Chapter 6¹ described how each function has a name, may have some parameters, and may have a return value. When you create your own functions, you need to define each of these. To create a function, you use the following syntax:

def <function_name>( <parameter_list> ):
    <statements>

The function name must meet the same requirements that variable names must meet, i.e., only letters, digits, and underscores, and it cannot start with a digit. The parameter list consists of zero or more variable names, with commas in between. The code block below the function definition must be indented.

Finally, be aware that Python must have “seen” your function definition before it sees the call to it in your code. Therefore it is convention to place all function definitions at the top of a program, right under the import statements.

How Python deals with functions

To be able to create functions, you have to know how Python deals with functions. Look at the small Python program below. It defines one function, called goodbyeWorld(). That function has no parameters. The code block for the function prints the line “Goodbye, world!”

The rest of the program is not part of a function. We often call the parts of a program that are not inside a function the “main” program. The main program prints the line “Hello, world!,” and then calls the function goodbyeWorld().

def goodbyeWorld():
    print( "Goodbye, world!" )

print( "Hello, world!" )
goodbyeWorld()

When you run this program, you see that it first prints “Hello, world!,” and then “Goodbye, world!” This happens even though Python processes code top-down, so that it sees the line print( "Goodbye, world!" ) before it sees the line print( "Hello, world!" ). This is because Python does not actually run the code inside functions, at least, not until the moment that the function gets called. Python does not even look at the code in functions. It just notices the function name, registers that the function is defined so that it can be used, and then continues, searching for the main program to run.

Parameters and arguments

Examine the code below. It defines a function hello() with one parameter, which is called name. The function uses the variable name in the code block. There is no explicit assignment of the variable name, it exists because it is a parameter of the function.

When a function is called, you must provide a value for every (mandatory) parameter that is defined for the function. Such a value is called an “argument.” Therefore, to call the function hello(), you must provide an argument for the parameter name. You place this argument between the parentheses of the function call. Note that in your main program you do not need to know that this parameter is called name. What it is called is unimportant. The only thing you need to know is that there is a parameter that needs a value, and preferably what kind of value the function is expecting (i.e., what the author of the function expects you to provide).

def hello( name ):
    print( "Hello, {}!".format( name ) )

hello( "Adrian" )
hello( "Binky" )
hello( "Caroline" )
hello( "Dante" )

The parameters of a function are no more and no less than variables that you can use in the function, and that get their value from outside the function (namely by a function call). The parameters are “local” to the function, i.e., they are not accessible outside the code block of the function, nor do they influence any variable values outside the function. More on that later.

Functions can have multiple parameters. For example, the following function multiplies two parameters and prints the result:

def multiply( x, y ):
    result = x * y
    print( result )

multiply( 2020, 5278238 )
multiply( 2, 3 )

Parameter types

In many programming languages, you specify what the data types of the parameters of the functions that you create are. This allows the language to check whether calls to the functions are made with correct arguments. In Python, you do not specify data types. This means that, for example, the multiply() function in the code block above can be called with string arguments. If you do so, you will generate a runtime error (as you cannot multiply two strings).

If you want to write a “safe” function, you can check the type of arguments that the function is provided with, using the isinstance() function. isinstance() gets a value or a variable as first parameter, and a type as second parameter. It returns True if the value or variable is of the specified type, and False otherwise. For example:

a = "Hello"
if isinstance( a, int ):
    print( "integer" )
elif isinstance( a, float ):
    print( "float" )
elif isinstance( a, str ):
    print( "string" )
else:
    print( "other" )

Of course, should you decide to do such type checking in a function, you must decide what you will do if the user provides the wrong type. The regular way to handle this is by “raising an exception.” This will be discussed in Chapter 18². For now, you may assume that the functions that you write are called with parameters of the correct types. As long as you write functions for your own use, you can always guarantee that.

Default parameter values

It is possible to provide default values for some of the parameters. You do this by placing an assignment operator and value next to the parameter name, as if it is a regular assignment. When calling the function, you can specify all parameters, or just some of them. In principle the values get passed to the function’s parameters from left to right; if you pass fewer values than there are parameters, as long as default values for the remaining parameters are given, the function call gets executed without runtime errors.

If you define a function with default values for some of the parameters, but not all, it is common to place the ones for which you give a default value to the right of the ones for which you do not.

If you want to override the default value for a specific parameter, and you know its name but not its place in the order of the parameters, or you simply want to leave the other parameters at their default value, you can actually in the function call give a value to a specific parameter by name, using an assignment between the parentheses, i.e., <function>( <parametername>=<value> ).

The following code gives examples of these possibilities:

def multiply_xyz( x, y=1, z=7 ):
    print( x * y * z )
    
multiply_xyz( 2, 2, 2 ) # x=2, y=2, z=2
multiply_xyz( 2, 5 )    # x=2, y=5, z=7
multiply_xyz( 2, z=5 )  # x=2, y=1, z=5

return

Parameters can be used to communicate information from outside a function to the code block of the function. Often, you also want a function to communicate information to the rest of the program outside the function. The keyword return accomplishes this.

When you use the command return in a function, that ends the processing of the function, and Python will continue with the code that comes after the call to the function. You can put one or more values or variables after the return statement. These values are communicated to the program outside the function. If you want to use them outside the function, you can put them into a variable when you assign the call to the function to that variable.

For instance, suppose a function is called using a statement <variable> = <function>(). The function makes a calculation and stores it as <result>. return <result> then ends the function, and the value stored in <result> “comes out of” the function. Due to the way <function>() was called, this value ends up in <variable>.

If this sounds a bit convoluted, it will probably become clear after studying the following example:

from math import sqrt

def pythagoras( a, b ):
    return sqrt( a*a + b*b )

c = pythagoras( 3, 4 )
print( c )

The function pythagoras() calculates the value of the square root of the sum of the squares of its two parameters. Then it returns that value, using the return statement. The main program “captures” the value by assigning it to variable c, then prints the contents of c.

Note that the return statement in the example above has a complete calculation with it. That calculation is done in the function, which leads to a value. It is the result of the calculation, i.e., the value, which is returned to the main program.

Now suppose that you want to only do this calculation for positive numbers (which would not be strange, as the function clearly is meant to calculate the length of the diagonal side of a right triangle, and who ever heard of a triangle with sides of length zero or less). Examine this code:

from math import sqrt

def pythagoras( a, b ):
    if a <= 0 or b <= 0:
        return
    return sqrt( a*a + b*b )

print( pythagoras( 3, 4 ) )
print( pythagoras( -3, 4 ) )

At first glance this code might seem fine: as it has nothing to calculate for negative numbers, it just returns no value. However, when you run this program you find it prints the special value None. I discussed this special value in Chapter 6³. The main program expected the function pythagoras() to return a number, so pythagoras() is failing its duties by returning nothing in certain circumstances. You should always be very clear about what data type your function returns, and ensure that in each and every circumstance the function actually returns a value of that type. By the way, the following code is equivalent to the code above (and has the same mistake):

from math import sqrt

def pythagoras( a, b ):
    if a > 0 and b > 0:
        return sqrt( a*a + b*b )

print( pythagoras( 3, 4 ) )
print( pythagoras( -3, 4 ) )

In this code, you do not see the return without a value explicitly, but it is there nonetheless. If Python reaches the end of a function code block without having found a return, it will return from the function without a value.

If you wonder what you should return in circumstances that you do not have a good return value for: that depends on the application. For instance, for the pythagoras() function, you could decide that it will return \(-1\) whenever it gets provided with arguments that it cannot process. As long as you communicate that to the user of a function, the user can ensure that the main program handles such exceptional cases in the spirit of the program as a whole. For instance:

from math import sqrt
from pcinput import getInteger

def pythagoras( a, b ):
    if a <= 0 or b <= 0:
        return -1
    return sqrt( a*a + b*b )

num1 = getInteger( "Give side 1: " )
num2 = getInteger( "Give side 2: " )
num3 = pythagoras( num1, num2 )
if num3 < 0:
    print( "The numbers you provided cannot be used." )
else:
    print( "The diagonal side's length is", num3 )

Note that every line of code in the function that occurs immediately after a return at the same level of indentation will always be ignored. E.g., in the function:

from math import sqrt

def pythagoras( a, b ):
    if a <= 0 or b <= 0:
        return -1
        print( "This line will never be printed" )
    return sqrt( a*a + b*b )

the line below return -1 clearly states how useless it is.

Difference between return and print

I noticed in the past that many students struggle with the difference between a function returning a value and a function printing a value. Compare the following two pieces of code:

def print3():
   print( 3 )
print3()

and:

def return3():
   return 3
print( return3() )

Both the function print3() and return3() are called in their respective codes, and result in the printing of the value 3. The difference is that the printing of this value in the case of print3() happens in the function, while the function returns nothing, while in the case of return3() the function only returns the value 3, which is then printed in the main program. For the user the result of these codes looks the same: both display the number 3. But for the programmer the two functions involved are quite different.

The function print3() can only be used for one purpose, namely to display the number 3. The function return3(), however, can be used wherever I need the number 3, regardless whether I need to display it, use it in a calculation, or assign it to a variable. For instance, the following code raises 2 to the power of 3 and prints the result:

def return3():
   return 3
x = 2 ** return3()
print( x )

On the other hand, the following code leads to a runtime error when executed:

def print3():
    print( 3 )
x = 2 ** print3() # Erroneous code!
print( x )

The reason is that while print3() displays the value of 3 on the screen (you even see it above the runtime error when you run the code), it does not produce the actual value 3 in such a way that the calculation can use it. The function print3() actually returns the special value None, which cannot be used in a calculation.

So, if you want to create a function that produces a value that can be used in other parts of the program, then the function must return that value. If you want to create a function that just displays something on the screen, you can use a print statement in the function to do that, but the function does not need to return anything.

Welcome to the machine

If you still have troubles imagining how functions work, think of them like this:

A function is like a big machine, for instance, a machine that makes pancakes. It has some input hoppers at the top, which are labeled “milk,” “eggs,” and “flour.” Those are the input parameters. You can decide what pancakes you want by putting the right stuff in the hoppers; for instance, if you want whole-grain pancakes, you put whole-grain flour into the “flour” hopper. Of course, you can be certain that things will go dramatically wrong if you put eggs into the “milk” hopper – or you try to put a cat into the “flour” hopper.

Anyway, once the hoppers are loaded the machine starts huffing and puffing. You patiently wait next to the output hopper which, surprise surprise, is labeled “return.” And after a short while, a pancake slides out. The pancake is the return value that the machine produced.

The machine also has a display. Maybe after you put something inappropriate into the “flour” hopper, the display says: “Cat stuck in the machine, please reset.” The display is where everything that you “print” in the machine appears.

Now, you understand that it is useless if, after loading the right ingredients into the input hopper, the machine just displays “Pancake is ready!” You want the actual pancake. That’s why the machine must “return” it via its output hopper, from which you can take it and “assign” it to your lunch plate. Just printing that the pancake exists is not sufficient.

By the way, one of the nice things about the pancake making machine is that even if you do not know how pancakes are made, you can still get pancakes as long as you manage to supply the right ingredients. That’s also what is so nice about functions: they may do complex things for you without you needing to know how they accomplish them.

Multiple return values

In your functions, you are not limited to returning just one value. You can return multiple values by putting commas in between. If you want to use these values in the program after the call to the function, you have to assign them to multiple variables. You put them to the left of the assignment, also with commas in between. This is easiest to illustrate with and example:

import datetime

def addDays( year, month, day, dayincrement ):
    startdate = datetime.datetime( year, month, day )
    enddate = startdate + datetime.timedelta( days=dayincrement )
    return enddate.year, enddate.month, enddate.day

y, m, d = addDays( 2015, 11, 13, 55 )
print( "{}/{}/{}".format( y, m, d ) )

The function addDays() gets four arguments, namely integers indicating a year, a month, and a day, and a number of days that you want to add to that date. It returns three values, namely a new year, month, and day. These are in this code captured in the main program in three variables, namely y, m, and d.

When you look at the code above, you might be mystified how exactly addDays() is doing its job. As I said, it’s a nice thing about functions that as long as the function works and you know what arguments it wants and what it returns, you can use the function without any knowledge of its internal process. So you can just ignore the code for addDays() (note: the contents of addDays() use the datetime module, which is discussed in Chapter 28⁴).

Calling functions from functions

Functions are allowed to call other functions, as long as those other functions are known to the calling function. For instance, the following code shows how the function euclideanDistance() uses the function pythagoras() to calculate the distance between two points in 2-dimensional space.

from math import sqrt

def pythagoras( a, b ):
    if a <= 0 or b <= 0:
        return -1
    return sqrt( a*a + b*b )

def euclideanDistance( x1, y1, x2, y2 ):
    return pythagoras( abs( x1 - x2 ), abs( y1 - y2 ) )

print( euclideanDistance( 1, 1, 4, 5 ) )

euclideanDistance() knows pythagoras(), because pythagoras() was defined before euclideanDistance() is called.

If you want, you can put functions inside other functions, i.e., you can “nest” functions. For instance, you can place pythagoras() in euclideanDistance(). That means that pythagoras() can be called inside euclideanDistance(), but not elsewhere in the program.

from math import sqrt

def euclideanDistance( x1, y1, x2, y2 ):

    def pythagoras_inside( a, b ):
        if a <= 0 or b <= 0:
            return -1
        return sqrt( a*a + b*b )

    return pythagoras_inside( abs( x1 - x2 ), abs( y1 - y2 ) )

print( euclideanDistance( 1, 1, 4, 5 ) )
# print( pythagoras_inside( 3, 4 ) )

It is not very common that nested functions are used, but it is possible.

Note: if you remove the hash mark before the last line of the code above, it adds a call to pythagoras_inside(). This will cause a runtime error, as pythagoras_inside() is only visible inside euclideanDistance().

Write a function called printx() that just prints the letter “x.” Then write a function called multiplex() which takes as argument an integer and prints as many times the letter “x” as the integer indicates by calling the function printx() that many times.

Naming functions

Convention prescribes that you should not start a function name with an underscore (such function names are reserved for the developers of Python itself), and that you try to use only lower case letters. If the function name consists of multiple words, you can either put underscores between the words, or start every word except the first with a capital (different programmers prefer different conventions in this respect, but it does not matter much as you can always recognize a function by the fact that it has parentheses after the name).

Certain function names are typical for particular functionalities.

A function that tests if a certain item has a certain property, which then returns either True or False depending on whether the property holds, commonly has a name that starts with the word is, which is then followed by the name of the property, starting with a capital. For instance, a function that tests if a number is even, would be called isEven().

Write the function isEven().

Write the function isOdd(), which determines whether a number is odd, by calling the function isEven() and inverting its result.

Note: if you want to use a function like isEven() in a conditional statement, for instance, because you want to execute an action only for numbers that are even, you do not need to write if isEven( num ) == True:. You can simply write if isEven( num ):, because the function already returns True or False. Using an is-function in such a way makes a program more readable.

A function that gets the value of a certain property and returns it, commonly starts with the word get, which is then followed by the name of the property, starting with a capital. For instance, a functions that gets the fractional part of a float (i.e., the decimals) would be called getFraction().

Write the function getFraction().

The opposite of a get function is a function that gives a property a certain value. Such a function commonly starts with set, and for the rest is similar to a get function. I cannot give an example as at this point I have not yet explained how you can use a function to give something a value, as functions cannot change the values of their parameters (at least, for the data types that we have used until now). This will follow in a later chapter.

If you stick to such naming conventions, it will make your code more readable.

Commenting functions

In all the chapters until now, you have seen very little commenting of code. While books and courses on programming often encourage students to write comments in code, I myself am of the opinion that code should be “self-documenting,” i.e., that you can easily derive from code what it does simply by reading it. You can accomplish that often by choosing strong names for variables and functions, judiciously using white spaces and empty lines, good indenting (which Python enforces), and not using any convoluted trickery just because it makes the code a little bit faster or to show off how smart you are.¹⁵

So while I see comments as an extra that you should use when you feel you need to explain something particular about your code, my opinion on comments for functions is different. The idea behind a function is that the user of the function does not need to look at the function’s code to use it. Therefore, what the function does and how it works, should be explained in comments at the top of the function, above the function name.

In the comments for a function, you explain three things:

• What the function does

• What arguments the function needs/accepts, including data types

• What the function returns, including data types

If a function has any side effects, i.e., things it affects in the main program, then this should be carefully documented in the comments too. I do not put that in the list above, because a function should not have any side effects.

Note: For the answers to the exercises in this chapter I have added comments to the functions in a form that I find acceptable. In follow-up chapters I often will not do that as I discuss the functions in text anyway, or I want you to study the contents of the function. However, I always write comments for functions that I write in code that I use for other purposes.