Retrenchment: Extending Refinement for Continuous and Control Systems

Discussion of a radiation dose calculation example demonstrates various expressive limitations of the reenement calculus, particularly for systems with continuous variables. A liberalization of reenement, called retrenchment, is proposed, which will support an analogous formal development calculus. Useful concrete system behaviour can be speciied outside the domain of pure reenement, in particular behaviour under controlled precision decay. A syntax and a formal deenition 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 ooer 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.