|  | 
 | .. _datamodel: | 
 |  | 
 | ********** | 
 | Data model | 
 | ********** | 
 |  | 
 |  | 
 | .. _objects: | 
 |  | 
 | Objects, values and types | 
 | ========================= | 
 |  | 
 | .. index:: | 
 |    single: object | 
 |    single: data | 
 |  | 
 | :dfn:`Objects` are Python's abstraction for data.  All data in a Python program | 
 | is represented by objects or by relations between objects. (In a sense, and in | 
 | conformance to Von Neumann's model of a "stored program computer," code is also | 
 | represented by objects.) | 
 |  | 
 | .. index:: | 
 |    builtin: id | 
 |    builtin: type | 
 |    single: identity of an object | 
 |    single: value of an object | 
 |    single: type of an object | 
 |    single: mutable object | 
 |    single: immutable object | 
 |  | 
 | Every object has an identity, a type and a value.  An object's *identity* never | 
 | changes once it has been created; you may think of it as the object's address in | 
 | memory.  The ':keyword:`is`' operator compares the identity of two objects; the | 
 | :func:`id` function returns an integer representing its identity (currently | 
 | implemented as its address). An object's :dfn:`type` is also unchangeable. [#]_ | 
 | An object's type determines the operations that the object supports (e.g., "does | 
 | it have a length?") and also defines the possible values for objects of that | 
 | type.  The :func:`type` function returns an object's type (which is an object | 
 | itself).  The *value* of some objects can change.  Objects whose value can | 
 | change are said to be *mutable*; objects whose value is unchangeable once they | 
 | are created are called *immutable*. (The value of an immutable container object | 
 | that contains a reference to a mutable object can change when the latter's value | 
 | is changed; however the container is still considered immutable, because the | 
 | collection of objects it contains cannot be changed.  So, immutability is not | 
 | strictly the same as having an unchangeable value, it is more subtle.) An | 
 | object's mutability is determined by its type; for instance, numbers, strings | 
 | and tuples are immutable, while dictionaries and lists are mutable. | 
 |  | 
 | .. index:: | 
 |    single: garbage collection | 
 |    single: reference counting | 
 |    single: unreachable object | 
 |  | 
 | Objects are never explicitly destroyed; however, when they become unreachable | 
 | they may be garbage-collected.  An implementation is allowed to postpone garbage | 
 | collection or omit it altogether --- it is a matter of implementation quality | 
 | how garbage collection is implemented, as long as no objects are collected that | 
 | are still reachable. | 
 |  | 
 | .. impl-detail:: | 
 |  | 
 |    CPython currently uses a reference-counting scheme with (optional) delayed | 
 |    detection of cyclically linked garbage, which collects most objects as soon | 
 |    as they become unreachable, but is not guaranteed to collect garbage | 
 |    containing circular references.  See the documentation of the :mod:`gc` | 
 |    module for information on controlling the collection of cyclic garbage. | 
 |    Other implementations act differently and CPython may change. | 
 |    Do not depend on immediate finalization of objects when they become | 
 |    unreachable (ex: always close files). | 
 |  | 
 | Note that the use of the implementation's tracing or debugging facilities may | 
 | keep objects alive that would normally be collectable. Also note that catching | 
 | an exception with a ':keyword:`try`...\ :keyword:`except`' statement may keep | 
 | objects alive. | 
 |  | 
 | Some objects contain references to "external" resources such as open files or | 
 | windows.  It is understood that these resources are freed when the object is | 
 | garbage-collected, but since garbage collection is not guaranteed to happen, | 
 | such objects also provide an explicit way to release the external resource, | 
 | usually a :meth:`close` method. Programs are strongly recommended to explicitly | 
 | close such objects.  The ':keyword:`try`...\ :keyword:`finally`' statement | 
 | provides a convenient way to do this. | 
 |  | 
 | .. index:: single: container | 
 |  | 
 | Some objects contain references to other objects; these are called *containers*. | 
 | Examples of containers are tuples, lists and dictionaries.  The references are | 
 | part of a container's value.  In most cases, when we talk about the value of a | 
 | container, we imply the values, not the identities of the contained objects; | 
 | however, when we talk about the mutability of a container, only the identities | 
 | of the immediately contained objects are implied.  So, if an immutable container | 
 | (like a tuple) contains a reference to a mutable object, its value changes if | 
 | that mutable object is changed. | 
 |  | 
 | Types affect almost all aspects of object behavior.  Even the importance of | 
 | object identity is affected in some sense: for immutable types, operations that | 
 | compute new values may actually return a reference to any existing object with | 
 | the same type and value, while for mutable objects this is not allowed.  E.g., | 
 | after ``a = 1; b = 1``, ``a`` and ``b`` may or may not refer to the same object | 
 | with the value one, depending on the implementation, but after ``c = []; d = | 
 | []``, ``c`` and ``d`` are guaranteed to refer to two different, unique, newly | 
 | created empty lists. (Note that ``c = d = []`` assigns the same object to both | 
 | ``c`` and ``d``.) | 
 |  | 
 |  | 
 | .. _types: | 
 |  | 
 | The standard type hierarchy | 
 | =========================== | 
 |  | 
 | .. index:: | 
 |    single: type | 
 |    pair: data; type | 
 |    pair: type; hierarchy | 
 |    pair: extension; module | 
 |    pair: C; language | 
 |  | 
 | Below is a list of the types that are built into Python.  Extension modules | 
 | (written in C, Java, or other languages, depending on the implementation) can | 
 | define additional types.  Future versions of Python may add types to the type | 
 | hierarchy (e.g., rational numbers, efficiently stored arrays of integers, etc.). | 
 |  | 
 | .. index:: | 
 |    single: attribute | 
 |    pair: special; attribute | 
 |    triple: generic; special; attribute | 
 |  | 
 | Some of the type descriptions below contain a paragraph listing 'special | 
 | attributes.'  These are attributes that provide access to the implementation and | 
 | are not intended for general use.  Their definition may change in the future. | 
 |  | 
 | None | 
 |    .. index:: object: None | 
 |  | 
 |    This type has a single value.  There is a single object with this value. This | 
 |    object is accessed through the built-in name ``None``. It is used to signify the | 
 |    absence of a value in many situations, e.g., it is returned from functions that | 
 |    don't explicitly return anything. Its truth value is false. | 
 |  | 
 | NotImplemented | 
 |    .. index:: object: NotImplemented | 
 |  | 
 |    This type has a single value.  There is a single object with this value. This | 
 |    object is accessed through the built-in name ``NotImplemented``. Numeric methods | 
 |    and rich comparison methods may return this value if they do not implement the | 
 |    operation for the operands provided.  (The interpreter will then try the | 
 |    reflected operation, or some other fallback, depending on the operator.)  Its | 
 |    truth value is true. | 
 |  | 
 | Ellipsis | 
 |    .. index:: object: Ellipsis | 
 |  | 
 |    This type has a single value.  There is a single object with this value. This | 
 |    object is accessed through the built-in name ``Ellipsis``. It is used to | 
 |    indicate the presence of the ``...`` syntax in a slice.  Its truth value is | 
 |    true. | 
 |  | 
 | :class:`numbers.Number` | 
 |    .. index:: object: numeric | 
 |  | 
 |    These are created by numeric literals and returned as results by arithmetic | 
 |    operators and arithmetic built-in functions.  Numeric objects are immutable; | 
 |    once created their value never changes.  Python numbers are of course strongly | 
 |    related to mathematical numbers, but subject to the limitations of numerical | 
 |    representation in computers. | 
 |  | 
 |    Python distinguishes between integers, floating point numbers, and complex | 
 |    numbers: | 
 |  | 
 |    :class:`numbers.Integral` | 
 |       .. index:: object: integer | 
 |  | 
 |       These represent elements from the mathematical set of integers (positive and | 
 |       negative). | 
 |  | 
 |       There are three types of integers: | 
 |  | 
 |       Plain integers | 
 |          .. index:: | 
 |             object: plain integer | 
 |             single: OverflowError (built-in exception) | 
 |  | 
 |          These represent numbers in the range -2147483648 through 2147483647. | 
 |          (The range may be larger on machines with a larger natural word size, | 
 |          but not smaller.)  When the result of an operation would fall outside | 
 |          this range, the result is normally returned as a long integer (in some | 
 |          cases, the exception :exc:`OverflowError` is raised instead).  For the | 
 |          purpose of shift and mask operations, integers are assumed to have a | 
 |          binary, 2's complement notation using 32 or more bits, and hiding no | 
 |          bits from the user (i.e., all 4294967296 different bit patterns | 
 |          correspond to different values). | 
 |  | 
 |       Long integers | 
 |          .. index:: object: long integer | 
 |  | 
 |          These represent numbers in an unlimited range, subject to available | 
 |          (virtual) memory only.  For the purpose of shift and mask operations, a | 
 |          binary representation is assumed, and negative numbers are represented | 
 |          in a variant of 2's complement which gives the illusion of an infinite | 
 |          string of sign bits extending to the left. | 
 |  | 
 |       Booleans | 
 |          .. index:: | 
 |             object: Boolean | 
 |             single: False | 
 |             single: True | 
 |  | 
 |          These represent the truth values False and True.  The two objects | 
 |          representing the values ``False`` and ``True`` are the only Boolean objects. | 
 |          The Boolean type is a subtype of plain integers, and Boolean values | 
 |          behave like the values 0 and 1, respectively, in almost all contexts, | 
 |          the exception being that when converted to a string, the strings | 
 |          ``"False"`` or ``"True"`` are returned, respectively. | 
 |  | 
 |       .. index:: pair: integer; representation | 
 |  | 
 |       The rules for integer representation are intended to give the most | 
 |       meaningful interpretation of shift and mask operations involving negative | 
 |       integers and the least surprises when switching between the plain and long | 
 |       integer domains.  Any operation, if it yields a result in the plain | 
 |       integer domain, will yield the same result in the long integer domain or | 
 |       when using mixed operands.  The switch between domains is transparent to | 
 |       the programmer. | 
 |  | 
 |    :class:`numbers.Real` (:class:`float`) | 
 |       .. index:: | 
 |          object: floating point | 
 |          pair: floating point; number | 
 |          pair: C; language | 
 |          pair: Java; language | 
 |  | 
 |       These represent machine-level double precision floating point numbers. You are | 
 |       at the mercy of the underlying machine architecture (and C or Java | 
 |       implementation) for the accepted range and handling of overflow. Python does not | 
 |       support single-precision floating point numbers; the savings in processor and | 
 |       memory usage that are usually the reason for using these are dwarfed by the | 
 |       overhead of using objects in Python, so there is no reason to complicate the | 
 |       language with two kinds of floating point numbers. | 
 |  | 
 |    :class:`numbers.Complex` | 
 |       .. index:: | 
 |          object: complex | 
 |          pair: complex; number | 
 |  | 
 |       These represent complex numbers as a pair of machine-level double precision | 
 |       floating point numbers.  The same caveats apply as for floating point numbers. | 
 |       The real and imaginary parts of a complex number ``z`` can be retrieved through | 
 |       the read-only attributes ``z.real`` and ``z.imag``. | 
 |  | 
 | Sequences | 
 |    .. index:: | 
 |       builtin: len | 
 |       object: sequence | 
 |       single: index operation | 
 |       single: item selection | 
 |       single: subscription | 
 |  | 
 |    These represent finite ordered sets indexed by non-negative numbers. The | 
 |    built-in function :func:`len` returns the number of items of a sequence. When | 
 |    the length of a sequence is *n*, the index set contains the numbers 0, 1, | 
 |    ..., *n*-1.  Item *i* of sequence *a* is selected by ``a[i]``. | 
 |  | 
 |    .. index:: single: slicing | 
 |  | 
 |    Sequences also support slicing: ``a[i:j]`` selects all items with index *k* such | 
 |    that *i* ``<=`` *k* ``<`` *j*.  When used as an expression, a slice is a | 
 |    sequence of the same type.  This implies that the index set is renumbered so | 
 |    that it starts at 0. | 
 |  | 
 |    .. index:: single: extended slicing | 
 |  | 
 |    Some sequences also support "extended slicing" with a third "step" parameter: | 
 |    ``a[i:j:k]`` selects all items of *a* with index *x* where ``x = i + n*k``, *n* | 
 |    ``>=`` ``0`` and *i* ``<=`` *x* ``<`` *j*. | 
 |  | 
 |    Sequences are distinguished according to their mutability: | 
 |  | 
 |    Immutable sequences | 
 |       .. index:: | 
 |          object: immutable sequence | 
 |          object: immutable | 
 |  | 
 |       An object of an immutable sequence type cannot change once it is created.  (If | 
 |       the object contains references to other objects, these other objects may be | 
 |       mutable and may be changed; however, the collection of objects directly | 
 |       referenced by an immutable object cannot change.) | 
 |  | 
 |       The following types are immutable sequences: | 
 |  | 
 |       Strings | 
 |          .. index:: | 
 |             builtin: chr | 
 |             builtin: ord | 
 |             object: string | 
 |             single: character | 
 |             single: byte | 
 |             single: ASCII@ASCII | 
 |  | 
 |          The items of a string are characters.  There is no separate character type; a | 
 |          character is represented by a string of one item. Characters represent (at | 
 |          least) 8-bit bytes.  The built-in functions :func:`chr` and :func:`ord` convert | 
 |          between characters and nonnegative integers representing the byte values.  Bytes | 
 |          with the values 0-127 usually represent the corresponding ASCII values, but the | 
 |          interpretation of values is up to the program.  The string data type is also | 
 |          used to represent arrays of bytes, e.g., to hold data read from a file. | 
 |  | 
 |          .. index:: | 
 |             single: ASCII@ASCII | 
 |             single: EBCDIC | 
 |             single: character set | 
 |             pair: string; comparison | 
 |             builtin: chr | 
 |             builtin: ord | 
 |  | 
 |          (On systems whose native character set is not ASCII, strings may use EBCDIC in | 
 |          their internal representation, provided the functions :func:`chr` and | 
 |          :func:`ord` implement a mapping between ASCII and EBCDIC, and string comparison | 
 |          preserves the ASCII order. Or perhaps someone can propose a better rule?) | 
 |  | 
 |       Unicode | 
 |          .. index:: | 
 |             builtin: unichr | 
 |             builtin: ord | 
 |             builtin: unicode | 
 |             object: unicode | 
 |             single: character | 
 |             single: integer | 
 |             single: Unicode | 
 |  | 
 |          The items of a Unicode object are Unicode code units.  A Unicode code unit is | 
 |          represented by a Unicode object of one item and can hold either a 16-bit or | 
 |          32-bit value representing a Unicode ordinal (the maximum value for the ordinal | 
 |          is given in ``sys.maxunicode``, and depends on how Python is configured at | 
 |          compile time).  Surrogate pairs may be present in the Unicode object, and will | 
 |          be reported as two separate items.  The built-in functions :func:`unichr` and | 
 |          :func:`ord` convert between code units and nonnegative integers representing the | 
 |          Unicode ordinals as defined in the Unicode Standard 3.0. Conversion from and to | 
 |          other encodings are possible through the Unicode method :meth:`encode` and the | 
 |          built-in function :func:`unicode`. | 
 |  | 
 |       Tuples | 
 |          .. index:: | 
 |             object: tuple | 
 |             pair: singleton; tuple | 
 |             pair: empty; tuple | 
 |  | 
 |          The items of a tuple are arbitrary Python objects. Tuples of two or more items | 
 |          are formed by comma-separated lists of expressions.  A tuple of one item (a | 
 |          'singleton') can be formed by affixing a comma to an expression (an expression | 
 |          by itself does not create a tuple, since parentheses must be usable for grouping | 
 |          of expressions).  An empty tuple can be formed by an empty pair of parentheses. | 
 |  | 
 |    Mutable sequences | 
 |       .. index:: | 
 |          object: mutable sequence | 
 |          object: mutable | 
 |          pair: assignment; statement | 
 |          single: subscription | 
 |          single: slicing | 
 |  | 
 |       Mutable sequences can be changed after they are created.  The subscription and | 
 |       slicing notations can be used as the target of assignment and :keyword:`del` | 
 |       (delete) statements. | 
 |  | 
 |       There are currently two intrinsic mutable sequence types: | 
 |  | 
 |       Lists | 
 |          .. index:: object: list | 
 |  | 
 |          The items of a list are arbitrary Python objects.  Lists are formed by placing a | 
 |          comma-separated list of expressions in square brackets. (Note that there are no | 
 |          special cases needed to form lists of length 0 or 1.) | 
 |  | 
 |       Byte Arrays | 
 |          .. index:: bytearray | 
 |  | 
 |          A bytearray object is a mutable array. They are created by the built-in | 
 |          :func:`bytearray` constructor.  Aside from being mutable (and hence | 
 |          unhashable), byte arrays otherwise provide the same interface and | 
 |          functionality as immutable bytes objects. | 
 |  | 
 |       .. index:: module: array | 
 |  | 
 |       The extension module :mod:`array` provides an additional example of a mutable | 
 |       sequence type. | 
 |  | 
 | Set types | 
 |    .. index:: | 
 |       builtin: len | 
 |       object: set type | 
 |  | 
 |    These represent unordered, finite sets of unique, immutable objects. As such, | 
 |    they cannot be indexed by any subscript. However, they can be iterated over, and | 
 |    the built-in function :func:`len` returns the number of items in a set. Common | 
 |    uses for sets are fast membership testing, removing duplicates from a sequence, | 
 |    and computing mathematical operations such as intersection, union, difference, | 
 |    and symmetric difference. | 
 |  | 
 |    For set elements, the same immutability rules apply as for dictionary keys. Note | 
 |    that numeric types obey the normal rules for numeric comparison: if two numbers | 
 |    compare equal (e.g., ``1`` and ``1.0``), only one of them can be contained in a | 
 |    set. | 
 |  | 
 |    There are currently two intrinsic set types: | 
 |  | 
 |    Sets | 
 |       .. index:: object: set | 
 |  | 
 |       These represent a mutable set. They are created by the built-in :func:`set` | 
 |       constructor and can be modified afterwards by several methods, such as | 
 |       :meth:`~set.add`. | 
 |  | 
 |    Frozen sets | 
 |       .. index:: object: frozenset | 
 |  | 
 |       These represent an immutable set.  They are created by the built-in | 
 |       :func:`frozenset` constructor.  As a frozenset is immutable and | 
 |       :term:`hashable`, it can be used again as an element of another set, or as | 
 |       a dictionary key. | 
 |  | 
 | Mappings | 
 |    .. index:: | 
 |       builtin: len | 
 |       single: subscription | 
 |       object: mapping | 
 |  | 
 |    These represent finite sets of objects indexed by arbitrary index sets. The | 
 |    subscript notation ``a[k]`` selects the item indexed by ``k`` from the mapping | 
 |    ``a``; this can be used in expressions and as the target of assignments or | 
 |    :keyword:`del` statements. The built-in function :func:`len` returns the number | 
 |    of items in a mapping. | 
 |  | 
 |    There is currently a single intrinsic mapping type: | 
 |  | 
 |    Dictionaries | 
 |       .. index:: object: dictionary | 
 |  | 
 |       These represent finite sets of objects indexed by nearly arbitrary values.  The | 
 |       only types of values not acceptable as keys are values containing lists or | 
 |       dictionaries or other mutable types that are compared by value rather than by | 
 |       object identity, the reason being that the efficient implementation of | 
 |       dictionaries requires a key's hash value to remain constant. Numeric types used | 
 |       for keys obey the normal rules for numeric comparison: if two numbers compare | 
 |       equal (e.g., ``1`` and ``1.0``) then they can be used interchangeably to index | 
 |       the same dictionary entry. | 
 |  | 
 |       Dictionaries are mutable; they can be created by the ``{...}`` notation (see | 
 |       section :ref:`dict`). | 
 |  | 
 |       .. index:: | 
 |          module: dbm | 
 |          module: gdbm | 
 |          module: bsddb | 
 |  | 
 |       The extension modules :mod:`dbm`, :mod:`gdbm`, and :mod:`bsddb` provide | 
 |       additional examples of mapping types. | 
 |  | 
 | Callable types | 
 |    .. index:: | 
 |       object: callable | 
 |       pair: function; call | 
 |       single: invocation | 
 |       pair: function; argument | 
 |  | 
 |    These are the types to which the function call operation (see section | 
 |    :ref:`calls`) can be applied: | 
 |  | 
 |    User-defined functions | 
 |       .. index:: | 
 |          pair: user-defined; function | 
 |          object: function | 
 |          object: user-defined function | 
 |  | 
 |       A user-defined function object is created by a function definition (see | 
 |       section :ref:`function`).  It should be called with an argument list | 
 |       containing the same number of items as the function's formal parameter | 
 |       list. | 
 |  | 
 |       Special attributes: | 
 |  | 
 |       .. tabularcolumns:: |l|L|l| | 
 |  | 
 |       +-----------------------+-------------------------------+-----------+ | 
 |       | Attribute             | Meaning                       |           | | 
 |       +=======================+===============================+===========+ | 
 |       | :attr:`__doc__`       | The function's documentation  | Writable  | | 
 |       | :attr:`func_doc`      | string, or ``None`` if        |           | | 
 |       |                       | unavailable.                  |           | | 
 |       +-----------------------+-------------------------------+-----------+ | 
 |       | :attr:`__name__`      | The function's name.          | Writable  | | 
 |       | :attr:`func_name`     |                               |           | | 
 |       +-----------------------+-------------------------------+-----------+ | 
 |       | :attr:`__module__`    | The name of the module the    | Writable  | | 
 |       |                       | function was defined in, or   |           | | 
 |       |                       | ``None`` if unavailable.      |           | | 
 |       +-----------------------+-------------------------------+-----------+ | 
 |       | :attr:`__defaults__`  | A tuple containing default    | Writable  | | 
 |       | :attr:`func_defaults` | argument values for those     |           | | 
 |       |                       | arguments that have defaults, |           | | 
 |       |                       | or ``None`` if no arguments   |           | | 
 |       |                       | have a default value.         |           | | 
 |       +-----------------------+-------------------------------+-----------+ | 
 |       | :attr:`__code__`      | The code object representing  | Writable  | | 
 |       | :attr:`func_code`     | the compiled function body.   |           | | 
 |       +-----------------------+-------------------------------+-----------+ | 
 |       | :attr:`__globals__`   | A reference to the dictionary | Read-only | | 
 |       | :attr:`func_globals`  | that holds the function's     |           | | 
 |       |                       | global variables --- the      |           | | 
 |       |                       | global namespace of the       |           | | 
 |       |                       | module in which the function  |           | | 
 |       |                       | was defined.                  |           | | 
 |       +-----------------------+-------------------------------+-----------+ | 
 |       | :attr:`__dict__`      | The namespace supporting      | Writable  | | 
 |       | :attr:`func_dict`     | arbitrary function            |           | | 
 |       |                       | attributes.                   |           | | 
 |       +-----------------------+-------------------------------+-----------+ | 
 |       | :attr:`__closure__`   | ``None`` or a tuple of cells  | Read-only | | 
 |       | :attr:`func_closure`  | that contain bindings for the |           | | 
 |       |                       | function's free variables.    |           | | 
 |       +-----------------------+-------------------------------+-----------+ | 
 |  | 
 |       Most of the attributes labelled "Writable" check the type of the assigned value. | 
 |  | 
 |       .. versionchanged:: 2.4 | 
 |          ``func_name`` is now writable. | 
 |  | 
 |       .. versionchanged:: 2.6 | 
 |          The double-underscore attributes ``__closure__``, ``__code__``, | 
 |          ``__defaults__``, and ``__globals__`` were introduced as aliases for | 
 |          the corresponding ``func_*`` attributes for forwards compatibility | 
 |          with Python 3. | 
 |  | 
 |       Function objects also support getting and setting arbitrary attributes, which | 
 |       can be used, for example, to attach metadata to functions.  Regular attribute | 
 |       dot-notation is used to get and set such attributes. *Note that the current | 
 |       implementation only supports function attributes on user-defined functions. | 
 |       Function attributes on built-in functions may be supported in the future.* | 
 |  | 
 |       Additional information about a function's definition can be retrieved from its | 
 |       code object; see the description of internal types below. | 
 |  | 
 |       .. index:: | 
 |          single: __doc__ (function attribute) | 
 |          single: __name__ (function attribute) | 
 |          single: __module__ (function attribute) | 
 |          single: __dict__ (function attribute) | 
 |          single: __defaults__ (function attribute) | 
 |          single: __code__ (function attribute) | 
 |          single: __globals__ (function attribute) | 
 |          single: __closure__ (function attribute) | 
 |          single: func_doc (function attribute) | 
 |          single: func_name (function attribute) | 
 |          single: func_dict (function attribute) | 
 |          single: func_defaults (function attribute) | 
 |          single: func_code (function attribute) | 
 |          single: func_globals (function attribute) | 
 |          single: func_closure (function attribute) | 
 |          pair: global; namespace | 
 |  | 
 |    User-defined methods | 
 |       .. index:: | 
 |          object: method | 
 |          object: user-defined method | 
 |          pair: user-defined; method | 
 |  | 
 |       A user-defined method object combines a class, a class instance (or ``None``) | 
 |       and any callable object (normally a user-defined function). | 
 |  | 
 |       Special read-only attributes: :attr:`im_self` is the class instance object, | 
 |       :attr:`im_func` is the function object; :attr:`im_class` is the class of | 
 |       :attr:`im_self` for bound methods or the class that asked for the method for | 
 |       unbound methods; :attr:`__doc__` is the method's documentation (same as | 
 |       ``im_func.__doc__``); :attr:`__name__` is the method name (same as | 
 |       ``im_func.__name__``); :attr:`__module__` is the name of the module the method | 
 |       was defined in, or ``None`` if unavailable. | 
 |  | 
 |       .. versionchanged:: 2.2 | 
 |          :attr:`im_self` used to refer to the class that defined the method. | 
 |  | 
 |       .. versionchanged:: 2.6 | 
 |          For Python 3 forward-compatibility, :attr:`im_func` is also available as | 
 |          :attr:`__func__`, and :attr:`im_self` as :attr:`__self__`. | 
 |  | 
 |       .. index:: | 
 |          single: __doc__ (method attribute) | 
 |          single: __name__ (method attribute) | 
 |          single: __module__ (method attribute) | 
 |          single: im_func (method attribute) | 
 |          single: im_self (method attribute) | 
 |  | 
 |       Methods also support accessing (but not setting) the arbitrary function | 
 |       attributes on the underlying function object. | 
 |  | 
 |       User-defined method objects may be created when getting an attribute of a class | 
 |       (perhaps via an instance of that class), if that attribute is a user-defined | 
 |       function object, an unbound user-defined method object, or a class method | 
 |       object. When the attribute is a user-defined method object, a new method object | 
 |       is only created if the class from which it is being retrieved is the same as, or | 
 |       a derived class of, the class stored in the original method object; otherwise, | 
 |       the original method object is used as it is. | 
 |  | 
 |       .. index:: | 
 |          single: im_class (method attribute) | 
 |          single: im_func (method attribute) | 
 |          single: im_self (method attribute) | 
 |  | 
 |       When a user-defined method object is created by retrieving a user-defined | 
 |       function object from a class, its :attr:`im_self` attribute is ``None`` | 
 |       and the method object is said to be unbound. When one is created by | 
 |       retrieving a user-defined function object from a class via one of its | 
 |       instances, its :attr:`im_self` attribute is the instance, and the method | 
 |       object is said to be bound. In either case, the new method's | 
 |       :attr:`im_class` attribute is the class from which the retrieval takes | 
 |       place, and its :attr:`im_func` attribute is the original function object. | 
 |  | 
 |       .. index:: single: im_func (method attribute) | 
 |  | 
 |       When a user-defined method object is created by retrieving another method object | 
 |       from a class or instance, the behaviour is the same as for a function object, | 
 |       except that the :attr:`im_func` attribute of the new instance is not the | 
 |       original method object but its :attr:`im_func` attribute. | 
 |  | 
 |       .. index:: | 
 |          single: im_class (method attribute) | 
 |          single: im_func (method attribute) | 
 |          single: im_self (method attribute) | 
 |  | 
 |       When a user-defined method object is created by retrieving a class method object | 
 |       from a class or instance, its :attr:`im_self` attribute is the class itself, and | 
 |       its :attr:`im_func` attribute is the function object underlying the class method. | 
 |  | 
 |       When an unbound user-defined method object is called, the underlying function | 
 |       (:attr:`im_func`) is called, with the restriction that the first argument must | 
 |       be an instance of the proper class (:attr:`im_class`) or of a derived class | 
 |       thereof. | 
 |  | 
 |       When a bound user-defined method object is called, the underlying function | 
 |       (:attr:`im_func`) is called, inserting the class instance (:attr:`im_self`) in | 
 |       front of the argument list.  For instance, when :class:`C` is a class which | 
 |       contains a definition for a function :meth:`f`, and ``x`` is an instance of | 
 |       :class:`C`, calling ``x.f(1)`` is equivalent to calling ``C.f(x, 1)``. | 
 |  | 
 |       When a user-defined method object is derived from a class method object, the | 
 |       "class instance" stored in :attr:`im_self` will actually be the class itself, so | 
 |       that calling either ``x.f(1)`` or ``C.f(1)`` is equivalent to calling ``f(C,1)`` | 
 |       where ``f`` is the underlying function. | 
 |  | 
 |       Note that the transformation from function object to (unbound or bound) method | 
 |       object happens each time the attribute is retrieved from the class or instance. | 
 |       In some cases, a fruitful optimization is to assign the attribute to a local | 
 |       variable and call that local variable. Also notice that this transformation only | 
 |       happens for user-defined functions; other callable objects (and all non-callable | 
 |       objects) are retrieved without transformation.  It is also important to note | 
 |       that user-defined functions which are attributes of a class instance are not | 
 |       converted to bound methods; this *only* happens when the function is an | 
 |       attribute of the class. | 
 |  | 
 |    Generator functions | 
 |       .. index:: | 
 |          single: generator; function | 
 |          single: generator; iterator | 
 |  | 
 |       A function or method which uses the :keyword:`yield` statement (see section | 
 |       :ref:`yield`) is called a :dfn:`generator | 
 |       function`.  Such a function, when called, always returns an iterator object | 
 |       which can be used to execute the body of the function:  calling the iterator's | 
 |       :meth:`~iterator.next` method will cause the function to execute until | 
 |       it provides a value | 
 |       using the :keyword:`yield` statement.  When the function executes a | 
 |       :keyword:`return` statement or falls off the end, a :exc:`StopIteration` | 
 |       exception is raised and the iterator will have reached the end of the set of | 
 |       values to be returned. | 
 |  | 
 |    Built-in functions | 
 |       .. index:: | 
 |          object: built-in function | 
 |          object: function | 
 |          pair: C; language | 
 |  | 
 |       A built-in function object is a wrapper around a C function.  Examples of | 
 |       built-in functions are :func:`len` and :func:`math.sin` (:mod:`math` is a | 
 |       standard built-in module). The number and type of the arguments are | 
 |       determined by the C function. Special read-only attributes: | 
 |       :attr:`__doc__` is the function's documentation string, or ``None`` if | 
 |       unavailable; :attr:`__name__` is the function's name; :attr:`__self__` is | 
 |       set to ``None`` (but see the next item); :attr:`__module__` is the name of | 
 |       the module the function was defined in or ``None`` if unavailable. | 
 |  | 
 |    Built-in methods | 
 |       .. index:: | 
 |          object: built-in method | 
 |          object: method | 
 |          pair: built-in; method | 
 |  | 
 |       This is really a different disguise of a built-in function, this time containing | 
 |       an object passed to the C function as an implicit extra argument.  An example of | 
 |       a built-in method is ``alist.append()``, assuming *alist* is a list object. In | 
 |       this case, the special read-only attribute :attr:`__self__` is set to the object | 
 |       denoted by *alist*. | 
 |  | 
 |    Class Types | 
 |       Class types, or "new-style classes," are callable.  These objects normally act | 
 |       as factories for new instances of themselves, but variations are possible for | 
 |       class types that override :meth:`__new__`.  The arguments of the call are passed | 
 |       to :meth:`__new__` and, in the typical case, to :meth:`__init__` to initialize | 
 |       the new instance. | 
 |  | 
 |    Classic Classes | 
 |       .. index:: | 
 |          single: __init__() (object method) | 
 |          object: class | 
 |          object: class instance | 
 |          object: instance | 
 |          pair: class object; call | 
 |  | 
 |       Class objects are described below.  When a class object is called, a new class | 
 |       instance (also described below) is created and returned.  This implies a call to | 
 |       the class's :meth:`__init__` method if it has one.  Any arguments are passed on | 
 |       to the :meth:`__init__` method.  If there is no :meth:`__init__` method, the | 
 |       class must be called without arguments. | 
 |  | 
 |    Class instances | 
 |       Class instances are described below.  Class instances are callable only when the | 
 |       class has a :meth:`__call__` method; ``x(arguments)`` is a shorthand for | 
 |       ``x.__call__(arguments)``. | 
 |  | 
 | Modules | 
 |    .. index:: | 
 |       statement: import | 
 |       object: module | 
 |  | 
 |    Modules are imported by the :keyword:`import` statement (see section | 
 |    :ref:`import`). A module object has a | 
 |    namespace implemented by a dictionary object (this is the dictionary referenced | 
 |    by the func_globals attribute of functions defined in the module).  Attribute | 
 |    references are translated to lookups in this dictionary, e.g., ``m.x`` is | 
 |    equivalent to ``m.__dict__["x"]``. A module object does not contain the code | 
 |    object used to initialize the module (since it isn't needed once the | 
 |    initialization is done). | 
 |  | 
 |    Attribute assignment updates the module's namespace dictionary, e.g., ``m.x = | 
 |    1`` is equivalent to ``m.__dict__["x"] = 1``. | 
 |  | 
 |    .. index:: single: __dict__ (module attribute) | 
 |  | 
 |    Special read-only attribute: :attr:`__dict__` is the module's namespace as a | 
 |    dictionary object. | 
 |  | 
 |    .. impl-detail:: | 
 |  | 
 |       Because of the way CPython clears module dictionaries, the module | 
 |       dictionary will be cleared when the module falls out of scope even if the | 
 |       dictionary still has live references.  To avoid this, copy the dictionary | 
 |       or keep the module around while using its dictionary directly. | 
 |  | 
 |    .. index:: | 
 |       single: __name__ (module attribute) | 
 |       single: __doc__ (module attribute) | 
 |       single: __file__ (module attribute) | 
 |       pair: module; namespace | 
 |  | 
 |    Predefined (writable) attributes: :attr:`__name__` is the module's name; | 
 |    :attr:`__doc__` is the module's documentation string, or ``None`` if | 
 |    unavailable; :attr:`__file__` is the pathname of the file from which the module | 
 |    was loaded, if it was loaded from a file. The :attr:`__file__` attribute is not | 
 |    present for C modules that are statically linked into the interpreter; for | 
 |    extension modules loaded dynamically from a shared library, it is the pathname | 
 |    of the shared library file. | 
 |  | 
 | Classes | 
 |    Both class types (new-style classes) and class objects (old-style/classic | 
 |    classes) are typically created by class definitions (see section | 
 |    :ref:`class`).  A class has a namespace implemented by a dictionary object. | 
 |    Class attribute references are translated to lookups in this dictionary, e.g., | 
 |    ``C.x`` is translated to ``C.__dict__["x"]`` (although for new-style classes | 
 |    in particular there are a number of hooks which allow for other means of | 
 |    locating attributes). When the attribute name is not found there, the | 
 |    attribute search continues in the base classes.  For old-style classes, the | 
 |    search is depth-first, left-to-right in the order of occurrence in the base | 
 |    class list. New-style classes use the more complex C3 method resolution | 
 |    order which behaves correctly even in the presence of 'diamond' | 
 |    inheritance structures where there are multiple inheritance paths | 
 |    leading back to a common ancestor. Additional details on the C3 MRO used by | 
 |    new-style classes can be found in the documentation accompanying the | 
 |    2.3 release at https://www.python.org/download/releases/2.3/mro/. | 
 |  | 
 |    .. XXX: Could we add that MRO doc as an appendix to the language ref? | 
 |  | 
 |    .. index:: | 
 |       object: class | 
 |       object: class instance | 
 |       object: instance | 
 |       pair: class object; call | 
 |       single: container | 
 |       object: dictionary | 
 |       pair: class; attribute | 
 |  | 
 |    When a class attribute reference (for class :class:`C`, say) would yield a | 
 |    user-defined function object or an unbound user-defined method object whose | 
 |    associated class is either :class:`C` or one of its base classes, it is | 
 |    transformed into an unbound user-defined method object whose :attr:`im_class` | 
 |    attribute is :class:`C`. When it would yield a class method object, it is | 
 |    transformed into a bound user-defined method object whose | 
 |    :attr:`im_self` attribute is :class:`C`.  When it would yield a | 
 |    static method object, it is transformed into the object wrapped by the static | 
 |    method object. See section :ref:`descriptors` for another way in which | 
 |    attributes retrieved from a class may differ from those actually contained in | 
 |    its :attr:`__dict__` (note that only new-style classes support descriptors). | 
 |  | 
 |    .. index:: triple: class; attribute; assignment | 
 |  | 
 |    Class attribute assignments update the class's dictionary, never the dictionary | 
 |    of a base class. | 
 |  | 
 |    .. index:: pair: class object; call | 
 |  | 
 |    A class object can be called (see above) to yield a class instance (see below). | 
 |  | 
 |    .. index:: | 
 |       single: __name__ (class attribute) | 
 |       single: __module__ (class attribute) | 
 |       single: __dict__ (class attribute) | 
 |       single: __bases__ (class attribute) | 
 |       single: __doc__ (class attribute) | 
 |  | 
 |    Special attributes: :attr:`__name__` is the class name; :attr:`__module__` is | 
 |    the module name in which the class was defined; :attr:`__dict__` is the | 
 |    dictionary containing the class's namespace; :attr:`~class.__bases__` is a | 
 |    tuple (possibly empty or a singleton) containing the base classes, in the | 
 |    order of their occurrence in the base class list; :attr:`__doc__` is the | 
 |    class's documentation string, or None if undefined. | 
 |  | 
 | Class instances | 
 |    .. index:: | 
 |       object: class instance | 
 |       object: instance | 
 |       pair: class; instance | 
 |       pair: class instance; attribute | 
 |  | 
 |    A class instance is created by calling a class object (see above). A class | 
 |    instance has a namespace implemented as a dictionary which is the first place in | 
 |    which attribute references are searched.  When an attribute is not found there, | 
 |    and the instance's class has an attribute by that name, the search continues | 
 |    with the class attributes.  If a class attribute is found that is a user-defined | 
 |    function object or an unbound user-defined method object whose associated class | 
 |    is the class (call it :class:`C`) of the instance for which the attribute | 
 |    reference was initiated or one of its bases, it is transformed into a bound | 
 |    user-defined method object whose :attr:`im_class` attribute is :class:`C` and | 
 |    whose :attr:`im_self` attribute is the instance. Static method and class method | 
 |    objects are also transformed, as if they had been retrieved from class | 
 |    :class:`C`; see above under "Classes". See section :ref:`descriptors` for | 
 |    another way in which attributes of a class retrieved via its instances may | 
 |    differ from the objects actually stored in the class's :attr:`__dict__`. If no | 
 |    class attribute is found, and the object's class has a :meth:`__getattr__` | 
 |    method, that is called to satisfy the lookup. | 
 |  | 
 |    .. index:: triple: class instance; attribute; assignment | 
 |  | 
 |    Attribute assignments and deletions update the instance's dictionary, never a | 
 |    class's dictionary.  If the class has a :meth:`__setattr__` or | 
 |    :meth:`__delattr__` method, this is called instead of updating the instance | 
 |    dictionary directly. | 
 |  | 
 |    .. index:: | 
 |       object: numeric | 
 |       object: sequence | 
 |       object: mapping | 
 |  | 
 |    Class instances can pretend to be numbers, sequences, or mappings if they have | 
 |    methods with certain special names.  See section :ref:`specialnames`. | 
 |  | 
 |    .. index:: | 
 |       single: __dict__ (instance attribute) | 
 |       single: __class__ (instance attribute) | 
 |  | 
 |    Special attributes: :attr:`~object.__dict__` is the attribute dictionary; | 
 |    :attr:`~instance.__class__` is the instance's class. | 
 |  | 
 | Files | 
 |    .. index:: | 
 |       object: file | 
 |       builtin: open | 
 |       single: popen() (in module os) | 
 |       single: makefile() (socket method) | 
 |       single: sys.stdin | 
 |       single: sys.stdout | 
 |       single: sys.stderr | 
 |       single: stdio | 
 |       single: stdin (in module sys) | 
 |       single: stdout (in module sys) | 
 |       single: stderr (in module sys) | 
 |  | 
 |    A file object represents an open file.  File objects are created by the | 
 |    :func:`open` built-in function, and also by :func:`os.popen`, | 
 |    :func:`os.fdopen`, and the :meth:`makefile` method of socket objects (and | 
 |    perhaps by other functions or methods provided by extension modules).  The | 
 |    objects ``sys.stdin``, ``sys.stdout`` and ``sys.stderr`` are initialized to | 
 |    file objects corresponding to the interpreter's standard input, output and | 
 |    error streams.  See :ref:`bltin-file-objects` for complete documentation of | 
 |    file objects. | 
 |  | 
 | Internal types | 
 |    .. index:: | 
 |       single: internal type | 
 |       single: types, internal | 
 |  | 
 |    A few types used internally by the interpreter are exposed to the user. Their | 
 |    definitions may change with future versions of the interpreter, but they are | 
 |    mentioned here for completeness. | 
 |  | 
 |    Code objects | 
 |       .. index:: | 
 |          single: bytecode | 
 |          object: code | 
 |  | 
 |       Code objects represent *byte-compiled* executable Python code, or :term:`bytecode`. | 
 |       The difference between a code object and a function object is that the function | 
 |       object contains an explicit reference to the function's globals (the module in | 
 |       which it was defined), while a code object contains no context; also the default | 
 |       argument values are stored in the function object, not in the code object | 
 |       (because they represent values calculated at run-time).  Unlike function | 
 |       objects, code objects are immutable and contain no references (directly or | 
 |       indirectly) to mutable objects. | 
 |  | 
 |       .. index:: | 
 |          single: co_argcount (code object attribute) | 
 |          single: co_code (code object attribute) | 
 |          single: co_consts (code object attribute) | 
 |          single: co_filename (code object attribute) | 
 |          single: co_firstlineno (code object attribute) | 
 |          single: co_flags (code object attribute) | 
 |          single: co_lnotab (code object attribute) | 
 |          single: co_name (code object attribute) | 
 |          single: co_names (code object attribute) | 
 |          single: co_nlocals (code object attribute) | 
 |          single: co_stacksize (code object attribute) | 
 |          single: co_varnames (code object attribute) | 
 |          single: co_cellvars (code object attribute) | 
 |          single: co_freevars (code object attribute) | 
 |  | 
 |       Special read-only attributes: :attr:`co_name` gives the function name; | 
 |       :attr:`co_argcount` is the number of positional arguments (including arguments | 
 |       with default values); :attr:`co_nlocals` is the number of local variables used | 
 |       by the function (including arguments); :attr:`co_varnames` is a tuple containing | 
 |       the names of the local variables (starting with the argument names); | 
 |       :attr:`co_cellvars` is a tuple containing the names of local variables that are | 
 |       referenced by nested functions; :attr:`co_freevars` is a tuple containing the | 
 |       names of free variables; :attr:`co_code` is a string representing the sequence | 
 |       of bytecode instructions; :attr:`co_consts` is a tuple containing the literals | 
 |       used by the bytecode; :attr:`co_names` is a tuple containing the names used by | 
 |       the bytecode; :attr:`co_filename` is the filename from which the code was | 
 |       compiled; :attr:`co_firstlineno` is the first line number of the function; | 
 |       :attr:`co_lnotab` is a string encoding the mapping from bytecode offsets to | 
 |       line numbers (for details see the source code of the interpreter); | 
 |       :attr:`co_stacksize` is the required stack size (including local variables); | 
 |       :attr:`co_flags` is an integer encoding a number of flags for the interpreter. | 
 |  | 
 |       .. index:: object: generator | 
 |  | 
 |       The following flag bits are defined for :attr:`co_flags`: bit ``0x04`` is set if | 
 |       the function uses the ``*arguments`` syntax to accept an arbitrary number of | 
 |       positional arguments; bit ``0x08`` is set if the function uses the | 
 |       ``**keywords`` syntax to accept arbitrary keyword arguments; bit ``0x20`` is set | 
 |       if the function is a generator. | 
 |  | 
 |       Future feature declarations (``from __future__ import division``) also use bits | 
 |       in :attr:`co_flags` to indicate whether a code object was compiled with a | 
 |       particular feature enabled: bit ``0x2000`` is set if the function was compiled | 
 |       with future division enabled; bits ``0x10`` and ``0x1000`` were used in earlier | 
 |       versions of Python. | 
 |  | 
 |       Other bits in :attr:`co_flags` are reserved for internal use. | 
 |  | 
 |       .. index:: single: documentation string | 
 |  | 
 |       If a code object represents a function, the first item in :attr:`co_consts` is | 
 |       the documentation string of the function, or ``None`` if undefined. | 
 |  | 
 |    .. _frame-objects: | 
 |  | 
 |    Frame objects | 
 |       .. index:: object: frame | 
 |  | 
 |       Frame objects represent execution frames.  They may occur in traceback objects | 
 |       (see below). | 
 |  | 
 |       .. index:: | 
 |          single: f_back (frame attribute) | 
 |          single: f_code (frame attribute) | 
 |          single: f_globals (frame attribute) | 
 |          single: f_locals (frame attribute) | 
 |          single: f_lasti (frame attribute) | 
 |          single: f_builtins (frame attribute) | 
 |          single: f_restricted (frame attribute) | 
 |  | 
 |       Special read-only attributes: :attr:`f_back` is to the previous stack frame | 
 |       (towards the caller), or ``None`` if this is the bottom stack frame; | 
 |       :attr:`f_code` is the code object being executed in this frame; :attr:`f_locals` | 
 |       is the dictionary used to look up local variables; :attr:`f_globals` is used for | 
 |       global variables; :attr:`f_builtins` is used for built-in (intrinsic) names; | 
 |       :attr:`f_restricted` is a flag indicating whether the function is executing in | 
 |       restricted execution mode; :attr:`f_lasti` gives the precise instruction (this | 
 |       is an index into the bytecode string of the code object). | 
 |  | 
 |       .. index:: | 
 |          single: f_trace (frame attribute) | 
 |          single: f_exc_type (frame attribute) | 
 |          single: f_exc_value (frame attribute) | 
 |          single: f_exc_traceback (frame attribute) | 
 |          single: f_lineno (frame attribute) | 
 |  | 
 |       Special writable attributes: :attr:`f_trace`, if not ``None``, is a function | 
 |       called at the start of each source code line (this is used by the debugger); | 
 |       :attr:`f_exc_type`, :attr:`f_exc_value`, :attr:`f_exc_traceback` represent the | 
 |       last exception raised in the parent frame provided another exception was ever | 
 |       raised in the current frame (in all other cases they are None); :attr:`f_lineno` | 
 |       is the current line number of the frame --- writing to this from within a trace | 
 |       function jumps to the given line (only for the bottom-most frame).  A debugger | 
 |       can implement a Jump command (aka Set Next Statement) by writing to f_lineno. | 
 |  | 
 |    Traceback objects | 
 |       .. index:: | 
 |          object: traceback | 
 |          pair: stack; trace | 
 |          pair: exception; handler | 
 |          pair: execution; stack | 
 |          single: exc_info (in module sys) | 
 |          single: exc_traceback (in module sys) | 
 |          single: last_traceback (in module sys) | 
 |          single: sys.exc_info | 
 |          single: sys.exc_traceback | 
 |          single: sys.last_traceback | 
 |  | 
 |       Traceback objects represent a stack trace of an exception.  A traceback object | 
 |       is created when an exception occurs.  When the search for an exception handler | 
 |       unwinds the execution stack, at each unwound level a traceback object is | 
 |       inserted in front of the current traceback.  When an exception handler is | 
 |       entered, the stack trace is made available to the program. (See section | 
 |       :ref:`try`.) It is accessible as ``sys.exc_traceback``, | 
 |       and also as the third item of the tuple returned by ``sys.exc_info()``.  The | 
 |       latter is the preferred interface, since it works correctly when the program is | 
 |       using multiple threads. When the program contains no suitable handler, the stack | 
 |       trace is written (nicely formatted) to the standard error stream; if the | 
 |       interpreter is interactive, it is also made available to the user as | 
 |       ``sys.last_traceback``. | 
 |  | 
 |       .. index:: | 
 |          single: tb_next (traceback attribute) | 
 |          single: tb_frame (traceback attribute) | 
 |          single: tb_lineno (traceback attribute) | 
 |          single: tb_lasti (traceback attribute) | 
 |          statement: try | 
 |  | 
 |       Special read-only attributes: :attr:`tb_next` is the next level in the stack | 
 |       trace (towards the frame where the exception occurred), or ``None`` if there is | 
 |       no next level; :attr:`tb_frame` points to the execution frame of the current | 
 |       level; :attr:`tb_lineno` gives the line number where the exception occurred; | 
 |       :attr:`tb_lasti` indicates the precise instruction.  The line number and last | 
 |       instruction in the traceback may differ from the line number of its frame object | 
 |       if the exception occurred in a :keyword:`try` statement with no matching except | 
 |       clause or with a finally clause. | 
 |  | 
 |    Slice objects | 
 |       .. index:: builtin: slice | 
 |  | 
 |       Slice objects are used to represent slices when *extended slice syntax* is used. | 
 |       This is a slice using two colons, or multiple slices or ellipses separated by | 
 |       commas, e.g., ``a[i:j:step]``, ``a[i:j, k:l]``, or ``a[..., i:j]``.  They are | 
 |       also created by the built-in :func:`slice` function. | 
 |  | 
 |       .. index:: | 
 |          single: start (slice object attribute) | 
 |          single: stop (slice object attribute) | 
 |          single: step (slice object attribute) | 
 |  | 
 |       Special read-only attributes: :attr:`~slice.start` is the lower bound; | 
 |       :attr:`~slice.stop` is the upper bound; :attr:`~slice.step` is the step | 
 |       value; each is ``None`` if omitted.  These attributes can have any type. | 
 |  | 
 |       Slice objects support one method: | 
 |  | 
 |  | 
 |       .. method:: slice.indices(self, length) | 
 |  | 
 |          This method takes a single integer argument *length* and computes information | 
 |          about the extended slice that the slice object would describe if applied to a | 
 |          sequence of *length* items.  It returns a tuple of three integers; respectively | 
 |          these are the *start* and *stop* indices and the *step* or stride length of the | 
 |          slice. Missing or out-of-bounds indices are handled in a manner consistent with | 
 |          regular slices. | 
 |  | 
 |          .. versionadded:: 2.3 | 
 |  | 
 |    Static method objects | 
 |       Static method objects provide a way of defeating the transformation of function | 
 |       objects to method objects described above. A static method object is a wrapper | 
 |       around any other object, usually a user-defined method object. When a static | 
 |       method object is retrieved from a class or a class instance, the object actually | 
 |       returned is the wrapped object, which is not subject to any further | 
 |       transformation. Static method objects are not themselves callable, although the | 
 |       objects they wrap usually are. Static method objects are created by the built-in | 
 |       :func:`staticmethod` constructor. | 
 |  | 
 |    Class method objects | 
 |       A class method object, like a static method object, is a wrapper around another | 
 |       object that alters the way in which that object is retrieved from classes and | 
 |       class instances. The behaviour of class method objects upon such retrieval is | 
 |       described above, under "User-defined methods". Class method objects are created | 
 |       by the built-in :func:`classmethod` constructor. | 
 |  | 
 |  | 
 | .. _newstyle: | 
 |  | 
 | New-style and classic classes | 
 | ============================= | 
 |  | 
 | Classes and instances come in two flavors: old-style (or classic) and new-style. | 
 |  | 
 | Up to Python 2.1 the concept of ``class`` was unrelated to the concept of | 
 | ``type``, and old-style classes were the only flavor available.  For an | 
 | old-style class, the statement ``x.__class__`` provides the class of *x*, but | 
 | ``type(x)`` is always ``<type 'instance'>``.  This reflects the fact that all | 
 | old-style instances, independent of their class, are implemented with a single | 
 | built-in type, called ``instance``. | 
 |  | 
 | New-style classes were introduced in Python 2.2 to unify the concepts of | 
 | ``class`` and ``type``.  A new-style class is simply a user-defined type, | 
 | no more, no less.  If *x* is an instance of a new-style class, then ``type(x)`` | 
 | is typically the same as ``x.__class__`` (although this is not guaranteed -- a | 
 | new-style class instance is permitted to override the value returned for | 
 | ``x.__class__``). | 
 |  | 
 | The major motivation for introducing new-style classes is to provide a unified | 
 | object model with a full meta-model.  It also has a number of practical | 
 | benefits, like the ability to subclass most built-in types, or the introduction | 
 | of "descriptors", which enable computed properties. | 
 |  | 
 | For compatibility reasons, classes are still old-style by default.  New-style | 
 | classes are created by specifying another new-style class (i.e. a type) as a | 
 | parent class, or the "top-level type" :class:`object` if no other parent is | 
 | needed.  The behaviour of new-style classes differs from that of old-style | 
 | classes in a number of important details in addition to what :func:`type` | 
 | returns.  Some of these changes are fundamental to the new object model, like | 
 | the way special methods are invoked.  Others are "fixes" that could not be | 
 | implemented before for compatibility concerns, like the method resolution order | 
 | in case of multiple inheritance. | 
 |  | 
 | While this manual aims to provide comprehensive coverage of Python's class | 
 | mechanics, it may still be lacking in some areas when it comes to its coverage | 
 | of new-style classes. Please see https://www.python.org/doc/newstyle/ for | 
 | sources of additional information. | 
 |  | 
 | .. index:: | 
 |    single: class; new-style | 
 |    single: class; classic | 
 |    single: class; old-style | 
 |  | 
 | Old-style classes are removed in Python 3, leaving only new-style classes. | 
 |  | 
 |  | 
 | .. _specialnames: | 
 |  | 
 | Special method names | 
 | ==================== | 
 |  | 
 | .. index:: | 
 |    pair: operator; overloading | 
 |    single: __getitem__() (mapping object method) | 
 |  | 
 | A class can implement certain operations that are invoked by special syntax | 
 | (such as arithmetic operations or subscripting and slicing) by defining methods | 
 | with special names. This is Python's approach to :dfn:`operator overloading`, | 
 | allowing classes to define their own behavior with respect to language | 
 | operators.  For instance, if a class defines a method named :meth:`__getitem__`, | 
 | and ``x`` is an instance of this class, then ``x[i]`` is roughly equivalent | 
 | to ``x.__getitem__(i)`` for old-style classes and ``type(x).__getitem__(x, i)`` | 
 | for new-style classes.  Except where mentioned, attempts to execute an | 
 | operation raise an exception when no appropriate method is defined (typically | 
 | :exc:`AttributeError` or :exc:`TypeError`). | 
 |  | 
 | When implementing a class that emulates any built-in type, it is important that | 
 | the emulation only be implemented to the degree that it makes sense for the | 
 | object being modelled.  For example, some sequences may work well with retrieval | 
 | of individual elements, but extracting a slice may not make sense.  (One example | 
 | of this is the :class:`~xml.dom.NodeList` interface in the W3C's Document | 
 | Object Model.) | 
 |  | 
 |  | 
 | .. _customization: | 
 |  | 
 | Basic customization | 
 | ------------------- | 
 |  | 
 | .. method:: object.__new__(cls[, ...]) | 
 |  | 
 |    .. index:: pair: subclassing; immutable types | 
 |  | 
 |    Called to create a new instance of class *cls*.  :meth:`__new__` is a static | 
 |    method (special-cased so you need not declare it as such) that takes the class | 
 |    of which an instance was requested as its first argument.  The remaining | 
 |    arguments are those passed to the object constructor expression (the call to the | 
 |    class).  The return value of :meth:`__new__` should be the new object instance | 
 |    (usually an instance of *cls*). | 
 |  | 
 |    Typical implementations create a new instance of the class by invoking the | 
 |    superclass's :meth:`__new__` method using ``super(currentclass, | 
 |    cls).__new__(cls[, ...])`` with appropriate arguments and then modifying the | 
 |    newly-created instance as necessary before returning it. | 
 |  | 
 |    If :meth:`__new__` returns an instance of *cls*, then the new instance's | 
 |    :meth:`__init__` method will be invoked like ``__init__(self[, ...])``, where | 
 |    *self* is the new instance and the remaining arguments are the same as were | 
 |    passed to :meth:`__new__`. | 
 |  | 
 |    If :meth:`__new__` does not return an instance of *cls*, then the new instance's | 
 |    :meth:`__init__` method will not be invoked. | 
 |  | 
 |    :meth:`__new__` is intended mainly to allow subclasses of immutable types (like | 
 |    int, str, or tuple) to customize instance creation.  It is also commonly | 
 |    overridden in custom metaclasses in order to customize class creation. | 
 |  | 
 |  | 
 | .. method:: object.__init__(self[, ...]) | 
 |  | 
 |    .. index:: pair: class; constructor | 
 |  | 
 |    Called after the instance has been created (by :meth:`__new__`), but before | 
 |    it is returned to the caller.  The arguments are those passed to the | 
 |    class constructor expression.  If a base class has an :meth:`__init__` method, | 
 |    the derived class's :meth:`__init__` method, if any, must explicitly call it to | 
 |    ensure proper initialization of the base class part of the instance; for | 
 |    example: ``BaseClass.__init__(self, [args...])``. | 
 |  | 
 |    Because :meth:`__new__` and :meth:`__init__` work together in constructing | 
 |    objects (:meth:`__new__` to create it, and :meth:`__init__` to customise it), | 
 |    no non-``None`` value may be returned by :meth:`__init__`; doing so will | 
 |    cause a :exc:`TypeError` to be raised at runtime. | 
 |  | 
 |  | 
 | .. method:: object.__del__(self) | 
 |  | 
 |    .. index:: | 
 |       single: destructor | 
 |       statement: del | 
 |  | 
 |    Called when the instance is about to be destroyed.  This is also called a | 
 |    destructor.  If a base class has a :meth:`__del__` method, the derived class's | 
 |    :meth:`__del__` method, if any, must explicitly call it to ensure proper | 
 |    deletion of the base class part of the instance.  Note that it is possible | 
 |    (though not recommended!) for the :meth:`__del__` method to postpone destruction | 
 |    of the instance by creating a new reference to it.  It may then be called at a | 
 |    later time when this new reference is deleted.  It is not guaranteed that | 
 |    :meth:`__del__` methods are called for objects that still exist when the | 
 |    interpreter exits. | 
 |  | 
 |    .. note:: | 
 |  | 
 |       ``del x`` doesn't directly call ``x.__del__()`` --- the former decrements | 
 |       the reference count for ``x`` by one, and the latter is only called when | 
 |       ``x``'s reference count reaches zero.  Some common situations that may | 
 |       prevent the reference count of an object from going to zero include: | 
 |       circular references between objects (e.g., a doubly-linked list or a tree | 
 |       data structure with parent and child pointers); a reference to the object | 
 |       on the stack frame of a function that caught an exception (the traceback | 
 |       stored in ``sys.exc_traceback`` keeps the stack frame alive); or a | 
 |       reference to the object on the stack frame that raised an unhandled | 
 |       exception in interactive mode (the traceback stored in | 
 |       ``sys.last_traceback`` keeps the stack frame alive).  The first situation | 
 |       can only be remedied by explicitly breaking the cycles; the latter two | 
 |       situations can be resolved by storing ``None`` in ``sys.exc_traceback`` or | 
 |       ``sys.last_traceback``.  Circular references which are garbage are | 
 |       detected when the option cycle detector is enabled (it's on by default), | 
 |       but can only be cleaned up if there are no Python-level :meth:`__del__` | 
 |       methods involved. Refer to the documentation for the :mod:`gc` module for | 
 |       more information about how :meth:`__del__` methods are handled by the | 
 |       cycle detector, particularly the description of the ``garbage`` value. | 
 |  | 
 |    .. warning:: | 
 |  | 
 |       Due to the precarious circumstances under which :meth:`__del__` methods are | 
 |       invoked, exceptions that occur during their execution are ignored, and a warning | 
 |       is printed to ``sys.stderr`` instead.  Also, when :meth:`__del__` is invoked in | 
 |       response to a module being deleted (e.g., when execution of the program is | 
 |       done), other globals referenced by the :meth:`__del__` method may already have | 
 |       been deleted or in the process of being torn down (e.g. the import | 
 |       machinery shutting down).  For this reason, :meth:`__del__` methods | 
 |       should do the absolute | 
 |       minimum needed to maintain external invariants.  Starting with version 1.5, | 
 |       Python guarantees that globals whose name begins with a single underscore are | 
 |       deleted from their module before other globals are deleted; if no other | 
 |       references to such globals exist, this may help in assuring that imported | 
 |       modules are still available at the time when the :meth:`__del__` method is | 
 |       called. | 
 |  | 
 |    See also the :option:`-R` command-line option. | 
 |  | 
 |  | 
 | .. method:: object.__repr__(self) | 
 |  | 
 |    .. index:: builtin: repr | 
 |  | 
 |    Called by the :func:`repr` built-in function and by string conversions (reverse | 
 |    quotes) to compute the "official" string representation of an object.  If at all | 
 |    possible, this should look like a valid Python expression that could be used to | 
 |    recreate an object with the same value (given an appropriate environment).  If | 
 |    this is not possible, a string of the form ``<...some useful description...>`` | 
 |    should be returned.  The return value must be a string object. If a class | 
 |    defines :meth:`__repr__` but not :meth:`__str__`, then :meth:`__repr__` is also | 
 |    used when an "informal" string representation of instances of that class is | 
 |    required. | 
 |  | 
 |    .. index:: | 
 |       pair: string; conversion | 
 |       pair: reverse; quotes | 
 |       pair: backward; quotes | 
 |       single: back-quotes | 
 |  | 
 |    This is typically used for debugging, so it is important that the representation | 
 |    is information-rich and unambiguous. | 
 |  | 
 |  | 
 | .. method:: object.__str__(self) | 
 |  | 
 |    .. index:: | 
 |       builtin: str | 
 |       statement: print | 
 |  | 
 |    Called by the :func:`str` built-in function and by the :keyword:`print` | 
 |    statement to compute the "informal" string representation of an object.  This | 
 |    differs from :meth:`__repr__` in that it does not have to be a valid Python | 
 |    expression: a more convenient or concise representation may be used instead. | 
 |    The return value must be a string object. | 
 |  | 
 |  | 
 | .. method:: object.__lt__(self, other) | 
 |             object.__le__(self, other) | 
 |             object.__eq__(self, other) | 
 |             object.__ne__(self, other) | 
 |             object.__gt__(self, other) | 
 |             object.__ge__(self, other) | 
 |  | 
 |    .. versionadded:: 2.1 | 
 |  | 
 |    .. index:: | 
 |       single: comparisons | 
 |  | 
 |    These are the so-called "rich comparison" methods, and are called for comparison | 
 |    operators in preference to :meth:`__cmp__` below. The correspondence between | 
 |    operator symbols and method names is as follows: ``x<y`` calls ``x.__lt__(y)``, | 
 |    ``x<=y`` calls ``x.__le__(y)``, ``x==y`` calls ``x.__eq__(y)``, ``x!=y`` and | 
 |    ``x<>y`` call ``x.__ne__(y)``, ``x>y`` calls ``x.__gt__(y)``, and ``x>=y`` calls | 
 |    ``x.__ge__(y)``. | 
 |  | 
 |    A rich comparison method may return the singleton ``NotImplemented`` if it does | 
 |    not implement the operation for a given pair of arguments. By convention, | 
 |    ``False`` and ``True`` are returned for a successful comparison. However, these | 
 |    methods can return any value, so if the comparison operator is used in a Boolean | 
 |    context (e.g., in the condition of an ``if`` statement), Python will call | 
 |    :func:`bool` on the value to determine if the result is true or false. | 
 |  | 
 |    There are no implied relationships among the comparison operators. The truth | 
 |    of ``x==y`` does not imply that ``x!=y`` is false.  Accordingly, when | 
 |    defining :meth:`__eq__`, one should also define :meth:`__ne__` so that the | 
 |    operators will behave as expected.  See the paragraph on :meth:`__hash__` for | 
 |    some important notes on creating :term:`hashable` objects which support | 
 |    custom comparison operations and are usable as dictionary keys. | 
 |  | 
 |    There are no swapped-argument versions of these methods (to be used when the | 
 |    left argument does not support the operation but the right argument does); | 
 |    rather, :meth:`__lt__` and :meth:`__gt__` are each other's reflection, | 
 |    :meth:`__le__` and :meth:`__ge__` are each other's reflection, and | 
 |    :meth:`__eq__` and :meth:`__ne__` are their own reflection. | 
 |  | 
 |    Arguments to rich comparison methods are never coerced. | 
 |  | 
 |    To automatically generate ordering operations from a single root operation, | 
 |    see :func:`functools.total_ordering`. | 
 |  | 
 | .. method:: object.__cmp__(self, other) | 
 |  | 
 |    .. index:: | 
 |       builtin: cmp | 
 |       single: comparisons | 
 |  | 
 |    Called by comparison operations if rich comparison (see above) is not | 
 |    defined.  Should return a negative integer if ``self < other``, zero if | 
 |    ``self == other``, a positive integer if ``self > other``.  If no | 
 |    :meth:`__cmp__`, :meth:`__eq__` or :meth:`__ne__` operation is defined, class | 
 |    instances are compared by object identity ("address").  See also the | 
 |    description of :meth:`__hash__` for some important notes on creating | 
 |    :term:`hashable` objects which support custom comparison operations and are | 
 |    usable as dictionary keys. (Note: the restriction that exceptions are not | 
 |    propagated by :meth:`__cmp__` has been removed since Python 1.5.) | 
 |  | 
 |  | 
 | .. method:: object.__rcmp__(self, other) | 
 |  | 
 |    .. versionchanged:: 2.1 | 
 |       No longer supported. | 
 |  | 
 |  | 
 | .. method:: object.__hash__(self) | 
 |  | 
 |    .. index:: | 
 |       object: dictionary | 
 |       builtin: hash | 
 |  | 
 |    Called by built-in function :func:`hash` and for operations on members of | 
 |    hashed collections including :class:`set`, :class:`frozenset`, and | 
 |    :class:`dict`.  :meth:`__hash__` should return an integer.  The only required | 
 |    property is that objects which compare equal have the same hash value; it is | 
 |    advised to somehow mix together (e.g. using exclusive or) the hash values for | 
 |    the components of the object that also play a part in comparison of objects. | 
 |  | 
 |    If a class does not define a :meth:`__cmp__` or :meth:`__eq__` method it | 
 |    should not define a :meth:`__hash__` operation either; if it defines | 
 |    :meth:`__cmp__` or :meth:`__eq__` but not :meth:`__hash__`, its instances | 
 |    will not be usable in hashed collections.  If a class defines mutable objects | 
 |    and implements a :meth:`__cmp__` or :meth:`__eq__` method, it should not | 
 |    implement :meth:`__hash__`, since hashable collection implementations require | 
 |    that a object's hash value is immutable (if the object's hash value changes, | 
 |    it will be in the wrong hash bucket). | 
 |  | 
 |    User-defined classes have :meth:`__cmp__` and :meth:`__hash__` methods | 
 |    by default; with them, all objects compare unequal (except with themselves) | 
 |    and ``x.__hash__()`` returns a result derived from ``id(x)``. | 
 |  | 
 |    Classes which inherit a :meth:`__hash__` method from a parent class but | 
 |    change the meaning of :meth:`__cmp__` or :meth:`__eq__` such that the hash | 
 |    value returned is no longer appropriate (e.g. by switching to a value-based | 
 |    concept of equality instead of the default identity based equality) can | 
 |    explicitly flag themselves as being unhashable by setting ``__hash__ = None`` | 
 |    in the class definition. Doing so means that not only will instances of the | 
 |    class raise an appropriate :exc:`TypeError` when a program attempts to | 
 |    retrieve their hash value, but they will also be correctly identified as | 
 |    unhashable when checking ``isinstance(obj, collections.Hashable)`` (unlike | 
 |    classes which define their own :meth:`__hash__` to explicitly raise | 
 |    :exc:`TypeError`). | 
 |  | 
 |    .. versionchanged:: 2.5 | 
 |       :meth:`__hash__` may now also return a long integer object; the 32-bit | 
 |       integer is then derived from the hash of that object. | 
 |  | 
 |    .. versionchanged:: 2.6 | 
 |       :attr:`__hash__` may now be set to :const:`None` to explicitly flag | 
 |       instances of a class as unhashable. | 
 |  | 
 |  | 
 | .. method:: object.__nonzero__(self) | 
 |  | 
 |    .. index:: single: __len__() (mapping object method) | 
 |  | 
 |    Called to implement truth value testing and the built-in operation ``bool()``; | 
 |    should return ``False`` or ``True``, or their integer equivalents ``0`` or | 
 |    ``1``.  When this method is not defined, :meth:`__len__` is called, if it is | 
 |    defined, and the object is considered true if its result is nonzero. | 
 |    If a class defines neither :meth:`__len__` nor :meth:`__nonzero__`, all its | 
 |    instances are considered true. | 
 |  | 
 |  | 
 | .. method:: object.__unicode__(self) | 
 |  | 
 |    .. index:: builtin: unicode | 
 |  | 
 |    Called to implement :func:`unicode` built-in; should return a Unicode object. | 
 |    When this method is not defined, string conversion is attempted, and the result | 
 |    of string conversion is converted to Unicode using the system default encoding. | 
 |  | 
 |  | 
 | .. _attribute-access: | 
 |  | 
 | Customizing attribute access | 
 | ---------------------------- | 
 |  | 
 | The following methods can be defined to customize the meaning of attribute | 
 | access (use of, assignment to, or deletion of ``x.name``) for class instances. | 
 |  | 
 |  | 
 | .. method:: object.__getattr__(self, name) | 
 |  | 
 |    Called when an attribute lookup has not found the attribute in the usual places | 
 |    (i.e. it is not an instance attribute nor is it found in the class tree for | 
 |    ``self``).  ``name`` is the attribute name. This method should return the | 
 |    (computed) attribute value or raise an :exc:`AttributeError` exception. | 
 |  | 
 |    .. index:: single: __setattr__() (object method) | 
 |  | 
 |    Note that if the attribute is found through the normal mechanism, | 
 |    :meth:`__getattr__` is not called.  (This is an intentional asymmetry between | 
 |    :meth:`__getattr__` and :meth:`__setattr__`.) This is done both for efficiency | 
 |    reasons and because otherwise :meth:`__getattr__` would have no way to access | 
 |    other attributes of the instance.  Note that at least for instance variables, | 
 |    you can fake total control by not inserting any values in the instance attribute | 
 |    dictionary (but instead inserting them in another object).  See the | 
 |    :meth:`__getattribute__` method below for a way to actually get total control in | 
 |    new-style classes. | 
 |  | 
 |  | 
 | .. method:: object.__setattr__(self, name, value) | 
 |  | 
 |    Called when an attribute assignment is attempted.  This is called instead of the | 
 |    normal mechanism (i.e. store the value in the instance dictionary).  *name* is | 
 |    the attribute name, *value* is the value to be assigned to it. | 
 |  | 
 |    .. index:: single: __dict__ (instance attribute) | 
 |  | 
 |    If :meth:`__setattr__` wants to assign to an instance attribute, it should not | 
 |    simply execute ``self.name = value`` --- this would cause a recursive call to | 
 |    itself.  Instead, it should insert the value in the dictionary of instance | 
 |    attributes, e.g., ``self.__dict__[name] = value``.  For new-style classes, | 
 |    rather than accessing the instance dictionary, it should call the base class | 
 |    method with the same name, for example, ``object.__setattr__(self, name, | 
 |    value)``. | 
 |  | 
 |  | 
 | .. method:: object.__delattr__(self, name) | 
 |  | 
 |    Like :meth:`__setattr__` but for attribute deletion instead of assignment.  This | 
 |    should only be implemented if ``del obj.name`` is meaningful for the object. | 
 |  | 
 |  | 
 | .. _new-style-attribute-access: | 
 |  | 
 | More attribute access for new-style classes | 
 | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ | 
 |  | 
 | The following methods only apply to new-style classes. | 
 |  | 
 |  | 
 | .. method:: object.__getattribute__(self, name) | 
 |  | 
 |    Called unconditionally to implement attribute accesses for instances of the | 
 |    class. If the class also defines :meth:`__getattr__`, the latter will not be | 
 |    called unless :meth:`__getattribute__` either calls it explicitly or raises an | 
 |    :exc:`AttributeError`. This method should return the (computed) attribute value | 
 |    or raise an :exc:`AttributeError` exception. In order to avoid infinite | 
 |    recursion in this method, its implementation should always call the base class | 
 |    method with the same name to access any attributes it needs, for example, | 
 |    ``object.__getattribute__(self, name)``. | 
 |  | 
 |    .. note:: | 
 |  | 
 |       This method may still be bypassed when looking up special methods as the | 
 |       result of implicit invocation via language syntax or built-in functions. | 
 |       See :ref:`new-style-special-lookup`. | 
 |  | 
 |  | 
 | .. _descriptors: | 
 |  | 
 | Implementing Descriptors | 
 | ^^^^^^^^^^^^^^^^^^^^^^^^ | 
 |  | 
 | The following methods only apply when an instance of the class containing the | 
 | method (a so-called *descriptor* class) appears in an *owner* class (the | 
 | descriptor must be in either the owner's class dictionary or in the class | 
 | dictionary for one of its parents).  In the examples below, "the attribute" | 
 | refers to the attribute whose name is the key of the property in the owner | 
 | class' :attr:`__dict__`. | 
 |  | 
 |  | 
 | .. method:: object.__get__(self, instance, owner) | 
 |  | 
 |    Called to get the attribute of the owner class (class attribute access) or of an | 
 |    instance of that class (instance attribute access). *owner* is always the owner | 
 |    class, while *instance* is the instance that the attribute was accessed through, | 
 |    or ``None`` when the attribute is accessed through the *owner*.  This method | 
 |    should return the (computed) attribute value or raise an :exc:`AttributeError` | 
 |    exception. | 
 |  | 
 |  | 
 | .. method:: object.__set__(self, instance, value) | 
 |  | 
 |    Called to set the attribute on an instance *instance* of the owner class to a | 
 |    new value, *value*. | 
 |  | 
 |  | 
 | .. method:: object.__delete__(self, instance) | 
 |  | 
 |    Called to delete the attribute on an instance *instance* of the owner class. | 
 |  | 
 |  | 
 | .. _descriptor-invocation: | 
 |  | 
 | Invoking Descriptors | 
 | ^^^^^^^^^^^^^^^^^^^^ | 
 |  | 
 | In general, a descriptor is an object attribute with "binding behavior", one | 
 | whose attribute access has been overridden by methods in the descriptor | 
 | protocol:  :meth:`__get__`, :meth:`__set__`, and :meth:`__delete__`. If any of | 
 | those methods are defined for an object, it is said to be a descriptor. | 
 |  | 
 | The default behavior for attribute access is to get, set, or delete the | 
 | attribute from an object's dictionary. For instance, ``a.x`` has a lookup chain | 
 | starting with ``a.__dict__['x']``, then ``type(a).__dict__['x']``, and | 
 | continuing through the base classes of ``type(a)`` excluding metaclasses. | 
 |  | 
 | However, if the looked-up value is an object defining one of the descriptor | 
 | methods, then Python may override the default behavior and invoke the descriptor | 
 | method instead.  Where this occurs in the precedence chain depends on which | 
 | descriptor methods were defined and how they were called.  Note that descriptors | 
 | are only invoked for new style objects or classes (ones that subclass | 
 | :class:`object()` or :class:`type()`). | 
 |  | 
 | The starting point for descriptor invocation is a binding, ``a.x``. How the | 
 | arguments are assembled depends on ``a``: | 
 |  | 
 | Direct Call | 
 |    The simplest and least common call is when user code directly invokes a | 
 |    descriptor method:    ``x.__get__(a)``. | 
 |  | 
 | Instance Binding | 
 |    If binding to a new-style object instance, ``a.x`` is transformed into the call: | 
 |    ``type(a).__dict__['x'].__get__(a, type(a))``. | 
 |  | 
 | Class Binding | 
 |    If binding to a new-style class, ``A.x`` is transformed into the call: | 
 |    ``A.__dict__['x'].__get__(None, A)``. | 
 |  | 
 | Super Binding | 
 |    If ``a`` is an instance of :class:`super`, then the binding ``super(B, | 
 |    obj).m()`` searches ``obj.__class__.__mro__`` for the base class ``A`` | 
 |    immediately preceding ``B`` and then invokes the descriptor with the call: | 
 |    ``A.__dict__['m'].__get__(obj, obj.__class__)``. | 
 |  | 
 | For instance bindings, the precedence of descriptor invocation depends on the | 
 | which descriptor methods are defined.  A descriptor can define any combination | 
 | of :meth:`__get__`, :meth:`__set__` and :meth:`__delete__`.  If it does not | 
 | define :meth:`__get__`, then accessing the attribute will return the descriptor | 
 | object itself unless there is a value in the object's instance dictionary.  If | 
 | the descriptor defines :meth:`__set__` and/or :meth:`__delete__`, it is a data | 
 | descriptor; if it defines neither, it is a non-data descriptor.  Normally, data | 
 | descriptors define both :meth:`__get__` and :meth:`__set__`, while non-data | 
 | descriptors have just the :meth:`__get__` method.  Data descriptors with | 
 | :meth:`__set__` and :meth:`__get__` defined always override a redefinition in an | 
 | instance dictionary.  In contrast, non-data descriptors can be overridden by | 
 | instances. | 
 |  | 
 | Python methods (including :func:`staticmethod` and :func:`classmethod`) are | 
 | implemented as non-data descriptors.  Accordingly, instances can redefine and | 
 | override methods.  This allows individual instances to acquire behaviors that | 
 | differ from other instances of the same class. | 
 |  | 
 | The :func:`property` function is implemented as a data descriptor. Accordingly, | 
 | instances cannot override the behavior of a property. | 
 |  | 
 |  | 
 | .. _slots: | 
 |  | 
 | __slots__ | 
 | ^^^^^^^^^ | 
 |  | 
 | By default, instances of both old and new-style classes have a dictionary for | 
 | attribute storage.  This wastes space for objects having very few instance | 
 | variables.  The space consumption can become acute when creating large numbers | 
 | of instances. | 
 |  | 
 | The default can be overridden by defining *__slots__* in a new-style class | 
 | definition.  The *__slots__* declaration takes a sequence of instance variables | 
 | and reserves just enough space in each instance to hold a value for each | 
 | variable.  Space is saved because *__dict__* is not created for each instance. | 
 |  | 
 |  | 
 | .. data:: __slots__ | 
 |  | 
 |    This class variable can be assigned a string, iterable, or sequence of strings | 
 |    with variable names used by instances.  If defined in a new-style class, | 
 |    *__slots__* reserves space for the declared variables and prevents the automatic | 
 |    creation of *__dict__* and *__weakref__* for each instance. | 
 |  | 
 |    .. versionadded:: 2.2 | 
 |  | 
 | Notes on using *__slots__* | 
 |  | 
 | * When inheriting from a class without *__slots__*, the *__dict__* attribute of | 
 |   that class will always be accessible, so a *__slots__* definition in the | 
 |   subclass is meaningless. | 
 |  | 
 | * Without a *__dict__* variable, instances cannot be assigned new variables not | 
 |   listed in the *__slots__* definition.  Attempts to assign to an unlisted | 
 |   variable name raises :exc:`AttributeError`. If dynamic assignment of new | 
 |   variables is desired, then add ``'__dict__'`` to the sequence of strings in the | 
 |   *__slots__* declaration. | 
 |  | 
 |   .. versionchanged:: 2.3 | 
 |      Previously, adding ``'__dict__'`` to the *__slots__* declaration would not | 
 |      enable the assignment of new attributes not specifically listed in the sequence | 
 |      of instance variable names. | 
 |  | 
 | * Without a *__weakref__* variable for each instance, classes defining | 
 |   *__slots__* do not support weak references to its instances. If weak reference | 
 |   support is needed, then add ``'__weakref__'`` to the sequence of strings in the | 
 |   *__slots__* declaration. | 
 |  | 
 |   .. versionchanged:: 2.3 | 
 |      Previously, adding ``'__weakref__'`` to the *__slots__* declaration would not | 
 |      enable support for weak references. | 
 |  | 
 | * *__slots__* are implemented at the class level by creating descriptors | 
 |   (:ref:`descriptors`) for each variable name.  As a result, class attributes | 
 |   cannot be used to set default values for instance variables defined by | 
 |   *__slots__*; otherwise, the class attribute would overwrite the descriptor | 
 |   assignment. | 
 |  | 
 | * The action of a *__slots__* declaration is limited to the class where it is | 
 |   defined.  As a result, subclasses will have a *__dict__* unless they also define | 
 |   *__slots__* (which must only contain names of any *additional* slots). | 
 |  | 
 | * If a class defines a slot also defined in a base class, the instance variable | 
 |   defined by the base class slot is inaccessible (except by retrieving its | 
 |   descriptor directly from the base class). This renders the meaning of the | 
 |   program undefined.  In the future, a check may be added to prevent this. | 
 |  | 
 | * Nonempty *__slots__* does not work for classes derived from "variable-length" | 
 |   built-in types such as :class:`long`, :class:`str` and :class:`tuple`. | 
 |  | 
 | * Any non-string iterable may be assigned to *__slots__*. Mappings may also be | 
 |   used; however, in the future, special meaning may be assigned to the values | 
 |   corresponding to each key. | 
 |  | 
 | * *__class__* assignment works only if both classes have the same *__slots__*. | 
 |  | 
 |   .. versionchanged:: 2.6 | 
 |      Previously, *__class__* assignment raised an error if either new or old class | 
 |      had *__slots__*. | 
 |  | 
 |  | 
 | .. _metaclasses: | 
 |  | 
 | Customizing class creation | 
 | -------------------------- | 
 |  | 
 | By default, new-style classes are constructed using :func:`type`. A class | 
 | definition is read into a separate namespace and the value of class name is | 
 | bound to the result of ``type(name, bases, dict)``. | 
 |  | 
 | When the class definition is read, if *__metaclass__* is defined then the | 
 | callable assigned to it will be called instead of :func:`type`. This allows | 
 | classes or functions to be written which monitor or alter the class creation | 
 | process: | 
 |  | 
 | * Modifying the class dictionary prior to the class being created. | 
 |  | 
 | * Returning an instance of another class -- essentially performing the role of a | 
 |   factory function. | 
 |  | 
 | These steps will have to be performed in the metaclass's :meth:`__new__` method | 
 | -- :meth:`type.__new__` can then be called from this method to create a class | 
 | with different properties.  This example adds a new element to the class | 
 | dictionary before creating the class:: | 
 |  | 
 |   class metacls(type): | 
 |       def __new__(mcs, name, bases, dict): | 
 |           dict['foo'] = 'metacls was here' | 
 |           return type.__new__(mcs, name, bases, dict) | 
 |  | 
 | You can of course also override other class methods (or add new methods); for | 
 | example defining a custom :meth:`__call__` method in the metaclass allows custom | 
 | behavior when the class is called, e.g. not always creating a new instance. | 
 |  | 
 |  | 
 | .. data:: __metaclass__ | 
 |  | 
 |    This variable can be any callable accepting arguments for ``name``, ``bases``, | 
 |    and ``dict``.  Upon class creation, the callable is used instead of the built-in | 
 |    :func:`type`. | 
 |  | 
 |    .. versionadded:: 2.2 | 
 |  | 
 | The appropriate metaclass is determined by the following precedence rules: | 
 |  | 
 | * If ``dict['__metaclass__']`` exists, it is used. | 
 |  | 
 | * Otherwise, if there is at least one base class, its metaclass is used (this | 
 |   looks for a *__class__* attribute first and if not found, uses its type). | 
 |  | 
 | * Otherwise, if a global variable named __metaclass__ exists, it is used. | 
 |  | 
 | * Otherwise, the old-style, classic metaclass (types.ClassType) is used. | 
 |  | 
 | The potential uses for metaclasses are boundless. Some ideas that have been | 
 | explored including logging, interface checking, automatic delegation, automatic | 
 | property creation, proxies, frameworks, and automatic resource | 
 | locking/synchronization. | 
 |  | 
 |  | 
 | Customizing instance and subclass checks | 
 | ---------------------------------------- | 
 |  | 
 | .. versionadded:: 2.6 | 
 |  | 
 | The following methods are used to override the default behavior of the | 
 | :func:`isinstance` and :func:`issubclass` built-in functions. | 
 |  | 
 | In particular, the metaclass :class:`abc.ABCMeta` implements these methods in | 
 | order to allow the addition of Abstract Base Classes (ABCs) as "virtual base | 
 | classes" to any class or type (including built-in types), including other | 
 | ABCs. | 
 |  | 
 | .. method:: class.__instancecheck__(self, instance) | 
 |  | 
 |    Return true if *instance* should be considered a (direct or indirect) | 
 |    instance of *class*. If defined, called to implement ``isinstance(instance, | 
 |    class)``. | 
 |  | 
 |  | 
 | .. method:: class.__subclasscheck__(self, subclass) | 
 |  | 
 |    Return true if *subclass* should be considered a (direct or indirect) | 
 |    subclass of *class*.  If defined, called to implement ``issubclass(subclass, | 
 |    class)``. | 
 |  | 
 |  | 
 | Note that these methods are looked up on the type (metaclass) of a class.  They | 
 | cannot be defined as class methods in the actual class.  This is consistent with | 
 | the lookup of special methods that are called on instances, only in this | 
 | case the instance is itself a class. | 
 |  | 
 | .. seealso:: | 
 |  | 
 |    :pep:`3119` - Introducing Abstract Base Classes | 
 |       Includes the specification for customizing :func:`isinstance` and | 
 |       :func:`issubclass` behavior through :meth:`~class.__instancecheck__` and | 
 |       :meth:`~class.__subclasscheck__`, with motivation for this functionality | 
 |       in the context of adding Abstract Base Classes (see the :mod:`abc` | 
 |       module) to the language. | 
 |  | 
 |  | 
 | .. _callable-types: | 
 |  | 
 | Emulating callable objects | 
 | -------------------------- | 
 |  | 
 |  | 
 | .. method:: object.__call__(self[, args...]) | 
 |  | 
 |    .. index:: pair: call; instance | 
 |  | 
 |    Called when the instance is "called" as a function; if this method is defined, | 
 |    ``x(arg1, arg2, ...)`` is a shorthand for ``x.__call__(arg1, arg2, ...)``. | 
 |  | 
 |  | 
 | .. _sequence-types: | 
 |  | 
 | Emulating container types | 
 | ------------------------- | 
 |  | 
 | The following methods can be defined to implement container objects.  Containers | 
 | usually are sequences (such as lists or tuples) or mappings (like dictionaries), | 
 | but can represent other containers as well.  The first set of methods is used | 
 | either to emulate a sequence or to emulate a mapping; the difference is that for | 
 | a sequence, the allowable keys should be the integers *k* for which ``0 <= k < | 
 | N`` where *N* is the length of the sequence, or slice objects, which define a | 
 | range of items. (For backwards compatibility, the method :meth:`__getslice__` | 
 | (see below) can also be defined to handle simple, but not extended slices.) It | 
 | is also recommended that mappings provide the methods :meth:`keys`, | 
 | :meth:`values`, :meth:`items`, :meth:`has_key`, :meth:`get`, :meth:`clear`, | 
 | :meth:`setdefault`, :meth:`iterkeys`, :meth:`itervalues`, :meth:`iteritems`, | 
 | :meth:`pop`, :meth:`popitem`, :meth:`!copy`, and :meth:`update` behaving similar | 
 | to those for Python's standard dictionary objects.  The :mod:`UserDict` module | 
 | provides a :class:`DictMixin` class to help create those methods from a base set | 
 | of :meth:`__getitem__`, :meth:`__setitem__`, :meth:`__delitem__`, and | 
 | :meth:`keys`. Mutable sequences should provide methods :meth:`append`, | 
 | :meth:`count`, :meth:`index`, :meth:`extend`, :meth:`insert`, :meth:`pop`, | 
 | :meth:`remove`, :meth:`reverse` and :meth:`sort`, like Python standard list | 
 | objects.  Finally, sequence types should implement addition (meaning | 
 | concatenation) and multiplication (meaning repetition) by defining the methods | 
 | :meth:`__add__`, :meth:`__radd__`, :meth:`__iadd__`, :meth:`__mul__`, | 
 | :meth:`__rmul__` and :meth:`__imul__` described below; they should not define | 
 | :meth:`__coerce__` or other numerical operators.  It is recommended that both | 
 | mappings and sequences implement the :meth:`__contains__` method to allow | 
 | efficient use of the ``in`` operator; for mappings, ``in`` should be equivalent | 
 | of :meth:`has_key`; for sequences, it should search through the values.  It is | 
 | further recommended that both mappings and sequences implement the | 
 | :meth:`__iter__` method to allow efficient iteration through the container; for | 
 | mappings, :meth:`__iter__` should be the same as :meth:`iterkeys`; for | 
 | sequences, it should iterate through the values. | 
 |  | 
 |  | 
 | .. method:: object.__len__(self) | 
 |  | 
 |    .. index:: | 
 |       builtin: len | 
 |       single: __nonzero__() (object method) | 
 |  | 
 |    Called to implement the built-in function :func:`len`.  Should return the length | 
 |    of the object, an integer ``>=`` 0.  Also, an object that doesn't define a | 
 |    :meth:`__nonzero__` method and whose :meth:`__len__` method returns zero is | 
 |    considered to be false in a Boolean context. | 
 |  | 
 |  | 
 | .. method:: object.__getitem__(self, key) | 
 |  | 
 |    .. index:: object: slice | 
 |  | 
 |    Called to implement evaluation of ``self[key]``. For sequence types, the | 
 |    accepted keys should be integers and slice objects.  Note that the special | 
 |    interpretation of negative indexes (if the class wishes to emulate a sequence | 
 |    type) is up to the :meth:`__getitem__` method. If *key* is of an inappropriate | 
 |    type, :exc:`TypeError` may be raised; if of a value outside the set of indexes | 
 |    for the sequence (after any special interpretation of negative values), | 
 |    :exc:`IndexError` should be raised. For mapping types, if *key* is missing (not | 
 |    in the container), :exc:`KeyError` should be raised. | 
 |  | 
 |    .. note:: | 
 |  | 
 |       :keyword:`for` loops expect that an :exc:`IndexError` will be raised for illegal | 
 |       indexes to allow proper detection of the end of the sequence. | 
 |  | 
 |  | 
 | .. method:: object.__missing__(self, key) | 
 |  | 
 |    Called by :class:`dict`\ .\ :meth:`__getitem__` to implement ``self[key]`` for dict subclasses | 
 |    when key is not in the dictionary. | 
 |  | 
 |  | 
 | .. method:: object.__setitem__(self, key, value) | 
 |  | 
 |    Called to implement assignment to ``self[key]``.  Same note as for | 
 |    :meth:`__getitem__`.  This should only be implemented for mappings if the | 
 |    objects support changes to the values for keys, or if new keys can be added, or | 
 |    for sequences if elements can be replaced.  The same exceptions should be raised | 
 |    for improper *key* values as for the :meth:`__getitem__` method. | 
 |  | 
 |  | 
 | .. method:: object.__delitem__(self, key) | 
 |  | 
 |    Called to implement deletion of ``self[key]``.  Same note as for | 
 |    :meth:`__getitem__`.  This should only be implemented for mappings if the | 
 |    objects support removal of keys, or for sequences if elements can be removed | 
 |    from the sequence.  The same exceptions should be raised for improper *key* | 
 |    values as for the :meth:`__getitem__` method. | 
 |  | 
 |  | 
 | .. method:: object.__iter__(self) | 
 |  | 
 |    This method is called when an iterator is required for a container. This method | 
 |    should return a new iterator object that can iterate over all the objects in the | 
 |    container.  For mappings, it should iterate over the keys of the container, and | 
 |    should also be made available as the method :meth:`iterkeys`. | 
 |  | 
 |    Iterator objects also need to implement this method; they are required to return | 
 |    themselves.  For more information on iterator objects, see :ref:`typeiter`. | 
 |  | 
 |  | 
 | .. method:: object.__reversed__(self) | 
 |  | 
 |    Called (if present) by the :func:`reversed` built-in to implement | 
 |    reverse iteration.  It should return a new iterator object that iterates | 
 |    over all the objects in the container in reverse order. | 
 |  | 
 |    If the :meth:`__reversed__` method is not provided, the :func:`reversed` | 
 |    built-in will fall back to using the sequence protocol (:meth:`__len__` and | 
 |    :meth:`__getitem__`).  Objects that support the sequence protocol should | 
 |    only provide :meth:`__reversed__` if they can provide an implementation | 
 |    that is more efficient than the one provided by :func:`reversed`. | 
 |  | 
 |    .. versionadded:: 2.6 | 
 |  | 
 |  | 
 | The membership test operators (:keyword:`in` and :keyword:`not in`) are normally | 
 | implemented as an iteration through a sequence.  However, container objects can | 
 | supply the following special method with a more efficient implementation, which | 
 | also does not require the object be a sequence. | 
 |  | 
 | .. method:: object.__contains__(self, item) | 
 |  | 
 |    Called to implement membership test operators.  Should return true if *item* | 
 |    is in *self*, false otherwise.  For mapping objects, this should consider the | 
 |    keys of the mapping rather than the values or the key-item pairs. | 
 |  | 
 |    For objects that don't define :meth:`__contains__`, the membership test first | 
 |    tries iteration via :meth:`__iter__`, then the old sequence iteration | 
 |    protocol via :meth:`__getitem__`, see :ref:`this section in the language | 
 |    reference <membership-test-details>`. | 
 |  | 
 |  | 
 | .. _sequence-methods: | 
 |  | 
 | Additional methods for emulation of sequence types | 
 | -------------------------------------------------- | 
 |  | 
 | The following optional methods can be defined to further emulate sequence | 
 | objects.  Immutable sequences methods should at most only define | 
 | :meth:`__getslice__`; mutable sequences might define all three methods. | 
 |  | 
 |  | 
 | .. method:: object.__getslice__(self, i, j) | 
 |  | 
 |    .. deprecated:: 2.0 | 
 |       Support slice objects as parameters to the :meth:`__getitem__` method. | 
 |       (However, built-in types in CPython currently still implement | 
 |       :meth:`__getslice__`.  Therefore, you have to override it in derived | 
 |       classes when implementing slicing.) | 
 |  | 
 |    Called to implement evaluation of ``self[i:j]``. The returned object should | 
 |    be of the same type as *self*.  Note that missing *i* or *j* in the slice | 
 |    expression are replaced by zero or :attr:`sys.maxsize`, respectively.  If | 
 |    negative indexes are used in the slice, the length of the sequence is added | 
 |    to that index. If the instance does not implement the :meth:`__len__` method, | 
 |    an :exc:`AttributeError` is raised. No guarantee is made that indexes | 
 |    adjusted this way are not still negative.  Indexes which are greater than the | 
 |    length of the sequence are not modified. If no :meth:`__getslice__` is found, | 
 |    a slice object is created instead, and passed to :meth:`__getitem__` instead. | 
 |  | 
 |  | 
 | .. method:: object.__setslice__(self, i, j, sequence) | 
 |  | 
 |    Called to implement assignment to ``self[i:j]``. Same notes for *i* and *j* as | 
 |    for :meth:`__getslice__`. | 
 |  | 
 |    This method is deprecated. If no :meth:`__setslice__` is found, or for extended | 
 |    slicing of the form ``self[i:j:k]``, a slice object is created, and passed to | 
 |    :meth:`__setitem__`, instead of :meth:`__setslice__` being called. | 
 |  | 
 |  | 
 | .. method:: object.__delslice__(self, i, j) | 
 |  | 
 |    Called to implement deletion of ``self[i:j]``. Same notes for *i* and *j* as for | 
 |    :meth:`__getslice__`. This method is deprecated. If no :meth:`__delslice__` is | 
 |    found, or for extended slicing of the form ``self[i:j:k]``, a slice object is | 
 |    created, and passed to :meth:`__delitem__`, instead of :meth:`__delslice__` | 
 |    being called. | 
 |  | 
 | Notice that these methods are only invoked when a single slice with a single | 
 | colon is used, and the slice method is available.  For slice operations | 
 | involving extended slice notation, or in absence of the slice methods, | 
 | :meth:`__getitem__`, :meth:`__setitem__` or :meth:`__delitem__` is called with a | 
 | slice object as argument. | 
 |  | 
 | The following example demonstrate how to make your program or module compatible | 
 | with earlier versions of Python (assuming that methods :meth:`__getitem__`, | 
 | :meth:`__setitem__` and :meth:`__delitem__` support slice objects as | 
 | arguments):: | 
 |  | 
 |    class MyClass: | 
 |        ... | 
 |        def __getitem__(self, index): | 
 |            ... | 
 |        def __setitem__(self, index, value): | 
 |            ... | 
 |        def __delitem__(self, index): | 
 |            ... | 
 |  | 
 |        if sys.version_info < (2, 0): | 
 |            # They won't be defined if version is at least 2.0 final | 
 |  | 
 |            def __getslice__(self, i, j): | 
 |                return self[max(0, i):max(0, j):] | 
 |            def __setslice__(self, i, j, seq): | 
 |                self[max(0, i):max(0, j):] = seq | 
 |            def __delslice__(self, i, j): | 
 |                del self[max(0, i):max(0, j):] | 
 |        ... | 
 |  | 
 | Note the calls to :func:`max`; these are necessary because of the handling of | 
 | negative indices before the :meth:`__\*slice__` methods are called.  When | 
 | negative indexes are used, the :meth:`__\*item__` methods receive them as | 
 | provided, but the :meth:`__\*slice__` methods get a "cooked" form of the index | 
 | values.  For each negative index value, the length of the sequence is added to | 
 | the index before calling the method (which may still result in a negative | 
 | index); this is the customary handling of negative indexes by the built-in | 
 | sequence types, and the :meth:`__\*item__` methods are expected to do this as | 
 | well.  However, since they should already be doing that, negative indexes cannot | 
 | be passed in; they must be constrained to the bounds of the sequence before | 
 | being passed to the :meth:`__\*item__` methods. Calling ``max(0, i)`` | 
 | conveniently returns the proper value. | 
 |  | 
 |  | 
 | .. _numeric-types: | 
 |  | 
 | Emulating numeric types | 
 | ----------------------- | 
 |  | 
 | The following methods can be defined to emulate numeric objects. Methods | 
 | corresponding to operations that are not supported by the particular kind of | 
 | number implemented (e.g., bitwise operations for non-integral numbers) should be | 
 | left undefined. | 
 |  | 
 |  | 
 | .. method:: object.__add__(self, other) | 
 |             object.__sub__(self, other) | 
 |             object.__mul__(self, other) | 
 |             object.__floordiv__(self, other) | 
 |             object.__mod__(self, other) | 
 |             object.__divmod__(self, other) | 
 |             object.__pow__(self, other[, modulo]) | 
 |             object.__lshift__(self, other) | 
 |             object.__rshift__(self, other) | 
 |             object.__and__(self, other) | 
 |             object.__xor__(self, other) | 
 |             object.__or__(self, other) | 
 |  | 
 |    .. index:: | 
 |       builtin: divmod | 
 |       builtin: pow | 
 |       builtin: pow | 
 |  | 
 |    These methods are called to implement the binary arithmetic operations (``+``, | 
 |    ``-``, ``*``, ``//``, ``%``, :func:`divmod`, :func:`pow`, ``**``, ``<<``, | 
 |    ``>>``, ``&``, ``^``, ``|``).  For instance, to evaluate the expression | 
 |    ``x + y``, where *x* is an instance of a class that has an :meth:`__add__` | 
 |    method, ``x.__add__(y)`` is called.  The :meth:`__divmod__` method should be the | 
 |    equivalent to using :meth:`__floordiv__` and :meth:`__mod__`; it should not be | 
 |    related to :meth:`__truediv__` (described below).  Note that :meth:`__pow__` | 
 |    should be defined to accept an optional third argument if the ternary version of | 
 |    the built-in :func:`pow` function is to be supported. | 
 |  | 
 |    If one of those methods does not support the operation with the supplied | 
 |    arguments, it should return ``NotImplemented``. | 
 |  | 
 |  | 
 | .. method:: object.__div__(self, other) | 
 |             object.__truediv__(self, other) | 
 |  | 
 |    The division operator (``/``) is implemented by these methods.  The | 
 |    :meth:`__truediv__` method is used when ``__future__.division`` is in effect, | 
 |    otherwise :meth:`__div__` is used.  If only one of these two methods is defined, | 
 |    the object will not support division in the alternate context; :exc:`TypeError` | 
 |    will be raised instead. | 
 |  | 
 |  | 
 | .. method:: object.__radd__(self, other) | 
 |             object.__rsub__(self, other) | 
 |             object.__rmul__(self, other) | 
 |             object.__rdiv__(self, other) | 
 |             object.__rtruediv__(self, other) | 
 |             object.__rfloordiv__(self, other) | 
 |             object.__rmod__(self, other) | 
 |             object.__rdivmod__(self, other) | 
 |             object.__rpow__(self, other) | 
 |             object.__rlshift__(self, other) | 
 |             object.__rrshift__(self, other) | 
 |             object.__rand__(self, other) | 
 |             object.__rxor__(self, other) | 
 |             object.__ror__(self, other) | 
 |  | 
 |    .. index:: | 
 |       builtin: divmod | 
 |       builtin: pow | 
 |  | 
 |    These methods are called to implement the binary arithmetic operations (``+``, | 
 |    ``-``, ``*``, ``/``, ``%``, :func:`divmod`, :func:`pow`, ``**``, ``<<``, ``>>``, | 
 |    ``&``, ``^``, ``|``) with reflected (swapped) operands.  These functions are | 
 |    only called if the left operand does not support the corresponding operation and | 
 |    the operands are of different types. [#]_ For instance, to evaluate the | 
 |    expression ``x - y``, where *y* is an instance of a class that has an | 
 |    :meth:`__rsub__` method, ``y.__rsub__(x)`` is called if ``x.__sub__(y)`` returns | 
 |    *NotImplemented*. | 
 |  | 
 |    .. index:: builtin: pow | 
 |  | 
 |    Note that ternary :func:`pow` will not try calling :meth:`__rpow__` (the | 
 |    coercion rules would become too complicated). | 
 |  | 
 |    .. note:: | 
 |  | 
 |       If the right operand's type is a subclass of the left operand's type and that | 
 |       subclass provides the reflected method for the operation, this method will be | 
 |       called before the left operand's non-reflected method.  This behavior allows | 
 |       subclasses to override their ancestors' operations. | 
 |  | 
 |  | 
 | .. method:: object.__iadd__(self, other) | 
 |             object.__isub__(self, other) | 
 |             object.__imul__(self, other) | 
 |             object.__idiv__(self, other) | 
 |             object.__itruediv__(self, other) | 
 |             object.__ifloordiv__(self, other) | 
 |             object.__imod__(self, other) | 
 |             object.__ipow__(self, other[, modulo]) | 
 |             object.__ilshift__(self, other) | 
 |             object.__irshift__(self, other) | 
 |             object.__iand__(self, other) | 
 |             object.__ixor__(self, other) | 
 |             object.__ior__(self, other) | 
 |  | 
 |    These methods are called to implement the augmented arithmetic assignments | 
 |    (``+=``, ``-=``, ``*=``, ``/=``, ``//=``, ``%=``, ``**=``, ``<<=``, ``>>=``, | 
 |    ``&=``, ``^=``, ``|=``).  These methods should attempt to do the operation | 
 |    in-place (modifying *self*) and return the result (which could be, but does | 
 |    not have to be, *self*).  If a specific method is not defined, the augmented | 
 |    assignment falls back to the normal methods.  For instance, to execute the | 
 |    statement ``x += y``, where *x* is an instance of a class that has an | 
 |    :meth:`__iadd__` method, ``x.__iadd__(y)`` is called.  If *x* is an instance | 
 |    of a class that does not define a :meth:`__iadd__` method, ``x.__add__(y)`` | 
 |    and ``y.__radd__(x)`` are considered, as with the evaluation of ``x + y``. | 
 |  | 
 |  | 
 | .. method:: object.__neg__(self) | 
 |             object.__pos__(self) | 
 |             object.__abs__(self) | 
 |             object.__invert__(self) | 
 |  | 
 |    .. index:: builtin: abs | 
 |  | 
 |    Called to implement the unary arithmetic operations (``-``, ``+``, :func:`abs` | 
 |    and ``~``). | 
 |  | 
 |  | 
 | .. method:: object.__complex__(self) | 
 |             object.__int__(self) | 
 |             object.__long__(self) | 
 |             object.__float__(self) | 
 |  | 
 |    .. index:: | 
 |       builtin: complex | 
 |       builtin: int | 
 |       builtin: long | 
 |       builtin: float | 
 |  | 
 |    Called to implement the built-in functions :func:`complex`, :func:`int`, | 
 |    :func:`long`, and :func:`float`.  Should return a value of the appropriate type. | 
 |  | 
 |  | 
 | .. method:: object.__oct__(self) | 
 |             object.__hex__(self) | 
 |  | 
 |    .. index:: | 
 |       builtin: oct | 
 |       builtin: hex | 
 |  | 
 |    Called to implement the built-in functions :func:`oct` and :func:`hex`.  Should | 
 |    return a string value. | 
 |  | 
 |  | 
 | .. method:: object.__index__(self) | 
 |  | 
 |    Called to implement :func:`operator.index`.  Also called whenever Python needs | 
 |    an integer object (such as in slicing).  Must return an integer (int or long). | 
 |  | 
 |    .. versionadded:: 2.5 | 
 |  | 
 |  | 
 | .. method:: object.__coerce__(self, other) | 
 |  | 
 |    Called to implement "mixed-mode" numeric arithmetic.  Should either return a | 
 |    2-tuple containing *self* and *other* converted to a common numeric type, or | 
 |    ``None`` if conversion is impossible.  When the common type would be the type of | 
 |    ``other``, it is sufficient to return ``None``, since the interpreter will also | 
 |    ask the other object to attempt a coercion (but sometimes, if the implementation | 
 |    of the other type cannot be changed, it is useful to do the conversion to the | 
 |    other type here).  A return value of ``NotImplemented`` is equivalent to | 
 |    returning ``None``. | 
 |  | 
 |  | 
 | .. _coercion-rules: | 
 |  | 
 | Coercion rules | 
 | -------------- | 
 |  | 
 | This section used to document the rules for coercion.  As the language has | 
 | evolved, the coercion rules have become hard to document precisely; documenting | 
 | what one version of one particular implementation does is undesirable.  Instead, | 
 | here are some informal guidelines regarding coercion.  In Python 3, coercion | 
 | will not be supported. | 
 |  | 
 | * | 
 |  | 
 |   If the left operand of a % operator is a string or Unicode object, no coercion | 
 |   takes place and the string formatting operation is invoked instead. | 
 |  | 
 | * | 
 |  | 
 |   It is no longer recommended to define a coercion operation. Mixed-mode | 
 |   operations on types that don't define coercion pass the original arguments to | 
 |   the operation. | 
 |  | 
 | * | 
 |  | 
 |   New-style classes (those derived from :class:`object`) never invoke the | 
 |   :meth:`__coerce__` method in response to a binary operator; the only time | 
 |   :meth:`__coerce__` is invoked is when the built-in function :func:`coerce` is | 
 |   called. | 
 |  | 
 | * | 
 |  | 
 |   For most intents and purposes, an operator that returns ``NotImplemented`` is | 
 |   treated the same as one that is not implemented at all. | 
 |  | 
 | * | 
 |  | 
 |   Below, :meth:`__op__` and :meth:`__rop__` are used to signify the generic method | 
 |   names corresponding to an operator; :meth:`__iop__` is used for the | 
 |   corresponding in-place operator.  For example, for the operator '``+``', | 
 |   :meth:`__add__` and :meth:`__radd__` are used for the left and right variant of | 
 |   the binary operator, and :meth:`__iadd__` for the in-place variant. | 
 |  | 
 | * | 
 |  | 
 |   For objects *x* and *y*, first ``x.__op__(y)`` is tried.  If this is not | 
 |   implemented or returns ``NotImplemented``, ``y.__rop__(x)`` is tried.  If this | 
 |   is also not implemented or returns ``NotImplemented``, a :exc:`TypeError` | 
 |   exception is raised.  But see the following exception: | 
 |  | 
 | * | 
 |  | 
 |   Exception to the previous item: if the left operand is an instance of a built-in | 
 |   type or a new-style class, and the right operand is an instance of a proper | 
 |   subclass of that type or class and overrides the base's :meth:`__rop__` method, | 
 |   the right operand's :meth:`__rop__` method is tried *before* the left operand's | 
 |   :meth:`__op__` method. | 
 |  | 
 |   This is done so that a subclass can completely override binary operators. | 
 |   Otherwise, the left operand's :meth:`__op__` method would always accept the | 
 |   right operand: when an instance of a given class is expected, an instance of a | 
 |   subclass of that class is always acceptable. | 
 |  | 
 | * | 
 |  | 
 |   When either operand type defines a coercion, this coercion is called before that | 
 |   type's :meth:`__op__` or :meth:`__rop__` method is called, but no sooner.  If | 
 |   the coercion returns an object of a different type for the operand whose | 
 |   coercion is invoked, part of the process is redone using the new object. | 
 |  | 
 | * | 
 |  | 
 |   When an in-place operator (like '``+=``') is used, if the left operand | 
 |   implements :meth:`__iop__`, it is invoked without any coercion.  When the | 
 |   operation falls back to :meth:`__op__` and/or :meth:`__rop__`, the normal | 
 |   coercion rules apply. | 
 |  | 
 | * | 
 |  | 
 |   In ``x + y``, if *x* is a sequence that implements sequence concatenation, | 
 |   sequence concatenation is invoked. | 
 |  | 
 | * | 
 |  | 
 |   In ``x * y``, if one operand is a sequence that implements sequence | 
 |   repetition, and the other is an integer (:class:`int` or :class:`long`), | 
 |   sequence repetition is invoked. | 
 |  | 
 | * | 
 |  | 
 |   Rich comparisons (implemented by methods :meth:`__eq__` and so on) never use | 
 |   coercion.  Three-way comparison (implemented by :meth:`__cmp__`) does use | 
 |   coercion under the same conditions as other binary operations use it. | 
 |  | 
 | * | 
 |  | 
 |   In the current implementation, the built-in numeric types :class:`int`, | 
 |   :class:`long`, :class:`float`, and :class:`complex` do not use coercion. | 
 |   All these types implement a :meth:`__coerce__` method, for use by the built-in | 
 |   :func:`coerce` function. | 
 |  | 
 |   .. versionchanged:: 2.7 | 
 |  | 
 |      The complex type no longer makes implicit calls to the :meth:`__coerce__` | 
 |      method for mixed-type binary arithmetic operations. | 
 |  | 
 |  | 
 | .. _context-managers: | 
 |  | 
 | With Statement Context Managers | 
 | ------------------------------- | 
 |  | 
 | .. versionadded:: 2.5 | 
 |  | 
 | A :dfn:`context manager` is an object that defines the runtime context to be | 
 | established when executing a :keyword:`with` statement. The context manager | 
 | handles the entry into, and the exit from, the desired runtime context for the | 
 | execution of the block of code.  Context managers are normally invoked using the | 
 | :keyword:`with` statement (described in section :ref:`with`), but can also be | 
 | used by directly invoking their methods. | 
 |  | 
 | .. index:: | 
 |    statement: with | 
 |    single: context manager | 
 |  | 
 | Typical uses of context managers include saving and restoring various kinds of | 
 | global state, locking and unlocking resources, closing opened files, etc. | 
 |  | 
 | For more information on context managers, see :ref:`typecontextmanager`. | 
 |  | 
 |  | 
 | .. method:: object.__enter__(self) | 
 |  | 
 |    Enter the runtime context related to this object. The :keyword:`with` statement | 
 |    will bind this method's return value to the target(s) specified in the | 
 |    :keyword:`as` clause of the statement, if any. | 
 |  | 
 |  | 
 | .. method:: object.__exit__(self, exc_type, exc_value, traceback) | 
 |  | 
 |    Exit the runtime context related to this object. The parameters describe the | 
 |    exception that caused the context to be exited. If the context was exited | 
 |    without an exception, all three arguments will be :const:`None`. | 
 |  | 
 |    If an exception is supplied, and the method wishes to suppress the exception | 
 |    (i.e., prevent it from being propagated), it should return a true value. | 
 |    Otherwise, the exception will be processed normally upon exit from this method. | 
 |  | 
 |    Note that :meth:`__exit__` methods should not reraise the passed-in exception; | 
 |    this is the caller's responsibility. | 
 |  | 
 |  | 
 | .. seealso:: | 
 |  | 
 |    :pep:`0343` - The "with" statement | 
 |       The specification, background, and examples for the Python :keyword:`with` | 
 |       statement. | 
 |  | 
 |  | 
 | .. _old-style-special-lookup: | 
 |  | 
 | Special method lookup for old-style classes | 
 | ------------------------------------------- | 
 |  | 
 | For old-style classes, special methods are always looked up in exactly the | 
 | same way as any other method or attribute. This is the case regardless of | 
 | whether the method is being looked up explicitly as in ``x.__getitem__(i)`` | 
 | or implicitly as in ``x[i]``. | 
 |  | 
 | This behaviour means that special methods may exhibit different behaviour | 
 | for different instances of a single old-style class if the appropriate | 
 | special attributes are set differently:: | 
 |  | 
 |    >>> class C: | 
 |    ...     pass | 
 |    ... | 
 |    >>> c1 = C() | 
 |    >>> c2 = C() | 
 |    >>> c1.__len__ = lambda: 5 | 
 |    >>> c2.__len__ = lambda: 9 | 
 |    >>> len(c1) | 
 |    5 | 
 |    >>> len(c2) | 
 |    9 | 
 |  | 
 |  | 
 | .. _new-style-special-lookup: | 
 |  | 
 | Special method lookup for new-style classes | 
 | ------------------------------------------- | 
 |  | 
 | For new-style classes, implicit invocations of special methods are only guaranteed | 
 | to work correctly if defined on an object's type, not in the object's instance | 
 | dictionary.  That behaviour is the reason why the following code raises an | 
 | exception (unlike the equivalent example with old-style classes):: | 
 |  | 
 |    >>> class C(object): | 
 |    ...     pass | 
 |    ... | 
 |    >>> c = C() | 
 |    >>> c.__len__ = lambda: 5 | 
 |    >>> len(c) | 
 |    Traceback (most recent call last): | 
 |      File "<stdin>", line 1, in <module> | 
 |    TypeError: object of type 'C' has no len() | 
 |  | 
 | The rationale behind this behaviour lies with a number of special methods such | 
 | as :meth:`__hash__` and :meth:`__repr__` that are implemented by all objects, | 
 | including type objects. If the implicit lookup of these methods used the | 
 | conventional lookup process, they would fail when invoked on the type object | 
 | itself:: | 
 |  | 
 |    >>> 1 .__hash__() == hash(1) | 
 |    True | 
 |    >>> int.__hash__() == hash(int) | 
 |    Traceback (most recent call last): | 
 |      File "<stdin>", line 1, in <module> | 
 |    TypeError: descriptor '__hash__' of 'int' object needs an argument | 
 |  | 
 | Incorrectly attempting to invoke an unbound method of a class in this way is | 
 | sometimes referred to as 'metaclass confusion', and is avoided by bypassing | 
 | the instance when looking up special methods:: | 
 |  | 
 |    >>> type(1).__hash__(1) == hash(1) | 
 |    True | 
 |    >>> type(int).__hash__(int) == hash(int) | 
 |    True | 
 |  | 
 | In addition to bypassing any instance attributes in the interest of | 
 | correctness, implicit special method lookup generally also bypasses the | 
 | :meth:`__getattribute__` method even of the object's metaclass:: | 
 |  | 
 |    >>> class Meta(type): | 
 |    ...    def __getattribute__(*args): | 
 |    ...       print "Metaclass getattribute invoked" | 
 |    ...       return type.__getattribute__(*args) | 
 |    ... | 
 |    >>> class C(object): | 
 |    ...     __metaclass__ = Meta | 
 |    ...     def __len__(self): | 
 |    ...         return 10 | 
 |    ...     def __getattribute__(*args): | 
 |    ...         print "Class getattribute invoked" | 
 |    ...         return object.__getattribute__(*args) | 
 |    ... | 
 |    >>> c = C() | 
 |    >>> c.__len__()                 # Explicit lookup via instance | 
 |    Class getattribute invoked | 
 |    10 | 
 |    >>> type(c).__len__(c)          # Explicit lookup via type | 
 |    Metaclass getattribute invoked | 
 |    10 | 
 |    >>> len(c)                      # Implicit lookup | 
 |    10 | 
 |  | 
 | Bypassing the :meth:`__getattribute__` machinery in this fashion | 
 | provides significant scope for speed optimisations within the | 
 | interpreter, at the cost of some flexibility in the handling of | 
 | special methods (the special method *must* be set on the class | 
 | object itself in order to be consistently invoked by the interpreter). | 
 |  | 
 |  | 
 | .. rubric:: Footnotes | 
 |  | 
 | .. [#] It *is* possible in some cases to change an object's type, under certain | 
 |    controlled conditions. It generally isn't a good idea though, since it can | 
 |    lead to some very strange behaviour if it is handled incorrectly. | 
 |  | 
 | .. [#] For operands of the same type, it is assumed that if the non-reflected method | 
 |    (such as :meth:`__add__`) fails the operation is not supported, which is why the | 
 |    reflected method is not called. | 
 |  |