Functions

=========

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.

Function calls

--------------

We have already seen one example of a **function call**:

::

>>> type(42)

<class '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 also called the **return value**.

Python provides 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'

Math functions

--------------

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 functions in a module, we have to import it with

an **import statement**:

::

>>> import math

This statement creates a **module object** named math. If you display

the module object, you get some information about it:

::

>>> 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 ``math.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 180 and multiply by :math:`\pi`:

::

>>> degrees = 45

>>> radians = degrees / 180.0 * math.pi

>>> math.sin(radians)

0.707106781187

The expression math.pi gets the variable pi from the math module. Its

value is a floating-point approximation of :math:`\pi`, accurate to

about 15 digits.

If you know 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

Composition

-----------

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

Adding new functions

--------------------

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

run when the function is called.

Here is an example:

::

def print_lyrics():

print("I'm a lumberjack, and I'm okay.")

print("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 underscore 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, indentation is always four

spaces. 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.

All quotation marks (single and double) must be “straight quotes”,

usually located next to Enter on the keyboard. “Curly quotes”, like the

ones in this sentence, are not legal in Python.

If you type a function definition in interactive mode, the interpreter

prints dots (...) 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.

Defining a function creates a **function object**, which has type

``function``:

::

>>> print(print_lyrics)

<function print_lyrics at 0xb7e99e9c>

>>> type(print_lyrics)

<class '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.

Definitions and uses

--------------------

Pulling together the code fragments from the previous section, the whole

program looks like this:

::

def print_lyrics():

print("I'm a lumberjack, and I'm okay.")

print("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 effect is to create function objects. The statements

inside the function do not run 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 run

it. In other words, the function definition has to run before the

function gets called.

As an exercise, move the last line of this program to the top, so the

function call appears before the definitions. Run the program and see

what error message you get.

Now move the function call back to the bottom and move the definition of

``print_lyrics`` after the definition of ``repeat_lyrics``. What happens

when you run this program?

Flow of execution

-----------------

To ensure that a function is defined before its first use, you have to

know the order statements run in, which is called the **flow of

execution**.

Execution always begins at the first statement of the program.

Statements are run 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 don’t run 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,

runs 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

run the statements in another function. Then, while running that new

function, the program might have to run 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.

In summary, 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.

Parameters and arguments

------------------------

Some of the 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 a definition for a function that takes an

argument:

::

def print_twice(bruce):

print(bruce)

print(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(42)

42

42

>>> print_twice(math.pi)

3.14159265359

3.14159265359

The same rules of composition that apply to built-in functions also

apply to programmer-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.

Variables and parameters are local

----------------------------------

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.

Stack diagrams

--------------

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 [fig.stack].

.. figure:: figs/stack.pdf

:alt: Stack diagram.

Stack diagram.

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, 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 at the bottom.

Fruitful functions and void functions

-------------------------------------

Some of the functions we have used, such as the math functions, return

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 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))

<class 'NoneType'>

The functions we have written so far are all void. We will start writing

fruitful functions in a few chapters.

Why functions?

--------------

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.

Debugging

---------

One of the most important skills you will acquire is debugging. Although

it can be frustrating, debugging is one of the most intellectually rich,

challenging, and interesting parts of programming.

In some ways debugging is like detective work. You are confronted with

clues and you have to infer the processes and events that led to the

results you see.

Debugging is also like an experimental science. Once you have an idea

about what is going wrong, you modify your program and try again. If

your hypothesis was correct, you can predict the result of the

modification, and you take a step closer to a working program. If your

hypothesis was wrong, you have to come up with a new one. As Sherlock

Holmes pointed out, “When you have eliminated the impossible, whatever

remains, however improbable, must be the truth.” (A. Conan Doyle, *The

Sign of Four*)

For some people, programming and debugging are the same thing. That is,

programming is the process of gradually debugging a program until it

does what you want. The idea is that you should start with a working

program and make small modifications, debugging them as you go.

For example, Linux is an operating system that contains millions of

lines of code, but it started out as a simple program Linus Torvalds

used to explore the Intel 80386 chip. According to Larry Greenfield,

“One of Linus’s earlier projects was a program that would switch between

printing AAAA and BBBB. This later evolved to Linux.” (*The Linux Users’

Guide* Beta Version 1).

.. _glossary03:

Glossary

--------

.. include:: glossary/03.txt

Exercises

---------

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('monty')

monty

Hint: Use string concatenation and repetition. Also, Python provides a

built-in function called len that returns the length of a string, so the

value of ``len('monty')`` is 5.

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():

print('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.

#. Copy the definition of ``print_twice`` from earlier in this chapter

to your script.

#. 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://thinkpython2.com/code/do_four.py.

Note: This exercise should 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 of values:

::

print('+', '-')

By default, print advances to the next line, but you can override

that behavior and put a space at the end, like this:

::

print('+', end=' ')

print('-')

The output of these statements is ``'+ -'``.

A print statement with no argument 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://thinkpython2.com/code/grid.py. Credit: This exercise is

based on an exercise in Oualline, *Practical C Programming, Third

Edition*, O’Reilly Media, 1997.