Reenement and Continuous Behaviour

Re nement Calculus is a formal framework for the development of provably correct software It is also used in the development of Action Systems which is a predicate transformer based framework for constructing distributed and reactive software systems Recently Action Systems were extended with a new action called the di erential action It allows the modelling of con tinuous behaviour Along with the di erential action we may use Action Systems also to model hybrid systems In this paper we investigate how the use of di erential action in Action Systems ts to the re nement ideology As the main result we show that simple laws can be used for proving a re nement step involving continuous behaviour within the Re nement Calculus