ABSTRACT

Because of the growing importance of object-oriented programming, a number of testing approaches have been proposed. Frankl et al. propose the application of the functional approach, using algebraic specifications for the generation of test cases and the validation of methods. Given a specification, Frankl et al. propose that equivalent terms should give observably equivalent objects, and offer general heuristics on the selection of equivalent terms for testing. Their guidelines, however, are only supported by limited empirical results, do not have a theoretical basis, and provide no guarantee of effectiveness. In this paper, we define the concept of a fundamental pair as a pair of equivalent terms which are formed by replacing 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. In other words, the testing coverage of fundamental pairs is identical to that of all equivalent terms, and hence we need only concentrate on the testing of fundamental pairs. Our strategy is mathematically based, simple, and much more efficient. Furthermore, it underscores the usefulness of axiom-based specifications.

	1.	This research is supported in part by a grant of the Research Grants Council of Hong Kong and a research and conference grant of The University of Hong Kong.
	2.	(Corresponding author.)
		Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong. Email:
	3.	School of Professional and Continuing Education, The University of Hong Kong.
	4.	Department of Computer Science, Jinan University.

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