Congruence Proofs for Weak BisimulationEquivalences on Higher { order ProcessCalculiMichael

Congruence proofs for bisimulation equivalences on higher{order process calculi tend to be signiicantly more complex than their counterparts in rst{order process algebra frameworks. The fact that higher{order synchronization invokes substitution seems to be the main problem. The reason is that it renders standard rst{order proof techniques circular in the higher{order case, and this situation is diicult to deal with. Moreover, some techniques that allow us to cover strong forms of bisimulation equivalence on higher{order calculi seem to fail for the corresponding weak forms. Applicative simulation equivalence on {calculi poses similar problems and our starting point is that Howe has invented a general and elegant technique for solving them. Our contribution is that we use Howe{style techniques to prove that three forms of weak bisimulation equivalence on variants of Thomsen's Plain CHOCS and CHOCS second{order process calculi are congruences. In the Plain CHOCS case we treat late weak context equivalence; in the CHOCS case we treat late and a minor variant of early weak higher{order equivalences.