Greatest Bisimulations for Binary Methods

In previous work [14] I introduced a generalised notion of coalgebra that is capable of modelling binary methods as they occur in object-oriented programming. An important problem with this generalisation is that bisimulations are not closed under union and that a greatest bisimulation does not exists in general. There are two possible approaches to improve this situation: First, to strengthen the definition of bisimulation, and second, to place constraints on the coalgebras (i.e., on the behaviour of the binary methods). In this paper I combine both approaches to show that (under reasonable assumptions) the greatest bisimulation does exist for all coalgebras of extended polynomial functors