Modular bisimulation theory for computations and values

  • Authors:
  • Martin Churchill;Peter D. Mosses

  • Affiliations:
  • Department of Computer Science, Swansea University, Swansea, UK;Department of Computer Science, Swansea University, Swansea, UK

  • Venue:
  • FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
  • Year:
  • 2013

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Abstract

For structural operational semantics (SOS) of process algebras, various notions of bisimulation have been studied, together with rule formats ensuring that bisimilarity is a congruence. For programming languages, however, SOS generally involves auxiliary entities (e.g. stores) and computed values, and the standard bisimulation and rule formats are not directly applicable. Here, we first introduce a notion of bisimulation based on the distinction between computations and values, with a corresponding liberal congruence format. We then provide metatheory for a modular variant of SOS (MSOS) which provides a systematic treatment of auxiliary entities. This is based on a higher order form of bisimulation, and we formulate an appropriate congruence format. Finally, we show how algebraic laws can be proved sound for bisimulation with reference only to the (M)SOS rules defining the programming constructs involved in them. Such laws remain sound for languages that involve further constructs.