9. Classes¶
Classes provide a means of bundling data and functionality together. Creating a new class creates a new type of object, allowing new instances of that type to be made. Each class instance can have attributes attached to it for maintaining its state. Class instances can also have methods (defined by its class) for modifying its state.
Compared with other programming languages, Python’s class mechanism adds classes with a minimum of new syntax and semantics. It is a mixture of the class mechanisms found in C++ and Modula-3. Python classes provide all the standard features of Object Oriented Programming: the class inheritance mechanism allows multiple base classes, a derived class can override any methods of its base class or classes, and a method can call the method of a base class with the same name. Objects can contain arbitrary amounts and kinds of data. As is true for modules, classes partake of the dynamic nature of Python: they are created at runtime, and can be modified further after creation.
In C++ terminology, normally class members (including the data members) are public (except see below Private Variables), and all member functions are virtual. As in Modula-3, there are no shorthands for referencing the object’s members from its methods: the method function is declared with an explicit first argument representing the object, which is provided implicitly by the call. As in Smalltalk, classes themselves are objects. This provides semantics for importing and renaming. Unlike C++ and Modula-3, built-in types can be used as base classes for extension by the user. Also, like in C++, most built-in operators with special syntax (arithmetic operators, subscripting etc.) can be redefined for class instances.
(Lacking universally accepted terminology to talk about classes, I will make occasional use of Smalltalk and C++ terms. I would use Modula-3 terms, since its object-oriented semantics are closer to those of Python than C++, but I expect that few readers have heard of it.)
9.1. A Word About Names and Objects¶
Objects have individuality, and multiple names (in multiple scopes) can be bound to the same object. This is known as aliasing in other languages. This is usually not appreciated on a first glance at Python, and can be safely ignored when dealing with immutable basic types (numbers, strings, tuples). However, aliasing has a possibly surprising effect on the semantics of Python code involving mutable objects such as lists, dictionaries, and most other types. This is usually used to the benefit of the program, since aliases behave like pointers in some respects. For example, passing an object is cheap since only a pointer is passed by the implementation; and if a function modifies an object passed as an argument, the caller will see the change — this eliminates the need for two different argument passing mechanisms as in Pascal.
9.2. Python Scopes and Namespaces¶
Before introducing classes, I first have to tell you something about Python’s scope rules. Class definitions play some neat tricks with namespaces, and you need to know how scopes and namespaces work to fully understand what’s going on. Incidentally, knowledge about this subject is useful for any advanced Python programmer.
Let’s begin with some definitions.
A namespace is a mapping from names to objects. Most namespaces are currently
implemented as Python dictionaries, but that’s normally not noticeable in any
way (except for performance), and it may change in the future. Examples of
namespaces are: the set of built-in names (containing functions such as abs()
, and
built-in exception names); the global names in a module; and the local names in
a function invocation. In a sense the set of attributes of an object also form
a namespace. The important thing to know about namespaces is that there is
absolutely no relation between names in different namespaces; for instance, two
different modules may both define a function maximize
without confusion —
users of the modules must prefix it with the module name.
By the way, I use the word attribute for any name following a dot — for
example, in the expression z.real
, real
is an attribute of the object
z
. Strictly speaking, references to names in modules are attribute
references: in the expression modname.funcname
, modname
is a module
object and funcname
is an attribute of it. In this case there happens to be
a straightforward mapping between the module’s attributes and the global names
defined in the module: they share the same namespace! [1]
Attributes may be read-only or writable. In the latter case, assignment to
attributes is possible. Module attributes are writable: you can write
modname.the_answer = 42
. Writable attributes may also be deleted with the
del
statement. For example, del modname.the_answer
will remove
the attribute the_answer
from the object named by modname
.
Namespaces are created at different moments and have different lifetimes. The
namespace containing the built-in names is created when the Python interpreter
starts up, and is never deleted. The global namespace for a module is created
when the module definition is read in; normally, module namespaces also last
until the interpreter quits. The statements executed by the top-level
invocation of the interpreter, either read from a script file or interactively,
are considered part of a module called __main__
, so they have their own
global namespace. (The built-in names actually also live in a module; this is
called builtins
.)
The local namespace for a function is created when the function is called, and deleted when the function returns or raises an exception that is not handled within the function. (Actually, forgetting would be a better way to describe what actually happens.) Of course, recursive invocations each have their own local namespace.
A scope is a textual region of a Python program where a namespace is directly accessible. “Directly accessible” here means that an unqualified reference to a name attempts to find the name in the namespace.
Although scopes are determined statically, they are used dynamically. At any time during execution, there are 3 or 4 nested scopes whose namespaces are directly accessible:
the innermost scope, which is searched first, contains the local names
the scopes of any enclosing functions, which are searched starting with the nearest enclosing scope, contain non-local, but also non-global names
the next-to-last scope contains the current module’s global names
the outermost scope (searched last) is the namespace containing built-in names
If a name is declared global, then all references and assignments go directly to
the next-to-last scope containing the module’s global names. To rebind variables
found outside of the innermost scope, the nonlocal
statement can be
used; if not declared nonlocal, those variables are read-only (an attempt to
write to such a variable will simply create a new local variable in the
innermost scope, leaving the identically named outer variable unchanged).
Usually, the local scope references the local names of the (textually) current function. Outside functions, the local scope references the same namespace as the global scope: the module’s namespace. Class definitions place yet another namespace in the local scope.
It is important to realize that scopes are determined textually: the global scope of a function defined in a module is that module’s namespace, no matter from where or by what alias the function is called. On the other hand, the actual search for names is done dynamically, at run time — however, the language definition is evolving towards static name resolution, at “compile” time, so don’t rely on dynamic name resolution! (In fact, local variables are already determined statically.)
A special quirk of Python is that – if no global
or nonlocal
statement is in effect – assignments to names always go into the innermost scope.
Assignments do not copy data — they just bind names to objects. The same is true
for deletions: the statement del x
removes the binding of x
from the
namespace referenced by the local scope. In fact, all operations that introduce
new names use the local scope: in particular, import
statements and
function definitions bind the module or function name in the local scope.
The global
statement can be used to indicate that particular
variables live in the global scope and should be rebound there; the
nonlocal
statement indicates that particular variables live in
an enclosing scope and should be rebound there.
9.2.1. Scopes and Namespaces Example¶
This is an example demonstrating how to reference the different scopes and
namespaces, and how global
and nonlocal
affect variable
binding:
def scope_test():
def do_local():
spam = "local spam"
def do_nonlocal():
nonlocal spam
spam = "nonlocal spam"
def do_global():
global spam
spam = "global spam"
spam = "test spam"
do_local()
print("After local assignment:", spam)
do_nonlocal()
print("After nonlocal assignment:", spam)
do_global()
print("After global assignment:", spam)
scope_test()
print("In global scope:", spam)
The output of the example code is:
After local assignment: test spam
After nonlocal assignment: nonlocal spam
After global assignment: nonlocal spam
In global scope: global spam
Note how the local assignment (which is default) didn’t change scope_test's
binding of spam. The nonlocal
assignment changed scope_test's
binding of spam, and the global
assignment changed the module-level
binding.
You can also see that there was no previous binding for spam before the
global
assignment.
9.3. A First Look at Classes¶
Classes introduce a little bit of new syntax, three new object types, and some new semantics.
9.3.1. Class Definition Syntax¶
The simplest form of class definition looks like this:
class ClassName:
<statement-1>
.
.
.
<statement-N>
Class definitions, like function definitions (def
statements) must be
executed before they have any effect. (You could conceivably place a class
definition in a branch of an if
statement, or inside a function.)
In practice, the statements inside a class definition will usually be function definitions, but other statements are allowed, and sometimes useful — we’ll come back to this later. The function definitions inside a class normally have a peculiar form of argument list, dictated by the calling conventions for methods — again, this is explained later.
When a class definition is entered, a new namespace is created, and used as the local scope — thus, all assignments to local variables go into this new namespace. In particular, function definitions bind the name of the new function here.
When a class definition is left normally (via the end), a class object is
created. This is basically a wrapper around the contents of the namespace
created by the class definition; we’ll learn more about class objects in the
next section. The original local scope (the one in effect just before the class
definition was entered) is reinstated, and the class object is bound here to the
class name given in the class definition header (ClassName
in the
example).
9.3.2. Class Objects¶
Class objects support two kinds of operations: attribute references and instantiation.
Attribute references use the standard syntax used for all attribute references
in Python: obj.name
. Valid attribute names are all the names that were in
the class’s namespace when the class object was created. So, if the class
definition looked like this:
class MyClass:
"""A simple example class"""
i = 12345
def f(self):
return 'hello world'
then MyClass.i
and MyClass.f
are valid attribute references, returning
an integer and a function object, respectively. Class attributes can also be
assigned to, so you can change the value of MyClass.i
by assignment.
__doc__
is also a valid attribute, returning the docstring
belonging to the class: "A simple example class"
.
Class instantiation uses function notation. Just pretend that the class object is a parameterless function that returns a new instance of the class. For example (assuming the above class):
x = MyClass()
creates a new instance of the class and assigns this object to the local
variable x
.
The instantiation operation (“calling” a class object) creates an empty object.
Many classes like to create objects with instances customized to a specific
initial state. Therefore a class may define a special method named
__init__()
, like this:
def __init__(self):
self.data = []
When a class defines an __init__()
method, class instantiation
automatically invokes __init__()
for the newly created class instance. So
in this example, a new, initialized instance can be obtained by:
x = MyClass()
Of course, the __init__()
method may have arguments for greater
flexibility. In that case, arguments given to the class instantiation operator
are passed on to __init__()
. For example,
>>> class Complex:
... def __init__(self, realpart, imagpart):
... self.r = realpart
... self.i = imagpart
...
>>> x = Complex(3.0, -4.5)
>>> x.r, x.i
(3.0, -4.5)
9.3.3. Instance Objects¶
Now what can we do with instance objects? The only operations understood by instance objects are attribute references. There are two kinds of valid attribute names: data attributes and methods.
data attributes correspond to “instance variables” in Smalltalk, and to “data
members” in C++. Data attributes need not be declared; like local variables,
they spring into existence when they are first assigned to. For example, if
x
is the instance of MyClass
created above, the following piece of
code will print the value 16
, without leaving a trace:
x.counter = 1
while x.counter < 10:
x.counter = x.counter * 2
print(x.counter)
del x.counter
The other kind of instance attribute reference is a method. A method is a function that “belongs to” an object.
Valid method names of an instance object depend on its class. By definition,
all attributes of a class that are function objects define corresponding
methods of its instances. So in our example, x.f
is a valid method
reference, since MyClass.f
is a function, but x.i
is not, since
MyClass.i
is not. But x.f
is not the same thing as MyClass.f
— it
is a method object, not a function object.
9.3.4. Method Objects¶
Usually, a method is called right after it is bound:
x.f()
In the MyClass
example, this will return the string 'hello world'
.
However, it is not necessary to call a method right away: x.f
is a method
object, and can be stored away and called at a later time. For example:
xf = x.f
while True:
print(xf())
will continue to print hello world
until the end of time.
What exactly happens when a method is called? You may have noticed that
x.f()
was called without an argument above, even though the function
definition for f()
specified an argument. What happened to the argument?
Surely Python raises an exception when a function that requires an argument is
called without any — even if the argument isn’t actually used…
Actually, you may have guessed the answer: the special thing about methods is
that the instance object is passed as the first argument of the function. In our
example, the call x.f()
is exactly equivalent to MyClass.f(x)
. In
general, calling a method with a list of n arguments is equivalent to calling
the corresponding function with an argument list that is created by inserting
the method’s instance object before the first argument.
In general, methods work as follows. When a non-data attribute of an instance is referenced, the instance’s class is searched. If the name denotes a valid class attribute that is a function object, references to both the instance object and the function object are packed into a method object. When the method object is called with an argument list, a new argument list is constructed from the instance object and the argument list, and the function object is called with this new argument list.
9.3.5. Class and Instance Variables¶
Generally speaking, instance variables are for data unique to each instance and class variables are for attributes and methods shared by all instances of the class:
class Dog:
kind = 'canine' # class variable shared by all instances
def __init__(self, name):
self.name = name # instance variable unique to each instance
>>> d = Dog('Fido')
>>> e = Dog('Buddy')
>>> d.kind # shared by all dogs
'canine'
>>> e.kind # shared by all dogs
'canine'
>>> d.name # unique to d
'Fido'
>>> e.name # unique to e
'Buddy'
As discussed in A Word About Names and Objects, shared data can have possibly surprising effects with involving mutable objects such as lists and dictionaries. For example, the tricks list in the following code should not be used as a class variable because just a single list would be shared by all Dog instances:
class Dog:
tricks = [] # mistaken use of a class variable
def __init__(self, name):
self.name = name
def add_trick(self, trick):
self.tricks.append(trick)
>>> d = Dog('Fido')
>>> e = Dog('Buddy')
>>> d.add_trick('roll over')
>>> e.add_trick('play dead')
>>> d.tricks # unexpectedly shared by all dogs
['roll over', 'play dead']
Correct design of the class should use an instance variable instead:
class Dog:
def __init__(self, name):
self.name = name
self.tricks = [] # creates a new empty list for each dog
def add_trick(self, trick):
self.tricks.append(trick)
>>> d = Dog('Fido')
>>> e = Dog('Buddy')
>>> d.add_trick('roll over')
>>> e.add_trick('play dead')
>>> d.tricks
['roll over']
>>> e.tricks
['play dead']
9.4. Random Remarks¶
If the same attribute name occurs in both an instance and in a class, then attribute lookup prioritizes the instance:
>>> class Warehouse:
... purpose = 'storage'
... region = 'west'
...
>>> w1 = Warehouse()
>>> print(w1.purpose, w1.region)
storage west
>>> w2 = Warehouse()
>>> w2.region = 'east'
>>> print(w2.purpose, w2.region)
storage east
Data attributes may be referenced by methods as well as by ordinary users (“clients”) of an object. In other words, classes are not usable to implement pure abstract data types. In fact, nothing in Python makes it possible to enforce data hiding — it is all based upon convention. (On the other hand, the Python implementation, written in C, can completely hide implementation details and control access to an object if necessary; this can be used by extensions to Python written in C.)
Clients should use data attributes with care — clients may mess up invariants maintained by the methods by stamping on their data attributes. Note that clients may add data attributes of their own to an instance object without affecting the validity of the methods, as long as name conflicts are avoided — again, a naming convention can save a lot of headaches here.
There is no shorthand for referencing data attributes (or other methods!) from within methods. I find that this actually increases the readability of methods: there is no chance of confusing local variables and instance variables when glancing through a method.
Often, the first argument of a method is called self
. This is nothing more
than a convention: the name self
has absolutely no special meaning to
Python. Note, however, that by not following the convention your code may be
less readable to other Python programmers, and it is also conceivable that a
class browser program might be written that relies upon such a convention.
Any function object that is a class attribute defines a method for instances of that class. It is not necessary that the function definition is textually enclosed in the class definition: assigning a function object to a local variable in the class is also ok. For example:
# Function defined outside the class
def f1(self, x, y):
return min(x, x+y)
class C:
f = f1
def g(self):
return 'hello world'
h = g
Now f
, g
and h
are all attributes of class C
that refer to
function objects, and consequently they are all methods of instances of
C
— h
being exactly equivalent to g
. Note that this practice
usually only serves to confuse the reader of a program.
Methods may call other methods by using method attributes of the self
argument:
class Bag:
def __init__(self):
self.data = []
def add(self, x):
self.data.append(x)
def addtwice(self, x):
self.add(x)
self.add(x)
Methods may reference global names in the same way as ordinary functions. The global scope associated with a method is the module containing its definition. (A class is never used as a global scope.) While one rarely encounters a good reason for using global data in a method, there are many legitimate uses of the global scope: for one thing, functions and modules imported into the global scope can be used by methods, as well as functions and classes defined in it. Usually, the class containing the method is itself defined in this global scope, and in the next section we’ll find some good reasons why a method would want to reference its own class.
Each value is an object, and therefore has a class (also called its type).
It is stored as object.__class__
.
9.5. Inheritance¶
Of course, a language feature would not be worthy of the name “class” without supporting inheritance. The syntax for a derived class definition looks like this:
class DerivedClassName(BaseClassName):
<statement-1>
.
.
.
<statement-N>
The name BaseClassName
must be defined in a
namespace accessible from the scope containing the
derived class definition. In place of a base class name, other arbitrary
expressions are also allowed. This can be useful, for example, when the base
class is defined in another module:
class DerivedClassName(modname.BaseClassName):
Execution of a derived class definition proceeds the same as for a base class. When the class object is constructed, the base class is remembered. This is used for resolving attribute references: if a requested attribute is not found in the class, the search proceeds to look in the base class. This rule is applied recursively if the base class itself is derived from some other class.
There’s nothing special about instantiation of derived classes:
DerivedClassName()
creates a new instance of the class. Method references
are resolved as follows: the corresponding class attribute is searched,
descending down the chain of base classes if necessary, and the method reference
is valid if this yields a function object.
Derived classes may override methods of their base classes. Because methods
have no special privileges when calling other methods of the same object, a
method of a base class that calls another method defined in the same base class
may end up calling a method of a derived class that overrides it. (For C++
programmers: all methods in Python are effectively virtual
.)
An overriding method in a derived class may in fact want to extend rather than
simply replace the base class method of the same name. There is a simple way to
call the base class method directly: just call BaseClassName.methodname(self,
arguments)
. This is occasionally useful to clients as well. (Note that this
only works if the base class is accessible as BaseClassName
in the global
scope.)
Python has two built-in functions that work with inheritance:
Use
isinstance()
to check an instance’s type:isinstance(obj, int)
will beTrue
only ifobj.__class__
isint
or some class derived fromint
.Use
issubclass()
to check class inheritance:issubclass(bool, int)
isTrue
sincebool
is a subclass ofint
. However,issubclass(float, int)
isFalse
sincefloat
is not a subclass ofint
.
9.5.1. Multiple Inheritance¶
Python supports a form of multiple inheritance as well. A class definition with multiple base classes looks like this:
class DerivedClassName(Base1, Base2, Base3):
<statement-1>
.
.
.
<statement-N>
For most purposes, in the simplest cases, you can think of the search for
attributes inherited from a parent class as depth-first, left-to-right, not
searching twice in the same class where there is an overlap in the hierarchy.
Thus, if an attribute is not found in DerivedClassName
, it is searched
for in Base1
, then (recursively) in the base classes of Base1
,
and if it was not found there, it was searched for in Base2
, and so on.
In fact, it is slightly more complex than that; the method resolution order
changes dynamically to support cooperative calls to super()
. This
approach is known in some other multiple-inheritance languages as
call-next-method and is more powerful than the super call found in
single-inheritance languages.
Dynamic ordering is necessary because all cases of multiple inheritance exhibit
one or more diamond relationships (where at least one of the parent classes
can be accessed through multiple paths from the bottommost class). For example,
all classes inherit from object
, so any case of multiple inheritance
provides more than one path to reach object
. To keep the base classes
from being accessed more than once, the dynamic algorithm linearizes the search
order in a way that preserves the left-to-right ordering specified in each
class, that calls each parent only once, and that is monotonic (meaning that a
class can be subclassed without affecting the precedence order of its parents).
Taken together, these properties make it possible to design reliable and
extensible classes with multiple inheritance. For more detail, see
The Python 2.3 Method Resolution Order.
9.6. Private Variables¶
“Private” instance variables that cannot be accessed except from inside an
object don’t exist in Python. However, there is a convention that is followed
by most Python code: a name prefixed with an underscore (e.g. _spam
) should
be treated as a non-public part of the API (whether it is a function, a method
or a data member). It should be considered an implementation detail and subject
to change without notice.
Since there is a valid use-case for class-private members (namely to avoid name
clashes of names with names defined by subclasses), there is limited support for
such a mechanism, called name mangling. Any identifier of the form
__spam
(at least two leading underscores, at most one trailing underscore)
is textually replaced with _classname__spam
, where classname
is the
current class name with leading underscore(s) stripped. This mangling is done
without regard to the syntactic position of the identifier, as long as it
occurs within the definition of a class.
See also
The private name mangling specifications for details and special cases.
Name mangling is helpful for letting subclasses override methods without breaking intraclass method calls. For example:
class Mapping:
def __init__(self, iterable):
self.items_list = []
self.__update(iterable)
def update(self, iterable):
for item in iterable:
self.items_list.append(item)
__update = update # private copy of original update() method
class MappingSubclass(Mapping):
def update(self, keys, values):
# provides new signature for update()
# but does not break __init__()
for item in zip(keys, values):
self.items_list.append(item)
The above example would work even if MappingSubclass
were to introduce a
__update
identifier since it is replaced with _Mapping__update
in the
Mapping
class and _MappingSubclass__update
in the MappingSubclass
class respectively.
Note that the mangling rules are designed mostly to avoid accidents; it still is possible to access or modify a variable that is considered private. This can even be useful in special circumstances, such as in the debugger.
Notice that code passed to exec()
or eval()
does not consider the
classname of the invoking class to be the current class; this is similar to the
effect of the global
statement, the effect of which is likewise restricted
to code that is byte-compiled together. The same restriction applies to
getattr()
, setattr()
and delattr()
, as well as when referencing
__dict__
directly.
9.7. Odds and Ends¶
Sometimes it is useful to have a data type similar to the Pascal “record” or C
“struct”, bundling together a few named data items. The idiomatic approach
is to use dataclasses
for this purpose:
from dataclasses import dataclass
@dataclass
class Employee:
name: str
dept: str
salary: int
>>> john = Employee('john', 'computer lab', 1000)
>>> john.dept
'computer lab'
>>> john.salary
1000
A piece of Python code that expects a particular abstract data type can often be
passed a class that emulates the methods of that data type instead. For
instance, if you have a function that formats some data from a file object, you
can define a class with methods read()
and
readline()
that get the
data from a string buffer instead, and pass it as an argument.
Instance method objects have attributes, too:
m.__self__
is the instance
object with the method m()
, and m.__func__
is
the function object
corresponding to the method.
9.8. Iterators¶
By now you have probably noticed that most container objects can be looped over
using a for
statement:
for element in [1, 2, 3]:
print(element)
for element in (1, 2, 3):
print(element)
for key in {'one':1, 'two':2}:
print(key)
for char in "123":
print(char)
for line in open("myfile.txt"):
print(line, end='')
This style of access is clear, concise, and convenient. The use of iterators
pervades and unifies Python. Behind the scenes, the for
statement
calls iter()
on the container object. The function returns an iterator
object that defines the method __next__()
which accesses
elements in the container one at a time. When there are no more elements,
__next__()
raises a StopIteration
exception which tells the
for
loop to terminate. You can call the __next__()
method
using the next()
built-in function; this example shows how it all works:
>>> s = 'abc'
>>> it = iter(s)
>>> it
<str_iterator object at 0x10c90e650>
>>> next(it)
'a'
>>> next(it)
'b'
>>> next(it)
'c'
>>> next(it)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
next(it)
StopIteration
Having seen the mechanics behind the iterator protocol, it is easy to add
iterator behavior to your classes. Define an __iter__()
method which
returns an object with a __next__()
method. If the class
defines __next__()
, then __iter__()
can just return self
:
class Reverse:
"""Iterator for looping over a sequence backwards."""
def __init__(self, data):
self.data = data
self.index = len(data)
def __iter__(self):
return self
def __next__(self):
if self.index == 0:
raise StopIteration
self.index = self.index - 1
return self.data[self.index]
>>> rev = Reverse('spam')
>>> iter(rev)
<__main__.Reverse object at 0x00A1DB50>
>>> for char in rev:
... print(char)
...
m
a
p
s
9.9. Generators¶
Generators are a simple and powerful tool for creating iterators. They
are written like regular functions but use the yield
statement
whenever they want to return data. Each time next()
is called on it, the
generator resumes where it left off (it remembers all the data values and which
statement was last executed). An example shows that generators can be trivially
easy to create:
def reverse(data):
for index in range(len(data)-1, -1, -1):
yield data[index]
>>> for char in reverse('golf'):
... print(char)
...
f
l
o
g
Anything that can be done with generators can also be done with class-based
iterators as described in the previous section. What makes generators so
compact is that the __iter__()
and __next__()
methods
are created automatically.
Another key feature is that the local variables and execution state are
automatically saved between calls. This made the function easier to write and
much more clear than an approach using instance variables like self.index
and self.data
.
In addition to automatic method creation and saving program state, when
generators terminate, they automatically raise StopIteration
. In
combination, these features make it easy to create iterators with no more effort
than writing a regular function.
9.10. Generator Expressions¶
Some simple generators can be coded succinctly as expressions using a syntax similar to list comprehensions but with parentheses instead of square brackets. These expressions are designed for situations where the generator is used right away by an enclosing function. Generator expressions are more compact but less versatile than full generator definitions and tend to be more memory friendly than equivalent list comprehensions.
Examples:
>>> sum(i*i for i in range(10)) # sum of squares
285
>>> xvec = [10, 20, 30]
>>> yvec = [7, 5, 3]
>>> sum(x*y for x,y in zip(xvec, yvec)) # dot product
260
>>> unique_words = set(word for line in page for word in line.split())
>>> valedictorian = max((student.gpa, student.name) for student in graduates)
>>> data = 'golf'
>>> list(data[i] for i in range(len(data)-1, -1, -1))
['f', 'l', 'o', 'g']
Footnotes