Proc. of the European symposium on programming on ESOP 86
Prespecification in data refinement
Information Processing Letters
A theoretical basis for stepwise refinement and the programming calculus
Science of Computer Programming
The existence of refinement mappings
Theoretical Computer Science
The Z notation: a reference manual
The Z notation: a reference manual
Using Z: specification, refinement, and proof
Using Z: specification, refinement, and proof
The B-book: assigning programs to meanings
The B-book: assigning programs to meanings
An axiomatic basis for computer programming
Communications of the ACM
Automatic Control Engineering
A Discipline of Programming
More Powerful Z Data Refinement: Pushing the State of the Art in Industrial Refinement
ZUM '98 Proceedings of the 11th International Conference of Z Users on The Z Formal Specification Notation
Retrenchment: An Engineering Variation on Refinement
B '98 Proceedings of the Second International B Conference on Recent Advances in the Development and Use of the B Method
Using a Process Algebra to Control B Operations
IFM '99 Proceedings of the 1st International Conference on Integrated Formal Methods
Retrenchment and Punctured Simulation
IFM '99 Proceedings of the 1st International Conference on Integrated Formal Methods
Refinement Calculus, Part I: Sequential Nondeterministic Programs
Stepwise Refinement of Distributed Systems, Models, Formalisms, Correctness, REX Workshop
Retrenchment: Extending the Reach of Refinement
ASE '99 Proceedings of the 14th IEEE international conference on Automated software engineering
From z to c: illustration of a rigorous development method (specification hierarchy)
From z to c: illustration of a rigorous development method (specification hierarchy)
Controlling Control Systems: An Application of Evolving Retrenchment
ZB '02 Proceedings of the 2nd International Conference of B and Z Users on Formal Specification and Development in Z and B
Minimally and Maximally Abstract Retrenchments
IFM '02 Proceedings of the Third International Conference on Integrated Formal Methods
Engineering and theoretical underpinnings of retrenchment
Science of Computer Programming
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Discussion of a radiation dose calculation example demonstrates various expressive limitations of the refinement calculus, particularly for systems with continuous variables. A liberalization of refinement, called retrenchment, is proposed, which will support an analogous formal development calculus. Useful concrete system behaviour can be specified outside the domain of pure refinement, in particular behaviour under controlled precision decay. A syntax and a formal definition are presented for retrenchment in the B notation of J.-R. Abrial. Necessary transitivity and monotonicity properties for a formal development calculus are stated. A generalisation, evolving retrenchment, is proposed, and a simple example demonstrates its utility, by analogy, in control systems applications. Evolution in retrenchment is demonstrated to offer the expressive power to describe useful simulation-like behaviour, with evolving precision, in software for control systems. Finally, the dosimetry problem demonstrates the architectural value of retrenchment for the formal construction of continuous systems.