Denotational semantics of membrane systems by using complete metric spaces

In this paper we present a mathematical model for a class of membrane systems, emphasizing on constructions of the denotational semantics as fixed points over complete metric spaces (to describe the semantics of multiset rewriting) and metric powerdomains (to describe the nondeterministic behaviour). We use the continuation-passing style, a technique providing enough flexibility for handling the concept of maximal parallelism and for describing the specific interactions in a membrane system. An important feature of the denotational approach is that it provides a compositional view of the membrane systems. Moreover, the semantics can be implemented naturally in a functional programming language; the implementation in Haskell is provided, and it is freely available for software experiments.