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

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

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

Some collection classes are mutable.  The methods that add, subtract,
or rearrange their members in place, and don't return a specific item,
never return the collection instance itself but "None".

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


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

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

* "None"

* "False"

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

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

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

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

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

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


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

These are the Boolean operations, ordered by ascending priority:

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

Notes:

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

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

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


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

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

This table summarizes the comparison operations:

+--------------+---------------------------+
| Operation    | Meaning                   |
+==============+===========================+
| "<"          | strictly less than        |
+--------------+---------------------------+
| "<="         | less than or equal        |
+--------------+---------------------------+
| ">"          | strictly greater than     |
+--------------+---------------------------+
| ">="         | greater than or equal     |
+--------------+---------------------------+
| "=="         | equal                     |
+--------------+---------------------------+
| "!="         | not equal                 |
+--------------+---------------------------+
| "is"         | object identity           |
+--------------+---------------------------+
| "is not"     | negated object identity   |
+--------------+---------------------------+

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

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

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

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

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


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

There are three distinct numeric types: *integers*, *floating point
numbers*, and *complex numbers*.  In addition, Booleans are a subtype
of integers.  Integers have unlimited precision.  Floating point
numbers are usually implemented using "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
"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, "fractions" that hold rationals,
and "decimal" that hold floating-point numbers with user-definable
precision.)

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

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

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

+-----------------------+-----------------------------------+-----------+----------------------+
| Operation             | Result                            | Notes     | Full documentation   |
+=======================+===================================+===========+======================+
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+
| "int(x)"              | *x* converted to integer          | (3)(6)    | "int()"              |
+-----------------------+-----------------------------------+-----------+----------------------+
| "float(x)"            | *x* converted to floating point   | (4)(6)    | "float()"            |
+-----------------------+-----------------------------------+-----------+----------------------+
| "complex(re, im)"     | a complex number with real part   | (6)       | "complex()"          |
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+
| "divmod(x, y)"        | the pair "(x // y, x % y)"        | (2)       | "divmod()"           |
+-----------------------+-----------------------------------+-----------+----------------------+
| "pow(x, y)"           | *x* to the power *y*              | (5)       | "pow()"              |
+-----------------------+-----------------------------------+-----------+----------------------+
+-----------------------+-----------------------------------+-----------+----------------------+

Notes:

1. Also referred to as integer division.  The resultant value is a
   whole integer, though the result's type is not necessarily int. The
   result is always rounded towards minus infinity: "1//2" is "0",
   "(-1)//2" is "-1", "1//(-2)" is "-1", and "(-1)//(-2)" is "0".

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

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

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

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

6. The numeric literals accepted include the digits "0" to "9" or
   any Unicode equivalent (code points with the "Nd" property).

   See http://www.unicode.org/Public/6.0.0/ucd/extracted/DerivedNumer
   icType.txt for a complete list of code points with the "Nd"
   property.

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

+----------------------+--------------------------------------+----------+
| Operation            | Result                               | Notes    |
+======================+======================================+==========+
+----------------------+--------------------------------------+----------+
+----------------------+--------------------------------------+----------+
+----------------------+--------------------------------------+----------+
+----------------------+--------------------------------------+----------+

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


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

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 << n"     | *x* shifted left by *n* bits     | (1)(2)     |
+--------------+----------------------------------+------------+
| "x >> n"     | *x* shifted right by *n* bits    | (1)(3)     |
+--------------+----------------------------------+------------+
+--------------+----------------------------------+------------+

Notes:

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

2. A left shift by *n* bits is equivalent to multiplication by
   "pow(2, n)" without overflow check.

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


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

The int type implements the "numbers.Integral" *abstract base class*.
In addition, it provides one more method:

int.bit_length()

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

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

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

   Equivalent to:

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

   New in version 3.1.

int.to_bytes(length, byteorder, *, signed=False)

   Return an array of bytes representing an integer.

   >>> (1024).to_bytes(2, byteorder='big')
   b'\x04\x00'
   >>> (1024).to_bytes(10, byteorder='big')
   b'\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00'
   >>> (-1024).to_bytes(10, byteorder='big', signed=True)
   b'\xff\xff\xff\xff\xff\xff\xff\xff\xfc\x00'
   >>> x = 1000
   >>> x.to_bytes((x.bit_length() // 8) + 1, byteorder='little')
   b'\xe8\x03'

   The integer is represented using *length* bytes.  An
   "OverflowError" is raised if the integer is not representable with
   the given number of bytes.

   The *byteorder* argument determines the byte order used to
   represent the integer.  If *byteorder* is ""big"", the most
   significant byte is at the beginning of the byte array.  If
   *byteorder* is ""little"", the most significant byte is at the end
   of the byte array.  To request the native byte order of the host
   system, use "sys.byteorder" as the byte order value.

   The *signed* argument determines whether two's complement is used
   to represent the integer.  If *signed* is "False" and a negative
   integer is given, an "OverflowError" is raised. The default value
   for *signed* is "False".

   New in version 3.2.

classmethod int.from_bytes(bytes, byteorder, *, signed=False)

   Return the integer represented by the given array of bytes.

   >>> int.from_bytes(b'\x00\x10', byteorder='big')
   16
   >>> int.from_bytes(b'\x00\x10', byteorder='little')
   4096
   >>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=True)
   -1024
   >>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=False)
   64512
   >>> int.from_bytes([255, 0, 0], byteorder='big')
   16711680

   The argument *bytes* must either be a *bytes-like object* or an
   iterable producing bytes.

   The *byteorder* argument determines the byte order used to
   represent the integer.  If *byteorder* is ""big"", the most
   significant byte is at the beginning of the byte array.  If
   *byteorder* is ""little"", the most significant byte is at the end
   of the byte array.  To request the native byte order of the host
   system, use "sys.byteorder" as the byte order value.

   The *signed* argument indicates whether two's complement is used to
   represent the integer.

   New in version 3.2.


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

The float type implements the "numbers.Real" *abstract base class*.
float also has the following additional methods.

float.as_integer_ratio()

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

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

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

float.hex()

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

classmethod float.fromhex(s)

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

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

A hexadecimal string takes the form:

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

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

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

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

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

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


Hashing of numeric types
------------------------

For numbers "x" and "y", possibly of different types, it's a
requirement that "hash(x) == hash(y)" whenever "x == y" (see the
"__hash__()" method documentation for more details).  For ease of
implementation and efficiency across a variety of numeric types
(including "int", "float", "decimal.Decimal" and "fractions.Fraction")
Python's hash for numeric types is based on a single mathematical
function that's defined for any rational number, and hence applies to
all instances of "int" and "fractions.Fraction", and all finite
instances of "float" and "decimal.Decimal".  Essentially, this
function is given by reduction modulo "P" for a fixed prime "P".  The
value of "P" is made available to Python as the "modulus" attribute of
"sys.hash_info".

**CPython implementation detail:** Currently, the prime used is "P =
2**31 - 1" on machines with 32-bit C longs and "P = 2**61 - 1" on
machines with 64-bit C longs.

Here are the rules in detail:

* If "x = m / n" is a nonnegative rational number and "n" is not
  divisible by "P", define "hash(x)" as "m * invmod(n, P) % P", where
  "invmod(n, P)" gives the inverse of "n" modulo "P".

* If "x = m / n" is a nonnegative rational number and "n" is
  divisible by "P" (but "m" is not) then "n" has no inverse modulo "P"
  and the rule above doesn't apply; in this case define "hash(x)" to
  be the constant value "sys.hash_info.inf".

* If "x = m / n" is a negative rational number define "hash(x)" as
  "-hash(-x)".  If the resulting hash is "-1", replace it with "-2".

* The particular values "sys.hash_info.inf", "-sys.hash_info.inf"
  and "sys.hash_info.nan" are used as hash values for positive
  infinity, negative infinity, or nans (respectively).  (All hashable
  nans have the same hash value.)

* For a "complex" number "z", the hash values of the real and
  imaginary parts are combined by computing "hash(z.real) +
  sys.hash_info.imag * hash(z.imag)", reduced modulo
  "2**sys.hash_info.width" so that it lies in
  "range(-2**(sys.hash_info.width - 1), 2**(sys.hash_info.width -
  1))".  Again, if the result is "-1", it's replaced with "-2".

To clarify the above rules, here's some example Python code,
equivalent to the built-in hash, for computing the hash of a rational
number, "float", or "complex":

   import sys, math

   def hash_fraction(m, n):
       """Compute the hash of a rational number m / n.

       Assumes m and n are integers, with n positive.
       Equivalent to hash(fractions.Fraction(m, n)).

       """
       P = sys.hash_info.modulus
       # Remove common factors of P.  (Unnecessary if m and n already coprime.)
       while m % P == n % P == 0:
           m, n = m // P, n // P

       if n % P == 0:
           hash_ = sys.hash_info.inf
       else:
           # Fermat's Little Theorem: pow(n, P-1, P) is 1, so
           # pow(n, P-2, P) gives the inverse of n modulo P.
           hash_ = (abs(m) % P) * pow(n, P - 2, P) % P
       if m < 0:
           hash_ = -hash_
       if hash_ == -1:
           hash_ = -2
       return hash_

   def hash_float(x):
       """Compute the hash of a float x."""

       if math.isnan(x):
           return sys.hash_info.nan
       elif math.isinf(x):
           return sys.hash_info.inf if x > 0 else -sys.hash_info.inf
       else:
           return hash_fraction(*x.as_integer_ratio())

   def hash_complex(z):
       """Compute the hash of a complex number z."""

       hash_ = hash_float(z.real) + sys.hash_info.imag * hash_float(z.imag)
       # do a signed reduction modulo 2**sys.hash_info.width
       M = 2**(sys.hash_info.width - 1)
       hash_ = (hash_ & (M - 1)) - (hash & M)
       if hash_ == -1:
           hash_ == -2
       return hash_


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

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

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

container.__iter__()

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

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

iterator.__iter__()

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

iterator.__next__()

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

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

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


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

Python's *generator*s provide a convenient way to implement the
iterator protocol.  If a container object's "__iter__()" method is
implemented as a generator, it will automatically return an iterator
object (technically, a generator object) supplying the "__iter__()"
and "__next__()" methods. More information about generators can be
found in *the documentation for the yield expression*.


Sequence Types --- "list", "tuple", "range"
===========================================

There are three basic sequence types: lists, tuples, and range
objects. Additional sequence types tailored for processing of *binary
data* and *text strings* are described in dedicated sections.


Common Sequence Operations
--------------------------

The operations in the following table are supported by most sequence
types, both mutable and immutable. The "collections.abc.Sequence" ABC
is provided to make it easier to correctly implement these operations
on custom sequence types.

This table lists the sequence operations sorted in ascending priority
(operations in the same box have the same priority).  In the table,
*s* and *t* are sequences of the same type, *n*, *i*, *j* and *k* are
integers and *x* is an arbitrary object that meets any type and value
restrictions imposed by *s*.

The "in" and "not in" operations have the same priorities as the
comparison operations. The "+" (concatenation) and "*" (repetition)
operations have the same priority as the corresponding numeric
operations.

+----------------------------+----------------------------------+------------+
| Operation                  | Result                           | Notes      |
+============================+==================================+============+
| "x in s"                   | "True" if an item of *s* is      | (1)        |
+----------------------------+----------------------------------+------------+
| "x not in s"               | "False" if an item of *s* is     | (1)        |
+----------------------------+----------------------------------+------------+
| "s + t"                    | the concatenation of *s* and *t* | (6)(7)     |
+----------------------------+----------------------------------+------------+
| "s * n" or "n * s"         | *n* shallow copies of *s*        | (2)(7)     |
+----------------------------+----------------------------------+------------+
| "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)     |
+----------------------------+----------------------------------+------------+
+----------------------------+----------------------------------+------------+
+----------------------------+----------------------------------+------------+
+----------------------------+----------------------------------+------------+
| "s.index(x[, i[, j]])"     | index of the first occurrence of | (8)        |
+----------------------------+----------------------------------+------------+
+----------------------------+----------------------------------+------------+

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

Notes:

1. While the "in" and "not in" operations are used only for simple
   containment testing in the general case, some specialised sequences
   (such as "str", "bytes" and "bytearray") also use them for
   subsequence testing:

      >>> "gg" in "eggs"
      True

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. Concatenating immutable sequences always results in a new
   object. This means that building up a sequence by repeated
   concatenation will have a quadratic runtime cost in the total
   sequence length. To get a linear runtime cost, you must switch to
   one of the alternatives below:

   * if concatenating "str" objects, you can build a list and use
     "str.join()" at the end or else write to a "io.StringIO" instance
     and retrieve its value when complete

   * if concatenating "bytes" objects, you can similarly use
     "bytes.join()" or "io.BytesIO", or you can do in-place
     concatenation with a "bytearray" object.  "bytearray" objects are
     mutable and have an efficient overallocation mechanism

   * if concatenating "tuple" objects, extend a "list" instead

   * for other types, investigate the relevant class documentation

7. Some sequence types (such as "range") only support item
   sequences that follow specific patterns, and hence don't support
   sequence concatenation or repetition.

8. "index" raises "ValueError" when *x* is not found in *s*. When
   supported, the additional arguments to the index method allow
   efficient searching of subsections of the sequence. Passing the
   extra arguments is roughly equivalent to using "s[i:j].index(x)",
   only without copying any data and with the returned index being
   relative to the start of the sequence rather than the start of the
   slice.


Immutable Sequence Types
------------------------

The only operation that immutable sequence types generally implement
that is not also implemented by mutable sequence types is support for
the "hash()" built-in.

This support allows immutable sequences, such as "tuple" instances, to
be used as "dict" keys and stored in "set" and "frozenset" instances.

Attempting to hash an immutable sequence that contains unhashable
values will result in "TypeError".


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

The operations in the following table are defined on mutable sequence
types. The "collections.abc.MutableSequence" ABC is provided to make
it easier to correctly implement these operations on custom sequence
types.

In the table *s* is an instance of a mutable sequence type, *t* is any
iterable object and *x* is an arbitrary object that meets any type and
value restrictions imposed by *s* (for example, "bytearray" only
accepts integers that meet the value restriction "0 <= x <= 255").

+--------------------------------+----------------------------------+-----------------------+
| Operation                      | Result                           | Notes                 |
+================================+==================================+=======================+
+--------------------------------+----------------------------------+-----------------------+
+--------------------------------+----------------------------------+-----------------------+
+--------------------------------+----------------------------------+-----------------------+
| "s[i:j:k] = t"                 | the elements of "s[i:j:k]" are   | (1)                   |
+--------------------------------+----------------------------------+-----------------------+
+--------------------------------+----------------------------------+-----------------------+
+--------------------------------+----------------------------------+-----------------------+
| "s.clear()"                    | removes all items from "s" (same | (5)                   |
+--------------------------------+----------------------------------+-----------------------+
| "s.copy()"                     | creates a shallow copy of "s"    | (5)                   |
+--------------------------------+----------------------------------+-----------------------+
+--------------------------------+----------------------------------+-----------------------+
+--------------------------------+----------------------------------+-----------------------+
| "s.pop([i])"                   | retrieves the item at *i* and    | (2)                   |
+--------------------------------+----------------------------------+-----------------------+
| "s.remove(x)"                  | remove the first item from *s*   | (3)                   |
+--------------------------------+----------------------------------+-----------------------+
| "s.reverse()"                  | reverses the items of *s* in     | (4)                   |
+--------------------------------+----------------------------------+-----------------------+

Notes:

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

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

3. "remove" raises "ValueError" when *x* is not found in *s*.

4. The "reverse()" method modifies the sequence in place for
   economy of space when reversing a large sequence.  To remind users
   that it operates by side effect, it does not return the reversed
   sequence.

5. "clear()" and "copy()" are included for consistency with the
   interfaces of mutable containers that don't support slicing
   operations (such as "dict" and "set")

   New in version 3.3: "clear()" and "copy()" methods.


Lists
-----

Lists are mutable sequences, typically used to store collections of
homogeneous items (where the precise degree of similarity will vary by
application).

class class list([iterable])

   Lists may be constructed in several ways:

   * Using a pair of square brackets to denote the empty list: "[]"

   * Using square brackets, separating items with commas: "[a]",
     "[a, b, c]"

   * Using a list comprehension: "[x for x in iterable]"

   * Using the type constructor: "list()" or "list(iterable)"

   The constructor builds a list whose items are the same and in the
   same order as *iterable*'s items.  *iterable* may be either a
   sequence, a container that supports iteration, or an iterator
   object.  If *iterable* is already a list, a copy is made and
   returned, similar to "iterable[:]". For example, "list('abc')"
   returns "['a', 'b', 'c']" and "list( (1, 2, 3) )" returns "[1, 2,
   3]". If no argument is given, the constructor creates a new empty
   list, "[]".

   Many other operations also produce lists, including the "sorted()"
   built-in.

   Lists implement all of the *common* and *mutable* sequence
   operations. Lists also provide the following additional method:

   sort(*, key=None, reverse=None)

      This method sorts the list in place, using only "<" comparisons
      between items. Exceptions are not suppressed - if any comparison
      operations fail, the entire sort operation will fail (and the
      list will likely be left in a partially modified state).

      "sort()" accepts two arguments that can only be passed by
      keyword (*keyword-only arguments*):

      *key* specifies a function of one argument that is used to
      extract a comparison key from each list element (for example,
      "key=str.lower"). The key corresponding to each item in the list
      is calculated once and then used for the entire sorting process.
      The default value of "None" means that list items are sorted
      directly without calculating a separate key value.

      The "functools.cmp_to_key()" utility is available to convert a
      2.x style *cmp* function to a *key* function.

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

      This method modifies the sequence in place for economy of space
      when sorting a large sequence.  To remind users that it operates
      by side effect, it does not return the sorted sequence (use
      "sorted()" to explicitly request a new sorted list instance).

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

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


Tuples
------

Tuples are immutable sequences, typically used to store collections of
heterogeneous data (such as the 2-tuples produced by the "enumerate()"
built-in). Tuples are also used for cases where an immutable sequence
of homogeneous data is needed (such as allowing storage in a "set" or
"dict" instance).

class class tuple([iterable])

   Tuples may be constructed in a number of ways:

   * Using a pair of parentheses to denote the empty tuple: "()"

   * Using a trailing comma for a singleton tuple: "a," or "(a,)"

   * Separating items with commas: "a, b, c" or "(a, b, c)"

   * Using the "tuple()" built-in: "tuple()" or "tuple(iterable)"

   The constructor builds a tuple whose items are the same and in the
   same order as *iterable*'s items.  *iterable* may be either a
   sequence, a container that supports iteration, or an iterator
   object.  If *iterable* is already a tuple, it is returned
   unchanged. For example, "tuple('abc')" returns "('a', 'b', 'c')"
   and "tuple( [1, 2, 3] )" returns "(1, 2, 3)". If no argument is
   given, the constructor creates a new empty tuple, "()".

   Note that it is actually the comma which makes a tuple, not the
   parentheses. The parentheses are optional, except in the empty
   tuple case, or when they are needed to avoid syntactic ambiguity.
   For example, "f(a, b, c)" is a function call with three arguments,
   while "f((a, b, c))" is a function call with a 3-tuple as the sole
   argument.

   Tuples implement all of the *common* sequence operations.

For heterogeneous collections of data where access by name is clearer
than access by index, "collections.namedtuple()" may be a more
appropriate choice than a simple tuple object.


Ranges
------

The "range" type represents an immutable sequence of numbers and is
commonly used for looping a specific number of times in "for" loops.

class class range(stop)
class class range(start, stop[, step])

   The arguments to the range constructor must be integers (either
   built-in "int" or any object that implements the "__index__"
   special method).  If the *step* argument is omitted, it defaults to
   "1". If the *start* argument is omitted, it defaults to "0". If
   *step* is zero, "ValueError" is raised.

   For a positive *step*, the contents of a range "r" are determined
   by the formula "r[i] = start + step*i" where "i >= 0" and "r[i] <
   stop".

   For a negative *step*, the contents of the range are still
   determined by the formula "r[i] = start + step*i", but the
   constraints are "i >= 0" and "r[i] > stop".

   A range object will be empty if "r[0]" does not meet the value
   constraint. Ranges do support negative indices, but these are
   interpreted as indexing from the end of the sequence determined by
   the positive indices.

   Ranges containing absolute values larger than "sys.maxsize" are
   permitted but some features (such as "len()") may raise
   "OverflowError".

   Range examples:

      >>> list(range(10))
      [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
      >>> list(range(1, 11))
      [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
      >>> list(range(0, 30, 5))
      [0, 5, 10, 15, 20, 25]
      >>> list(range(0, 10, 3))
      [0, 3, 6, 9]
      >>> list(range(0, -10, -1))
      [0, -1, -2, -3, -4, -5, -6, -7, -8, -9]
      >>> list(range(0))
      []
      >>> list(range(1, 0))
      []

   Ranges implement all of the *common* sequence operations except
   concatenation and repetition (due to the fact that range objects
   can only represent sequences that follow a strict pattern and
   repetition and concatenation will usually violate that pattern).

The advantage of the "range" type over a regular "list" or "tuple" is
that a "range" object will always take the same (small) amount of
memory, no matter the size of the range it represents (as it only
stores the "start", "stop" and "step" values, calculating individual
items and subranges as needed).

Range objects implement the "collections.abc.Sequence" ABC, and
provide features such as containment tests, element index lookup,
slicing and support for negative indices (see *Sequence Types ---
list, tuple, range*):

>>> r = range(0, 20, 2)
>>> r
range(0, 20, 2)
>>> 11 in r
False
>>> 10 in r
True
>>> r.index(10)
5
>>> r[5]
10
>>> r[:5]
range(0, 10, 2)
>>> r[-1]
18

Testing range objects for equality with "==" and "!=" compares them as
sequences.  That is, two range objects are considered equal if they
represent the same sequence of values.  (Note that two range objects
that compare equal might have different "start", "stop" and "step"
attributes, for example "range(0) == range(2, 1, 3)" or "range(0, 3,
2) == range(0, 4, 2)".)

Changed in version 3.2: Implement the Sequence ABC. Support slicing
and negative indices. Test "int" objects for membership in constant
time instead of iterating through all items.

Changed in version 3.3: Define '==' and '!=' to compare range objects
based on the sequence of values they define (instead of comparing
based on object identity).

New in version 3.3: The "start", "stop" and "step" attributes.


Text Sequence Type --- "str"
============================

Textual data in Python is handled with "str" objects, or *strings*.
Strings are immutable *sequences* of Unicode code points.  String
literals are written in a variety of ways:

* Single quotes: "'allows embedded "double" quotes'"

* Double quotes: ""allows embedded 'single' quotes"".

* Triple quoted: "'''Three single quotes'''", """"Three double
  quotes""""

Triple quoted strings may span multiple lines - all associated
whitespace will be included in the string literal.

String literals that are part of a single expression and have only
whitespace between them will be implicitly converted to a single
string literal. That is, "("spam " "eggs") == "spam eggs"".

See *String and Bytes literals* for more about the various forms of
string literal, including supported escape sequences, and the "r"
("raw") prefix that disables most escape sequence processing.

Strings may also be created from other objects using the "str"
constructor.

Since there is no separate "character" type, indexing a string
produces strings of length 1. That is, for a non-empty string *s*,
"s[0] == s[0:1]".

There is also no mutable string type, but "str.join()" or
"io.StringIO" can be used to efficiently construct strings from
multiple fragments.

Changed in version 3.3: For backwards compatibility with the Python 2
series, the "u" prefix is once again permitted on string literals. It
has no effect on the meaning of string literals and cannot be combined
with the "r" prefix.

class class str(object='')
class class str(object=b'', encoding='utf-8', errors='strict')

   Return a *string* version of *object*.  If *object* is not
   provided, returns the empty string.  Otherwise, the behavior of
   "str()" depends on whether *encoding* or *errors* is given, as
   follows.

   If neither *encoding* nor *errors* is given, "str(object)" returns
   "object.__str__()", which is the "informal" or nicely printable
   string representation of *object*.  For string objects, this is the
   string itself.  If *object* does not have a "__str__()" method,
   then "str()" falls back to returning "repr(object)".

   If at least one of *encoding* or *errors* is given, *object* should
   be a *bytes-like object* (e.g. "bytes" or "bytearray").  In this
   case, if *object* is a "bytes" (or "bytearray") object, then
   "str(bytes, encoding, errors)" is equivalent to
   "bytes.decode(encoding, errors)".  Otherwise, the bytes object
   underlying the buffer object is obtained before calling
   "bytes.decode()".  See *Binary Sequence Types --- bytes, bytearray,
   memoryview* and *Buffer Protocol* for information on buffer
   objects.

   Passing a "bytes" object to "str()" without the *encoding* or
   *errors* arguments falls under the first case of returning the
   informal string representation (see also the *-b* command-line
   option to Python).  For example:

      >>> str(b'Zoot!')
      "b'Zoot!'"

   For more information on the "str" class and its methods, see *Text
   Sequence Type --- str* and the *String Methods* section below.  To
   output formatted strings, see the *String Formatting* section.  In
   addition, see the *Text Processing Services* section.


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

Strings implement all of the *common* sequence operations, along with
the additional methods described below.

Strings also support two styles of string formatting, one providing a
large degree of flexibility and customization (see "str.format()",
*Format String Syntax* and *String Formatting*) and the other based on
C "printf" style formatting that handles a narrower range of types and
is slightly harder to use correctly, but is often faster for the cases
it can handle (*printf-style String Formatting*).

The *Text Processing Services* section of the standard library covers
a number of other modules that provide various text related utilities
(including regular expression support in the "re" module).

str.capitalize()

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

str.casefold()

   Return a casefolded copy of the string. Casefolded strings may be
   used for caseless matching.

   Casefolding is similar to lowercasing but more aggressive because
   it is intended to remove all case distinctions in a string. For
   example, the German lowercase letter "'ß'" is equivalent to ""ss"".
   Since it is already lowercase, "lower()" would do nothing to "'ß'";
   "casefold()" converts it to ""ss"".

   The casefolding algorithm is described in section 3.13 of the
   Unicode Standard.

   New in version 3.3.

str.center(width[, fillchar])

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

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

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

str.encode(encoding="utf-8", errors="strict")

   Return an encoded version of the string as a bytes object. Default
   encoding is "'utf-8'". *errors* may be given to set a different
   error handling scheme. The default for *errors* is "'strict'",
   meaning that encoding errors raise a "UnicodeError". Other possible
   values are "'ignore'", "'replace'", "'xmlcharrefreplace'",
   "'backslashreplace'" and any other name registered via
   "codecs.register_error()", see section *Codec Base Classes*. For a
   list of possible encodings, see section *Standard Encodings*.

   Changed in version 3.1: Support for keyword arguments added.

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

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

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'

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 "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 "in" operator:

        >>> 'Py' in 'Python'
        True

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

str.format_map(mapping)

   Similar to "str.format(**mapping)", except that "mapping" is used
   directly and not copied to a "dict".  This is useful if for example
   "mapping" is a dict subclass:

   >>> class Default(dict):
   ...     def __missing__(self, key):
   ...         return key
   ...
   >>> '{name} was born in {country}'.format_map(Default(name='Guido'))
   'Guido was born in country'

   New in version 3.2.

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

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

str.isalnum()

   Return true if all characters in the string are alphanumeric and
   there is at least one character, false otherwise.  A character "c"
   is alphanumeric if one of the following returns "True":
   "c.isalpha()", "c.isdecimal()", "c.isdigit()", or "c.isnumeric()".

str.isalpha()

   Return true if all characters in the string are alphabetic and
   there is at least one character, false otherwise.  Alphabetic
   characters are those characters defined in the Unicode character
   database as "Letter", i.e., those with general category property
   being one of "Lm", "Lt", "Lu", "Ll", or "Lo".  Note that this is
   different from the "Alphabetic" property defined in the Unicode
   Standard.

str.isdecimal()

   Return true if all characters in the string are decimal characters
   and there is at least one character, false otherwise. Decimal
   characters are those from general category "Nd". This category
   includes digit characters, and all characters that can be used to
   form decimal-radix numbers, e.g. U+0660, ARABIC-INDIC DIGIT ZERO.

str.isdigit()

   Return true if all characters in the string are digits and there is
   at least one character, false otherwise.  Digits include decimal
   characters and digits that need special handling, such as the
   compatibility superscript digits.  Formally, a digit is a character
   that has the property value Numeric_Type=Digit or
   Numeric_Type=Decimal.

str.isidentifier()

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

   Use "keyword.iskeyword()" to test for reserved identifiers such as
   "def" and "class".

str.islower()

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

str.isnumeric()

   Return true if all characters in the string are numeric characters,
   and there is at least one character, false otherwise. Numeric
   characters include digit characters, and all characters that have
   the Unicode numeric value property, e.g. U+2155, VULGAR FRACTION
   ONE FIFTH.  Formally, numeric characters are those with the
   property value Numeric_Type=Digit, Numeric_Type=Decimal or
   Numeric_Type=Numeric.

str.isprintable()

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

str.isspace()

   Return true if there are only whitespace characters in the string
   and there is at least one character, false otherwise.  Whitespace
   characters  are those characters defined in the Unicode character
   database as "Other" or "Separator" and those with bidirectional
   property being one of "WS", "B", or "S".

str.istitle()

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

str.isupper()

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

str.join(iterable)

   Return a string which is the concatenation of the strings in the
   *iterable* *iterable*.  A "TypeError" will be raised if there are
   any non-string values in *iterable*, including "bytes" objects.
   The separator between elements is the string providing this method.

str.ljust(width[, fillchar])

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

str.lower()

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

   The lowercasing algorithm used is described in section 3.13 of the
   Unicode Standard.

str.lstrip([chars])

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

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

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

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

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

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

str.partition(sep)

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

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

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

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

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

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

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

str.rjust(width[, fillchar])

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

str.rpartition(sep)

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

str.rsplit(sep=None, maxsplit=-1)

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

str.rstrip([chars])

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

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

str.split(sep=None, maxsplit=-1)

   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  ']".

str.splitlines([keepends])

   Return a list of the lines in the string, breaking at line
   boundaries. This method uses the *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 "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.

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

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

str.strip([chars])

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

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

str.swapcase()

   Return a copy of the string with uppercase characters converted to
   lowercase and vice versa. Note that it is not necessarily true that
   "s.swapcase().swapcase() == s".

str.title()

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

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

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

   A workaround for apostrophes can be constructed using regular
   expressions:

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

str.translate(map)

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

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

   Note: An even more flexible approach is to create a custom
     character mapping codec using the "codecs" module (see
     "encodings.cp1251" for an example).

str.upper()

   Return a copy of the string 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).

   The uppercasing algorithm used is described in section 3.13 of the
   Unicode Standard.

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)".


"printf"-style String Formatting
--------------------------------

Note: The formatting operations described here exhibit a variety of
  quirks that lead to a number of common errors (such as failing to
  display tuples and dictionaries correctly).  Using the newer
  "str.format()" interface helps avoid these errors, and also provides
  a generally more powerful, flexible and extensible approach to
  formatting text.

String objects have one unique built-in operation: the "%" operator
(modulo). This is also known as the string *formatting* or
*interpolation* operator. Given "format % values" (where *format* is a
string), "%" conversion specifications in *format* are replaced with
zero or more elements of *values*. The effect is similar to using the
"sprintf()" in the C language.

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:

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

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

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

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

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

6. Length modifier (optional).

7. Conversion type.

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

>>> print('%(language)s has %(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     |
+-----------+-----------------------------------------------------------------------+
| "'0'"     | The conversion will be zero padded for numeric values.                |
+-----------+-----------------------------------------------------------------------+
| "'-'"     | The converted value is left adjusted (overrides the "'0'" conversion  |
+-----------+-----------------------------------------------------------------------+
| "' '"     | (a space) A blank should be left before a positive number (or empty   |
+-----------+-----------------------------------------------------------------------+
| "'+'"     | A sign character ("'+'" or "'-'") will precede the conversion         |
+-----------+-----------------------------------------------------------------------+

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   |
+==============+=======================================================+=========+
+--------------+-------------------------------------------------------+---------+
+--------------+-------------------------------------------------------+---------+
| "'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)     |
+--------------+-------------------------------------------------------+---------+
| "'G'"        | Floating point format. Uses uppercase exponential     | (4)     |
+--------------+-------------------------------------------------------+---------+
+--------------+-------------------------------------------------------+---------+
| "'r'"        | String (converts any Python object using "repr()").   | (5)     |
+--------------+-------------------------------------------------------+---------+
| "'s'"        | String (converts any Python object using "str()").    | (5)     |
+--------------+-------------------------------------------------------+---------+
| "'a'"        | String (converts any Python object using "ascii()").  | (5)     |
+--------------+-------------------------------------------------------+---------+
+--------------+-------------------------------------------------------+---------+

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. If precision is "N", the output is truncated to "N" characters.

7. See **PEP 237**.

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

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


Binary Sequence Types --- "bytes", "bytearray", "memoryview"
============================================================

The core built-in types for manipulating binary data are "bytes" and
"bytearray". They are supported by "memoryview" which uses the *buffer
protocol* to access the memory of other binary objects without needing
to make a copy.

The "array" module supports efficient storage of basic data types like
32-bit integers and IEEE754 double-precision floating values.


Bytes
-----

Bytes objects are immutable sequences of single bytes. Since many
major binary protocols are based on the ASCII text encoding, bytes
objects offer several methods that are only valid when working with
ASCII compatible data and are closely related to string objects in a
variety of other ways.

Firstly, the syntax for bytes literals is largely the same as that for
string literals, except that a "b" prefix is added:

* Single quotes: "b'still allows embedded "double" quotes'"

* Double quotes: "b"still allows embedded 'single' quotes"".

* Triple quoted: "b'''3 single quotes'''", "b"""3 double quotes""""

Only ASCII characters are permitted in bytes literals (regardless of
the declared source code encoding). Any binary values over 127 must be
entered into bytes literals using the appropriate escape sequence.

As with string literals, bytes literals may also use a "r" prefix to
disable processing of escape sequences. See *String and Bytes
literals* for more about the various forms of bytes literal, including
supported escape sequences.

While bytes literals and representations are based on ASCII text,
bytes objects actually behave like immutable sequences of integers,
with each value in the sequence restricted such that "0 <= x < 256"
(attempts to violate this restriction will trigger "ValueError". This
is done deliberately to emphasise that while many binary formats
include ASCII based elements and can be usefully manipulated with some
text-oriented algorithms, this is not generally the case for arbitrary
binary data (blindly applying text processing algorithms to binary
data formats that are not ASCII compatible will usually lead to data
corruption).

In addition to the literal forms, bytes objects can be created in a
number of other ways:

* A zero-filled bytes object of a specified length: "bytes(10)"

* From an iterable of integers: "bytes(range(20))"

* Copying existing binary data via the buffer protocol:
  "bytes(obj)"

Also see the *bytes* built-in.

Since bytes objects are sequences of integers, for a bytes object *b*,
"b[0]" will be an integer, while "b[0:1]" will be a bytes object of
length 1.  (This contrasts with text strings, where both indexing and
slicing will produce a string of length 1)

The representation of bytes objects uses the literal format ("b'...'")
since it is often more useful than e.g. "bytes([46, 46, 46])".  You
can always convert a bytes object into a list of integers using
"list(b)".

Note: For Python 2.x users: In the Python 2.x series, a variety of
  implicit conversions between 8-bit strings (the closest thing 2.x
  offers to a built-in binary data type) and Unicode strings were
  permitted. This was a backwards compatibility workaround to account
  for the fact that Python originally only supported 8-bit text, and
  Unicode text was a later addition. In Python 3.x, those implicit
  conversions are gone - conversions between 8-bit binary data and
  Unicode text must be explicit, and bytes and string objects will
  always compare unequal.


Bytearray Objects
-----------------

"bytearray" objects are a mutable counterpart to "bytes" objects.
There is no dedicated literal syntax for bytearray objects, instead
they are always created by calling the constructor:

* Creating an empty instance: "bytearray()"

* Creating a zero-filled instance with a given length:
  "bytearray(10)"

* From an iterable of integers: "bytearray(range(20))"

* Copying existing binary data via the buffer protocol:
  "bytearray(b'Hi!')"

As bytearray objects are mutable, they support the *mutable* sequence
operations in addition to the common bytes and bytearray operations
described in *Bytes and Bytearray Operations*.

Also see the *bytearray* built-in.


Bytes and Bytearray Operations
------------------------------

Both bytes and bytearray objects support the *common* sequence
operations. They interoperate not just with operands of the same type,
but with any object that supports the *buffer protocol*. Due to this
flexibility, they can be freely mixed in operations without causing
errors. However, the return type of the result may depend on the order
of operands.

Due to the common use of ASCII text as the basis for binary protocols,
bytes and bytearray objects provide almost all methods found on text
strings, with the exceptions of:

* "str.encode()" (which converts text strings to bytes objects)

* "str.format()" and "str.format_map()" (which are used to format
  text for display to users)

* "str.isidentifier()", "str.isnumeric()", "str.isdecimal()",
  "str.isprintable()" (which are used to check various properties of
  text strings which are not typically applicable to binary
  protocols).

All other string methods are supported, although sometimes with slight
differences in functionality and semantics (as described below).

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

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

  and:

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

Whenever a bytes or bytearray method needs to interpret the bytes as
characters (e.g. the "is...()" methods, "split()", "strip()"), the
ASCII character set is assumed (text strings use Unicode semantics).

Note: Using these ASCII based methods to manipulate binary data that
  is not stored in an ASCII based format may lead to data corruption.

The search operations ("in", "count()", "find()", "index()", "rfind()"
and "rindex()") all accept both integers in the range 0 to 255
(inclusive) as well as bytes and byte array sequences.

Changed in version 3.3: All of the search methods also accept an
integer in the range 0 to 255 (inclusive) as their first argument.

Each bytes and bytearray instance provides a "decode()" convenience
method that is the inverse of "str.encode()":

bytes.decode(encoding="utf-8", errors="strict")
bytearray.decode(encoding="utf-8", errors="strict")

   Return a string decoded from the given bytes.  Default encoding is
   "'utf-8'". *errors* may be given to set a different error handling
   scheme.  The default for *errors* is "'strict'", meaning that
   encoding errors raise a "UnicodeError".  Other possible values are
   "'ignore'", "'replace'" and any other name registered via
   "codecs.register_error()", see section *Codec Base Classes*. For a
   list of possible encodings, see section *Standard Encodings*.

   Changed in version 3.1: Added support for keyword arguments.

Since 2 hexadecimal digits correspond precisely to a single byte,
hexadecimal numbers are a commonly used format for describing binary
data. Accordingly, the bytes and bytearray types have an additional
class method to read data in that format:

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

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

   >>> bytes.fromhex('2Ef0 F1f2  ')
   b'.\xf0\xf1\xf2'

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

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

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

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

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

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

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

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

   New in version 3.1.


Memory Views
------------

"memoryview" objects allow Python code to access the internal data of
an object that supports the *buffer protocol* without copying.

class class memoryview(obj)

   Create a "memoryview" that references *obj*.  *obj* must support
   the buffer protocol.  Built-in objects that support the buffer
   protocol include "bytes" and "bytearray".

   A "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 "bytes" and "bytearray", an element is a
   single byte, but other types such as "array.array" may have bigger
   elements.

   "len(view)" is equal to the length of "tolist". If "view.ndim = 0",
   the length is 1. If "view.ndim = 1", the length is equal to the
   number of elements in the view. For higher dimensions, the length
   is equal to the length of the nested list representation of the
   view. The "itemsize" attribute will give you the number of bytes in
   a single element.

   A "memoryview" supports slicing to expose its data. If "format" is
   one of the native format specifiers from the "struct" module,
   indexing will return a single element with the correct type. Full
   slicing will result in a subview:

      >>> v = memoryview(b'abcefg')
      >>> v[1]
      98
      >>> v[-1]
      103
      >>> v[1:4]
      <memory at 0x7f3ddc9f4350>
      >>> bytes(v[1:4])
      b'bce'

   Other native formats:

      >>> import array
      >>> a = array.array('l', [-11111111, 22222222, -33333333, 44444444])
      >>> a[0]
      -11111111
      >>> a[-1]
      44444444
      >>> a[2:3].tolist()
      [-33333333]
      >>> a[::2].tolist()
      [-11111111, -33333333]
      >>> a[::-1].tolist()
      [44444444, -33333333, 22222222, -11111111]

   New in version 3.3.

   If the underlying object is writable, the memoryview supports slice
   assignment. Resizing is not allowed:

      >>> data = bytearray(b'abcefg')
      >>> v = memoryview(data)
      >>> v.readonly
      False
      >>> v[0] = ord(b'z')
      >>> data
      bytearray(b'zbcefg')
      >>> v[1:4] = b'123'
      >>> data
      bytearray(b'z123fg')
      >>> v[2:3] = b'spam'
      Traceback (most recent call last):
        File "<stdin>", line 1, in <module>
      ValueError: memoryview assignment: lvalue and rvalue have different structures
      >>> v[2:6] = b'spam'
      >>> data
      bytearray(b'z1spam')

   One-dimensional memoryviews of hashable (read-only) types with
   formats 'B', 'b' or 'c' are also hashable. The hash is defined as
   "hash(m) == hash(m.tobytes())":

      >>> v = memoryview(b'abcefg')
      >>> hash(v) == hash(b'abcefg')
      True
      >>> hash(v[2:4]) == hash(b'ce')
      True
      >>> hash(v[::-2]) == hash(b'abcefg'[::-2])
      True

   Changed in version 3.3: One-dimensional memoryviews with formats
   'B', 'b' or 'c' are now hashable.

   "memoryview" has several methods:

   __eq__(exporter)

      A memoryview and a **PEP 3118** exporter are equal if their
      shapes are equivalent and if all corresponding values are equal
      when the operands' respective format codes are interpreted using
      "struct" syntax.

      For the subset of "struct" format strings currently supported by
      "tolist()", "v" and "w" are equal if "v.tolist() == w.tolist()":

         >>> import array
         >>> a = array.array('I', [1, 2, 3, 4, 5])
         >>> b = array.array('d', [1.0, 2.0, 3.0, 4.0, 5.0])
         >>> c = array.array('b', [5, 3, 1])
         >>> x = memoryview(a)
         >>> y = memoryview(b)
         >>> x == a == y == b
         True
         >>> x.tolist() == a.tolist() == y.tolist() == b.tolist()
         True
         >>> z = y[::-2]
         >>> z == c
         True
         >>> z.tolist() == c.tolist()
         True

      If either format string is not supported by the "struct" module,
      then the objects will always compare as unequal (even if the
      format strings and buffer contents are identical):

         >>> from ctypes import BigEndianStructure, c_long
         >>> class BEPoint(BigEndianStructure):
         ...     _fields_ = [("x", c_long), ("y", c_long)]
         ...
         >>> point = BEPoint(100, 200)
         >>> a = memoryview(point)
         >>> b = memoryview(point)
         >>> a == point
         False
         >>> a == b
         False

      Note that, as with floating point numbers, "v is w" does *not*
      imply "v == w" for memoryview objects.

      Changed in version 3.3: Previous versions compared the raw
      memory disregarding the item format and the logical array
      structure.

   tobytes()

      Return the data in the buffer as a bytestring.  This is
      equivalent to calling the "bytes" constructor on the memoryview.

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

      For non-contiguous arrays the result is equal to the flattened
      list representation with all elements converted to bytes.
      "tobytes()" supports all format strings, including those that
      are not in "struct" module syntax.

   tolist()

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

         >>> memoryview(b'abc').tolist()
         [97, 98, 99]
         >>> import array
         >>> a = array.array('d', [1.1, 2.2, 3.3])
         >>> m = memoryview(a)
         >>> m.tolist()
         [1.1, 2.2, 3.3]

      Changed in version 3.3: "tolist()" now supports all single
      character native formats in "struct" module syntax as well as
      multi-dimensional representations.

   release()

      Release the underlying buffer exposed by the memoryview object.
      Many objects take special actions when a view is held on them
      (for example, a "bytearray" would temporarily forbid resizing);
      therefore, calling release() is handy to remove these
      restrictions (and free any dangling resources) as soon as
      possible.

      After this method has been called, any further operation on the
      view raises a "ValueError" (except "release()" itself which can
      be called multiple times):

         >>> m = memoryview(b'abc')
         >>> m.release()
         >>> m[0]
         Traceback (most recent call last):
           File "<stdin>", line 1, in <module>
         ValueError: operation forbidden on released memoryview object

      The context management protocol can be used for a similar
      effect, using the "with" statement:

         >>> with memoryview(b'abc') as m:
         ...     m[0]
         ...
         97
         >>> m[0]
         Traceback (most recent call last):
           File "<stdin>", line 1, in <module>
         ValueError: operation forbidden on released memoryview object

      New in version 3.2.

   cast(format[, shape])

      Cast a memoryview to a new format or shape. *shape* defaults to
      "[byte_length//new_itemsize]", which means that the result view
      will be one-dimensional. The return value is a new memoryview,
      but the buffer itself is not copied. Supported casts are 1D ->
      C-contiguous and C-contiguous -> 1D.

      Both formats are restricted to single element native formats in
      "struct" syntax. One of the formats must be a byte format ('B',
      'b' or 'c'). The byte length of the result must be the same as
      the original length.

      Cast 1D/long to 1D/unsigned bytes:

         >>> import array
         >>> a = array.array('l', [1,2,3])
         >>> x = memoryview(a)
         >>> x.format
         'l'
         >>> x.itemsize
         8
         >>> len(x)
         3
         >>> x.nbytes
         24
         >>> y = x.cast('B')
         >>> y.format
         'B'
         >>> y.itemsize
         1
         >>> len(y)
         24
         >>> y.nbytes
         24

      Cast 1D/unsigned bytes to 1D/char:

         >>> b = bytearray(b'zyz')
         >>> x = memoryview(b)
         >>> x[0] = b'a'
         Traceback (most recent call last):
           File "<stdin>", line 1, in <module>
         ValueError: memoryview: invalid value for format "B"
         >>> y = x.cast('c')
         >>> y[0] = b'a'
         >>> b
         bytearray(b'ayz')

      Cast 1D/bytes to 3D/ints to 1D/signed char:

         >>> import struct
         >>> buf = struct.pack("i"*12, *list(range(12)))
         >>> x = memoryview(buf)
         >>> y = x.cast('i', shape=[2,2,3])
         >>> y.tolist()
         [[[0, 1, 2], [3, 4, 5]], [[6, 7, 8], [9, 10, 11]]]
         >>> y.format
         'i'
         >>> y.itemsize
         4
         >>> len(y)
         2
         >>> y.nbytes
         48
         >>> z = y.cast('b')
         >>> z.format
         'b'
         >>> z.itemsize
         1
         >>> len(z)
         48
         >>> z.nbytes
         48

      Cast 1D/unsigned char to 2D/unsigned long:

         >>> buf = struct.pack("L"*6, *list(range(6)))
         >>> x = memoryview(buf)
         >>> y = x.cast('L', shape=[2,3])
         >>> len(y)
         2
         >>> y.nbytes
         48
         >>> y.tolist()
         [[0, 1, 2], [3, 4, 5]]

      New in version 3.3.

   There are also several readonly attributes available:

   obj

      The underlying object of the memoryview:

         >>> b  = bytearray(b'xyz')
         >>> m = memoryview(b)
         >>> m.obj is b
         True

      New in version 3.3.

   nbytes

      "nbytes == product(shape) * itemsize == len(m.tobytes())". This
      is the amount of space in bytes that the array would use in a
      contiguous representation. It is not necessarily equal to
      len(m):

         >>> import array
         >>> a = array.array('i', [1,2,3,4,5])
         >>> m = memoryview(a)
         >>> len(m)
         5
         >>> m.nbytes
         20
         >>> y = m[::2]
         >>> len(y)
         3
         >>> y.nbytes
         12
         >>> len(y.tobytes())
         12

      Multi-dimensional arrays:

         >>> import struct
         >>> buf = struct.pack("d"*12, *[1.5*x for x in range(12)])
         >>> x = memoryview(buf)
         >>> y = x.cast('d', shape=[3,4])
         >>> y.tolist()
         [[0.0, 1.5, 3.0, 4.5], [6.0, 7.5, 9.0, 10.5], [12.0, 13.5, 15.0, 16.5]]
         >>> len(y)
         3
         >>> y.nbytes
         96

      New in version 3.3.

   readonly

      A bool indicating whether the memory is read only.

   format

      A string containing the format (in "struct" module style) for
      each element in the view. A memoryview can be created from
      exporters with arbitrary format strings, but some methods (e.g.
      "tolist()") are restricted to native single element formats.

      Changed in version 3.3: format "'B'" is now handled according to
      the struct module syntax. This means that "memoryview(b'abc')[0]
      == b'abc'[0] == 97".

   itemsize

      The size in bytes of each element of the memoryview:

         >>> import array, struct
         >>> m = memoryview(array.array('H', [32000, 32001, 32002]))
         >>> m.itemsize
         2
         >>> m[0]
         32000
         >>> struct.calcsize('H') == m.itemsize
         True

   ndim

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

   shape

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

      Changed in version 3.3: An empty tuple instead of None when ndim
      = 0.

   strides

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

      Changed in version 3.3: An empty tuple instead of None when ndim
      = 0.

   suboffsets

      Used internally for PIL-style arrays. The value is informational
      only.

   c_contiguous

      A bool indicating whether the memory is C-contiguous.

      New in version 3.3.

   f_contiguous

      A bool indicating whether the memory is Fortran contiguous.

      New in version 3.3.

   contiguous

      A bool indicating whether the memory is contiguous.

      New in version 3.3.


Set Types --- "set", "frozenset"
================================

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

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

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

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 "set" constructor.

The constructors for both classes work the same:

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

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

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

   len(s)

      Return the cardinality of set *s*.

   x in s

      Test *x* for membership in *s*.

   x not in s

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

   isdisjoint(other)

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

   issubset(other)
   set <= other

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

   set < other

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

   issuperset(other)
   set >= other

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

   set > other

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

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

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

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

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

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

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

   symmetric_difference(other)
   set ^ other

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

   copy()

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

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

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

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

   The subset and equality comparisons do not generalize to a total
   ordering function.  For example, any two nonempty disjoint sets are
   not equal and are not subsets of each other, so *all* of the
   following return "False": "a<b", "a==b", or "a>b".

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

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

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

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

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

      Update the set, adding elements from all others.

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

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

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

      Update the set, removing elements found in others.

   symmetric_difference_update(other)
   set ^= other

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

   add(elem)

      Add element *elem* to the set.

   remove(elem)

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

   discard(elem)

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

   pop()

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

   clear()

      Remove all elements from the set.

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

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


Mapping Types --- "dict"
========================

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

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

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

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

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

   len(d)

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

   d[key]

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

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

         >>> class Counter(dict):
         ...     def __missing__(self, key):
         ...         return 0
         >>> c = Counter()
         >>> c['red']
         0
         >>> c['red'] += 1
         >>> c['red']
         1

      See "collections.Counter" for a complete implementation
      including other methods helpful for accumulating and managing
      tallies.

   d[key] = value

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

   del d[key]

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

   key in d

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

   key not in d

      Equivalent to "not key in d".

   iter(d)

      Return an iterator over the keys of the dictionary.  This is a
      shortcut for "iter(d.keys())".

   clear()

      Remove all items from the dictionary.

   copy()

      Return a shallow copy of the dictionary.

   classmethod fromkeys(seq[, value])

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

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

   get(key[, default])

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

   items()

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

   keys()

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

   pop(key[, default])

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

   popitem()

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

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

   setdefault(key[, default])

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

   update([other])

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

      "update()" accepts either another dictionary object or an
      iterable of key/value pairs (as 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)".

   values()

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

See also: "types.MappingProxyType" can be used to create a read-only
  view of a "dict".


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

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

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

len(dictview)

   Return the number of entries in the dictionary.

iter(dictview)

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

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

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

x in dictview

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

Keys views are set-like since their entries are unique and hashable.
If all values are hashable, so that "(key, value)" pairs are unique
and hashable, then the items view is also set-like.  (Values views are
not treated as set-like since the entries are generally not unique.)
For set-like views, all of the operations defined for the abstract
base class "collections.abc.Set" are available (for example, "==",
"<", or "^").

An example of dictionary view usage:

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

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

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

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

   >>> # set operations
   >>> keys & {'eggs', 'bacon', 'salad'}
   {'bacon'}
   >>> keys ^ {'sausage', 'juice'}
   {'juice', 'sausage', 'bacon', 'spam'}


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

Python's "with" statement supports the concept of a runtime context
defined by a context manager.  This is implemented using a pair of
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:

contextmanager.__enter__()

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

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

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

contextmanager.__exit__(exc_type, exc_val, exc_tb)

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

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

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

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

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

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


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

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


Modules
-------

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

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

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


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

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


Functions
---------

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

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

See *Function definitions* for more information.


Methods
-------

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

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

Like function objects, bound method objects support getting arbitrary
attributes.  However, since method attributes are actually stored on
the underlying function object ("meth.__func__"), setting method
attributes on bound methods is disallowed.  Attempting to set an
attribute on a method results in an "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: 'method' object has no attribute 'whoami'
   >>> c.method.__func__.whoami = 'my name is method'
   >>> c.method.whoami
   'my name is method'

See *The standard type hierarchy* for more information.


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

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

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

See *The standard type hierarchy* for more information.


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

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

Types are written like this: "<class 'int'>".


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

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

It is written as "None".


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

This object is commonly used by slicing (see *Slicings*).  It supports
no special operations.  There is exactly one ellipsis object, named
"Ellipsis" (a built-in name).  "type(Ellipsis)()" produces the
"Ellipsis" singleton.

It is written as "Ellipsis" or "...".


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
*Comparisons* for more information.  There is exactly one
"NotImplemented" object. "type(NotImplemented)()" produces the
singleton instance.

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 "bool()" can be
used to convert any value to a Boolean, if the value can be
interpreted as a truth value (see section *Truth Value Testing*
above).

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


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

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


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

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

object.__dict__

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

instance.__class__

   The class to which a class instance belongs.

class.__bases__

   The tuple of base classes of a class object.

class.__name__

   The name of the class or type.

class.__qualname__

   The *qualified name* of the class or type.

   New in version 3.3.

class.__mro__

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

class.mro()

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

class.__subclasses__()

   Each 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__()
      [<class 'bool'>]

-[ Footnotes ]-

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

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

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

[4] 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.
