Techniques modulo pour les bisimulations

Damien Pous 1, 2
2 PLUME - Preuves et Langages
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : While programming languages tend to give higher abstraction levels to the programmer, the programs that are written nowadays tend to be more complex: these programs are distributed, concurrent, interactive, and often, mobile. Moreover the critical role they may play sometimes requires a really precise analysis of their properties. This dissertation is devoted to the study of proof techniques for the analysis of such programs. We develop a theory of “up-to” techniques for coinduction, in the abstract setting of complete lattices. This theory contains new and general modularity results; it establishes the grounds for the reminder of the dissertation, where we focus on up-to techniques for bisimilarity. Up-to techniques for weak bisimilarity are known to be problematic. We show that these problems are related to similar phenomenons in term rewriting theory, and, using tools from this domain (strong normalisation and well-founded inductions), we develop up-to techniques going beyond existing ones. The benefits of these new tech- niques are illustrated by applying one of them in order to prove the correctness of a non-trivial distributed algorithm, for which standard techniques are not sufficient to give a satisfactory proof. Independently, by applying our general theory of up-to techniques in the function space, we show how to obtain second-order techniques, that allow us to revisit the “up to context” techniques: we define a generic method that greatly simplifies the study of such techniques. We illustrate this method by using it to recover up to contexts techniques in the case of CCS.
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Theses
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https://hal.archives-ouvertes.fr/tel-01441480
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Submitted on : Thursday, January 19, 2017 - 5:50:31 PM
Last modification on : Wednesday, November 21, 2018 - 1:13:56 AM
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  • HAL Id : tel-01441480, version 1

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Damien Pous. Techniques modulo pour les bisimulations. Informatique [cs]. ENS Lyon, 2008. Français. ⟨tel-01441480⟩

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