Continuation Semantics for Concurrency Applied to Parallel Rewriting of Multisets

We present a (compositional) continuation semantics for an abstract concurrent language embodying two important features encountered in membrane computing: the semantics of parallel composition is based on the concept of maximal parallelism and computations are specified by means of multiset rewriting rules. As far as we know this is the first paper that presents a compositional semantics for this combination of concepts. Other features, such as the nested structure of a membrane computing system are lacking from the language under study, but we argue that continuations provide sufficient flexibility for representing such structures. Instead of using a mathematical notation, we find convenient to use the functional programming language Haskell as ametalanguage for the denotational semantics.