A coalgebraic approach to the semantics of the ambient calculus

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.