An Algebraic Understanding of Interactive Functionality

The thesis of this paper is simple: that understanding both the construction and the interpretation of algebras is useful not only as a speciication technique for the implementation of interactive systems, but also as providing fundamental insights into the design and use of such systems in a general way. This is in contrast rstly to state-oriented speciication techniques like Z and VDM , which are less mathematically tractable and so obscure the general observations we wish to make here. It is in contrast secondly to behavioural notations like CSP and CCS which, while very tractable, abstract away from issues of value or state and only describe permissible action orderings. The paper presents a generic algebra for direct manipulation interactive systems, and indicates the importance of initial and nal interpretations of algebraic speciications in the iterative design process.