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Abstract. Over the last decade, the increasing demand for the validation of safety critical systems lead to the development of domain-speci c programming languages (e.g. synchronous languages) and automatic veri cation tools (e.g. model checkers). Conventionally, the veri cation of a reactive system is implemented by specifying a discrete model of the system (i.e. a nite-state machine) and then checking this model against temporal properties (e.g. using an automata-based tool). We investigate the use of a theorem prover, Coq, for the speci cation of in nite state systems and for the veri cation of co-inductive properties.

The languages for modeling reactive systems are of different styles, like the imperative, state-based ones and the declarative, data-flow ones. They are adapted to different application domains. This paper, through the example of the languages Statecharts and Signal, shows a way to give a model of an imperative specification (Statecharts) in a declarative, equational one (Signal). This model constitutes a formal model of the Statemate semantics of Statecharts, upon which formal analysis techniques can be applied. Being a transformation from an imperative to a declarative structure, it involves the definition of generic models for the explicit management of state (in the case of control as well as of data). In order to obtain a structural construction of the model, a hierarchical and modular organization is proposed, including proper management and propagation of control along the hierarchy. The results presented here cover the essential features of Statecharts as well as of another language of Statemate: Activitycharts. As a translation, it makes multiformalism specification possible, and provides support for the integrated operation of the languages. The motivation lies also in the perspective of gaining access to the various formal analysis and implementation tools of the synchronous technology, using the DCϩ exchange format, as in the Sacres programming environment.