6.2.1. Built-in constants¶

The keywords True, False, and None name built-in constants. The token ... names the Ellipsis constant.

Evaluation of these atoms yields the corresponding value.

>>> False = 123
  File "<input>", line 1
   False = 123
   ^^^^^
SyntaxError: cannot assign to False

6.2.2. Identifiers (Names)¶

An identifier occurring as an atom is a name. See section Names (identifiers and keywords) for lexical definition and section Naming and binding for documentation of naming and binding.

When the name is bound to an object, evaluation of the atom yields that object. When a name is not bound, an attempt to evaluate it raises a NameError exception.

6.2.3. Literals¶

A literal is a textual representation of a value. Python supports numeric, string and bytes literals. Format strings and template strings are treated as string literals.

Numeric literals consist of a single NUMBER token, which names an integer, floating-point number, or an imaginary number. See the Numeric literals section in Lexical analysis documentation for details.

String and bytes literals may consist of several tokens. See section String literal concatenation for details.

Note that negative and complex numbers, like -3 or 3+4.2j, are syntactically not literals, but unary or binary arithmetic operations involving the - or + operator.

Evaluation of a literal yields an object of the given type (int, float, complex, str, bytes, or Template) with the given value. The value may be approximated in the case of floating-point and imaginary literals.

The formal grammar for literals is:

literal: strings | NUMBER

>>> x = 7
>>> y = 7
>>> x is y
True

>>> x = 123456789
>>> y = 123456789
>>> x is y
False

>>> x = 7
>>> x is 7
<input>:1: SyntaxWarning: "is" with 'int' literal. Did you mean "=="?
True

>>> "hello" 'world'
"helloworld"

>>> greeting = "Hello"
>>> space = " "
>>> name = "Blaise"
>>> print(greeting + space + name)   # not: print(greeting space name)
Hello Blaise

>>> "Hello" r', ' f"{name}!"
"Hello, Blaise!"

re.compile("[A-Za-z_]"       # letter or underscore
           "[A-Za-z0-9_]*"   # letter, digit or underscore
          )

>>> t"Hello" t"{name}!"
Template(strings=('Hello', '!'), interpolations=(...))

strings: (STRING | fstring)+ | tstring+

6.2.4. Parenthesized forms¶

A parenthesized form is an optional expression list enclosed in parentheses:

parenth_form: "(" [starred_expression] ")"

A parenthesized expression list yields whatever that expression list yields: if the list contains at least one comma, it yields a tuple; otherwise, it yields the single expression that makes up the expression list.

An empty pair of parentheses yields an empty tuple object. Since tuples are immutable, the same rules as for literals apply (i.e., two occurrences of the empty tuple may or may not yield the same object).

Note that tuples are not formed by the parentheses, but rather by use of the comma. The exception is the empty tuple, for which parentheses are required — allowing unparenthesized “nothing” in expressions would cause ambiguities and allow common typos to pass uncaught.

6.2.5. Displays for lists, sets and dictionaries¶

For constructing a list, a set or a dictionary Python provides special syntax called “displays”, each of them in two flavors:

• either the container contents are listed explicitly, or

• they are computed via a set of looping and filtering instructions, called a comprehension.

Common syntax elements for comprehensions are:

comprehension: assignment_expression comp_for
comp_for:      ["async"] "for" target_list "in" or_test [comp_iter]
comp_iter:     comp_for | comp_if
comp_if:       "if" or_test [comp_iter]

The comprehension consists of a single expression followed by at least one for clause and zero or more for or if clauses. In this case, the elements of the new container are those that would be produced by considering each of the for or if clauses a block, nesting from left to right, and evaluating the expression to produce an element each time the innermost block is reached.

However, aside from the iterable expression in the leftmost for clause, the comprehension is executed in a separate implicitly nested scope. This ensures that names assigned to in the target list don’t “leak” into the enclosing scope.

The iterable expression in the leftmost for clause is evaluated directly in the enclosing scope and then passed as an argument to the implicitly nested scope. Subsequent for clauses and any filter condition in the leftmost for clause cannot be evaluated in the enclosing scope as they may depend on the values obtained from the leftmost iterable. For example: [x*y for x in range(10) for y in range(x, x+10)].

To ensure the comprehension always results in a container of the appropriate type, yield and yield from expressions are prohibited in the implicitly nested scope.

Since Python 3.6, in an async def function, an async for clause may be used to iterate over a asynchronous iterator. A comprehension in an async def function may consist of either a for or async for clause following the leading expression, may contain additional for or async for clauses, and may also use await expressions.

If a comprehension contains async for clauses, or if it contains await expressions or other asynchronous comprehensions anywhere except the iterable expression in the leftmost for clause, it is called an asynchronous comprehension. An asynchronous comprehension may suspend the execution of the coroutine function in which it appears. See also PEP 530.

6.2.6. List displays¶

A list display is a possibly empty series of expressions enclosed in square brackets:

list_display: "[" [flexible_expression_list | comprehension] "]"

A list display yields a new list object, the contents being specified by either a list of expressions or a comprehension. When a comma-separated list of expressions is supplied, its elements are evaluated from left to right and placed into the list object in that order. When a comprehension is supplied, the list is constructed from the elements resulting from the comprehension.

6.2.7. Set displays¶

A set display is denoted by curly braces and distinguishable from dictionary displays by the lack of colons separating keys and values:

set_display: "{" (flexible_expression_list | comprehension) "}"

A set display yields a new mutable set object, the contents being specified by either a sequence of expressions or a comprehension. When a comma-separated list of expressions is supplied, its elements are evaluated from left to right and added to the set object. When a comprehension is supplied, the set is constructed from the elements resulting from the comprehension.

An empty set cannot be constructed with {}; this literal constructs an empty dictionary.

6.2.8. Dictionary displays¶

A dictionary display is a possibly empty series of dict items (key/value pairs) enclosed in curly braces:

dict_display:       "{" [dict_item_list | dict_comprehension] "}"
dict_item_list:     dict_item ("," dict_item)* [","]
dict_item:          expression ":" expression | "**" or_expr
dict_comprehension: expression ":" expression comp_for

A dictionary display yields a new dictionary object.

If a comma-separated sequence of dict items is given, they are evaluated from left to right to define the entries of the dictionary: each key object is used as a key into the dictionary to store the corresponding value. This means that you can specify the same key multiple times in the dict item list, and the final dictionary’s value for that key will be the last one given.

A double asterisk ** denotes dictionary unpacking. Its operand must be a mapping. Each mapping item is added to the new dictionary. Later values replace values already set by earlier dict items and earlier dictionary unpackings.

A dict comprehension, in contrast to list and set comprehensions, needs two expressions separated with a colon followed by the usual “for” and “if” clauses. When the comprehension is run, the resulting key and value elements are inserted in the new dictionary in the order they are produced.

Restrictions on the types of the key values are listed earlier in section The standard type hierarchy. (To summarize, the key type should be hashable, which excludes all mutable objects.) Clashes between duplicate keys are not detected; the last value (textually rightmost in the display) stored for a given key value prevails.

6.2.9. Generator expressions¶

The syntax for generator expressions is the same as for list comprehensions, except that they are enclosed in parentheses instead of brackets. For example:

>>> iterator = (x ** 2 for x in range(10))
>>> iterator
<generator object <genexpr> at ...>

At runtime, a generator expression evaluates to a generator iterator which yields the same values as the corresponding list comprehension:

>>> list(iterator)
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

Thus, the example above is roughly equivalent to defining and calling the following generator function:

def make_generator_of_squares(iterator):
    for x in iterator:
        yield x ** 2

make_generator_of_squares(iter(range(10)))

The enclosing parentheses can be omitted in calls when the generator expression is the only positional argument and there are no keyword arguments. See the Calls section for details. For example:

# The parentheses after `sum` are part of the call syntax:
>>> sum(x ** 2 for x in range(10))
285

# The generator needs its own parentheses if it's not the only argument:
>>> sum((x ** 2 for x in range(10)), start=1000)
1285

The iterable expression in the leftmost for clause is evaluated immediately, so that an error raised by this expression will be emitted at the point where the generator expression is defined, rather than at the point where the first value is retrieved:

>>> (x ** 2 for x in nonexistent_iterable)
Traceback (most recent call last):
  ...
NameError: name 'nonexistent_iterable' is not defined

After the expression is evaluated, an iterator is created from the result, as if iter() was called on it. Any error raised when creating the iterator is also emitted immediately:

>>> (x ** 2 for x in None)
Traceback (most recent call last):
  ...
TypeError: 'NoneType' object is not iterable

All other expressions are evaluated lazily, in the same fashion as normal generators (that is, when the iterator is asked to yield a value):

>>> iterator = (nonexistent_value for x in range(10))
>>> iterator
<generator object <genexpr> at ...>
>>> list(iterator)
Traceback (most recent call last):
  ...
NameError: name 'nonexistent_value' is not defined

>>> iterator = (x * y for x in range(10) for y in nonexistent_iterable)
>>> iterator
<generator object <genexpr> at ...>
>>> list(iterator)
Traceback (most recent call last):
  ...
NameError: name 'nonexistent_iterable' is not defined

To avoid interfering with the expected operation of the generator expression itself, yield and yield from expressions are prohibited inside the implicitly nested scope.

If a generator expression contains either async for clauses or await expressions it is called an asynchronous generator expression. An asynchronous generator expression returns a new asynchronous generator object, which is an asynchronous iterator (see Asynchronous Iterators).

The formal grammar for generator expressions is:

generator_expression: "(" expression comp_for ")"

6.2.10. Yield expressions¶

yield_atom:       "(" yield_expression ")"
yield_from:       "yield" "from" expression
yield_expression: "yield" yield_list | yield_from

The yield expression is used when defining a generator function or an asynchronous generator function and thus can only be used in the body of a function definition. Using a yield expression in a function’s body causes that function to be a generator function, and using it in an async def function’s body causes that coroutine function to be an asynchronous generator function. For example:

def gen():  # defines a generator function
    yield 123

async def agen(): # defines an asynchronous generator function
    yield 123

Due to their side effects on the containing scope, yield expressions are not permitted as part of the implicitly defined scopes used to implement comprehensions and generator expressions.

Generator functions are described below, while asynchronous generator functions are described separately in section Asynchronous generator functions.

When a generator function is called, it returns an iterator known as a generator. That generator then controls the execution of the generator function. The execution starts when one of the generator’s methods is called. At that time, the execution proceeds to the first yield expression, where it is suspended again, returning the value of yield_list to the generator’s caller, or None if yield_list is omitted. By suspended, we mean that all local state is retained, including the current bindings of local variables, the instruction pointer, the internal evaluation stack, and the state of any exception handling. When the execution is resumed by calling one of the generator’s methods, the function can proceed exactly as if the yield expression were just another external call. The value of the yield expression after resuming depends on the method which resumed the execution. If __next__() is used (typically via either a for or the next() builtin) then the result is None. Otherwise, if send() is used, then the result will be the value passed in to that method.

All of this makes generator functions quite similar to coroutines; they yield multiple times, they have more than one entry point and their execution can be suspended. The only difference is that a generator function cannot control where the execution should continue after it yields; the control is always transferred to the generator’s caller.

Yield expressions are allowed anywhere in a try construct. If the generator is not resumed before it is finalized (by reaching a zero reference count or by being garbage collected), the generator-iterator’s close() method will be called, allowing any pending finally clauses to execute.

When yield from <expr> is used, the supplied expression must be an iterable. The values produced by iterating that iterable are passed directly to the caller of the current generator’s methods. Any values passed in with send() and any exceptions passed in with throw() are passed to the underlying iterator if it has the appropriate methods. If this is not the case, then send() will raise AttributeError or TypeError, while throw() will just raise the passed in exception immediately.

When the underlying iterator is complete, the value attribute of the raised StopIteration instance becomes the value of the yield expression. It can be either set explicitly when raising StopIteration, or automatically when the subiterator is a generator (by returning a value from the subgenerator).

The parentheses may be omitted when the yield expression is the sole expression on the right hand side of an assignment statement.

>>> def echo(value=None):
...     print("Execution starts when 'next()' is called for the first time.")
...     try:
...         while True:
...             try:
...                 value = (yield value)
...             except Exception as e:
...                 value = e
...     finally:
...         print("Don't forget to clean up when 'close()' is called.")
...
>>> generator = echo(1)
>>> print(next(generator))
Execution starts when 'next()' is called for the first time.
1
>>> print(next(generator))
None
>>> print(generator.send(2))
2
>>> generator.throw(TypeError, "spam")
TypeError('spam',)
>>> generator.close()
Don't forget to clean up when 'close()' is called.

6.3.1. Attribute references¶

An attribute reference is a primary followed by a period and a name:

attributeref: primary "." identifier

The primary must evaluate to an object of a type that supports attribute references, which most objects do. This object is then asked to produce the attribute whose name is the identifier. The type and value produced is determined by the object. Multiple evaluations of the same attribute reference may yield different objects.

This production can be customized by overriding the __getattribute__() method or the __getattr__() method. The __getattribute__() method is called first and either returns a value or raises AttributeError if the attribute is not available.

If an AttributeError is raised and the object has a __getattr__() method, that method is called as a fallback.

6.3.2. Subscriptions and slicings¶

The subscription syntax is usually used for selecting an element from a container – for example, to get a value from a dict:

>>> digits_by_name = {'one': 1, 'two': 2}
>>> digits_by_name['two']  # Subscripting a dictionary using the key 'two'
2

In the subscription syntax, the object being subscribed – a primary – is followed by a subscript in square brackets. In the simplest case, the subscript is a single expression.

Depending on the type of the object being subscribed, the subscript is sometimes called a key (for mappings), index (for sequences), or type argument (for generic types). Syntactically, these are all equivalent:

>>> colors = ['red', 'blue', 'green', 'black']
>>> colors[3]  # Subscripting a list using the index 3
'black'

>>> list[str]  # Parameterizing the list type using the type argument str
list[str]

At runtime, the interpreter will evaluate the primary and the subscript, and call the primary’s __getitem__() or __class_getitem__() special method with the subscript as argument. For more details on which of these methods is called, see __class_getitem__ versus __getitem__.

To show how subscription works, we can define a custom object that implements __getitem__() and prints out the value of the subscript:

>>> class SubscriptionDemo:
...     def __getitem__(self, key):
...         print(f'subscripted with: {key!r}')
...
>>> demo = SubscriptionDemo()
>>> demo[1]
subscripted with: 1
>>> demo['a' * 3]
subscripted with: 'aaa'

See __getitem__() documentation for how built-in types handle subscription.

Subscriptions may also be used as targets in assignment or deletion statements. In these cases, the interpreter will call the subscripted object’s __setitem__() or __delitem__() special method, respectively, instead of __getitem__().

>>> colors = ['red', 'blue', 'green', 'black']
>>> colors[3] = 'white'  # Setting item at index
>>> colors
['red', 'blue', 'green', 'white']
>>> del colors[3]  # Deleting item at index 3
>>> colors
['red', 'blue', 'green']

All advanced forms of subscript documented in the following sections are also usable for assignment and deletion.

>>> number_names = ['zero', 'one', 'two', 'three', 'four', 'five']
>>> number_names[1:3]
['one', 'two']
>>> number_names[1:]
['one', 'two', 'three', 'four', 'five']
>>> number_names[:3]
['zero', 'one', 'two']
>>> number_names[:]
['zero', 'one', 'two', 'three', 'four', 'five']
>>> number_names[::2]
['zero', 'two', 'four']
>>> number_names[:-3]
['zero', 'one', 'two']
>>> del number_names[4:]
>>> number_names
['zero', 'one', 'two', 'three']

# continuing with the SubscriptionDemo instance defined above:
>>> demo[2:3]
subscripted with: slice(2, 3, None)
>>> demo[::'spam']
subscripted with: slice(None, None, 'spam')

# continuing with the SubscriptionDemo instance defined above:
>>> demo[1, 2, 3]
subscripted with: (1, 2, 3)
>>> demo[1:2, 3]
subscripted with: (slice(1, 2, None), 3)

>>> demo['spam',]
subscripted with: ('spam',)

# continuing with the SubscriptionDemo instance defined above:
>>> demo[*range(10)]
subscripted with: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

>>> demo['a', 'b', *range(3), 'c']
subscripted with: ('a', 'b', 0, 1, 2, 'c')

subscription:     primary '[' subscript ']'
subscript:        single_subscript | tuple_subscript
single_subscript: proper_slice | assignment_expression
proper_slice:     [expression] ":" [expression] [ ":" [expression] ]
tuple_subscript:  ','.(single_subscript | starred_expression)+ [',']

6.3.3. Calls¶

A call calls a callable object (e.g., a function) with a possibly empty series of arguments:

call:                 primary "(" [argument_list [","] | comprehension] ")"
argument_list:        positional_arguments ["," starred_and_keywords]
                        ["," keywords_arguments]
                      | starred_and_keywords ["," keywords_arguments]
                      | keywords_arguments
positional_arguments: positional_item ("," positional_item)*
positional_item:      assignment_expression | "*" expression
starred_and_keywords: ("*" expression | keyword_item)
                      ("," "*" expression | "," keyword_item)*
keywords_arguments:   (keyword_item | "**" expression)
                      ("," keyword_item | "," "**" expression)*
keyword_item:         identifier "=" expression

An optional trailing comma may be present after the positional and keyword arguments but does not affect the semantics.

The primary must evaluate to a callable object (user-defined functions, built-in functions, methods of built-in objects, class objects, methods of class instances, and all objects having a __call__() method are callable). All argument expressions are evaluated before the call is attempted. Please refer to section Function definitions for the syntax of formal parameter lists.

If keyword arguments are present, they are first converted to positional arguments, as follows. First, a list of unfilled slots is created for the formal parameters. If there are N positional arguments, they are placed in the first N slots. Next, for each keyword argument, the identifier is used to determine the corresponding slot (if the identifier is the same as the first formal parameter name, the first slot is used, and so on). If the slot is already filled, a TypeError exception is raised. Otherwise, the argument is placed in the slot, filling it (even if the expression is None, it fills the slot). When all arguments have been processed, the slots that are still unfilled are filled with the corresponding default value from the function definition. (Default values are calculated, once, when the function is defined; thus, a mutable object such as a list or dictionary used as default value will be shared by all calls that don’t specify an argument value for the corresponding slot; this should usually be avoided.) If there are any unfilled slots for which no default value is specified, a TypeError exception is raised. Otherwise, the list of filled slots is used as the argument list for the call.

If there are more positional arguments than there are formal parameter slots, a TypeError exception is raised, unless a formal parameter using the syntax *identifier is present; in this case, that formal parameter receives a tuple containing the excess positional arguments (or an empty tuple if there were no excess positional arguments).

If any keyword argument does not correspond to a formal parameter name, a TypeError exception is raised, unless a formal parameter using the syntax **identifier is present; in this case, that formal parameter receives a dictionary containing the excess keyword arguments (using the keywords as keys and the argument values as corresponding values), or a (new) empty dictionary if there were no excess keyword arguments.

If the syntax *expression appears in the function call, expression must evaluate to an iterable. Elements from these iterables are treated as if they were additional positional arguments. For the call f(x1, x2, *y, x3, x4), if y evaluates to a sequence y1, …, yM, this is equivalent to a call with M+4 positional arguments x1, x2, y1, …, yM, x3, x4.

A consequence of this is that although the *expression syntax may appear after explicit keyword arguments, it is processed before the keyword arguments (and any **expression arguments – see below). So:

>>> def f(a, b):
...     print(a, b)
...
>>> f(b=1, *(2,))
2 1
>>> f(a=1, *(2,))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: f() got multiple values for keyword argument 'a'
>>> f(1, *(2,))
1 2

It is unusual for both keyword arguments and the *expression syntax to be used in the same call, so in practice this confusion does not often arise.

If the syntax **expression appears in the function call, expression must evaluate to a mapping, the contents of which are treated as additional keyword arguments. If a parameter matching a key has already been given a value (by an explicit keyword argument, or from another unpacking), a TypeError exception is raised.

When **expression is used, each key in this mapping must be a string. Each value from the mapping is assigned to the first formal parameter eligible for keyword assignment whose name is equal to the key. A key need not be a Python identifier (e.g. "max-temp °F" is acceptable, although it will not match any formal parameter that could be declared). If there is no match to a formal parameter the key-value pair is collected by the ** parameter, if there is one, or if there is not, a TypeError exception is raised.

Formal parameters using the syntax *identifier or **identifier cannot be used as positional argument slots or as keyword argument names.

A call always returns some value, possibly None, unless it raises an exception. How this value is computed depends on the type of the callable object.

If it is—

a user-defined function:

The code block for the function is executed, passing it the argument list. The first thing the code block will do is bind the formal parameters to the arguments; this is described in section Function definitions. When the code block executes a return statement, this specifies the return value of the function call. If execution reaches the end of the code block without executing a return statement, the return value is None.

a built-in function or method:

The result is up to the interpreter; see Built-in Functions for the descriptions of built-in functions and methods.

a class object:

A new instance of that class is returned.

a class instance method:

The corresponding user-defined function is called, with an argument list that is one longer than the argument list of the call: the instance becomes the first argument.

a class instance:

The class must define a __call__() method; the effect is then the same as if that method was called.

6.10.1. Value comparisons¶

The operators <, >, ==, >=, <=, and != compare the values of two objects. The objects do not need to have the same type.

Chapter Objects, values and types states that objects have a value (in addition to type and identity). The value of an object is a rather abstract notion in Python: For example, there is no canonical access method for an object’s value. Also, there is no requirement that the value of an object should be constructed in a particular way, e.g. comprised of all its data attributes. Comparison operators implement a particular notion of what the value of an object is. One can think of them as defining the value of an object indirectly, by means of their comparison implementation.

Because all types are (direct or indirect) subtypes of object, they inherit the default comparison behavior from object. Types can customize their comparison behavior by implementing rich comparison methods like __lt__(), described in Basic customization.

The default behavior for equality comparison (== and !=) is based on the identity of the objects. Hence, equality comparison of instances with the same identity results in equality, and equality comparison of instances with different identities results in inequality. A motivation for this default behavior is the desire that all objects should be reflexive (i.e. x is y implies x == y).

A default order comparison (<, >, <=, and >=) is not provided; an attempt raises TypeError. A motivation for this default behavior is the lack of a similar invariant as for equality.

The behavior of the default equality comparison, that instances with different identities are always unequal, may be in contrast to what types will need that have a sensible definition of object value and value-based equality. Such types will need to customize their comparison behavior, and in fact, a number of built-in types have done that.

The following list describes the comparison behavior of the most important built-in types.

• Numbers of built-in numeric types (Numeric Types — int, float, complex) and of the standard library types fractions.Fraction and decimal.Decimal can be compared within and across their types, with the restriction that complex numbers do not support order comparison. Within the limits of the types involved, they compare mathematically (algorithmically) correct without loss of precision.

  The not-a-number values float('NaN') and decimal.Decimal('NaN') are special. Any ordered comparison of a number to a not-a-number value is false. A counter-intuitive implication is that not-a-number values are not equal to themselves. For example, if x = float('NaN'), 3 < x, x < 3 and x == x are all false, while x != x is true. This behavior is compliant with IEEE 754.

• None and NotImplemented are singletons. PEP 8 advises that comparisons for singletons should always be done with is or is not, never the equality operators.

• Binary sequences (instances of bytes or bytearray) can be compared within and across their types. They compare lexicographically using the numeric values of their elements.

• Strings (instances of str) compare lexicographically using the numerical Unicode code points (the result of the built-in function ord()) of their characters. [3]

  Strings and binary sequences cannot be directly compared.

• Sequences (instances of tuple, list, or range) can be compared only within each of their types, with the restriction that ranges do not support order comparison. Equality comparison across these types results in inequality, and ordering comparison across these types raises TypeError.

  Sequences compare lexicographically using comparison of corresponding elements. The built-in containers typically assume identical objects are equal to themselves. That lets them bypass equality tests for identical objects to improve performance and to maintain their internal invariants.

  Lexicographical comparison between built-in collections works as follows:

  • For two collections to compare equal, they must be of the same type, have the same length, and each pair of corresponding elements must compare equal (for example, [1,2] == (1,2) is false because the type is not the same).

  • Collections that support order comparison are ordered the same as their first unequal elements (for example, [1,2,x] <= [1,2,y] has the same value as x <= y). If a corresponding element does not exist, the shorter collection is ordered first (for example, [1,2] < [1,2,3] is true).

• Mappings (instances of dict) compare equal if and only if they have equal (key, value) pairs. Equality comparison of the keys and values enforces reflexivity.

  Order comparisons (<, >, <=, and >=) raise TypeError.

• Sets (instances of set or frozenset) can be compared within and across their types.

  They define order comparison operators to mean subset and superset tests. Those relations do not define total orderings (for example, the two sets {1,2} and {2,3} are not equal, nor subsets of one another, nor supersets of one another). Accordingly, sets are not appropriate arguments for functions which depend on total ordering (for example, min(), max(), and sorted() produce undefined results given a list of sets as inputs).

  Comparison of sets enforces reflexivity of its elements.

• Most other built-in types have no comparison methods implemented, so they inherit the default comparison behavior.

User-defined classes that customize their comparison behavior should follow some consistency rules, if possible:

• Equality comparison should be reflexive. In other words, identical objects should compare equal:

  x is y implies x == y

• Comparison should be symmetric. In other words, the following expressions should have the same result:

  x == y and y == x

  x != y and y != x

  x < y and y > x

  x <= y and y >= x

• Comparison should be transitive. The following (non-exhaustive) examples illustrate that:

  x > y and y > z implies x > z

  x < y and y <= z implies x < z

• Inverse comparison should result in the boolean negation. In other words, the following expressions should have the same result:

  x == y and not x != y

  x < y and not x >= y (for total ordering)

  x > y and not x <= y (for total ordering)

  The last two expressions apply to totally ordered collections (e.g. to sequences, but not to sets or mappings). See also the @total_ordering decorator.

• The hash() result should be consistent with equality. Objects that are equal should either have the same hash value, or be marked as unhashable.

Python does not enforce these consistency rules. In fact, the not-a-number values are an example for not following these rules.

6.10.2. Membership test operations¶

The operators in and not in test for membership. x in s evaluates to True if x is a member of s, and False otherwise. x not in s returns the negation of x in s. All built-in sequences and set types support this as well as dictionary, for which in tests whether the dictionary has a given key. For container types such as list, tuple, set, frozenset, dict, or collections.deque, the expression x in y is equivalent to any(x is e or x == e for e in y).

For the string and bytes types, x in y is True if and only if x is a substring of y. An equivalent test is y.find(x) != -1. Empty strings are always considered to be a substring of any other string, so "" in "abc" will return True.

For user-defined classes which define the __contains__() method, x in y returns True if y.__contains__(x) returns a true value, and False otherwise.

For user-defined classes which do not define __contains__() but do define __iter__(), x in y is True if some value z, for which the expression x is z or x == z is true, is produced while iterating over y. If an exception is raised during the iteration, it is as if in raised that exception.

Lastly, the old-style iteration protocol is tried: if a class defines __getitem__(), x in y is True if and only if there is a non-negative integer index i such that x is y[i] or x == y[i], and no lower integer index raises the IndexError exception. (If any other exception is raised, it is as if in raised that exception).

The operator not in is defined to have the inverse truth value of in.

6.10.3. Identity comparisons¶

The operators is and is not test for an object’s identity: x is y is true if and only if x and y are the same object. An Object’s identity is determined using the id() function. x is not y yields the inverse truth value. [4]