The refinement calculus is a well-established theory for formal development of imperative program code and is supported by a number of automated tools. Via a detailed case study, this article shows how refinement theory and tool support can be extended for a program with real-time constraints. The approach adapts a timed variant of the refinement calculus and makes corresponding enhancements to a theorem-prover based refinement tool.

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In this paper we describe investigations into the use of automatic theorem proving technology in the refutation of proof obligations. Specifically, we discuss the use of resolution based theorem proving and model checking to find false obligations and counterexamples. These techniques can be used as basis of an automatic method for finding faults in design during the formal development of software. This approach is complementary to verifcation by proof as such proofs can only be completed when all faults have been corrected. We give a simple example using the B formal development method to demonstrate its potential. 1