5. 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.

5.1. Arithmetic conversions

When a description of an arithmetic operator below uses the phrase “the numeric arguments are converted to a common type,” the arguments are coerced using the coercion rules listed at Coercion rules. If both arguments are standard numeric types, the following coercions are applied:

• 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, if either argument is a long integer, the other is converted to long integer;
• otherwise, both must be plain integers and no conversion is necessary.

Some additional rules apply for certain operators (e.g., a string left argument to the ‘%’ operator). Extensions can define their own coercions.

5.2. Atoms

Atoms are the most basic elements of expressions. The simplest atoms are identifiers or literals. Forms enclosed in reverse quotes or 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
               | generator_expression | dict_display | set_display
               | string_conversion | yield_atom

5.2.1. 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.

5.2.2. Literals

Python supports string literals and various numeric literals:

literal ::=  stringliteral | integer | longinteger
             | floatnumber | imagnumber

Evaluation of a literal yields an object of the given type (string, integer, long 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.

5.2.3. 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.

5.2.4. List displays

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

list_display        ::=  "[" [expression_list | list_comprehension] "]"
list_comprehension  ::=  expression list_for
list_for            ::=  "for" target_list "in" old_expression_list [list_iter]
old_expression_list ::=  old_expression [("," old_expression)+ [","]]
old_expression      ::=  or_test | old_lambda_expr
list_iter           ::=  list_for | list_if
list_if             ::=  "if" old_expression [list_iter]

A list display yields a new list object. Its contents are specified by providing either a list of expressions or a list 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 list comprehension is supplied, it 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 list 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 a list element each time the innermost block is reached [1].

5.2.5. Displays for sets and dictionaries

For constructing 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” in the enclosing scope.

5.2.6. 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 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 the detail.

5.2.7. 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 comma-separated 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.

5.2.8. 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 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.

5.2.9. String conversions

A string conversion is an expression list enclosed in reverse (a.k.a. backward) quotes:

string_conversion ::=  "`" expression_list "`"

A string conversion evaluates the contained expression list and converts the resulting object into a string according to rules specific to its type.

If the object is a string, a number, None, or a tuple, list or dictionary containing only objects whose type is one of these, the resulting string is a valid Python expression which can be passed to the built-in function eval() to yield an expression with the same value (or an approximation, if floating point numbers are involved).

(In particular, converting a string adds quotes around it and converts “funny” characters to escape sequences that are safe to print.)

Recursive objects (for example, lists or dictionaries that contain a reference to themselves, directly or indirectly) use ... to indicate a recursive reference, and the result cannot be passed to eval() to get an equal value (SyntaxError will be raised instead).

The built-in function repr() performs exactly the same conversion in its argument as enclosing it in parentheses and reverse quotes does. The built-in function str() performs a similar but more user-friendly conversion.

5.2.10. Yield expressions

yield_atom       ::=  "(" yield_expression ")"
yield_expression ::=  "yield" [expression_list]

New in version 2.5.

The yield expression is only used when defining a generator function, and can only be used in the body of a function definition. Using a yield expression in a function definition is sufficient to cause that definition to create a generator function instead of a normal function.

When a generator function is called, it returns an iterator known as a generator. That generator then controls the execution of a 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 generator’s caller. By suspended we mean that all local state is retained, including the current bindings of local variables, the instruction pointer, and the internal evaluation stack. When the execution is resumed by calling one of the generator’s methods, the function can proceed exactly as if the yield expression was just another external call. The value of the yield expression after resuming depends on the method which resumed the execution.

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 should the execution continue after it yields; the control is always transferred to the generator’s caller.

5.2.10.1. Generator-iterator 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 to None. The execution then continues to the next yield expression, where the generator is suspended again, and the value of the expression_list is returned to next()’s caller. If the generator exits without yielding another value, a StopIteration exception is raised.

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 raises StopIteration if the generator exits without yielding another value. When send() is called to start the generator, it must be called with None 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 generator was paused, and returns the next value yielded by the generator function. If the generator exits without yielding another value, a StopIteration exception is raised. If the generator function does not catch the passed-in 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 raises StopIteration (by exiting normally, or due to already being closed) or GeneratorExit (by not catching the exception), close returns to its caller. If the generator yields a value, a RuntimeError 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.

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

See also

PEP 342 - Coroutines via Enhanced Generators

The proposal to enhance the API and syntax of generators, making them usable as simple coroutines.

5.3. Primaries

Primaries represent the most tightly bound operations of the language. Their syntax is:

primary ::=  atom | attributeref | subscription | slicing | call

5.3.1. 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, e.g., a module, list, or an instance. This object is then asked to produce the attribute whose name is the identifier. 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.

5.3.2. 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 of a sequence or mapping type.

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 a plain integer. If this value is negative, the length of the sequence is added to it (so that, e.g., 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).

A string’s items are characters. A character is not a separate data type but a string of exactly one character.

5.3.3. 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          ::=  simple_slicing | extended_slicing
simple_slicing   ::=  primary "[" short_slice "]"
extended_slicing ::=  primary "[" slice_list "]"
slice_list       ::=  slice_item ("," slice_item)* [","]
slice_item       ::=  expression | proper_slice | ellipsis
proper_slice     ::=  short_slice | long_slice
short_slice      ::=  [lower_bound] ":" [upper_bound]
long_slice       ::=  short_slice ":" [stride]
lower_bound      ::=  expression
upper_bound      ::=  expression
stride           ::=  expression
ellipsis         ::=  "..."

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 nor ellipses). Similarly, when the slice list has exactly one short slice and no trailing comma, the interpretation as a simple slicing takes priority over that as an extended slicing.

The semantics for a simple slicing are as follows. The primary must evaluate to a sequence object. The lower and upper bound expressions, if present, must evaluate to plain integers; defaults are zero and the sys.maxint, respectively. If either bound is negative, the sequence’s length is added to it. The slicing now selects all items with index k such that i <= k < j where i and j are the specified lower and upper bounds. This may be an empty sequence. It is not an error if i or j lie outside the range of valid indexes (such items don’t exist so they aren’t selected).

The semantics for an extended slicing are as follows. The primary must evaluate to a mapping object, and it is indexed 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 an ellipsis slice item is the built-in Ellipsis object. 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.

5.3.4. Calls

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

call                 ::=  primary "(" [argument_list [","]
                          | expression genexpr_for] ")"
argument_list        ::=  positional_arguments ["," keyword_arguments]
                            ["," "*" expression] ["," keyword_arguments]
                            ["," "**" expression]
                          | keyword_arguments ["," "*" expression]
                            ["," "**" expression]
                          | "*" expression ["," keyword_arguments] ["," "**" expression]
                          | "**" expression
positional_arguments ::=  expression ("," expression)*
keyword_arguments    ::=  keyword_item ("," keyword_item)*
keyword_item         ::=  identifier "=" expression

A 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 certain class instances themselves are callable; extensions may define additional callable object types). 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 built-in 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 <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 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. Formal parameters using the syntax (sublist) cannot be used as keyword argument names; the outermost sublist corresponds to a single unnamed argument slot, and the argument value is assigned to the sublist using the usual tuple assignment rules after all other parameter processing is done.

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.

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.

5.4. 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 ::=  primary ["**" 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 built-in 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. The result type is that of the arguments after coercion.

With mixed operand types, the coercion rules for binary arithmetic operators apply. For int and long int operands, the result has the same type as the operands (after coercion) 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. (This last feature was added in Python 2.2. In Python 2.1 and before, if both arguments were of integer types and the second argument was negative, an exception was raised).

Raising 0.0 to a negative power results in a ZeroDivisionError. Raising a negative number to a fractional power results in a ValueError.

5.5. 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 plain or long 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.

5.6. Binary arithmetic operations

The binary arithmetic operations have the conventional priority levels. Note that some of these operations also apply to certain non-numeric 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 "//" 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 (plain or long) 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 / (division) and // (floor division) operators yield the quotient of their arguments. The numeric arguments are first converted to a common type. Plain or long integer division yields an integer of the same type; 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 [2].

The integer division and modulo operators are connected by the following identity: x == (x/y)*y + (x%y). Integer division and modulo are also connected with the built-in function divmod(): divmod(x, y) == (x/y, x%y). These identities don’t hold for floating point numbers; there similar identities hold approximately where x/y is replaced by floor(x/y) or floor(x/y) - 1 [3].

In addition to performing the modulo operation on numbers, the % operator is also overloaded by string and unicode objects to perform string formatting (also known as interpolation). The syntax for string formatting is described in the Python Library Reference, section String Formatting Operations.

Deprecated since version 2.3: The floor division operator, the modulo operator, and the divmod() function are no longer 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 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.

5.7. Shifting operations

The shifting operations have lower priority than the arithmetic operations:

shift_expr ::=  a_expr | shift_expr ( "<<" | ">>" ) a_expr

These operators accept plain or long integers as arguments. The arguments are converted to a common type. 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 division by pow(2, n). A left shift by n bits is defined as multiplication with pow(2, n). Negative shift counts raise a ValueError exception.

Note

In the current implementation, the right-hand operand is required to be at most sys.maxsize. If the right-hand operand is larger than sys.maxsize an OverflowError exception is raised.

5.8. 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 plain or long integers. The arguments are converted to a common type.

The ^ operator yields the bitwise XOR (exclusive OR) of its arguments, which must be plain or long integers. The arguments are converted to a common type.

The | operator yields the bitwise (inclusive) OR of its arguments, which must be plain or long integers. The arguments are converted to a common type.

5.9. 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).

The forms <> and != are equivalent; for consistency with C, != is preferred; where != is mentioned below <> is also accepted. The <> spelling is considered obsolescent.

5.9.1. 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.

Types can customize their comparison behavior by implementing a __cmp__() method or 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).

The default order comparison (<, >, <=, and >=) gives a consistent but arbitrary order.

(This unusual definition of comparison was used to simplify the definition of operations like sorting and the in and not in operators. In the future, the comparison rules for objects of different types are likely to change.)

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, long, 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.

• Strings (instances of str or unicode) compare lexicographically using the numeric equivalents (the result of the built-in function ord()) of their characters. [4] When comparing an 8-bit string and a Unicode string, the 8-bit string is converted to Unicode. If the conversion fails, the strings are considered unequal.

• Instances of tuple or list can be compared only within each of their types. Equality comparison across these types results in unequality, and ordering comparison across these types gives an arbitrary order.

  These 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 non-reflexive elements, the result is different than for strict element comparison.

  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 are ordered the same as their first unequal elements (for example, cmp([1,2,x], [1,2,y]) returns the same as cmp(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.

  Outcomes other than equality are resolved consistently, but are not otherwise defined. [5]

• Most other objects of built-in types compare unequal unless they are the same object; the choice whether one object is considered smaller or larger than another one is made arbitrarily but consistently within one execution of a program.

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.

5.9.2. 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 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 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 == 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.

5.9.3. Identity comparisons

The operators is and is not test for object identity: x is y is true if and only if x and y are the same object. x is not y yields the inverse truth value. [6]

5.10. 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. (See the __nonzero__() special method for a way to change this.)

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 invent a value anyway, it does not bother to return a value of the same type as its argument, so e.g., not 'foo' yields False, not ''.)

5.11. Conditional Expressions

New in version 2.5.

conditional_expression ::=  or_test ["if" or_test "else" expression]
expression             ::=  conditional_expression | lambda_expr

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 (not 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.

5.12. Lambdas

lambda_expr     ::=  "lambda" [parameter_list]: expression
old_lambda_expr ::=  "lambda" [parameter_list]: old_expression

Lambda expressions (sometimes called lambda forms) have the same syntactic position as expressions. They are a shorthand to create anonymous functions; the expression lambda arguments: expression yields a function object. The unnamed object behaves like a function object defined with

def name(arguments):
    return expression

See section Function definitions for the syntax of parameter lists. Note that functions created with lambda expressions cannot contain statements.

5.13. 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: ().)

5.14. Evaluation order

Python evaluates expressions from left to right. Notice that while evaluating an assignment, the right-hand side is evaluated before the left-hand 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

5.15. Operator precedence

The following table summarizes the operator precedences 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 comparisons, including tests, which all have the same precedence and chain from left to right — see section Comparisons — and exponentiation, which groups from right to left).

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, division, remainder [7]
+x, -x, ~x	Positive, negative, bitwise NOT
**	Exponentiation [8]
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, string conversion

Footnotes

[1]	In Python 2.3 and later releases, a list comprehension “leaks” the control variables of each for it contains into the containing scope. However, this behavior is deprecated, and relying on it will not work in Python 3.

[2]

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 double-precision number, in order that -1e-100 % 1e100 have the same sign as 1e100, the computed result is -1e-100 + 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 -1e-100 in this case. Which approach is more appropriate depends on the application.

[3]	If x is very close to an exact integer multiple of y, it’s possible for floor(x/y) to be one larger than (x-x%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.

[4]

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 unicode strings compare at the level of Unicode code points. This may be counter-intuitive to humans. For example, u"\u00C7" == u"\u0043\u0327" is False, even though both strings represent the same abstract character “LATIN CAPITAL LETTER C WITH CEDILLA”. To compare strings at the level of abstract characters (that is, in a way intuitive to humans), use unicodedata.normalize().

[5]

Earlier versions of Python used lexicographic comparison of the sorted (key, value) lists, but this was very expensive for the common case of comparing for equality. An even earlier version of Python compared dictionaries by identity only, but this caused surprises because people expected to be able to test a dictionary for emptiness by comparing it to {}.

[6]	Due to automatic garbage-collection, 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.

[7]	The % operator is also used for string formatting; the same precedence applies.

[8]	The power operator ** binds less tightly than an arithmetic or bitwise unary operator on its right, that is, 2**-1 is 0.5.