1. Armin Rigo
  2. cpython-withatomic


cpython-withatomic / Doc / library / stdtypes.rst

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 :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, 0.0, 0j.
  • any empty sequence, for example, '', (), [].
  • any empty mapping, for example, {}.
  • instances of user-defined classes, if the class defines a :meth:`__bool__` 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.


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 :exc:`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 :meth:`__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 :meth:`__lt__`, :meth:`__le__`, :meth:`__gt__`, and :meth:`__ge__` (in general, :meth:`__lt__` and :meth:`__eq__` are sufficient, if you want the conventional meanings of the comparison operators).

The behavior of the :keyword:`is` and :keyword:`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, :keyword:`in` and :keyword:`not in`, are supported only by sequence types (below).

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

There are three distinct numeric types: :dfn:`integers`, :dfn:`floating point numbers`, and :dfn:`complex numbers`. In addition, Booleans are a subtype of integers. 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 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 :func:`int`, :func:`float`, and :func:`complex` can be used to produce numbers of a specific type.

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

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


  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 :func:`abs` if appropriate.

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

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

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

  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/DerivedNumericType.txt for a complete list of code points with the Nd property.

All :class:`numbers.Real` types (:class:`int` 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  

For additional numeric operations see the :mod:`math` and :mod:`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 | 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) 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 :class:`numbers.Integral` :term:`abstract base class`. In addition, it provides 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)

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 :meth:`__hash__` method documentation for more details). For ease of implementation and efficiency across a variety of numeric types (including :class:`int`, :class:`float`, :class:`decimal.Decimal` and :class:`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 :class:`int` and :class:`fraction.Fraction`, and all finite instances of :class:`float` and :class:`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 :attr:`modulus` attribute of :data:`sys.hash_info`.

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 :class:`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 builtin hash, for computing the hash of a rational number, :class:`float`, or :class:`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
        # 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
        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:

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.

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

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:`bytes`, :class:`bytearray`, :class:`list`, :class:`tuple`, :class:`range`

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

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

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

While string objects are sequences of characters (represented by strings of length 1), bytes and bytearray objects are sequences of integers (between 0 and 255), representing the ASCII value of single bytes. That means that for a bytes or bytearray object b, b[0] will be an integer, while b[0:1] will be a bytes or bytearray object of length 1. The representation of bytes objects uses the literal format (b'...') since it is generally more useful than e.g. bytes([50, 19, 100]). You can always convert a bytes object into a list of integers using list(b).

Also, while in previous Python versions, byte strings and Unicode strings could be exchanged for each other rather freely (barring encoding issues), strings and bytes are now completely separate concepts. There's no implicit en-/decoding if you pass an object of the wrong type. A string always compares unequal to a bytes or bytearray object.

Lists are constructed with square brackets, separating items with commas: [a, b, c]. Tuples are constructed by the comma operator (not within square brackets), with or without enclosing parentheses, but an empty tuple must have the enclosing parentheses, such as a, b, c or (). A single item tuple must have a trailing comma, such as (d,).

Objects of type range are created using the :func:`range` function. They don't support concatenation or repetition, and using :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, j and k 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 object, the in and not in operations act like a substring test.

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

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

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

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

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

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

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

String Methods

String objects support the methods listed below.

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

Old String Formatting Operations


The formatting operations described here are obsolete and may go away in future versions of Python. Use the new :ref:`string-formatting` in new code.

String objects have one unique built-in operation: the % operator (modulo). This is also known as the string formatting or interpolation operator. Given format % values (where format is a string), % conversion specifications in format are replaced with zero or more elements of values. The effect is similar to the using :c:func:`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 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 :func:`repr`). (5)
's' String (converts any Python object using :func:`str`). (5)
'a' String (converts any Python object using :func:`ascii`). (5)
'%' 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. If precision is N, the output is truncated to N characters.

  1. 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`.

Range Type

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

Range objects have relatively little behavior: they support indexing, contains, iteration, the :func:`len` function, and the following methods:

Mutable Sequence Types

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

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

Operation Result Notes
s[i] = x item i of s is replaced by x  
s[i:j] = t slice of s from i to j is replaced by the contents of the iterable t  
del s[i:j] same as s[i:j] = []  
s[i:j:k] = t the elements of s[i:j:k] are 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]  
s.extend(x) same as s[len(s):len(s)] = x (2)
s.clear() remove all items from s  
s.copy() return a shallow copy of s  
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 (3)
s.insert(i, x) same as s[i:i] = [x] (4)
s.pop([i]) same as x = s[i]; del s[i]; return x (5)
s.remove(x) same as del s[s.index(x)] (3)
s.reverse() reverses the items of s in place (6)
s.sort([key[, reverse]]) sort the items of s in place (6), (7), (8)


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

  2. x can be any iterable object.

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

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

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

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

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

    key specifies a function of one argument that is used to extract a comparison key from each list element: key=str.lower. The default value is None. Use :func:`functools.cmp_to_key` to convert an old-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.

    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).

  8. :meth:`sort` is not supported by :class:`bytearray` objects.

Bytes and Byte Array Methods

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

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


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")


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

The bytes and bytearray types have an additional class method:

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

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.

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 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 complete ordering function. For example, any two disjoint sets are not equal and are not subsets of each other, so all of the following return False: a<b, a==b, or a>b.

Since sets only define partial ordering (subset relationships), the output of the :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 :dfn:`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 or from a set of keyword arguments. If no arguments are given, return a new empty dictionary. If the positional argument arg is a mapping object, return a dictionary mapping the same keys to the same values as does the mapping object. Otherwise the positional argument must be a sequence, a container that supports iteration, or an iterator object. The elements of the argument must each also be of one of those kinds, and each must in turn contain exactly two objects. The first is used as a key in the new dictionary, and the second as the key's value. If a given key is seen more than once, the last value associated with it is retained in the new dictionary.

If keyword arguments are given, the keywords themselves with their associated values are added as items to the dictionary. If a key is specified both in the positional argument and as a keyword argument, the value associated with the keyword is retained in the dictionary. For example, these all return a dictionary equal to {"one": 1, "two": 2}:

  • dict(one=1, two=2)
  • dict({'one': 1, 'two': 2})
  • dict(zip(('one', 'two'), (1, 2)))
  • dict([['two', 2], ['one', 1]])

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

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

Dictionary view objects

The objects returned by :meth:`dict.keys`, :meth:`dict.values` and :meth:`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:

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 :class:`collections.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)

>>> # 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'}
>>> keys ^ {'sausage', 'juice'}
{'juice', 'sausage', 'bacon', 'spam'}

memoryview type

:class:`memoryview` objects allow Python code to access the internal data of an object that supports the :ref:`buffer protocol <bufferobjects>` 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:`bytes` and :class:`bytearray`.

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:`bytes` and :class:`bytearray`, an element is a single byte, but other types such as :class:`array.array` may have bigger 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:`bytes` object. Full slicing will result in a subview:

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

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

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

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

Memoryviews of hashable (read-only) types are also hashable and their hash value matches the corresponding bytes object:

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

:class:`memoryview` has several 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 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:

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

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

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

class C:
    def method(self):

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

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:`__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 :func:`exec` or :func:`eval` built-in functions.

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: <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 :ref:`slicings`). It supports no special operations. There is exactly one ellipsis object, named :const:`Ellipsis` (a built-in name). type(Ellipsis)() produces the :const:`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 :ref:`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 :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.


[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.