The laws of programming unify process calculi

Abstract We survey the well-known algebraic laws of sequential programming, and propose some less familiar laws for concurrent programming. On the basis of these laws, we derive the rules of a number of classical programming and process calculi, for example, those due to Hoare, Milner, and Kahn. The algebraic laws are simpler than each of the calculi derived from it, and they are stronger than all the calculi put together. Conversely, most of the laws are derivable from one or more of the calculi. This suggests that the laws are useful as a presentation of program semantics, and correspond to a widely held common understanding of the meaning of programs. For further evidence, Appendix A describes a realistic and generic model of program behaviour, which has been proved to satisfy the laws.

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