Testing can be formal, too

The paper presents a theory of program testing based on formal specifications. The formal semantics of the specifications is the basis for a notion of an exhaustive test set. Under some minimal hypotheses on the program under test, the success of this test set is equivalent to the satisfaction of the specification.The selection of a finite subset of the exhaustive test set can be seen as the introduction of more hypotheses on the program, called selection hypotheses. Several examples of commonly used selection hypotheses are presented.Another problem is the observability of the results of a program with respect to its specification: contrary to some common belief, the use of a formal specification is not always sufficient to decide whether a test execution is a success. As soon as the specification deals with more abstract entities than the program, program results may appear in a form which is not obviously equivalent to the specified results. A solution to this problem is proposed in the case of algebraic specifications.