The B-Book
Assigning Programs to Meanings

The definitive book on the B Method; essential for all working in formal methods and safety-critical software.

J. R. Abrial (Author), A. Hoare (Foreword by), Pierre Chapron (Foreword by)

9780521021753, Cambridge University Press

Paperback / softback, published 3 November 2005

816 pages
24.6 x 17.2 x 4.6 cm, 1.274 kg

'It will act as the reference book for many involved in the application of the B-Method … The B-Book provides a comprehensive reference for the B approach to specifying, designing and coding software systems.' Jonathan Bowen, The Times Higher Education Supplement

The B Method is a means for specifying, designing and coding software systems. The long-awaited B-Book is the standard reference for everything concerning this method. It contains the mathematical basis on which it is founded, the precise definitions of the notations used, and a large number of examples illustrating its use in practice. J.-R. Abrial, the inventor of B, has written the book in such a way that it can be used for self-study or for reference. It is in four parts, the first dealing with the mathematical foundations and the definition of the various mathematical structures that are needed to formalise software systems; special emphasis is placed on the notion of proof. The second part contains a presentation of the Generalised Substitution Language and of the Abstract Machine Notation; examples are given to show how large specifications can be constructed systematically. The next part introduces the two basic programming features of sequencing and loop. The last part covers the very important notion of refinement. It shows how to construct large software systems by means of layered architectures of modules. With the appearance of The B-Book, formal methods practitioners, computer scientists, and systems developers at last will have access to the definitive account of what will become one of the standard approaches to the construction of software systems.

Tribute
Foreword
Introduction
Part I. Mathematics: 1. Mathematical reasoning
2. Set notation
3. Mathematical objects
Part II. Abstract Machines: 4. Introduction to abstract machines
5. Formal definition of abstract machines
6. Theory of abstract machines
7. Constructing large abstract machines
8. Examples of abstract machines
Part III. Programming: 9. Sequencing and loop
10. Programming examples
Part IV. Refinement: 11. Refinement
12. Constructing large software systems
13. Examples of refinement
Appendixes
Index.

Subject Areas: Mathematical theory of computation [UYA], Software Engineering [UMZ]