State Transitions modeled as Re nements

We are going to show how state transitions can be modeled in the framework of algebraic speci cations. We use the algebraic speci cation, composition, and re nement framework provided by the Specware tool [28, 29] and Evolving Algebras [10] as a general framework for transition systems. Numerous case studies show that evolving algebras are well suited to model large and complex reactive and concurrent systems [1, 7, 5, 6, 15, 16, 17, 22, 21]. We show how evolving algebras can be embedded in Specware, and how Specware supports reasoning about Hoare triples [20]. Although Evolving Algebras are based on onesorted signatures we use for simplicity many sorted signatures for both algebraic speci cation and Evolving Algebras. We do not address the problem how one-sorted Evolving Algebras are translated to many-sorted ones [34]. The paper is structured as follows. In the second section we give the main ideas, and in the last section we draw conclusions and indicate further work. We assume familiarity of the reader with both Specware and Evolving Algebras. A selfcontained and less technical version of this ideas will be given in [26].