On effectiveness of equivalent fundamental pairs as test cases for object-oriented software

One of the means to enhance reliability and quality of software systems is testing. Object-oriented methodology makes resulting software systems more reliable, maintainable and reusable. However, it also renders the testing more complex and difficult. There are various sequences and combinations to execute the methods in a class or across different classes. This character leads us to select sequences of operations (namely ground terms), rather than individual operations, as test cases in object-oriented class level testing. The pairs of equivalent ground terms can be derived as test cases from a given algebraic specification for a class. If two ground terms are equivalent, but their implemented sequences produce observationally non-equivalent objects, then there is an error in the implementation. However, the set of all equivalent pairs is generally infinite. How do we select a finite number of them? Recently, we have proposed an approach to deal with this problem. In our approach, a fundamental pair is defined as a pair of equivalent terms produced by substituting all the variables on both sides of an axiom by normal forms. We prove that an implementation is consistent with respect to all equivalent terms if and only if it is consistent with respect to all fundamental pairs.