On the Refinement Calculus [Paperback]

On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.The Specification Statement.- 1 Introduction.- 2 Specification statements.- 3 The implementation ordering.- 4 Suitability of the definitions.- 5 Using specification statements.- 6 Miracles.- 7 Guarded commands are miracles.- 8 Positive applications of miracles.- 9 Conclusion.- 10 Acknowledgements.- Specification Statements and Refinement.- 1 Introduction.- 2 The refinement theorems.- 3 The refinement calculus.- 4 An example: square root.- 5 Derivation of laws.- 6 Conclusion.- 7 Acknowledgements.- Procedures, Parameters, and Abstraction: Separate Concerns.- 1 Introduction.- 2 Procedure call.- 3 Procedural abstraction.- 4 Parameters.- 5 Conclusion.- 6 Acknowledgements.- Data Refinement by Miracles.- 1 Introduction.- 2 An abstract program.- 3 A difficult data refinement.- 4 Miraculous programs.- 5 Eliminating miracles.- 6 Conclusion.- 7 Acknowledgements.- Auxiliary Variables in Data Refinement.- 1 Introduction.- 2 The direct technique.- 3 The auxiliary variable technique.- 4 The correspondence.- 5 Conclusion.- 6 Acknowledgements.- Data Refinement of Predicate Transformers.- 1 Introduction.- 2 Predicate transformers.- 3 Algorithmic refinement of predicate transformers.- 4 Data refinement of predicate transformers.- 5 The programming language.- 6 Distribution of lS