Embedding imperative synchronous languages in interactive theorem provers

We present a new way to define the semantics of imperative synchronous languages by means of separating the control and the data flow. The control flow is defined by predicates that describe entering conditions, conditions for internal moves, and termination conditions. The data flow is based on the extraction of guarded commands. This definition principle can be applied to any imperative synchronous language like Esterel or some statechart variants. Following this definition principle, we have embedded our language Quartz (an Esterel variant) in the interactive theorem prover HOL. We use this embedding for formal verification (both interactive theorem proving and symbolic model checking), program analysis, reasoning about the language at a meta-level and verified code generation (formal synthesis).

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