Algebra Unifies Operational Calculi

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 a general calculus of program execution. The basic judgment of the theory is a quintuple, and we deduce its rules by algebraic reasoning. The general calculus can be specialised to obtain more familiar operational calculi, such as the structural operational semantics of Plotkin, process calculus semantics of Milner, reduction semantics with evaluation contexts of Felleisen and Hieb, and the natural semantics of Kahn. The algebra unifies these calculi, as it is simpler than each calculus derived from it, and stronger than all of them put together.

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