6. Expressions — Python 3.4.3 documentation

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# 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 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.

## 6.2. 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 comma-separated list of expressions is supplied, its elements are evaluated from left to right and placed into the list object in that order. When a comprehension is supplied, the list is constructed from the elements resulting from the comprehension.

### 6.2.6. 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 comma-separated list of expressions is supplied, its elements are evaluated from left to right and added to the set object. When a comprehension is supplied, the set is constructed from the elements resulting from the comprehension.

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

### 6.2.7. 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.

### 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 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 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 generator-iterator’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 sub-iterator is a generator (by returning a value from the sub-generator).

> 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 sub-generators easy.

#### 6.2.9.1. 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.

  This method is normally called implicitly, e.g. by a `for` loop, or by the built-in `next()` 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 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 the 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.

#### 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). 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 ["," 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 (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 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 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. 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, 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`.)

## 6.5. 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 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.

## 6.6. 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 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. 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 built-in 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 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.

## 6.7. 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 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.

## 6.8. 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 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.

## 6.9. 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 operators `<`, `>`, `==`, `>=`, `<=`, and `!=` compare the values of two objects. The objects need not have the same type. If both are numbers, they are converted to a common type. Otherwise, the `==` and `!=` operators always consider objects of different types to be unequal, while the `<`, `>`, `>=` and `<=` operators raise a `TypeError` when comparing objects of different types that do not implement these operators for the given pair of types. You can control comparison behavior of objects of non-built-in types by defining rich comparison methods like `__gt__()`, described in section Basic customization.

Comparison of objects of the same type depends on the type:

- Numbers are compared arithmetically.

- The values `float('NaN')` and `Decimal('NaN')` are special. They are identical to themselves, `x is x` but are not equal to themselves, `x != x`. Additionally, comparing any value to a not-a-number value will return `False`. For example, both `3 < float('NaN')` and `float('NaN') < 3` will return `False`.

- Bytes objects are compared lexicographically using the numeric values of their elements.

- Strings are compared lexicographically using the numeric equivalents (the result of the built-in function `ord()`) of their characters. [3] String and bytes object can’t be compared!

- Tuples and lists are compared lexicographically using comparison of corresponding elements. This means that to compare equal, each element must compare equal and the two sequences must be of the same type and have the same length.

  If not equal, the sequences are ordered the same as their first differing elements. For example, `[1,2,x] <= [1,2,y]` has the same value as `x <= y`. If the corresponding element does not exist, the shorter sequence is ordered first (for example, `[1,2] < [1,2,3]`).

- Mappings (dictionaries) compare equal if and only if they have the same `(key, value)` pairs. Order comparisons `('<', '<=', '>=', '>')` raise `TypeError`.

- Sets and frozensets define comparison operators to mean subset and superset tests. Those relations do not define total orderings (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.

- 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.

Comparison of objects of differing types depends on whether either of the types provide explicit support for the comparison. Most numeric types can be compared with one another. When cross-type comparison is not supported, the comparison method returns `NotImplemented`.

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` is true if and only if `y.__contains__(x)` is true.

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`.

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. [4]

## 6.10. 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. 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 `''`.)

## 6.11. 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.

## 6.12. 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.

## 6.13. 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: `()`.)

## 6.14. 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

## 6.15. 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 left-to-right 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, division, remainder [5]
`+x`, `-x`, `~x` | Positive, negative, bitwise NOT
`**` | Exponentiation [6]
`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 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.

[2] | If x is very close to an exact integer multiple of y, it’s possible for `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`.

[3] | While comparisons between strings make sense at the byte level, they may be counter-intuitive to users. For example, the strings `"\u00C7"` and `"\u0327\u0043"` compare differently, even though they both represent the same unicode character (LATIN CAPITAL LETTER C WITH CEDILLA). To compare strings in a human recognizable way, compare using `unicodedata.normalize()`.

[4] | 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.

[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`.

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