Verifying a Class: combining Testing and Proving

Abstract

The problem of correctness of a class C w.r.t. a specification S is discussed. A formal counterpart of the problem is the question well known in metamathematics, whether an algebraic structure is a model of a given theory. Now, this metamathematical problem has to be adapted to the context of software engineering. As a theory we consider the (algorithmic) specification S. The algebraic structure A _C induced by the class C is our candidate for a model of S. Remark, that this problem differs from the correctness' problem of an algorithm w.r.t. a pre- and a post-conditions. In the paper we consider the specification ATPQ of priority queues and the class PQS, and we verify the correctness of this class with respect to the specification ATPQ.

Programmers and software companies prefer to test software instead of proving it. Surely, proving is more difficult, testing is easier. In this article we combine these two approaches. Hence, the following actions appear in our method of verification: experiment, observe, formulate hypotheses, prove. It is our hope that this method is of general use and adapts well to many practical cases of verification of object-oriented software.