Fully-abstract statecharts semantics via intuitionistic Kripke models

Abstract

The semantics of Statecharts macro steps, as introduced by Pnueli and Shalev, lacks compositionality. This paper first analyzes the compositionality problem and traces it back to the invalidity of the Law of the Excluded Middle. It then characterizes the semantics via a particular class of linear, intuitionistic Kripke models, namely stabilization sequences. This yields, for the first time in the literature, a simple fully-abstract semantics which interprets Pnueli and Shalev’s concept of failure naturally. The results not only give insights into the semantic subtleties of Statecharts, but also provide a basis for developing algebraic theories for macro steps and for comparing different Statecharts variants.