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WHY DENOTATIONAL?

Abstract

This is an essay where the author expresses his views on applied denotational semantics. In the author's opinion, whether a software system has or does not have a sufficiently abstract denotational semantics should be regarded as a pragmatic attribute of the system rather than merely as a mathematical attribute of its description. In a software system with denotational semantics structured programming is feasible and for such systems there is a routine method of developing program-correctness logic. All that may not be the case if denotationality is not ensured. On the other hand, a non-denotational semantics can be always artificially made denotational on the expense of lowering its level of abstraction. This leads to an important pragmatic question: to what extent and in which situations can we sacrifice denotationality and/or abstraction of a semantics? All discussions are carried on an algebraic ground but the paper is not very technical and contains a short introduction to the algebraic theory of denotational semantics.