Equations for Describing Dynamic Nets of Communicating Systems

We give a notation and a logical calculus for the description and deductive manipulation of dynamic networks of communicating components. We represent such nets by hierarchical systems of recursive equations for streams. We give logical rules that describe the communication within a net and the dynamic creation of components, channels and rearrangement of the net structure. Such net transformations are based on a calculus of declarations of identifiers for data elements and especially for streams and equational logic. We demonstrate the modelling of interactive systems that correspond to dynamically changing net structures as obtained in systems with dynamic process creation (such as in object oriented approaches) within a framework of classical equational logic.