Juan C. Bicarregui – författare

Not so many years ago, it would have been difficult to find more than a handful of examples of the use of formal methods in industry. Today however, the industrial application of formal methods is becoming increasingly common in a variety of application areas, particularly those with a safety, security or financially critical aspects. Furthermore, in situations where a particularly high level of assurance is required, formal proof is broadly accepted as being of value. Perhaps the major benefit of formalisation is that it enables formal symbolic manip­ ulation of elements of a design and hence can provide developers with a variety of analyses which facilitate the detection of faults. Proof is just one of these possible formal activities, others, such as test case generation and animation, have also been shown to be effective bug finders. Proof can be used for both validation and verifi­ cation. Validation of a specification can be achieved by proving formal statements conjectured about the required behaviours of the system. Verification of the cor­ rectness of successive designs can be achieved by proof of a prescribed set of proof obligations generated from the specifications.

This manual examines the practical aspects of using and constructing proofs in the specification and development of computing systems. The reader is guided through the elements of proof construction with the help of numerous worked examples. The techniques can be applied to specification and development in a range of formalisms, and are illustrated using the logic and the basic data types of the VDM specification language. The construction of theorems and proofs from actual specifications and refinements is also described, and a detailed case study, including several refinement steps, shows how formal proofs can be used in practice. In addition, the book contains a directory of axioms and formally proved theorems.