Composition of Reactive System Components

This paper will present the case for using a formal component-based speciication technique for reactive systems, such as the Object Calculus of Fiadeiro and Maibaum. The Object Calculus provides a modular, highly declarative and abstract speciication language, suitable for reenement using model-based design notations such as B or VDM. In the Object Calculus, pre/post style speciications of the eeect of actions can be given, together with temporal logic speciications of expected histories of behaviour of the system. Temporal logic is an established technique for the speciication of reactive systems: it has the advantage of being declarative and supporting reasoning, and it is suuciently expressive for many practical cases. The Object Calculus adds a strong concept of encapsulation and theory composition to a basic temporal logic formalism 8], which allows reactive system components to be separately speciied, instantiated and combined using category-theoretic operations, in particular, the co-limit construction: \given a category of widgets, the operation of putting a system of widgets together to form some super-widget corresponds to taking the co-limit of the diagram of widgets that shows how to interconnect them" 10] Using this integration of category-theoretic structuring and temporal or modal logics, the development of the Object Calculus has been carried out by research groups at Imperial College and the University of Lisbon over the last 10 years. It has been taken up by other research groups and applied to systems of signiicant complexity, such as the steam boiler system described here.