Computing with continuous change

A central challenge in computer science and knowledge representation is the integration of conceptual frameworks for continuous and discrete change, as exemplified by the theory of differential equations and real analysis on the one hand, and the theory of programming languages on the other. We take the first steps towards such an integrated theory by presenting a recipe for the construction of continuous programming languages — languages in which state dynamics can be described by differential equations. The basic idea is to start with an untimed language and extend it uniformly over dense (real) time. We present a concrete mathematical model and language (the Hybrid concurrent constraint programming model, Hybrid cc) instantiating these ideas. The language is intended to be used for modeling and programming hybrid systems. The language is declarative — programs can be understood as formulas that place constraints on the (temporal) evolution of the system, with parallel composition regarded as conjunction. It is expressive — it allows the definition of continuous versions of the preemption control constructs