REASONING ABOUT CONTINUOUS SYSTEMS

The mathematics of program construction has been developed over three decades to design correct digital programs, hand-in-hand with their proofs, in a systematic fashion. A goal of this paper is to explore the use of this mathematics to reason about continuous systems. Many systems in physics and biology are continuous. Can the mathematics of programming be used to understand such systems? In particular can nondeterminism be used to reason about incompletely specified, continuous systems? This exploratory paper is written as much for scientists in the physical and biological sciences who want an introduction to the mathematics of program construction as for computing scientists who are intrigued by the possibility of using their mathematics outside the programming domain. Some of this material is introductory. The paper is speculative in the sense that it is likely to produce more questions than answers. © 1990.