In a previous paper we introduced the tile model, a framework encompassing 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 and of concurrency theory, and our formalism recollects many properties of these sources. For example, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Moreover, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and side-effects to determine the actual behaviour of a system. In this work we narrow our scope, presenting a re...