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arXiv · 2001.07063

Modular coinduction up-to for higher-order languages via first-order transition systems

Jean-Marie Madiot·Damien Pous·Davide Sangiorgi
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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 abstract fixed-point theory and compatible functions. 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. 2020-01-20. Modular coinduction up-to for higher-order languages via first-order transition systems. https://doi.org/10.46298/lmcs-17(3%3A25)2021

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