
Data model
**********


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 (ex:
always close files).

Note that the use of the implementation's tracing or debugging
facilities may keep objects alive that would normally be collectable.
Also note that catching an exception with a '"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".)


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.

None
   This type has a single value.  There is a single object with this
   value. This object is accessed through the built-in name "None". It
   is used to signify the absence of a value in many situations, e.g.,
   it is returned from functions that don't explicitly return
   anything. Its truth value is false.

NotImplemented
   This type has a single value.  There is a single object with this
   value. This object is accessed through the built-in name
   "NotImplemented". Numeric methods and rich comparison methods may
   return this value if they do not implement the operation for the
   operands provided.  (The interpreter will then try the reflected
   operation, or some other fallback, depending on the operator.)  Its
   truth value is true.

Ellipsis
   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.

"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.

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

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

      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.

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

   "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 is
      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.

   "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".

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:

   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
         codepoints. All the codepoints in range "U+0000 - U+10FFFF"
         can be represented in a string.  Python doesn't have a "chr"
         type, and every character in the string is represented as a
         string object with length "1".  The built-in function "ord()"
         converts a character to its codepoint (as an integer);
         "chr()" converts an integer in range "0 - 10FFFF" to the
         corresponding character. "str.encode()" can be used to
         convert a "str" to "bytes" using the given 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 function
         "bytes()" can be used to construct bytes objects.  Also,
         bytes objects can be decoded to strings via the "decode()"
         method.

   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.

      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.

      The extension module "array" provides an additional example of a
      mutable sequence type, as does the "collections" module.

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.

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:

   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 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.

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

   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.

      Special attributes:

      +---------------------------+---------------------------------+-------------+
      +===========================+=================================+=============+
      | "__doc__"                 | The function's documentation    | Writable    |
      +---------------------------+---------------------------------+-------------+
      | "__name__"                | The function's name             | Writable    |
      +---------------------------+---------------------------------+-------------+
      | "__qualname__"            | The function's *qualified name* | Writable    |
      +---------------------------+---------------------------------+-------------+
      | "__module__"              | The name of the module the      | Writable    |
      +---------------------------+---------------------------------+-------------+
      | "__defaults__"            | A tuple containing default      | Writable    |
      +---------------------------+---------------------------------+-------------+
      | "__code__"                | The code object representing    | Writable    |
      +---------------------------+---------------------------------+-------------+
      | "__globals__"             | A reference to the dictionary   | Read-only   |
      +---------------------------+---------------------------------+-------------+
      | "__dict__"                | The namespace supporting        | Writable    |
      +---------------------------+---------------------------------+-------------+
      | "__closure__"             | "None" or a tuple of cells that | Read-only   |
      +---------------------------+---------------------------------+-------------+
      | "__annotations__"         | A dict containing annotations   | Writable    |
      +---------------------------+---------------------------------+-------------+
      | "__kwdefaults__"          | A dict containing defaults for  | Writable    |
      +---------------------------+---------------------------------+-------------+

      Most of the attributes labelled "Writable" check the type of the
      assigned value.

      Function objects also support getting and setting arbitrary
      attributes, which can be used, for example, to attach metadata
      to functions.  Regular attribute dot-notation is used to get and
      set such attributes. *Note that the current implementation only
      supports function attributes on user-defined functions. Function
      attributes on built-in functions may be supported in the
      future.*

      Additional information about a function's definition can be
      retrieved from its code object; see the description of internal
      types below.

   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: "__self__" is the class instance
      object, "__func__" is the function object; "__doc__" is the
      method's documentation (same as "__func__.__doc__"); "__name__"
      is the method name (same as "__func__.__name__"); "__module__"
      is 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 class
      method 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 a user-defined method object is created by retrieving
      another method object from a class or instance, the behaviour is
      the same as for a function object, except that the "__func__"
      attribute of the new instance is not the original method object
      but its "__func__" attribute.

      When an instance method object is created by retrieving a class
      method 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 class method
      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.

   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.

   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; "__name__" is the function's
      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.

   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*.

   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.

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

Modules
   Modules are a basic organizational unit of Python code, and are
   created by the *import system* as invoked either by the "import"
   statement (see "import"), 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".

   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.

   Predefined (writable) attributes: "__name__" is the module's name;
   "__doc__" is the module's documentation string, or "None" if
   unavailable; "__file__" is 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 is
   the pathname of the shared library file.

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
   http://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__" attributes is "C".  When it would yield a
   static method 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__" is the class name; "__module__" is
   the module name in which the class was defined; "__dict__" is the
   dictionary containing the class's namespace; "__bases__" is a tuple
   (possibly empty or a singleton) containing the base classes, in the
   order of their occurrence in the base class list; "__doc__" is the
   class's documentation string, or None if undefined.

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.

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.

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.

   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.

      Special read-only attributes: "co_name" gives the function name;
      "co_argcount" is the number of positional arguments (including
      arguments with default values); "co_nlocals" is the number of
      local variables used by the function (including arguments);
      "co_varnames" is a tuple containing the names of the local
      variables (starting with the argument names); "co_cellvars" is a
      tuple containing the names of local variables that are
      referenced by nested functions; "co_freevars" is a tuple
      containing the names of free variables; "co_code" is a string
      representing the sequence of bytecode instructions; "co_consts"
      is a tuple containing the literals used by the bytecode;
      "co_names" is a tuple containing the names used by the bytecode;
      "co_filename" is the filename from which the code was compiled;
      "co_firstlineno" is the first line number of the function;
      "co_lnotab" is a string encoding the mapping from bytecode
      offsets to line numbers (for details see the source code of the
      interpreter); "co_stacksize" is the required stack size
      (including local variables); "co_flags" is 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.

      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.

   Frame objects
      Frame objects represent execution frames.  They may occur in
      traceback objects (see below).

      Special read-only attributes: "f_back" is to the previous stack
      frame (towards the caller), or "None" if this is the bottom
      stack frame; "f_code" is the code object being executed in this
      frame; "f_locals" is the dictionary used to look up local
      variables; "f_globals" is used for global variables;
      "f_builtins" is used for built-in (intrinsic) names; "f_lasti"
      gives the precise instruction (this is an index into the
      bytecode string of the code object).

      Special writable attributes: "f_trace", if not "None", is a
      function called at the start of each source code line (this is
      used by the debugger); "f_lineno" is the current line number of
      the frame --- writing to this from within a trace function jumps
      to the given line (only for the bottom-most frame).  A debugger
      can implement a Jump command (aka Set Next Statement) by writing
      to f_lineno.

   Traceback objects
      Traceback objects represent a stack trace of an exception.  A
      traceback object is created when an exception occurs.  When the
      search for an exception handler unwinds the execution stack, at
      each unwound level a traceback object is inserted in front of
      the current traceback.  When an exception handler is entered,
      the stack trace is made available to the program. (See section
      *The try statement*.) It is accessible as the third item of the
      tuple returned by "sys.exc_info()". 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".

      Special read-only attributes: "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; "tb_frame" points to the
      execution frame of the current level; "tb_lineno" gives the line
      number where the exception occurred; "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.

   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.

   Static method objects
      Static method objects provide a way of defeating the
      transformation of function objects to method objects described
      above. A static method object is a wrapper around any other
      object, usually a user-defined method object. When a static
      method object is retrieved from a class or a class instance, the
      object actually returned is the wrapped object, which is not
      subject to any further transformation. Static method objects are
      not themselves callable, although the objects they wrap usually
      are. Static method objects are created by the built-in
      "staticmethod()" constructor.

   Class method objects
      A class method object, like a static method object, is a wrapper
      around another object that alters the way in which that object
      is retrieved from classes and class instances. The behaviour of
      class method objects upon such retrieval is described above,
      under "User-defined methods". Class method objects are created
      by the built-in "classmethod()" constructor.


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").

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.)


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(currentclass, cls).__new__(cls[, ...])" with appropriate
   arguments and then modifying the newly-created instance as
   necessary before returning it.

   If "__new__()" 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 "__new__()".

   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 when the instance is created.  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:
   "BaseClass.__init__(self, [args...])".  As a special constraint on
   constructors, no value may be returned; 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 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.
   Note that it is possible (though not recommended!) for the
   "__del__()" method to postpone destruction of the instance by
   creating a new reference to it.  It may then be called at a later
   time when this new reference is deleted.  It is not guaranteed that
   "__del__()" methods are called for objects that still exist when
   the interpreter exits.

   Note: "del x" doesn't directly call "x.__del__()" --- the former
     decrements the reference count for "x" by one, and the latter is
     only called when "x"'s reference count reaches zero.  Some common
     situations that may prevent the reference count of an object from
     going to zero include: circular references between objects (e.g.,
     a doubly-linked list or a tree data structure with parent and
     child pointers); a reference to the object on the stack frame of
     a function that caught an exception (the traceback stored in
     "sys.exc_info()[2]" keeps the stack frame alive); or a reference
     to the object on the stack frame that raised an unhandled
     exception in interactive mode (the traceback stored in
     "sys.last_traceback" keeps the stack frame alive).  The first
     situation can only be remedied by explicitly breaking the cycles;
     the latter two situations can be resolved by storing "None" in
     "sys.last_traceback". Circular references which are garbage are
     detected when the option cycle detector is enabled (it's on by
     default), but can only be cleaned up if there are no Python-
     level "__del__()" methods involved. Refer to the documentation
     for the "gc" module for more information about how "__del__()"
     methods are handled by the cycle detector, particularly the
     description of the "garbage" value.

   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. Also, when "__del__()" is invoked in
     response to a module being deleted (e.g., when execution of the
     program is done), other globals referenced by the "__del__()"
     method may already have been deleted or in the process of being
     torn down (e.g. the import machinery shutting down).  For this
     reason, "__del__()" methods should do the absolute minimum needed
     to maintain external invariants.  Starting with version 1.5,
     Python guarantees that globals whose name begins with a single
     underscore are deleted from their module before other globals are
     deleted; if no other references to such globals exist, this may
     help in assuring that imported modules are still available at the
     time when the "__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, the
   "str.format()" method of class "str") 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.

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.

   There are no implied relationships among the comparison operators.
   The truth of "x==y" does not imply that "x!=y" is false.
   Accordingly, when defining "__eq__()", one should also define
   "__ne__()" so that the operators will behave as expected.  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.

   Arguments to rich comparison methods are never coerced.

   To automatically generate ordering operations from a single root
   operation, see "functools.total_ordering()".

object.__hash__(self)

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

   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.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.Hashable)" call.

   Note: By default, the "__hash__()" values of str, bytes and
     datetime 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://www.ocert.org/advisories/ocert-2011-003.html for
     details.Changing hash values affects the iteration order of
     dicts, sets and other mappings.  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.


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 an attribute lookup has not found the attribute in the
   usual places (i.e. it is not an instance attribute nor is it found
   in the class tree for "self").  "name" is the attribute name. This
   method should return the (computed) attribute value or raise an
   "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*.

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)".

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.

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.


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)

   Called to get the attribute of the owner class (class attribute
   access) or of an instance of that class (instance attribute
   access). *owner* is always the owner class, while *instance* is the
   instance that the attribute was accessed through, or "None" when
   the attribute is accessed through the *owner*.  This method should
   return the (computed) attribute value or raise an "AttributeError"
   exception.

object.__set__(self, instance, value)

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

object.__delete__(self, instance)

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


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
   If "a" is an instance of "super", then the binding "super(B,
   obj).m()" searches "obj.__class__.__mro__" for the base class "A"
   immediately preceding "B" and then invokes the descriptor with the
   call: "A.__dict__['m'].__get__(obj, obj.__class__)".

For instance bindings, the precedence of descriptor invocation depends
on the which descriptor methods are defined.  A descriptor can define
any combination of "__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 "__set__()" and "__get__()"
defined always override a redefinition in an instance dictionary.  In
contrast, non-data descriptors can be overridden by instances.

Python methods (including "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.


__slots__
~~~~~~~~~

By default, instances of classes have a dictionary for attribute
storage.  This wastes space for objects having very few instance
variables.  The space consumption can become acute when creating large
numbers of instances.

The default can be overridden by defining *__slots__* in a class
definition. The *__slots__* declaration takes a sequence of instance
variables and reserves just enough space in each instance to hold a
value for each variable.  Space is saved because *__dict__* is not
created for each instance.

object.__slots__

   This class variable can be assigned a string, iterable, or sequence
   of strings with variable names used by instances.  If defined in a
   class, *__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__*
  attribute of that class will always be accessible, so a *__slots__*
  definition in the subclass is meaningless.

* Without a *__dict__* variable, instances cannot be assigned new
  variables not listed in the *__slots__* definition.  Attempts to
  assign to an unlisted variable name raises "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 (*Implementing Descriptors*) for each variable name.  As
  a result, class attributes cannot be used to set default values for
  instance variables defined by *__slots__*; otherwise, the class
  attribute would overwrite the descriptor assignment.

* The action of a *__slots__* declaration is limited to the class
  where it is defined.  As a result, subclasses will have a *__dict__*
  unless they also define *__slots__* (which must only contain names
  of any *additional* slots).

* If a class defines a slot also defined in a base class, the
  instance variable defined by the base class slot is inaccessible
  (except by retrieving its descriptor directly from the base class).
  This renders the meaning of the program undefined.  In the future, a
  check may be added to prevent this.

* Nonempty *__slots__* does not work for classes derived from
  "variable-length" built-in types such as "int", "bytes" and "tuple".

* Any non-string iterable may be assigned to *__slots__*. Mappings
  may also be used; however, in the future, special meaning may be
  assigned to the values corresponding to each key.

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


Customizing class creation
--------------------------

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 customised 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:

* the appropriate metaclass is determined

* the class namespace is prepared

* the class body is executed

* the class object is created


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".


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).

If the metaclass has no "__prepare__" attribute, then the class
namespace is initialised as an empty "dict()" instance.

See also: **PEP 3115** - Metaclasses in Python 3000

     Introduced the "__prepare__" namespace hook


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, and cannot be accessed at all
from static methods.


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.

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.

See also: **PEP 3135** - New super

     Describes the implicit "__class__" closure reference


Metaclass example
~~~~~~~~~~~~~~~~~

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

Here is an example of a metaclass that uses an
"collections.OrderedDict" to remember the order that class members
were defined:

   class OrderedClass(type):

        @classmethod
        def __prepare__(metacls, name, bases, **kwds):
           return collections.OrderedDict()

        def __new__(cls, name, bases, namespace, **kwds):
           result = type.__new__(cls, name, bases, dict(namespace))
           result.members = tuple(namespace)
           return result

   class A(metaclass=OrderedClass):
       def one(self): pass
       def two(self): pass
       def three(self): pass
       def four(self): pass

   >>> A.members
   ('__module__', 'one', 'two', 'three', 'four')

When the class definition for *A* gets executed, the process begins
with calling the metaclass's "__prepare__()" method which returns an
empty "collections.OrderedDict".  That mapping records the methods and
attributes of *A* as they are defined within the body of the class
statement. Once those definitions are executed, the ordered dictionary
is fully populated and the metaclass's "__new__()" method gets
invoked.  That method builds the new type and it saves the ordered
dictionary keys in an attribute called "members".


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.


Emulating callable objects
--------------------------

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

   Called when the instance is "called" as a function; if this method
   is defined, "x(arg1, arg2, ...)" is a shorthand for
   "x.__call__(arg1, arg2, ...)".


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" 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 be the same as "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.

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 and slice objects.  Note that
   the special interpretation of negative indexes (if the class wishes
   to emulate a sequence type) is up to the "__getitem__()" method. If
   *key* is of an inappropriate type, "TypeError" may be raised; if of
   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.

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.__iter__(self)

   This method is called when an iterator is required for a container.
   This method should return a new iterator object that can iterate
   over all the objects in the container.  For mappings, it should
   iterate over the keys of the container, and should also be made
   available as the method "keys()".

   Iterator objects also need to implement this method; they are
   required to return themselves.  For more information on iterator
   objects, see *Iterator Types*.

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 sequence.  However, container
objects can supply the following special method with a more efficient
implementation, which also does not require the object be a sequence.

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*.


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.__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, "x.__add__(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.__rtruediv__(self, other)
object.__rfloordiv__(self, other)
object.__rmod__(self, other)
object.__rdivmod__(self, other)
object.__rpow__(self, other)
object.__rlshift__(self, other)
object.__rrshift__(self, other)
object.__rand__(self, other)
object.__rxor__(self, other)
object.__ror__(self, other)

   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 and the operands are of
   different types. [2]  For instance, to evaluate the expression "x -
   y", where *y* is an instance of a class that has an "__rsub__()"
   method, "y.__rsub__(x)" is called if "x.__sub__(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 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.__itruediv__(self, other)
object.__ifloordiv__(self, other)
object.__imod__(self, other)
object.__ipow__(self, other[, modulo])
object.__ilshift__(self, other)
object.__irshift__(self, other)
object.__iand__(self, other)
object.__ixor__(self, other)
object.__ior__(self, other)

   These methods are called to implement the augmented arithmetic
   assignments ("+=", "-=", "*=", "/=", "//=", "%=", "**=", "<<=",
   ">>=", "&=", "^=", "|=").  These methods should attempt to do the
   operation in-place (modifying *self*) and return the result (which
   could be, but does not have to be, *self*).  If a specific method
   is not defined, the augmented assignment falls back to the normal
   methods.  For instance, to execute the statement "x += y", where
   *x* is an instance of a class that has an "__iadd__()" method,
   "x.__iadd__(y)" is called.  If *x* is an instance of a class that
   does not define a "__iadd__()" method, "x.__add__(y)" and
   "y.__radd__(x)" are considered, as with the evaluation of "x + y".

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)
object.__round__(self[, n])

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

object.__index__(self)

   Called to implement "operator.index()".  Also called whenever
   Python needs an integer object (such as in slicing, or in the
   built-in "bin()", "hex()" and "oct()" functions). Must return an
   integer.


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 0343** - The "with" statement

     The specification, background, and examples for the Python "with"
     statement.


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).

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