Testing a function is the act of verifying that the function's behavior matches expectations. Our language of functions is now sufficiently complex that we need to start testing our implementations.

A test is a mechanism for systematically performing this verification. Tests typically take the form of another function that contains one or more sample calls to the function being tested. The returned value is then verified against an expected result. Unlike most functions, which are meant to be general, tests involve selecting and validating calls with specific argument values. Tests also serve as documentation: they demonstrate how to call a function and what argument values are appropriate.

Assertions. Programmers use assert statements to verify expectations, such as the output of a function being tested. An assert statement has an expression in a boolean context, followed by a quoted line of text (single or double quotes are both fine, but be consistent) that will be displayed if the expression evaluates to a false value.

>>> assert fib(8) == 13, 'The 8th Fibonacci number should be 13'

When the expression being asserted evaluates to a true value, executing an assert statement has no effect. When it is a false value, assert causes an error that halts execution.

A test function for fib should test several arguments, including extreme values of n.

>>> def fib_test():
        assert fib(2) == 1, 'The 2nd Fibonacci number should be 1'
        assert fib(3) == 1, 'The 3rd Fibonacci number should be 1'
        assert fib(50) == 7778742049, 'Error at the 50th Fibonacci number'

When writing Python in files, rather than directly into the interpreter, tests are typically written in the same file or a neighboring file with the suffix _test.py.

Doctests. Python provides a convenient method for placing simple tests directly in the docstring of a function. The first line of a docstring should contain a one-line description of the function, followed by a blank line. A detailed description of arguments and behavior may follow. In addition, the docstring may include a sample interactive session that calls the function:

>>> def sum_naturals(n):
        """Return the sum of the first n natural numbers.

        >>> sum_naturals(10)
        55
        >>> sum_naturals(100)
        5050
        """
        total, k = 0, 1
        while k <= n:
            total, k = total + k, k + 1
        return total

Then, the interaction can be verified via the doctest module. Below, the globals function returns a representation of the global environment, which the interpreter needs in order to evaluate expressions.

>>> from doctest import testmod
>>> testmod()
TestResults(failed=0, attempted=2)

To verify the doctest interactions for only a single function, we use a doctest function called run_docstring_examples. This function is (unfortunately) a bit complicated to call. Its first argument is the function to test. The second should always be the result of the expression globals(), a built-in function that returns the global environment. The third argument is True to indicate that we would like "verbose" output: a catalog of all tests run.

>>> from doctest import run_docstring_examples
>>> run_docstring_examples(sum_naturals, globals(), True)
Finding tests in NoName
Trying:
    sum_naturals(10)
Expecting:
    55
ok
Trying:
    sum_naturals(100)
Expecting:
    5050
ok

When the return value of a function does not match the expected result, the run_docstring_examples function will report this problem as a test failure.

When writing Python in files, all doctests in a file can be run by starting Python with the doctest command line option:

python3 -m doctest <python_source_file>

The key to effective testing is to write (and run) tests immediately after implementing new functions. It is even good practice to write some tests before you implement, in order to have some example inputs and outputs in your mind. A test that applies a single function is called a unit test. Exhaustive unit testing is a hallmark of good program design.