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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Calculus > On the Refinement Calculus: (Formal Approaches to Computing & Information Technology (FACIT))
On the Refinement Calculus: (Formal Approaches to Computing & Information Technology (FACIT))

On the Refinement Calculus: (Formal Approaches to Computing & Information Technology (FACIT))


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About the Book

This volume collects the work accomplished at Oxford on the refinement calculus: the rigorous development, from state-based assertional specifications, of executable imperative code. The refinement calculus is a notation and set of rules for deriving imperative programs from their specifications. It is distinguished from earlier methods (though based on them) because the derivations are carried out within a single 'programming' language: there is no separate language of specifications. So far, it has uncovered 'miracles', novel techniques of data refinement, a simpler treatment of procedures, 'conjunction' of programs, and a light-weight treatment of types in simple imperative programs. State-based assertional specification - in the Z style - was established at Oxford by J.-R. Abrial and much developed during the 1980's. Its principal effects on the minds of those who encountered it were: first, an exhilaration that one, at last, could be both abstract and yet precise; second, the realization that its mathematical nature allowed rigorous reasoning about and exploration of proposed designs; and third, a desire to proceed rigorously from such specifications to executable code. The integration of specifications and code was proposed by R.-J. R. Back in the late 1970's, when he inserted specifications into Dijkstra's language based on weakest preconditions. At Oxford, this same idea, although much later, was amplified both by the strong research tradition in specification and by the challenge offered by the University's undergraduate degree course in computer science, which started in 1985. 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 provides excellent reference material for all t hose seeking the background and mathematical underpinnings of the refinement calculus.

Table of Contents:
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 data refinement.- 7 Data refinement of specifications.- 8 Data refinement in practice.- 9 Conclusions.- 10 Acknowledgements.- Data Refinement by Calculation.- 1 Introduction.- 2 Refinement.- 3 Language extensions.- 4 Data refinement calculators.- 5 Example of refinement: the "mean" module.- 6 Specialized techniques.- 7 Conclusions.- 8 Acknowledgements.- 9 Appendix: refinement laws.- A Single Complete Rule for Data Refinement.- 1 Introduction.- 2 Data refinement.- 3 Predicate transformers.- 4 Completeness.- 5 Soundness.- 6 Partial programs.- 7 An example.- 8 Conclusion.- 9 Acknowledgements.- Types and Invariants in the Refinement Calculus.- 1 Introduction.- 2 Invariant semantics.- 3 The refinement calculus.- 4 A development method.- 5 Laws for local invariants.- 6 Eliminating local invariants.- 7 Type-checking.- 8 Recursion.- 9 Examples.- 10 A discussion of motives.- 11 Related work.- 12 Conclusions.- Acknowledgements.- A Additional refinement laws.- References.- Authors' Addresses.


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Product Details
  • ISBN-13: 9783540198093
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • Returnable: N
  • Weight: 425 gr
  • ISBN-10: 3540198091
  • Publisher Date: 09 Dec 1993
  • Binding: Hardback
  • Language: English
  • Series Title: Formal Approaches to Computing & Information Technology (FACIT)
  • Width: 155 mm


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