Editing Semantics (computer science) (section)

==Approaches==
There are many approaches to formal semantics; these belong to three major classes:

* '''[[Denotational semantics]]''',<ref name=Schmidt1986>{{cite book |author-first=David A.|author-last=Schmidt |title=Denotational Semantics: A Methodology for Language Development |publisher=William C. Brown Publishers |date=1986 |isbn=9780205104505}}</ref> whereby each phrase in the language is interpreted as a ''[[denotation (semiotics)|denotation]]'', i.e. a conceptual meaning that can be thought of abstractly.  Such denotations are often mathematical objects inhabiting a mathematical space, but it is not a requirement that they should be so.  As a practical necessity, denotations are described using some form of mathematical notation, which can in turn be formalized as a denotational metalanguage.  For example, denotational semantics of [[functional programming language|functional languages]] often translate the language into [[domain theory]]. Denotational semantic descriptions can also serve as compositional translations from a programming language into the denotational metalanguage and used as a basis for designing [[compiler]]s.
* '''[[Operational semantics]]''',<ref name=Plotkin1981>{{cite report |author-link=Gordon Plotkin|first=Gordon D.|last=Plotkin |title=A structural approach to operational semantics |series=Technical Report DAIMI FN-19 |publisher=Computer Science Department, [[Aarhus University]] |date=1981}}</ref> whereby the execution of the language is described directly (rather than by translation).  Operational semantics loosely corresponds to [[interpreter (computing)|interpretation]], although again the "implementation language" of the interpreter is generally a mathematical formalism.  Operational semantics may define an [[abstract machine]] (such as the [[SECD machine]]), and give meaning to phrases by describing the transitions they induce on states of the machine.  Alternatively, as with the pure [[lambda calculus]], operational semantics can be defined via syntactic transformations on phrases of the language itself;
* '''[[Axiomatic semantics]]''',<ref name=Goguen77>{{cite journal |author1-link=Joseph Goguen|author1-first=Joseph A.|author1-last=Goguen |author2-first=James W.|author2-last=Thatcher |author3-first=Eric G.|author3-last=Wagner |author4-first=Jesse B.|author4-last=Wright |title=Initial algebra semantics and continuous algebras |journal=[[Journal of the ACM]] |volume=24 |issue=1 |date=1977 |pages=68–95 |doi=10.1145/321992.321997|s2cid=11060837 |doi-access=free }}</ref> whereby one gives meaning to phrases by describing the ''[[axiom]]s'' that apply to them.  Axiomatic semantics makes no distinction between a phrase's meaning and the logical formulas that describe it; its meaning ''is'' exactly what can be proven about it in some logic.  The canonical example of axiomatic semantics is [[Hoare logic]].

Apart from the choice between denotational, operational, or axiomatic approaches, most variations in formal semantic systems arise from the choice of supporting mathematical formalism.{{cn|date=April 2024}}