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 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. Here are most of the built-in objects considered false: constants defined to be false: None and False .

zero of any numeric type: 0 , 0.0 , 0j , Decimal(0) , Fraction(0, 1)

empty sequences and collections: '' , () , [] , {} , set() , range(0) Operations and built-in functions that have a Boolean result always return 0 or False for false and 1 or True for true, unless otherwise stated. (Important exception: the Boolean operations or and and always return one of their operands.)

Boolean Operations — and , or , not ¶ These are the Boolean operations, ordered by ascending priority: Operation Result Notes x or y if x is false, then y, else 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: This is a short-circuit operator, so it only evaluates the second argument if the first one is false. This is a short-circuit operator, so it only evaluates the second argument if the first one is true. 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. 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. Non-identical instances of a class normally compare as non-equal unless the class defines the __eq__() method. Instances of a class cannot be ordered with respect to other instances of the same class, or other types of object, unless the class defines enough of the methods __lt__() , __le__() , __gt__() , and __ge__() (in general, __lt__() and __eq__() are sufficient, if you want the conventional meanings of the comparison operators). The behavior of the is and is not operators cannot be customized; also they can be applied to any two objects and never raise an exception. Two more operations with the same syntactic priority, in and not in , are supported 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 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. A comparison between numbers of different types behaves as though the exact values of those numbers were being compared. 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 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 abs() int(x) x converted to integer (3)(6) int() float(x) x converted to floating point (4)(6) float() complex(re, im) a complex number with real part re, imaginary part im. im defaults to zero. (6) complex() c.conjugate() conjugate of the complex number c divmod(x, y) the pair (x // y, x % y) (2) divmod() pow(x, y) x to the power y (5) pow() x ** y 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 is 0 , (-1)//2 is -1 , 1//(-2) is -1 , and (-1)//(-2) is 0 . 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() and math.ceil() for well-defined 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) and 0 ** 0 to be 1 , as is common for programming languages. 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/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 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 <= x math.ceil(x) the least Integral >= x 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 x | y bitwise or of x and y (4) x ^ y bitwise exclusive or of x and y (4) x & y bitwise and of x and y (4) 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: 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 bit-width 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, then x.bit_length() is the unique positive integer k such that 2**(k-1) <= abs(x) < 2**k . Equivalently, when abs(x) is small enough to have a correctly rounded logarithm, then k = 1 + int(log(abs(x), 2)) . If x is zero, then x.bit_length() returns 0 . Equivalent to: def bit_length ( self ): s = bin ( self ) # binary representation: bin(-37) --> '-0b100101' s = s . lstrip ( '-0b' ) # remove leading zeros and minus sign return len ( s ) # len('100101') --> 6 New in version 3.1. int. to_bytes ( length, byteorder, *, signed=False ) ¶ Return an array of bytes representing an integer. >>> ( 1024 ) . to_bytes ( 2 , byteorder = 'big' ) b'\x04\x00' >>> ( 1024 ) . to_bytes ( 10 , byteorder = 'big' ) b'\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00' >>> ( - 1024 ) . to_bytes ( 10 , byteorder = 'big' , signed = True ) b'\xff\xff\xff\xff\xff\xff\xff\xff\xfc\x00' >>> x = 1000 >>> x . to_bytes (( x . bit_length () + 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, use sys.byteorder as the byte order value. The signed argument determines whether two’s complement is used to represent the integer. If signed is False and a negative integer is given, an OverflowError is raised. The default value for signed is False . New in version 3.2. classmethod int. from_bytes ( bytes, byteorder, *, signed=False ) ¶ Return the integer represented by the given array of bytes. >>> int . from_bytes ( b ' \x00\x10 ' , byteorder = 'big' ) 16 >>> int . from_bytes ( b ' \x00\x10 ' , byteorder = 'little' ) 4096 >>> int . from_bytes ( b ' \xfc\x00 ' , byteorder = 'big' , signed = True ) -1024 >>> int . from_bytes ( b ' \xfc\x00 ' , byteorder = 'big' , signed = False ) 64512 >>> int . from_bytes ([ 255 , 0 , 0 ], byteorder = 'big' ) 16711680 The argument bytes must either be a bytes-like object or an iterable producing bytes. The byteorder argument determines the byte order used to represent the integer. If byteorder is "big" , the most significant byte is at the beginning of the byte array. If byteorder is "little" , the most significant byte is at the end of the byte array. To request the native byte order of the host system, use sys.byteorder as the byte order value. The signed argument indicates whether two’s complement is used to represent the integer. New in version 3.2. int. as_integer_ratio ( ) ¶ Return a pair of integers whose ratio is exactly equal to the original integer and with a positive denominator. The integer ratio of integers (whole numbers) is always the integer as the numerator and 1 as the denominator. New in version 3.8. Additional Methods on Float¶ The float type implements the numbers.Real abstract base class. float also has the following additional methods. float. as_integer_ratio ( ) ¶ Return a pair of integers whose ratio is exactly equal to the original float and with a positive denominator. Raises OverflowError on infinities and a ValueError on NaNs. float. is_integer ( ) ¶ Return True if the float instance is finite with integral value, and False otherwise: >>> ( - 2.0 ) . is_integer () True >>> ( 3.2 ) . is_integer () False Two methods support conversion to and from hexadecimal strings. Since Python’s floats are stored internally as binary numbers, converting a float to or from a decimal string usually involves a small rounding error. In contrast, hexadecimal strings allow exact representation and specification of floating-point numbers. This can be useful when debugging, and in numerical work. float. hex ( ) ¶ Return a representation of a floating-point number as a hexadecimal string. For finite floating-point numbers, this representation will always include a leading 0x and a trailing p and exponent. classmethod float. fromhex ( s ) ¶ Class method to return the float represented by a hexadecimal string s. The string s may have leading and trailing whitespace. Note that float.hex() is an instance method, while float.fromhex() is a class method. A hexadecimal string takes the form: [ sign ] [ '0x' ] integer [ '.' fraction ] [ 'p' exponent ] where the optional sign may by either + or - , integer and fraction are strings of hexadecimal digits, and exponent is a decimal integer with an optional leading sign. Case is not significant, and there must be at least one hexadecimal digit in either the integer or the fraction. This syntax is similar to the syntax specified in section 6.4.4.2 of the C99 standard, and also to the syntax used in Java 1.5 onwards. In particular, the output of float.hex() is usable as a hexadecimal floating-point literal in C or Java code, and hexadecimal strings produced by C’s %a format character or Java’s Double.toHexString are accepted by float.fromhex() . Note that the exponent is written in decimal rather than hexadecimal, and that it gives the power of 2 by which to multiply the coefficient. For example, the hexadecimal string 0x3.a7p10 represents the floating-point number (3 + 10./16 + 7./16**2) * 2.0**10 , or 3740.0 : >>> float . fromhex ( '0x3.a7p10' ) 3740.0 Applying the reverse conversion to 3740.0 gives a different hexadecimal string representing the same number: >>> float . hex ( 3740.0 ) '0x1.d380000000000p+11' Hashing of numeric types¶ For numbers x and y , possibly of different types, it’s a requirement that hash(x) == hash(y) whenever x == y (see the __hash__() method documentation for more details). For ease of implementation and efficiency across a variety of numeric types (including int , float , decimal.Decimal and fractions.Fraction ) Python’s hash for numeric types is based on a single mathematical function that’s defined for any rational number, and hence applies to all instances of int and fractions.Fraction , and all finite instances of float and decimal.Decimal . Essentially, this function is given by reduction modulo P for a fixed prime P . The value of P is made available to Python as the modulus attribute of sys.hash_info . CPython implementation detail: Currently, the prime used is P = 2**31 - 1 on machines with 32-bit C longs and P = 2**61 - 1 on machines with 64-bit C longs. Here are the rules in detail: If x = m / n is a nonnegative rational number and n is not divisible by P , define hash(x) as m * invmod(n, P) % P , where invmod(n, P) gives the inverse of n modulo P .

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

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

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

For a complex number z , the hash values of the real and imaginary parts are combined by computing hash(z.real) + sys.hash_info.imag * hash(z.imag) , reduced modulo 2**sys.hash_info.width so that it lies in range(-2**(sys.hash_info.width - 1), 2**(sys.hash_info.width - 1)) . Again, if the result is -1 , it’s replaced with -2 . To clarify the above rules, here’s some example Python code, equivalent to the built-in hash, for computing the hash of a rational number, float , or complex : import sys , math def hash_fraction ( m , n ): """Compute the hash of a rational number m / n. Assumes m and n are integers, with n positive. Equivalent to hash(fractions.Fraction(m, n)). """ P = sys . hash_info . modulus # Remove common factors of P. (Unnecessary if m and n already coprime.) while m % P == n % P == 0 : m , n = m // P , n // P if n % P == 0 : hash_value = 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_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 user-defined classes to support iteration. Sequences, described below in more detail, always support the iteration methods. One method needs to be defined for container objects to provide iteration support: container. __iter__ ( ) ¶ Return an iterator object. The object is required to support the iterator protocol described below. If a container supports different types of iteration, additional methods can be provided to specifically request iterators for those iteration types. (An example of an object supporting multiple forms of iteration would be a tree structure which supports both breadth-first and depth-first traversal.) This method corresponds to the tp_iter slot of the type structure for Python objects in the Python/C API. The iterator objects themselves are required to support the following two methods, which together form the iterator protocol: iterator. __iter__ ( ) ¶ Return the iterator object itself. This is required to allow both containers and iterators to be used with the for and in statements. This method corresponds to the tp_iter slot of the type structure for Python objects in the Python/C API. iterator. __next__ ( ) ¶ Return the next item from the container. If there are no further items, raise the StopIteration exception. This method corresponds to the tp_iternext slot of the type structure for Python objects in the Python/C API. Python defines several iterator objects to support iteration over general and specific sequence types, dictionaries, and other more specialized forms. The specific types are not important beyond their implementation of the iterator protocol. Once an iterator’s __next__() method raises StopIteration , it must continue to do so on subsequent calls. Implementations that do not obey this property are deemed broken. Generator Types¶ Python’s 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. 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 equivalent to adding s to itself n times (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 occurrence of x in s (at or after index i and before index j) (8) s.count(x) 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 and not in operations are used only for simple containment testing in the general case, some specialised sequences (such as str , bytes and bytearray ) also use them for subsequence testing: >>> "gg" in "eggs" True Values of n less than 0 are treated as 0 (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 one-element list containing an empty list, so all three elements of [[]] * 3 are references 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]] 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 or len(s) + j is substituted. But note that -0 is still 0 . 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. 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). When k is positive, i and j are reduced to len(s) if they are greater. When k is negative, i and j are reduced to len(s) - 1 if they are greater. 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 . Concatenating immutable sequences always results in a new object. This means that building up a sequence by repeated concatenation will have a quadratic runtime cost in the total sequence length. To get a linear runtime cost, you must switch to one of the alternatives below: if concatenating str objects, you can build a list and use str.join() at the end or else write to an io.StringIO instance and retrieve its value when complete

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

if concatenating tuple objects, extend a list instead

for other types, investigate the relevant class documentation Some sequence types (such as range ) only support item sequences that follow specific patterns, and hence don’t support sequence concatenation or repetition. index raises ValueError 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 using s[i:j].index(x) , only without copying any data and with the returned index being relative to the start of the sequence rather than the start of the slice. Immutable Sequence Types¶ The only operation that immutable sequence types generally implement that is not also implemented by mutable sequence types is support for the hash() built-in. This support allows immutable sequences, such as tuple instances, to be used as dict keys and stored in set and frozenset instances. Attempting to hash an immutable sequence that contains unhashable values will result in TypeError . Mutable Sequence Types¶ The operations in the following table are defined on mutable sequence types. The collections.abc.MutableSequence ABC is provided to make it easier to correctly implement these operations on custom sequence types. In the table s is an instance of a mutable sequence type, t is any iterable object and x is an arbitrary object that meets any type and value restrictions imposed by s (for example, bytearray only accepts integers that meet the value restriction 0 <= x <= 255 ). Operation Result Notes s[i] = 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) or s += t extends s with the contents of t (for the most part the same as s[len(s):len(s)] = t ) s *= n updates s with its contents repeated n times (6) 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] is equal to x (3) s.reverse() 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() raises ValueError 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() and copy() are included for consistency with the interfaces of mutable containers that don’t support slicing operations (such as dict and set ). copy() is not part of the collections.abc.MutableSequence ABC, but most concrete mutable sequence classes provide it. New in version 3.3: clear() and copy() 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 for s * 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() or list(iterable) The constructor builds a list whose items are the same and in the same order as iterable’s items. iterable may be either a sequence, a container that supports iteration, or an iterator object. If iterable is already a list, a copy is made and returned, similar to iterable[:] . For example, list('abc') returns ['a', 'b', 'c'] and list( (1, 2, 3) ) returns [1, 2, 3] . If no argument is given, the constructor creates a new empty list, [] . Many other operations also produce lists, including the sorted() built-in. Lists implement all of the common and mutable sequence operations. Lists also provide the following additional method: sort ( *, key=None, reverse=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 (keyword-only arguments): key specifies a function of one argument that is used to extract a comparison key from each list element (for example, key=str.lower ). The key corresponding to each item in the list is calculated once and then used for the entire sorting process. The default value of None means that list items are sorted directly without calculating a separate key value. The functools.cmp_to_key() utility is available to convert a 2.x style cmp function to a key function. reverse is a boolean value. If set to True , then the list elements are sorted as if each comparison were reversed. This method modifies the sequence in place for economy of space when sorting a large sequence. To remind users that it operates by side effect, it does not return the sorted sequence (use sorted() to explicitly request a new sorted list instance). The sort() method is guaranteed to be stable. A sort is stable if it guarantees not to change the relative order of elements that compare equal — this is helpful for sorting in multiple passes (for example, sort by department, then by salary grade). 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 2-tuples produced by the enumerate() built-in). Tuples are also used for cases where an immutable sequence of homogeneous data is needed (such as allowing storage in a set or dict instance). class tuple ( [ iterable ] ) ¶ Tuples may be constructed in a number of ways: Using a pair of parentheses to denote the empty tuple: ()

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

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

Using the tuple() built-in: tuple() or tuple(iterable) The constructor builds a tuple whose items are the same and in the same order as iterable’s items. iterable may be either a sequence, a container that supports iteration, or an iterator object. If iterable is already a tuple, it is returned unchanged. For example, tuple('abc') returns ('a', 'b', 'c') and tuple( [1, 2, 3] ) returns (1, 2, 3) . If no argument is given, the constructor creates a new empty tuple, () . Note that it is actually the comma which makes a tuple, not the parentheses. The parentheses are optional, except in the empty tuple case, or when they are needed to avoid syntactic ambiguity. For example, f(a, b, c) is a function call with three arguments, while f((a, b, c)) is a function call with a 3-tuple as the sole argument. Tuples implement all of the common sequence operations. For heterogeneous collections of data where access by name is clearer than access by index, collections.namedtuple() may be a more appropriate choice than a simple tuple object. Ranges¶ The range type represents an immutable sequence of numbers and is commonly used for looping a specific number of times in for loops. class range ( stop ) ¶ class range ( start, stop [ , step ] ) The arguments to the range constructor must be integers (either built-in int or any object that implements the __index__ special method). If the step argument is omitted, it defaults to 1 . If the start argument is omitted, it defaults to 0 . If step is zero, ValueError is raised. For a positive step, the contents of a range r are determined by the formula r[i] = start + step*i where i >= 0 and r[i] < stop . For a negative step, the contents of the range are still determined by the formula r[i] = start + step*i , but the constraints are i >= 0 and r[i] > stop . A range object will be empty if r[0] does not meet the value constraint. Ranges do support negative indices, but these are interpreted as indexing from the end of the sequence determined by the positive indices. Ranges containing absolute values larger than sys.maxsize are permitted but some features (such as len() ) may raise OverflowError . Range examples: >>> list ( range ( 10 )) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] >>> list ( range ( 1 , 11 )) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] >>> list ( range ( 0 , 30 , 5 )) [0, 5, 10, 15, 20, 25] >>> list ( range ( 0 , 10 , 3 )) [0, 3, 6, 9] >>> list ( range ( 0 , - 10 , - 1 )) [0, -1, -2, -3, -4, -5, -6, -7, -8, -9] >>> list ( range ( 0 )) [] >>> list ( range ( 1 , 0 )) [] Ranges implement all of the common sequence operations except concatenation and repetition (due to the fact that range objects can only represent sequences that follow a strict pattern and repetition and concatenation will usually violate that pattern). start ¶ The value of the start parameter (or 0 if the parameter was not supplied) stop ¶ The value of the stop parameter step ¶ The value of the step parameter (or 1 if the parameter was not supplied) The advantage of the range type over a regular list or tuple is that a range object will always take the same (small) amount of memory, no matter the size of the range it represents (as it only stores the start , stop and step values, calculating individual items and subranges as needed). Range objects implement the collections.abc.Sequence ABC, and provide features such as containment tests, element index lookup, slicing and support for negative indices (see Sequence Types — list, tuple, range): >>> r = range ( 0 , 20 , 2 ) >>> r range(0, 20, 2) >>> 11 in r False >>> 10 in r True >>> r . index ( 10 ) 5 >>> r [ 5 ] 10 >>> r [: 5 ] range(0, 10, 2) >>> r [ - 1 ] 18 Testing range objects for equality with == and != compares them as sequences. That is, two range objects are considered equal if they represent the same sequence of values. (Note that two range objects that compare equal might have different start , stop and step attributes, for example range(0) == range(2, 1, 3) or range(0, 3, 2) == range(0, 4, 2) .) Changed in version 3.2: Implement the Sequence ABC. Support slicing and negative indices. Test int objects for membership in constant time instead of iterating through all items. Changed in version 3.3: Define ‘==’ and ‘!=’ to compare range objects based on the sequence of values they define (instead of comparing based on object identity). New in version 3.3: The start , stop and step attributes. See also The linspace recipe shows how to implement a lazy version of range suitable for floating point applications.

Set Types — set , frozenset ¶ A set object is an unordered collection of distinct hashable objects. Common uses include membership testing, removing duplicates from a sequence, and computing mathematical operations such as intersection, union, difference, and symmetric difference. (For other containers see the built-in dict , list , and tuple classes, and the collections module.) Like other collections, sets support x in set , len(set) , and for x in set . Being an unordered collection, sets do not record element position or order of insertion. Accordingly, sets do not support indexing, slicing, or other sequence-like behavior. There are currently two built-in set types, set and frozenset . The set type is mutable — the contents can be changed using methods like add() and remove() . Since it is mutable, it has no hash value and cannot be used as either a dictionary key or as an element of another set. The frozenset type is immutable and hashable — its contents cannot be altered after it is created; it can therefore be used as a dictionary key or as an element of another set. Non-empty sets (not frozensets) can be created by placing a comma-separated list of elements within braces, for example: {'jack', 'sjoerd'} , in addition to the set constructor. The constructors for both classes work the same: class set ( [ iterable ] ) ¶ class frozenset ( [ iterable ] ) ¶ Return a new set or frozenset object whose elements are taken from iterable. The elements of a set must be hashable. To represent sets of sets, the inner sets must be frozenset objects. If iterable is not specified, a new empty set is returned. Instances of set and frozenset provide the following operations: len(s) Return the number of elements in set s (cardinality of s). x in s Test x for membership in s. x not in s Test x for non-membership in s. isdisjoint ( other ) ¶ Return True if the set has no elements in common with other. Sets are disjoint if and only if their intersection is the empty set. issubset ( other ) ¶ set <= other Test whether every element in the set is in other. set < other Test whether the set is a proper subset of other, that is, set <= other and set != other . issuperset ( other ) ¶ set >= other Test whether every element in other is in the set. set > other Test whether the set is a proper superset of other, that is, set >= other and set != other . union ( *others ) ¶ set | other | ... Return a new set with elements from the set and all others. intersection ( *others ) ¶ set & other & ... Return a new set with elements common to the set and all others. difference ( *others ) ¶ set - other - ... Return a new set with elements in the set that are not in the others. symmetric_difference ( other ) ¶ set ^ other Return a new set with elements in either the set or other but not both. copy ( ) ¶ Return a shallow copy of the set. Note, the non-operator versions of union() , intersection() , difference() , and symmetric_difference() , issubset() , and issuperset() methods will accept any iterable as an argument. In contrast, their operator based counterparts require their arguments to be sets. This precludes error-prone constructions like set('abc') & 'cbs' in favor of the more readable set('abc').intersection('cbs') . Both set and frozenset support set to set comparisons. Two sets are equal if and only if every element of each set is contained in the other (each is a subset of the other). A set is less than another set if and only if the first set is a proper subset of the second set (is a subset, but is not equal). A set is greater than another set if and only if the first set is a proper superset of the second set (is a superset, but is not equal). Instances of set are compared to instances of frozenset based on their members. For example, set('abc') == frozenset('abc') returns True and so does set('abc') in set([frozenset('abc')]) . The subset and equality comparisons do not generalize to a total ordering function. For example, any two nonempty disjoint sets are not equal and are not subsets of each other, so all of the following return False : a<b , a==b , or a>b . Since sets only define partial ordering (subset relationships), the output of the list.sort() method is undefined for lists of sets. Set elements, like dictionary keys, must be hashable. Binary operations that mix set instances with frozenset return the type of the first operand. For example: frozenset('ab') | set('bc') returns an instance of frozenset . The following table lists operations available for set that do not apply to immutable instances of frozenset : set |= other | ... Update the set, adding elements from all others. set &= other & ... Update the set, keeping only elements found in it and all others. set -= other | ... Update the set, removing elements found in others. set ^= other Update the set, keeping only elements found in either set, but not in both. add ( elem ) ¶ Add element elem to the set. remove ( elem ) ¶ Remove element elem from the set. Raises KeyError if elem is not contained in the set. discard ( elem ) ¶ Remove element elem from the set if it is present. pop ( ) ¶ Remove and return an arbitrary element from the set. Raises KeyError if the set is empty. clear ( ) ¶ Remove all elements from the set. Note, the non-operator versions of the update() , intersection_update() , difference_update() , and symmetric_difference_update() methods will accept any iterable as an argument. Note, the elem argument to the __contains__() , remove() , and discard() methods may be a set. To support searching for an equivalent frozenset, a temporary one is created from elem.

Mapping Types — dict ¶ A mapping object maps hashable values to arbitrary objects. Mappings are mutable objects. There is currently only one standard mapping type, the dictionary. (For other containers see the built-in list , set , and tuple classes, and the collections module.) A dictionary’s keys are almost arbitrary values. Values that are not hashable, that is, values containing lists, dictionaries or other mutable types (that are compared by value rather than by object identity) may not be used as keys. Numeric types used for keys obey the normal rules for numeric comparison: if two numbers compare equal (such as 1 and 1.0 ) then they can be used interchangeably to index the same dictionary entry. (Note however, that since computers store floating-point numbers as approximations it is usually unwise to use them as dictionary keys.) Dictionaries can be created by placing a comma-separated list of key: value pairs within braces, for example: {'jack': 4098, 'sjoerd': 4127} or {4098: 'jack', 4127: 'sjoerd'} , or by the dict constructor. class dict ( **kwarg ) ¶ class dict ( mapping, **kwarg ) class dict ( iterable, **kwarg ) Return a new dictionary initialized from an optional positional argument and a possibly empty set of keyword arguments. If no positional argument is given, an empty dictionary is created. If a positional argument is given and it is a mapping object, a dictionary is created with the same key-value pairs as the mapping object. Otherwise, the positional argument must be an iterable object. Each item in the iterable must itself be an iterable 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): list(d) Return a list of all the keys used in the dictionary d. len(d) Return the number of items in the dictionary d. d[key] Return the item of d with key key. Raises a KeyError if key is not in the map. If a subclass of dict defines a method __missing__() and key is not present, the d[key] operation calls that method with the key key as argument. The d[key] operation then returns or raises whatever is returned or raised by the __missing__(key) call. No other operations or methods invoke __missing__() . If __missing__() is not defined, KeyError is raised. __missing__() must be a method; it cannot be an instance variable: >>> class Counter ( dict ): ... def __missing__ ( self , key ): ... return 0 >>> c = Counter () >>> c [ 'red' ] 0 >>> c [ 'red' ] += 1 >>> c [ 'red' ] 1 The example above shows part of the implementation of collections.Counter . A different __missing__ method is used by collections.defaultdict . d[key] = value Set d[key] to value. del d[key] Remove d[key] from d. Raises a KeyError if key is not in the map. key in d Return True if d has a key key, else False . key not in d Equivalent to not key in d . iter(d) Return an iterator over the keys of the dictionary. This is a shortcut for iter(d.keys()) . clear ( ) ¶ Remove all items from the dictionary. copy ( ) ¶ Return a shallow copy of the dictionary. classmethod fromkeys ( iterable [ , value ] ) ¶ Create a new dictionary with keys from iterable and values set to value. fromkeys() is a class method that returns a new dictionary. value defaults to None . All of the values refer to just a single instance, so it generally doesn’t make sense for value to be a mutable object such as an empty list. To get distinct values, use a dict comprehension instead. get ( key [ , default ] ) ¶ Return the value for key if key is in the dictionary, else default. If default is not given, it defaults to None , so that this method never raises a KeyError . items ( ) ¶ Return a new view of the dictionary’s items ( (key, value) pairs). See the documentation of view objects. keys ( ) ¶ Return a new view of the dictionary’s keys. See the documentation of view objects. pop ( key [ , default ] ) ¶ If key is in the dictionary, remove it and return its value, else return default. If default is not given and key is not in the dictionary, a KeyError is raised. popitem ( ) ¶ Remove and return a (key, value) pair from the dictionary. Pairs are returned in LIFO order. popitem() is useful to destructively iterate over a dictionary, as often used in set algorithms. If the dictionary is empty, calling popitem() raises a KeyError . Changed in version 3.7: LIFO order is now guaranteed. In prior versions, popitem() would return an arbitrary key/value pair. reversed(d) Return a reverse iterator over the keys of the dictionary. This is a shortcut for reversed(d.keys()) . New in version 3.8. setdefault ( key [ , default ] ) ¶ If key is in the dictionary, return its value. If not, insert key with a value of default and return default. default defaults to None . Update the dictionary with the key/value pairs from other, overwriting existing keys. Return None . update() accepts either another dictionary object or an iterable of key/value pairs (as tuples or other iterables of length two). If keyword arguments are specified, the dictionary is then updated with those key/value pairs: d.update(red=1, blue=2) . values ( ) ¶ Return a new view of the dictionary’s values. See the documentation of view objects. An equality comparison between one dict.values() view and another will always return False . This also applies when comparing dict.values() to itself: >>> d = { 'a' : 1 } >>> d . values () == d . values () False Dictionaries compare equal if and only if they have the same (key, value) pairs (regardless of ordering). Order comparisons (‘<’, ‘<=’, ‘>=’, ‘>’) raise TypeError . Dictionaries preserve insertion order. Note that updating a key does not affect the order. Keys added after deletion are inserted at the end. >>> d = { "one" : 1 , "two" : 2 , "three" : 3 , "four" : 4 } >>> d {'one': 1, 'two': 2, 'three': 3, 'four': 4} >>> list ( d ) ['one', 'two', 'three', 'four'] >>> list ( d . values ()) [1, 2, 3, 4] >>> d [ "one" ] = 42 >>> d {'one': 42, 'two': 2, 'three': 3, 'four': 4} >>> del d [ "two" ] >>> d [ "two" ] = None >>> d {'one': 42, 'three': 3, 'four': 4, 'two': None} Changed in version 3.7: Dictionary order is guaranteed to be insertion order. This behavior was an implementation detail of CPython from 3.6. Dictionaries and dictionary views are reversible. >>> d = { "one" : 1 , "two" : 2 , "three" : 3 , "four" : 4 } >>> d {'one': 1, 'two': 2, 'three': 3, 'four': 4} >>> list ( reversed ( d )) ['four', 'three', 'two', 'one'] >>> list ( reversed ( d . values ())) [4, 3, 2, 1] >>> list ( reversed ( d . items ())) [('four', 4), ('three', 3), ('two', 2), ('one', 1)] Changed in version 3.8: Dictionaries are now reversible. See also types.MappingProxyType can be used to create a read-only view of a dict . Dictionary view objects¶ The objects returned by dict.keys() , dict.values() and dict.items() are view objects. They provide a dynamic view on the dictionary’s entries, which means that when the dictionary changes, the view reflects these changes. Dictionary views can be iterated over to yield their respective data, and support membership tests: len(dictview) Return the number of entries in the dictionary. iter(dictview) Return an iterator over the keys, values or items (represented as tuples of (key, value) ) in the dictionary. Keys and values are iterated over in insertion order. This allows the creation of (value, key) pairs using zip() : pairs = zip(d.values(), d.keys()) . Another way to create the same list is pairs = [(v, k) for (k, v) in d.items()] . Iterating views while adding or deleting entries in the dictionary may raise a RuntimeError or fail to iterate over all entries. Changed in version 3.7: Dictionary order is guaranteed to be insertion order. x in dictview Return True if x is in the underlying dictionary’s keys, values or items (in the latter case, x should be a (key, value) tuple). reversed(dictview) Return a reverse iterator over the keys, values or items of the dictionary. The view will be iterated in reverse order of the insertion. Changed in version 3.8: Dictionary views are now reversible. Keys views are set-like since their entries are unique and hashable. If all values are hashable, so that (key, value) pairs are unique and hashable, then the items view is also set-like. (Values views are not treated as set-like since the entries are generally not unique.) For set-like views, all of the operations defined for the abstract base class collections.abc.Set are available (for example, == , < , or ^ ). An example of dictionary view usage: >>> dishes = { 'eggs' : 2 , 'sausage' : 1 , 'bacon' : 1 , 'spam' : 500 } >>> keys = dishes . keys () >>> values = dishes . values () >>> # iteration >>> n = 0 >>> for val in values : ... n += val >>> print ( n ) 504 >>> # keys and values are iterated over in the same order (insertion order) >>> list ( keys ) ['eggs', 'sausage', 'bacon', 'spam'] >>> list ( values ) [2, 1, 1, 500] >>> # view objects are dynamic and reflect dict changes >>> del dishes [ 'eggs' ] >>> del dishes [ 'sausage' ] >>> list ( keys ) ['bacon', 'spam'] >>> # set operations >>> keys & { 'eggs' , 'bacon' , 'salad' } {'bacon'} >>> keys ^ { 'sausage' , 'juice' } {'juice', 'sausage', 'bacon', 'spam'}

Context Manager Types¶ Python’s with statement supports the concept of a runtime context defined by a context manager. This is implemented using a pair of methods that allow user-defined classes to define a runtime context that is entered before the statement body is executed and exited when the statement ends: contextmanager. __enter__ ( ) ¶ Enter the runtime context and return either this object or another object related to the runtime context. The value returned by this method is bound to the identifier in the as clause of with statements using this context manager. An example of a context manager that returns itself is a file object. File objects return themselves from __enter__() to allow open() to be used as the context expression in a with statement. An example of a context manager that returns a related object is the one returned by decimal.localcontext() . These managers set the active decimal context to a copy of the original decimal context and then return the copy. This allows changes to be made to the current decimal context in the body of the with statement without affecting code outside the with statement. contextmanager. __exit__ ( exc_type, exc_val, exc_tb ) ¶ Exit the runtime context and return a Boolean flag indicating if any exception that occurred should be suppressed. If an exception occurred while executing the body of the with statement, the arguments contain the exception type, value and traceback information. Otherwise, all three arguments are None . Returning a true value from this method will cause the with statement to suppress the exception and continue execution with the statement immediately following the with statement. Otherwise the exception continues propagating after this method has finished executing. Exceptions that occur during execution of this method will replace any exception that occurred in the body of the with statement. The exception passed in should never be reraised explicitly - instead, this method should return a false value to indicate that the method completed successfully and does not want to suppress the raised exception. This allows context management code to easily detect whether or not an __exit__() method has actually failed. Python defines several context managers to support easy thread synchronisation, prompt closure of files or other objects, and simpler manipulation of the active decimal arithmetic context. The specific types are not treated specially beyond their implementation of the context management protocol. See the contextlib module for some examples. Python’s generators and the contextlib.contextmanager decorator provide a convenient way to implement these protocols. If a generator function is decorated with the contextlib.contextmanager decorator, it will return a context manager implementing the necessary __enter__() and __exit__() methods, rather than the iterator produced by an undecorated generator function. Note that there is no specific slot for any of these methods in the type structure for Python objects in the Python/C API. Extension types wanting to define these methods must provide them as a normal Python accessible method. Compared to the overhead of setting up the runtime context, the overhead of a single class dictionary lookup is negligible.

Other Built-in Types¶ The interpreter supports several other kinds of objects. Most of these support only one or two operations. Modules¶ The only special operation on a module is attribute access: m.name , where m is a module and name accesses a name defined in m’s symbol table. Module attributes can be assigned to. (Note that the import statement is not, strictly speaking, an operation on a module object; import foo does not require a module object named foo to exist, rather it requires an (external) definition for a module named foo somewhere.) A special attribute of every module is __dict__ . This is the dictionary containing the module’s symbol table. Modifying this dictionary will actually change the module’s symbol table, but direct assignment to the __dict__ attribute is not possible (you can write m.__dict__['a'] = 1 , which defines m.a to be 1 , but you can’t write m.__dict__ = {} ). Modifying __dict__ directly is not recommended. Modules built into the interpreter are written like this: <module 'sys' (built-in)> . If loaded from a file, they are written as <module 'os' from '/usr/local/lib/pythonX.Y/os.pyc'> . Classes and Class Instances¶ See Objects, values and types and Class definitions for these. Functions¶ Function objects are created by function definitions. The only operation on a function object is to call it: func(argument-list) . There are really two flavors of function objects: built-in functions and user-defined functions. Both support the same operation (to call the function), but the implementation is different, hence the different object types. See Function definitions for more information. Methods¶ Methods are functions that are called using the attribute notation. There are two flavors: built-in methods (such as append() on lists) and class instance methods. Built-in methods are described with the types that support them. If you access a method (a function defined in a class namespace) through an instance, you get a special object: a bound method (also called instance method) object. When called, it will add the self argument to the argument list. Bound methods have two special read-only attributes: m.__self__ is the object on which the method operates, and m.__func__ is the function implementing the method. Calling m(arg-1, arg-2, ..., arg-n) is completely equivalent to calling m.__func__(m.__self__, arg-1, arg-2, ..., arg-n) . Like function objects, bound method objects support getting arbitrary attributes. However, since method attributes are actually stored on the underlying function object ( meth.__func__ ), setting method attributes on bound methods is disallowed. Attempting to set an attribute on a method results in an AttributeError being raised. In order to set a method attribute, you need to explicitly set it on the underlying function object: >>> class C : ... def method ( self ): ... pass ... >>> c = C () >>> c . method . whoami = 'my name is method' # can't set on the method Traceback (most recent call last): File "<stdin>" , line 1 , in <module> AttributeError : 'method' object has no attribute 'whoami' >>> c . method . __func__ . whoami = 'my name is method' >>> c . method . whoami 'my name is method' See The standard type hierarchy for more information. Code Objects¶ Code objects are used by the implementation to represent “pseudo-compiled” executable Python code such as a function body. They differ from function objects because they don’t contain a reference to their global execution environment. Code objects are returned by the built-in compile() function and can be extracted from function objects through their __code__ attribute. See also the code module. A code object can be executed or evaluated by passing it (instead of a source string) to the exec() or eval() built-in functions. See The standard type hierarchy for more information. Type Objects¶ Type objects represent the various object types. An object’s type is accessed by the built-in function type() . There are no special operations on types. The standard module types defines names for all standard built-in types. Types are written like this: <class 'int'> . The Null Object¶ This object is returned by functions that don’t explicitly return a value. It supports no special operations. There is exactly one null object, named None (a built-in name). type(None)() produces the same singleton. It is written as None . The Ellipsis Object¶ This object is commonly used by slicing (see Slicings). It supports no special operations. There is exactly one ellipsis object, named Ellipsis (a built-in name). type(Ellipsis)() produces the Ellipsis singleton. It is written as Ellipsis or ... . The NotImplemented Object¶ This object is returned from comparisons and binary operations when they are asked to operate on types they don’t support. See Comparisons for more information. There is exactly one NotImplemented object. type(NotImplemented)() produces the singleton instance. It is written as NotImplemented . Boolean Values¶ Boolean values are the two constant objects False and True . They are used to represent truth values (although other values can also be considered false or true). In numeric contexts (for example when used as the argument to an arithmetic operator), they behave like the integers 0 and 1, respectively. The built-in function bool() can be used to convert any value to a Boolean, if the value can be interpreted as a truth value (see section Truth Value Testing above). They are written as False and True , respectively. Internal Objects¶ See The standard type hierarchy for this information. It describes stack frame objects, traceback objects, and slice objects.