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

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

The principal built-in types are numerics, sequences, mappings,
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``, ``0.0``, ``0j``.

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

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

* instances of user-defined classes, if the class defines a
  ``__bool__()`` 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
===========

There are eight comparison operations in Python.  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                   |
+==============+===========================+
| ``<``        | strictly less than        |
+--------------+---------------------------+
| ``<=``       | less than or equal        |
+--------------+---------------------------+
| ``>``        | strictly greater than     |
+--------------+---------------------------+
| ``>=``       | greater than or equal     |
+--------------+---------------------------+
| ``==``       | equal                     |
+--------------+---------------------------+
| ``!=``       | not equal                 |
+--------------+---------------------------+
| ``is``       | object identity           |
+--------------+---------------------------+
| ``is not``   | negated object identity   |
+--------------+---------------------------+

Objects of different types, except different numeric types, never
compare equal. Furthermore, some types (for example, function objects)
support only a degenerate notion of comparison where any two objects
of that type are unequal.  The ``<``, ``<=``, ``>`` and ``>=``
operators will raise a ``TypeError`` exception when any operand is a
complex number, the objects are of different types that cannot be
compared, or other cases where there is no defined ordering.

Non-identical instances of a class normally compare as non-equal
unless the class defines the ``__eq__()`` method.

Instances of a class cannot be ordered with respect to other instances
of the same class, or other types of object, unless the class defines
enough of the methods ``__lt__()``, ``__le__()``, ``__gt__()``, and
``__ge__()`` (in general, ``__lt__()`` and ``__eq__()`` are
sufficient, if you want the conventional meanings of the comparison
operators).

The behavior of the ``is`` and ``is not`` operators cannot be
customized; also they can be applied to any two objects and never
raise an exception.

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


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

There are three distinct numeric types: *integers*, *floating point
numbers*, and *complex numbers*.  In addition, Booleans are a subtype
of integers.  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``. (The
standard library includes additional numeric types, ``fractions`` that
hold rationals, and ``decimal`` that hold floating-point numbers with
user-definable precision.)

Numbers are created by numeric literals or as the result of built-in
functions and operators.  Unadorned integer literals (including hex,
octal and binary numbers) yield integers.  Numeric literals containing
a decimal point or an exponent sign yield floating point numbers.
Appending ``'j'`` or ``'J'`` to a numeric literal yields an imaginary
number (a complex number with a zero real part) which you can add to
an integer or float to get a complex number with real and imaginary
parts.

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 integer is
narrower than floating point, which is narrower than complex.
Comparisons between numbers of mixed type use the same rule. [2] The
constructors ``int()``, ``float()``, and ``complex()`` can be used to
produce numbers of a specific type.

All numeric types (except complex) support the following operations,
sorted by ascending priority (operations in the same box have the same
priority; all numeric operations have a higher priority than
comparison operations):

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

Notes:

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

2. Not for complex numbers.  Instead convert to floats using ``abs()``
   if appropriate.

3. Conversion from floating point to integer may round or truncate as
   in C; see functions ``floor()`` and ``ceil()`` in the ``math``
   module for well-defined conversions.

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

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

All ``numbers.Real`` types (``int`` 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*      |          |
+----------------------+--------------------------------------+----------+

For additional numeric operations see the ``math`` and ``cmath``
modules.


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

Integers support additional operations that make sense only for bit-
strings. Negative numbers are treated as their 2's complement value
(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 (operations in the same box have the same 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)`` without overflow check.

3. A right shift by *n* bits is equivalent to division by ``pow(2,
   n)`` without overflow check.


Additional Methods on Integer Types
-----------------------------------

int.bit_length()

   Return the number of bits necessary to represent an integer in
   binary, excluding the sign and leading zeros:

      >>> n = -37
      >>> bin(n)
      '-0b100101'
      >>> n.bit_length()
      6

   More precisely, if ``x`` is nonzero, then ``x.bit_length()`` is the
   unique positive integer ``k`` such that ``2**(k-1) <= abs(x) <
   2**k``. Equivalently, when ``abs(x)`` is small enough to have a
   correctly rounded logarithm, then ``k = 1 + int(log(abs(x), 2))``.
   If ``x`` is zero, then ``x.bit_length()`` returns ``0``.

   Equivalent to:

      def bit_length(self):
          s = bin(x)          # binary representation:  bin(-37) --> '-0b100101'
          s = s.lstrip('-0b') # remove leading zeros and minus sign
          return len(s)       # len('100101') --> 6

   New in version 3.1.


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.

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.

classmethod float.fromhex(s)

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

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
==============

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.

Once an iterator's ``__next__()`` method raises ``StopIteration``, it
must continue to do so on subsequent calls.  Implementations that do
not obey this property are deemed broken.


Generator Types
---------------

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. More information about generators can be
found in *the documentation for the yield expression*.


Sequence Types --- ``str``, ``bytes``, ``bytearray``, ``list``, ``tuple``, ``range``
====================================================================================

There are six sequence types: strings, byte sequences (``bytes``
objects), byte arrays (``bytearray`` objects), lists, tuples, and
range objects.  For other containers see the built in ``dict`` and
``set`` classes, and the ``collections`` module.

Strings contain Unicode characters.  Their literals are written in
single or double quotes: ``'xyzzy'``, ``"frobozz"``.  See *String and
Bytes literals* for more about string literals.  In addition to the
functionality described here, there are also string-specific methods
described in the *String Methods* section.

Bytes and bytearray objects contain single bytes -- the former is
immutable while the latter is a mutable sequence.  Bytes objects can
be constructed the constructor, ``bytes()``, and from literals; use a
``b`` prefix with normal string syntax: ``b'xyzzy'``.  To construct
byte arrays, use the ``bytearray()`` function.

Warning: While string objects are sequences of characters (represented by
  strings of length 1), bytes and bytearray objects are sequences of
  *integers* (between 0 and 255), representing the ASCII value of
  single bytes.  That means that for a bytes or bytearray object *b*,
  ``b[0]`` will be an integer, while ``b[0:1]`` will be a bytes or
  bytearray object of length 1.  The representation of bytes objects
  uses the literal format (``b'...'``) since it is generally more
  useful than e.g. ``bytes([50, 19, 100])``.  You can always convert a
  bytes object into a list of integers using ``list(b)``.Also, while
  in previous Python versions, byte strings and Unicode strings could
  be exchanged for each other rather freely (barring encoding issues),
  strings and bytes are now completely separate concepts.  There's no
  implicit en-/decoding if you pass an object of the wrong type.  A
  string always compares unequal to a bytes or bytearray object.

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,)``.

Objects of type range are created using the ``range()`` 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 object, the ``in`` and ``not in`` operations
   act like a substring test.

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. **CPython implementation detail:** 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.


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

String objects support the methods listed below.  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, bytes, bytearray, list,
tuple, range* section. To output formatted strings, see the *String
Formatting* 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.

str.center(width[, fillchar])

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

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.encode([encoding[, errors]])

   Return an encoded version of the string as a bytes object.  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*.

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.

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(*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.

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.

str.isalpha()

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

str.isdecimal()

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

str.isdigit()

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

str.isidentifier()

   Return true if the string is a valid identifier according to the
   language definition, section *Identifiers and keywords*.

str.islower()

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

str.isnumeric()

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

str.isprintable()

   Return true if all characters in the string are printable or the
   string is empty, false otherwise.  Nonprintable characters are
   those characters defined in the Unicode character database as
   "Other" or "Separator", excepting the ASCII space (0x20) which is
   considered printable.  (Note that printable characters in this
   context are those which should not be escaped when ``repr()`` is
   invoked on a string.  It has no bearing on the handling of strings
   written to ``sys.stdout`` or ``sys.stderr``.)

str.isspace()

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

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.

str.isupper()

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

str.join(iterable)

   Return a string which is the concatenation of the strings in the
   *iterable* *iterable*.  A ``TypeError`` will be raised if there are
   any non-string values in *seq*, including ``bytes`` objects.  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)``.

str.lower()

   Return a copy of the string converted to lowercase.

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'

static str.maketrans(x[, y[, z]])

   This static method returns a translation table usable for
   ``str.translate()``.

   If there is only one argument, it must be a dictionary mapping
   Unicode ordinals (integers) or characters (strings of length 1) to
   Unicode ordinals, strings (of arbitrary lengths) or None.
   Character keys will then be converted to ordinals.

   If there are two arguments, they must be strings of equal length,
   and in the resulting dictionary, each character in x will be mapped
   to the character at the same position in y.  If there is a third
   argument, it must be a string, whose characters will be mapped to
   None in the result.

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.

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)``.

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.

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.

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'

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.

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'

str.swapcase()

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

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."

str.translate(map)

   Return a copy of the *s* where all characters have been mapped
   through the *map* which must be a dictionary of Unicode ordinals
   (integers) to Unicode ordinals, strings or ``None``.  Unmapped
   characters are left untouched. Characters mapped to ``None`` are
   deleted.

   You can use ``str.maketrans()`` to create a translation map from
   character-to-character mappings in different formats.

   Note: An even 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.

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)``.


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

Note: The formatting operations described here are obsolete and may go
  away in future versions of Python.  Use the new *String Formatting*
  in new code.

String 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), ``%`` 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* 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()``).  |         |
+--------------+-------------------------------------------------------+---------+
| ``'%'``      | 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 precision determines the maximal number of characters used.

1. See **PEP 237**.

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

Changed in version 3.1: ``%f`` conversions for numbers whose absolute
value is over 1e50 are no longer replaced by ``%g`` conversions.

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


Range Type
----------

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

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


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

List and bytearray 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).

Note that while lists allow their items to be of any type, bytearray
object "items" are all integers in the range 0 <= x < 256.

+--------------------------------+----------------------------------+-----------------------+
| 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)] =     |                       |
|                                | [x]``                            |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.extend(x)``                | same as ``s[len(s):len(s)] = x`` | (2)                   |
+--------------------------------+----------------------------------+-----------------------+
| ``s.count(x)``                 | return number of *i*'s for which |                       |
|                                | ``s[i] == x``                    |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.index(x[, i[, j]])``       | return smallest *k* such that    | (3)                   |
|                                | ``s[k] == x`` and ``i <= k < j`` |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.insert(i, x)``             | same as ``s[i:i] = [x]``         | (4)                   |
+--------------------------------+----------------------------------+-----------------------+
| ``s.pop([i])``                 | same as ``x = s[i]; del s[i];    | (5)                   |
|                                | return x``                       |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.remove(x)``                | same as ``del s[s.index(x)]``    | (3)                   |
+--------------------------------+----------------------------------+-----------------------+
| ``s.reverse()``                | reverses the items of *s* in     | (6)                   |
|                                | place                            |                       |
+--------------------------------+----------------------------------+-----------------------+
| ``s.sort([key[, reverse]])``   | sort the items of *s* in place   | (6), (7), (8)         |
+--------------------------------+----------------------------------+-----------------------+

Notes:

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

2. *x* can be any iterable object.

3. 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 sequence length is added, as for slice indices.  If it
   is still negative, it is truncated to zero, as for slice indices.

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

5. The optional argument *i* defaults to ``-1``, so that by default
   the last item is removed and returned.

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

7. The ``sort()`` method takes optional arguments for controlling the
   comparisons.  Each must be specified as a keyword argument.

   *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.

   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).

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

8. ``sort()`` is not supported by ``bytearray`` objects.


Bytes and Byte Array Methods
----------------------------

Bytes and bytearray objects, being "strings of bytes", have all
methods found on strings, with the exception of ``encode()``,
``format()`` and ``isidentifier()``, which do not make sense with
these types.  For converting the objects to strings, they have a
``decode()`` method.

Wherever one of these methods needs to interpret the bytes as
characters (e.g. the ``is...()`` methods), the ASCII character set is
assumed.

Note: The methods on bytes and bytearray objects don't accept strings as
  their arguments, just as the methods on strings don't accept bytes
  as their arguments.  For example, you have to write

     a = "abc"
     b = a.replace("a", "f")

  and

     a = b"abc"
     b = a.replace(b"a", b"f")

bytes.decode([encoding[, errors]])
bytearray.decode([encoding[, errors]])

   Return a string decoded from the given bytes.  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'`` and any other name registered via
   ``codecs.register_error()``, see section *Codec Base Classes*. For
   a list of possible encodings, see section *Standard Encodings*.

The bytes and bytearray types have an additional class method:

classmethod bytes.fromhex(string)
classmethod bytearray.fromhex(string)

   This ``bytes`` class method returns a bytes or bytearray object,
   decoding the given string object.  The string must contain two
   hexadecimal digits per byte, spaces are ignored.

   >>> bytes.fromhex('f0 f1f2  ')
   b'\xf0\xf1\xf2'

The maketrans and translate methods differ in semantics from the
versions available on strings:

bytes.translate(table[, delete])
bytearray.translate(table[, delete])

   Return a copy of the bytes or bytearray object where all bytes
   occurring in the optional argument *delete* are removed, and the
   remaining bytes have been mapped through the given translation
   table, which must be a bytes object of length 256.

   You can use the ``bytes.maketrans()`` method to create a
   translation table.

   Set the *table* argument to ``None`` for translations that only
   delete characters:

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

static bytes.maketrans(from, to)
static bytearray.maketrans(from, to)

   This static method returns a translation table usable for
   ``bytes.translate()`` that will map each character in *from* into
   the character at the same position in *to*; *from* and *to* must be
   bytes objects and have the same length.

   New in version 3.1.


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.)

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 built-in 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.

   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.

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

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

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

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

   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``.

   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 all others.

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

      Update the set, keeping only elements found in it and all
      others.

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

      Update the set, removing elements found in others.

   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.


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.

   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.

      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``.

   key not in d

      Equivalent to ``not key in d``.

   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.

   classmethod 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``.

   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``.

   items()

      Return a new view of the dictionary's items (``(key, value)``
      pairs).  See below for documentation of view objects.

   keys()

      Return a new view of the dictionary's keys.  See below for
      documentation of view objects.

   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.

   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 updated with those key/value pairs:
         ``d.update(red=1, blue=2)``.

   values()

      Return a new view of the dictionary's values.  See below for
      documentation of view objects.


Dictionary view objects
-----------------------

The objects returned by ``dict.keys()``, ``dict.values()`` and
``dict.items()`` are *view objects*.  They provide a dynamic view on
the dictionary's entries, which means that when the dictionary
changes, the view reflects these changes.

Dictionary views can be iterated over to yield their respective data,
and support membership tests:

len(dictview)

   Return the number of entries in the dictionary.

iter(dictview)

   Return an iterator over the keys, values or items (represented as
   tuples of ``(key, value)``) in the dictionary.

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

   Iterating views while adding or deleting entries in the dictionary
   may raise a ``RuntimeError`` or fail to iterate over all entries.

x in dictview

   Return ``True`` if *x* is in the underlying dictionary's keys,
   values or items (in the latter case, *x* should be a ``(key,
   value)`` tuple).

Keys views are set-like since their entries are unique and hashable.
If all values are hashable, so that (key, value) pairs are unique and
hashable, then the items view is also set-like.  (Values views are not
treated as set-like since the entries are generally not unique.)  Then
these set operations are available ("other" refers either to another
view or a set):

dictview & other

   Return the intersection of the dictview and the other object as a
   new set.

dictview | other

   Return the union of the dictview and the other object as a new set.

dictview - other

   Return the difference between the dictview and the other object
   (all elements in *dictview* that aren't in *other*) as a new set.

dictview ^ other

   Return the symmetric difference (all elements either in *dictview*
   or *other*, but not in both) of the dictview and the other object
   as a new set.

An example of dictionary view usage:

   >>> dishes = {'eggs': 2, 'sausage': 1, 'bacon': 1, 'spam': 500}
   >>> keys = dishes.keys()
   >>> values = dishes.values()

   >>> # iteration
   >>> n = 0
   >>> for val in values:
   ...     n += val
   >>> print(n)
   504

   >>> # keys and values are iterated over in the same order
   >>> list(keys)
   ['eggs', 'bacon', 'sausage', 'spam']
   >>> list(values)
   [2, 1, 1, 500]

   >>> # view objects are dynamic and reflect dict changes
   >>> del dishes['eggs']
   >>> del dishes['sausage']
   >>> list(keys)
   ['spam', 'bacon']

   >>> # set operations
   >>> keys & {'eggs', 'bacon', 'salad'}
   {'bacon'}


memoryview Types
================

``memoryview``s allow Python code to access the internal data of an
object that supports the buffer protocol without copying.  Memory can
be interpreted as simple bytes or complex data structures.

class class memoryview(obj)

   Create a ``memoryview`` that references *obj*.  *obj* must support
   the buffer protocol.  Builtin objects that support the buffer
   protocol include ``bytes`` and ``bytearray``.

   ``len(view)`` returns the total number of bytes in the memoryview,
   *view*.

   A ``memoryview`` supports slicing to expose its data.  Taking a
   single index will return a single byte.  Full slicing will result
   in a subview:

      >>> v = memoryview(b'abcefg')
      >>> v[1]
      b'b'
      >>> v[-1]
      b'g'
      >>> v[1:4]
      <memory at 0x77ab28>
      >>> bytes(v[1:4])
      b'bce'
      >>> v[3:-1]
      <memory at 0x744f18>
      >>> bytes(v[4:-1])

   If the object the memory view is over supports changing its data,
   the memoryview supports slice assignment:

      >>> data = bytearray(b'abcefg')
      >>> v = memoryview(data)
      >>> v.readonly
      False
      >>> v[0] = b'z'
      >>> data
      bytearray(b'zbcefg')
      >>> v[1:4] = b'123'
      >>> data
      bytearray(b'a123fg')
      >>> v[2] = b'spam'
      Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
      ValueError: cannot modify size of memoryview object

   Notice how the size of the memoryview object can not be changed.

   ``memoryview`` has two methods:

   tobytes()

      Return the data in the buffer as a bytestring.

   tolist()

      Return the data in the buffer as a list of integers.

         >>> memoryview(b'abc').tolist()
         [97, 98, 99]

   There are also several readonly attributes available:

   format

      A string containing the format (in ``struct`` module style) for
      each element in the view.  This defaults to ``'B'``, a simple
      bytestring.

   itemsize

      The size in bytes of each element of the memoryview.

   shape

      A tuple of integers the length of ``ndim`` giving the shape of
      the memory as a N-dimensional array.

   ndim

      An integer indicating how many dimensions of a multi-dimensional
      array the memory represents.

   strides

      A tuple of integers the length of ``ndim`` giving the size in
      bytes to access each element for each dimension of the array.


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

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.contextmanager``
*decorator* provide a convenient way to implement these protocols.  If
a generator function is decorated with the
``contextlib.contextmanager`` 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.

If you access a method (a function defined in a class namespace)
through an instance, you get a special object: a *bound method* (also
called *instance method*) object. When called, it will add the
``self`` argument to the argument list.  Bound methods have two
special read-only attributes: ``m.__self__`` is the object on which
the method operates, and ``m.__func__`` is the function implementing
the method.  Calling ``m(arg-1, arg-2, ..., arg-n)`` is completely
equivalent to calling ``m.__func__(m.__self__, arg-1, arg-2, ...,
arg-n)``.

Like function objects, bound method objects support getting arbitrary
attributes.  However, since method attributes are actually stored on
the underlying function object (``meth.__func__``), setting method
attributes on bound 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.__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 ``__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()`` or ``eval()``  built-in functions.

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: ``<class '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 commonly used by slicing (see *Slicings*).  It supports
no special operations.  There is exactly one ellipsis object, named
``Ellipsis`` (a built-in name).

It is written as ``Ellipsis`` or ``...``.


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.

instance.__class__

   The class to which a class instance belongs.

class.__bases__

   The tuple of base classes of a class object.

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.
