Bisimulations Up-to: Beyond First-Order Transition Systems

  • Jean-Marie Madiot
  • Damien Pous
  • Davide Sangiorgi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8704)


The bisimulation proof method can be enhanced by employing ‘bisimulations up-to’ techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on the notion of compatible function for fixed-point theory.

We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. The only ingredient that has to be manually supplied is the compatibility of basic up-to techniques that are specific to the new languages. We investigate the method on the π-calculus, the λ-calculus, and a (call-by-value) λ-calculus with references.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jean-Marie Madiot
    • 1
  • Damien Pous
    • 1
  • Davide Sangiorgi
    • 2
  1. 1.ENS LyonUniversité de Lyon, CNRS, INRIAFrance
  2. 2.Università di Bologna, INRIAItaly

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