The tile model

In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework Mes92], and of concur-rency theory: among the others, the structured operational semantics Plo81], the context systems LX90] and the structured transition systems CM92] approaches. Our model recollects many properties of these sources: rst, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Second, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and side-eeects to determine the actual behaviour of a system. Finally, an equivalence relation over sequences of transitions is deened, equipping the system under analysis with a concurrent semantics , where each equivalence class denotes a family of \computationally equivalent" behaviours, intended to correspond to the execution of the same set of (causally unrelated) events. As a further abstraction step, our model is conveniently represented using double-categories: its operational semantics is recovered with a free construction, by means of a suitable adjunction.