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arXiv · 1806.11064

Up-To Techniques for Behavioural Metrics via Fibrations

Filippo Bonchi·Barbara König·Daniela Petrisan
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Abstract

Up-to techniques are a well-known method for enhancing coinductive proofs of behavioural equivalences. We introduce up-to techniques for behavioural metrics between systems modelled as coalgebras and we provide abstract results to prove their oundness in a compositional way. In order to obtain a general framework, we need a systematic way to lift functors: we show that the Wasserstein lifting of a functor, introduced in a previous work, corresponds to a change of base in a fibrational sense. This observation enables us to reuse existing results about soundness of up-to techniques in a fibrational setting. We focus on the fibrations of predicates and relations valued in a quantale, for which pseudo-metric spaces are an example. To illustrate our approach we provide an example on distances between regular languages.

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Filippo Bonchi, Barbara König, Daniela Petrisan. 2018-06-28. Up-To Techniques for Behavioural Metrics via Fibrations. https://arxiv.org/abs/1806.11064

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