.. XXX: reference/datamodel and this have quite a few overlaps!


.. _bltin-types:

**************
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.

.. index:: pair: built-in; types

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

.. index:: statement: print

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 :ref:`repr() <func-repr>` function or the slightly different
:func:`str` function).  The latter function is implicitly used when an object is
written by the :func:`print` function.


.. _truth:

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

.. index::
   statement: if
   statement: while
   pair: truth; value
   pair: Boolean; operations
   single: false

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

  .. index:: single: None (Built-in object)

* ``None``

  .. index:: single: False (Built-in object)

* ``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 :meth:`__nonzero__`
  or :meth:`__len__` method, when that method returns the integer zero or
  :class:`bool` value ``False``. [1]_

.. index:: single: true

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

.. index::
   operator: or
   operator: and
   single: False
   single: 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:

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

.. index:: pair: Boolean; operations

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``                  |       |
+-------------+---------------------------------+-------+

.. index::
   operator: and
   operator: or
   operator: not

Notes:

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

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


.. _stdcomparisons:

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

.. index::
   pair: chaining; comparisons
   pair: operator; comparison
   operator: ==
   operator: <
   operator: <=
   operator: >
   operator: >=
   operator: !=
   operator: is
   operator: is not

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
    ``!=``.

.. index::
   pair: object; numeric
   pair: objects; comparing

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 :exc:`TypeError` exception when any operand is
a complex number.

.. index::
   single: __cmp__() (instance method)
   single: __eq__() (instance method)
   single: __ne__() (instance method)
   single: __lt__() (instance method)
   single: __le__() (instance method)
   single: __gt__() (instance method)
   single: __ge__() (instance method)

Non-identical instances of a class normally compare as non-equal unless the
class defines the :meth:`__eq__` method or the :meth:`__cmp__` 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 either enough of
the rich comparison methods (:meth:`__lt__`, :meth:`__le__`, :meth:`__gt__`, and
:meth:`__ge__`) or the :meth:`__cmp__` method.

.. impl-detail::

   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.

.. index::
   operator: in
   operator: not in

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


.. _typesnumeric:

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

.. index::
   object: numeric
   object: Boolean
   object: integer
   object: long integer
   object: floating point
   object: complex number
   pair: C; language

There are four distinct numeric types: :dfn:`plain integers`, :dfn:`long
integers`, :dfn:`floating point numbers`, and :dfn:`complex numbers`. In
addition, Booleans are a subtype of plain integers. Plain integers (also just
called :dfn:`integers`) are implemented using :c:type:`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 usually implemented using :c:type:`double` in C; information about
the precision and internal representation of floating point numbers for the
machine on which your program is running is available in
:data:`sys.float_info`.  Complex numbers have a real and imaginary part, which
are each a floating point number.  To extract these parts from a complex number
*z*, use ``z.real`` and ``z.imag``. (The standard library includes additional
numeric types, :mod:`fractions` that hold rationals, and :mod:`decimal` that
hold floating-point numbers with user-definable precision.)

.. index::
   pair: numeric; literals
   pair: integer; literals
   triple: long; integer; literals
   pair: floating point; literals
   pair: complex number; literals
   pair: hexadecimal; literals
   pair: octal; literals

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.

.. index::
   single: arithmetic
   builtin: int
   builtin: long
   builtin: float
   builtin: complex
   operator: +
   operator: -
   operator: *
   operator: /
   operator: //
   operator: %
   operator: **

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 :func:`int`,
:func:`long`, :func:`float`, and :func:`complex` can be used to produce numbers
of a specific type.

All built-in numeric types support the following operations. See
:ref:`power` 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   | (4)(5) |
|                    | *y*                             |        |
+--------------------+---------------------------------+--------+
| ``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)   |
+--------------------+---------------------------------+--------+

.. index::
   triple: operations on; numeric; types
   single: conjugate() (complex number method)

Notes:

(1)
   .. index::
      pair: integer; division
      triple: long; integer; division

   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)
   .. index::
      module: math
      single: floor() (in module math)
      single: ceil() (in module math)
      single: trunc() (in module math)
      pair: numeric; conversions

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

(3)
   See :ref:`built-in-funcs` for a full description.

(4)
   .. deprecated:: 2.3
      The floor division operator, the modulo operator, and the :func:`divmod`
      function are no longer defined for complex numbers.  Instead, convert to
      a floating point number using the :func:`abs` function 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.

   .. versionadded:: 2.6

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

All :class:`numbers.Real` types (:class:`int`, :class:`long`, and
:class:`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 ties away from zero. If n |        |
|                    | is omitted, it defaults to 0.      |        |
+--------------------+------------------------------------+--------+
| ``math.floor(x)``  | the greatest integral float <= *x* |        |
+--------------------+------------------------------------+--------+
| ``math.ceil(x)``   | the least integral float >= *x*    |        |
+--------------------+------------------------------------+--------+

.. XXXJH exceptions: overflow (when? what operations?) zerodivision


.. _bitstring-ops:

Bitwise Operations on Integer Types
--------------------------------------

.. index::
   triple: operations on; integer; types
   pair: bitwise; operations
   pair: shifting; operations
   pair: masking; operations
   operator: ^
   operator: &
   operator: <<
   operator: >>

Bitwise operations only make sense for integers.  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 bitwise operations sorted in ascending priority
(operations in the same box have the same priority):

+------------+--------------------------------+----------+
| Operation  | Result                         | Notes    |
+============+================================+==========+
| ``x | y``  | bitwise :dfn:`or` of *x* and   |          |
|            | *y*                            |          |
+------------+--------------------------------+----------+
| ``x ^ y``  | bitwise :dfn:`exclusive or` of |          |
|            | *x* and *y*                    |          |
+------------+--------------------------------+----------+
| ``x & y``  | bitwise :dfn:`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 :exc:`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 Integer Types
-----------------------------------

The integer types implement the :class:`numbers.Integral` :term:`abstract base
class`. In addition, they provide one more method:

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

    .. versionadded:: 2.7


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

The float type implements the :class:`numbers.Real` :term:`abstract base
class`. float also has the following additional methods.

.. method:: float.as_integer_ratio()

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

   .. versionadded:: 2.6

.. method:: float.is_integer()

   Return ``True`` if the float instance is finite with integral
   value, and ``False`` otherwise::

      >>> (-2.0).is_integer()
      True
      >>> (3.2).is_integer()
      False

   .. versionadded:: 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.


.. method:: 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.

   .. versionadded:: 2.6


.. method:: float.fromhex(s)

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

   .. versionadded:: 2.6


Note that :meth:`float.hex` is an instance method, while
:meth:`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
:meth:`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
:meth:`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'


.. _typeiter:

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

.. versionadded:: 2.2

.. index::
   single: iterator protocol
   single: protocol; iterator
   single: sequence; iteration
   single: container; iteration over

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:

.. XXX duplicated in reference/datamodel!

.. method:: 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
   :c:member:`~PyTypeObject.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 :dfn:`iterator protocol`:


.. method:: iterator.__iter__()

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


.. method:: iterator.next()

   Return the next item from the container.  If there are no further items, raise
   the :exc:`StopIteration` exception.  This method corresponds to the
   :c:member:`~PyTypeObject.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 :meth:`next` method
raises :exc:`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.)


.. _generator-types:

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

Python's :term:`generator`\s provide a convenient way to implement the iterator
protocol.  If a container object's :meth:`__iter__` method is implemented as a
generator, it will automatically return an iterator object (technically, a
generator object) supplying the :meth:`__iter__` and :meth:`next` methods.  More
information about generators can be found in :ref:`the documentation for the
yield expression <yieldexpr>`.


.. _typesseq:

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

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

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


.. index::
   object: sequence
   object: string
   object: Unicode
   object: tuple
   object: list
   object: bytearray
   object: buffer
   object: xrange

String literals are written in single or double quotes: ``'xyzzy'``,
``"frobozz"``.  See :ref:`strings` 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 :ref:`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,)``.

Bytearray objects are created with the built-in function :func:`bytearray`.

Buffer objects are not directly supported by Python syntax, but can be created
by calling the built-in function :func:`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 :func:`xrange` function.  They don't
support slicing, concatenation or repetition, and using ``in``, ``not in``,
:func:`min` or :func:`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 :ref:`typesseq-mutable`.

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   | \(6)     |
|                  | *t*                            |          |
+------------------+--------------------------------+----------+
| ``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*            |          |
+------------------+--------------------------------+----------+
| ``s.index(x)``   | index of the first occurrence  |          |
|                  | of *x* in *s*                  |          |
+------------------+--------------------------------+----------+
| ``s.count(x)``   | total number of occurrences of |          |
|                  | *x* in *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 :ref:`comparisons` in the language
reference.)

.. index::
   triple: operations on; sequence; types
   builtin: len
   builtin: min
   builtin: max
   pair: concatenation; operation
   pair: repetition; operation
   pair: subscript; operation
   pair: slice; operation
   pair: extended slice; operation
   operator: in
   operator: not in

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)
   .. impl-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 :meth:`str.join` method which assures consistent
      linear concatenation performance across versions and implementations.

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


.. _string-methods:

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

.. index:: pair: string; methods

Below are listed the string methods which both 8-bit strings and
Unicode objects support.  Some of them are also available on :class:`bytearray`
objects.

In addition, Python's strings support the sequence type methods
described in the :ref:`typesseq` section. To output formatted strings
use template strings or the ``%`` operator described in the
:ref:`string-formatting` section. Also, see the :mod:`re` module for
string functions based on regular expressions.

.. method:: str.capitalize()

   Return a copy of the string with its first character capitalized and the
   rest lowercased.

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


.. method:: str.center(width[, fillchar])

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

   .. versionchanged:: 2.4
      Support for the *fillchar* argument.


.. method:: 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.


.. method:: 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 :exc:`UnicodeError`.  Other possible values are
   ``'ignore'``, ``'replace'`` and any other name registered via
   :func:`codecs.register_error`, see section :ref:`codec-base-classes`.

   .. versionadded:: 2.2

   .. versionchanged:: 2.3
      Support for other error handling schemes added.

   .. versionchanged:: 2.7
      Support for keyword arguments added.

.. method:: 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 :exc:`UnicodeError`.  Other possible values are
   ``'ignore'``, ``'replace'``, ``'xmlcharrefreplace'``, ``'backslashreplace'`` and
   any other name registered via :func:`codecs.register_error`, see section
   :ref:`codec-base-classes`. For a list of possible encodings, see section
   :ref:`standard-encodings`.

   .. versionadded:: 2.0

   .. versionchanged:: 2.3
      Support for ``'xmlcharrefreplace'`` and ``'backslashreplace'`` and other error
      handling schemes added.

   .. versionchanged:: 2.7
      Support for keyword arguments added.

.. method:: 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.

   .. versionchanged:: 2.5
      Accept tuples as *suffix*.


.. method:: 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.  Tab
   positions occur every *tabsize* characters (default is 8, giving tab
   positions at columns 0, 8, 16 and so on).  To expand the string, the current
   column is set to zero and the string is examined character by character.  If
   the character is a tab (``\t``), one or more space characters are inserted
   in the result until the current column is equal to the next tab position.
   (The tab character itself is not copied.)  If the character is a newline
   (``\n``) or return (``\r``), it is copied and the current column is reset to
   zero.  Any other character is copied unchanged and the current column is
   incremented by one regardless of how the character is represented when
   printed.

      >>> '01\t012\t0123\t01234'.expandtabs()
      '01      012     0123    01234'
      >>> '01\t012\t0123\t01234'.expandtabs(4)
      '01  012 0123    01234'


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

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

   .. note::

      The :meth:`~str.find` method should be used only if you need to know the
      position of *sub*.  To check if *sub* is a substring or not, use the
      :keyword:`in` operator::

         >>> 'Py' in 'Python'
         True


.. method:: str.format(*args, **kwargs)

   Perform a string formatting operation.  The string on which this method is
   called 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
   the 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 :ref:`formatstrings` 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, and
   should be preferred to the ``%`` formatting described in
   :ref:`string-formatting` in new code.

   .. versionadded:: 2.6


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

   Like :meth:`find`, but raise :exc:`ValueError` when the substring is not found.


.. method:: 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.


.. method:: 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.


.. method:: 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.


.. method:: str.islower()

   Return true if all cased characters [4]_ in the string are lowercase and there is at
   least one cased character, false otherwise.

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


.. method:: 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.


.. method:: 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.


.. method:: str.isupper()

   Return true if all cased characters [4]_ in the string are uppercase and there is at
   least one cased character, false otherwise.

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


.. method:: str.join(iterable)

   Return a string which is the concatenation of the strings in the
   :term:`iterable` *iterable*.  The separator between elements is the string
   providing this method.


.. 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 or equal to ``len(s)``.

   .. versionchanged:: 2.4
      Support for the *fillchar* argument.


.. method:: str.lower()

   Return a copy of the string with all the cased characters [4]_ converted to
   lowercase.

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


.. method:: 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'

   .. versionchanged:: 2.2.2
      Support for the *chars* argument.


.. method:: 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.

   .. versionadded:: 2.5


.. method:: 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.


.. method:: 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.


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

   Like :meth:`rfind` but raises :exc:`ValueError` when the substring *sub* is not
   found.


.. method:: 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 or equal to ``len(s)``.

   .. versionchanged:: 2.4
      Support for the *fillchar* argument.


.. method:: 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.

   .. versionadded:: 2.5


.. method:: 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, :meth:`rsplit` behaves like
   :meth:`split` which is described in detail below.

   .. versionadded:: 2.4


.. method:: 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'

   .. versionchanged:: 2.2.2
      Support for the *chars* argument.


.. method:: 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 or ``-1``, 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  ']``.


.. index::
   single: universal newlines; str.splitlines method

.. method:: str.splitlines([keepends])

   Return a list of the lines in the string, breaking at line boundaries.
   This method uses the :term:`universal newlines` approach to splitting lines.
   Line breaks are not included in the resulting list unless *keepends* is
   given and true.

   For example, ``'ab c\n\nde fg\rkl\r\n'.splitlines()`` returns
   ``['ab c', '', 'de fg', 'kl']``, while the same call with ``splitlines(True)``
   returns ``['ab c\n', '\n', 'de fg\r', 'kl\r\n']``.

   Unlike :meth:`~str.split` when a delimiter string *sep* is given, this
   method returns an empty list for the empty string, and a terminal line
   break does not result in an extra line.


.. method:: 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.

   .. versionchanged:: 2.5
      Accept tuples as *prefix*.


.. method:: 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'

   .. versionchanged:: 2.2.2
      Support for the *chars* argument.


.. method:: 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.


.. method:: 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.


.. method:: 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 :func:`~string.maketrans` helper function in the :mod:`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'

   .. versionadded:: 2.6
      Support for a ``None`` *table* argument.

   For Unicode objects, the :meth:`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 :mod:`codecs` module (see :mod:`encodings.cp1251` for an
   example).


.. method:: str.upper()

   Return a copy of the string with all the cased characters [4]_ converted to
   uppercase.  Note that ``str.upper().isupper()`` might be ``False`` if ``s``
   contains uncased characters or if the Unicode category of the resulting
   character(s) is not "Lu" (Letter, uppercase), but e.g. "Lt" (Letter, titlecase).

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


.. method:: 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 or equal to ``len(s)``.


   .. versionadded:: 2.2.2

The following methods are present only on unicode objects:

.. method:: 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.

.. method:: unicode.isdecimal()

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


.. _string-formatting:

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

.. index::
   single: formatting, string (%)
   single: interpolation, string (%)
   single: string; formatting
   single: string; interpolation
   single: printf-style formatting
   single: sprintf-style formatting
   single: % formatting
   single: % interpolation

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
:c:func:`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. [5]_  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:

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

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

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

#. 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.

#. 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.

#. Length modifier (optional).

#. 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 %(number)03d quote types.' % \
   ...       {"language": "Python", "number": 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            | \(5)  |
|            | :ref:`repr() <func-repr>`).                         |       |
+------------+-----------------------------------------------------+-------+
| ``'s'``    | String (converts any Python object using            | \(6)  |
|            | :func:`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 ``%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 :class:`unicode` string, the resulting
   string will also be :class:`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.

.. XXX Examples?

.. versionchanged:: 2.7
   ``%f`` conversions for numbers whose absolute value is over 1e50 are no
   longer replaced by ``%g`` conversions.

.. index::
   module: string
   module: re

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


.. _typesseq-xrange:

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

.. index:: object: xrange

The :class:`xrange` type is an immutable sequence which is commonly used for
looping.  The advantage of the :class:`xrange` type is that an :class:`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 :func:`len` function.


.. _typesseq-mutable:

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

.. index::
   triple: mutable; sequence; types
   object: list

List and :class:`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):

.. index::
   triple: operations on; sequence; types
   triple: operations on; list; type
   pair: subscript; assignment
   pair: slice; assignment
   pair: extended slice; assignment
   statement: del
   single: append() (list method)
   single: extend() (list method)
   single: count() (list method)
   single: index() (list method)
   single: insert() (list method)
   single: pop() (list method)
   single: remove() (list method)
   single: reverse() (list method)
   single: sort() (list method)

+------------------------------+--------------------------------+---------------------+
| 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]``   | \(1)                |
|                              | are 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)] =   | \(3)                |
|                              | x``                            |                     |
+------------------------------+--------------------------------+---------------------+
| ``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 :exc:`ValueError` when *x* is not found in *s*. When a negative index is
   passed as the second or third parameter to the :meth:`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.

   .. versionchanged:: 2.3
      Previously, :meth:`index` didn't have arguments for specifying start and stop
      positions.

(5)
   When a negative index is passed as the first parameter to the :meth:`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.

   .. versionchanged:: 2.3
      Previously, all negative indices were truncated to zero.

(6)
   The :meth:`pop` method's optional argument *i* defaults to ``-1``, so that
   by default the last item is removed and returned.

(7)
   The :meth:`sort` and :meth:`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 :meth:`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.  Use :func:`functools.cmp_to_key` to convert an
   old-style *cmp* function to a *key* function.

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

   .. versionchanged:: 2.4
      Support for *key* and *reverse* was added.

(9)
   Starting with Python 2.3, the :meth:`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)
   .. impl-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 2.3 and
      newer makes the list appear empty for the duration, and raises
      :exc:`ValueError` if it can detect that the list has been mutated during a
      sort.


.. _types-set:

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

.. index:: object: set

A :dfn:`set` object is an unordered collection of distinct :term:`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 :class:`dict`, :class:`list`,
and :class:`tuple` classes, and the :mod:`collections` module.)


.. versionadded:: 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 built-in set types, :class:`set` and :class:`frozenset`.
The :class:`set` type is mutable --- the contents can be changed using methods
like :meth:`~set.add` and :meth:`~set.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 :class:`frozenset` type is immutable and :term:`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.

As of Python 2.7, non-empty sets (not frozensets) can be created by placing a
comma-separated list of elements within braces, for example: ``{'jack',
'sjoerd'}``, in addition to the :class:`set` constructor.

The constructors for both classes work the same:

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

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

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

   .. describe:: len(s)

      Return the cardinality of set *s*.

   .. describe:: x in s

      Test *x* for membership in *s*.

   .. describe:: x not in s

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

   .. method:: 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.

      .. versionadded:: 2.6

   .. method:: issubset(other)
               set <= other

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

   .. method:: set < other

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

   .. method:: issuperset(other)
               set >= other

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

   .. method:: set > other

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

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

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

      .. versionchanged:: 2.6
         Accepts multiple input iterables.

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

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

      .. versionchanged:: 2.6
         Accepts multiple input iterables.

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

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

      .. versionchanged:: 2.6
         Accepts multiple input iterables.

   .. method:: symmetric_difference(other)
               set ^ other

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

   .. method:: copy()

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


   Note, the non-operator versions of :meth:`union`, :meth:`intersection`,
   :meth:`difference`, and :meth:`symmetric_difference`, :meth:`issubset`, and
   :meth:`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 :class:`set` and :class:`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 :class:`set` are compared to instances of :class:`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 total ordering
   function.  For example, any two non-empty 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 :meth:`__cmp__`
   method.

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

   Set elements, like dictionary keys, must be :term:`hashable`.

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

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

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

      Update the set, adding elements from all others.

      .. versionchanged:: 2.6
         Accepts multiple input iterables.

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

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

      .. versionchanged:: 2.6
         Accepts multiple input iterables.

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

      Update the set, removing elements found in others.

      .. versionchanged:: 2.6
         Accepts multiple input iterables.

   .. method:: symmetric_difference_update(other)
               set ^= other

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

   .. method:: add(elem)

      Add element *elem* to the set.

   .. method:: remove(elem)

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

   .. method:: discard(elem)

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

   .. method:: pop()

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

   .. method:: clear()

      Remove all elements from the set.


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

   Note, the *elem* argument to the :meth:`__contains__`, :meth:`remove`, and
   :meth:`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.


.. seealso::

   :ref:`comparison-to-builtin-set`
      Differences between the :mod:`sets` module and the built-in set types.


.. _typesmapping:

Mapping Types --- :class:`dict`
===============================

.. index::
   object: mapping
   object: dictionary
   triple: operations on; mapping; types
   triple: operations on; dictionary; type
   statement: del
   builtin: len

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

A dictionary's keys are *almost* arbitrary values.  Values that are not
:term:`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 :class:`dict` constructor.

.. class:: dict(**kwarg)
           dict(mapping, **kwarg)
           dict(iterable, **kwarg)

   Return a new dictionary initialized from an optional positional argument
   and a possibly empty set of keyword arguments.

   If no positional argument is given, an empty dictionary is created.
   If a positional argument is given and it is a mapping object, a dictionary
   is created with the same key-value pairs as the mapping object.  Otherwise,
   the positional argument must be an :term:`iterator` object.  Each item in
   the iterable must itself be an iterator with exactly two objects.  The
   first object of each item becomes a key in the new dictionary, and the
   second object the corresponding value.  If a key occurs more than once, the
   last value for that key becomes the corresponding value in the new
   dictionary.

   If keyword arguments are given, the keyword arguments and their values are
   added to the dictionary created from the positional argument.  If a key
   being added is already present, the value from the keyword argument
   replaces the value from the positional argument.

   To illustrate, the following examples all return a dictionary equal to
   ``{"one": 1, "two": 2, "three": 3}``::

      >>> a = dict(one=1, two=2, three=3)
      >>> b = {'one': 1, 'two': 2, 'three': 3}
      >>> c = dict(zip(['one', 'two', 'three'], [1, 2, 3]))
      >>> d = dict([('two', 2), ('one', 1), ('three', 3)])
      >>> e = dict({'three': 3, 'one': 1, 'two': 2})
      >>> a == b == c == d == e
      True

   Providing keyword arguments as in the first example only works for keys that
   are valid Python identifiers.  Otherwise, any valid keys can be used.

   .. versionadded:: 2.2

   .. versionchanged:: 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):

   .. describe:: len(d)

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

   .. describe:: d[key]

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

      .. versionadded:: 2.5
         If a subclass of dict defines a method :meth:`__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
         :meth:`__missing__`. If :meth:`__missing__` is not defined,
         :exc:`KeyError` is raised.  :meth:`__missing__` must be a method; it
         cannot be an instance variable. For an example, see
         :class:`collections.defaultdict`.

   .. describe:: d[key] = value

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

   .. describe:: del d[key]

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

   .. describe:: key in d

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

      .. versionadded:: 2.2

   .. describe:: key not in d

      Equivalent to ``not key in d``.

      .. versionadded:: 2.2

   .. describe:: iter(d)

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

   .. method:: clear()

      Remove all items from the dictionary.

   .. method:: copy()

      Return a shallow copy of the dictionary.

   .. method:: fromkeys(seq[, value])

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

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

      .. versionadded:: 2.3

   .. method:: 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 :exc:`KeyError`.

   .. method:: has_key(key)

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

   .. method:: items()

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

      .. impl-detail::

         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 :meth:`items`, :meth:`keys`, :meth:`values`, :meth:`iteritems`,
      :meth:`iterkeys`, and :meth:`itervalues` are called with no intervening
      modifications to the dictionary, the lists will directly correspond.  This
      allows the creation of ``(value, key)`` pairs using :func:`zip`: ``pairs =
      zip(d.values(), d.keys())``.  The same relationship holds for the
      :meth:`iterkeys` and :meth:`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()]``.

   .. method:: iteritems()

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

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

      .. versionadded:: 2.2

   .. method:: iterkeys()

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

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

      .. versionadded:: 2.2

   .. method:: itervalues()

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

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

      .. versionadded:: 2.2

   .. method:: keys()

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

   .. method:: 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 :exc:`KeyError` is raised.

      .. versionadded:: 2.3

   .. method:: popitem()

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

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

   .. method:: 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``.

   .. method:: update([other])

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

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

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

   .. method:: values()

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

   .. method:: viewitems()

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

      .. versionadded:: 2.7

   .. method:: viewkeys()

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

      .. versionadded:: 2.7

   .. method:: viewvalues()

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

      .. versionadded:: 2.7


.. _dict-views:

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

The objects returned by :meth:`dict.viewkeys`, :meth:`dict.viewvalues` and
:meth:`dict.viewitems` 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:

.. describe:: len(dictview)

   Return the number of entries in the dictionary.

.. describe:: 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 :func:`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 :exc:`RuntimeError` or fail to iterate over all entries.

.. describe:: 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):

.. describe:: dictview & other

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

.. describe:: dictview | other

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

.. describe:: 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.

.. describe:: 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.viewkeys()
   >>> values = dishes.viewvalues()

   >>> # 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'}


.. _bltin-file-objects:

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

.. index::
   object: file
   builtin: file
   module: os
   module: socket

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

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

Files have the following methods:


.. method:: 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 :exc:`ValueError` after the
   file has been closed.  Calling :meth:`close` more than once is allowed.

   As of Python 2.5, you can avoid having to call this method explicitly if you use
   the :keyword:`with` statement.  For example, the following code will
   automatically close *f* when the :keyword:`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
      :keyword:`with` statement.  If your code is intended to work with any file-like
      object, you can use the function :func:`contextlib.closing` instead of using
      the object directly.


.. method:: file.flush()

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

   .. note::

      :meth:`flush` does not necessarily write the file's data to disk.  Use
      :meth:`flush` followed by :func:`os.fsync` to ensure this behavior.


.. method:: file.fileno()

   .. index::
      pair: file; descriptor
      module: fcntl

   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
   :mod:`fcntl` module or :func:`os.read` and friends.

   .. note::

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


.. 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.


.. method:: 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
   :keyword:`for` loop (for example, ``for line in f: print line.strip()``), the
   :meth:`~file.next` method is called repeatedly.  This method returns the next input
   line, or raises :exc:`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 :keyword:`for` loop the most efficient way of looping over the lines of a
   file (a very common operation), the :meth:`~file.next` method uses a hidden read-ahead
   buffer.  As a consequence of using a read-ahead buffer, combining :meth:`~file.next`
   with other file methods (like :meth:`~file.readline`) does not work right.  However,
   using :meth:`seek` to reposition the file to an absolute position will flush the
   read-ahead buffer.

   .. versionadded:: 2.3


.. method:: 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 :c:func:`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
      :c:func:`fread` C function, and will behave the same in corner cases,
      such as whether the EOF value is cached.


.. method:: 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. When *size* is not 0, an empty string is returned *only* when EOF
   is encountered immediately.

   .. note::

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


.. method:: file.readlines([sizehint])

   Read until EOF using :meth:`~file.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.


.. method:: file.xreadlines()

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

   .. versionadded:: 2.1

   .. deprecated:: 2.3
      Use ``for line in file`` instead.


.. method:: file.seek(offset[, whence])

   Set the file's current position, like ``stdio``'s :c:func:`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 :meth:`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 :meth:`tell` are
   legal.  Use of other offsets causes undefined behavior.

   Note that not all file objects are seekable.

   .. versionchanged:: 2.6
      Passing float values as offset has been deprecated.


.. method:: file.tell()

   Return the file's current position, like ``stdio``'s :c:func:`ftell`.

   .. note::

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


.. method:: 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.


.. method:: 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 :meth:`flush` or
   :meth:`close` method is called.


.. method:: 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 :meth:`readlines`; :meth:`writelines` does not
   add line separators.)

Files support the iterator protocol.  Each iteration returns the same result as
:meth:`~file.readline`, and iteration ends when the :meth:`~file.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.


.. attribute:: file.closed

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


.. attribute:: 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.

   .. versionadded:: 2.3


.. attribute:: file.errors

   The Unicode error handler used along with the encoding.

   .. versionadded:: 2.6


.. attribute:: file.mode

   The I/O mode for the file.  If the file was created using the :func:`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.


.. attribute:: file.name

   If the file object was created using :func:`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.

   .. index::
      single: universal newlines; file.newlines attribute


.. attribute:: file.newlines

   If Python was built with :term:`universal newlines` enabled (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 newlines read mode the value of this attribute
   will be ``None``.


.. attribute:: file.softspace

   Boolean that indicates whether a space character needs to be printed before
   another value when using the :keyword:`print` statement. Classes that are trying
   to simulate a file object should also have a writable :attr:`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
   :attr:`softspace` attribute.

   .. note::

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


.. _typememoryview:

memoryview type
===============

.. versionadded:: 2.7

:class:`memoryview` objects allow Python code to access the internal data
of an object that supports the buffer protocol without copying.  Memory
is generally interpreted as simple bytes.

.. class:: memoryview(obj)

   Create a :class:`memoryview` that references *obj*.  *obj* must support the
   buffer protocol.  Built-in objects that support the buffer protocol include
   :class:`str` and :class:`bytearray` (but not :class:`unicode`).

   A :class:`memoryview` has the notion of an *element*, which is the
   atomic memory unit handled by the originating object *obj*.  For many
   simple types such as :class:`str` and :class:`bytearray`, an element
   is a single byte, but other third-party types may expose larger elements.

   ``len(view)`` returns the total number of elements in the memoryview,
   *view*.  The :class:`~memoryview.itemsize` attribute will give you the
   number of bytes in a single element.

   A :class:`memoryview` supports slicing to expose its data.  Taking a single
   index will return a single element as a :class:`str` object.  Full
   slicing will result in a subview::

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

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

      >>> data = bytearray('abcefg')
      >>> v = memoryview(data)
      >>> v.readonly
      False
      >>> v[0] = 'z'
      >>> data
      bytearray(b'zbcefg')
      >>> v[1:4] = '123'
      >>> data
      bytearray(b'z123fg')
      >>> v[2] = '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 cannot be changed.

   :class:`memoryview` has two methods:

   .. method:: tobytes()

      Return the data in the buffer as a bytestring (an object of class
      :class:`str`). ::

         >>> m = memoryview("abc")
         >>> m.tobytes()
         'abc'

   .. method:: tolist()

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

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

   There are also several readonly attributes available:

   .. attribute:: format

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

   .. attribute:: itemsize

      The size in bytes of each element of the memoryview.

   .. attribute:: shape

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

   .. attribute:: ndim

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

   .. attribute:: strides

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

   .. attribute:: readonly

      A bool indicating whether the memory is read only.

   .. memoryview.suboffsets isn't documented because it only seems useful for C


.. _typecontextmanager:

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

.. versionadded:: 2.5

.. index::
   single: context manager
   single: context management protocol
   single: protocol; context management

Python's :keyword:`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 :dfn:`context management protocol` consists of a pair of methods that need
to be provided for a context manager object to define a runtime context:


.. method:: 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 :keyword:`as` clause of :keyword:`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 :func:`open` to be used as
   the context expression in a :keyword:`with` statement.

   An example of a context manager that returns a related object is the one
   returned by :func:`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 :keyword:`with` statement without affecting code outside the
   :keyword:`with` statement.


.. method:: 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 :keyword:`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 :keyword:`with` statement
   to suppress the exception and continue execution with the statement immediately
   following the :keyword:`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 :keyword:`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 :meth:`__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
:mod:`contextlib` module for some examples.

Python's :term:`generator`\s and the ``contextlib.contextmanager`` :term:`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 :meth:`__enter__` and
:meth:`__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.


.. _typesother:

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

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


.. _typesmodules:

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 :keyword:`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 attribute of every module is :attr:`~object.__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
:attr:`__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 :attr:`__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'>``.


.. _typesobjects:

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

See :ref:`objects` and :ref:`class` for these.


.. _typesfunctions:

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 :ref:`function` for more information.


.. _typesmethods:

Methods
-------

.. index:: object: method

Methods are functions that are called using the attribute notation. There are
two flavors: built-in methods (such as :meth:`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 :exc:`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 an attribute on a method results in
an :exc:`AttributeError` 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.whoami = 'my name is method'  # can't set on the method
   Traceback (most recent call last):
     File "<stdin>", line 1, in <module>
   AttributeError: 'instancemethod' object has no attribute 'whoami'
   >>> c.method.im_func.whoami = 'my name is method'
   >>> c.method.whoami
   'my name is method'


See :ref:`types` for more information.


.. _bltin-code-objects:

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

.. index:: object: code

.. index::
   builtin: compile
   single: func_code (function object attribute)

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 :func:`compile` function
and can be extracted from function objects through their :attr:`func_code`
attribute. See also the :mod:`code` module.

.. index::
   statement: exec
   builtin: eval

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

See :ref:`types` for more information.


.. _bltin-type-objects:

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

.. index::
   builtin: type
   module: types

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

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


.. _bltin-null-object:

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``.


.. _bltin-ellipsis-object:

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

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

It is written as ``Ellipsis``.  When in a subscript, it can also be written as
``...``, for example ``seq[...]``.


The NotImplemented Object
-------------------------

This object is returned from comparisons and binary operations when they are
asked to operate on types they don't support. See :ref:`comparisons` for more
information.

It is written as ``NotImplemented``.


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 :func:`bool` can be used to convert any value to a
Boolean, if the value can be interpreted as a truth value (see section
:ref:`truth` above).

.. index::
   single: False
   single: True
   pair: Boolean; values

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


.. _typesinternal:

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

See :ref:`types` for this information.  It describes stack frame objects,
traceback objects, and slice objects.


.. _specialattrs:

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
:func:`dir` built-in function.


.. attribute:: object.__dict__

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


.. attribute:: object.__methods__

   .. deprecated:: 2.2
      Use the built-in function :func:`dir` to get a list of an object's attributes.
      This attribute is no longer available.


.. attribute:: object.__members__

   .. deprecated:: 2.2
      Use the built-in function :func:`dir` to get a list of an object's attributes.
      This attribute is no longer available.


.. attribute:: instance.__class__

   The class to which a class instance belongs.


.. attribute:: class.__bases__

   The tuple of base classes of a class object.


.. attribute:: class.__name__

   The name of the class or type.


The following attributes are only supported by :term:`new-style class`\ es.

.. attribute:: class.__mro__

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


.. method:: 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 :attr:`~class.__mro__`.


.. method:: 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'>]


.. rubric:: Footnotes

.. [1] Additional information on these special methods may be found in the Python
   Reference Manual (:ref:`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] Cased characters are those with general category property being one of
   "Lu" (Letter, uppercase), "Ll" (Letter, lowercase), or "Lt" (Letter, titlecase).

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

.. [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!).
