#### Note 20.5.1. Specification-Based Tests.

Specification-based tests are tests that are designed based only on the information in the function specification, without considering any of the details in the function implementation.

Once you have designed a testable function, with a clear docstring specification, writing unit tests is not difficult. In this section, you'll learn how to do just that.

Let's start with our

`sumnums`

function:def sumnums(lo, hi): """computes the sum of a range of numbers Precondition: lo <= hi Postcondition: returns the sum of the numbers in the range [lo..hi] """ sum = 0 for i in range(lo, hi+1): sum += i return sum

As we've seen, to write a unit test, you devise test cases for the function, and then write assert statements that call the function and check that the function produced the expected results. The following assert statements would be appropriate for a unit test for

`sumnums`

:assert sumnums(1, 3) == 6 assert sumnums(1, 1) == 1

But what about the following?

assert sumnums(3, 1) == 0

Note that

`sumnums`

produces the value `0`

for cases where the `lo`

values exceeds the `hi`

value, as is the case in this assert. So, like the first two asserts above, this assert would pass. However, it is not an appropriate assertion, because the specification says nothing about what the function produces if `lo`

is greater than `hi`

.The unit test should be written such that it passes even if the function implementation is altered in a way that causes some other value than 0 to be returned if

`lo`

exceeds `hi`

. For example, we might want to redesign the function to be more efficient — for example, use Gauss's formula for summing numbers, as in the following:def sumnums(lo, hi): """computes the sum of a range of numbers Precondition: lo <= hi Postcondition: returns the sum of the numbers in the range [lo..hi] """ return (hi * (hi + 1) / 2) - (lo * (lo - 1) / 2)

This version will produce correct results if the precondition is satisfied. Like the original function, it produces incorrect results if the precondition is violated — but unlike the original function, the values produced if the precondition is violated are not necessarily 0.

A key idea to remember when writing a unit test is that your test must always respect the function's preconditions. The docstring states what the function should do, with the assumption that parameter values meet the preconditions. It does not state what the function should do if the parameter values violate the preconditions.

Writing an assert that violates the functions preconditions is not a good idea, because to determine what the function will produce for that case, you must look into the implementation of the function and analyze its behavior. That is called implementation-based testing, and it leads to brittle tests that are likely to fail if you rework the function implementation. When you write tests are based only on the function specification, without looking at the implementation, you are doing specification-based testing.

Specification-based tests are tests that are designed based only on the information in the function specification, without considering any of the details in the function implementation.

Specification-based tests are preferred over implementation-based tests, because they are more resilient. They will continue to pass even if you rework the function implementation.

Check your understanding

- assert repeat('*', 0) == ''
- Correct. The specification indicates that the function should produce an empty string.
- assert repeat('*', -1) == ''
- Incorrect. The parameter -1 violates the precondition, and such a test is inappropriate, even though the function would return an empty string in this case.
- assert repeat('-', 5) == '-----'
- Correct. The parameters satisfy the precondition and the value '-----' is appropriate given the postcondition.
- assert repeat('*', 5) == '***'
- Incorrect. The string '***' does not conform to the postcondition.

Consider the following function. Indicate which of the asserts would be appropriate for a unit test.

```
def repeat(s: str, num: int) -> str:
"""duplicates a string
Precondition: `num` >= 0
Postcondition: Returns a string containing `num` copies of `s`
"""
if num >= 0:
return s * num
else:
return ''
```

Write assert statements below to test a function with the following specification. Your asserts should check that the function produces an appropriate value for each of the three postcondition cases.

```
def grade(score):
"""Determines letter grade given a numeric score
Precondition: 0 <= `score` <= 100
Postcondition: Returns 'A' if 90 <= `score` <= 100,
'B' if 80 <= `score` < 90, 'F' if 0 <= `score` < 80
"""
```

Note: Line numbers in any assert error messages that appear while you are developing and testing your answer will not be accurate.

Solution.

The following asserts are just some of several that could have been used.

```
assert grade(92) == 'A'
assert grade(85) == 'B'
assert grade(69) == 'F'
```

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