3. Data model
*************


3.1. Objects, values and types
==============================

*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.)

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 '"is"' operator compares the
identity of two objects; the "id()" function returns an integer
representing its identity.

**CPython implementation detail:** For CPython, "id(x)" is the memory
address where "x" is stored.

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 "type()" function returns an object's
type (which is an object itself).  Like its identity, an object's
*type* is also unchangeable. [1]

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.

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.

**CPython implementation 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 "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 (so
you should always close files explicitly).

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 '"try"..."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 "close()" method. Programs
are strongly recommended to explicitly close such objects.  The
'"try"..."finally"' statement and the '"with"' statement provide
convenient ways to do this.

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".)


3.2. The standard type hierarchy
================================

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.), although such additions
will often be provided via the standard library instead.

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.


3.2.1. 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.


3.2.2. 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 should
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.)  It
should not be evaluated in a boolean context.

See Implementing the arithmetic operations for more details.

Changed in version 3.9: Evaluating "NotImplemented" in a boolean
context is deprecated. While it currently evaluates as true, it will
emit a "DeprecationWarning". It will raise a "TypeError" in a future
version of Python.


3.2.3. Ellipsis
---------------

This type has a single value.  There is a single object with this
value. This object is accessed through the literal "..." or the built-
in name "Ellipsis".  Its truth value is true.


3.2.4. "numbers.Number"
-----------------------

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.

The string representations of the numeric classes, computed by
"__repr__()" and "__str__()", have the following properties:

* They are valid numeric literals which, when passed to their class
  constructor, produce an object having the value of the original
  numeric.

* The representation is in base 10, when possible.

* Leading zeros, possibly excepting a single zero before a decimal
  point, are not shown.

* Trailing zeros, possibly excepting a single zero after a decimal
  point, are not shown.

* A sign is shown only when the number is negative.

Python distinguishes between integers, floating point numbers, and
complex numbers:


3.2.4.1. "numbers.Integral"
~~~~~~~~~~~~~~~~~~~~~~~~~~~

These represent elements from the mathematical set of integers
(positive and negative).

Note:

  The rules for integer representation are intended to give the most
  meaningful interpretation of shift and mask operations involving
  negative integers.

There are two types of integers:

Integers ("int")
   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 ("bool")
   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 the integer type, 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.


3.2.4.2. "numbers.Real" ("float")
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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.


3.2.4.3. "numbers.Complex" ("complex")
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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".


3.2.5. Sequences
----------------

These represent finite ordered sets indexed by non-negative numbers.
The built-in function "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]".

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.

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:


3.2.5.1. Immutable sequences
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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
   A string is a sequence of values that represent Unicode code
   points. All the code points in the range "U+0000 - U+10FFFF" can be
   represented in a string.  Python doesn't have a char type; instead,
   every code point in the string is represented as a string object
   with length "1".  The built-in function "ord()" converts a code
   point from its string form to an integer in the range "0 - 10FFFF";
   "chr()" converts an integer in the range "0 - 10FFFF" to the
   corresponding length "1" string object. "str.encode()" can be used
   to convert a "str" to "bytes" using the given text encoding, and
   "bytes.decode()" can be used to achieve the opposite.

Tuples
   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.

Bytes
   A bytes object is an immutable array.  The items are 8-bit bytes,
   represented by integers in the range 0 <= x < 256.  Bytes literals
   (like "b'abc'") and the built-in "bytes()" constructor can be used
   to create bytes objects.  Also, bytes objects can be decoded to
   strings via the "decode()" method.


3.2.5.2. Mutable sequences
~~~~~~~~~~~~~~~~~~~~~~~~~~

Mutable sequences can be changed after they are created.  The
subscription and slicing notations can be used as the target of
assignment and "del" (delete) statements.

Note:

  The "collections" and "array" module provide additional examples of
  mutable sequence types.

There are currently two intrinsic mutable sequence types:

Lists
   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
   A bytearray object is a mutable array. They are created by the
   built-in "bytearray()" constructor.  Aside from being mutable (and
   hence unhashable), byte arrays otherwise provide the same interface
   and functionality as immutable "bytes" objects.


3.2.6. Set types
----------------

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 "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
   These represent a mutable set. They are created by the built-in
   "set()" constructor and can be modified afterwards by several
   methods, such as "add()".

Frozen sets
   These represent an immutable set.  They are created by the built-in
   "frozenset()" constructor.  As a frozenset is immutable and
   *hashable*, it can be used again as an element of another set, or
   as a dictionary key.


3.2.7. Mappings
---------------

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 "del" statements. The built-in function
"len()" returns the number of items in a mapping.

There is currently a single intrinsic mapping type:


3.2.7.1. Dictionaries
~~~~~~~~~~~~~~~~~~~~~

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 preserve insertion order, meaning that keys will be
produced in the same order they were added sequentially over the
dictionary. Replacing an existing key does not change the order,
however removing a key and re-inserting it will add it to the end
instead of keeping its old place.

Dictionaries are mutable; they can be created by the "{...}" notation
(see section Dictionary displays).

The extension modules "dbm.ndbm" and "dbm.gnu" provide additional
examples of mapping types, as does the "collections" module.

Changed in version 3.7: Dictionaries did not preserve insertion order
in versions of Python before 3.6. In CPython 3.6, insertion order was
preserved, but it was considered an implementation detail at that time
rather than a language guarantee.


3.2.8. Callable types
---------------------

These are the types to which the function call operation (see section
Calls) can be applied:


3.2.8.1. User-defined functions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A user-defined function object is created by a function definition
(see section Function definitions).  It should be called with an
argument list containing the same number of items as the function's
formal parameter list.


3.2.8.1.1. Special read-only attributes
"""""""""""""""""""""""""""""""""""""""

+----------------------------------------------------+----------------------------------------------------+
| Attribute                                          | Meaning                                            |
|====================================================|====================================================|
| function.__globals__                               | A reference to the "dictionary" that holds the     |
|                                                    | function's global variables -- the global          |
|                                                    | namespace of the module in which the function was  |
|                                                    | defined.                                           |
+----------------------------------------------------+----------------------------------------------------+
| function.__closure__                               | "None" or a "tuple" of cells that contain bindings |
|                                                    | for the function's free variables.  A cell object  |
|                                                    | has the attribute "cell_contents". This can be     |
|                                                    | used to get the value of the cell, as well as set  |
|                                                    | the value.                                         |
+----------------------------------------------------+----------------------------------------------------+


3.2.8.1.2. Special writable attributes
""""""""""""""""""""""""""""""""""""""

Most of these attributes check the type of the assigned value:

+----------------------------------------------------+----------------------------------------------------+
| Attribute                                          | Meaning                                            |
|====================================================|====================================================|
| function.__doc__                                   | The function's documentation string, or "None" if  |
|                                                    | unavailable. Not inherited by subclasses.          |
+----------------------------------------------------+----------------------------------------------------+
| function.__name__                                  | The function's name. See also: "__name__           |
|                                                    | attributes".                                       |
+----------------------------------------------------+----------------------------------------------------+
| function.__qualname__                              | The function's *qualified name*. See also:         |
|                                                    | "__qualname__ attributes".  New in version 3.3.    |
+----------------------------------------------------+----------------------------------------------------+
| function.__module__                                | The name of the module the function was defined    |
|                                                    | in, or "None" if unavailable.                      |
+----------------------------------------------------+----------------------------------------------------+
| function.__defaults__                              | A "tuple" containing default *parameter* values    |
|                                                    | for those parameters that have defaults, or "None" |
|                                                    | if no parameters have a default value.             |
+----------------------------------------------------+----------------------------------------------------+
| function.__code__                                  | The code object representing the compiled function |
|                                                    | body.                                              |
+----------------------------------------------------+----------------------------------------------------+
| function.__dict__                                  | The namespace supporting arbitrary function        |
|                                                    | attributes. See also: "__dict__ attributes".       |
+----------------------------------------------------+----------------------------------------------------+
| function.__annotations__                           | A "dictionary" containing annotations of           |
|                                                    | *parameters*. The keys of the dictionary are the   |
|                                                    | parameter names, and "'return'" for the return     |
|                                                    | annotation, if provided. See also: Annotations     |
|                                                    | Best Practices.                                    |
+----------------------------------------------------+----------------------------------------------------+
| function.__kwdefaults__                            | A "dictionary" containing defaults for keyword-    |
|                                                    | only *parameters*.                                 |
+----------------------------------------------------+----------------------------------------------------+

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.

**CPython implementation detail:** CPython's 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 (accessible via the "__code__" attribute).


3.2.8.2. Instance methods
~~~~~~~~~~~~~~~~~~~~~~~~~

An instance method object combines a class, a class instance and any
callable object (normally a user-defined function).

Special read-only attributes:

+----------------------------------------------------+----------------------------------------------------+
| method.__self__                                    | Refers to the class instance object to which the   |
|                                                    | method is bound                                    |
+----------------------------------------------------+----------------------------------------------------+
| method.__func__                                    | Refers to the original function object             |
+----------------------------------------------------+----------------------------------------------------+
| method.__doc__                                     | The method's documentation (same as                |
|                                                    | "method.__func__.__doc__"). A "string" if the      |
|                                                    | original function had a docstring, else "None".    |
+----------------------------------------------------+----------------------------------------------------+
| method.__name__                                    | The name of the method (same as                    |
|                                                    | "method.__func__.__name__")                        |
+----------------------------------------------------+----------------------------------------------------+
| method.__module__                                  | The name of the module the method was defined in,  |
|                                                    | or "None" if unavailable.                          |
+----------------------------------------------------+----------------------------------------------------+

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 or a "classmethod" object.

When an instance method object is created by retrieving a user-defined
function object from a class via one of its instances, its "__self__"
attribute is the instance, and the method object is said to be
*bound*.  The new method's "__func__" attribute is the original
function object.

When an instance method object is created by retrieving a
"classmethod" object from a class or instance, its "__self__"
attribute is the class itself, and its "__func__" attribute is the
function object underlying the class method.

When an instance method object is called, the underlying function
("__func__") is called, inserting the class instance ("__self__") in
front of the argument list.  For instance, when "C" is a class which
contains a definition for a function "f()", and "x" is an instance of
"C", calling "x.f(1)" is equivalent to calling "C.f(x, 1)".

When an instance method object is derived from a "classmethod" object,
the "class instance" stored in "__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 instance method
object happens each time the attribute is retrieved from the 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.


3.2.8.3. Generator functions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A function or method which uses the "yield" statement (see section The
yield statement) is called a *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
"iterator.__next__()" method will cause the function to execute until
it provides a value using the "yield" statement.  When the function
executes a "return" statement or falls off the end, a "StopIteration"
exception is raised and the iterator will have reached the end of the
set of values to be returned.


3.2.8.4. Coroutine functions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A function or method which is defined using "async def" is called a
*coroutine function*.  Such a function, when called, returns a
*coroutine* object.  It may contain "await" expressions, as well as
"async with" and "async for" statements. See also the Coroutine
Objects section.


3.2.8.5. Asynchronous generator functions
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A function or method which is defined using "async def" and which uses
the "yield" statement is called a *asynchronous generator function*.
Such a function, when called, returns an *asynchronous iterator*
object which can be used in an "async for" statement to execute the
body of the function.

Calling the asynchronous iterator's "aiterator.__anext__" method will
return an *awaitable* which when awaited will execute until it
provides a value using the "yield" expression.  When the function
executes an empty "return" statement or falls off the end, a
"StopAsyncIteration" exception is raised and the asynchronous iterator
will have reached the end of the set of values to be yielded.


3.2.8.6. Built-in functions
~~~~~~~~~~~~~~~~~~~~~~~~~~~

A built-in function object is a wrapper around a C function.  Examples
of built-in functions are "len()" and "math.sin()" ("math" is a
standard built-in module). The number and type of the arguments are
determined by the C function. Special read-only attributes:

* "__doc__" is the function's documentation string, or "None" if
  unavailable. See "function.__doc__".

* "__name__" is the function's name. See "function.__name__".

* "__self__" is set to "None" (but see the next item).

* "__module__" is the name of the module the function was defined in
  or "None" if unavailable. See "function.__module__".


3.2.8.7. Built-in methods
~~~~~~~~~~~~~~~~~~~~~~~~~

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 "__self__" is set to the object denoted by *alist*. (The
attribute has the same semantics as it does with "other instance
methods".)


3.2.8.8. Classes
~~~~~~~~~~~~~~~~

Classes are callable.  These objects normally act as factories for new
instances of themselves, but variations are possible for class types
that override "__new__()".  The arguments of the call are passed to
"__new__()" and, in the typical case, to "__init__()" to initialize
the new instance.


3.2.8.9. Class Instances
~~~~~~~~~~~~~~~~~~~~~~~~

Instances of arbitrary classes can be made callable by defining a
"__call__()" method in their class.


3.2.9. Modules
--------------

Modules are a basic organizational unit of Python code, and are
created by the import system as invoked either by the "import"
statement, or by calling functions such as "importlib.import_module()"
and built-in "__import__()".  A module object has a namespace
implemented by a "dictionary" object (this is the dictionary
referenced by the "__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".

Predefined (writable) attributes:

   "__name__"
      The module's name.

   "__doc__"
      The module's documentation string, or "None" if unavailable.

   "__file__"
      The pathname of the file from which the module was loaded, if it
      was loaded from a file. The "__file__" attribute may be missing
      for certain types of modules, such as C modules that are
      statically linked into the interpreter.  For extension modules
      loaded dynamically from a shared library, it's the pathname of
      the shared library file.

   "__annotations__"
      A dictionary containing *variable annotations* collected during
      module body execution.  For best practices on working with
      "__annotations__", please see Annotations Best Practices.

Special read-only attribute: "__dict__" is the module's namespace as a
dictionary object.

**CPython implementation 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.


3.2.10. Custom classes
----------------------

Custom class types are typically created by class definitions (see
section Class definitions).  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 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.
This search of the base classes uses the 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 Python can
be found in the documentation accompanying the 2.3 release at
https://www.python.org/download/releases/2.3/mro/.

When a class attribute reference (for class "C", say) would yield a
class method object, it is transformed into an instance method object
whose "__self__" attribute is "C". When it would yield a
"staticmethod" object, it is transformed into the object wrapped by
the static method object. See section Implementing Descriptors for
another way in which attributes retrieved from a class may differ from
those actually contained in its "__dict__".

Class attribute assignments update the class's dictionary, never the
dictionary of a base class.

A class object can be called (see above) to yield a class instance
(see below).

Special attributes:

   "__name__"
      The class name.

   "__module__"
      The name of the module in which the class was defined.

   "__dict__"
      The dictionary containing the class's namespace.

   "__bases__"
      A tuple containing the base classes, in the order of their
      occurrence in the base class list.

   "__doc__"
      The class's documentation string, or "None" if undefined.

   "__annotations__"
      A dictionary containing *variable annotations* collected during
      class body execution.  For best practices on working with
      "__annotations__", please see Annotations Best Practices.


3.2.11. Class instances
-----------------------

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, it is transformed into an instance method object
whose "__self__" attribute is the instance.  Static method and class
method objects are also transformed; see above under "Classes".  See
section Implementing 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 "__dict__".  If no class attribute is
found, and the object's class has a "__getattr__()" method, that is
called to satisfy the lookup.

Attribute assignments and deletions update the instance's dictionary,
never a class's dictionary.  If the class has a "__setattr__()" or
"__delattr__()" method, this is called instead of updating the
instance dictionary directly.

Class instances can pretend to be numbers, sequences, or mappings if
they have methods with certain special names.  See section Special
method names.

Special attributes: "__dict__" is the attribute dictionary;
"__class__" is the instance's class.


3.2.12. I/O objects (also known as file objects)
------------------------------------------------

A *file object* represents an open file.  Various shortcuts are
available to create file objects: the "open()" built-in function, and
also "os.popen()", "os.fdopen()", and the "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; they are all open in text mode and therefore
follow the interface defined by the "io.TextIOBase" abstract class.


3.2.13. Internal types
----------------------

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.


3.2.13.1. Code objects
~~~~~~~~~~~~~~~~~~~~~~

Code objects represent *byte-compiled* executable Python code, or
*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.


3.2.13.1.1. Special read-only attributes
""""""""""""""""""""""""""""""""""""""""

+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_name                                 | The function name                                  |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_qualname                             | The fully qualified function name                  |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_argcount                             | The total number of positional *parameters*        |
|                                                    | (including positional-only parameters and          |
|                                                    | parameters with default values) that the function  |
|                                                    | has                                                |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_posonlyargcount                      | The number of positional-only *parameters*         |
|                                                    | (including arguments with default values) that the |
|                                                    | function has                                       |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_kwonlyargcount                       | The number of keyword-only *parameters* (including |
|                                                    | arguments with default values) that the function   |
|                                                    | has                                                |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_nlocals                              | The number of local variables used by the function |
|                                                    | (including parameters)                             |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_varnames                             | A "tuple" containing the names of the local        |
|                                                    | variables in the function (starting with the       |
|                                                    | parameter names)                                   |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_cellvars                             | A "tuple" containing the names of local variables  |
|                                                    | that are referenced by nested functions inside the |
|                                                    | function                                           |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_freevars                             | A "tuple" containing the names of free variables   |
|                                                    | in the function                                    |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_code                                 | A string representing the sequence of *bytecode*   |
|                                                    | instructions in the function                       |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_consts                               | A "tuple" containing the literals used by the      |
|                                                    | *bytecode* in the function                         |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_names                                | A "tuple" containing the names used by the         |
|                                                    | *bytecode* in the function                         |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_filename                             | The name of the file from which the code was       |
|                                                    | compiled                                           |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_firstlineno                          | The line number of the first line of the function  |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_lnotab                               | A string encoding the mapping from *bytecode*      |
|                                                    | offsets to line numbers. For details, see the      |
|                                                    | source code of the interpreter.                    |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_stacksize                            | The required stack size of the code object         |
+----------------------------------------------------+----------------------------------------------------+
| codeobject.co_flags                                | An "integer" encoding a number of flags for the    |
|                                                    | interpreter.                                       |
+----------------------------------------------------+----------------------------------------------------+

The following flag bits are defined for "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. See Code Objects Bit
Flags for details on the semantics of each flags that might be
present.

Future feature declarations ("from __future__ import division") also
use bits in "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 "co_flags" are reserved for internal use.

If a code object represents a function, the first item in "co_consts"
is the documentation string of the function, or "None" if undefined.


3.2.13.1.2. Methods on code objects
"""""""""""""""""""""""""""""""""""

codeobject.co_positions()

   Returns an iterable over the source code positions of each
   *bytecode* instruction in the code object.

   The iterator returns "tuple"s containing the "(start_line,
   end_line, start_column, end_column)". The *i-th* tuple corresponds
   to the position of the source code that compiled to the *i-th*
   instruction. Column information is 0-indexed utf-8 byte offsets on
   the given source line.

   This positional information can be missing. A non-exhaustive lists
   of cases where this may happen:

   * Running the interpreter with "-X" "no_debug_ranges".

   * Loading a pyc file compiled while using "-X" "no_debug_ranges".

   * Position tuples corresponding to artificial instructions.

   * Line and column numbers that can't be represented due to
     implementation specific limitations.

   When this occurs, some or all of the tuple elements can be "None".

   New in version 3.11.

   Note:

     This feature requires storing column positions in code objects
     which may result in a small increase of disk usage of compiled
     Python files or interpreter memory usage. To avoid storing the
     extra information and/or deactivate printing the extra traceback
     information, the "-X" "no_debug_ranges" command line flag or the
     "PYTHONNODEBUGRANGES" environment variable can be used.

codeobject.co_lines()

   Returns an iterator that yields information about successive ranges
   of *bytecode*s. Each item yielded is a "(start, end, lineno)"
   "tuple":

   * "start" (an "int") represents the offset (inclusive) of the start
     of the *bytecode* range

   * "end" (an "int") represents the offset (exclusive) of the end of
     the *bytecode* range

   * "lineno" is an "int" representing the line number of the
     *bytecode* range, or "None" if the bytecodes in the given range
     have no line number

   The items yielded will have the following properties:

   * The first range yielded will have a "start" of 0.

   * The "(start, end)" ranges will be non-decreasing and consecutive.
     That is, for any pair of "tuple"s, the "start" of the second will
     be equal to the "end" of the first.

   * No range will be backwards: "end >= start" for all triples.

   * The last "tuple" yielded will have "end" equal to the size of the
     *bytecode*.

   Zero-width ranges, where "start == end", are allowed. Zero-width
   ranges are used for lines that are present in the source code, but
   have been eliminated by the *bytecode* compiler.

   New in version 3.10.

   See also:

     **PEP 626** - Precise line numbers for debugging and other tools.
        The PEP that introduced the "co_lines()" method.


3.2.13.2. Frame objects
~~~~~~~~~~~~~~~~~~~~~~~

Frame objects represent execution frames.  They may occur in traceback
objects, and are also passed to registered trace functions.


3.2.13.2.1. Special read-only attributes
""""""""""""""""""""""""""""""""""""""""

+----------------------------------------------------+----------------------------------------------------+
| frame.f_back                                       | Points to the previous stack frame (towards the    |
|                                                    | caller), or "None" if this is the bottom stack     |
|                                                    | frame                                              |
+----------------------------------------------------+----------------------------------------------------+
| frame.f_code                                       | The code object being executed in this frame.      |
|                                                    | Accessing this attribute raises an auditing event  |
|                                                    | "object.__getattr__" with arguments "obj" and      |
|                                                    | ""f_code"".                                        |
+----------------------------------------------------+----------------------------------------------------+
| frame.f_locals                                     | The dictionary used by the frame to look up local  |
|                                                    | variables                                          |
+----------------------------------------------------+----------------------------------------------------+
| frame.f_globals                                    | The dictionary used by the frame to look up global |
|                                                    | variables                                          |
+----------------------------------------------------+----------------------------------------------------+
| frame.f_builtins                                   | The dictionary used by the frame to look up built- |
|                                                    | in (intrinsic) names                               |
+----------------------------------------------------+----------------------------------------------------+
| frame.f_lasti                                      | The "precise instruction" of the frame object      |
|                                                    | (this is an index into the *bytecode* string of    |
|                                                    | the code object)                                   |
+----------------------------------------------------+----------------------------------------------------+


3.2.13.2.2. Special writable attributes
"""""""""""""""""""""""""""""""""""""""

+----------------------------------------------------+----------------------------------------------------+
| frame.f_trace                                      | If not "None", this is a function called for       |
|                                                    | various events during code execution (this is used |
|                                                    | by debuggers). Normally an event is triggered for  |
|                                                    | each new source line (see "f_trace_lines").        |
+----------------------------------------------------+----------------------------------------------------+
| frame.f_trace_lines                                | Set this attribute to "False" to disable           |
|                                                    | triggering a tracing event for each source line.   |
+----------------------------------------------------+----------------------------------------------------+
| frame.f_trace_opcodes                              | Set this attribute to "True" to allow per-opcode   |
|                                                    | events to be requested. Note that this may lead to |
|                                                    | undefined interpreter behaviour if exceptions      |
|                                                    | raised by the trace function escape to the         |
|                                                    | function being traced.                             |
+----------------------------------------------------+----------------------------------------------------+
| frame.f_lineno                                     | 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 this attribute.      |
+----------------------------------------------------+----------------------------------------------------+


3.2.13.2.3. Frame object methods
""""""""""""""""""""""""""""""""

Frame objects support one method:

frame.clear()

   This method clears all references to local variables held by the
   frame.  Also, if the frame belonged to a *generator*, the generator
   is finalized.  This helps break reference cycles involving frame
   objects (for example when catching an exception and storing its
   traceback for later use).

   "RuntimeError" is raised if the frame is currently executing.

   New in version 3.4.


3.2.13.3. Traceback objects
~~~~~~~~~~~~~~~~~~~~~~~~~~~

Traceback objects represent the stack trace of an exception. A
traceback object is implicitly created when an exception occurs, and
may also be explicitly created by calling "types.TracebackType".

Changed in version 3.7: Traceback objects can now be explicitly
instantiated from Python code.

For implicitly created tracebacks, 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 The try statement.) It is accessible as the
third item of the tuple returned by "sys.exc_info()", and as the
"__traceback__" attribute of the caught exception.

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".

For explicitly created tracebacks, it is up to the creator of the
traceback to determine how the "tb_next" attributes should be linked
to form a full stack trace.

Special read-only attributes:

+----------------------------------------------------+----------------------------------------------------+
| traceback.tb_frame                                 | Points to the execution frame of the current       |
|                                                    | level.  Accessing this attribute raises an         |
|                                                    | auditing event "object.__getattr__" with arguments |
|                                                    | "obj" and ""tb_frame"".                            |
+----------------------------------------------------+----------------------------------------------------+
| traceback.tb_lineno                                | Gives the line number where the exception occurred |
+----------------------------------------------------+----------------------------------------------------+
| traceback.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
"try" statement with no matching except clause or with a "finally"
clause.

traceback.tb_next

   The special writable attribute "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.

   Changed in version 3.7: This attribute is now writable


3.2.13.4. Slice objects
~~~~~~~~~~~~~~~~~~~~~~~

Slice objects are used to represent slices for "__getitem__()"
methods.  They are also created by the built-in "slice()" function.

Special read-only attributes: "start" is the lower bound; "stop" is
the upper bound; "step" is the step value; each is "None" if omitted.
These attributes can have any type.

Slice objects support one method:

slice.indices(self, length)

   This method takes a single integer argument *length* and computes
   information about the 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.


3.2.13.5. 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 also callable. Static method objects are created by
the built-in "staticmethod()" constructor.


3.2.13.6. 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 "instance
methods". Class method objects are created by the built-in
"classmethod()" constructor.


3.3. Special method names
=========================

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
*operator overloading*, allowing classes to define their own behavior
with respect to language operators.  For instance, if a class defines
a method named "__getitem__()", and "x" is an instance of this class,
then "x[i]" is roughly equivalent to "type(x).__getitem__(x, i)".
Except where mentioned, attempts to execute an operation raise an
exception when no appropriate method is defined (typically
"AttributeError" or "TypeError").

Setting a special method to "None" indicates that the corresponding
operation is not available.  For example, if a class sets "__iter__()"
to "None", the class is not iterable, so calling "iter()" on its
instances will raise a "TypeError" (without falling back to
"__getitem__()"). [2]

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
"NodeList" interface in the W3C's Document Object Model.)


3.3.1. Basic customization
--------------------------

object.__new__(cls[, ...])

   Called to create a new instance of class *cls*.  "__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 "__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 "__new__()" method using
   "super().__new__(cls[, ...])" with appropriate arguments and then
   modifying the newly created instance as necessary before returning
   it.

   If "__new__()" is invoked during object construction and it returns
   an instance of *cls*, then the new instance’s "__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 the object constructor.

   If "__new__()" does not return an instance of *cls*, then the new
   instance's "__init__()" method will not be invoked.

   "__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.

object.__init__(self[, ...])

   Called after the instance has been created (by "__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
   "__init__()" method, the derived class's "__init__()" method, if
   any, must explicitly call it to ensure proper initialization of the
   base class part of the instance; for example:
   "super().__init__([args...])".

   Because "__new__()" and "__init__()" work together in constructing
   objects ("__new__()" to create it, and "__init__()" to customize
   it), no non-"None" value may be returned by "__init__()"; doing so
   will cause a "TypeError" to be raised at runtime.

object.__del__(self)

   Called when the instance is about to be destroyed.  This is also
   called a finalizer or (improperly) a destructor.  If a base class
   has a "__del__()" method, the derived class's "__del__()" method,
   if any, must explicitly call it to ensure proper deletion of the
   base class part of the instance.

   It is possible (though not recommended!) for the "__del__()" method
   to postpone destruction of the instance by creating a new reference
   to it.  This is called object *resurrection*.  It is
   implementation-dependent whether "__del__()" is called a second
   time when a resurrected object is about to be destroyed; the
   current *CPython* implementation only calls it once.

   It is not guaranteed that "__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.

   **CPython implementation detail:** It is possible for a reference
   cycle to prevent the reference count of an object from going to
   zero.  In this case, the cycle will be later detected and deleted
   by the *cyclic garbage collector*.  A common cause of reference
   cycles is when an exception has been caught in a local variable.
   The frame's locals then reference the exception, which references
   its own traceback, which references the locals of all frames caught
   in the traceback.

   See also: Documentation for the "gc" module.

   Warning:

     Due to the precarious circumstances under which "__del__()"
     methods are invoked, exceptions that occur during their execution
     are ignored, and a warning is printed to "sys.stderr" instead.
     In particular:

     * "__del__()" can be invoked when arbitrary code is being
       executed, including from any arbitrary thread.  If "__del__()"
       needs to take a lock or invoke any other blocking resource, it
       may deadlock as the resource may already be taken by the code
       that gets interrupted to execute "__del__()".

     * "__del__()" can be executed during interpreter shutdown.  As a
       consequence, the global variables it needs to access (including
       other modules) may already have been deleted or set to "None".
       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 "__del__()" method is called.

object.__repr__(self)

   Called by the "repr()" built-in function 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 "__repr__()" but
   not "__str__()", then "__repr__()" is also used when an "informal"
   string representation of instances of that class is required.

   This is typically used for debugging, so it is important that the
   representation is information-rich and unambiguous.

object.__str__(self)

   Called by "str(object)" and the built-in functions "format()" and
   "print()" to compute the "informal" or nicely printable string
   representation of an object.  The return value must be a string
   object.

   This method differs from "object.__repr__()" in that there is no
   expectation that "__str__()" return a valid Python expression: a
   more convenient or concise representation can be used.

   The default implementation defined by the built-in type "object"
   calls "object.__repr__()".

object.__bytes__(self)

   Called by bytes to compute a byte-string representation of an
   object. This should return a "bytes" object.

object.__format__(self, format_spec)

   Called by the "format()" built-in function, and by extension,
   evaluation of formatted string literals and the "str.format()"
   method, to produce a "formatted" string representation of an
   object. The *format_spec* argument is a string that contains a
   description of the formatting options desired. The interpretation
   of the *format_spec* argument is up to the type implementing
   "__format__()", however most classes will either delegate
   formatting to one of the built-in types, or use a similar
   formatting option syntax.

   See Format Specification Mini-Language for a description of the
   standard formatting syntax.

   The return value must be a string object.

   Changed in version 3.4: The __format__ method of "object" itself
   raises a "TypeError" if passed any non-empty string.

   Changed in version 3.7: "object.__format__(x, '')" is now
   equivalent to "str(x)" rather than "format(str(x), '')".

object.__lt__(self, other)
object.__le__(self, other)
object.__eq__(self, other)
object.__ne__(self, other)
object.__gt__(self, other)
object.__ge__(self, other)

   These are the so-called "rich comparison" methods. 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" calls "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 "bool()"
   on the value to determine if the result is true or false.

   By default, "object" implements "__eq__()" by using "is", returning
   "NotImplemented" in the case of a false comparison: "True if x is y
   else NotImplemented". For "__ne__()", by default it delegates to
   "__eq__()" and inverts the result unless it is "NotImplemented".
   There are no other implied relationships among the comparison
   operators or default implementations; for example, the truth of
   "(x<y or x==y)" does not imply "x<=y". To automatically generate
   ordering operations from a single root operation, see
   "functools.total_ordering()".

   See the paragraph on "__hash__()" for some important notes on
   creating *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, "__lt__()" and "__gt__()" are each other's
   reflection, "__le__()" and "__ge__()" are each other's reflection,
   and "__eq__()" and "__ne__()" are their own reflection. If the
   operands are of different types, and right operand's type is a
   direct or indirect subclass of the left operand's type, the
   reflected method of the right operand has priority, otherwise the
   left operand's method has priority.  Virtual subclassing is not
   considered.

object.__hash__(self)

   Called by built-in function "hash()" and for operations on members
   of hashed collections including "set", "frozenset", and "dict".
   The "__hash__()" method should return an integer. The only required
   property is that objects which compare equal have the same hash
   value; it is advised to mix together the hash values of the
   components of the object that also play a part in comparison of
   objects by packing them into a tuple and hashing the tuple.
   Example:

      def __hash__(self):
          return hash((self.name, self.nick, self.color))

   Note:

     "hash()" truncates the value returned from an object's custom
     "__hash__()" method to the size of a "Py_ssize_t".  This is
     typically 8 bytes on 64-bit builds and 4 bytes on 32-bit builds.
     If an object's   "__hash__()" must interoperate on builds of
     different bit sizes, be sure to check the width on all supported
     builds.  An easy way to do this is with "python -c "import sys;
     print(sys.hash_info.width)"".

   If a class does not define an "__eq__()" method it should not
   define a "__hash__()" operation either; if it defines "__eq__()"
   but not "__hash__()", its instances will not be usable as items in
   hashable collections.  If a class defines mutable objects and
   implements an "__eq__()" method, it should not implement
   "__hash__()", since the implementation of *hashable* collections
   requires that a key's hash value is immutable (if the object's hash
   value changes, it will be in the wrong hash bucket).

   User-defined classes have "__eq__()" and "__hash__()" methods by
   default; with them, all objects compare unequal (except with
   themselves) and "x.__hash__()" returns an appropriate value such
   that "x == y" implies both that "x is y" and "hash(x) == hash(y)".

   A class that overrides "__eq__()" and does not define "__hash__()"
   will have its "__hash__()" implicitly set to "None".  When the
   "__hash__()" method of a class is "None", instances of the class
   will raise an appropriate "TypeError" when a program attempts to
   retrieve their hash value, and will also be correctly identified as
   unhashable when checking "isinstance(obj,
   collections.abc.Hashable)".

   If a class that overrides "__eq__()" needs to retain the
   implementation of "__hash__()" from a parent class, the interpreter
   must be told this explicitly by setting "__hash__ =
   <ParentClass>.__hash__".

   If a class that does not override "__eq__()" wishes to suppress
   hash support, it should include "__hash__ = None" in the class
   definition. A class which defines its own "__hash__()" that
   explicitly raises a "TypeError" would be incorrectly identified as
   hashable by an "isinstance(obj, collections.abc.Hashable)" call.

   Note:

     By default, the "__hash__()" values of str and bytes objects are
     "salted" with an unpredictable random value.  Although they
     remain constant within an individual Python process, they are not
     predictable between repeated invocations of Python.This is
     intended to provide protection against a denial-of-service caused
     by carefully chosen inputs that exploit the worst case
     performance of a dict insertion, *O*(*n*^2) complexity.  See
     http://ocert.org/advisories/ocert-2011-003.html for
     details.Changing hash values affects the iteration order of sets.
     Python has never made guarantees about this ordering (and it
     typically varies between 32-bit and 64-bit builds).See also
     "PYTHONHASHSEED".

   Changed in version 3.3: Hash randomization is enabled by default.

object.__bool__(self)

   Called to implement truth value testing and the built-in operation
   "bool()"; should return "False" or "True".  When this method is not
   defined, "__len__()" is called, if it is defined, and the object is
   considered true if its result is nonzero.  If a class defines
   neither "__len__()" nor "__bool__()", all its instances are
   considered true.


3.3.2. 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.

object.__getattr__(self, name)

   Called when the default attribute access fails with an
   "AttributeError" (either "__getattribute__()" raises an
   "AttributeError" because *name* is not an instance attribute or an
   attribute in the class tree for "self"; or "__get__()" of a *name*
   property raises "AttributeError").  This method should either
   return the (computed) attribute value or raise an "AttributeError"
   exception.

   Note that if the attribute is found through the normal mechanism,
   "__getattr__()" is not called.  (This is an intentional asymmetry
   between "__getattr__()" and "__setattr__()".) This is done both for
   efficiency reasons and because otherwise "__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
   "__getattribute__()" method below for a way to actually get total
   control over attribute access.

object.__getattribute__(self, name)

   Called unconditionally to implement attribute accesses for
   instances of the class. If the class also defines "__getattr__()",
   the latter will not be called unless "__getattribute__()" either
   calls it explicitly or raises an "AttributeError". This method
   should return the (computed) attribute value or raise an
   "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 Special method lookup.

   For certain sensitive attribute accesses, raises an auditing event
   "object.__getattr__" with arguments "obj" and "name".

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.

   If "__setattr__()" wants to assign to an instance attribute, it
   should call the base class method with the same name, for example,
   "object.__setattr__(self, name, value)".

   For certain sensitive attribute assignments, raises an auditing
   event "object.__setattr__" with arguments "obj", "name", "value".

object.__delattr__(self, name)

   Like "__setattr__()" but for attribute deletion instead of
   assignment.  This should only be implemented if "del obj.name" is
   meaningful for the object.

   For certain sensitive attribute deletions, raises an auditing event
   "object.__delattr__" with arguments "obj" and "name".

object.__dir__(self)

   Called when "dir()" is called on the object. A sequence must be
   returned. "dir()" converts the returned sequence to a list and
   sorts it.


3.3.2.1. Customizing module attribute access
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Special names "__getattr__" and "__dir__" can be also used to
customize access to module attributes. The "__getattr__" function at
the module level should accept one argument which is the name of an
attribute and return the computed value or raise an "AttributeError".
If an attribute is not found on a module object through the normal
lookup, i.e. "object.__getattribute__()", then "__getattr__" is
searched in the module "__dict__" before raising an "AttributeError".
If found, it is called with the attribute name and the result is
returned.

The "__dir__" function should accept no arguments, and return a
sequence of strings that represents the names accessible on module. If
present, this function overrides the standard "dir()" search on a
module.

For a more fine grained customization of the module behavior (setting
attributes, properties, etc.), one can set the "__class__" attribute
of a module object to a subclass of "types.ModuleType". For example:

   import sys
   from types import ModuleType

   class VerboseModule(ModuleType):
       def __repr__(self):
           return f'Verbose {self.__name__}'

       def __setattr__(self, attr, value):
           print(f'Setting {attr}...')
           super().__setattr__(attr, value)

   sys.modules[__name__].__class__ = VerboseModule

Note:

  Defining module "__getattr__" and setting module "__class__" only
  affect lookups made using the attribute access syntax -- directly
  accessing the module globals (whether by code within the module, or
  via a reference to the module's globals dictionary) is unaffected.

Changed in version 3.5: "__class__" module attribute is now writable.

New in version 3.7: "__getattr__" and "__dir__" module attributes.

See also:

  **PEP 562** - Module __getattr__ and __dir__
     Describes the "__getattr__" and "__dir__" functions on modules.


3.3.2.2. 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' "__dict__".

object.__get__(self, instance, owner=None)

   Called to get the attribute of the owner class (class attribute
   access) or of an instance of that class (instance attribute
   access). The optional *owner* argument is 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
   "AttributeError" exception.

   **PEP 252** specifies that "__get__()" is callable with one or two
   arguments.  Python's own built-in descriptors support this
   specification; however, it is likely that some third-party tools
   have descriptors that require both arguments.  Python's own
   "__getattribute__()" implementation always passes in both arguments
   whether they are required or not.

object.__set__(self, instance, value)

   Called to set the attribute on an instance *instance* of the owner
   class to a new value, *value*.

   Note, adding "__set__()" or "__delete__()" changes the kind of
   descriptor to a "data descriptor".  See Invoking Descriptors for
   more details.

object.__delete__(self, instance)

   Called to delete the attribute on an instance *instance* of the
   owner class.

Instances of descriptors may also have the "__objclass__" attribute
present:

object.__objclass__

   The attribute "__objclass__" is interpreted by the "inspect" module
   as specifying the class where this object was defined (setting this
   appropriately can assist in runtime introspection of dynamic class
   attributes). For callables, it may indicate that an instance of the
   given type (or a subclass) is expected or required as the first
   positional argument (for example, CPython sets this attribute for
   unbound methods that are implemented in C).


3.3.2.3. 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:  "__get__()", "__set__()", and
"__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.

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 an object instance, "a.x" is transformed into the
   call: "type(a).__dict__['x'].__get__(a, type(a))".

Class Binding
   If binding to a class, "A.x" is transformed into the call:
   "A.__dict__['x'].__get__(None, A)".

Super Binding
   A dotted lookup such as "super(A, a).x" searches
   "a.__class__.__mro__" for a base class "B" following "A" and then
   returns "B.__dict__['x'].__get__(a, A)".  If not a descriptor, "x"
   is returned unchanged.

For instance bindings, the precedence of descriptor invocation depends
on which descriptor methods are defined.  A descriptor can define any
combination of "__get__()", "__set__()" and "__delete__()".  If it
does not define "__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 "__set__()" and/or
"__delete__()", it is a data descriptor; if it defines neither, it is
a non-data descriptor.  Normally, data descriptors define both
"__get__()" and "__set__()", while non-data descriptors have just the
"__get__()" method.  Data descriptors with "__get__()" and "__set__()"
(and/or "__delete__()") defined always override a redefinition in an
instance dictionary.  In contrast, non-data descriptors can be
overridden by instances.

Python methods (including those decorated with "@staticmethod" and
"@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 "property()" function is implemented as a data descriptor.
Accordingly, instances cannot override the behavior of a property.


3.3.2.4. __slots__
~~~~~~~~~~~~~~~~~~

*__slots__* allow us to explicitly declare data members (like
properties) and deny the creation of "__dict__" and *__weakref__*
(unless explicitly declared in *__slots__* or available in a parent.)

The space saved over using "__dict__" can be significant. Attribute
lookup speed can be significantly improved as well.

object.__slots__

   This class variable can be assigned a string, iterable, or sequence
   of strings with variable names used by instances.  *__slots__*
   reserves space for the declared variables and prevents the
   automatic creation of "__dict__" and *__weakref__* for each
   instance.

Notes on using *__slots__*:

* When inheriting from a class without *__slots__*, the "__dict__" and
  *__weakref__* attribute of the instances will always be accessible.

* 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 "AttributeError". If
  dynamic assignment of new variables is desired, then add
  "'__dict__'" to the sequence of strings in the *__slots__*
  declaration.

* 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.

* *__slots__* are implemented at the class level by creating
  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 not limited to the class
  where it is defined.  *__slots__* declared in parents are available
  in child classes. However, child subclasses will get a "__dict__"
  and *__weakref__* unless they also define *__slots__* (which should
  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.

* "TypeError" will be raised if nonempty *__slots__* are defined for a
  class derived from a ""variable-length" built-in type" such as
  "int", "bytes", and "tuple".

* Any non-string *iterable* may be assigned to *__slots__*.

* If a "dictionary" is used to assign *__slots__*, the dictionary keys
  will be used as the slot names. The values of the dictionary can be
  used to provide per-attribute docstrings that will be recognised by
  "inspect.getdoc()" and displayed in the output of "help()".

* "__class__" assignment works only if both classes have the same
  *__slots__*.

* Multiple inheritance with multiple slotted parent classes can be
  used, but only one parent is allowed to have attributes created by
  slots (the other bases must have empty slot layouts) - violations
  raise "TypeError".

* If an *iterator* is used for *__slots__* then a *descriptor* is
  created for each of the iterator's values. However, the *__slots__*
  attribute will be an empty iterator.


3.3.3. Customizing class creation
---------------------------------

Whenever a class inherits from another class, "__init_subclass__()" is
called on the parent class. This way, it is possible to write classes
which change the behavior of subclasses. This is closely related to
class decorators, but where class decorators only affect the specific
class they're applied to, "__init_subclass__" solely applies to future
subclasses of the class defining the method.

classmethod object.__init_subclass__(cls)

   This method is called whenever the containing class is subclassed.
   *cls* is then the new subclass. If defined as a normal instance
   method, this method is implicitly converted to a class method.

   Keyword arguments which are given to a new class are passed to the
   parent class's "__init_subclass__". For compatibility with other
   classes using "__init_subclass__", one should take out the needed
   keyword arguments and pass the others over to the base class, as
   in:

      class Philosopher:
          def __init_subclass__(cls, /, default_name, **kwargs):
              super().__init_subclass__(**kwargs)
              cls.default_name = default_name

      class AustralianPhilosopher(Philosopher, default_name="Bruce"):
          pass

   The default implementation "object.__init_subclass__" does nothing,
   but raises an error if it is called with any arguments.

   Note:

     The metaclass hint "metaclass" is consumed by the rest of the
     type machinery, and is never passed to "__init_subclass__"
     implementations. The actual metaclass (rather than the explicit
     hint) can be accessed as "type(cls)".

   New in version 3.6.

When a class is created, "type.__new__()" scans the class variables
and makes callbacks to those with a "__set_name__()" hook.

object.__set_name__(self, owner, name)

   Automatically called at the time the owning class *owner* is
   created. The object has been assigned to *name* in that class:

      class A:
          x = C()  # Automatically calls: x.__set_name__(A, 'x')

   If the class variable is assigned after the class is created,
   "__set_name__()" will not be called automatically. If needed,
   "__set_name__()" can be called directly:

      class A:
         pass

      c = C()
      A.x = c                  # The hook is not called
      c.__set_name__(A, 'x')   # Manually invoke the hook

   See Creating the class object for more details.

   New in version 3.6.


3.3.3.1. Metaclasses
~~~~~~~~~~~~~~~~~~~~

By default, classes are constructed using "type()". The class body is
executed in a new namespace and the class name is bound locally to the
result of "type(name, bases, namespace)".

The class creation process can be customized by passing the
"metaclass" keyword argument in the class definition line, or by
inheriting from an existing class that included such an argument. In
the following example, both "MyClass" and "MySubclass" are instances
of "Meta":

   class Meta(type):
       pass

   class MyClass(metaclass=Meta):
       pass

   class MySubclass(MyClass):
       pass

Any other keyword arguments that are specified in the class definition
are passed through to all metaclass operations described below.

When a class definition is executed, the following steps occur:

* MRO entries are resolved;

* the appropriate metaclass is determined;

* the class namespace is prepared;

* the class body is executed;

* the class object is created.


3.3.3.2. Resolving MRO entries
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

object.__mro_entries__(self, bases)

   If a base that appears in a class definition is not an instance of
   "type", then an "__mro_entries__()" method is searched on the base.
   If an "__mro_entries__()" method is found, the base is substituted
   with the result of a call to "__mro_entries__()" when creating the
   class. The method is called with the original bases tuple passed to
   the *bases* parameter, and must return a tuple of classes that will
   be used instead of the base. The returned tuple may be empty: in
   these cases, the original base is ignored.

See also:

  "types.resolve_bases()"
     Dynamically resolve bases that are not instances of "type".

  **PEP 560**
     Core support for typing module and generic types.


3.3.3.3. Determining the appropriate metaclass
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The appropriate metaclass for a class definition is determined as
follows:

* if no bases and no explicit metaclass are given, then "type()" is
  used;

* if an explicit metaclass is given and it is *not* an instance of
  "type()", then it is used directly as the metaclass;

* if an instance of "type()" is given as the explicit metaclass, or
  bases are defined, then the most derived metaclass is used.

The most derived metaclass is selected from the explicitly specified
metaclass (if any) and the metaclasses (i.e. "type(cls)") of all
specified base classes. The most derived metaclass is one which is a
subtype of *all* of these candidate metaclasses. If none of the
candidate metaclasses meets that criterion, then the class definition
will fail with "TypeError".


3.3.3.4. Preparing the class namespace
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Once the appropriate metaclass has been identified, then the class
namespace is prepared. If the metaclass has a "__prepare__" attribute,
it is called as "namespace = metaclass.__prepare__(name, bases,
**kwds)" (where the additional keyword arguments, if any, come from
the class definition). The "__prepare__" method should be implemented
as a "classmethod". The namespace returned by "__prepare__" is passed
in to "__new__", but when the final class object is created the
namespace is copied into a new "dict".

If the metaclass has no "__prepare__" attribute, then the class
namespace is initialised as an empty ordered mapping.

See also:

  **PEP 3115** - Metaclasses in Python 3000
     Introduced the "__prepare__" namespace hook


3.3.3.5. Executing the class body
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The class body is executed (approximately) as "exec(body, globals(),
namespace)". The key difference from a normal call to "exec()" is that
lexical scoping allows the class body (including any methods) to
reference names from the current and outer scopes when the class
definition occurs inside a function.

However, even when the class definition occurs inside the function,
methods defined inside the class still cannot see names defined at the
class scope. Class variables must be accessed through the first
parameter of instance or class methods, or through the implicit
lexically scoped "__class__" reference described in the next section.


3.3.3.6. Creating the class object
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Once the class namespace has been populated by executing the class
body, the class object is created by calling "metaclass(name, bases,
namespace, **kwds)" (the additional keywords passed here are the same
as those passed to "__prepare__").

This class object is the one that will be referenced by the zero-
argument form of "super()". "__class__" is an implicit closure
reference created by the compiler if any methods in a class body refer
to either "__class__" or "super". This allows the zero argument form
of "super()" to correctly identify the class being defined based on
lexical scoping, while the class or instance that was used to make the
current call is identified based on the first argument passed to the
method.

**CPython implementation detail:** In CPython 3.6 and later, the
"__class__" cell is passed to the metaclass as a "__classcell__" entry
in the class namespace. If present, this must be propagated up to the
"type.__new__" call in order for the class to be initialised
correctly. Failing to do so will result in a "RuntimeError" in Python
3.8.

When using the default metaclass "type", or any metaclass that
ultimately calls "type.__new__", the following additional
customization steps are invoked after creating the class object:

1. The "type.__new__" method collects all of the attributes in the
   class namespace that define a "__set_name__()" method;

2. Those "__set_name__" methods are called with the class being
   defined and the assigned name of that particular attribute;

3. The "__init_subclass__()" hook is called on the immediate parent of
   the new class in its method resolution order.

After the class object is created, it is passed to the class
decorators included in the class definition (if any) and the resulting
object is bound in the local namespace as the defined class.

When a new class is created by "type.__new__", the object provided as
the namespace parameter is copied to a new ordered mapping and the
original object is discarded. The new copy is wrapped in a read-only
proxy, which becomes the "__dict__" attribute of the class object.

See also:

  **PEP 3135** - New super
     Describes the implicit "__class__" closure reference


3.3.3.7. Uses for metaclasses
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The potential uses for metaclasses are boundless. Some ideas that have
been explored include enum, logging, interface checking, automatic
delegation, automatic property creation, proxies, frameworks, and
automatic resource locking/synchronization.


3.3.4. Customizing instance and subclass checks
-----------------------------------------------

The following methods are used to override the default behavior of the
"isinstance()" and "issubclass()" built-in functions.

In particular, the metaclass "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.

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)".

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.

See also:

  **PEP 3119** - Introducing Abstract Base Classes
     Includes the specification for customizing "isinstance()" and
     "issubclass()" behavior through "__instancecheck__()" and
     "__subclasscheck__()", with motivation for this functionality in
     the context of adding Abstract Base Classes (see the "abc"
     module) to the language.


3.3.5. Emulating generic types
------------------------------

When using *type annotations*, it is often useful to *parameterize* a
*generic type* using Python's square-brackets notation. For example,
the annotation "list[int]" might be used to signify a "list" in which
all the elements are of type "int".

See also:

  **PEP 484** - Type Hints
     Introducing Python's framework for type annotations

  Generic Alias Types
     Documentation for objects representing parameterized generic
     classes

  Generics, user-defined generics and "typing.Generic"
     Documentation on how to implement generic classes that can be
     parameterized at runtime and understood by static type-checkers.

A class can *generally* only be parameterized if it defines the
special class method "__class_getitem__()".

classmethod object.__class_getitem__(cls, key)

   Return an object representing the specialization of a generic class
   by type arguments found in *key*.

   When defined on a class, "__class_getitem__()" is automatically a
   class method. As such, there is no need for it to be decorated with
   "@classmethod" when it is defined.


3.3.5.1. The purpose of *__class_getitem__*
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The purpose of "__class_getitem__()" is to allow runtime
parameterization of standard-library generic classes in order to more
easily apply *type hints* to these classes.

To implement custom generic classes that can be parameterized at
runtime and understood by static type-checkers, users should either
inherit from a standard library class that already implements
"__class_getitem__()", or inherit from "typing.Generic", which has its
own implementation of "__class_getitem__()".

Custom implementations of "__class_getitem__()" on classes defined
outside of the standard library may not be understood by third-party
type-checkers such as mypy. Using "__class_getitem__()" on any class
for purposes other than type hinting is discouraged.


3.3.5.2. *__class_getitem__* versus *__getitem__*
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Usually, the subscription of an object using square brackets will call
the "__getitem__()" instance method defined on the object's class.
However, if the object being subscribed is itself a class, the class
method "__class_getitem__()" may be called instead.
"__class_getitem__()" should return a GenericAlias object if it is
properly defined.

Presented with the *expression* "obj[x]", the Python interpreter
follows something like the following process to decide whether
"__getitem__()" or "__class_getitem__()" should be called:

   from inspect import isclass

   def subscribe(obj, x):
       """Return the result of the expression 'obj[x]'"""

       class_of_obj = type(obj)

       # If the class of obj defines __getitem__,
       # call class_of_obj.__getitem__(obj, x)
       if hasattr(class_of_obj, '__getitem__'):
           return class_of_obj.__getitem__(obj, x)

       # Else, if obj is a class and defines __class_getitem__,
       # call obj.__class_getitem__(x)
       elif isclass(obj) and hasattr(obj, '__class_getitem__'):
           return obj.__class_getitem__(x)

       # Else, raise an exception
       else:
           raise TypeError(
               f"'{class_of_obj.__name__}' object is not subscriptable"
           )

In Python, all classes are themselves instances of other classes. The
class of a class is known as that class's *metaclass*, and most
classes have the "type" class as their metaclass. "type" does not
define "__getitem__()", meaning that expressions such as "list[int]",
"dict[str, float]" and "tuple[str, bytes]" all result in
"__class_getitem__()" being called:

   >>> # list has class "type" as its metaclass, like most classes:
   >>> type(list)
   <class 'type'>
   >>> type(dict) == type(list) == type(tuple) == type(str) == type(bytes)
   True
   >>> # "list[int]" calls "list.__class_getitem__(int)"
   >>> list[int]
   list[int]
   >>> # list.__class_getitem__ returns a GenericAlias object:
   >>> type(list[int])
   <class 'types.GenericAlias'>

However, if a class has a custom metaclass that defines
"__getitem__()", subscribing the class may result in different
behaviour. An example of this can be found in the "enum" module:

   >>> from enum import Enum
   >>> class Menu(Enum):
   ...     """A breakfast menu"""
   ...     SPAM = 'spam'
   ...     BACON = 'bacon'
   ...
   >>> # Enum classes have a custom metaclass:
   >>> type(Menu)
   <class 'enum.EnumMeta'>
   >>> # EnumMeta defines __getitem__,
   >>> # so __class_getitem__ is not called,
   >>> # and the result is not a GenericAlias object:
   >>> Menu['SPAM']
   <Menu.SPAM: 'spam'>
   >>> type(Menu['SPAM'])
   <enum 'Menu'>

See also:

  **PEP 560** - Core Support for typing module and generic types
     Introducing "__class_getitem__()", and outlining when a
     subscription results in "__class_getitem__()" being called
     instead of "__getitem__()"


3.3.6. Emulating callable objects
---------------------------------

object.__call__(self[, args...])

   Called when the instance is "called" as a function; if this method
   is defined, "x(arg1, arg2, ...)" roughly translates to
   "type(x).__call__(x, arg1, ...)".


3.3.7. 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.  It is also recommended that mappings
provide the methods "keys()", "values()", "items()", "get()",
"clear()", "setdefault()", "pop()", "popitem()", "copy()", and
"update()" behaving similar to those for Python's standard
"dictionary" objects.  The "collections.abc" module provides a
"MutableMapping" *abstract base class* to help create those methods
from a base set of "__getitem__()", "__setitem__()", "__delitem__()",
and "keys()". Mutable sequences should provide methods "append()",
"count()", "index()", "extend()", "insert()", "pop()", "remove()",
"reverse()" and "sort()", like Python standard "list" objects.
Finally, sequence types should implement addition (meaning
concatenation) and multiplication (meaning repetition) by defining the
methods "__add__()", "__radd__()", "__iadd__()", "__mul__()",
"__rmul__()" and "__imul__()" described below; they should not define
other numerical operators.  It is recommended that both mappings and
sequences implement the "__contains__()" method to allow efficient use
of the "in" operator; for mappings, "in" should search the mapping's
keys; for sequences, it should search through the values.  It is
further recommended that both mappings and sequences implement the
"__iter__()" method to allow efficient iteration through the
container; for mappings, "__iter__()" should iterate through the
object's keys; for sequences, it should iterate through the values.

object.__len__(self)

   Called to implement the built-in function "len()".  Should return
   the length of the object, an integer ">=" 0.  Also, an object that
   doesn't define a "__bool__()" method and whose "__len__()" method
   returns zero is considered to be false in a Boolean context.

   **CPython implementation detail:** In CPython, the length is
   required to be at most "sys.maxsize". If the length is larger than
   "sys.maxsize" some features (such as "len()") may raise
   "OverflowError".  To prevent raising "OverflowError" by truth value
   testing, an object must define a "__bool__()" method.

object.__length_hint__(self)

   Called to implement "operator.length_hint()". Should return an
   estimated length for the object (which may be greater or less than
   the actual length). The length must be an integer ">=" 0. The
   return value may also be "NotImplemented", which is treated the
   same as if the "__length_hint__" method didn't exist at all. This
   method is purely an optimization and is never required for
   correctness.

   New in version 3.4.

Note:

  Slicing is done exclusively with the following three methods.  A
  call like

     a[1:2] = b

  is translated to

     a[slice(1, 2, None)] = b

  and so forth.  Missing slice items are always filled in with "None".

object.__getitem__(self, key)

   Called to implement evaluation of "self[key]". For *sequence*
   types, the accepted keys should be integers. Optionally, they may
   support "slice" objects as well.  Negative index support is also
   optional. If *key* is of an inappropriate type, "TypeError" may be
   raised; if *key* is a value outside the set of indexes for the
   sequence (after any special interpretation of negative values),
   "IndexError" should be raised. For *mapping* types, if *key* is
   missing (not in the container), "KeyError" should be raised.

   Note:

     "for" loops expect that an "IndexError" will be raised for
     illegal indexes to allow proper detection of the end of the
     sequence.

   Note:

     When subscripting a *class*, the special class method
     "__class_getitem__()" may be called instead of "__getitem__()".
     See __class_getitem__ versus __getitem__ for more details.

object.__setitem__(self, key, value)

   Called to implement assignment to "self[key]".  Same note as for
   "__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 "__getitem__()" method.

object.__delitem__(self, key)

   Called to implement deletion of "self[key]".  Same note as for
   "__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 "__getitem__()" method.

object.__missing__(self, key)

   Called by "dict"."__getitem__()" to implement "self[key]" for dict
   subclasses when key is not in the dictionary.

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.

object.__reversed__(self)

   Called (if present) by the "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 "__reversed__()" method is not provided, the "reversed()"
   built-in will fall back to using the sequence protocol ("__len__()"
   and "__getitem__()").  Objects that support the sequence protocol
   should only provide "__reversed__()" if they can provide an
   implementation that is more efficient than the one provided by
   "reversed()".

The membership test operators ("in" and "not in") are normally
implemented as an iteration through a container. However, container
objects can supply the following special method with a more efficient
implementation, which also does not require the object be iterable.

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 "__contains__()", the membership test
   first tries iteration via "__iter__()", then the old sequence
   iteration protocol via "__getitem__()", see this section in the
   language reference.


3.3.8. 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.

object.__add__(self, other)
object.__sub__(self, other)
object.__mul__(self, other)
object.__matmul__(self, other)
object.__truediv__(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)

   These methods are called to implement the binary arithmetic
   operations ("+", "-", "*", "@", "/", "//", "%", "divmod()",
   "pow()", "**", "<<", ">>", "&", "^", "|").  For instance, to
   evaluate the expression "x + y", where *x* is an instance of a
   class that has an "__add__()" method, "type(x).__add__(x, y)" is
   called.  The "__divmod__()" method should be the equivalent to
   using "__floordiv__()" and "__mod__()"; it should not be related to
   "__truediv__()".  Note that "__pow__()" should be defined to accept
   an optional third argument if the ternary version of the built-in
   "pow()" function is to be supported.

   If one of those methods does not support the operation with the
   supplied arguments, it should return "NotImplemented".

object.__radd__(self, other)
object.__rsub__(self, other)
object.__rmul__(self, other)
object.__rmatmul__(self, other)
object.__rtruediv__(self, other)
object.__rfloordiv__(self, other)
object.__rmod__(self, other)
object.__rdivmod__(self, other)
object.__rpow__(self, other[, modulo])
object.__rlshift__(self, other)
object.__rrshift__(self, other)
object.__rand__(self, other)
object.__rxor__(self, other)
object.__ror__(self, other)

   These methods are called to implement the binary arithmetic
   operations ("+", "-", "*", "@", "/", "//", "%", "divmod()",
   "pow()", "**", "<<", ">>", "&", "^", "|") with reflected (swapped)
   operands.  These functions are only called if the left operand does
   not support the corresponding operation [3] and the operands are of
   different types. [4] For instance, to evaluate the expression "x -
   y", where *y* is an instance of a class that has an "__rsub__()"
   method, "type(y).__rsub__(y, x)" is called if "type(x).__sub__(x,
   y)" returns *NotImplemented*.

   Note that ternary "pow()" will not try calling "__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 a different implementation of 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.

object.__iadd__(self, other)
object.__isub__(self, other)
object.__imul__(self, other)
object.__imatmul__(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, if *x* is an instance of a class
   with an "__iadd__()" method, "x += y" is equivalent to "x =
   x.__iadd__(y)" . Otherwise, "x.__add__(y)" and "y.__radd__(x)" are
   considered, as with the evaluation of "x + y". In certain
   situations, augmented assignment can result in unexpected errors
   (see Why does a_tuple[i] += ['item'] raise an exception when the
   addition works?), but this behavior is in fact part of the data
   model.

object.__neg__(self)
object.__pos__(self)
object.__abs__(self)
object.__invert__(self)

   Called to implement the unary arithmetic operations ("-", "+",
   "abs()" and "~").

object.__complex__(self)
object.__int__(self)
object.__float__(self)

   Called to implement the built-in functions "complex()", "int()" and
   "float()".  Should return a value of the appropriate type.

object.__index__(self)

   Called to implement "operator.index()", and whenever Python needs
   to losslessly convert the numeric object to an integer object (such
   as in slicing, or in the built-in "bin()", "hex()" and "oct()"
   functions). Presence of this method indicates that the numeric
   object is an integer type.  Must return an integer.

   If "__int__()", "__float__()" and "__complex__()" are not defined
   then corresponding built-in functions "int()", "float()" and
   "complex()" fall back to "__index__()".

object.__round__(self[, ndigits])
object.__trunc__(self)
object.__floor__(self)
object.__ceil__(self)

   Called to implement the built-in function "round()" and "math"
   functions "trunc()", "floor()" and "ceil()". Unless *ndigits* is
   passed to "__round__()" all these methods should return the value
   of the object truncated to an "Integral" (typically an "int").

   The built-in function "int()" falls back to "__trunc__()" if
   neither "__int__()" nor "__index__()" is defined.

   Changed in version 3.11: The delegation of "int()" to "__trunc__()"
   is deprecated.


3.3.9. With Statement Context Managers
--------------------------------------

A *context manager* is an object that defines the runtime context to
be established when executing a "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 "with" statement (described in section The with
statement), but can also be used by directly invoking their methods.

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 Context Manager Types.

object.__enter__(self)

   Enter the runtime context related to this object. The "with"
   statement will bind this method's return value to the target(s)
   specified in the "as" clause of the statement, if any.

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 "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 "__exit__()" methods should not reraise the passed-in
   exception; this is the caller's responsibility.

See also:

  **PEP 343** - The "with" statement
     The specification, background, and examples for the Python "with"
     statement.


3.3.10. Customizing positional arguments in class pattern matching
------------------------------------------------------------------

When using a class name in a pattern, positional arguments in the
pattern are not allowed by default, i.e. "case MyClass(x, y)" is
typically invalid without special support in "MyClass". To be able to
use that kind of pattern, the class needs to define a *__match_args__*
attribute.

object.__match_args__

   This class variable can be assigned a tuple of strings. When this
   class is used in a class pattern with positional arguments, each
   positional argument will be converted into a keyword argument,
   using the corresponding value in *__match_args__* as the keyword.
   The absence of this attribute is equivalent to setting it to "()".

For example, if "MyClass.__match_args__" is "("left", "center",
"right")" that means that "case MyClass(x, y)" is equivalent to "case
MyClass(left=x, center=y)". Note that the number of arguments in the
pattern must be smaller than or equal to the number of elements in
*__match_args__*; if it is larger, the pattern match attempt will
raise a "TypeError".

New in version 3.10.

See also:

  **PEP 634** - Structural Pattern Matching
     The specification for the Python "match" statement.


3.3.11. Special method lookup
-----------------------------

For custom 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:

   >>> class C:
   ...     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 "__hash__()" and "__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 "__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 "__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).


3.4. Coroutines
===============


3.4.1. Awaitable Objects
------------------------

An *awaitable* object generally implements an "__await__()" method.
*Coroutine objects* returned from "async def" functions are awaitable.

Note:

  The *generator iterator* objects returned from generators decorated
  with "types.coroutine()" are also awaitable, but they do not
  implement "__await__()".

object.__await__(self)

   Must return an *iterator*.  Should be used to implement *awaitable*
   objects.  For instance, "asyncio.Future" implements this method to
   be compatible with the "await" expression.

   Note:

     The language doesn't place any restriction on the type or value
     of the objects yielded by the iterator returned by "__await__",
     as this is specific to the implementation of the asynchronous
     execution framework (e.g. "asyncio") that will be managing the
     *awaitable* object.

New in version 3.5.

See also:

  **PEP 492** for additional information about awaitable objects.


3.4.2. Coroutine Objects
------------------------

*Coroutine objects* are *awaitable* objects. A coroutine's execution
can be controlled by calling "__await__()" and iterating over the
result.  When the coroutine has finished executing and returns, the
iterator raises "StopIteration", and the exception's "value" attribute
holds the return value.  If the coroutine raises an exception, it is
propagated by the iterator.  Coroutines should not directly raise
unhandled "StopIteration" exceptions.

Coroutines also have the methods listed below, which are analogous to
those of generators (see Generator-iterator methods).  However, unlike
generators, coroutines do not directly support iteration.

Changed in version 3.5.2: It is a "RuntimeError" to await on a
coroutine more than once.

coroutine.send(value)

   Starts or resumes execution of the coroutine.  If *value* is
   "None", this is equivalent to advancing the iterator returned by
   "__await__()".  If *value* is not "None", this method delegates to
   the "send()" method of the iterator that caused the coroutine to
   suspend.  The result (return value, "StopIteration", or other
   exception) is the same as when iterating over the "__await__()"
   return value, described above.

coroutine.throw(value)
coroutine.throw(type[, value[, traceback]])

   Raises the specified exception in the coroutine.  This method
   delegates to the "throw()" method of the iterator that caused the
   coroutine to suspend, if it has such a method.  Otherwise, the
   exception is raised at the suspension point.  The result (return
   value, "StopIteration", or other exception) is the same as when
   iterating over the "__await__()" return value, described above.  If
   the exception is not caught in the coroutine, it propagates back to
   the caller.

coroutine.close()

   Causes the coroutine to clean itself up and exit.  If the coroutine
   is suspended, this method first delegates to the "close()" method
   of the iterator that caused the coroutine to suspend, if it has
   such a method.  Then it raises "GeneratorExit" at the suspension
   point, causing the coroutine to immediately clean itself up.
   Finally, the coroutine is marked as having finished executing, even
   if it was never started.

   Coroutine objects are automatically closed using the above process
   when they are about to be destroyed.


3.4.3. Asynchronous Iterators
-----------------------------

An *asynchronous iterator* can call asynchronous code in its
"__anext__" method.

Asynchronous iterators can be used in an "async for" statement.

object.__aiter__(self)

   Must return an *asynchronous iterator* object.

object.__anext__(self)

   Must return an *awaitable* resulting in a next value of the
   iterator.  Should raise a "StopAsyncIteration" error when the
   iteration is over.

An example of an asynchronous iterable object:

   class Reader:
       async def readline(self):
           ...

       def __aiter__(self):
           return self

       async def __anext__(self):
           val = await self.readline()
           if val == b'':
               raise StopAsyncIteration
           return val

New in version 3.5.

Changed in version 3.7: Prior to Python 3.7, "__aiter__()" could
return an *awaitable* that would resolve to an *asynchronous
iterator*.Starting with Python 3.7, "__aiter__()" must return an
asynchronous iterator object.  Returning anything else will result in
a "TypeError" error.


3.4.4. Asynchronous Context Managers
------------------------------------

An *asynchronous context manager* is a *context manager* that is able
to suspend execution in its "__aenter__" and "__aexit__" methods.

Asynchronous context managers can be used in an "async with"
statement.

object.__aenter__(self)

   Semantically similar to "__enter__()", the only difference being
   that it must return an *awaitable*.

object.__aexit__(self, exc_type, exc_value, traceback)

   Semantically similar to "__exit__()", the only difference being
   that it must return an *awaitable*.

An example of an asynchronous context manager class:

   class AsyncContextManager:
       async def __aenter__(self):
           await log('entering context')

       async def __aexit__(self, exc_type, exc, tb):
           await log('exiting context')

New in version 3.5.

-[ Footnotes ]-

[1] 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.

[2] The "__hash__()", "__iter__()", "__reversed__()", and
    "__contains__()" methods have special handling for this; others
    will still raise a "TypeError", but may do so by relying on the
    behavior that "None" is not callable.

[3] "Does not support" here means that the class has no such method,
    or the method returns "NotImplemented".  Do not set the method to
    "None" if you want to force fallback to the right operand's
    reflected method—that will instead have the opposite effect of
    explicitly *blocking* such fallback.

[4] For operands of the same type, it is assumed that if the non-
    reflected method -- such as "__add__()" -- fails then the overall
    operation is not supported, which is why the reflected method is
    not called.
