Nominal SOS

Plotkin’s style of Structural Operational Semantics (SOS) has become a de facto standard in giving operational semantics to formalisms and process calculi. In many such formalisms and calculi, the concepts of names, variables and binders are essential ingredients. In this paper, we propose a formal framework for dealing with names in SOS. The framework is based on the Nominal Logic of Gabbay and Pitts and hence is called Nominal SOS. We define nominal bisimilarity, an adaptation of the notion of bisimilarity that is aware of binding. We provide evidence of the expressiveness of the framework by formulating the early π-calculus and Abramsky’s lazy λ-calculus within Nominal SOS. For both calculi we establish the operational correspondence with the original calculi. Moreover, in the context of the π-calculus, we prove that nominal bisimilarity coincides with Sangiorgi’s open bisimilarity and in the context of the λ-calculus we prove that nominal bisimilarity coincides with Abramsky’s applicative bisimilarity.