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cpython / Doc / library / stdtypes.rst

Built-in Types

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


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

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

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

Truth Value Testing

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

  • None
  • False
  • zero of any numeric type, for example, 0, 0L, 0.0, 0j.
  • any empty sequence, for example, '', (), [].
  • any empty mapping, for example, {}.
  • instances of user-defined classes, if the class defines a :meth:`__nonzero__` or :meth:`__len__` method, when that method returns the integer zero or :class:`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 --- :keyword:`and`, :keyword:`or`, :keyword:`not`

These are the Boolean operations, ordered by ascending priority:

Operation Result Notes
x or y if x is false, then y, else x (1)
x and y if x is false, then x, else y (2)
not x if x is false, then True, else False (3)


  1. This is a short-circuit operator, so it only evaluates the second argument if the first one is :const:`False`.
  2. This is a short-circuit operator, so it only evaluates the second argument if the first one is :const:`True`.
  3. not has a lower priority than non-Boolean operators, so not a == b is interpreted as not (a == b), and a == not b is a syntax error.


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

This table summarizes the comparison operations:

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


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

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

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

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

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

There are four distinct numeric types: :dfn:`plain integers`, :dfn:`long integers`, :dfn:`floating point numbers`, and :dfn:`complex numbers`. In addition, Booleans are a subtype of plain integers. Plain integers (also just called :dfn:`integers`) are implemented using :c:type:`long` in C, which gives them at least 32 bits of precision (sys.maxint is always set to the maximum plain integer value for the current platform, the minimum value is -sys.maxint - 1). Long integers have unlimited precision. Floating point numbers are usually implemented using :c:type:`double` in C; information about the precision and internal representation of floating point numbers for the machine on which your program is running is available in :data:`sys.float_info`. Complex numbers have a real and imaginary part, which are each a floating point number. To extract these parts from a complex number z, use z.real and z.imag. (The standard library includes additional numeric types, :mod:`fractions` that hold rationals, and :mod:`decimal` that hold floating-point numbers with user-definable precision.)

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

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

All built-in numeric types support the following operations. See :ref:`power` and later sections for the operators' priorities.

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


  1. For (plain or long) integer division, the result is an integer. The result is always rounded towards minus infinity: 1/2 is 0, (-1)/2 is -1, 1/(-2) is -1, and (-1)/(-2) is 0. Note that the result is a long integer if either operand is a long integer, regardless of the numeric value.
  2. Conversion from floats using :func:`int` or :func:`long` truncates toward zero like the related function, :func:`math.trunc`. Use the function :func:`math.floor` to round downward and :func:`math.ceil` to round upward.
  3. See :ref:`built-in-funcs` for a full description.
  4. Also referred to as integer division. The resultant value is a whole integer, though the result's type is not necessarily int.
  5. float also accepts the strings "nan" and "inf" with an optional prefix "+" or "-" for Not a Number (NaN) and positive or negative infinity.
  6. Python defines pow(0, 0) and 0 ** 0 to be 1, as is common for programming languages.

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

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

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 | y bitwise :dfn:`or` of x and y  
x ^ y bitwise :dfn:`exclusive or` of x and y  
x & y bitwise :dfn:`and` of x and y  
x << n x shifted left by n bits (1)(2)
x >> n x shifted right by n bits (1)(3)
~x the bits of x inverted  


  1. Negative shift counts are illegal and cause a :exc:`ValueError` to be raised.
  2. A left shift by n bits is equivalent to multiplication by pow(2, n). A long integer is returned if the result exceeds the range of plain integers.
  3. A right shift by n bits is equivalent to division by pow(2, n).

Additional Methods on Integer Types

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

Additional Methods on Float

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

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.

Note that :meth:`float.hex` is an instance method, while :meth:`float.fromhex` is a class method.

A hexadecimal string takes the form:

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

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

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

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

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

>>> float.hex(3740.0)

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:

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

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

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

Generator Types

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

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

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

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

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

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

Buffer objects are not directly supported by Python syntax, but can be created by calling the built-in function :func:`buffer`. They don't support concatenation or repetition.

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

Most sequence types support the following operations. The in and not in operations have the same priorities as the comparison operations. The + and * operations have the same priority as the corresponding numeric operations. [3] Additional methods are provided for :ref:`typesseq-mutable`.

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

Operation Result Notes
x in s True if an item of s is equal to x, else False (1)
x not in s False if an item of s is equal to x, else True (1)
s + t the concatenation of s and t (6)
s * n, n * s n shallow copies of s concatenated (2)
s[i] ith 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 with step k (3)(5)
len(s) length of s  
min(s) smallest item of s  
max(s) largest item of s  
s.index(i) index of the first occurence of i in s  
s.count(i) total number of occurences of i in s  

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


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

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

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

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

    >>> lists = [[] for i in range(3)]
    >>> lists[0].append(3)
    >>> lists[1].append(5)
    >>> lists[2].append(7)
    >>> lists
    [[3], [5], [7]]
  3. If i or j is negative, the index is relative to the end of the string: len(s) + i or len(s) + j is substituted. But note that -0 is still 0.

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

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

String Methods

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

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

The following methods are present only on unicode objects:

String Formatting Operations

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

If format requires a single argument, values may be a single non-tuple object. [5] Otherwise, values must be a tuple with exactly the number of items specified by the format string, or a single mapping object (for example, a dictionary).

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

  1. The '%' character, which marks the start of the specifier.
  2. Mapping key (optional), consisting of a parenthesised sequence of characters (for example, (somename)).
  3. Conversion flags (optional), which affect the result of some conversion types.
  4. Minimum field width (optional). If specified as an '*' (asterisk), the actual width is read from the next element of the tuple in values, and the object to convert comes after the minimum field width and optional precision.
  5. Precision (optional), given as a '.' (dot) followed by the precision. If specified as '*' (an asterisk), the actual width is read from the next element of the tuple in values, and the value to convert comes after the precision.
  6. Length modifier (optional).
  7. Conversion type.

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

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

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

The conversion flag characters are:

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

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

The conversion types are:

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


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

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

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

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

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

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

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

    The precision determines the maximal number of characters used.

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

    The precision determines the maximal number of characters used.

  7. See PEP 237.

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

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

XRange Type

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

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

Mutable Sequence Types

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

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


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

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

  3. x can be any iterable object.

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

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

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

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

  8. The :meth:`sort` method takes optional arguments for controlling the comparisons.

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

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

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

    In general, the key and reverse conversion processes are much faster than specifying an equivalent cmp function. This is because cmp is called multiple times for each list element while key and reverse touch each element only once. Use :func:`functools.cmp_to_key` to convert an old-style cmp function to a key function.

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

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

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

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

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

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

The constructors for both classes work the same:

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

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

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

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

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

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

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

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

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

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

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

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

Mapping Types --- :class:`dict`

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

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

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

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

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

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

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

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

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):

Dictionary view objects

The objects returned by :meth:`dict.viewkeys`, :meth:`dict.viewvalues` and :meth:`dict.viewitems` are view objects. They provide a dynamic view on the dictionary's entries, which means that when the dictionary changes, the view reflects these changes.

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

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

An example of dictionary view usage:

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

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

>>> # 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'}

File Objects

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

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

Files have the following methods:

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

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

memoryview type

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

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

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

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

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

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

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

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

Notice how the size of the memoryview object cannot be changed.

:class:`memoryview` has two methods:

There are also several readonly attributes available:

Context Manager Types

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

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

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

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

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

Other Built-in Types

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


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

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

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

Classes and Class Instances

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


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

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

See :ref:`function` for more information.


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

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

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

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

>>> class C:
...     def method(self):
...         pass
>>> c = C()
>>> c.method.whoami = 'my name is method'  # can't set on the method
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: 'instancemethod' object has no attribute 'whoami'
>>> c.method.im_func.whoami = 'my name is method'
>>> c.method.whoami
'my name is method'

See :ref:`types` for more information.

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

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

See :ref:`types` for more information.

Type Objects

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

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

The Null Object

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

It is written as None.

The Ellipsis Object

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

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

The NotImplemented Object

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

It is written as NotImplemented.

Boolean Values

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

They are written as False and True, respectively.

Internal Objects

See :ref:`types` 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 :func:`dir` built-in function.

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


[1]Additional information on these special methods may be found in the Python Reference Manual (:ref:`customization`).
[2]As a consequence, the list [1, 2] is considered equal to [1.0, 2.0], and similarly for tuples.
[3]They must have since the parser can't tell the type of the operands.
[4]Cased characters are those with general category property being one of "Lu" (Letter, uppercase), "Ll" (Letter, lowercase), or "Lt" (Letter, titlecase).
[5]To format only a tuple you should therefore provide a singleton tuple whose only element is the tuple to be formatted.
[6]The advantage of leaving the newline on is that returning an empty string is then an unambiguous EOF indication. It is also possible (in cases where it might matter, for example, if you want to make an exact copy of a file while scanning its lines) to tell whether the last line of a file ended in a newline or not (yes this happens!).