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Section 7.8 Boolean Functions

Subsection 7.8.1 Introduction

We have already seen that boolean values result from the evaluation of boolean expressions. Since the result of any expression evaluation can be returned by a function (using the return statement), functions can return boolean values. This turns out to be a very convenient way to hide the details of complicated tests. For example:
The name of this function is isDivisible. It is common to give boolean functions names that sound like yes/no questions. isDivisible returns either True or False to indicate whether the x is or is not divisible by y.
We can make the function more concise by taking advantage of the fact that the condition of the if statement is itself a boolean expression. We can return it directly, avoiding the if statement altogether:
def isDivisible(x, y):
    return x % y == 0
Boolean functions are often used in conditional statements:
if isDivisible(x, y):
    ... # do something ...
    ... # do something else ...
It might be tempting to write something like if isDivisible(x, y) == True: but the extra comparison is redundant. You only need an == expression if you are comparing some other type than boolean. (isDivisible(x, y) == False can also be made more concise as not isDivisible(x, y)). The following example shows the isDivisible function at work. Notice how descriptive the code is when we move the testing details into a boolean function. Try it with a few other actual parameters to see what is printed.
Here is the same program in codelens. When we evaluate the if statement in the main part of the program, the evaluation of the boolean expression causes a call to the isDivisible function. This is very easy to see in codelens.
Check your understanding

Checkpoint 7.8.1.

    What is a Boolean function?
  • A function that returns True or False
  • A Boolean function is just like any other function, but it always returns True or False.
  • A function that takes True or False as an argument
  • A Boolean function may take any number of arguments (including 0, though that is rare), of any type.
  • The same as a Boolean expression
  • A Boolean expression is a statement that evaluates to True or False, e.g. 5+3==8. A function is a series of expressions grouped together with a name that are only executed when you call the function.

Checkpoint 7.8.2.

    Is the following statement legal in a Python function (assuming x, y and z are defined to be numbers)?
    return x + y < z
  • Yes
  • It is perfectly valid to return the result of evaluating a Boolean expression.
  • No
  • x +y < z is a valid Boolean expression, which will evaluate to True or False. It is perfectly legal to return True or False from a function, and to have the statement to be evaluated in the same line as the return keyword.

Subsection 7.8.2 More Unit Testing

When we write unit tests, we should also consider output equivalence classes that result in significantly different results.
The isDivisible function can return either True or False. These two different outputs give us two equivalence classes. We then choose inputs that should give each of the different results. It is important to have at least one test for each output equivalence class.

Note 7.8.3. Extend the program ….

Starting on line 7, write two unit tests (that should pass), one for each output equivalence class.

Note 7.8.4.

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