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 built-in 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.

6.3. 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). User-defined objects can support subscription by defining a __getitem__() method. For built-in 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, built-in 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 ["," starred_and_keywords ] ["," keywords_arguments ] | starred_and_keywords ["," keywords_arguments ] | keywords_arguments positional_arguments ::= positional_item ("," positional_item)* positional_item ::= assignment_expression | "*" expression starred_and_keywords ::= ("*" expression | keyword_item ) ("," "*" expression | "," keyword_item )* keywords_arguments ::= ( keyword_item | "**" expression ) ("," keyword_item | "," "**" expression )* keyword_item ::= identifier "=" expression An optional trailing comma may be present after the positional and keyword arguments but does not affect the semantics. The primary must evaluate to a callable object (user-defined functions, built-in functions, methods of built-in objects, class objects, methods of class instances, and all objects having a __call__() method are callable). All argument expressions are evaluated before the call is attempted. Please refer to section Function definitions for the syntax of formal parameter lists. If keyword arguments are present, they are first converted to positional arguments, as follows. First, a list of unfilled slots is created for the formal parameters. If there are N positional arguments, they are placed in the first N slots. Next, for each keyword argument, the identifier is used to determine the corresponding slot (if the identifier is the same as the first formal parameter name, the first slot is used, and so on). If the slot is already filled, a TypeError exception is raised. Otherwise, the 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 these iterables are treated as if they were additional positional arguments. For the call f(x1, x2, *y, x3, x4) , if y evaluates to a sequence y1, …, yM, this is equivalent to a call with M+4 positional arguments x1, x2, y1, …, yM, x3, x4. A consequence of this is that although the *expression syntax may appear after explicit keyword arguments, it is processed before the keyword arguments (and any **expression arguments – see below). So: >>> def f ( a , b ): ... print ( a , b ) ... >>> f ( b = 1 , * ( 2 ,)) 2 1 >>> f ( a = 1 , * ( 2 ,)) Traceback (most recent call last): File "<stdin>" , line 1 , in <module> TypeError : f() got multiple values for keyword argument 'a' >>> f ( 1 , * ( 2 ,)) 1 2 It is unusual for both keyword arguments and the *expression syntax to be used in the same call, so in practice this confusion does not arise. If the syntax **expression appears in the function call, expression must evaluate to a mapping, the contents of which are treated as additional keyword arguments. If a keyword is already present (as an explicit keyword argument, or from another unpacking), 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. Changed in version 3.5: Function calls accept any number of * and ** unpackings, positional arguments may follow iterable unpackings ( * ), and keyword arguments may follow dictionary unpackings ( ** ). Originally proposed by PEP 448. 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.

6.4. Await expression¶ Suspend the execution of coroutine on an awaitable object. Can only be used inside a coroutine function. await_expr ::= "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_expr | 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, 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 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 "@" 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 . 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 built-in function divmod() : divmod(x, y) == (x//y, x%y) . . In addition to performing the modulo operation on numbers, the % operator is also overloaded by string objects to perform old-style string formatting (also known as interpolation). The syntax for string formatting is described in the Python Library Reference, section printf-style 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) .

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 value-based equality. Such types will need to customize their comparison behavior, and in fact, a number of built-in types have done that. The following list describes the comparison behavior of the most important built-in types. Numbers of built-in numeric types (Numeric Types — int, float, complex) and of the standard library types fractions.Fraction and decimal.Decimal can be compared within and across their types, with the restriction that complex numbers do not support order comparison. Within the limits of the types involved, they compare mathematically (algorithmically) correct without loss of precision. The not-a-number values float('NaN') and decimal.Decimal('NaN') are special. Any ordered comparison of a number to a not-a-number value is false. A counter-intuitive implication is that not-a-number values are not equal to themselves. For example, if x = float('NaN') , 3 < x , x < 3 and x == x are all false, while x != x is true. This behavior is compliant with IEEE 754.

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

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

Strings (instances of str ) compare lexicographically using the numerical Unicode code points (the result of the built-in function ord() ) of their characters. Strings and binary sequences cannot be directly compared.

Sequences (instances of tuple , list , or range ) can be compared only within each of their types, with the restriction that ranges do not support order comparison. Equality comparison across these types results in inequality, and ordering comparison across these types raises TypeError . Sequences compare lexicographically using comparison of corresponding elements. The built-in containers typically assume identical objects are equal to themselves. That lets them bypass equality tests for identical objects to improve performance and to maintain their internal invariants. Lexicographical comparison between built-in collections works as follows: For two collections to compare equal, they must be of the same type, have the same length, and each pair of corresponding elements must compare equal (for example, [1,2] == (1,2) is false because the type is not the same). Collections that support order comparison are ordered the same as their first unequal elements (for example, [1,2,x] <= [1,2,y] has the same value as x <= y ). If a corresponding element does not exist, the shorter collection is ordered first (for example, [1,2] < [1,2,3] is true).

Mappings (instances of dict ) compare equal if and only if they have equal (key, value) pairs. Equality comparison of the keys and values enforces reflexivity. Order comparisons ( < , > , <= , and >= ) raise TypeError .

Sets (instances of set or frozenset ) can be compared within and across their types. They define order comparison operators to mean subset and superset tests. Those relations do not define total orderings (for example, the two sets {1,2} and {2,3} are not equal, nor subsets of one another, nor supersets of one another). Accordingly, sets are not appropriate arguments for functions which depend on total ordering (for example, min() , max() , and sorted() produce undefined results given a list of sets as inputs). Comparison of sets enforces reflexivity of its elements.

Most other built-in types have no comparison methods implemented, so they inherit the default comparison behavior. User-defined classes that customize their comparison behavior should follow some consistency rules, if possible: Equality comparison should be reflexive. In other words, identical objects should compare equal: x is y implies x == y

Comparison should be symmetric. In other words, the following expressions should have the same result: x == y and y == x x != y and y != x x < y and y > x x <= y and y >= x

Comparison should be transitive. The following (non-exhaustive) examples illustrate that: x > y and y > z implies x > z x < y and y <= z implies x < z

Inverse comparison should result in the boolean negation. In other words, the following expressions should have the same result: x == y and not x != y x < y and not x >= y (for total ordering) x > y and not x <= y (for total ordering) The last two expressions apply to totally ordered collections (e.g. to sequences, but not to sets or mappings). See also the total_ordering() decorator.

The hash() result should be consistent with equality. Objects that are equal should either have the same hash value, or be marked as unhashable. Python does not enforce these consistency rules. In fact, the not-a-number values are an example for not following these rules. 6.10.2. Membership test operations¶ The operators in and not in test for membership. x in s evaluates to True if x is a member of s, and False otherwise. x not in s returns the negation of x in s . All built-in sequences and set types support this as well as dictionary, for which in tests whether the dictionary has a given key. For container types such as list, tuple, set, frozenset, dict, or collections.deque, the expression x in y is equivalent to any(x is e or x == e for e in y) . For the string and bytes types, x in y is True if and only if x is a substring of y. An equivalent test is y.find(x) != -1 . Empty strings are always considered to be a substring of any other string, so "" in "abc" will return True . For user-defined classes which define the __contains__() method, x in y returns True if y.__contains__(x) returns a true value, and False otherwise. For user-defined classes which do not define __contains__() but do define __iter__() , x in y is True if some value z , for which the expression x is z or x == z is true, is produced while iterating over y . If an exception is raised during the iteration, it is as if in raised that exception. Lastly, the old-style iteration protocol is tried: if a class defines __getitem__() , x in y is True if and only if there is a non-negative integer index i such that x is y[i] or x == y[i] , and no lower integer index raises the IndexError exception. (If any other exception is raised, it is as if in raised that exception). The operator not in is defined to have the inverse truth value of in . 6.10.3. Identity comparisons¶ The operators is and is not test for an object’s identity: x is y is true if and only if x and y are the same object. An Object’s identity is determined using the id() function. x is not y yields the inverse truth value.

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. User-defined 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. Assignment expressions¶ assignment_expression ::= [ identifier ":="] expression An assignment expression (sometimes also called a “named expression” or “walrus”) assigns an expression to an identifier , while also returning the value of the expression . One common use case is when handling matched regular expressions: if matching := pattern . search ( data ): do_something ( matching ) Or, when processing a file stream in chunks: while chunk := file . read ( 9000 ): process ( chunk ) New in version 3.8: See PEP 572 for more details about assignment expressions.

6.13. 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.

6.14. 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 parameters: expression yields a function object. The unnamed object behaves like a function object defined with: def <lambda>(parameters): return expression See section Function definitions for the syntax of parameter lists. Note that functions created with lambda expressions cannot contain statements or annotations.

6.15. Expression lists¶ expression_list ::= expression ("," expression )* [","] starred_list ::= starred_item ("," starred_item )* [","] starred_expression ::= expression | ( starred_item ",")* [ starred_item ] starred_item ::= assignment_expression | "*" or_expr Except when part of a list or set display, 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. An asterisk * denotes iterable unpacking. Its operand must be an iterable. The iterable is expanded into a sequence of items, which are included in the new tuple, list, or set, at the site of the unpacking. New in version 3.5: Iterable unpacking in expression lists, originally proposed by PEP 448. 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: () .)

6.16. 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