Up-To Techniques for Behavioural Metrics via Fibrations

Filippo Bonchi, Barbara König, Daniela Petrisan, Michael Wagner
2018 International Conference on Concurrency Theory  
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 soundness 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 » ... is 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.
doi:10.4230/lipics.concur.2018.17 dblp:conf/concur/Bonchi0P18 fatcat:n6dyzhli2zgatgwndph4nnmyxi