Model-Oriented Proof Methods and their Comparison
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- Willem-Paul de Roever, Christian-Albrechts Universität zu Kiel, Germany
- Kai Engelhardt, University of Technology, Sydney
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The goal of this book is to provide a comprehensive and systematic introduction to the important and highly applicable method of data refinement and the simulation methods used for proving its correctness. The authors concentrate in the first part on the general principles needed to prove data refinement correct. They begin with an explanation of the fundamental notions, showing that data refinement proofs reduce to proving simulation. The topics of Hoare Logic and the Refinement Calculus are introduced and a general theory of simulations is developed and related to them. Accessibility and comprehension are emphasized in order to guide newcomers to the area. The book's second part contains a detailed survey of important methods in this field, such as VDM, and the methods due to Abadi & Lamport, Hehner, Lynch and Reynolds, Back's refinement calculus and Z. All these methods are carefully analysed, and shown to be either imcomplete, with counterexamples to their application, or to be always applicable whenever data refinement holds. This is shown by proving, for the first time, that all these methods can be described and analyzed in terms of two simple notions: forward and backward simulation. The book is self-contained, going from advanced undergraduate level and taking the reader to the state of the art in methods for proving simulation.Read more
- Broad-based and comparative treatment of methods
- Exercises provided for students
- Historical illustrations
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"The presentation of the theory is backed up by some substantial examples...and this together with the extensive historical notes makes the book an extremely useful reference manual and graduate text."
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- Date Published: March 2011
- format: Adobe eBook Reader
- isbn: 9780511836503
- contains: 18 b/w illus. 93 exercises
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
Part I. Theory:
1. Introduction to data refinement
2. Simulation as a proof method for data refinement
3. Relations and recursion
4. Properties of simulation
5. Notation and semantics
6. A Hoare logic
7. Simulation and Hoare logic
8. An extension to total correctness
9. Simulation and total correctness
10. Refinement calculus
Part II. Applications:
11. Reynolds' method
13. Z, Hehner's method and Back's refinement calculus
14. Refinement methods due to Abadi & Lamport and Lynch. Appendix A. An introduction to Hoare logic
Appendix B. A primer on ordinals and transfinite induction
Appendix C. Notational convention
Appendix D. Precedences
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