Poppleton, Michael R, and Banach, Richard N.
Structuring Retrenchments in B by Decomposition.
In, FME2003: International Symposium of Formal Methods Europe, Pisa, Italy,
Springer Lecture Notes in Computer Science, .
Simple retrenchment is briefly reviewed in the B language of J.-R. Abrial [ref] as a liberalization of classical refinement, for the formal description of application developments too demanding for refinement. This work initiates the study of the structuring of retrenchment-based developments in B by decomposition. A given coarse-grained retrenchment relation between specifications is decomposed into a family of more fine-grained retrenchments. The resulting family may distinguish more incisively between refining, approximately refining, and non-refining behaviours. Two decomposition results are given, each sharpening a coarse-grained retrenchment within a particular syntactic structure for operations at concrete and abstract levels. A third result decomposes a retrenchment exploiting structure latent in both levels. The theory is illustrated by a simple example based on an abstract model of distributed computing, and methodological aspects are considered.
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