
Built-in Types
**************

The following sections describe the standard types that are built into
the interpreter.

Note: Historically (until release 2.2), Python's built-in types have
  differed from user-defined types because it was not possible to use
  the built-in types as the basis for object-oriented inheritance.
  This limitation no longer exists.

The principal built-in types are numerics, sequences, mappings, files,
classes, instances and exceptions.

Some operations are supported by several object types; in particular,
practically all objects can be compared, tested for truth value, and
converted to a string (with the ``repr()`` function or the slightly
different ``str()`` function).  The latter function is implicitly used
when an object is written by the ``print()`` function.


Truth Value Testing
===================

Any object can be tested for truth value, for use in an ``if`` or
``while`` condition or as operand of the Boolean operations below. The
following values are considered false:

* ``None``

* ``False``

* zero of any numeric type, for example, ``0``, ``0L``, ``0.0``,
  ``0j``.

* any empty sequence, for example, ``''``, ``()``, ``[]``.

* any empty mapping, for example, ``{}``.

* instances of user-defined classes, if the class defines a
  ``__nonzero__()`` or ``__len__()`` method, when that method returns
  the integer zero or ``bool`` value ``False``. [1]

All other values are considered true --- so objects of many types are
always true.

Operations and built-in functions that have a Boolean result always
return ``0`` or ``False`` for false and ``1`` or ``True`` for true,
unless otherwise stated. (Important exception: the Boolean operations
``or`` and ``and`` always return one of their operands.)


Boolean Operations --- ``and``, ``or``, ``not``
===============================================

These are the Boolean operations, ordered by ascending priority:

+---------------+-----------------------------------+---------+
| Operation     | Result                            | Notes   |
+===============+===================================+=========+
| ``x or y``    | if *x* is false, then *y*, else   | (1)     |
|               | *x*                               |         |
+---------------+-----------------------------------+---------+
| ``x and y``   | if *x* is false, then *x*, else   | (2)     |
|               | *y*                               |         |
+---------------+-----------------------------------+---------+
| ``not x``     | if *x* is false, then ``True``,   | (3)     |
|               | else ``False``                    |         |
+---------------+-----------------------------------+---------+

Notes:

1. This is a short-circuit operator, so it only evaluates the second
   argument if the first one is ``False``.

2. This is a short-circuit operator, so it only evaluates the second
   argument if the first one is ``True``.

3. ``not`` has a lower priority than non-Boolean operators, so ``not a
   == b`` is interpreted as ``not (a == b)``, and ``a == not b`` is a
   syntax error.


Comparisons
===========

Comparison operations are supported by all objects.  They all have the
same priority (which is higher than that of the Boolean operations).
Comparisons can be chained arbitrarily; for example, ``x < y <= z`` is
equivalent to ``x < y and y <= z``, except that *y* is evaluated only
once (but in both cases *z* is not evaluated at all when ``x < y`` is
found to be false).

This table summarizes the comparison operations:

+--------------+---------------------------+---------+
| Operation    | Meaning                   | Notes   |
+==============+===========================+=========+
| ``<``        | strictly less than        |         |
+--------------+---------------------------+---------+
| ``<=``       | less than or equal        |         |
+--------------+---------------------------+---------+
| ``>``        | strictly greater than     |         |
+--------------+---------------------------+---------+
| ``>=``       | greater than or equal     |         |
+--------------+---------------------------+---------+
| ``==``       | equal                     |         |
+--------------+---------------------------+---------+
| ``!=``       | not equal                 | (1)     |
+--------------+---------------------------+---------+
| ``is``       | object identity           |         |
+--------------+---------------------------+---------+
| ``is not``   | negated object identity   |         |
+--------------+---------------------------+---------+

Notes:

1. ``!=`` can also be written ``<>``, but this is an obsolete usage
   kept for backwards compatibility only. New code should always use
   ``!=``.

Objects of different types, except different numeric types and
different string types, never compare equal; such objects are ordered
consistently but arbitrarily (so that sorting a heterogeneous array
yields a consistent result). Furthermore, some types (for example,
file objects) support only a degenerate notion of comparison where any
two objects of that type are unequal.  Again, such objects are ordered
arbitrarily but consistently. The ``<``, ``<=``, ``>`` and ``>=``
operators will raise a ``TypeError`` exception when any operand is a
complex number.

Instances of a class normally compare as non-equal unless the class
defines the ``__cmp__()`` method.  Refer to *Basic customization*) for
information on the use of this method to effect object comparisons.

**Implementation note:** Objects of different types except numbers are
ordered by their type names; objects of the same types that don't
support proper comparison are ordered by their address.

Two more operations with the same syntactic priority, ``in`` and ``not
in``, are supported only by sequence types (below).


Numeric Types --- ``int``, ``float``, ``long``, ``complex``
===========================================================

There are four distinct numeric types: *plain integers*, *long
integers*,  *floating point numbers*, and *complex numbers*. In
addition, Booleans are a subtype of plain integers. Plain integers
(also just called *integers*) are implemented using ``long`` in C,
which gives them at least 32 bits of precision (``sys.maxint`` is
always set to the maximum plain integer value for the current
platform, the minimum value is ``-sys.maxint - 1``).  Long integers
have unlimited precision. Floating point numbers are implemented using
``double`` in C. All bets on their precision are off unless you happen
to know the machine you are working with.

Complex numbers have a real and imaginary part, which are each
implemented using ``double`` in C.  To extract these parts from a
complex number *z*, use ``z.real`` and ``z.imag``.

Numbers are created by numeric literals or as the result of built-in
functions and operators.  Unadorned integer literals (including
binary, hex, and octal numbers) yield plain integers unless the value
they denote is too large to be represented as a plain integer, in
which case they yield a long integer. Integer literals with an ``'L'``
or ``'l'`` suffix yield long integers (``'L'`` is preferred because
``1l`` looks too much like eleven!).  Numeric literals containing a
decimal point or an exponent sign yield floating point numbers.
Appending ``'j'`` or ``'J'`` to a numeric literal yields a complex
number with a zero real part. A complex numeric literal is the sum of
a real and an imaginary part.

Python fully supports mixed arithmetic: when a binary arithmetic
operator has operands of different numeric types, the operand with the
"narrower" type is widened to that of the other, where plain integer
is narrower than long integer is narrower than floating point is
narrower than complex. Comparisons between numbers of mixed type use
the same rule. [2] The constructors ``int()``, ``long()``,
``float()``, and ``complex()`` can be used to produce numbers of a
specific type.

All builtin numeric types support the following operations. See *The
power operator* and later sections for the operators' priorities.

+----------------------+-----------------------------------+----------+
| Operation            | Result                            | Notes    |
+======================+===================================+==========+
| ``x + y``            | sum of *x* and *y*                |          |
+----------------------+-----------------------------------+----------+
| ``x - y``            | difference of *x* and *y*         |          |
+----------------------+-----------------------------------+----------+
| ``x * y``            | product of *x* and *y*            |          |
+----------------------+-----------------------------------+----------+
| ``x / y``            | quotient of *x* and *y*           | (1)      |
+----------------------+-----------------------------------+----------+
| ``x // y``           | (floored) quotient of *x* and *y* | (4)(5)   |
+----------------------+-----------------------------------+----------+
| ``x % y``            | remainder of ``x / y``            | (4)      |
+----------------------+-----------------------------------+----------+
| ``-x``               | *x* negated                       |          |
+----------------------+-----------------------------------+----------+
| ``+x``               | *x* unchanged                     |          |
+----------------------+-----------------------------------+----------+
| ``abs(x)``           | absolute value or magnitude of    | (3)      |
|                      | *x*                               |          |
+----------------------+-----------------------------------+----------+
| ``int(x)``           | *x* converted to integer          | (2)      |
+----------------------+-----------------------------------+----------+
| ``long(x)``          | *x* converted to long integer     | (2)      |
+----------------------+-----------------------------------+----------+
| ``float(x)``         | *x* converted to floating point   | (6)      |
+----------------------+-----------------------------------+----------+
| ``complex(re,im)``   | a complex number with real part   |          |
|                      | *re*, imaginary part *im*. *im*   |          |
|                      | defaults to zero.                 |          |
+----------------------+-----------------------------------+----------+
| ``c.conjugate()``    | conjugate of the complex number   |          |
|                      | *c*. (Identity on real numbers)   |          |
+----------------------+-----------------------------------+----------+
| ``divmod(x, y)``     | the pair ``(x // y, x % y)``      | (3)(4)   |
+----------------------+-----------------------------------+----------+
| ``pow(x, y)``        | *x* to the power *y*              | (3)(7)   |
+----------------------+-----------------------------------+----------+
| ``x ** y``           | *x* to the power *y*              | (7)      |
+----------------------+-----------------------------------+----------+

Notes:

1. For (plain or long) integer division, the result is an integer. The
   result is always rounded towards minus infinity: 1/2 is 0, (-1)/2
   is -1, 1/(-2) is -1, and (-1)/(-2) is 0.  Note that the result is a
   long integer if either operand is a long integer, regardless of the
   numeric value.

2. Conversion from floats using ``int()`` or ``long()`` truncates
   toward zero like the related function, ``math.trunc()``.  Use the
   function ``math.floor()`` to round downward and ``math.ceil()`` to
   round upward.

3. See *Built-in Functions* for a full description.

4. Complex floor division operator, modulo operator, and ``divmod()``.

   Deprecated since version 2.3: Instead convert to float using
   ``abs()`` if appropriate.

5. Also referred to as integer division.  The resultant value is a
   whole integer, though the result's type is not necessarily int.

6. float also accepts the strings "nan" and "inf" with an optional
   prefix "+" or "-" for Not a Number (NaN) and positive or negative
   infinity.

   New in version 2.6.

7. Python defines ``pow(0, 0)`` and ``0 ** 0`` to be ``1``, as is
   common for programming languages.

All ``numbers.Real`` types (``int``, ``long``, and ``float``) also
include the following operations:

+----------------------+--------------------------------------+----------+
| Operation            | Result                               | Notes    |
+======================+======================================+==========+
| ``math.trunc(x)``    | *x* truncated to Integral            |          |
+----------------------+--------------------------------------+----------+
| ``round(x[, n])``    | *x* rounded to n digits, rounding    |          |
|                      | half to even. If n is omitted, it    |          |
|                      | defaults to 0.                       |          |
+----------------------+--------------------------------------+----------+
| ``math.floor(x)``    | the greatest integral float <= *x*   |          |
+----------------------+--------------------------------------+----------+
| ``math.ceil(x)``     | the least integral float >= *x*      |          |
+----------------------+--------------------------------------+----------+


Bit-string Operations on Integer Types
--------------------------------------

Plain and long integer types support additional operations that make
sense only for bit-strings.  Negative numbers are treated as their 2's
complement value (for long integers, this assumes a sufficiently large
number of bits that no overflow occurs during the operation).

The priorities of the binary bitwise operations are all lower than the
numeric operations and higher than the comparisons; the unary
operation ``~`` has the same priority as the other unary numeric
operations (``+`` and ``-``).

This table lists the bit-string operations sorted in ascending
priority:

+--------------+----------------------------------+------------+
| Operation    | Result                           | Notes      |
+==============+==================================+============+
| ``x | y``    | bitwise *or* of *x* and *y*      |            |
+--------------+----------------------------------+------------+
| ``x ^ y``    | bitwise *exclusive or* of *x*    |            |
|              | and *y*                          |            |
+--------------+----------------------------------+------------+
| ``x & y``    | bitwise *and* of *x* and *y*     |            |
+--------------+----------------------------------+------------+
| ``x << n``   | *x* shifted left by *n* bits     | (1)(2)     |
+--------------+----------------------------------+------------+
| ``x >> n``   | *x* shifted right by *n* bits    | (1)(3)     |
+--------------+----------------------------------+------------+
| ``~x``       | the bits of *x* inverted         |            |
+--------------+----------------------------------+------------+

Notes:

1. Negative shift counts are illegal and cause a ``ValueError`` to be
   raised.

2. A left shift by *n* bits is equivalent to multiplication by
   ``pow(2, n)``.  A long integer is returned if the result exceeds
   the range of plain integers.

3. A right shift by *n* bits is equivalent to division by ``pow(2,
   n)``.


Additional Methods on Float
---------------------------

The float type has some additional methods.

float.as_integer_ratio()

   Return a pair of integers whose ratio is exactly equal to the
   original float and with a positive denominator.  Raises
   ``OverflowError`` on infinities and a ``ValueError`` on NaNs.

   New in version 2.6.

Two methods support conversion to and from hexadecimal strings.  Since
Python's floats are stored internally as binary numbers, converting a
float to or from a *decimal* string usually involves a small rounding
error.  In contrast, hexadecimal strings allow exact representation
and specification of floating-point numbers.  This can be useful when
debugging, and in numerical work.

float.hex()

   Return a representation of a floating-point number as a hexadecimal
   string.  For finite floating-point numbers, this representation
   will always include a leading ``0x`` and a trailing ``p`` and
   exponent.

   New in version 2.6.

float.fromhex(s)

   Class method to return the float represented by a hexadecimal
   string *s*.  The string *s* may have leading and trailing
   whitespace.

   New in version 2.6.

Note that ``float.hex()`` is an instance method, while
``float.fromhex()`` is a class method.

A hexadecimal string takes the form:

   [sign] ['0x'] integer ['.' fraction] ['p' exponent]

where the optional ``sign`` may by either ``+`` or ``-``, ``integer``
and ``fraction`` are strings of hexadecimal digits, and ``exponent``
is a decimal integer with an optional leading sign.  Case is not
significant, and there must be at least one hexadecimal digit in
either the integer or the fraction.  This syntax is similar to the
syntax specified in section 6.4.4.2 of the C99 standard, and also to
the syntax used in Java 1.5 onwards.  In particular, the output of
``float.hex()`` is usable as a hexadecimal floating-point literal in C
or Java code, and hexadecimal strings produced by C's ``%a`` format
character or Java's ``Double.toHexString`` are accepted by
``float.fromhex()``.

Note that the exponent is written in decimal rather than hexadecimal,
and that it gives the power of 2 by which to multiply the coefficient.
For example, the hexadecimal string ``0x3.a7p10`` represents the
floating-point number ``(3 + 10./16 + 7./16**2) * 2.0**10``, or
``3740.0``:

   >>> float.fromhex('0x3.a7p10')
   3740.0

Applying the reverse conversion to ``3740.0`` gives a different
hexadecimal string representing the same number:

   >>> float.hex(3740.0)
   '0x1.d380000000000p+11'


Iterator Types
==============

New in version 2.2.

Python supports a concept of iteration over containers.  This is
implemented using two distinct methods; these are used to allow user-
defined classes to support iteration.  Sequences, described below in
more detail, always support the iteration methods.

One method needs to be defined for container objects to provide
iteration support:

container.__iter__()

   Return an iterator object.  The object is required to support the
   iterator protocol described below.  If a container supports
   different types of iteration, additional methods can be provided to
   specifically request iterators for those iteration types.  (An
   example of an object supporting multiple forms of iteration would
   be a tree structure which supports both breadth-first and depth-
   first traversal.)  This method corresponds to the ``tp_iter`` slot
   of the type structure for Python objects in the Python/C API.

The iterator objects themselves are required to support the following
two methods, which together form the *iterator protocol*:

iterator.__iter__()

   Return the iterator object itself.  This is required to allow both
   containers and iterators to be used with the ``for`` and ``in``
   statements. This method corresponds to the ``tp_iter`` slot of the
   type structure for Python objects in the Python/C API.

iterator.next()

   Return the next item from the container.  If there are no further
   items, raise the ``StopIteration`` exception.  This method
   corresponds to the ``tp_iternext`` slot of the type structure for
   Python objects in the Python/C API.

Python defines several iterator objects to support iteration over
general and specific sequence types, dictionaries, and other more
specialized forms.  The specific types are not important beyond their
implementation of the iterator protocol.

The intention of the protocol is that once an iterator's ``next()``
method raises ``StopIteration``, it will continue to do so on
subsequent calls. Implementations that do not obey this property are
deemed broken.  (This constraint was added in Python 2.3; in Python
2.2, various iterators are broken according to this rule.)

Python's *generator*s provide a convenient way to implement the
iterator protocol.  If a container object's ``__iter__()`` method is
implemented as a generator, it will automatically return an iterator
object (technically, a generator object) supplying the ``__iter__()``
and ``next()`` methods.


Sequence Types --- ``str``, ``unicode``, ``list``, ``tuple``, ``buffer``, ``xrange``
====================================================================================

There are six sequence types: strings, Unicode strings, lists, tuples,
buffers, and xrange objects.

For other containers see the built in ``dict`` and ``set`` classes,
and the ``collections`` module.

String literals are written in single or double quotes: ``'xyzzy'``,
``"frobozz"``.  See *String literals* for more about string literals.
Unicode strings are much like strings, but are specified in the syntax
using a preceding ``'u'`` character: ``u'abc'``, ``u"def"``. In
addition to the functionality described here, there are also string-
specific methods described in the *String Methods* section. Lists are
constructed with square brackets, separating items with commas: ``[a,
b, c]``. Tuples are constructed by the comma operator (not within
square brackets), with or without enclosing parentheses, but an empty
tuple must have the enclosing parentheses, such as ``a, b, c`` or
``()``.  A single item tuple must have a trailing comma, such as
``(d,)``.

Buffer objects are not directly supported by Python syntax, but can be
created by calling the builtin function ``buffer()``.  They don't
support concatenation or repetition.

Objects of type xrange are similar to buffers in that there is no
specific syntax to create them, but they are created using the
``xrange()`` function.  They don't support slicing, concatenation or
repetition, and using ``in``, ``not in``, ``min()`` or ``max()`` on
them is inefficient.

Most sequence types support the following operations.  The ``in`` and
``not in`` operations have the same priorities as the comparison
operations.  The ``+`` and ``*`` operations have the same priority as
the corresponding numeric operations. [3] Additional methods are
provided for *Mutable Sequence Types*.

This table lists the sequence operations sorted in ascending priority
(operations in the same box have the same priority).  In the table,
*s* and *t* are sequences of the same type; *n*, *i* and *j* are
integers:

+--------------------+----------------------------------+------------+
| Operation          | Result                           | Notes      |
+====================+==================================+============+
| ``x in s``         | ``True`` if an item of *s* is    | (1)        |
|                    | equal to *x*, else ``False``     |            |
+--------------------+----------------------------------+------------+
| ``x not in s``     | ``False`` if an item of *s* is   | (1)        |
|                    | equal to *x*, else ``True``      |            |
+--------------------+----------------------------------+------------+
| ``s + t``          | the concatenation of *s* and *t* | (6)        |
+--------------------+----------------------------------+------------+
| ``s * n, n * s``   | *n* shallow copies of *s*        | (2)        |
|                    | concatenated                     |            |
+--------------------+----------------------------------+------------+
| ``s[i]``           | *i*'th item of *s*, origin 0     | (3)        |
+--------------------+----------------------------------+------------+
| ``s[i:j]``         | slice of *s* from *i* to *j*     | (3)(4)     |
+--------------------+----------------------------------+------------+
| ``s[i:j:k]``       | slice of *s* from *i* to *j*     | (3)(5)     |
|                    | with step *k*                    |            |
+--------------------+----------------------------------+------------+
| ``len(s)``         | length of *s*                    |            |
+--------------------+----------------------------------+------------+
| ``min(s)``         | smallest item of *s*             |            |
+--------------------+----------------------------------+------------+
| ``max(s)``         | largest item of *s*              |            |
+--------------------+----------------------------------+------------+

Sequence types also support comparisons. In particular, tuples and
lists are compared lexicographically by comparing corresponding
elements. This means that to compare equal, every element must compare
equal and the two sequences must be of the same type and have the same
length. (For full details see *Comparisons* in the language
reference.)

Notes:

1. When *s* is a string or Unicode string object the ``in`` and ``not
   in`` operations act like a substring test.  In Python versions
   before 2.3, *x* had to be a string of length 1. In Python 2.3 and
   beyond, *x* may be a string of any length.

2. Values of *n* less than ``0`` are treated as ``0`` (which yields an
   empty sequence of the same type as *s*).  Note also that the copies
   are shallow; nested structures are not copied.  This often haunts
   new Python programmers; consider:

   >>> lists = [[]] * 3
   >>> lists
   [[], [], []]
   >>> lists[0].append(3)
   >>> lists
   [[3], [3], [3]]

   What has happened is that ``[[]]`` is a one-element list containing
   an empty list, so all three elements of ``[[]] * 3`` are (pointers
   to) this single empty list.  Modifying any of the elements of
   ``lists`` modifies this single list. You can create a list of
   different lists this way:

   >>> lists = [[] for i in range(3)]
   >>> lists[0].append(3)
   >>> lists[1].append(5)
   >>> lists[2].append(7)
   >>> lists
   [[3], [5], [7]]

3. If *i* or *j* is negative, the index is relative to the end of the
   string: ``len(s) + i`` or ``len(s) + j`` is substituted.  But note
   that ``-0`` is still ``0``.

4. The slice of *s* from *i* to *j* is defined as the sequence of
   items with index *k* such that ``i <= k < j``.  If *i* or *j* is
   greater than ``len(s)``, use ``len(s)``.  If *i* is omitted or
   ``None``, use ``0``.  If *j* is omitted or ``None``, use
   ``len(s)``.  If *i* is greater than or equal to *j*, the slice is
   empty.

5. The slice of *s* from *i* to *j* with step *k* is defined as the
   sequence of items with index  ``x = i + n*k`` such that ``0 <= n <
   (j-i)/k``.  In other words, the indices are ``i``, ``i+k``,
   ``i+2*k``, ``i+3*k`` and so on, stopping when *j* is reached (but
   never including *j*).  If *i* or *j* is greater than ``len(s)``,
   use ``len(s)``.  If *i* or *j* are omitted or ``None``, they become
   "end" values (which end depends on the sign of *k*).  Note, *k*
   cannot be zero. If *k* is ``None``, it is treated like ``1``.

6. If *s* and *t* are both strings, some Python implementations such
   as CPython can usually perform an in-place optimization for
   assignments of the form ``s=s+t`` or ``s+=t``.  When applicable,
   this optimization makes quadratic run-time much less likely.  This
   optimization is both version and implementation dependent. For
   performance sensitive code, it is preferable to use the
   ``str.join()`` method which assures consistent linear concatenation
   performance across versions and implementations.

   Changed in version 2.4: Formerly, string concatenation never
   occurred in-place.


String Methods
--------------

Below are listed the string methods which both 8-bit strings and
Unicode objects support. Note that none of these methods take keyword
arguments.

In addition, Python's strings support the sequence type methods
described in the *Sequence Types --- str, unicode, list, tuple,
buffer, xrange* section. To output formatted strings use template
strings or the ``%`` operator described in the *String Formatting
Operations* section. Also, see the ``re`` module for string functions
based on regular expressions.

str.capitalize()

   Return a copy of the string with only its first character
   capitalized.

   For 8-bit strings, this method is locale-dependent.

str.center(width[, fillchar])

   Return centered in a string of length *width*. Padding is done
   using the specified *fillchar* (default is a space).

   Changed in version 2.4: Support for the *fillchar* argument.

str.count(sub[, start[, end]])

   Return the number of non-overlapping occurrences of substring *sub*
   in the range [*start*, *end*].  Optional arguments *start* and
   *end* are interpreted as in slice notation.

str.decode([encoding[, errors]])

   Decodes the string using the codec registered for *encoding*.
   *encoding* defaults to the default string encoding.  *errors* may
   be given to set a different error handling scheme.  The default is
   ``'strict'``, meaning that encoding errors raise ``UnicodeError``.
   Other possible values are ``'ignore'``, ``'replace'`` and any other
   name registered via ``codecs.register_error()``, see section *Codec
   Base Classes*.

   New in version 2.2.

   Changed in version 2.3: Support for other error handling schemes
   added.

str.encode([encoding[, errors]])

   Return an encoded version of the string.  Default encoding is the
   current default string encoding.  *errors* may be given to set a
   different error handling scheme.  The default for *errors* is
   ``'strict'``, meaning that encoding errors raise a
   ``UnicodeError``.  Other possible values are ``'ignore'``,
   ``'replace'``, ``'xmlcharrefreplace'``, ``'backslashreplace'`` and
   any other name registered via ``codecs.register_error()``, see
   section *Codec Base Classes*. For a list of possible encodings, see
   section *Standard Encodings*.

   New in version 2.0.

   Changed in version 2.3: Support for ``'xmlcharrefreplace'`` and
   ``'backslashreplace'`` and other error handling schemes added.

str.endswith(suffix[, start[, end]])

   Return ``True`` if the string ends with the specified *suffix*,
   otherwise return ``False``.  *suffix* can also be a tuple of
   suffixes to look for.  With optional *start*, test beginning at
   that position.  With optional *end*, stop comparing at that
   position.

   Changed in version 2.5: Accept tuples as *suffix*.

str.expandtabs([tabsize])

   Return a copy of the string where all tab characters are replaced
   by one or more spaces, depending on the current column and the
   given tab size.  The column number is reset to zero after each
   newline occurring in the string. If *tabsize* is not given, a tab
   size of ``8`` characters is assumed.  This doesn't understand other
   non-printing characters or escape sequences.

str.find(sub[, start[, end]])

   Return the lowest index in the string where substring *sub* is
   found, such that *sub* is contained in the range [*start*, *end*].
   Optional arguments *start* and *end* are interpreted as in slice
   notation.  Return ``-1`` if *sub* is not found.

str.format(format_string, *args, **kwargs)

   Perform a string formatting operation.  The *format_string*
   argument can contain literal text or replacement fields delimited
   by braces ``{}``.  Each replacement field contains either the
   numeric index of a positional argument, or the name of a keyword
   argument.  Returns a copy of *format_string* where each replacement
   field is replaced with the string value of the corresponding
   argument.

   >>> "The sum of 1 + 2 is {0}".format(1+2)
   'The sum of 1 + 2 is 3'

   See *Format String Syntax* for a description of the various
   formatting options that can be specified in format strings.

   This method of string formatting is the new standard in Python 3.0,
   and should be preferred to the ``%`` formatting described in
   *String Formatting Operations* in new code.

   New in version 2.6.

str.index(sub[, start[, end]])

   Like ``find()``, but raise ``ValueError`` when the substring is not
   found.

str.isalnum()

   Return true if all characters in the string are alphanumeric and
   there is at least one character, false otherwise.

   For 8-bit strings, this method is locale-dependent.

str.isalpha()

   Return true if all characters in the string are alphabetic and
   there is at least one character, false otherwise.

   For 8-bit strings, this method is locale-dependent.

str.isdigit()

   Return true if all characters in the string are digits and there is
   at least one character, false otherwise.

   For 8-bit strings, this method is locale-dependent.

str.islower()

   Return true if all cased characters in the string are lowercase and
   there is at least one cased character, false otherwise.

   For 8-bit strings, this method is locale-dependent.

str.isspace()

   Return true if there are only whitespace characters in the string
   and there is at least one character, false otherwise.

   For 8-bit strings, this method is locale-dependent.

str.istitle()

   Return true if the string is a titlecased string and there is at
   least one character, for example uppercase characters may only
   follow uncased characters and lowercase characters only cased ones.
   Return false otherwise.

   For 8-bit strings, this method is locale-dependent.

str.isupper()

   Return true if all cased characters in the string are uppercase and
   there is at least one cased character, false otherwise.

   For 8-bit strings, this method is locale-dependent.

str.join(seq)

   Return a string which is the concatenation of the strings in the
   sequence *seq*. The separator between elements is the string
   providing this method.

str.ljust(width[, fillchar])

   Return the string left justified in a string of length *width*.
   Padding is done using the specified *fillchar* (default is a
   space).  The original string is returned if *width* is less than
   ``len(s)``.

   Changed in version 2.4: Support for the *fillchar* argument.

str.lower()

   Return a copy of the string converted to lowercase.

   For 8-bit strings, this method is locale-dependent.

str.lstrip([chars])

   Return a copy of the string with leading characters removed.  The
   *chars* argument is a string specifying the set of characters to be
   removed.  If omitted or ``None``, the *chars* argument defaults to
   removing whitespace.  The *chars* argument is not a prefix; rather,
   all combinations of its values are stripped:

   >>> '   spacious   '.lstrip()
   'spacious   '
   >>> 'www.example.com'.lstrip('cmowz.')
   'example.com'

   Changed in version 2.2.2: Support for the *chars* argument.

str.partition(sep)

   Split the string at the first occurrence of *sep*, and return a
   3-tuple containing the part before the separator, the separator
   itself, and the part after the separator.  If the separator is not
   found, return a 3-tuple containing the string itself, followed by
   two empty strings.

   New in version 2.5.

str.replace(old, new[, count])

   Return a copy of the string with all occurrences of substring *old*
   replaced by *new*.  If the optional argument *count* is given, only
   the first *count* occurrences are replaced.

str.rfind(sub[, start[, end]])

   Return the highest index in the string where substring *sub* is
   found, such that *sub* is contained within s[start,end].  Optional
   arguments *start* and *end* are interpreted as in slice notation.
   Return ``-1`` on failure.

str.rindex(sub[, start[, end]])

   Like ``rfind()`` but raises ``ValueError`` when the substring *sub*
   is not found.

str.rjust(width[, fillchar])

   Return the string right justified in a string of length *width*.
   Padding is done using the specified *fillchar* (default is a
   space). The original string is returned if *width* is less than
   ``len(s)``.

   Changed in version 2.4: Support for the *fillchar* argument.

str.rpartition(sep)

   Split the string at the last occurrence of *sep*, and return a
   3-tuple containing the part before the separator, the separator
   itself, and the part after the separator.  If the separator is not
   found, return a 3-tuple containing two empty strings, followed by
   the string itself.

   New in version 2.5.

str.rsplit([sep[, maxsplit]])

   Return a list of the words in the string, using *sep* as the
   delimiter string. If *maxsplit* is given, at most *maxsplit* splits
   are done, the *rightmost* ones.  If *sep* is not specified or
   ``None``, any whitespace string is a separator.  Except for
   splitting from the right, ``rsplit()`` behaves like ``split()``
   which is described in detail below.

   New in version 2.4.

str.rstrip([chars])

   Return a copy of the string with trailing characters removed.  The
   *chars* argument is a string specifying the set of characters to be
   removed.  If omitted or ``None``, the *chars* argument defaults to
   removing whitespace.  The *chars* argument is not a suffix; rather,
   all combinations of its values are stripped:

   >>> '   spacious   '.rstrip()
   '   spacious'
   >>> 'mississippi'.rstrip('ipz')
   'mississ'

   Changed in version 2.2.2: Support for the *chars* argument.

str.split([sep[, maxsplit]])

   Return a list of the words in the string, using *sep* as the
   delimiter string.  If *maxsplit* is given, at most *maxsplit*
   splits are done (thus, the list will have at most ``maxsplit+1``
   elements).  If *maxsplit* is not specified, then there is no limit
   on the number of splits (all possible splits are made).

   If *sep* is given, consecutive delimiters are not grouped together
   and are deemed to delimit empty strings (for example,
   ``'1,,2'.split(',')`` returns ``['1', '', '2']``).  The *sep*
   argument may consist of multiple characters (for example,
   ``'1<>2<>3'.split('<>')`` returns ``['1', '2', '3']``). Splitting
   an empty string with a specified separator returns ``['']``.

   If *sep* is not specified or is ``None``, a different splitting
   algorithm is applied: runs of consecutive whitespace are regarded
   as a single separator, and the result will contain no empty strings
   at the start or end if the string has leading or trailing
   whitespace.  Consequently, splitting an empty string or a string
   consisting of just whitespace with a ``None`` separator returns
   ``[]``.

   For example, ``' 1  2   3  '.split()`` returns ``['1', '2', '3']``,
   and ``'  1  2   3  '.split(None, 1)`` returns ``['1', '2   3  ']``.

str.splitlines([keepends])

   Return a list of the lines in the string, breaking at line
   boundaries.  Line breaks are not included in the resulting list
   unless *keepends* is given and true.

str.startswith(prefix[, start[, end]])

   Return ``True`` if string starts with the *prefix*, otherwise
   return ``False``. *prefix* can also be a tuple of prefixes to look
   for.  With optional *start*, test string beginning at that
   position.  With optional *end*, stop comparing string at that
   position.

   Changed in version 2.5: Accept tuples as *prefix*.

str.strip([chars])

   Return a copy of the string with the leading and trailing
   characters removed. The *chars* argument is a string specifying the
   set of characters to be removed. If omitted or ``None``, the
   *chars* argument defaults to removing whitespace. The *chars*
   argument is not a prefix or suffix; rather, all combinations of its
   values are stripped:

   >>> '   spacious   '.strip()
   'spacious'
   >>> 'www.example.com'.strip('cmowz.')
   'example'

   Changed in version 2.2.2: Support for the *chars* argument.

str.swapcase()

   Return a copy of the string with uppercase characters converted to
   lowercase and vice versa.

   For 8-bit strings, this method is locale-dependent.

str.title()

   Return a titlecased version of the string where words start with an
   uppercase character and the remaining characters are lowercase.

   The algorithm uses a simple language-independent definition of a
   word as groups of consecutive letters.  The definition works in
   many contexts but it means that apostrophes in contractions and
   possessives form word boundaries, which may not be the desired
   result:

      >>> "they're bill's friends from the UK".title()
      "They'Re Bill'S Friends From The Uk"

   A workaround for apostrophes can be constructed using regular
   expressions:

      >>> import re
      >>> def titlecase(s):
              return re.sub(r"[A-Za-z]+('[A-Za-z]+)?",
                            lambda mo: mo.group(0)[0].upper() +
                                       mo.group(0)[1:].lower(),
                            s)

      >>> titlecase("they're bill's friends.")
      "They're Bill's Friends."

   For 8-bit strings, this method is locale-dependent.

str.translate(table[, deletechars])

   Return a copy of the string where all characters occurring in the
   optional argument *deletechars* are removed, and the remaining
   characters have been mapped through the given translation table,
   which must be a string of length 256.

   You can use the ``maketrans()`` helper function in the ``string``
   module to create a translation table. For string objects, set the
   *table* argument to ``None`` for translations that only delete
   characters:

   >>> 'read this short text'.translate(None, 'aeiou')
   'rd ths shrt txt'

   New in version 2.6: Support for a ``None`` *table* argument.

   For Unicode objects, the ``translate()`` method does not accept the
   optional *deletechars* argument.  Instead, it returns a copy of the
   *s* where all characters have been mapped through the given
   translation table which must be a mapping of Unicode ordinals to
   Unicode ordinals, Unicode strings or ``None``. Unmapped characters
   are left untouched. Characters mapped to ``None`` are deleted.
   Note, a more flexible approach is to create a custom character
   mapping codec using the ``codecs`` module (see ``encodings.cp1251``
   for an example).

str.upper()

   Return a copy of the string converted to uppercase.

   For 8-bit strings, this method is locale-dependent.

str.zfill(width)

   Return the numeric string left filled with zeros in a string of
   length *width*.  A sign prefix is handled correctly.  The original
   string is returned if *width* is less than ``len(s)``.

   New in version 2.2.2.

The following methods are present only on unicode objects:

unicode.isnumeric()

   Return ``True`` if there are only numeric characters in S,
   ``False`` otherwise. Numeric characters include digit characters,
   and all characters that have the Unicode numeric value property,
   e.g. U+2155, VULGAR FRACTION ONE FIFTH.

unicode.isdecimal()

   Return ``True`` if there are only decimal characters in S,
   ``False`` otherwise. Decimal characters include digit characters,
   and all characters that that can be used to form decimal-radix
   numbers, e.g. U+0660, ARABIC-INDIC DIGIT ZERO.


String Formatting Operations
----------------------------

String and Unicode objects have one unique built-in operation: the
``%`` operator (modulo).  This is also known as the string
*formatting* or *interpolation* operator.  Given ``format % values``
(where *format* is a string or Unicode object), ``%`` conversion
specifications in *format* are replaced with zero or more elements of
*values*.  The effect is similar to the using ``sprintf()`` in the C
language.  If *format* is a Unicode object, or if any of the objects
being converted using the ``%s`` conversion are Unicode objects, the
result will also be a Unicode object.

If *format* requires a single argument, *values* may be a single non-
tuple object. [4]  Otherwise, *values* must be a tuple with exactly
the number of items specified by the format string, or a single
mapping object (for example, a dictionary).

A conversion specifier contains two or more characters and has the
following components, which must occur in this order:

1. The ``'%'`` character, which marks the start of the specifier.

2. Mapping key (optional), consisting of a parenthesised sequence of
   characters (for example, ``(somename)``).

3. Conversion flags (optional), which affect the result of some
   conversion types.

4. Minimum field width (optional).  If specified as an ``'*'``
   (asterisk), the actual width is read from the next element of the
   tuple in *values*, and the object to convert comes after the
   minimum field width and optional precision.

5. Precision (optional), given as a ``'.'`` (dot) followed by the
   precision.  If specified as ``'*'`` (an asterisk), the actual width
   is read from the next element of the tuple in *values*, and the
   value to convert comes after the precision.

6. Length modifier (optional).

7. Conversion type.

When the right argument is a dictionary (or other mapping type), then
the formats in the string *must* include a parenthesised mapping key
into that dictionary inserted immediately after the ``'%'`` character.
The mapping key selects the value to be formatted from the mapping.
For example:

>>> print '%(language)s has %(#)03d quote types.' % \
...       {'language': "Python", "#": 2}
Python has 002 quote types.

In this case no ``*`` specifiers may occur in a format (since they
require a sequential parameter list).

The conversion flag characters are:

+-----------+-----------------------------------------------------------------------+
| Flag      | Meaning                                                               |
+===========+=======================================================================+
| ``'#'``   | The value conversion will use the "alternate form" (where defined     |
|           | below).                                                               |
+-----------+-----------------------------------------------------------------------+
| ``'0'``   | The conversion will be zero padded for numeric values.                |
+-----------+-----------------------------------------------------------------------+
| ``'-'``   | The converted value is left adjusted (overrides the ``'0'``           |
|           | conversion if both are given).                                        |
+-----------+-----------------------------------------------------------------------+
| ``' '``   | (a space) A blank should be left before a positive number (or empty   |
|           | string) produced by a signed conversion.                              |
+-----------+-----------------------------------------------------------------------+
| ``'+'``   | A sign character (``'+'`` or ``'-'``) will precede the conversion     |
|           | (overrides a "space" flag).                                           |
+-----------+-----------------------------------------------------------------------+

A length modifier (``h``, ``l``, or ``L``) may be present, but is
ignored as it is not necessary for Python -- so e.g. ``%ld`` is
identical to ``%d``.

The conversion types are:

+--------------+-------------------------------------------------------+---------+
| Conversion   | Meaning                                               | Notes   |
+==============+=======================================================+=========+
| ``'d'``      | Signed integer decimal.                               |         |
+--------------+-------------------------------------------------------+---------+
| ``'i'``      | Signed integer decimal.                               |         |
+--------------+-------------------------------------------------------+---------+
| ``'o'``      | Signed octal value.                                   | (1)     |
+--------------+-------------------------------------------------------+---------+
| ``'u'``      | Obsolete type -- it is identical to ``'d'``.          | (7)     |
+--------------+-------------------------------------------------------+---------+
| ``'x'``      | Signed hexadecimal (lowercase).                       | (2)     |
+--------------+-------------------------------------------------------+---------+
| ``'X'``      | Signed hexadecimal (uppercase).                       | (2)     |
+--------------+-------------------------------------------------------+---------+
| ``'e'``      | Floating point exponential format (lowercase).        | (3)     |
+--------------+-------------------------------------------------------+---------+
| ``'E'``      | Floating point exponential format (uppercase).        | (3)     |
+--------------+-------------------------------------------------------+---------+
| ``'f'``      | Floating point decimal format.                        | (3)     |
+--------------+-------------------------------------------------------+---------+
| ``'F'``      | Floating point decimal format.                        | (3)     |
+--------------+-------------------------------------------------------+---------+
| ``'g'``      | Floating point format. Uses lowercase exponential     | (4)     |
|              | format if exponent is less than -4 or not less than   |         |
|              | precision, decimal format otherwise.                  |         |
+--------------+-------------------------------------------------------+---------+
| ``'G'``      | Floating point format. Uses uppercase exponential     | (4)     |
|              | format if exponent is less than -4 or not less than   |         |
|              | precision, decimal format otherwise.                  |         |
+--------------+-------------------------------------------------------+---------+
| ``'c'``      | Single character (accepts integer or single character |         |
|              | string).                                              |         |
+--------------+-------------------------------------------------------+---------+
| ``'r'``      | String (converts any python object using ``repr()``). | (5)     |
+--------------+-------------------------------------------------------+---------+
| ``'s'``      | String (converts any python object using ``str()``).  | (6)     |
+--------------+-------------------------------------------------------+---------+
| ``'%'``      | No argument is converted, results in a ``'%'``        |         |
|              | character in the result.                              |         |
+--------------+-------------------------------------------------------+---------+

Notes:

1. The alternate form causes a leading zero (``'0'``) to be inserted
   between left-hand padding and the formatting of the number if the
   leading character of the result is not already a zero.

2. The alternate form causes a leading ``'0x'`` or ``'0X'`` (depending
   on whether the ``'x'`` or ``'X'`` format was used) to be inserted
   between left-hand padding and the formatting of the number if the
   leading character of the result is not already a zero.

3. The alternate form causes the result to always contain a decimal
   point, even if no digits follow it.

   The precision determines the number of digits after the decimal
   point and defaults to 6.

4. The alternate form causes the result to always contain a decimal
   point, and trailing zeroes are not removed as they would otherwise
   be.

   The precision determines the number of significant digits before
   and after the decimal point and defaults to 6.

5. The ``%r`` conversion was added in Python 2.0.

   The precision determines the maximal number of characters used.

6. If the object or format provided is a ``unicode`` string, the
   resulting string will also be ``unicode``.

   The precision determines the maximal number of characters used.

7. See **PEP 237**.

Since Python strings have an explicit length, ``%s`` conversions do
not assume that ``'\0'`` is the end of the string.

For safety reasons, floating point precisions are clipped to 50;
``%f`` conversions for numbers whose absolute value is over 1e50 are
replaced by ``%g`` conversions. [5]  All other errors raise
exceptions.

Additional string operations are defined in standard modules
``string`` and ``re``.


XRange Type
-----------

The ``xrange`` type is an immutable sequence which is commonly used
for looping.  The advantage of the ``xrange`` type is that an
``xrange`` object will always take the same amount of memory, no
matter the size of the range it represents.  There are no consistent
performance advantages.

XRange objects have very little behavior: they only support indexing,
iteration, and the ``len()`` function.


Mutable Sequence Types
----------------------

List objects support additional operations that allow in-place
modification of the object. Other mutable sequence types (when added
to the language) should also support these operations. Strings and
tuples are immutable sequence types: such objects cannot be modified
once created. The following operations are defined on mutable sequence
types (where *x* is an arbitrary object):

+--------------------------------+----------------------------------+-----------------------+
| Operation                      | Result                           | Notes                 |
+================================+==================================+=======================+
| ``s[i] = x``                   | item *i* of *s* is replaced by   |                       |
|                                | *x*                              |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s[i:j] = t``                 | slice of *s* from *i* to *j* is  |                       |
|                                | replaced by the contents of the  |                       |
|                                | iterable *t*                     |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``del s[i:j]``                 | same as ``s[i:j] = []``          |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s[i:j:k] = t``               | the elements of ``s[i:j:k]`` are | (1)                   |
|                                | replaced by those of *t*         |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``del s[i:j:k]``               | removes the elements of          |                       |
|                                | ``s[i:j:k]`` from the list       |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.append(x)``                | same as ``s[len(s):len(s)] =     | (2)                   |
|                                | [x]``                            |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.extend(x)``                | same as ``s[len(s):len(s)] = x`` | (3)                   |
+--------------------------------+----------------------------------+-----------------------+
| ``s.count(x)``                 | return number of *i*'s for which |                       |
|                                | ``s[i] == x``                    |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.index(x[, i[, j]])``       | return smallest *k* such that    | (4)                   |
|                                | ``s[k] == x`` and ``i <= k < j`` |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.insert(i, x)``             | same as ``s[i:i] = [x]``         | (5)                   |
+--------------------------------+----------------------------------+-----------------------+
| ``s.pop([i])``                 | same as ``x = s[i]; del s[i];    | (6)                   |
|                                | return x``                       |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.remove(x)``                | same as ``del s[s.index(x)]``    | (4)                   |
+--------------------------------+----------------------------------+-----------------------+
| ``s.reverse()``                | reverses the items of *s* in     | (7)                   |
|                                | place                            |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.sort([cmp[, key[,          | sort the items of *s* in place   | (7)(8)(9)(10)         |
| reverse]]])``                  |                                  |                       |
+--------------------------------+----------------------------------+-----------------------+

Notes:

1. *t* must have the same length as the slice it is  replacing.

2. The C implementation of Python has historically accepted multiple
   parameters and implicitly joined them into a tuple; this no longer
   works in Python 2.0.  Use of this misfeature has been deprecated
   since Python 1.4.

3. *x* can be any iterable object.

4. Raises ``ValueError`` when *x* is not found in *s*. When a negative
   index is passed as the second or third parameter to the ``index()``
   method, the list length is added, as for slice indices.  If it is
   still negative, it is truncated to zero, as for slice indices.

   Changed in version 2.3: Previously, ``index()`` didn't have
   arguments for specifying start and stop positions.

5. When a negative index is passed as the first parameter to the
   ``insert()`` method, the list length is added, as for slice
   indices.  If it is still negative, it is truncated to zero, as for
   slice indices.

   Changed in version 2.3: Previously, all negative indices were
   truncated to zero.

6. The ``pop()`` method is only supported by the list and array types.
   The optional argument *i* defaults to ``-1``, so that by default
   the last item is removed and returned.

7. The ``sort()`` and ``reverse()`` methods modify the list in place
   for economy of space when sorting or reversing a large list.  To
   remind you that they operate by side effect, they don't return the
   sorted or reversed list.

8. The ``sort()`` method takes optional arguments for controlling the
   comparisons.

   *cmp* specifies a custom comparison function of two arguments (list
   items) which should return a negative, zero or positive number
   depending on whether the first argument is considered smaller than,
   equal to, or larger than the second argument: ``cmp=lambda x,y:
   cmp(x.lower(), y.lower())``.  The default value is ``None``.

   *key* specifies a function of one argument that is used to extract
   a comparison key from each list element: ``key=str.lower``.  The
   default value is ``None``.

   *reverse* is a boolean value.  If set to ``True``, then the list
   elements are sorted as if each comparison were reversed.

   In general, the *key* and *reverse* conversion processes are much
   faster than specifying an equivalent *cmp* function.  This is
   because *cmp* is called multiple times for each list element while
   *key* and *reverse* touch each element only once.

   Changed in version 2.3: Support for ``None`` as an equivalent to
   omitting *cmp* was added.

   Changed in version 2.4: Support for *key* and *reverse* was added.

9. Starting with Python 2.3, the ``sort()`` method is guaranteed to be
   stable.  A sort is stable if it guarantees not to change the
   relative order of elements that compare equal --- this is helpful
   for sorting in multiple passes (for example, sort by department,
   then by salary grade).

10. While a list is being sorted, the effect of attempting to mutate,
    or even inspect, the list is undefined.  The C implementation of
    Python 2.3 and newer makes the list appear empty for the duration,
    and raises ``ValueError`` if it can detect that the list has been
    mutated during a sort.


Set Types --- ``set``, ``frozenset``
====================================

A *set* object is an unordered collection of distinct *hashable*
objects. Common uses include membership testing, removing duplicates
from a sequence, and computing mathematical operations such as
intersection, union, difference, and symmetric difference. (For other
containers see the built in ``dict``, ``list``, and ``tuple`` classes,
and the ``collections`` module.)

New in version 2.4.

Like other collections, sets support ``x in set``, ``len(set)``, and
``for x in set``.  Being an unordered collection, sets do not record
element position or order of insertion.  Accordingly, sets do not
support indexing, slicing, or other sequence-like behavior.

There are currently two builtin set types, ``set`` and ``frozenset``.
The ``set`` type is mutable --- the contents can be changed using
methods like ``add()`` and ``remove()``.  Since it is mutable, it has
no hash value and cannot be used as either a dictionary key or as an
element of another set. The ``frozenset`` type is immutable and
*hashable* --- its contents cannot be altered after it is created; it
can therefore be used as a dictionary key or as an element of another
set.

The constructors for both classes work the same:

class class set([iterable])
class class frozenset([iterable])

   Return a new set or frozenset object whose elements are taken from
   *iterable*.  The elements of a set must be hashable.  To represent
   sets of sets, the inner sets must be ``frozenset`` objects.  If
   *iterable* is not specified, a new empty set is returned.

   Instances of ``set`` and ``frozenset`` provide the following
   operations:

   len(s)

      Return the cardinality of set *s*.

   x in s

      Test *x* for membership in *s*.

   x not in s

      Test *x* for non-membership in *s*.

   isdisjoint(other)

      Return True if the set has no elements in common with *other*.
      Sets are disjoint if and only if their intersection is the empty
      set.

      New in version 2.6.

   issubset(other)
   set <= other

      Test whether every element in the set is in *other*.

   set < other

      Test whether the set is a true subset of *other*, that is, ``set
      <= other and set != other``.

   issuperset(other)
   set >= other

      Test whether every element in *other* is in the set.

   set > other

      Test whether the set is a true superset of *other*, that is,
      ``set >= other and set != other``.

   union(other, ...)
   set | other | ...

      Return a new set with elements from the set and all others.

      Changed in version 2.6: Accepts multiple input iterables.

   intersection(other, ...)
   set & other & ...

      Return a new set with elements common to the set and all others.

      Changed in version 2.6: Accepts multiple input iterables.

   difference(other, ...)
   set - other - ...

      Return a new set with elements in the set that are not in the
      others.

      Changed in version 2.6: Accepts multiple input iterables.

   symmetric_difference(other)
   set ^ other

      Return a new set with elements in either the set or *other* but
      not both.

   copy()

      Return a new set with a shallow copy of *s*.

   Note, the non-operator versions of ``union()``, ``intersection()``,
   ``difference()``, and ``symmetric_difference()``, ``issubset()``,
   and ``issuperset()`` methods will accept any iterable as an
   argument.  In contrast, their operator based counterparts require
   their arguments to be sets.  This precludes error-prone
   constructions like ``set('abc') & 'cbs'`` in favor of the more
   readable ``set('abc').intersection('cbs')``.

   Both ``set`` and ``frozenset`` support set to set comparisons. Two
   sets are equal if and only if every element of each set is
   contained in the other (each is a subset of the other). A set is
   less than another set if and only if the first set is a proper
   subset of the second set (is a subset, but is not equal). A set is
   greater than another set if and only if the first set is a proper
   superset of the second set (is a superset, but is not equal).

   Instances of ``set`` are compared to instances of ``frozenset``
   based on their members.  For example, ``set('abc') ==
   frozenset('abc')`` returns ``True`` and so does ``set('abc') in
   set([frozenset('abc')])``.

   The subset and equality comparisons do not generalize to a complete
   ordering function.  For example, any two disjoint sets are not
   equal and are not subsets of each other, so *all* of the following
   return ``False``: ``a<b``, ``a==b``, or ``a>b``. Accordingly, sets
   do not implement the ``__cmp__()`` method.

   Since sets only define partial ordering (subset relationships), the
   output of the ``list.sort()`` method is undefined for lists of
   sets.

   Set elements, like dictionary keys, must be *hashable*.

   Binary operations that mix ``set`` instances with ``frozenset``
   return the type of the first operand.  For example:
   ``frozenset('ab') | set('bc')`` returns an instance of
   ``frozenset``.

   The following table lists operations available for ``set`` that do
   not apply to immutable instances of ``frozenset``:

   update(other, ...)
   set |= other | ...

      Update the set, adding elements from *other*.

      Changed in version 2.6: Accepts multiple input iterables.

   intersection_update(other, ...)
   set &= other & ...

      Update the set, keeping only elements found in it and *other*.

      Changed in version 2.6: Accepts multiple input iterables.

   difference_update(other, ...)
   set -= other | ...

      Update the set, removing elements found in others.

      Changed in version 2.6: Accepts multiple input iterables.

   symmetric_difference_update(other)
   set ^= other

      Update the set, keeping only elements found in either set, but
      not in both.

   add(elem)

      Add element *elem* to the set.

   remove(elem)

      Remove element *elem* from the set.  Raises ``KeyError`` if
      *elem* is not contained in the set.

   discard(elem)

      Remove element *elem* from the set if it is present.

   pop()

      Remove and return an arbitrary element from the set.  Raises
      ``KeyError`` if the set is empty.

   clear()

      Remove all elements from the set.

   Note, the non-operator versions of the ``update()``,
   ``intersection_update()``, ``difference_update()``, and
   ``symmetric_difference_update()`` methods will accept any iterable
   as an argument.

   Note, the *elem* argument to the ``__contains__()``, ``remove()``,
   and ``discard()`` methods may be a set.  To support searching for
   an equivalent frozenset, the *elem* set is temporarily mutated
   during the search and then restored.  During the search, the *elem*
   set should not be read or mutated since it does not have a
   meaningful value.

See also:

   *Comparison to the built-in set types*
      Differences between the ``sets`` module and the built-in set
      types.


Mapping Types --- ``dict``
==========================

A *mapping* object maps *hashable* values to arbitrary objects.
Mappings are mutable objects.  There is currently only one standard
mapping type, the *dictionary*.  (For other containers see the built
in ``list``, ``set``, and ``tuple`` classes, and the ``collections``
module.)

A dictionary's keys are *almost* arbitrary values.  Values that are
not *hashable*, that is, values containing lists, dictionaries or
other mutable types (that are compared by value rather than by object
identity) may not be used as keys.  Numeric types used for keys obey
the normal rules for numeric comparison: if two numbers compare equal
(such as ``1`` and ``1.0``) then they can be used interchangeably to
index the same dictionary entry.  (Note however, that since computers
store floating-point numbers as approximations it is usually unwise to
use them as dictionary keys.)

Dictionaries can be created by placing a comma-separated list of
``key: value`` pairs within braces, for example: ``{'jack': 4098,
'sjoerd': 4127}`` or ``{4098: 'jack', 4127: 'sjoerd'}``, or by the
``dict`` constructor.

class class dict([arg])

   Return a new dictionary initialized from an optional positional
   argument or from a set of keyword arguments. If no arguments are
   given, return a new empty dictionary. If the positional argument
   *arg* is a mapping object, return a dictionary mapping the same
   keys to the same values as does the mapping object. Otherwise the
   positional argument must be a sequence, a container that supports
   iteration, or an iterator object.  The elements of the argument
   must each also be of one of those kinds, and each must in turn
   contain exactly two objects. The first is used as a key in the new
   dictionary, and the second as the key's value.  If a given key is
   seen more than once, the last value associated with it is retained
   in the new dictionary.

   If keyword arguments are given, the keywords themselves with their
   associated values are added as items to the dictionary. If a key is
   specified both in the positional argument and as a keyword
   argument, the value associated with the keyword is retained in the
   dictionary. For example, these all return a dictionary equal to
   ``{"one": 2, "two": 3}``:

   * ``dict(one=2, two=3)``

   * ``dict({'one': 2, 'two': 3})``

   * ``dict(zip(('one', 'two'), (2, 3)))``

   * ``dict([['two', 3], ['one', 2]])``

   The first example only works for keys that are valid Python
   identifiers; the others work with any valid keys.

   New in version 2.2.

   Changed in version 2.3: Support for building a dictionary from
   keyword arguments added.

   These are the operations that dictionaries support (and therefore,
   custom mapping types should support too):

   len(d)

      Return the number of items in the dictionary *d*.

   d[key]

      Return the item of *d* with key *key*.  Raises a ``KeyError`` if
      *key* is not in the map.

      New in version 2.5: If a subclass of dict defines a method
      ``__missing__()``, if the key *key* is not present, the
      ``d[key]`` operation calls that method with the key *key* as
      argument.  The ``d[key]`` operation then returns or raises
      whatever is returned or raised by the ``__missing__(key)`` call
      if the key is not present. No other operations or methods invoke
      ``__missing__()``. If ``__missing__()`` is not defined,
      ``KeyError`` is raised.  ``__missing__()`` must be a method; it
      cannot be an instance variable. For an example, see
      ``collections.defaultdict``.

   d[key] = value

      Set ``d[key]`` to *value*.

   del d[key]

      Remove ``d[key]`` from *d*.  Raises a ``KeyError`` if *key* is
      not in the map.

   key in d

      Return ``True`` if *d* has a key *key*, else ``False``.

      New in version 2.2.

   key not in d

      Equivalent to ``not key in d``.

      New in version 2.2.

   iter(d)

      Return an iterator over the keys of the dictionary.  This is a
      shortcut for ``iterkeys()``.

   clear()

      Remove all items from the dictionary.

   copy()

      Return a shallow copy of the dictionary.

   fromkeys(seq[, value])

      Create a new dictionary with keys from *seq* and values set to
      *value*.

      ``fromkeys()`` is a class method that returns a new dictionary.
      *value* defaults to ``None``.

      New in version 2.3.

   get(key[, default])

      Return the value for *key* if *key* is in the dictionary, else
      *default*. If *default* is not given, it defaults to ``None``,
      so that this method never raises a ``KeyError``.

   has_key(key)

      Test for the presence of *key* in the dictionary.  ``has_key()``
      is deprecated in favor of ``key in d``.

   items()

      Return a copy of the dictionary's list of ``(key, value)``
      pairs.

      Note: Keys and values are listed in an arbitrary order which is non-
        random, varies across Python implementations, and depends on
        the dictionary's history of insertions and deletions. If
        ``items()``, ``keys()``, ``values()``, ``iteritems()``,
        ``iterkeys()``, and ``itervalues()`` are called with no
        intervening modifications to the dictionary, the lists will
        directly correspond.  This allows the creation of ``(value,
        key)`` pairs using ``zip()``: ``pairs = zip(d.values(),
        d.keys())``.  The same relationship holds for the
        ``iterkeys()`` and ``itervalues()`` methods: ``pairs =
        zip(d.itervalues(), d.iterkeys())`` provides the same value
        for ``pairs``. Another way to create the same list is ``pairs
        = [(v, k) for (k, v) in d.iteritems()]``.

   iteritems()

      Return an iterator over the dictionary's ``(key, value)`` pairs.
      See the note for ``dict.items()``.

      Using ``iteritems()`` while adding or deleting entries in the
      dictionary may raise a ``RuntimeError`` or fail to iterate over
      all entries.

      New in version 2.2.

   iterkeys()

      Return an iterator over the dictionary's keys.  See the note for
      ``dict.items()``.

      Using ``iterkeys()`` while adding or deleting entries in the
      dictionary may raise a ``RuntimeError`` or fail to iterate over
      all entries.

      New in version 2.2.

   itervalues()

      Return an iterator over the dictionary's values.  See the note
      for ``dict.items()``.

      Using ``itervalues()`` while adding or deleting entries in the
      dictionary may raise a ``RuntimeError`` or fail to iterate over
      all entries.

      New in version 2.2.

   keys()

      Return a copy of the dictionary's list of keys.  See the note
      for ``dict.items()``.

   pop(key[, default])

      If *key* is in the dictionary, remove it and return its value,
      else return *default*.  If *default* is not given and *key* is
      not in the dictionary, a ``KeyError`` is raised.

      New in version 2.3.

   popitem()

      Remove and return an arbitrary ``(key, value)`` pair from the
      dictionary.

      ``popitem()`` is useful to destructively iterate over a
      dictionary, as often used in set algorithms.  If the dictionary
      is empty, calling ``popitem()`` raises a ``KeyError``.

   setdefault(key[, default])

      If *key* is in the dictionary, return its value.  If not, insert
      *key* with a value of *default* and return *default*.  *default*
      defaults to ``None``.

   update([other])

      Update the dictionary with the key/value pairs from *other*,
      overwriting existing keys.  Return ``None``.

      ``update()`` accepts either another dictionary object or an
      iterable of key/value pairs (as a tuple or other iterable of
      length two).  If keyword arguments are specified, the dictionary
      is then is updated with those key/value pairs: ``d.update(red=1,
      blue=2)``.

      Changed in version 2.4: Allowed the argument to be an iterable
      of key/value pairs and allowed keyword arguments.

   values()

      Return a copy of the dictionary's list of values.  See the note
      for ``dict.items()``.


File Objects
============

File objects are implemented using C's ``stdio`` package and can be
created with the built-in ``open()`` function.  File objects are also
returned by some other built-in functions and methods, such as
``os.popen()`` and ``os.fdopen()`` and the ``makefile()`` method of
socket objects. Temporary files can be created using the ``tempfile``
module, and high-level file operations such as copying, moving, and
deleting files and directories can be achieved with the ``shutil``
module.

When a file operation fails for an I/O-related reason, the exception
``IOError`` is raised.  This includes situations where the operation
is not defined for some reason, like ``seek()`` on a tty device or
writing a file opened for reading.

Files have the following methods:

file.close()

   Close the file.  A closed file cannot be read or written any more.
   Any operation which requires that the file be open will raise a
   ``ValueError`` after the file has been closed.  Calling ``close()``
   more than once is allowed.

   As of Python 2.5, you can avoid having to call this method
   explicitly if you use the ``with`` statement.  For example, the
   following code will automatically close *f* when the ``with`` block
   is exited:

      from __future__ import with_statement # This isn't required in Python 2.6

      with open("hello.txt") as f:
          for line in f:
              print line

   In older versions of Python, you would have needed to do this to
   get the same effect:

      f = open("hello.txt")
      try:
          for line in f:
              print line
      finally:
          f.close()

   Note: Not all "file-like" types in Python support use as a context
     manager for the ``with`` statement.  If your code is intended to
     work with any file-like object, you can use the function
     ``contextlib.closing()`` instead of using the object directly.

file.flush()

   Flush the internal buffer, like ``stdio``'s ``fflush()``.  This may
   be a no-op on some file-like objects.

file.fileno()

   Return the integer "file descriptor" that is used by the underlying
   implementation to request I/O operations from the operating system.
   This can be useful for other, lower level interfaces that use file
   descriptors, such as the ``fcntl`` module or ``os.read()`` and
   friends.

   Note: File-like objects which do not have a real file descriptor should
     *not* provide this method!

file.isatty()

   Return ``True`` if the file is connected to a tty(-like) device,
   else ``False``.

   Note: If a file-like object is not associated with a real file, this
     method should *not* be implemented.

file.next()

   A file object is its own iterator, for example ``iter(f)`` returns
   *f* (unless *f* is closed).  When a file is used as an iterator,
   typically in a ``for`` loop (for example, ``for line in f: print
   line``), the ``next()`` method is called repeatedly.  This method
   returns the next input line, or raises ``StopIteration`` when EOF
   is hit when the file is open for reading (behavior is undefined
   when the file is open for writing).  In order to make a ``for``
   loop the most efficient way of looping over the lines of a file (a
   very common operation), the ``next()`` method uses a hidden read-
   ahead buffer.  As a consequence of using a read-ahead buffer,
   combining ``next()`` with other file methods (like ``readline()``)
   does not work right.  However, using ``seek()`` to reposition the
   file to an absolute position will flush the read-ahead buffer.

   New in version 2.3.

file.read([size])

   Read at most *size* bytes from the file (less if the read hits EOF
   before obtaining *size* bytes).  If the *size* argument is negative
   or omitted, read all data until EOF is reached.  The bytes are
   returned as a string object.  An empty string is returned when EOF
   is encountered immediately.  (For certain files, like ttys, it
   makes sense to continue reading after an EOF is hit.)  Note that
   this method may call the underlying C function ``fread()`` more
   than once in an effort to acquire as close to *size* bytes as
   possible. Also note that when in non-blocking mode, less data than
   was requested may be returned, even if no *size* parameter was
   given.

   Note: This function is simply a wrapper for the underlying ``fread()``
     C function, and will behave the same in corner cases, such as
     whether the EOF value is cached.

file.readline([size])

   Read one entire line from the file.  A trailing newline character
   is kept in the string (but may be absent when a file ends with an
   incomplete line). [6]  If the *size* argument is present and non-
   negative, it is a maximum byte count (including the trailing
   newline) and an incomplete line may be returned. An empty string is
   returned *only* when EOF is encountered immediately.

   Note: Unlike ``stdio``'s ``fgets()``, the returned string contains null
     characters (``'\0'``) if they occurred in the input.

file.readlines([sizehint])

   Read until EOF using ``readline()`` and return a list containing
   the lines thus read.  If the optional *sizehint* argument is
   present, instead of reading up to EOF, whole lines totalling
   approximately *sizehint* bytes (possibly after rounding up to an
   internal buffer size) are read.  Objects implementing a file-like
   interface may choose to ignore *sizehint* if it cannot be
   implemented, or cannot be implemented efficiently.

file.xreadlines()

   This method returns the same thing as ``iter(f)``.

   New in version 2.1.

   Deprecated since version 2.3: Use ``for line in file`` instead.

file.seek(offset[, whence])

   Set the file's current position, like ``stdio``'s ``fseek()``. The
   *whence* argument is optional and defaults to  ``os.SEEK_SET`` or
   ``0`` (absolute file positioning); other values are ``os.SEEK_CUR``
   or ``1`` (seek relative to the current position) and
   ``os.SEEK_END`` or ``2``  (seek relative to the file's end).  There
   is no return value.

   For example, ``f.seek(2, os.SEEK_CUR)`` advances the position by
   two and ``f.seek(-3, os.SEEK_END)`` sets the position to the third
   to last.

   Note that if the file is opened for appending (mode ``'a'`` or
   ``'a+'``), any ``seek()`` operations will be undone at the next
   write.  If the file is only opened for writing in append mode (mode
   ``'a'``), this method is essentially a no-op, but it remains useful
   for files opened in append mode with reading enabled (mode
   ``'a+'``).  If the file is opened in text mode (without ``'b'``),
   only offsets returned by ``tell()`` are legal.  Use of other
   offsets causes undefined behavior.

   Note that not all file objects are seekable.

   Changed in version 2.6: Passing float values as offset has been
   deprecated.

file.tell()

   Return the file's current position, like ``stdio``'s ``ftell()``.

   Note: On Windows, ``tell()`` can return illegal values (after an
     ``fgets()``) when reading files with Unix-style line-endings. Use
     binary mode (``'rb'``) to circumvent this problem.

file.truncate([size])

   Truncate the file's size.  If the optional *size* argument is
   present, the file is truncated to (at most) that size.  The size
   defaults to the current position. The current file position is not
   changed.  Note that if a specified size exceeds the file's current
   size, the result is platform-dependent:  possibilities include that
   the file may remain unchanged, increase to the specified size as if
   zero-filled, or increase to the specified size with undefined new
   content. Availability:  Windows, many Unix variants.

file.write(str)

   Write a string to the file.  There is no return value.  Due to
   buffering, the string may not actually show up in the file until
   the ``flush()`` or ``close()`` method is called.

file.writelines(sequence)

   Write a sequence of strings to the file.  The sequence can be any
   iterable object producing strings, typically a list of strings.
   There is no return value. (The name is intended to match
   ``readlines()``; ``writelines()`` does not add line separators.)

Files support the iterator protocol.  Each iteration returns the same
result as ``file.readline()``, and iteration ends when the
``readline()`` method returns an empty string.

File objects also offer a number of other interesting attributes.
These are not required for file-like objects, but should be
implemented if they make sense for the particular object.

file.closed

   bool indicating the current state of the file object.  This is a
   read-only attribute; the ``close()`` method changes the value. It
   may not be available on all file-like objects.

file.encoding

   The encoding that this file uses. When Unicode strings are written
   to a file, they will be converted to byte strings using this
   encoding. In addition, when the file is connected to a terminal,
   the attribute gives the encoding that the terminal is likely to use
   (that  information might be incorrect if the user has misconfigured
   the  terminal). The attribute is read-only and may not be present
   on all file-like objects. It may also be ``None``, in which case
   the file uses the system default encoding for converting Unicode
   strings.

   New in version 2.3.

file.errors

   The Unicode error handler used along with the encoding.

   New in version 2.6.

file.mode

   The I/O mode for the file.  If the file was created using the
   ``open()`` built-in function, this will be the value of the *mode*
   parameter.  This is a read-only attribute and may not be present on
   all file-like objects.

file.name

   If the file object was created using ``open()``, the name of the
   file. Otherwise, some string that indicates the source of the file
   object, of the form ``<...>``.  This is a read-only attribute and
   may not be present on all file-like objects.

file.newlines

   If Python was built with the *--with-universal-newlines* option to
   **configure** (the default) this read-only attribute exists, and
   for files opened in universal newline read mode it keeps track of
   the types of newlines encountered while reading the file. The
   values it can take are ``'\r'``, ``'\n'``, ``'\r\n'``, ``None``
   (unknown, no newlines read yet) or a tuple containing all the
   newline types seen, to indicate that multiple newline conventions
   were encountered. For files not opened in universal newline read
   mode the value of this attribute will be ``None``.

file.softspace

   Boolean that indicates whether a space character needs to be
   printed before another value when using the ``print`` statement.
   Classes that are trying to simulate a file object should also have
   a writable ``softspace`` attribute, which should be initialized to
   zero.  This will be automatic for most classes implemented in
   Python (care may be needed for objects that override attribute
   access); types implemented in C will have to provide a writable
   ``softspace`` attribute.

   Note: This attribute is not used to control the ``print`` statement,
     but to allow the implementation of ``print`` to keep track of its
     internal state.


Context Manager Types
=====================

New in version 2.5.

Python's ``with`` statement supports the concept of a runtime context
defined by a context manager.  This is implemented using two separate
methods that allow user-defined classes to define a runtime context
that is entered before the statement body is executed and exited when
the statement ends.

The *context management protocol* consists of a pair of methods that
need to be provided for a context manager object to define a runtime
context:

contextmanager.__enter__()

   Enter the runtime context and return either this object or another
   object related to the runtime context. The value returned by this
   method is bound to the identifier in the ``as`` clause of ``with``
   statements using this context manager.

   An example of a context manager that returns itself is a file
   object. File objects return themselves from __enter__() to allow
   ``open()`` to be used as the context expression in a ``with``
   statement.

   An example of a context manager that returns a related object is
   the one returned by ``decimal.localcontext()``. These managers set
   the active decimal context to a copy of the original decimal
   context and then return the copy. This allows changes to be made to
   the current decimal context in the body of the ``with`` statement
   without affecting code outside the ``with`` statement.

contextmanager.__exit__(exc_type, exc_val, exc_tb)

   Exit the runtime context and return a Boolean flag indicating if
   any exception that occurred should be suppressed. If an exception
   occurred while executing the body of the ``with`` statement, the
   arguments contain the exception type, value and traceback
   information. Otherwise, all three arguments are ``None``.

   Returning a true value from this method will cause the ``with``
   statement to suppress the exception and continue execution with the
   statement immediately following the ``with`` statement. Otherwise
   the exception continues propagating after this method has finished
   executing. Exceptions that occur during execution of this method
   will replace any exception that occurred in the body of the
   ``with`` statement.

   The exception passed in should never be reraised explicitly -
   instead, this method should return a false value to indicate that
   the method completed successfully and does not want to suppress the
   raised exception. This allows context management code (such as
   ``contextlib.nested``) to easily detect whether or not an
   ``__exit__()`` method has actually failed.

Python defines several context managers to support easy thread
synchronisation, prompt closure of files or other objects, and simpler
manipulation of the active decimal arithmetic context. The specific
types are not treated specially beyond their implementation of the
context management protocol. See the ``contextlib`` module for some
examples.

Python's *generator*s and the ``contextlib.contextfactory``
*decorator* provide a convenient way to implement these protocols.  If
a generator function is decorated with the
``contextlib.contextfactory`` decorator, it will return a context
manager implementing the necessary ``__enter__()`` and ``__exit__()``
methods, rather than the iterator produced by an undecorated generator
function.

Note that there is no specific slot for any of these methods in the
type structure for Python objects in the Python/C API. Extension types
wanting to define these methods must provide them as a normal Python
accessible method. Compared to the overhead of setting up the runtime
context, the overhead of a single class dictionary lookup is
negligible.


Other Built-in Types
====================

The interpreter supports several other kinds of objects. Most of these
support only one or two operations.


Modules
-------

The only special operation on a module is attribute access:
``m.name``, where *m* is a module and *name* accesses a name defined
in *m*'s symbol table. Module attributes can be assigned to.  (Note
that the ``import`` statement is not, strictly speaking, an operation
on a module object; ``import foo`` does not require a module object
named *foo* to exist, rather it requires an (external) *definition*
for a module named *foo* somewhere.)

A special member of every module is ``__dict__``. This is the
dictionary containing the module's symbol table. Modifying this
dictionary will actually change the module's symbol table, but direct
assignment to the ``__dict__`` attribute is not possible (you can
write ``m.__dict__['a'] = 1``, which defines ``m.a`` to be ``1``, but
you can't write ``m.__dict__ = {}``).  Modifying ``__dict__`` directly
is not recommended.

Modules built into the interpreter are written like this: ``<module
'sys' (built-in)>``.  If loaded from a file, they are written as
``<module 'os' from '/usr/local/lib/pythonX.Y/os.pyc'>``.


Classes and Class Instances
---------------------------

See *Objects, values and types* and *Class definitions* for these.


Functions
---------

Function objects are created by function definitions.  The only
operation on a function object is to call it: ``func(argument-list)``.

There are really two flavors of function objects: built-in functions
and user-defined functions.  Both support the same operation (to call
the function), but the implementation is different, hence the
different object types.

See *Function definitions* for more information.


Methods
-------

Methods are functions that are called using the attribute notation.
There are two flavors: built-in methods (such as ``append()`` on
lists) and class instance methods.  Built-in methods are described
with the types that support them.

The implementation adds two special read-only attributes to class
instance methods: ``m.im_self`` is the object on which the method
operates, and ``m.im_func`` is the function implementing the method.
Calling ``m(arg-1, arg-2, ..., arg-n)`` is completely equivalent to
calling ``m.im_func(m.im_self, arg-1, arg-2, ..., arg-n)``.

Class instance methods are either *bound* or *unbound*, referring to
whether the method was accessed through an instance or a class,
respectively.  When a method is unbound, its ``im_self`` attribute
will be ``None`` and if called, an explicit ``self`` object must be
passed as the first argument.  In this case, ``self`` must be an
instance of the unbound method's class (or a subclass of that class),
otherwise a ``TypeError`` is raised.

Like function objects, methods objects support getting arbitrary
attributes. However, since method attributes are actually stored on
the underlying function object (``meth.im_func``), setting method
attributes on either bound or unbound methods is disallowed.
Attempting to set a method attribute results in a ``TypeError`` being
raised.  In order to set a method attribute, you need to explicitly
set it on the underlying function object:

   class C:
       def method(self):
           pass

   c = C()
   c.method.im_func.whoami = 'my name is c'

See *The standard type hierarchy* for more information.


Code Objects
------------

Code objects are used by the implementation to represent "pseudo-
compiled" executable Python code such as a function body. They differ
from function objects because they don't contain a reference to their
global execution environment.  Code objects are returned by the built-
in ``compile()`` function and can be extracted from function objects
through their ``func_code`` attribute. See also the ``code`` module.

A code object can be executed or evaluated by passing it (instead of a
source string) to the ``exec`` statement or the built-in ``eval()``
function.

See *The standard type hierarchy* for more information.


Type Objects
------------

Type objects represent the various object types.  An object's type is
accessed by the built-in function ``type()``.  There are no special
operations on types.  The standard module ``types`` defines names for
all standard built-in types.

Types are written like this: ``<type 'int'>``.


The Null Object
---------------

This object is returned by functions that don't explicitly return a
value.  It supports no special operations.  There is exactly one null
object, named ``None`` (a built-in name).

It is written as ``None``.


The Ellipsis Object
-------------------

This object is used by extended slice notation (see *Slicings*).  It
supports no special operations.  There is exactly one ellipsis object,
named ``Ellipsis`` (a built-in name).

It is written as ``Ellipsis``.


Boolean Values
--------------

Boolean values are the two constant objects ``False`` and ``True``.
They are used to represent truth values (although other values can
also be considered false or true).  In numeric contexts (for example
when used as the argument to an arithmetic operator), they behave like
the integers 0 and 1, respectively. The built-in function ``bool()``
can be used to cast any value to a Boolean, if the value can be
interpreted as a truth value (see section Truth Value Testing above).

They are written as ``False`` and ``True``, respectively.


Internal Objects
----------------

See *The standard type hierarchy* for this information.  It describes
stack frame objects, traceback objects, and slice objects.


Special Attributes
==================

The implementation adds a few special read-only attributes to several
object types, where they are relevant.  Some of these are not reported
by the ``dir()`` built-in function.

object.__dict__

   A dictionary or other mapping object used to store an object's
   (writable) attributes.

object.__methods__

   Deprecated since version 2.2: Use the built-in function ``dir()``
   to get a list of an object's attributes. This attribute is no
   longer available.

object.__members__

   Deprecated since version 2.2: Use the built-in function ``dir()``
   to get a list of an object's attributes. This attribute is no
   longer available.

instance.__class__

   The class to which a class instance belongs.

class.__bases__

   The tuple of base classes of a class object.  If there are no base
   classes, this will be an empty tuple.

class.__name__

   The name of the class or type.

The following attributes are only supported by *new-style class*es.

class.__mro__

   This attribute is a tuple of classes that are considered when
   looking for base classes during method resolution.

class.mro()

   This method can be overridden by a metaclass to customize the
   method resolution order for its instances.  It is called at class
   instantiation, and its result is stored in ``__mro__``.

class.__subclasses__()

   Each new-style class keeps a list of weak references to its
   immediate subclasses.  This method returns a list of all those
   references still alive. Example:

      >>> int.__subclasses__()
      [<type 'bool'>]

-[ Footnotes ]-

[1] Additional information on these special methods may be found in
    the Python Reference Manual (*Basic customization*).

[2] As a consequence, the list ``[1, 2]`` is considered equal to
    ``[1.0, 2.0]``, and similarly for tuples.

[3] They must have since the parser can't tell the type of the
    operands.

[4] To format only a tuple you should therefore provide a singleton
    tuple whose only element is the tuple to be formatted.

[5] These numbers are fairly arbitrary.  They are intended to avoid
    printing endless strings of meaningless digits without hampering
    correct use and without having to know the exact precision of
    floating point values on a particular machine.

[6] The advantage of leaving the newline on is that returning an empty
    string is then an unambiguous EOF indication.  It is also possible
    (in cases where it might matter, for example, if you want to make
    an exact copy of a file while scanning its lines) to tell whether
    the last line of a file ended in a newline or not (yes this
    happens!).
