Bisimulations up-to: beyond first-order transition systems

Jean-Marie Madiot 1, 2, 3, * Damien Pous 1, 3, * Davide Sangiorgi 2, 4, *
* Corresponding author
2 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
3 PLUME - Preuves et Langages
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : 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 pi-calculus, the lambda-calculus, and a (call-by-value) lambda-calculus with references.
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Jean-Marie Madiot, Damien Pous, Davide Sangiorgi. Bisimulations up-to: beyond first-order transition systems. CONCUR, Sep 2014, Rome, Italy. ⟨10.1007/978-3-662-44584-6_8⟩. ⟨hal-00990859⟩

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