Lax Bialgebras and Up-To Techniques for Weak Bisimulations
Résumé
Up-to techniques are useful tools for optimising proofs of behavioural equivalence of processes.
Bisimulations up-to context can be safely used in any language specified by GSOS rules. We
showed this result in a previous paper by exploiting the well-known observation by Turi and
Plotkin that such languages form bialgebras. In this paper, we prove the soundness of up-to
contextual closure for weak bisimulations of systems specified by cool rule formats, as defined by
Bloom to ensure congruence of weak bisimilarity. However, the weak transition systems obtained
from such cool rules give rise to lax bialgebras, rather than to bialgebras. Hence, to reach our
goal, we extend our previously developed categorical framework to an ordered setting.