

   563    extended_slicing: `primary` "[" `slice_list` "]" 

   564    slice_list: `slice_item` ("," `slice_item`)* [","]

   565    slice_item: `expression` | `proper_slice` | `ellipsis`

   566    proper_slice: `short_slice` | `long_slice`

   567    short_slice: [`lower_bound`] ":" [`upper_bound`]

   568    long_slice: `short_slice` ":" [`stride`]

   569    lower_bound: `expression`

   570    upper_bound: `expression`

   571    stride: `expression`

   572    ellipsis: "..."

   573 

   574 .. index:: pair: extended; slicing

   575 

   576 There is ambiguity in the formal syntax here: anything that looks like an

   577 expression list also looks like a slice list, so any subscription can be

   578 interpreted as a slicing.  Rather than further complicating the syntax, this is

   579 disambiguated by defining that in this case the interpretation as a subscription

   580 takes priority over the interpretation as a slicing (this is the case if the

   581 slice list contains no proper slice nor ellipses).  Similarly, when the slice

   582 list has exactly one short slice and no trailing comma, the interpretation as a

   583 simple slicing takes priority over that as an extended slicing.

   584 

   585 The semantics for a simple slicing are as follows.  The primary must evaluate to

   586 a sequence object.  The lower and upper bound expressions, if present, must

   587 evaluate to plain integers; defaults are zero and the ``sys.maxint``,

   588 respectively.  If either bound is negative, the sequence's length is added to

   589 it.  The slicing now selects all items with index *k* such that ``i <= k < j``

   590 where *i* and *j* are the specified lower and upper bounds.  This may be an

   591 empty sequence.  It is not an error if *i* or *j* lie outside the range of valid

   592 indexes (such items don't exist so they aren't selected).

   593 

   594 .. index::

   595    single: start (slice object attribute)

   596    single: stop (slice object attribute)

   597    single: step (slice object attribute)

   598 

   599 The semantics for an extended slicing are as follows.  The primary must evaluate

   600 to a mapping object, and it is indexed with a key that is constructed from the

   601 slice list, as follows.  If the slice list contains at least one comma, the key

   602 is a tuple containing the conversion of the slice items; otherwise, the

   603 conversion of the lone slice item is the key.  The conversion of a slice item

   604 that is an expression is that expression.  The conversion of an ellipsis slice

   605 item is the built-in ``Ellipsis`` object.  The conversion of a proper slice is a

   606 slice object (see section :ref:`types`) whose :attr:`start`, :attr:`stop` and

   607 :attr:`step` attributes are the values of the expressions given as lower bound,

   608 upper bound and stride, respectively, substituting ``None`` for missing

   609 expressions.

   610 

   611 

   612 .. _calls:

   613 

   614 Calls

   615 -----

   616 

   617 .. index:: single: call

   618 

   619 .. index:: object: callable

   620 

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

   622 of arguments:

   623 

   624 .. productionlist::

   625    call: `primary` "(" [`argument_list` [","]

   626        : | `expression` `genexpr_for`] ")"

   627    argument_list: `positional_arguments` ["," `keyword_arguments`]

   628                 :   ["," "*" `expression`] ["," `keyword_arguments`]

   629                 :   ["," "**" `expression`]

   630                 : | `keyword_arguments` ["," "*" `expression`]

   631                 :   ["," "**" `expression`]

   632                 : | "*" `expression` ["," "*" `expression`] ["," "**" `expression`]

   633                 : | "**" `expression`

   634    positional_arguments: `expression` ("," `expression`)*

   635    keyword_arguments: `keyword_item` ("," `keyword_item`)*

   636    keyword_item: `identifier` "=" `expression`

   637 

   638 A trailing comma may be present after the positional and keyword arguments but

   639 does not affect the semantics.

   640 

   641 The primary must evaluate to a callable object (user-defined functions, built-in

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

   643 instances, and certain class instances themselves are callable; extensions may

   644 define additional callable object types).  All argument expressions are

   645 evaluated before the call is attempted.  Please refer to section :ref:`function`

   646 for the syntax of formal parameter lists.

   647 

   648 If keyword arguments are present, they are first converted to positional

   649 arguments, as follows.  First, a list of unfilled slots is created for the

   650 formal parameters.  If there are N positional arguments, they are placed in the

   651 first N slots.  Next, for each keyword argument, the identifier is used to

   652 determine the corresponding slot (if the identifier is the same as the first

   653 formal parameter name, the first slot is used, and so on).  If the slot is

   654 already filled, a :exc:`TypeError` exception is raised. Otherwise, the value of

   655 the argument is placed in the slot, filling it (even if the expression is

   656 ``None``, it fills the slot).  When all arguments have been processed, the slots

   657 that are still unfilled are filled with the corresponding default value from the

   658 function definition.  (Default values are calculated, once, when the function is

   659 defined; thus, a mutable object such as a list or dictionary used as default

   660 value will be shared by all calls that don't specify an argument value for the

   661 corresponding slot; this should usually be avoided.)  If there are any unfilled

   662 slots for which no default value is specified, a :exc:`TypeError` exception is

   663 raised.  Otherwise, the list of filled slots is used as the argument list for

   664 the call.

   665 

   666 .. note::

   667    

   668    An implementation may provide builtin functions whose positional parameters do

   669    not have names, even if they are 'named' for the purpose of documentation, and

   670    which therefore cannot be supplied by keyword.  In CPython, this is the case for

   671    functions implemented in C that use :cfunc:`PyArg_ParseTuple` to parse their

   672    arguments.

   673 

   674 If there are more positional arguments than there are formal parameter slots, a

   675 :exc:`TypeError` exception is raised, unless a formal parameter using the syntax

   676 ``*identifier`` is present; in this case, that formal parameter receives a tuple

   677 containing the excess positional arguments (or an empty tuple if there were no

   678 excess positional arguments).

   679 

   680 If any keyword argument does not correspond to a formal parameter name, a

   681 :exc:`TypeError` exception is raised, unless a formal parameter using the syntax

   682 ``**identifier`` is present; in this case, that formal parameter receives a

   683 dictionary containing the excess keyword arguments (using the keywords as keys

   684 and the argument values as corresponding values), or a (new) empty dictionary if

   685 there were no excess keyword arguments.

   686 

   687 If the syntax ``*expression`` appears in the function call, ``expression`` must

   688 evaluate to a sequence.  Elements from this sequence are treated as if they were

   689 additional positional arguments; if there are positional arguments *x1*,...,

   690 *xN*, and ``expression`` evaluates to a sequence *y1*, ..., *yM*, this is

   691 equivalent to a call with M+N positional arguments *x1*, ..., *xN*, *y1*, ...,

   692 *yM*.

   693 

   694 A consequence of this is that although the ``*expression`` syntax may appear

   695 *after* some keyword arguments, it is processed *before* the keyword arguments

   696 (and the ``**expression`` argument, if any -- see below).  So::

   697 

   698    >>> def f(a, b):

   699    ...  print a, b

   700    ...

   701    >>> f(b=1, *(2,))

   702    2 1

   703    >>> f(a=1, *(2,))

   704    Traceback (most recent call last):

   705      File "<stdin>", line 1, in ?

   706    TypeError: f() got multiple values for keyword argument 'a'

   707    >>> f(1, *(2,))

   708    1 2

   709 

   710 It is unusual for both keyword arguments and the ``*expression`` syntax to be

   711 used in the same call, so in practice this confusion does not arise.

   712 

   713 If the syntax ``**expression`` appears in the function call, ``expression`` must

   714 evaluate to a mapping, the contents of which are treated as additional keyword

   715 arguments.  In the case of a keyword appearing in both ``expression`` and as an

   716 explicit keyword argument, a :exc:`TypeError` exception is raised.

   717 

   718 Formal parameters using the syntax ``*identifier`` or ``**identifier`` cannot be

   719 used as positional argument slots or as keyword argument names.  Formal

   720 parameters using the syntax ``(sublist)`` cannot be used as keyword argument

   721 names; the outermost sublist corresponds to a single unnamed argument slot, and

   722 the argument value is assigned to the sublist using the usual tuple assignment

   723 rules after all other parameter processing is done.

   724 

   725 A call always returns some value, possibly ``None``, unless it raises an

   726 exception.  How this value is computed depends on the type of the callable

   727 object.

   728 

   729 If it is---

   730 

   731 a user-defined function:

   732    .. index::

   733       pair: function; call

   734       triple: user-defined; function; call

   735       object: user-defined function

   736       object: function

   737 

   738    The code block for the function is executed, passing it the argument list.  The

   739    first thing the code block will do is bind the formal parameters to the

   740    arguments; this is described in section :ref:`function`.  When the code block

   741    executes a :keyword:`return` statement, this specifies the return value of the

   742    function call.

   743 

   744 a built-in function or method:

   745    .. index::

   746       pair: function; call

   747       pair: built-in function; call

   748       pair: method; call

   749       pair: built-in method; call

   750       object: built-in method

   751       object: built-in function

   752       object: method

   753       object: function

   754 

   755    The result is up to the interpreter; see :ref:`built-in-funcs` for the

   756    descriptions of built-in functions and methods.

   757 

   758 a class object:

   759    .. index::

   760       object: class

   761       pair: class object; call

   762 

   763    A new instance of that class is returned.

   764 

   765 a class instance method:

   766    .. index::

   767       object: class instance

   768       object: instance

   769       pair: class instance; call

   770 

   771    The corresponding user-defined function is called, with an argument list that is

   772    one longer than the argument list of the call: the instance becomes the first

   773    argument.

   774 

   775 a class instance:

   776    .. index::

   777       pair: instance; call

   778       single: __call__() (object method)

   779 

   780    The class must define a :meth:`__call__` method; the effect is then the same as

   781    if that method was called.

   782 

   783 

   784 .. _power:

   785 

   786 The power operator

   787 ==================

   788 

   789 The power operator binds more tightly than unary operators on its left; it binds

   790 less tightly than unary operators on its right.  The syntax is:

   791 

   792 .. productionlist::

   793    power: `primary` ["**" `u_expr`]

   794 

   795 Thus, in an unparenthesized sequence of power and unary operators, the operators

   796 are evaluated from right to left (this does not constrain the evaluation order

   797 for the operands): ``-1**2`` results in ``-1``.

   798 

   799 The power operator has the same semantics as the built-in :func:`pow` function,

   800 when called with two arguments: it yields its left argument raised to the power

   801 of its right argument.  The numeric arguments are first converted to a common

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

   803 

   804 With mixed operand types, the coercion rules for binary arithmetic operators

   805 apply. For int and long int operands, the result has the same type as the

   806 operands (after coercion) unless the second argument is negative; in that case,

   807 all arguments are converted to float and a float result is delivered. For

   808 example, ``10**2`` returns ``100``, but ``10**-2`` returns ``0.01``. (This last

   809 feature was added in Python 2.2. In Python 2.1 and before, if both arguments

   810 were of integer types and the second argument was negative, an exception was

   811 raised).

   812 

   813 Raising ``0.0`` to a negative power results in a :exc:`ZeroDivisionError`.

   814 Raising a negative number to a fractional power results in a :exc:`ValueError`.

   815 

   816 

   817 .. _unary:

   818 

   819 Unary arithmetic operations

   820 ===========================

   821 

   822 .. index::

   823    triple: unary; arithmetic; operation

   824    triple: unary; bitwise; operation

   825 

   826 All unary arithmetic (and bitwise) operations have the same priority:

   827 

   828 .. productionlist::

   829    u_expr: `power` | "-" `u_expr` | "+" `u_expr` | "~" `u_expr`

   830 

   831 .. index::

   832    single: negation

   833    single: minus

   834 

   835 The unary ``-`` (minus) operator yields the negation of its numeric argument.

   836 

   837 .. index:: single: plus

   838 

   839 The unary ``+`` (plus) operator yields its numeric argument unchanged.

   840 

   841 .. index:: single: inversion

   842 

   843 The unary ``~`` (invert) operator yields the bitwise inversion of its plain or

   844 long integer argument.  The bitwise inversion of ``x`` is defined as

   845 ``-(x+1)``.  It only applies to integral numbers.

   846 

   847 .. index:: exception: TypeError

   848 

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

   850 :exc:`TypeError` exception is raised.

   851 

   852 

   853 .. _binary:

   854 

   855 Binary arithmetic operations

   856 ============================

   857 

   858 .. index:: triple: binary; arithmetic; operation

   859 

   860 The binary arithmetic operations have the conventional priority levels.  Note

   861 that some of these operations also apply to certain non-numeric types.  Apart

   862 from the power operator, there are only two levels, one for multiplicative

   863 operators and one for additive operators:

   864 

   865 .. productionlist::

   866    m_expr: `u_expr` | `m_expr` "*" `u_expr` | `m_expr` "//" `u_expr` | `m_expr` "/" `u_expr`

   867          : | `m_expr` "%" `u_expr`

   868    a_expr: `m_expr` | `a_expr` "+" `m_expr` | `a_expr` "-" `m_expr`

   869 

   870 .. index:: single: multiplication

   871 

   872 The ``*`` (multiplication) operator yields the product of its arguments.  The

   873 arguments must either both be numbers, or one argument must be an integer (plain

   874 or long) and the other must be a sequence. In the former case, the numbers are

   875 converted to a common type and then multiplied together.  In the latter case,

   876 sequence repetition is performed; a negative repetition factor yields an empty

   877 sequence.

   878 

   879 .. index::

   880    exception: ZeroDivisionError

   881    single: division

   882 

   883 The ``/`` (division) and ``//`` (floor division) operators yield the quotient of

   884 their arguments.  The numeric arguments are first converted to a common type.

   885 Plain or long integer division yields an integer of the same type; the result is

   886 that of mathematical division with the 'floor' function applied to the result.

   887 Division by zero raises the :exc:`ZeroDivisionError` exception.

   888 

   889 .. index:: single: modulo

   890 

   891 The ``%`` (modulo) operator yields the remainder from the division of the first

   892 argument by the second.  The numeric arguments are first converted to a common

   893 type.  A zero right argument raises the :exc:`ZeroDivisionError` exception.  The

   894 arguments may be floating point numbers, e.g., ``3.14%0.7`` equals ``0.34``

   895 (since ``3.14`` equals ``4*0.7 + 0.34``.)  The modulo operator always yields a

   896 result with the same sign as its second operand (or zero); the absolute value of

   897 the result is strictly smaller than the absolute value of the second operand

   898 [#]_.

   899 

   900 The integer division and modulo operators are connected by the following

   901 identity: ``x == (x/y)*y + (x%y)``.  Integer division and modulo are also

   902 connected with the built-in function :func:`divmod`: ``divmod(x, y) == (x/y,

   903 x%y)``.  These identities don't hold for floating point numbers; there similar

   904 identities hold approximately where ``x/y`` is replaced by ``floor(x/y)`` or

   905 ``floor(x/y) - 1`` [#]_.

   906 

   907 In addition to performing the modulo operation on numbers, the ``%`` operator is

   908 also overloaded by string and unicode objects to perform string formatting (also

   909 known as interpolation). The syntax for string formatting is described in the

   910 Python Library Reference, section :ref:`string-formatting`.

   911 

   912 .. deprecated:: 2.3

   913    The floor division operator, the modulo operator, and the :func:`divmod`

   914    function are no longer defined for complex numbers.  Instead, convert to a

   915    floating point number using the :func:`abs` function if appropriate.

   916 

   917 .. index:: single: addition

   918 

   919 The ``+`` (addition) operator yields the sum of its arguments. The arguments

   920 must either both be numbers or both sequences of the same type.  In the former

   921 case, the numbers are converted to a common type and then added together.  In

   922 the latter case, the sequences are concatenated.

   923 

   924 .. index:: single: subtraction

   925 

   926 The ``-`` (subtraction) operator yields the difference of its arguments.  The

   927 numeric arguments are first converted to a common type.

   928 

   929 

   930 .. _shifting:

   931 

   932 Shifting operations

   933 ===================

   934 

   935 .. index:: pair: shifting; operation

   936 

   937 The shifting operations have lower priority than the arithmetic operations:

   938 

   939 .. productionlist::

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

   941 

   942 These operators accept plain or long integers as arguments.  The arguments are

   943 converted to a common type.  They shift the first argument to the left or right

   944 by the number of bits given by the second argument.

   945 

   946 .. index:: exception: ValueError

   947 

   948 A right shift by *n* bits is defined as division by ``pow(2, n)``.  A left shift

   949 by *n* bits is defined as multiplication with ``pow(2, n)``.  Negative shift

   950 counts raise a :exc:`ValueError` exception.

   951 

   952 

   953 .. _bitwise:

   954 

   955 Binary bitwise operations

   956 =========================

   957 

   958 .. index:: triple: binary; bitwise; operation

   959 

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

   961 

   962 .. productionlist::

   963    and_expr: `shift_expr` | `and_expr` "&" `shift_expr`

   964    xor_expr: `and_expr` | `xor_expr` "^" `and_expr`

   965    or_expr: `xor_expr` | `or_expr` "|" `xor_expr`

   966 

   967 .. index:: pair: bitwise; and

   968 

   969 The ``&`` operator yields the bitwise AND of its arguments, which must be plain

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

   971 

   972 .. index::

   973    pair: bitwise; xor

   974    pair: exclusive; or

   975 

   976 The ``^`` operator yields the bitwise XOR (exclusive OR) of its arguments, which

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

   978 

   979 .. index::

   980    pair: bitwise; or

   981    pair: inclusive; or

   982 

   983 The ``|`` operator yields the bitwise (inclusive) OR of its arguments, which

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

   985 

   986 

   987 .. _comparisons:

   988 .. _is:

   989 .. _isnot:

   990 .. _in:

   991 .. _notin:

   992 

   993 Comparisons

   994 ===========

   995 

   996 .. index:: single: comparison

   997 

   998 .. index:: pair: C; language

   999 

  1000 Unlike C, all comparison operations in Python have the same priority, which is

  1001 lower than that of any arithmetic, shifting or bitwise operation.  Also unlike

  1002 C, expressions like ``a < b < c`` have the interpretation that is conventional

  1003 in mathematics:

  1004 

  1005 .. productionlist::

  1006    comparison: `or_expr` ( `comp_operator` `or_expr` )*

  1007    comp_operator: "<" | ">" | "==" | ">=" | "<=" | "<>" | "!="

  1008                 : | "is" ["not"] | ["not"] "in"

  1009 

  1010 Comparisons yield boolean values: ``True`` or ``False``.

  1011 

  1012 .. index:: pair: chaining; comparisons

  1013 

  1014 Comparisons can be chained arbitrarily, e.g., ``x < y <= z`` is equivalent to

  1015 ``x < y and y <= z``, except that ``y`` is evaluated only once (but in both

  1016 cases ``z`` is not evaluated at all when ``x < y`` is found to be false).

  1017 

  1018 Formally, if *a*, *b*, *c*, ..., *y*, *z* are expressions and *op1*, *op2*, ...,

  1019 *opN* are comparison operators, then ``a op1 b op2 c ... y opN z`` is equivalent

  1020 to ``a op1 b and b op2 c and ... y opN z``, except that each expression is

  1021 evaluated at most once.

  1022 

  1023 Note that ``a op1 b op2 c`` doesn't imply any kind of comparison between *a* and

  1024 *c*, so that, e.g., ``x < y > z`` is perfectly legal (though perhaps not

  1025 pretty).

  1026 

  1027 The forms ``<>`` and ``!=`` are equivalent; for consistency with C, ``!=`` is

  1028 preferred; where ``!=`` is mentioned below ``<>`` is also accepted.  The ``<>``

  1029 spelling is considered obsolescent.

  1030 

  1031 The operators ``<``, ``>``, ``==``, ``>=``, ``<=``, and ``!=`` compare the

  1032 values of two objects.  The objects need not have the same type. If both are

  1033 numbers, they are converted to a common type.  Otherwise, objects of different

  1034 types *always* compare unequal, and are ordered consistently but arbitrarily.

  1035 You can control comparison behavior of objects of non-builtin types by defining

  1036 a ``__cmp__`` method or rich comparison methods like ``__gt__``, described in

  1037 section :ref:`specialnames`.

  1038 

  1039 (This unusual definition of comparison was used to simplify the definition of

  1040 operations like sorting and the :keyword:`in` and :keyword:`not in` operators.

  1041 In the future, the comparison rules for objects of different types are likely to

  1042 change.)

  1043 

  1044 Comparison of objects of the same type depends on the type:

  1045 

  1046 * Numbers are compared arithmetically.

  1047 

  1048 * Strings are compared lexicographically using the numeric equivalents (the

  1049   result of the built-in function :func:`ord`) of their characters.  Unicode and

  1050   8-bit strings are fully interoperable in this behavior. [#]_

  1051 

  1052 * Tuples and lists are compared lexicographically using comparison of

  1053   corresponding elements.  This means that to compare equal, each element must

  1054   compare equal and the two sequences must be of the same type and have the same

  1055   length.

  1056 

  1057   If not equal, the sequences are ordered the same as their first differing

  1058   elements.  For example, ``cmp([1,2,x], [1,2,y])`` returns the same as

  1059   ``cmp(x,y)``.  If the corresponding element does not exist, the shorter sequence

  1060   is ordered first (for example, ``[1,2] < [1,2,3]``).

  1061 

  1062 * Mappings (dictionaries) compare equal if and only if their sorted (key, value)

  1063   lists compare equal. [#]_ Outcomes other than equality are resolved

  1064   consistently, but are not otherwise defined. [#]_

  1065 

  1066 * Most other objects of builtin types compare unequal unless they are the same

  1067   object; the choice whether one object is considered smaller or larger than

  1068   another one is made arbitrarily but consistently within one execution of a

  1069   program.

  1070 

  1071 The operators :keyword:`in` and :keyword:`not in` test for collection

  1072 membership.  ``x in s`` evaluates to true if *x* is a member of the collection

  1073 *s*, and false otherwise.  ``x not in s`` returns the negation of ``x in s``.

  1074 The collection membership test has traditionally been bound to sequences; an

  1075 object is a member of a collection if the collection is a sequence and contains

  1076 an element equal to that object.  However, it make sense for many other object

  1077 types to support membership tests without being a sequence.  In particular,

  1078 dictionaries (for keys) and sets support membership testing.

  1079 

  1080 For the list and tuple types, ``x in y`` is true if and only if there exists an

  1081 index *i* such that ``x == y[i]`` is true.

  1082 

  1083 For the Unicode and string types, ``x in y`` is true if and only if *x* is a

  1084 substring of *y*.  An equivalent test is ``y.find(x) != -1``.  Note, *x* and *y*

  1085 need not be the same type; consequently, ``u'ab' in 'abc'`` will return

  1086 ``True``. Empty strings are always considered to be a substring of any other

  1087 string, so ``"" in "abc"`` will return ``True``.

  1088 

  1089 .. versionchanged:: 2.3

  1090    Previously, *x* was required to be a string of length ``1``.

  1091 

  1092 For user-defined classes which define the :meth:`__contains__` method, ``x in

  1093 y`` is true if and only if ``y.__contains__(x)`` is true.

  1094 

  1095 For user-defined classes which do not define :meth:`__contains__` and do define

  1096 :meth:`__getitem__`, ``x in y`` is true if and only if there is a non-negative

  1097 integer index *i* such that ``x == y[i]``, and all lower integer indices do not

  1098 raise :exc:`IndexError` exception. (If any other exception is raised, it is as

  1099 if :keyword:`in` raised that exception).

  1100 

  1101 .. index::

  1102    operator: in

  1103    operator: not in

  1104    pair: membership; test

  1105    object: sequence

  1106 

  1107 The operator :keyword:`not in` is defined to have the inverse true value of

  1108 :keyword:`in`.

  1109 

  1110 .. index::

  1111    operator: is

  1112    operator: is not

  1113    pair: identity; test

  1114 

  1115 The operators :keyword:`is` and :keyword:`is not` test for object identity: ``x

  1116 is y`` is true if and only if *x* and *y* are the same object.  ``x is not y``

  1117 yields the inverse truth value. [#]_

  1118 

  1119 

  1120 .. _booleans:

  1121 .. _and:

  1122 .. _or:

  1123 .. _not:

  1124 

  1125 Boolean operations

  1126 ==================

  1127 

  1128 .. index::

  1129    pair: Conditional; expression

  1130    pair: Boolean; operation

  1131 

  1132 Boolean operations have the lowest priority of all Python operations:

  1133 

  1134 .. productionlist::

  1135    expression: `conditional_expression` | `lambda_form`