Hybrid systems are composed by continuous physical component and discrete control component where the system state evolves over time according to interacting law of discrete and continuous dynamics. Combinations of computation and control can lead to very complicated system designs We treat more explicit hybrid models by providing a hybrid relation calculus, where both clock and signal are introduced to coordinate activities of various components of hybrid systems. This paper presents a hybrid parallel programming language with a set of novel combinators to model physical world and its interaction with the control program. We discuss the algebraic properties of the language, and show how to convert a hybrid automata to a hybrid program. The paper also demonstrates how to transform a hybrid program into a normal form using the algebraic laws of the language, and explores the link between the hybrid relation calculus and the classical relation calculus.
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