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Line 27: \|date=October 1969 \|s2cid=207726175 \|doi-access=free ▼ ~~\|url=https://dl.acm.org/doi/pdf/10.1145/363235.363259~~ ▲\|doi-access=free }}</ref>{{r\|winskel}} Line 49 ⟶ 48: * '''[[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}} ==Variations== Line 57 ⟶ 56: * '''[[Algebraic semantics (computer science)\|Algebraic semantics]]'''<ref name=Goguen77/> is a form of [[axiomatic semantics]] based on [[algebra]]ic laws for describing and reasoning about [[program semantics]] in a [[formal methods\|formal]] manner. It also supports [[denotational semantics]] and [[operational semantics]]; * '''[[Attribute grammar]]s'''<ref>{{cite book \|author1-first=Pierre\|author1-last=Deransart \|author2-first=Martin\|author2-last=Jourdan \|author3-first=Bernard\|author3-last=Lorho \|title="Attribute Grammars: Definitions, Systems and Bibliography \|date=1988 \|series=Lecture Notes in Computer Science 323 \|publisher=[[Springer-Verlag]] \|isbn=9780387500560}}</ref> define systems that systematically compute "[[metadata]]" (called ''attributes'') for the various cases of [[Syntax (programming languages)\|the language's syntax]]. Attribute grammars can be understood as a denotational semantics where the target language is simply the original language enriched with attribute annotations. Aside from formal semantics, attribute grammars have also been used for code generation in [[compiler]]s, and to augment [[Regular languages\|regular]] or [[Context-free languages\|context-free grammars]] with [[Context-sensitive languages\|context-sensitive]] conditions; * '''[[Categorical semantics\|Categorical]] (or "functorial") semantics'''<ref name=Lawvere1963>{{cite journal \|author-link=William Lawvere\|author-first=F. William\|author-last=Lawvere \|title=Functorial semantics of algebraic theories \|journal=[[Proceedings of the National Academy of Sciences of the United States of America]] \|volume=50 \|issue=5 \|date=1963 \|pages=869–872 \|doi=10.1073/pnas.50.5.869\|pmid=16591125 \|pmc=221940 \|bibcode=1963PNAS...50..869L \|doi-access=free }}</ref> uses [[category theory]] as the core mathematical formalism. ~~A categorical~~Categorical semantics is usually proven to correspond to some axiomatic semantics that gives a syntactic presentation of the categorical structures. Also, denotational semantics are often instances of a general categorical semantics;<ref>{{cite journal \|author1=Andrzej Tarlecki \|author2=[[Rod Burstall\|Rod M. Burstall]] \|author3=[[Joseph Goguen\|Joseph A. Goguen]] \|title=Some fundamental algebraic tools for the semantics of computation: Part 3. Indexed categories \|journal=[[Theoretical Computer Science]] \|volume=91 \|issue=2 \|date=1991 \|pages=239–264 \|doi=10.1016/0304-3975(91)90085-G\|doi-access=free }}</ref> * '''[[Concurrency semantics]]'''<ref>{{cite conference \|author1-first=Mark\|author1-last=Batty \|author2-first=Kayvan\|author2-last=Memarian \|author3-first=Kyndylan\|author3-last=Nienhuis \|author4-first=Jean\|author4-last=Pichon-Pharabod \|author5-first=Peter\|author5-last=Sewell \|title=The problem of programming language concurrency semantics \|book-title=Proceedings of the European Symposium on Programming Languages and Systems \|pages=283–307 \|publisher=[[Springer Publishing\|Springer]] \|date=2015 \|doi=10.1007/978-3-662-46669-8_12\|doi-access=free \|url=http://kar.kent.ac.uk/50271/1/c_concurrency_challenges.pdf }}</ref> is a catch-all term for any formal semantics that describes concurrent computations. Historically important concurrent formalisms have included the [[actor model]] and [[process calculi]]; * '''[[Game semantics]]'''<ref name=Abramsky2009>{{cite book \|author-link=Samson Abramsky\|author-first=Samson\|author-last=Abramsky \|chapter=Semantics of interaction: An introduction to game semantics \|title=Semantics and Logics of Computation \|date=2009 \|pages=1–32 \|doi=10.1017/CBO9780511526619.002 \|publisher=Cambridge University Press \|isbn=9780521580571 \|url=https://ora.ox.ac.uk/objects/uuid:ab3ece5b-cd8d-49e6-ba33-010ea4c1a1ac \|editor1=Andrew M. Pitts \|editor2=P. Dybjer}}</ref> uses a metaphor inspired by [[game theory]];