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Builtin Types
The following sections describe the standard types that are built into the interpreter.
The principal builtin 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 for equality, tested for truth value, and converted to a string (with the repr()
function or the slightly different str()
function). The latter function is implicitly used when an object is written by the print()
function.
Truth Value Testing
Any object can be tested for truth value, for use in an if
or while
condition or as operand of the Boolean operations below.
By default, an object is considered true unless its class defines either a __bool__()
method that returns False
or a __len__()
method that returns zero, when called with the object. 1 Here are most of the builtin objects considered false:
constants defined to be false:
None
andFalse
.zero of any numeric type:
0
,0.0
,0j
,Decimal(0)
,Fraction(0, 1)
empty sequences and collections:
''
,()
,[]
,{}
,set()
,range(0)
Operations and builtin functions that have a Boolean result always return 0
or False
for false and 1
or True
for true, unless otherwise stated. (Important exception: the Boolean operations or
and and
always return one of their operands.)
Boolean Operations — and
, or
, not
These are the Boolean operations, ordered by ascending priority:
Operation 
Result 
Notes 


if x is false, then y, else x 
(1) 

if x is false, then x, else y 
(2) 

if x is false, then 
(3) 
Notes:
This is a shortcircuit operator, so it only evaluates the second argument if the first one is false.
This is a shortcircuit operator, so it only evaluates the second argument if the first one is true.
not
has a lower priority than nonBoolean operators, sonot a == b
is interpreted asnot (a == b)
, anda == 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 

object identity 

negated object identity 
Objects of different types, except different numeric types, never compare equal. The ==
operator is always defined but for some object types (for example, class objects) is equivalent to is
. The <
, <=
, >
and >=
operators are only defined where they make sense; for example, they raise a TypeError
exception when one of the arguments is a complex number.
Nonidentical instances of a class normally compare as nonequal unless the class defines the __eq__()
method.
Instances of a class cannot be ordered with respect to other instances of the same class, or other types of object, unless the class defines enough of the methods __lt__()
, __le__()
, __gt__()
, and __ge__()
(in general, __lt__()
and __eq__()
are sufficient, if you want the conventional meanings of the comparison operators).
The behavior of the is
and is not
operators cannot be customized; also they can be applied to any two objects and never raise an exception.
Two more operations with the same syntactic priority, in
and not in
, are supported by types that are iterable or implement the __contains__()
method.
Numeric Types — int
, float
, complex
There are three distinct numeric types: integers, floating point numbers, and complex numbers. In addition, Booleans are a subtype of integers. Integers have unlimited precision. Floating point numbers are usually implemented using double
in C; information about the precision and internal representation of floating point numbers for the machine on which your program is running is available in sys.float_info
. Complex numbers have a real and imaginary part, which are each a floating point number. To extract these parts from a complex number z, use z.real
and z.imag
. (The standard library includes the additional numeric types fractions.Fraction
, for rationals, and decimal.Decimal
, for floatingpoint numbers with userdefinable precision.)
Numbers are created by numeric literals or as the result of builtin 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. A comparison between numbers of different types behaves as though the exact values of those numbers were being compared. 2
The constructors int()
, float()
, and complex()
can be used to produce numbers of a specific type.
All numeric types (except complex) support the following operations (for priorities of the operations, see Operator precedence):
Operation 
Result 
Notes 
Full documentation 


sum of x and y 


difference of x and y 


product of x and y 


quotient of x and y 


floored quotient of x and y 
(1) 


remainder of 
(2) 


x negated 


x unchanged 


absolute value or magnitude of x 


x converted to integer 
(3)(6) 


x converted to floating point 
(4)(6) 


a complex number with real part re, imaginary part im. im defaults to zero. 
(6) 


conjugate of the complex number c 


the pair 
(2) 


x to the power y 
(5) 


x to the power y 
(5) 
Notes:
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
is0
,(1)//2
is1
,1//(2)
is1
, and(1)//(2)
is0
.Not for complex numbers. Instead convert to floats using
abs()
if appropriate.Conversion from floating point to integer may round or truncate as in C; see functions
math.floor()
andmath.ceil()
for welldefined conversions.float also accepts the strings “nan” and “inf” with an optional prefix “+” or “” for Not a Number (NaN) and positive or negative infinity.
Python defines
pow(0, 0)
and0 ** 0
to be1
, as is common for programming languages.The numeric literals accepted include the digits
0
to9
or any Unicode equivalent (code points with theNd
property).See http://www.unicode.org/Public/12.1.0/ucd/extracted/DerivedNumericType.txt for a complete list of code points with the
Nd
property.
All numbers.Real
types (int
and float
) also include the following operations:
Operation 
Result 

x truncated to 

x rounded to n digits, rounding half to even. If n is omitted, it defaults to 0. 

the greatest 

the least 
For additional numeric operations see the math
and cmath
modules.
Bitwise Operations on Integer Types
Bitwise operations only make sense for integers. The result of bitwise operations is calculated as though carried out in two’s complement with an infinite number of sign bits.
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:
Operation 
Result 
Notes 


bitwise or of x and y 
(4) 

bitwise exclusive or of x and y 
(4) 

bitwise and of x and y 
(4) 

x shifted left by n bits 
(1)(2) 

x shifted right by n bits 
(1)(3) 

the bits of x inverted 
Notes:
Negative shift counts are illegal and cause a
ValueError
to be raised.A left shift by n bits is equivalent to multiplication by
pow(2, n)
.A right shift by n bits is equivalent to floor division by
pow(2, n)
.Performing these calculations with at least one extra sign extension bit in a finite two’s complement representation (a working bitwidth of
1 + max(x.bit_length(), y.bit_length())
or more) is sufficient to get the same result as if there were an infinite number of sign bits.
Additional Methods on Integer Types
The int type implements the numbers.Integral
abstract base class. In addition, it provides a few more methods:
int.
bit_length
( )
Return the number of bits necessary to represent an integer in binary, excluding the sign and leading zeros:
>>> n = 37 >>> bin(n) '0b100101' >>> n.bit_length() 6
More precisely, if
x
is nonzero, thenx.bit_length()
is the unique positive integerk
such that2**(k1) <= abs(x) < 2**k
. Equivalently, whenabs(x)
is small enough to have a correctly rounded logarithm, thenk = 1 + int(log(abs(x), 2))
. Ifx
is zero, thenx.bit_length()
returns0
.Equivalent to:
def bit_length(self): s = bin(self) # binary representation: bin(37) > '0b100101' s = s.lstrip('0b') # remove leading zeros and minus sign return len(s) # len('100101') > 6
New in version 3.1.
int.
to_bytes
( length, byteorder, *, signed=False )
Return an array of bytes representing an integer.
>>> (1024).to_bytes(2, byteorder='big') b'\x04\x00' >>> (1024).to_bytes(10, byteorder='big') b'\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00' >>> (1024).to_bytes(10, byteorder='big', signed=True) b'\xff\xff\xff\xff\xff\xff\xff\xff\xfc\x00' >>> x = 1000 >>> x.to_bytes((x.bit_length() + 7) // 8, byteorder='little') b'\xe8\x03'
The integer is represented using length bytes. An
OverflowError
is raised if the integer is not representable with the given number of bytes.The byteorder argument determines the byte order used to represent the integer. If byteorder is
"big"
, the most significant byte is at the beginning of the byte array. If byteorder is"little"
, the most significant byte is at the end of the byte array. To request the native byte order of the host system, usesys.byteorder
as the byte order value.The signed argument determines whether two’s complement is used to represent the integer. If signed is
False
and a negative integer is given, anOverflowError
is raised. The default value for signed isFalse
.New in version 3.2.
 classmethod
int.
from_bytes
( bytes, byteorder, *, signed=False ) 
Return the integer represented by the given array of bytes.
>>> int.from_bytes(b'\x00\x10', byteorder='big') 16 >>> int.from_bytes(b'\x00\x10', byteorder='little') 4096 >>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=True) 1024 >>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=False) 64512 >>> int.from_bytes([255, 0, 0], byteorder='big') 16711680
The argument bytes must either be a byteslike object or an iterable producing bytes.
The byteorder argument determines the byte order used to represent the integer. If byteorder is
"big"
, the most significant byte is at the beginning of the byte array. If byteorder is"little"
, the most significant byte is at the end of the byte array. To request the native byte order of the host system, usesys.byteorder
as the byte order value.The signed argument indicates whether two’s complement is used to represent the integer.
New in version 3.2.
Additional Methods on Float
The float type implements the numbers.Real
abstract base class. float also has the following additional methods.
float.
as_integer_ratio
( )
Return a pair of integers whose ratio is exactly equal to the original float and with a positive denominator. Raises
OverflowError
on infinities and aValueError
on NaNs.
float.
is_integer
( )
Return
True
if the float instance is finite with integral value, andFalse
otherwise:>>> (2.0).is_integer() True >>> (3.2).is_integer() False
Two methods support conversion to and from hexadecimal strings. Since Python’s floats are stored internally as binary numbers, converting a float to or from a decimal string usually involves a small rounding error. In contrast, hexadecimal strings allow exact representation and specification of floatingpoint numbers. This can be useful when debugging, and in numerical work.
float.
hex
( )
Return a representation of a floatingpoint number as a hexadecimal string. For finite floatingpoint numbers, this representation will always include a leading
0x
and a trailingp
and exponent.
 classmethod
float.
fromhex
( s ) 
Class method to return the float represented by a hexadecimal string s. The string s may have leading and trailing whitespace.
Note that float.hex()
is an instance method, while float.fromhex()
is a class method.
A hexadecimal string takes the form:
[sign] ['0x'] integer ['.' fraction] ['p' exponent]
where the optional sign
may by either +
or 
, integer
and fraction
are strings of hexadecimal digits, and exponent
is a decimal integer with an optional leading sign. Case is not significant, and there must be at least one hexadecimal digit in either the integer or the fraction. This syntax is similar to the syntax specified in section 6.4.4.2 of the C99 standard, and also to the syntax used in Java 1.5 onwards. In particular, the output of float.hex()
is usable as a hexadecimal floatingpoint literal in C or Java code, and hexadecimal strings produced by C’s %a
format character or Java’s Double.toHexString
are accepted by float.fromhex()
.
Note that the exponent is written in decimal rather than hexadecimal, and that it gives the power of 2 by which to multiply the coefficient. For example, the hexadecimal string 0x3.a7p10
represents the floatingpoint number (3 + 10./16 + 7./16**2) * 2.0**10
, or 3740.0
:
>>> float.fromhex('0x3.a7p10')
3740.0
Applying the reverse conversion to 3740.0
gives a different hexadecimal string representing the same number:
>>> float.hex(3740.0)
'0x1.d380000000000p+11'
Hashing of numeric types
For numbers x
and y
, possibly of different types, it’s a requirement that hash(x) == hash(y)
whenever x == y
(see the __hash__()
method documentation for more details). For ease of implementation and efficiency across a variety of numeric types (including int
, float
, decimal.Decimal
and fractions.Fraction
) Python’s hash for numeric types is based on a single mathematical function that’s defined for any rational number, and hence applies to all instances of int
and fractions.Fraction
, and all finite instances of float
and decimal.Decimal
. Essentially, this function is given by reduction modulo P
for a fixed prime P
. The value of P
is made available to Python as the modulus
attribute of sys.hash_info
.
CPython implementation detail: Currently, the prime used is P = 2**31  1
on machines with 32bit C longs and P = 2**61  1
on machines with 64bit C longs.
Here are the rules in detail:
If
x = m / n
is a nonnegative rational number andn
is not divisible byP
, definehash(x)
asm * invmod(n, P) % P
, whereinvmod(n, P)
gives the inverse ofn
moduloP
.If
x = m / n
is a nonnegative rational number andn
is divisible byP
(butm
is not) thenn
has no inverse moduloP
and the rule above doesn’t apply; in this case definehash(x)
to be the constant valuesys.hash_info.inf
.If
x = m / n
is a negative rational number definehash(x)
ashash(x)
. If the resulting hash is1
, replace it with2
.The particular values
sys.hash_info.inf
,sys.hash_info.inf
andsys.hash_info.nan
are used as hash values for positive infinity, negative infinity, or nans (respectively). (All hashable nans have the same hash value.)For a
complex
numberz
, the hash values of the real and imaginary parts are combined by computinghash(z.real) + sys.hash_info.imag * hash(z.imag)
, reduced modulo2**sys.hash_info.width
so that it lies inrange(2**(sys.hash_info.width  1), 2**(sys.hash_info.width  1))
. Again, if the result is1
, it’s replaced with2
.
To clarify the above rules, here’s some example Python code, equivalent to the builtin hash, for computing the hash of a rational number, float
, or complex
:
import sys, math
def hash_fraction(m, n):
"""Compute the hash of a rational number m / n.
Assumes m and n are integers, with n positive.
Equivalent to hash(fractions.Fraction(m, n)).
"""
P = sys.hash_info.modulus
# Remove common factors of P. (Unnecessary if m and n already coprime.)
while m % P == n % P == 0:
m, n = m // P, n // P
if n % P == 0:
hash_value = sys.hash_info.inf
else:
# Fermat's Little Theorem: pow(n, P1, P) is 1, so
# pow(n, P2, P) gives the inverse of n modulo P.
hash_value = (abs(m) % P) * pow(n, P  2, P) % P
if m < 0:
hash_value = hash_value
if hash_value == 1:
hash_value = 2
return hash_value
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_value = 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_value = (hash_value & (M  1))  (hash_value & M)
if hash_value == 1:
hash_value = 2
return hash_value
Iterator Types
Python supports a concept of iteration over containers. This is implemented using two distinct methods; these are used to allow userdefined classes to support iteration. Sequences, described below in more detail, always support the iteration methods.
One method needs to be defined for container objects to provide iteration support:
container.
__iter__
( )
Return an iterator object. The object is required to support the iterator protocol described below. If a container supports different types of iteration, additional methods can be provided to specifically request iterators for those iteration types. (An example of an object supporting multiple forms of iteration would be a tree structure which supports both breadthfirst and depthfirst traversal.) This method corresponds to the
tp_iter
slot of the type structure for Python objects in the Python/C API.
The iterator objects themselves are required to support the following two methods, which together form the iterator protocol:
iterator.
__iter__
( )
Return the iterator object itself. This is required to allow both containers and iterators to be used with the
for
andin
statements. This method corresponds to thetp_iter
slot of the type structure for Python objects in the Python/C API.
iterator.
__next__
( )
Return the next item from the container. If there are no further items, raise the
StopIteration
exception. This method corresponds to thetp_iternext
slot of the type structure for Python objects in the Python/C API.
Python defines several iterator objects to support iteration over general and specific sequence types, dictionaries, and other more specialized forms. The specific types are not important beyond their implementation of the iterator protocol.
Once an iterator’s __next__()
method raises StopIteration
, it must continue to do so on subsequent calls. Implementations that do not obey this property are deemed broken.
Generator Types
Python’s generators provide a convenient way to implement the iterator protocol. If a container object’s __iter__()
method is implemented as a generator, it will automatically return an iterator object (technically, a generator object) supplying the __iter__()
and __next__()
methods. More information about generators can be found in the documentation for the yield expression.
Sequence Types — list
, tuple
, range
There are three basic sequence types: lists, tuples, and range objects. Additional sequence types tailored for processing of binary data and text strings are described in dedicated sections.
Common Sequence Operations
The operations in the following table are supported by most sequence types, both mutable and immutable. The collections.abc.Sequence
ABC is provided to make it easier to correctly implement these operations on custom sequence types.
This table lists the sequence operations sorted in ascending priority. 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. 3
Operation 
Result 
Notes 



(1) 


(1) 

the concatenation of s and t 
(6)(7) 

equivalent to adding s to itself n times 
(2)(7) 

ith item of s, origin 0 
(3) 

slice of s from i to j 
(3)(4) 

slice of s from i to j with step k 
(3)(5) 

length of s 


smallest item of s 


largest item of s 


index of the first occurrence of x in s (at or after index i and before index j) 
(8) 

total number of occurrences 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 Comparisons in the language reference.)
Notes:
While the
in
andnot in
operations are used only for simple containment testing in the general case, some specialised sequences (such asstr
,bytes
andbytearray
) also use them for subsequence testing:>>> "gg" in "eggs" True
Values of n less than
0
are treated as0
(which yields an empty sequence of the same type as s). Note that items in the sequence s are not copied; they are referenced multiple times. 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 oneelement list containing an empty list, so all three elements of[[]] * 3
are references to this single empty list. Modifying any of the elements oflists
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]]
Further explanation is available in the FAQ entry How do I create a multidimensional list?.
If i or j is negative, the index is relative to the end of sequence s:
len(s) + i
orlen(s) + j
is substituted. But note that0
is still0
.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 thanlen(s)
, uselen(s)
. If i is omitted orNone
, use0
. If j is omitted orNone
, uselen(s)
. If i is greater than or equal to j, the slice is empty.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 that0 <= n < (ji)/k
. In other words, the indices arei
,i+k
,i+2*k
,i+3*k
and so on, stopping when j is reached (but never including j). When k is positive, i and j are reduced tolen(s)
if they are greater. When k is negative, i and j are reduced tolen(s)  1
if they are greater. If i or j are omitted orNone
, they become “end” values (which end depends on the sign of k). Note, k cannot be zero. If k isNone
, it is treated like1
.Concatenating immutable sequences always results in a new object. This means that building up a sequence by repeated concatenation will have a quadratic runtime cost in the total sequence length. To get a linear runtime cost, you must switch to one of the alternatives below:
if concatenating
str
objects, you can build a list and usestr.join()
at the end or else write to anio.StringIO
instance and retrieve its value when completeif concatenating
bytes
objects, you can similarly usebytes.join()
orio.BytesIO
, or you can do inplace concatenation with abytearray
object.bytearray
objects are mutable and have an efficient overallocation mechanismfor other types, investigate the relevant class documentation
Some sequence types (such as
range
) only support item sequences that follow specific patterns, and hence don’t support sequence concatenation or repetition.index
raisesValueError
when x is not found in s. Not all implementations support passing the additional arguments i and j. These arguments allow efficient searching of subsections of the sequence. Passing the extra arguments is roughly equivalent to usings[i:j].index(x)
, only without copying any data and with the returned index being relative to the start of the sequence rather than the start of the slice.
Immutable Sequence Types
The only operation that immutable sequence types generally implement that is not also implemented by mutable sequence types is support for the hash()
builtin.
This support allows immutable sequences, such as tuple
instances, to be used as dict
keys and stored in set
and frozenset
instances.
Attempting to hash an immutable sequence that contains unhashable values will result in TypeError
.
Mutable Sequence Types
The operations in the following table are defined on mutable sequence types. The collections.abc.MutableSequence
ABC is provided to make it easier to correctly implement these operations on custom sequence types.
In the table s is an instance of a mutable sequence type, t is any iterable object and x is an arbitrary object that meets any type and value restrictions imposed by s (for example, bytearray
only accepts integers that meet the value restriction 0 <= x <= 255
).
Operation 
Result 
Notes 


item i of s is replaced by x 


slice of s from i to j is replaced by the contents of the iterable t 


same as 


the elements of 
(1) 

removes the elements of 


appends x to the end of the sequence (same as 


removes all items from s (same as 
(5) 

creates a shallow copy of s (same as 
(5) 

extends s with the contents of t (for the most part the same as 


updates s with its contents repeated n times 
(6) 

inserts x into s at the index given by i (same as 


retrieves the item at i and also removes it from s 
(2) 

remove the first item from s where 
(3) 

reverses the items of s in place 
(4) 
Notes:
t must have the same length as the slice it is replacing.
The optional argument i defaults to
1
, so that by default the last item is removed and returned.remove()
raisesValueError
when x is not found in s.The
reverse()
method modifies the sequence in place for economy of space when reversing a large sequence. To remind users that it operates by side effect, it does not return the reversed sequence.clear()
andcopy()
are included for consistency with the interfaces of mutable containers that don’t support slicing operations (such asdict
andset
).copy()
is not part of thecollections.abc.MutableSequence
ABC, but most concrete mutable sequence classes provide it.New in version 3.3:
clear()
andcopy()
methods.The value n is an integer, or an object implementing
__index__()
. Zero and negative values of n clear the sequence. Items in the sequence are not copied; they are referenced multiple times, as explained fors * n
under Common Sequence Operations.
Lists
Lists are mutable sequences, typically used to store collections of homogeneous items (where the precise degree of similarity will vary by application).
 class
list
( [ iterable ] ) 
Lists may be constructed in several ways:
Using a pair of square brackets to denote the empty list:
[]
Using square brackets, separating items with commas:
[a]
,[a, b, c]
Using a list comprehension:
[x for x in iterable]
Using the type constructor:
list()
orlist(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']
andlist( (1, 2, 3) )
returns[1, 2, 3]
. If no argument is given, the constructor creates a new empty list,[]
.Many other operations also produce lists, including the
sorted()
builtin.Lists implement all of the common and mutable sequence operations. Lists also provide the following additional method:
sort
( *, key=None, reverse=False )
This method sorts the list in place, using only
<
comparisons between items. Exceptions are not suppressed  if any comparison operations fail, the entire sort operation will fail (and the list will likely be left in a partially modified state).sort()
accepts two arguments that can only be passed by keyword (keywordonly arguments):key specifies a function of one argument that is used to extract a comparison key from each list element (for example,
key=str.lower
). The key corresponding to each item in the list is calculated once and then used for the entire sorting process. The default value ofNone
means that list items are sorted directly without calculating a separate key value.The
functools.cmp_to_key()
utility is available to convert a 2.x style cmp function to a key function.reverse is a boolean value. If set to
True
, then the list elements are sorted as if each comparison were reversed.This method modifies the sequence in place for economy of space when sorting a large sequence. To remind users that it operates by side effect, it does not return the sorted sequence (use
sorted()
to explicitly request a new sorted list instance).The
sort()
method is guaranteed to be stable. A sort is stable if it guarantees not to change the relative order of elements that compare equal — this is helpful for sorting in multiple passes (for example, sort by department, then by salary grade).For sorting examples and a brief sorting tutorial, see Sorting HOW TO.
CPython implementation detail: While a list is being sorted, the effect of attempting to mutate, or even inspect, the list is undefined. The C implementation of Python makes the list appear empty for the duration, and raises
ValueError
if it can detect that the list has been mutated during a sort.
Tuples
Tuples are immutable sequences, typically used to store collections of heterogeneous data (such as the 2tuples produced by the enumerate()
builtin). Tuples are also used for cases where an immutable sequence of homogeneous data is needed (such as allowing storage in a set
or dict
instance).
 class
tuple
( [ iterable ] ) 
Tuples may be constructed in a number of ways:
Using a pair of parentheses to denote the empty tuple:
()
Using a trailing comma for a singleton tuple:
a,
or(a,)
Separating items with commas:
a, b, c
or(a, b, c)
Using the
tuple()
builtin:tuple()
ortuple(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')
andtuple( [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, whilef((a, b, c))
is a function call with a 3tuple as the sole argument.Tuples implement all of the common sequence operations.
For heterogeneous collections of data where access by name is clearer than access by index, collections.namedtuple()
may be a more appropriate choice than a simple tuple object.
Ranges
The range
type represents an immutable sequence of numbers and is commonly used for looping a specific number of times in for
loops.
 class
range
( stop )  class
range
( start, stop [, step ] ) 
The arguments to the range constructor must be integers (either builtin
int
or any object that implements the__index__
special method). If the step argument is omitted, it defaults to1
. If the start argument is omitted, it defaults to0
. If step is zero,ValueError
is raised.For a positive step, the contents of a range
r
are determined by the formular[i] = start + step*i
wherei >= 0
andr[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 arei >= 0
andr[i] > stop
.A range object will be empty if
r[0]
does not meet the value constraint. Ranges do support negative indices, but these are interpreted as indexing from the end of the sequence determined by the positive indices.Ranges containing absolute values larger than
sys.maxsize
are permitted but some features (such aslen()
) may raiseOverflowError
.Range examples:
>>> list(range(10)) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] >>> list(range(1, 11)) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] >>> list(range(0, 30, 5)) [0, 5, 10, 15, 20, 25] >>> list(range(0, 10, 3)) [0, 3, 6, 9] >>> list(range(0, 10, 1)) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] >>> list(range(0)) [] >>> list(range(1, 0)) []
Ranges implement all of the common sequence operations except concatenation and repetition (due to the fact that range objects can only represent sequences that follow a strict pattern and repetition and concatenation will usually violate that pattern).
The advantage of the range
type over a regular list
or tuple
is that a range
object will always take the same (small) amount of memory, no matter the size of the range it represents (as it only stores the start
, stop
and step
values, calculating individual items and subranges as needed).
Range objects implement the collections.abc.Sequence
ABC, and provide features such as containment tests, element index lookup, slicing and support for negative indices (see Sequence Types — list, tuple, range):
>>> r = range(0, 20, 2)
>>> r
range(0, 20, 2)
>>> 11 in r
False
>>> 10 in r
True
>>> r.index(10)
5
>>> r[5]
10
>>> r[:5]
range(0, 10, 2)
>>> r[1]
18
Testing range objects for equality with ==
and !=
compares them as sequences. That is, two range objects are considered equal if they represent the same sequence of values. (Note that two range objects that compare equal might have different start
, stop
and step
attributes, for example range(0) == range(2, 1, 3)
or range(0, 3, 2) == range(0, 4, 2)
.)
Changed in version 3.2: Implement the Sequence ABC. Support slicing and negative indices. Test int
objects for membership in constant time instead of iterating through all items.
Changed in version 3.3: Define ‘==’ and ‘!=’ to compare range objects based on the sequence of values they define (instead of comparing based on object identity).
See also
The linspace recipe shows how to implement a lazy version of range suitable for floating point applications.
Text Sequence Type — str
Textual data in Python is handled with str
objects, or strings. Strings are immutable sequences of Unicode code points. String literals are written in a variety of ways:
Single quotes:
'allows embedded "double" quotes'
Double quotes:
"allows embedded 'single' quotes"
.Triple quoted:
'''Three single quotes'''
,"""Three double quotes"""
Triple quoted strings may span multiple lines  all associated whitespace will be included in the string literal.
String literals that are part of a single expression and have only whitespace between them will be implicitly converted to a single string literal. That is, ("spam " "eggs") == "spam eggs"
.
See String and Bytes literals for more about the various forms of string literal, including supported escape sequences, and the r
(“raw”) prefix that disables most escape sequence processing.
Strings may also be created from other objects using the str
constructor.
Since there is no separate “character” type, indexing a string produces strings of length 1. That is, for a nonempty string s, s[0] == s[0:1]
.
There is also no mutable string type, but str.join()
or io.StringIO
can be used to efficiently construct strings from multiple fragments.
Changed in version 3.3: For backwards compatibility with the Python 2 series, the u
prefix is once again permitted on string literals. It has no effect on the meaning of string literals and cannot be combined with the r
prefix.
 class
str
( object='' )  class
str
( object=b'', encoding='utf8', errors='strict' ) 
Return a string version of object. If object is not provided, returns the empty string. Otherwise, the behavior of
str()
depends on whether encoding or errors is given, as follows.If neither encoding nor errors is given,
str(object)
returnsobject.__str__()
, which is the “informal” or nicely printable string representation of object. For string objects, this is the string itself. If object does not have a__str__()
method, thenstr()
falls back to returningrepr(object)
.If at least one of encoding or errors is given, object should be a byteslike object (e.g.
bytes
orbytearray
). In this case, if object is abytes
(orbytearray
) object, thenstr(bytes, encoding, errors)
is equivalent tobytes.decode(encoding, errors)
. Otherwise, the bytes object underlying the buffer object is obtained before callingbytes.decode()
. See Binary Sequence Types — bytes, bytearray, memoryview and Buffer Protocol for information on buffer objects.Passing a
bytes
object tostr()
without the encoding or errors arguments falls under the first case of returning the informal string representation (see also theb
commandline option to Python). For example:>>> str(b'Zoot!') "b'Zoot!'"
For more information on the
str
class and its methods, see Text Sequence Type — str and the String Methods section below. To output formatted strings, see the Formatted string literals and Format String Syntax sections. In addition, see the Text Processing Services section.
String Methods
Strings implement all of the common sequence operations, along with the additional methods described below.
Strings also support two styles of string formatting, one providing a large degree of flexibility and customization (see str.format()
, Format String Syntax and Custom 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 (printfstyle String Formatting).
The Text Processing Services section of the standard library covers a number of other modules that provide various text related utilities (including regular expression support in the re
module).
str.
capitalize
( )
Return a copy of the string with its first character capitalized and the rest lowercased.
Changed in version 3.8: The first character is now put into titlecase rather than uppercase. This means that characters like digraphs will only have their first letter capitalized, instead of the full character.
str.
casefold
( )
Return a casefolded copy of the string. Casefolded strings may be used for caseless matching.
Casefolding is similar to lowercasing but more aggressive because it is intended to remove all case distinctions in a string. For example, the German lowercase letter
'ß'
is equivalent to"ss"
. Since it is already lowercase,lower()
would do nothing to'ß'
;casefold()
converts it to"ss"
.The casefolding algorithm is described in section 3.13 of the Unicode Standard.
New in version 3.3.
str.
center
( width [, fillchar ] )
Return centered in a string of length width. Padding is done using the specified fillchar (default is an ASCII space). The original string is returned if width is less than or equal to
len(s)
.
str.
count
( sub [, start [, end ] ] )
Return the number of nonoverlapping occurrences of substring sub in the range [start, end]. Optional arguments start and end are interpreted as in slice notation.
str.
encode
( encoding="utf8", errors="strict" )
Return an encoded version of the string as a bytes object. Default encoding is
'utf8'
. errors may be given to set a different error handling scheme. The default for errors is'strict'
, meaning that encoding errors raise aUnicodeError
. Other possible values are'ignore'
,'replace'
,'xmlcharrefreplace'
,'backslashreplace'
and any other name registered viacodecs.register_error()
, see section Error Handlers. For a list of possible encodings, see section Standard Encodings.Changed in version 3.1: Support for keyword arguments added.
str.
endswith
( suffix [, start [, end ] ] )
Return
True
if the string ends with the specified suffix, otherwise returnFalse
. suffix can also be a tuple of suffixes to look for. With optional start, test beginning at that position. With optional end, stop comparing at that position.
str.
expandtabs
( tabsize=8 )
Return a copy of the string where all tab characters are replaced by one or more spaces, depending on the current column and the given tab size. Tab positions occur every tabsize characters (default is 8, giving tab positions at columns 0, 8, 16 and so on). To expand the string, the current column is set to zero and the string is examined character by character. If the character is a tab (
\t
), one or more space characters are inserted in the result until the current column is equal to the next tab position. (The tab character itself is not copied.) If the character is a newline (\n
) or return (\r
), it is copied and the current column is reset to zero. Any other character is copied unchanged and the current column is incremented by one regardless of how the character is represented when printed.>>> '01\t012\t0123\t01234'.expandtabs() '01 012 0123 01234' >>> '01\t012\t0123\t01234'.expandtabs(4) '01 012 0123 01234'
str.
find
( sub [, start [, end ] ] )
Return the lowest index in the string where substring sub is found within the slice
s[start:end]
. Optional arguments start and end are interpreted as in slice notation. Return1
if sub is not found.
str.
format
( *args, **kwargs )
Perform a string formatting operation. The string on which this method is called can contain literal text or replacement fields delimited by braces
{}
. Each replacement field contains either the numeric index of a positional argument, or the name of a keyword argument. Returns a copy of the string where each replacement field is replaced with the string value of the corresponding argument.>>> "The sum of 1 + 2 is {0}".format(1+2) 'The sum of 1 + 2 is 3'
See Format String Syntax for a description of the various formatting options that can be specified in format strings.
Note
When formatting a number (
int
,float
,complex
,decimal.Decimal
and subclasses) with then
type (ex:'{:n}'.format(1234)
), the function temporarily sets theLC_CTYPE
locale to theLC_NUMERIC
locale to decodedecimal_point
andthousands_sep
fields oflocaleconv()
if they are nonASCII or longer than 1 byte, and theLC_NUMERIC
locale is different than theLC_CTYPE
locale. This temporary change affects other threads.Changed in version 3.7: When formatting a number with the
n
type, the function sets temporarily theLC_CTYPE
locale to theLC_NUMERIC
locale in some cases.
str.
format_map
( mapping )
Similar to
str.format(**mapping)
, except thatmapping
is used directly and not copied to adict
. This is useful if for examplemapping
is a dict subclass:>>> class Default(dict): ... def __missing__(self, key): ... return key ... >>> '{name} was born in {country}'.format_map(Default(name='Guido')) 'Guido was born in country'
New in version 3.2.
str.
index
( sub [, start [, end ] ] )
Like
find()
, but raiseValueError
when the substring is not found.
str.
isalnum
( )
Return
True
if all characters in the string are alphanumeric and there is at least one character,False
otherwise. A characterc
is alphanumeric if one of the following returnsTrue
:c.isalpha()
,c.isdecimal()
,c.isdigit()
, orc.isnumeric()
.
str.
isalpha
( )
Return
True
if all characters in the string are alphabetic and there is at least one character,False
otherwise. Alphabetic characters are those characters defined in the Unicode character database as “Letter”, i.e., those with general category property being one of “Lm”, “Lt”, “Lu”, “Ll”, or “Lo”. Note that this is different from the “Alphabetic” property defined in the Unicode Standard.
str.
isascii
( )
Return
True
if the string is empty or all characters in the string are ASCII,False
otherwise. ASCII characters have code points in the range U+0000U+007F.New in version 3.7.
str.
isdecimal
( )
Return
True
if all characters in the string are decimal characters and there is at least one character,False
otherwise. Decimal characters are those that can be used to form numbers in base 10, e.g. U+0660, ARABICINDIC DIGIT ZERO. Formally a decimal character is a character in the Unicode General Category “Nd”.
str.
isdigit
( )
Return
True
if all characters in the string are digits and there is at least one character,False
otherwise. Digits include decimal characters and digits that need special handling, such as the compatibility superscript digits. This covers digits which cannot be used to form numbers in base 10, like the Kharosthi numbers. Formally, a digit is a character that has the property value Numeric_Type=Digit or Numeric_Type=Decimal.
str.
isidentifier
( )
Return
True
if the string is a valid identifier according to the language definition, section Identifiers and keywords.Call
keyword.iskeyword()
to test whether strings
is a reserved identifier, such asdef
andclass
.Example:
>>> from keyword import iskeyword >>> 'hello'.isidentifier(), iskeyword('hello') True, False >>> 'def'.isidentifier(), iskeyword('def') True, True
str.
islower
( )
Return
True
if all cased characters 4 in the string are lowercase and there is at least one cased character,False
otherwise.
str.
isnumeric
( )
Return
True
if all characters in the string are numeric characters, and there is at least one character,False
otherwise. Numeric characters include digit characters, and all characters that have the Unicode numeric value property, e.g. U+2155, VULGAR FRACTION ONE FIFTH. Formally, numeric characters are those with the property value Numeric_Type=Digit, Numeric_Type=Decimal or Numeric_Type=Numeric.
str.
isprintable
( )
Return
True
if all characters in the string are printable or the string is empty,False
otherwise. Nonprintable characters are those characters defined in the Unicode character database as “Other” or “Separator”, excepting the ASCII space (0x20) which is considered printable. (Note that printable characters in this context are those which should not be escaped whenrepr()
is invoked on a string. It has no bearing on the handling of strings written tosys.stdout
orsys.stderr
.)
str.
isspace
( )
Return
True
if there are only whitespace characters in the string and there is at least one character,False
otherwise.A character is whitespace if in the Unicode character database (see
unicodedata
), either its general category isZs
(“Separator, space”), or its bidirectional class is one ofWS
,B
, orS
.
str.
istitle
( )
Return
True
if the string is a titlecased string and there is at least one character, for example uppercase characters may only follow uncased characters and lowercase characters only cased ones. ReturnFalse
otherwise.
str.
isupper
( )
Return
True
if all cased characters 4 in the string are uppercase and there is at least one cased character,False
otherwise.
str.
join
( iterable )
Return a string which is the concatenation of the strings in iterable. A
TypeError
will be raised if there are any nonstring values in iterable, includingbytes
objects. The separator between elements is the string providing this method.
str.
ljust
( width [, fillchar ] )
Return the string left justified in a string of length width. Padding is done using the specified fillchar (default is an ASCII space). The original string is returned if width is less than or equal to
len(s)
.
str.
lower
( )
Return a copy of the string with all the cased characters 4 converted to lowercase.
The lowercasing algorithm used is described in section 3.13 of the Unicode Standard.
str.
lstrip
( [ chars ] )
Return a copy of the string with leading characters removed. The chars argument is a string specifying the set of characters to be removed. If omitted or
None
, the chars argument defaults to removing whitespace. The chars argument is not a prefix; rather, all combinations of its values are stripped:>>> ' spacious '.lstrip() 'spacious ' >>> 'www.example.com'.lstrip('cmowz.') 'example.com'
 static
str.
maketrans
( x [, y [, z ] ] ) 
This static method returns a translation table usable for
str.translate()
.If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters (strings of length 1) to Unicode ordinals, strings (of arbitrary lengths) or
None
. Character keys will then be converted to ordinals.If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to
None
in the result.
str.
partition
( sep )
Split the string at the first occurrence of sep, and return a 3tuple containing the part before the separator, the separator itself, and the part after the separator. If the separator is not found, return a 3tuple containing the string itself, followed by two empty strings.
str.
replace
( old, new [, count ] )
Return a copy of the string with all occurrences of substring old replaced by new. If the optional argument count is given, only the first count occurrences are replaced.
str.
rfind
( sub [, start [, end ] ] )
Return the highest index in the string where substring sub is found, such that sub is contained within
s[start:end]
. Optional arguments start and end are interpreted as in slice notation. Return1
on failure.
str.
rindex
( sub [, start [, end ] ] )
Like
rfind()
but raisesValueError
when the substring sub is not found.