Bisimulation Congruences for Homer a calculus of Higher-order mobile embedded resources

We extend Howe’s method for proving that late labelled transition bisimulations are congruences to a core process passing calculus with local names, extended with non-linear active process mobility and nested locations, as found in the Seal calculus, M-calculus, and Kell-calculus. The calculus we consider, called Homer for Higher-order Mobile Embedded Resources, has a very simple syntax and semantics, which conservatively extend the standard syntax and semantics for process passing calculi. The extension of Howe’s method gives a sound characterisation of barbed bisimulation congruence in terms of a late contextual bisimulation. We show that early contextual bisimulation is complete with respect to barbed bisimulation congruence, but that the late bisimulation is in fact strictly included in the early bisimulation. We discuss the issue of scope extension through location boundaries in detail, in particular the difference between fresh name generation and static local names. We propose free name extension as a primitive construct in calculi with non-linear process mobility, explicit locations and local names.