Testing Re nements by Re ning Tests

One of the potential bene ts of formal methods is that they o er the possibility of reducing the costs of testing. A speci cation acts as both the benchmark against which any implementation is tested, and also as the means by which tests are generated. There has therefore been interest in developing test generation techniques from formal speci cations, and a number of di erent methods have been derived for state based languages such as Z, B and VDM. However, in addition to deriving tests from a formal speci cation, we might wish to re ne the speci cation further before its implementation. The purpose of this paper is to explore the relationship between testing and re nement. As our model for test generation we use a DNF partition analysis for operations written in Z, which produces a number of disjoint test cases for each operation. In this paper we discuss how the partition analysis of an operation alters upon re nement, and we develop techniques that allow us to re ne abstract tests in order to generate test cases for a re nement. To do so we use (and extend existing) methods for calculating the weakest data re nement of a speci cation.