# 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)

Notes:

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

## Comparisons

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

This table summarizes the comparison operations:

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

Objects of different types, except different numeric types, never compare equal. Furthermore, some types (for example, function objects) support only a degenerate notion of comparison where any two objects of that type are unequal. The <, <=, > and >= operators will raise a :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)

Notes:

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

2. Not for complex numbers. Instead convert to floats using :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

Notes:

1. Negative shift counts are illegal and cause a :exc:ValueError to be raised.
2. A left shift by n bits is equivalent to multiplication by pow(2, n) 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 6.4.4.2 of the C99 standard, and also to the syntax used in Java 1.5 onwards. In particular, the output of :meth:float.hex is usable as a hexadecimal floating-point literal in C or Java code, and hexadecimal strings produced by C's %a format character or Java's Double.toHexString are accepted by :meth:float.fromhex.

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

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


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

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


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

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

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

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

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


## Iterator Types

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

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

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:~iterator.__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:generators 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:~generator.__next__ methods. More information about generators can be found in :ref:the documentation for the yield expression <yieldexpr>.

## Sequence Types --- :class:list, :class:tuple, :class:range

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

### Common Sequence Operations

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

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

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

Operation Result Notes
x in s True if an item of s is 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)(7)
s * n or n * s n shallow copies of s concatenated (2)(7)
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(x[, i[, j]]) index of the first occurence of x in s (at or after index i and before index j) (8)
s.count(x) total number of occurences of x in s

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

Notes:

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

>>> "gg" in "eggs"
True

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

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


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

>>> lists = [[] for i in range(3)]
>>> lists[0].append(3)
>>> lists[1].append(5)
>>> lists[2].append(7)
>>> lists
[[3], [5], [7]]

3. If i or j is negative, the index is relative to the end of the string: len(s) + i or len(s) + j is substituted. But note that -0 is still 0.

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

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

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

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

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

### Immutable Sequence Types

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

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

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

### Mutable Sequence Types

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

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

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) appends x to the end of the sequence (same as s[len(s):len(s)] = [x])
s.clear() removes all items from s (same as del s[:]) (5)
s.copy() creates a shallow copy of s (same as s[:]) (5)
s.extend(t) extends s with the contents of t (same as s[len(s):len(s)] = t)
s.insert(i, x) inserts x into s at the index given by i (same as s[i:i] = [x])
s.pop([i]) retrieves the item at i and also removes it from s (2)
s.remove(x) remove the first item from s where s[i] == x (3)
s.reverse() reverses the items of s in place (4)

Notes:

1. t must have the same length as the slice it is replacing.
2. The optional argument i defaults to -1, so that by default the last item is removed and returned.
3. remove raises :exc:ValueError when x is not found in s.
4. The :meth:reverse method modifies the sequence in place for economy of space when reversing a large sequence. To remind users that it operates by side effect, it does not return the reversed sequence.
5. :meth:clear and :meth:!copy are included for consistency with the interfaces of mutable containers that don't support slicing operations (such as :class:dict and :class:set)

### Lists

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

Lists may be constructed in several ways:

• Using a pair of square brackets to denote the empty list: []
• Using square brackets, separating items with commas: [a], [a, b, c]
• Using a list comprehension: [x for x in iterable]
• Using the type constructor: list() or list(iterable)

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

Many other operations also produce lists, including the :func:sorted built-in.

Lists implement all of the :ref:common <typesseq-common> and :ref:mutable <typesseq-mutable> sequence operations. Lists also provide the following additional method:

### Tuples

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

Tuples may be constructed in a number of ways:

• Using a pair of parentheses to denote the empty tuple: ()
• Using a trailing comma for a singleton tuple: a, or (a,)
• Separating items with commas: a, b, c or (a, b, c)
• Using the :func:tuple built-in: tuple() or tuple(iterable)

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

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

Tuples implement all of the :ref:common <typesseq-common> sequence operations.

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

### Ranges

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

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

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

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

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

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

Range examples:

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


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

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

Range objects implement the :class:collections.Sequence ABC, and provide features such as containment tests, element index lookup, slicing and support for negative indices (see :ref:typesseq):

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


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

## Text Sequence Type --- :class:str

Textual data in Python is handled with :class:str objects, or :dfn:strings. Strings are immutable :ref:sequences <typesseq> of Unicode code points. String literals are written in a variety of ways:

• Single quotes: 'allows embedded "double" quotes'
• Double quotes: "allows embedded 'single' quotes".
• Triple quoted: '''Three single quotes''', """Three double quotes"""

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

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

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

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

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

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

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

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

If at least one of encoding or errors is given, object should be a :class:bytes or :class:bytearray object, or more generally any object that supports the :ref:buffer protocol <bufferobjects>. In this case, if object is a :class:bytes (or :class:bytearray) object, then str(bytes, encoding, errors) is equivalent to :meth:bytes.decode(encoding, errors) <bytes.decode>. Otherwise, the bytes object underlying the buffer object is obtained before calling :meth:bytes.decode. See :ref:binaryseq and :ref:bufferobjects for information on buffer objects.

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

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


For more information on the str class and its methods, see :ref:textseq and the :ref:string-methods section below. To output formatted strings, see the :ref:string-formatting section. In addition, see the :ref:stringservices section.

### String Methods

Strings implement all of the :ref:common <typesseq-common> sequence operations, along with the additional methods described below.

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

The :ref:textservices section of the standard library covers a number of other modules that provide various text related utilities (including regular expression support in the :mod:re module).

### printf-style String Formatting

Note

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

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

Notes:

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

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

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

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

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

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

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

1. See PEP 237.

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

## Binary Sequence Types --- :class:bytes, :class:bytearray, :class:memoryview

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

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

### Bytes

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

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

• Single quotes: b'still allows embedded "double" quotes'
• Double quotes: b"still allows embedded 'single' quotes".
• Triple quoted: b'''3 single quotes''', b"""3 double quotes"""

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

As with string literals, bytes literals may also use a r prefix to disable processing of escape sequences. See :ref:strings for more about the various forms of bytes literal, including supported escape sequences.

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

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

• A zero-filled bytes object of a specified length: bytes(10)
• From an iterable of integers: bytes(range(20))
• Copying existing binary data via the buffer protocol: bytes(obj)

Also see the :ref:bytes <func-bytes> built-in.

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

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

Note

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

### Bytearray Objects

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

• Creating an empty instance: bytearray()
• Creating a zero-filled instance with a given length: bytearray(10)
• From an iterable of integers: bytearray(range(20))
• Copying existing binary data via the buffer protocol: bytearray(b'Hi!')

As bytearray objects are mutable, they support the :ref:mutable <typesseq-mutable> sequence operations in addition to the common bytes and bytearray operations described in :ref:bytes-methods.

Also see the :ref:bytearray <func-bytearray> built-in.

### Bytes and Bytearray Operations

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

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

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

Note

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

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


and:

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


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

Note

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

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

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

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

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

### Memory Views

:class:memoryview objects allow Python code to access the internal data of an object that supports the :ref:buffer protocol <bufferobjects> without copying.

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

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

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


Other native formats:

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


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

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


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

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


:class:memoryview has several methods:

There are also several readonly attributes available:

## 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 :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
True


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

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

### 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.abc.Set are available (for example, ==, <, or ^).

An example of dictionary view usage:

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

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

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

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

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


## Context Manager Types

Python's :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:generators 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.

### Modules

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

A special attribute of every module is :attr:__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.

### Functions

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

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

See :ref:function for more information.

### Methods

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 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: 'method' object has no attribute 'whoami'
>>> c.method.__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:__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.

Footnotes

 [1] Additional information on these special methods may be found in the Python Reference Manual (:ref:customization).
 [2] As a consequence, the list [1, 2] is considered equal to [1.0, 2.0], and similarly for tuples.
 [3] They must have since the parser can't tell the type of the operands.
 [4] Cased characters are those with general category property being one of "Lu" (Letter, uppercase), "Ll" (Letter, lowercase), or "Lt" (Letter, titlecase).
 [5] To format only a tuple you should therefore provide a singleton tuple whose only element is the tuple to be formatted.