In addition, the book contains a directory of axioms and formally proved theorems.

Formal specifications were first used in the description of program ming languages because of the central role that languages and their compilers play in causing a machine to perform the computations required by a programmer. In a relatively short time, specification notations have found their place in industry and are used for the description of a wide variety of software and hardware systems. A formal method - like VDM - must offer a mathematically-based specification language. On this language rests the other key element of the formal method: the ability to reason about a specification. Proofs can be empioyed in reasoning about the potential behaviour of a system and in the process of showing that the design satisfies the specification. The existence of a formal specification is a prerequisite for the use of proofs; but this prerequisite is not in itself sufficient. Both proofs and programs are large formal texts. Would-be proofs may therefore contain errors in the same way as code. During the difficult but inevitable process of revising specifications and devel opments, ensuring consistency is a major challenge. It is therefore evident that another requirement - for the successful use of proof techniques in the development of systems from formal descriptions - is the availability of software tools which support the manipu lation of large bodies of formulae and help the user in the design of the proofs themselves.

Klappentext

BProof in VDM: A Practitioners' Guide/B is a textbook and manual on the practical aspects of using and constructing proofs in the specification and development of computing systems. Many introductory courses on formal techniques are, by their nature, unable to cover the pragmatics of proof. Practitioners competent in writing and comprehending formal specifications are therefore often at a loss when it comes to conducting the relevant proofs. BProof in VDM: A /B BPractitioners' Guide/B addresses that need. 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 proof can be used in practice. In addition, the book contains a directory of axioms and formally proved theorems.

Inhalt
1 Introduction.- 1.1 Background.- 1.2 How proofs arise in practice: an introductory example.- 1.3 A logical framework for proofs.- 1.4 Summary.- I A Logical Basis for Proof in VDM.- 2 Propositional LPF.- 3 Predicate LPF with Equality.- 4 Basic Type Constructors.- 5 Numbers.- 6 Finite Sets.- 7 Finite Maps.- 8 Finite Sequences.- 9 Booleans.- II Proof in Practice.- 10 Proofs From Specifications.- 11 Verifying Reifications.- 12 A Case Study in Air-Traffic Control.- 13 Advanced Topics.- III Directory of Theorems.- 14 Directory of Theorems.- Index of Symbols.- Index of Rules.