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Modular Bisimulation Theory for Computations and Values

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7794)


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.


  • structural operational semantics
  • programming languages
  • congruence formats
  • Modular SOS
  • higher-order bisimulation


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Churchill, M., Mosses, P.D. (2013). Modular Bisimulation Theory for Computations and Values. In: Pfenning, F. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2013. Lecture Notes in Computer Science, vol 7794. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37074-8

  • Online ISBN: 978-3-642-37075-5

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