6. Expressions
This chapter explains the meaning of the elements of expressions in Python.
Syntax Notes: In this and the following chapters, extended BNF notation will be used to describe syntax, not lexical analysis. When (one alternative of) a syntax rule has the form
name ::= othername
and no semantics are given, the semantics of this form of name
are the same
as for othername
.
6.1. Arithmetic conversions
When a description of an arithmetic operator below uses the phrase “the numeric arguments are converted to a common type,” this means that the operator implementation for builtin types works as follows:
 If either argument is a complex number, the other is converted to complex;
 otherwise, if either argument is a floating point number, the other is converted to floating point;
 otherwise, both must be integers and no conversion is necessary.
Some additional rules apply for certain operators (e.g., a string as a left argument to the ‘%’ operator). Extensions must define their own conversion behavior.
6.2. Atoms
Atoms are the most basic elements of expressions. The simplest atoms are identifiers or literals. Forms enclosed in parentheses, brackets or braces are also categorized syntactically as atoms. The syntax for atoms is:
atom ::=identifier
literal
enclosure
enclosure ::=parenth_form
list_display
dict_display
set_display
generator_expression
yield_atom
6.2.1. Identifiers (Names)
An identifier occurring as an atom is a name. See section 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.
Private name mangling: When an identifier that textually occurs in a class
definition begins with two or more underscore characters and does not end in two
or more underscores, it is considered a private name of that class.
Private names are transformed to a longer form before code is generated for
them. The transformation inserts the class name, with leading underscores
removed and a single underscore inserted, in front of the name. For example,
the identifier __spam
occurring in a class named Ham
will be transformed
to _Ham__spam
. This transformation is independent of the syntactical
context in which the identifier is used. If the transformed name is extremely
long (longer than 255 characters), implementation defined truncation may happen.
If the class name consists only of underscores, no transformation is done.
6.2.2. Literals
Python supports string and bytes literals and various numeric literals:
literal ::=stringliteral
bytesliteral
integer
floatnumber
imagnumber
Evaluation of a literal yields an object of the given type (string, bytes, integer, floating point number, complex number) with the given value. The value may be approximated in the case of floating point and imaginary (complex) literals. See section Literals for details.
All literals correspond to immutable data types, and hence the object’s identity is less important than its value. Multiple evaluations of literals with the same value (either the same occurrence in the program text or a different occurrence) may obtain the same object or a different object with the same value.
6.2.3. Parenthesized forms
A parenthesized form is an optional expression list enclosed in parentheses:
parenth_form ::= "(" [expression_list
] ")"
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 rules 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 operator. 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.
6.2.4. 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 ::=expression
comp_for
comp_for ::= "for"target_list
"in"or_test
[comp_iter
] comp_iter ::=comp_for
comp_if
comp_if ::= "if"expression_nocond
[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.
Note that the comprehension is executed in a separate scope, so names assigned to in the target list don’t “leak” into the enclosing scope.
6.2.5. List displays
A list display is a possibly empty series of expressions enclosed in square brackets:
list_display ::= "[" [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 commaseparated 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.
6.2.6. 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 ::= "{" (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 commaseparated 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.
6.2.7. Dictionary displays
A dictionary display is a possibly empty series of key/datum pairs enclosed in curly braces:
dict_display ::= "{" [key_datum_list
dict_comprehension
] "}" key_datum_list ::=key_datum
(","key_datum
)* [","] key_datum ::=expression
":"expression
dict_comprehension ::=expression
":"expression
comp_for
A dictionary display yields a new dictionary object.
If a commaseparated sequence of key/datum pairs 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 datum. This means that you can specify the same key multiple times in the key/datum list, and the final dictionary’s value for that key will be the last one given.
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 datum (textually rightmost in the display) stored for a given key value prevails.
6.2.8. Generator expressions
A generator expression is a compact generator notation in parentheses:
generator_expression ::= "("expression
comp_for
")"
A generator expression yields a new generator object. Its syntax is the same as for comprehensions, except that it is enclosed in parentheses instead of brackets or curly braces.
Variables used in the generator expression are evaluated lazily when the
__next__()
method is called for the generator object (in the same
fashion as normal generators). However, the leftmost for
clause is
immediately evaluated, so that an error produced by it can be seen before any
other possible error in the code that handles the generator expression.
Subsequent for
clauses cannot be evaluated immediately since they
may depend on the previous for
loop. For example: (x*y for x in
range(10) for y in bar(x))
.
The parentheses can be omitted on calls with only one argument. See section Calls for details.
6.2.9. Yield expressions
yield_atom ::= "("yield_expression
")" yield_expression ::= "yield" [expression_list
 "from"expression
]
The yield expression is only used when defining a 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.
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 expression_list
to the generator’s
caller. 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 generatoriterator’s close()
method will be called,
allowing any pending finally
clauses to execute.
When yield from <expr>
is used, it treats the supplied expression as
a subiterator. All values produced by that subiterator 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).
Changed in version 3.3: Added
yield from <expr>
to delegate control flow to a subiterator.
The parentheses may be omitted when the yield expression is the sole expression on the right hand side of an assignment statement.
See also
 PEP 0255  Simple Generators
 The proposal for adding generators and the
yield
statement to Python.  PEP 0342  Coroutines via Enhanced Generators
 The proposal to enhance the API and syntax of generators, making them usable as simple coroutines.
 PEP 0380  Syntax for Delegating to a Subgenerator
 The proposal to introduce the
yield_from
syntax, making delegation to subgenerators easy.
6.2.9.1. Generatoriterator methods
This subsection describes the methods of a generator iterator. They can be used to control the execution of a generator function.
Note that calling any of the generator methods below when the generator
is already executing raises a ValueError
exception.

generator.
__next__
() Starts the execution of a generator function or resumes it at the last executed yield expression. When a generator function is resumed with a
__next__()
method, the current yield expression always evaluates toNone
. The execution then continues to the next yield expression, where the generator is suspended again, and the value of theexpression_list
is returned to__next__()
‘s caller. If the generator exits without yielding another value, aStopIteration
exception is raised.This method is normally called implicitly, e.g. by a
for
loop, or by the builtinnext()
function.

generator.
send
(value) Resumes the execution and “sends” a value into the generator function. The value argument becomes the result of the current yield expression. The
send()
method returns the next value yielded by the generator, or raisesStopIteration
if the generator exits without yielding another value. Whensend()
is called to start the generator, it must be called withNone
as the argument, because there is no yield expression that could receive the value.

generator.
throw
(type[, value[, traceback]]) Raises an exception of type
type
at the point where the generator was paused, and returns the next value yielded by the generator function. If the generator exits without yielding another value, aStopIteration
exception is raised. If the generator function does not catch the passedin exception, or raises a different exception, then that exception propagates to the caller.

generator.
close
() Raises a
GeneratorExit
at the point where the generator function was paused. If the generator function then exits gracefully, is already closed, or raisesGeneratorExit
(by not catching the exception), close returns to its caller. If the generator yields a value, aRuntimeError
is raised. If the generator raises any other exception, it is propagated to the caller.close()
does nothing if the generator has already exited due to an exception or normal exit.
6.2.9.2. Examples
Here is a simple example that demonstrates the behavior of generators and generator functions:
>>> 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.
For examples using yield from
, see PEP 380: Syntax for Delegating to a Subgenerator in “What’s New in
Python.”
6.3. Primaries
Primaries represent the most tightly bound operations of the language. Their syntax is:
primary ::=atom
attributeref
subscription
slicing
call
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. This production can be customized by
overriding the __getattr__()
method. If this attribute is not available,
the exception AttributeError
is raised. Otherwise, the type and value of
the object produced is determined by the object. Multiple evaluations of the
same attribute reference may yield different objects.
6.3.2. Subscriptions
A subscription selects an item of a sequence (string, tuple or list) or mapping (dictionary) object:
subscription ::=primary
"["expression_list
"]"
The primary must evaluate to an object that supports subscription (lists or
dictionaries for example). Userdefined objects can support subscription by
defining a __getitem__()
method.
For builtin objects, there are two types of objects that support subscription:
If the primary is a mapping, the expression list must evaluate to an object whose value is one of the keys of the mapping, and the subscription selects the value in the mapping that corresponds to that key. (The expression list is a tuple except if it has exactly one item.)
If the primary is a sequence, the expression (list) must evaluate to an integer or a slice (as discussed in the following section).
The formal syntax makes no special provision for negative indices in
sequences; however, builtin sequences all provide a __getitem__()
method that interprets negative indices by adding the length of the sequence
to the index (so that x[1]
selects the last item of x
). The
resulting value must be a nonnegative integer less than the number of items in
the sequence, and the subscription selects the item whose index is that value
(counting from zero). Since the support for negative indices and slicing
occurs in the object’s __getitem__()
method, subclasses overriding
this method will need to explicitly add that support.
A string’s items are characters. A character is not a separate data type but a string of exactly one character.
6.3.3. Slicings
A slicing selects a range of items in a sequence object (e.g., a string, tuple
or list). Slicings may be used as expressions or as targets in assignment or
del
statements. The syntax for a slicing:
slicing ::=primary
"["slice_list
"]" slice_list ::=slice_item
(","slice_item
)* [","] slice_item ::=expression
proper_slice
proper_slice ::= [lower_bound
] ":" [upper_bound
] [ ":" [stride
] ] lower_bound ::=expression
upper_bound ::=expression
stride ::=expression
There is ambiguity in the formal syntax here: anything that looks like an expression list also looks like a slice list, so any subscription can be interpreted as a slicing. Rather than further complicating the syntax, this is disambiguated by defining that in this case the interpretation as a subscription takes priority over the interpretation as a slicing (this is the case if the slice list contains no proper slice).
The semantics for a slicing are as follows. The primary is indexed (using the
same __getitem__()
method as
normal subscription) with a key that is constructed from the slice list, as
follows. If the slice list contains at least one comma, the key is a tuple
containing the conversion of the slice items; otherwise, the conversion of the
lone slice item is the key. The conversion of a slice item that is an
expression is that expression. The conversion of a proper slice is a slice
object (see section The standard type hierarchy) whose start
,
stop
and step
attributes are the values of the
expressions given as lower bound, upper bound and stride, respectively,
substituting None
for missing expressions.
6.3.4. 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
[","keyword_arguments
] ["," "*"expression
] [","keyword_arguments
] ["," "**"expression
] keyword_arguments
["," "*"expression
] [","keyword_arguments
] ["," "**"expression
]  "*"expression
[","keyword_arguments
] ["," "**"expression
]  "**"expression
positional_arguments ::=expression
(","expression
)* keyword_arguments ::=keyword_item
(","keyword_item
)* 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 (userdefined functions, builtin
functions, methods of builtin 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 value of
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.
CPython implementation detail: An implementation may provide builtin functions whose positional parameters
do not have names, even if they are ‘named’ for the purpose of documentation,
and which therefore cannot be supplied by keyword. In CPython, this is the
case for functions implemented in C that use PyArg_ParseTuple()
to
parse their arguments.
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 this iterable are treated as if they
were additional positional arguments; if there are positional arguments
x1, ..., xN, and expression
evaluates to a sequence y1, ..., yM,
this is equivalent to a call with M+N positional arguments x1, ..., xN,
y1, ..., yM.
A consequence of this is that although the *expression
syntax may appear
after some keyword arguments, it is processed before the keyword arguments
(and the **expression
argument, if any – 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 ?
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 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. In the case of a keyword appearing in both expression
and as an
explicit keyword argument, 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 userdefined 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. a builtin function or method:
The result is up to the interpreter; see Builtin Functions for the descriptions of builtin functions and methods.
 a class object:
A new instance of that class is returned.
 a class instance method:
The corresponding userdefined 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.
6.4. Await expression
Suspend the execution of coroutine on an awaitable object. Can only be used inside a coroutine function.
await ::= ["await"] primary
New in version 3.5.
6.5. The power operator
The power operator binds more tightly than unary operators on its left; it binds less tightly than unary operators on its right. The syntax is:
power ::=await
["**"u_expr
]
Thus, in an unparenthesized sequence of power and unary operators, the operators
are evaluated from right to left (this does not constrain the evaluation order
for the operands): 1**2
results in 1
.
The power operator has the same semantics as the builtin pow()
function,
when called with two arguments: it yields its left argument raised to the power
of its right argument. The numeric arguments are first converted to a common
type, and the result is of that type.
For int operands, the result has the same type as the operands unless the second
argument is negative; in that case, all arguments are converted to float and a
float result is delivered. For example, 10**2
returns 100
, but
10**2
returns 0.01
.
Raising 0.0
to a negative power results in a ZeroDivisionError
.
Raising a negative number to a fractional power results in a complex
number. (In earlier versions it raised a ValueError
.)
6.6. Unary arithmetic and bitwise operations
All unary arithmetic and bitwise operations have the same priority:
u_expr ::=power
 ""u_expr
 "+"u_expr
 "~"u_expr
The unary 
(minus) operator yields the negation of its numeric argument.
The unary +
(plus) operator yields its numeric argument unchanged.
The unary ~
(invert) operator yields the bitwise inversion of its integer
argument. The bitwise inversion of x
is defined as (x+1)
. It only
applies to integral numbers.
In all three cases, if the argument does not have the proper type, a
TypeError
exception is raised.
6.7. Binary arithmetic operations
The binary arithmetic operations have the conventional priority levels. Note that some of these operations also apply to certain nonnumeric types. Apart from the power operator, there are only two levels, one for multiplicative operators and one for additive operators:
m_expr ::=u_expr
m_expr
"*"u_expr
m_expr
"@"m_expr
m_expr
"//"u_expr
m_expr
"/"u_expr
m_expr
"%"u_expr
a_expr ::=m_expr
a_expr
"+"m_expr
a_expr
""m_expr
The *
(multiplication) operator yields the product of its arguments. The
arguments must either both be numbers, or one argument must be an integer and
the other must be a sequence. In the former case, the numbers are converted to a
common type and then multiplied together. In the latter case, sequence
repetition is performed; a negative repetition factor yields an empty sequence.
The @
(at) operator is intended to be used for matrix multiplication. No
builtin Python types implement this operator.
New in version 3.5.
The /
(division) and //
(floor division) operators yield the quotient of
their arguments. The numeric arguments are first converted to a common type.
Division of integers yields a float, while floor division of integers results in an
integer; the result is that of mathematical division with the ‘floor’ function
applied to the result. Division by zero raises the ZeroDivisionError
exception.
The %
(modulo) operator yields the remainder from the division of the first
argument by the second. The numeric arguments are first converted to a common
type. A zero right argument raises the ZeroDivisionError
exception. The
arguments may be floating point numbers, e.g., 3.14%0.7
equals 0.34
(since 3.14
equals 4*0.7 + 0.34
.) The modulo operator always yields a
result with the same sign as its second operand (or zero); the absolute value of
the result is strictly smaller than the absolute value of the second operand
[1].
The floor division and modulo operators are connected by the following
identity: x == (x//y)*y + (x%y)
. Floor division and modulo are also
connected with the builtin function divmod()
: divmod(x, y) == (x//y,
x%y)
. [2].
In addition to performing the modulo operation on numbers, the %
operator is
also overloaded by string objects to perform oldstyle string formatting (also
known as interpolation). The syntax for string formatting is described in the
Python Library Reference, section printfstyle String Formatting.
The floor division operator, the modulo operator, and the divmod()
function are not defined for complex numbers. Instead, convert to a floating
point number using the abs()
function if appropriate.
The +
(addition) operator yields the sum of its arguments. The arguments
must either both be numbers or both be sequences of the same type. In the
former case, the numbers are converted to a common type and then added together.
In the latter case, the sequences are concatenated.
The 
(subtraction) operator yields the difference of its arguments. The
numeric arguments are first converted to a common type.
6.8. Shifting operations
The shifting operations have lower priority than the arithmetic operations:
shift_expr ::=a_expr
shift_expr
( "<<"  ">>" )a_expr
These operators accept integers as arguments. They shift the first argument to the left or right by the number of bits given by the second argument.
A right shift by n bits is defined as floor division by pow(2,n)
. A left
shift by n bits is defined as multiplication with pow(2,n)
.
Note
In the current implementation, the righthand operand is required
to be at most sys.maxsize
. If the righthand operand is larger than
sys.maxsize
an OverflowError
exception is raised.
6.9. Binary bitwise operations
Each of the three bitwise operations has a different priority level:
and_expr ::=shift_expr
and_expr
"&"shift_expr
xor_expr ::=and_expr
xor_expr
"^"and_expr
or_expr ::=xor_expr
or_expr
""xor_expr
The &
operator yields the bitwise AND of its arguments, which must be
integers.
The ^
operator yields the bitwise XOR (exclusive OR) of its arguments, which
must be integers.
The 
operator yields the bitwise (inclusive) OR of its arguments, which
must be integers.
6.10. Comparisons
Unlike C, all comparison operations in Python have the same priority, which is
lower than that of any arithmetic, shifting or bitwise operation. Also unlike
C, expressions like a < b < c
have the interpretation that is conventional
in mathematics:
comparison ::=or_expr
(comp_operator
or_expr
)* comp_operator ::= "<"  ">"  "=="  ">="  "<="  "!="  "is" ["not"]  ["not"] "in"
Comparisons yield boolean values: True
or False
.
Comparisons can be chained arbitrarily, e.g., 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).
Formally, if a, b, c, ..., y, z are expressions and op1, op2, ...,
opN are comparison operators, then a op1 b op2 c ... y opN z
is equivalent
to a op1 b and b op2 c and ... y opN z
, except that each expression is
evaluated at most once.
Note that a op1 b op2 c
doesn’t imply any kind of comparison between a and
c, so that, e.g., x < y > z
is perfectly legal (though perhaps not
pretty).
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 valuebased equality. Such types will need to customize their comparison behavior, and in fact, a number of builtin types have done that.
The following list describes the comparison behavior of the most important builtin types.
Numbers of builtin numeric types (Numeric Types — int, float, complex) and of the standard library types
fractions.Fraction
anddecimal.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 notanumber values
float('NaN')
andDecimal('NaN')
are special. They are identical to themselves (x is x
is true) but are not equal to themselves (x == x
is false). Additionally, comparing any number to a notanumber value will returnFalse
. For example, both3 < float('NaN')
andfloat('NaN') < 3
will returnFalse
.Binary sequences (instances of
bytes
orbytearray
) 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 builtin functionord()
) of their characters. [3]Strings and binary sequences cannot be directly compared.
Sequences (instances of
tuple
,list
, orrange
) 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 unequality, and ordering comparison across these types raisesTypeError
.Sequences compare lexicographically using comparison of corresponding elements, whereby reflexivity of the elements is enforced.
In enforcing reflexivity of elements, the comparison of collections assumes that for a collection element
x
,x == x
is always true. Based on that assumption, element identity is compared first, and element comparison is performed only for distinct elements. This approach yields the same result as a strict element comparison would, if the compared elements are reflexive. For nonreflexive elements, the result is different than for strict element comparison, and may be surprising: The nonreflexive notanumber values for example result in the following comparison behavior when used in a list:>>> nan = float('NaN') >>> nan is nan True >>> nan == nan False < the defined nonreflexive behavior of NaN >>> [nan] == [nan] True < list enforces reflexivity and tests identity first
Lexicographical comparison between builtin 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 asx <= y
). If a corresponding element does not exist, the shorter collection is ordered first (for example,[1,2] < [1,2,3]
is true).
 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,
Mappings (instances of
dict
) compare equal if and only if they have equal (key, value) pairs. Equality comparison of the keys and elements enforces reflexivity.Order comparisons (
<
,>
,<=
, and>=
) raiseTypeError
.Sets (instances of
set
orfrozenset
) 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()
, andsorted()
produce undefined results given a list of sets as inputs).Comparison of sets enforces reflexivity of its elements.
Most other builtin types have no comparison methods implemented, so they inherit the default comparison behavior.
Userdefined 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
impliesx == y
Comparison should be symmetric. In other words, the following expressions should have the same result:
x == y
andy == x
x != y
andy != x
x < y
andy > x
x <= y
andy >= x
Comparison should be transitive. The following (nonexhaustive) examples illustrate that:
x > y and y > z
impliesx > z
x < y and y <= z
impliesx < z
Inverse comparison should result in the boolean negation. In other words, the following expressions should have the same result:
x == y
andnot x != y
x < y
andnot x >= y
(for total ordering)x > y
andnot 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.
Python does not enforce these consistency rules. In fact, the notanumber 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 builtin 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 userdefined classes which define the __contains__()
method, x in
y
is true if and only if y.__contains__(x)
is true.
For userdefined classes which do not define __contains__()
but do define
__iter__()
, x in y
is true if some value z
with x == z
is
produced while iterating over y
. If an exception is raised during the
iteration, it is as if in
raised that exception.
Lastly, the oldstyle iteration protocol is tried: if a class defines
__getitem__()
, x in y
is true if and only if there is a nonnegative
integer index i such that x == y[i]
, and all lower integer indices do not
raise 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 true value of
in
.
6.11. Boolean operations
or_test ::=and_test
or_test
"or"and_test
and_test ::=not_test
and_test
"and"not_test
not_test ::=comparison
 "not"not_test
In the context of Boolean operations, and also when expressions are used by
control flow statements, the following values are interpreted as false:
False
, None
, numeric zero of all types, and empty strings and containers
(including strings, tuples, lists, dictionaries, sets and frozensets). All
other values are interpreted as true. Userdefined objects can customize their
truth value by providing a __bool__()
method.
The operator not
yields True
if its argument is false, False
otherwise.
The expression x and y
first evaluates x; if x is false, its value is
returned; otherwise, y is evaluated and the resulting value is returned.
The expression x or y
first evaluates x; if x is true, its value is
returned; otherwise, y is evaluated and the resulting value is returned.
(Note that neither and
nor or
restrict the value and type
they return to False
and True
, but rather return the last evaluated
argument. This is sometimes useful, e.g., if s
is a string that should be
replaced by a default value if it is empty, the expression s or 'foo'
yields
the desired value. Because not
has to create a new value, it
returns a boolean value regardless of the type of its argument
(for example, not 'foo'
produces False
rather than ''
.)
6.12. Conditional expressions
conditional_expression ::=or_test
["if"or_test
"else"expression
] expression ::=conditional_expression
lambda_expr
expression_nocond ::=or_test
lambda_expr_nocond
Conditional expressions (sometimes called a “ternary operator”) have the lowest priority of all Python operations.
The expression x if C else y
first evaluates the condition, C rather than x.
If C is true, x is evaluated and its value is returned; otherwise, y is
evaluated and its value is returned.
See PEP 308 for more details about conditional expressions.
6.13. Lambdas
lambda_expr ::= "lambda" [parameter_list
]:expression
lambda_expr_nocond ::= "lambda" [parameter_list
]:expression_nocond
Lambda expressions (sometimes called lambda forms) are used to create anonymous
functions. The expression lambda arguments: expression
yields a function
object. The unnamed object behaves like a function object defined with
def <lambda>(arguments):
return expression
See section Function definitions for the syntax of parameter lists. Note that functions created with lambda expressions cannot contain statements or annotations.
6.14. Expression lists
expression_list ::=expression
( ","expression
)* [","]
An expression list containing at least one comma yields a tuple. The length of the tuple is the number of expressions in the list. The expressions are evaluated from left to right.
The trailing comma is required only to create a single tuple (a.k.a. a
singleton); it is optional in all other cases. A single expression without a
trailing comma doesn’t create a tuple, but rather yields the value of that
expression. (To create an empty tuple, use an empty pair of parentheses:
()
.)
6.15. Evaluation order
Python evaluates expressions from left to right. Notice that while evaluating an assignment, the righthand side is evaluated before the lefthand side.
In the following lines, expressions will be evaluated in the arithmetic order of their suffixes:
expr1, expr2, expr3, expr4
(expr1, expr2, expr3, expr4)
{expr1: expr2, expr3: expr4}
expr1 + expr2 * (expr3  expr4)
expr1(expr2, expr3, *expr4, **expr5)
expr3, expr4 = expr1, expr2
6.16. Operator precedence
The following table summarizes the operator precedence in Python, from lowest precedence (least binding) to highest precedence (most binding). Operators in the same box have the same precedence. Unless the syntax is explicitly given, operators are binary. Operators in the same box group left to right (except for exponentiation, which groups from right to left).
Note that comparisons, membership tests, and identity tests, all have the same precedence and have a lefttoright chaining feature as described in the Comparisons section.
Operator  Description 

lambda 
Lambda expression 
if – else 
Conditional expression 
or 
Boolean OR 
and 
Boolean AND 
not x 
Boolean NOT 
in , not in ,
is , is not , < ,
<= , > , >= , != , == 
Comparisons, including membership tests and identity tests 
 
Bitwise OR 
^ 
Bitwise XOR 
& 
Bitwise AND 
<< , >> 
Shifts 
+ ,  
Addition and subtraction 
* , @ , / , // , % 
Multiplication, matrix multiplication division, remainder [5] 
+x , x , ~x 
Positive, negative, bitwise NOT 
** 
Exponentiation [6] 
await x 
Await expression 
x[index] , x[index:index] ,
x(arguments...) , x.attribute 
Subscription, slicing, call, attribute reference 
(expressions...) ,
[expressions...] ,
{key: value...} ,
{expressions...} 
Binding or tuple display, list display, dictionary display, set display 
Footnotes
[1]  While abs(x%y) < abs(y) is true mathematically, for floats it may not be
true numerically due to roundoff. For example, and assuming a platform on which
a Python float is an IEEE 754 doubleprecision number, in order that 1e100 %
1e100 have the same sign as 1e100 , the computed result is 1e100 +
1e100 , which is numerically exactly equal to 1e100 . The function
math.fmod() returns a result whose sign matches the sign of the
first argument instead, and so returns 1e100 in this case. Which approach
is more appropriate depends on the application. 
[2]  If x is very close to an exact integer multiple of y, it’s possible for
x//y to be one larger than (xx%y)//y due to rounding. In such
cases, Python returns the latter result, in order to preserve that
divmod(x,y)[0] * y + x % y be very close to x . 
[3]  The Unicode standard distinguishes between code points (e.g. U+0041) and abstract characters (e.g. “LATIN CAPITAL LETTER A”). While most abstract characters in Unicode are only represented using one code point, there is a number of abstract characters that can in addition be represented using a sequence of more than one code point. For example, the abstract character “LATIN CAPITAL LETTER C WITH CEDILLA” can be represented as a single precomposed character at code position U+00C7, or as a sequence of a base character at code position U+0043 (LATIN CAPITAL LETTER C), followed by a combining character at code position U+0327 (COMBINING CEDILLA). The comparison operators on strings compare at the level of Unicode code
points. This may be counterintuitive to humans. For example,
To compare strings at the level of abstract characters (that is, in a way
intuitive to humans), use 
[4]  Due to automatic garbagecollection, free lists, and the dynamic nature of
descriptors, you may notice seemingly unusual behaviour in certain uses of
the is operator, like those involving comparisons between instance
methods, or constants. Check their documentation for more info. 
[5]  The % operator is also used for string formatting; the same
precedence applies. 
[6]  The power operator ** binds less tightly than an arithmetic or
bitwise unary operator on its right, that is, 2**1 is 0.5 . 