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In Praise of Algebra

Tony Hoare

George Boole was a pioneer of the algebraic presentation of logic. I will suggest algebra as a simple way of presenting the semantics of broad families of programming languages. It neatly characterises the similarities and differences between members of the family. Denotational, operational, and deductive semantic presentations can be readily derived by algebraic proof. When the language is extended, all the derivations and theorems remain valid. The simplicity derives from the Oxford tradition that fact Programs are Predicates – in that they directly describe their own execution.

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