Denotational semantics

In computer science, denotational semantics (initially known as mathematical semantics or Scott–Strachey semantics) is an approach of formalizing the meanings of programming languages by constructing mathematical objects (called denotations) that describe the meanings of expressions from the languages. Other approaches providing formal semantics of programming languages include axiomatic semantics and operational semantics.

Broadly speaking, denotational semantics is concerned with finding mathematical objects called domains that represent what programs do. For example, programs (or program phrases) might be represented by partial functions[1][2] or by games[3] between the environment and the system.

An important tenet of denotational semantics is that semantics should be compositional: the denotation of a program phrase should be built out of the denotations of its subphrases.

  1. ^ Dana S. Scott. Outline of a mathematical theory of computation. Technical Monograph PRG-2, Oxford University Computing Laboratory, Oxford, England, November 1970.
  2. ^ Dana Scott and Christopher Strachey. Toward a mathematical semantics for computer languages Oxford Programming Research Group Technical Monograph. PRG-6. 1971.
  3. ^ Jan Jürjens. J. Games In The Semantics Of Programming Languages – An Elementary Introduction. Synthese 133, 131–158 (2002). https://doi.org/10.1023/A:1020883810034

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