Typed stochastic semantics for the calculus of looping sequences

The Stochastic Calculus of Looping Sequences is a quantitative term rewrite formalism suitable to describe the evolution of microbiological systems, taking into account the speed of the described activities. In this paper we propose an operational semantics for this calculus that considers the types of the species to derive the stochastic evolution of the system. The presence of positive and negative catalysers can modify these speeds. We claim that types provide an abstraction suitable to represent the interaction between elements without specifying exactly the element positions. Our claim is supported through an example modelling the lactose operon.