In the context of programming, a function is a named sequence of statements that performs a computation. When you define a function, you specify the name and the sequence of statements. Later, you can “call” the function by name. We have already seen one example of a function call:
>>> type(32) <type 'int'>
The name of the function is type
. The expression in parentheses is called
the argument of the function. The
result, for this function, is the type of the argument.
It is common to say that a function “takes” an argument and “returns” a result. The result is called the return value.
Python provides built-in functions that convert values
from one type to another. The int
function takes any value and converts it to an integer, if it can, or
complains otherwise:
>>> int('32') 32 >>> int('Hello') ValueError: invalid literal for int(): Hello
int
can convert floating-point
values to integers, but it doesn’t round off; it chops off the fraction
part:
>>> int(3.99999) 3 >>> int(-2.3) -2
float
converts integers and
strings to floating-point numbers:
>>> float(32) 32.0 >>> float('3.14159') 3.14159
Finally, str
converts its
argument to a string:
>>> str(32) '32' >>> str(3.14159) '3.14159'
Python has a math module that provides most of the familiar mathematical functions. A module is a file that contains a collection of related functions.
Before we can use the module, we have to import it:
>>> import math
This statement creates a module object named math. If you print the module object, you get some information about it:
>>> print math <module 'math' (built-in)>
The module object contains the functions and variables defined in the module. To access one of the functions, you have to specify the name of the module and the name of the function, separated by a dot (also known as a period). This format is called dot notation.
>>> ratio = signal_power / noise_power >>> decibels = 10 * math.log10(ratio) >>> radians = 0.7 >>> height = math.sin(radians)
The first example uses log10
to compute a signal-to-noise ratio in
decibels (assuming that signal_power
and noise_power
are defined). The math module also
provides log
, which computes
logarithms base e
.
The second example finds the sine of radians
. The name of the variable is a hint
that sin
and the other trigonometric
functions (cos
, tan
, etc.) take arguments in radians. To
convert from degrees to radians, divide by 360 and multiply by
:
>>> degrees = 45 >>> radians = degrees / 360.0 * 2 * math.pi >>> math.sin(radians) 0.707106781187
The expression math.pi
gets the
variable pi
from the math module. The
value of this variable is an approximation of , accurate to about 15 digits.
If you know your trigonometry, you can check the previous result by comparing it to the square root of two divided by two:
>>> math.sqrt(2) / 2.0 0.707106781187
So far, we have looked at the elements of a program—variables, expressions, and statements—in isolation, without talking about how to combine them.
One of the most useful features of programming languages is their ability to take small building blocks and compose them. For example, the argument of a function can be any kind of expression, including arithmetic operators:
x = math.sin(degrees / 360.0 * 2 * math.pi)
And even function calls:
x = math.exp(math.log(x+1))
Almost anywhere you can put a value, you can put an arbitrary expression, with one exception: the left side of an assignment statement has to be a variable name. Any other expression on the left side is a syntax error (we will see exceptions to this rule later).
>>> minutes = hours * 60 # right >>> hours * 60 = minutes # wrong! SyntaxError: can't assign to operator
So far, we have only been using the functions that come with Python, but it is also possible to add new functions. A function definition specifies the name of a new function and the sequence of statements that execute when the function is called.
Here is an example:
def
print_lyrics
():
"I'm a lumberjack, and I'm okay."
"I sleep all night and I work all day."
def
is a keyword that indicates
that this is a function definition. The name of the function is print_lyrics
. The rules for
function names are the same as for variable names: letters, numbers and
some punctuation marks are legal, but the first character can’t be a
number. You can’t use a keyword as the name of a function, and you
should avoid having a variable and a function with the same
name.
The empty parentheses after the name indicate that this function doesn’t take any arguments.
The first line of the function definition is called the header; the rest is called the body. The header has to end with a colon and the body has to be indented. By convention, the indentation is always four spaces; see Debugging. The body can contain any number of statements.
The strings in the print statements are enclosed in double quotes. Single quotes and double quotes do the same thing; most people use single quotes except in cases like this where a single quote (which is also an apostrophe) appears in the string.
If you type a function definition in interactive mode, the interpreter prints ellipses (...) to let you know that the definition isn’t complete:
>>> def print_lyrics(): ... print "I'm a lumberjack, and I'm okay." ... print "I sleep all night and I work all day." ...
To end the function, you have to enter an empty line (this is not necessary in a script).
Defining a function creates a variable with the same name.
>>> print print_lyrics <function print_lyrics at 0xb7e99e9c> >>> type(print_lyrics) <type 'function'>
The value of print_lyrics
is a function
object, which has type 'function'
.
The syntax for calling the new function is the same as for built-in functions:
>>> print_lyrics() I'm a lumberjack, and I'm okay. I sleep all night and I work all day.
Once you have defined a function, you can use it inside another
function. For example, to repeat the previous refrain, we could write a
function called repeat_lyrics
:
def
repeat_lyrics
():
print_lyrics
()
print_lyrics
()
And then call repeat_lyrics
:
>>> repeat_lyrics() I'm a lumberjack, and I'm okay. I sleep all night and I work all day. I'm a lumberjack, and I'm okay. I sleep all night and I work all day.
But that’s not really how the song goes.
Pulling together the code fragments from the previous section, the whole program looks like this:
def
print_lyrics
():
"I'm a lumberjack, and I'm okay."
"I sleep all night and I work all day."
def
repeat_lyrics
():
print_lyrics
()
print_lyrics
()
repeat_lyrics
()
This program contains two function definitions: print_lyrics
and repeat_lyrics
. Function
definitions get executed just like other statements, but the result
creates function objects. The statements inside the function do not get
executed until the function is called, and the function definition
generates no output.
As you might expect, you have to create a function before you can execute it. In other words, the function definition has to be executed before the function is called the first time.
In order to ensure that a function is defined before its first use, you have to know the order in which statements are executed, which is called the flow of execution.
Execution always begins at the first statement of the program. Statements are executed one at a time, in order, from top to bottom.
Function definitions do not alter the flow of execution of the program, but remember that statements inside the function are not executed until the function is called.
A function call is like a detour in the flow of execution. Instead of going to the next statement, the flow jumps to the body of the function, executes all the statements there, and then comes back to pick up where it left off.
That sounds simple enough, until you remember that one function can call another. While in the middle of one function, the program might have to execute the statements in another function. But while executing that new function, the program might have to execute yet another function!
Fortunately, Python is good at keeping track of where it is, so each time a function completes, the program picks up where it left off in the function that called it. When it gets to the end of the program, it terminates.
What’s the moral of this sordid tale? When you read a program, you don’t always want to read from top to bottom. Sometimes it makes more sense if you follow the flow of execution.
Some of the built-in functions we have seen require
arguments. For example, when you call math.sin
you pass a number as an argument.
Some functions take more than one argument: math.pow
takes two, the base and the
exponent.
Inside the function, the arguments are assigned to variables called parameters. Here is an example of a user-defined function that takes an argument:
def
print_twice
(
bruce
):
bruce
bruce
This function assigns the argument to a parameter named bruce
. When the function is called, it prints
the value of the parameter (whatever it is) twice.
This function works with any value that can be printed.
>>> print_twice('Spam') Spam Spam >>> print_twice(17) 17 17 >>> print_twice(math.pi) 3.14159265359 3.14159265359
The same rules of composition that apply to built-in functions
also apply to user-defined functions, so we can use any kind of
expression as an argument for print_twice
:
>>> print_twice('Spam '*4) Spam Spam Spam Spam Spam Spam Spam Spam >>> print_twice(math.cos(math.pi)) -1.0 -1.0
The argument is evaluated before the function is called, so in the
examples the expressions 'Spam
'*4
and math.cos(math.pi)
are only evaluated once.
You can also use a variable as an argument:
>>> michael = 'Eric, the half a bee.' >>> print_twice(michael) Eric, the half a bee. Eric, the half a bee.
The name of the variable we pass as an argument (michael
) has nothing to do with the name of
the parameter (bruce
). It doesn’t
matter what the value was called back home (in the caller); here in
print_twice
, we call
everybody bruce
.
When you create a variable inside a function, it is local, which means that it only exists inside the function. For example:
def
cat_twice
(
part1
,
part2
):
cat
=
part1
+
part2
print_twice
(
cat
)
This function takes two arguments, concatenates them, and prints the result twice. Here is an example that uses it:
>>> line1 = 'Bing tiddle ' >>> line2 = 'tiddle bang.' >>> cat_twice(line1, line2) Bing tiddle tiddle bang. Bing tiddle tiddle bang.
When cat_twice
terminates, the variable cat
is
destroyed. If we try to print it, we get an exception:
>>> print cat NameError: name 'cat' is not defined
Parameters are also local. For example, outside print_twice
, there is no such
thing as bruce
.
To keep track of which variables can be used where, it is sometimes useful to draw a stack diagram. Like state diagrams, stack diagrams show the value of each variable, but they also show the function each variable belongs to.
Each function is represented by a frame. A frame is a box with the name of a function beside it and the parameters and variables of the function inside it. The stack diagram for the previous example is shown in Figure 3-1.
The frames are arranged in a stack that indicates which function
called which, and so on. In this example, print_twice
was called by cat_twice
, and cat_twice
was called by __main__
, which is a special name
for the topmost frame. When you create a variable outside of any
function, it belongs to __main__
.
Each parameter refers to the same value as its corresponding
argument. So, part1
has the same
value as line1
, part2
has the same value as line2
, and bruce
has the same value as cat
.
If an error occurs during a function call, Python prints the name
of the function, and the name of the function that called it, and the
name of the function that called that, all the way
back to __main__
.
For example, if you try to access cat
from within print_twice
, you get a NameError
:
Traceback (innermost last): File "test.py", line 13, in __main__ cat_twice(line1, line2) File "test.py", line 5, in cat_twice print_twice(cat) File "test.py", line 9, in print_twice print cat NameError: name 'cat' is not defined
This list of functions is called a traceback. It tells you what program file the error occurred in, and what line, and what functions were executing at the time. It also shows the line of code that caused the error.
The order of the functions in the traceback is the same as the order of the frames in the stack diagram. The function that is currently running is listed at the bottom.
Some of the functions we are using, such as the math
functions, yield results; for lack of a better name, I call them
fruitful functions. Other functions,
like print_twice
,
perform an action but don’t return a value. They are called void functions.
When you call a fruitful function, you almost always want to do something with the result; for example, you might assign it to a variable or use it as part of an expression:
x = math.cos(radians) golden = (math.sqrt(5) + 1) / 2
When you call a function in interactive mode, Python displays the result:
>>> math.sqrt(5) 2.2360679774997898
But in a script, if you call a fruitful function all by itself, the return value is lost forever!
math.sqrt(5)
This script computes the square root of 5, but since it doesn’t store or display the result, it is not very useful.
Void functions might display something on the screen or have some
other effect, but they don’t have a return value. If you try to assign
the result to a variable, you get a special value called None
.
>>> result = print_twice('Bing') Bing Bing >>> print result None
The value None
is not the same
as the string 'None'
. It
is a special value that has its own type:
>>> print type(None) <type 'NoneType'>
The functions we have written so far are all void. We will start writing fruitful functions in a few chapters.
It may not be clear why it is worth the trouble to divide a program into functions. There are several reasons:
Creating a new function gives you an opportunity to name a group of statements, which makes your program easier to read and debug.
Functions can make a program smaller by eliminating repetitive code. Later, if you make a change, you only have to make it in one place.
Dividing a long program into functions allows you to debug the parts one at a time and then assemble them into a working whole.
Well-designed functions are often useful for many programs. Once you write and debug one, you can reuse it.
Python provides two ways to import modules; we have already seen one:
>>> import math >>> print math <module 'math' (built-in)> >>> print math.pi 3.14159265359
If you import math
, you get a
module object named math
. The module
object contains constants like pi
and
functions like sin
and exp
.
But if you try to access pi
directly, you get an error.
>>> print pi Traceback (most recent call last): File "<stdin>", line 1, in <module> NameError: name 'pi' is not defined
As an alternative, you can import an object from a module like this:
>>> from math import pi
Now you can access pi
directly,
without dot notation.
>>> print pi 3.14159265359
Or you can use the star operator to import everything from the module:
>>> from math import * >>> cos(pi) -1.0
The advantage of importing everything from the math module is that your code can be more concise. The disadvantage is that there might be conflicts between names defined in different modules, or between a name from a module and one of your variables.
If you are using a text editor to write your scripts, you might run into problems with spaces and tabs. The best way to avoid these problems is to use spaces exclusively (no tabs). Most text editors that know about Python do this by default, but some don’t.
Tabs and spaces are usually invisible, which makes them hard to debug, so try to find an editor that manages indentation for you.
Also, don’t forget to save your program before you run it. Some development environments do this automatically, but some don’t. In that case the program you are looking at in the text editor is not the same as the program you are running.
Debugging can take a long time if you keep running the same, incorrect, program over and over!
Make sure that the code you are looking at is the code you are
running. If you’re not sure, put something like print 'hello'
at the beginning of the program and
run it again. If you don’t see hello
, you’re not running the right
program!
A named sequence of statements that performs some useful operation. Functions may or may not take arguments and may or may not produce a result.
A statement that creates a new function, specifying its name, parameters, and the statements it executes.
A value created by a function definition. The name of the function is a variable that refers to a function object.
A name used inside a function to refer to the value passed as an argument.
A statement that executes a function. It consists of the function name followed by an argument list.
A value provided to a function when the function is called. This value is assigned to the corresponding parameter in the function.
A variable defined inside a function. A local variable can only be used inside its function.
The result of a function. If a function call is used as an expression, the return value is the value of the expression.
A file that contains a collection of related functions and other definitions.
A statement that reads a module file and creates a module object.
A value created by an import
statement that provides access to
the values defined in a module.
The syntax for calling a function in another module by specifying the module name followed by a dot (period) and the function name.
Using an expression as part of a larger expression, or a statement as part of a larger statement.
The order in which statements are executed during a program run.
A graphical representation of a stack of functions, their variables, and the values they refer to.
A box in a stack diagram that represents a function call. It contains the local variables and parameters of the function.
A list of the functions that are executing, printed when an exception occurs.
Exercise 3-3.
Python provides a built-in function called len
that returns the length of a string, so
the value of len('allen')
is 5.
Write a function named right_justify
that takes a string named
s
as a parameter and prints the
string with enough leading spaces so that the last letter of the
string is in column 70 of the display.
>>> right_justify('allen') allen
Exercise 3-4.
A function object is a value you can assign to a
variable or pass as an argument. For example, do_twice
is a function that takes a function
object as an argument and calls it twice:
def
do_twice
(
f
):
f
()
f
()
Here’s an example that uses do_twice
to call a function named print_spam
twice.
def
print_spam
():
'spam'
do_twice
(
print_spam
)
Type this example into a script and test it.
Modify do_twice
so that it takes two arguments, a
function object and a value, and calls the function twice, passing
the value as an argument.
Write a more general version of print_spam
, called print_twice
, that takes a string as a
parameter and prints it twice.
Use the modified version of do_twice
to call print_twice
twice, passing 'spam'
as an
argument.
Define a new function called do_four
that takes a function object and a
value and calls the function four times, passing the value as a
parameter. There should be only two statements in the body of this
function, not four.
Solution: http://thinkpython.com/code/do_four.py.
Exercise 3-5.
This exercise can be done using only the statements and other features we have learned so far.
Write a function that draws a grid like the following:
+ - - - - + - - - - + | | | | | | | | | | | | + - - - - + - - - - + | | | | | | | | | | | | + - - - - + - - - - +
Hint: to print more than one value on a line, you can print a comma-separated sequence:
print '+', '-'
If the sequence ends with a comma, Python leaves the line unfinished, so the value printed next appears on the same line.
print '+', print '-'
The output of these statements is '+ -'
.
A print
statement all by
itself ends the current line and goes to the next line.
Write a function that draws a similar grid with four rows and four columns.
Solution: http://thinkpython.com/code/grid.py. Credit: This exercise is based on an exercise in Oualline, Practical C Programming, Third Edition, O’Reilly Media, 1997.