Editing Denotational semantics (section)

{{short description|Study of programming languages via mathematical objects}}
{{Semantics}}

In [[computer science]], '''denotational semantics''' (initially known as '''mathematical semantics''' or '''Scott–Strachey semantics''') is an approach of formalizing the meanings of [[programming language]]s by constructing [[mathematical object]]s (called ''denotations'') that describe the meanings of [[Expression (computer science)|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 [[domain theory|domains]] that represent what programs do.  For example, programs (or program phrases) might be represented by [[partial function]]s<ref name="ropas.snu.ac.kr">Dana S. Scott. [https://ropas.snu.ac.kr/~kwang/520/readings/sco70.pdf Outline of a mathematical theory of computation]. Technical Monograph PRG-2, Oxford University Computing Laboratory, Oxford, England, November 1970.</ref><ref name="Research Group Technical Monograph 1971">[[Dana Scott]] and [[Christopher Strachey]]. ''Toward a mathematical semantics for computer languages'' Oxford Programming Research Group Technical Monograph. PRG-6.  1971.</ref> or by [[Game theory|games]]<ref>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 https://doi.org/10.1023/A:1020883810034]</ref> 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 [[phrase|subphrases]].