An Effective Coalgebraic Bisimulation Proof Method

The bisimulation “up-to-…” technique provides an effective way to relieve the amount of work in proving bisimilarity of two processes. This paper develops a fresh and direct approach to generalize this set-theoretic “up-to-...” principle to the setting of coalgebra theory. The notion of consistent function is introduced, as a generalization of Sangiorgi's sound function. Then, in order to prove that there are only bisimilar pairs in a relation, it is sufficient to find a morphism from it to the “lifting” of its image under some consistent function. One example is given showing that every self-bisimulation in normed BPA is just such a relation. What's more, we investigate the connection between span-bisimulation and ref-bisimulation. As a result, λ-bisimulation turns out to be covered by our new principle.