From ATM machines dispensing cash from our bank accounts, to online shopping websites, interactive systems permeate our everyday life. The underlying technology to support these systems, both hardware and software, is well advanced. However design principles and techniques for assuring their correct behaviour are at a much more primitive stage.

The provision of solid foundations for such activities, mathematical models of system behaviour and associated reasoning tools, has been a central theme of theoretical computer science over the last two decades. One approach has been the design of formal calculi in which the fundamental concepts underlying interactive systems can be described, and studied. The most obvious analogy is the use of the λ-calculus as a simple model for the study of sequential computation, or indeed the study of sequential programming languages. CCS (a Calculus for Communicating Systems) [28] was perhaps the first calculus proposed for the study of interactive systems, and was followed by numerous variations. This calculus consists of:

• A simple formal language for describing systems in terms of their structure; how they are constructed from individual, but interconnected, components.

• A semantic theory that seeks to understand the behaviour of systems described in the language, in terms of their ability to interact with users.

Here a system consists of a finite number of independent processes that intercommunicate using a fixed set of named communication channels. This set of channels constitutes a connection topology through which all communication takes place; it includes both communication between system components, and between the system and its users.