Up-To Techniques for Behavioural Metrics via Fibrations [article]

Filippo Bonchi, Barbara König, Daniela Petrisan
2018 arXiv   pre-print
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.
more » ... s 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.
arXiv:1806.11064v1 fatcat:lfvzqseo3bdjvhlesq64gnyl4m