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.
Author and article information
]Faculty of Mathematics and Computing
Open University, Walton Hall, Milton Keynes MK7 6AL, UK
]Department of Computer Science, Manchester University
Manchester M13 9PL, UK