We present a meta-logic that contains a new quantifier (for encoding "generic judgment") and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite π-calculus within this meta-logic. Since we

Recently, various process calculi have been introduced which are suited for the modelling of mobile computation and in particular the mobility of program code; a prominent example is the ambient calculus. Due to the complexity of the involved spatial reduction, there is — in contrast to the situation in standard process algebra — up to now no satisfying coalgebraic representation of a mobile process calculus. Here, we discuss a coalgebraic denotational semantics for the ambient calculus, viewed as a step towards a generic coalgebraic framework for modelling mobile systems. Crucial features of our modelling are a set of GSOS style transition rules for the ambient calculus, a hardwiring of the so-called hardening relation in the functorial signature, and a set-based treatment of hidden name sharing. The formal representation of this framework is cast in the algebraic-coalgebraic specification language CoCasl.

In recent years, logical frameworks and tile logic have been separately proposed by our research groups, respectively in Udine and in Pisa, as suitable metalanguages with higher-order features for encoding and studying nominal calculi. This paper discusses the main features of the two approaches, tracing di#erences and analogies on the basis of two case studies: late #-calculus and lazy simply typed #-calculus.

In this paper, we model fresh names in the #-calculus using abstractions with respect to a new binding operator #. Both the theory and the metatheory of the #-calculus benefit from this simple extension. The operational semantics of this new calculus is finitely branching. Bisimulation can be given without mentioning any constraint on names, thus allowing for a straightforward definition of a coalgebraic semantics, within a category of coalgebras over permutation algebras. Following previous work by Montanari and Pistore, we present also a finite representation for finitary processes and a finite state verification procedure for bisimilarity, based on the new notion of #-automaton.