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{{confuse|Computational semantics}}
{{Short description|Field concerned with the rigorous mathematicalMathematical study of the meaning of programming languages}}
{{Semantics}}
{{More footnotes|date=August 2020}}
{{Formal languages}}
In [[programming language theory]], '''semantics''' is the field concerned with the rigorous mathematical study of the meaning of [[programming language]]s.<ref>{{cite book |author=[[Joseph Goguen|Joseph A. Goguen]] |chapter=Semantics of computation |title=Category Theory Applied to Computation and Control |publisher=[[Springer Publishing|Springer]] |date=1975 |pages=151-163 |doi=10.1007/3-540-07142-3_75}}</ref> It does so by evaluating the meaning of [[programming language syntax|syntactically]] valid [[string (computer science)|strings]] defined by a specific programming language, showing the computation involved. In such a case that the evaluation would be of syntactically invalid strings, the result would be non-computation. Semantics describes the processes a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain [[computer platform|platform]], hence creating a [[model of computation]].▼
 
▲In [[programming language theory]], '''semantics''' is the field concerned with the rigorous mathematical study of the meaning of [[programming language]]s.<ref>{{cite book |author-link=[[Joseph Goguen|first=Joseph A. |last=Goguen]] |chapter=Semantics of computation |title=Category Theory Applied to Computation and Control |series=Lecture Notes in Computer Science |publisher=[[Springer Publishing|Springer]] |date=1975 |volume=25 |pages=151-163151–163 |doi=10.1007/3-540-07142-3_75|isbn=978-3-540-07142-6 }}</ref> ItSemantics does so by evaluating the meaning ofassigns [[programmingcomputation]]al languagemeaning syntax|syntactically]]to valid [[string (computer science)|strings]] defined byin a specific [[programming language, showing the computation involvedsyntax]]. InIt suchis aclosely caserelated that the evaluation would be of syntactically invalid stringsto, the result would be non-computation. Semantics describes the processes a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and outputoften ofcrosses aover programwith, or an explanation of how the program will be executed on a certain [[computerSemantics of platformlogic|platform]],semantics henceof creatingmathematical a [[model of computationproofs]].
 
'''Semantics''' describes the processes a computer follows when [[Execution (computing)|executing]] a program in that specific language. This can be done by describing the relationship between the input and output of a program, or giving an explanation of how the program will be executed on a certain [[computer platform|platform]], thereby creating a [[model of computation]].
 
== History ==▼
 
In 1967, [[Robert W. Floyd]] published the paper ''Assigning meanings to programs''; his chief aim was "a rigorous standard for proofs about computer programs, including [[formal verification|proofs of correctness]], equivalence, and termination".<ref name=floyd>{{cite book |year=1967 |author-link=Robert W. Floyd |first=Robert W. |last=Floyd |chapter=Assigning Meanings to Programs |chapter-url=https://people.eecs.berkeley.edu/~necula/Papers/FloydMeaning.pdf |editor-first=J.T. |editor-last=Schwartz |title=Mathematical Aspects of Computer Science |publisher=American Mathematical Society |isbn=0821867288 |pages=19–32 |url=https://books.google.com/books?id=ynigSICJflYC |series=Proceedings of Symposium on Applied Mathematics |volume=19 }}</ref><ref>{{cite web |author-link=Donald Knuth|author-first=Donald E.|author-last=Knuth |title=Memorial Resolution: Robert W. Floyd (1936–2001) |url=https://stacks.stanford.edu/file/druid:zy788sr3998/SC0193_MemorialResolution_Floyd_Robert.pdf |work=Stanford University Faculty Memorials |publisher=Stanford Historical Society }}</ref> Floyd further wrote:{{r|floyd}}
<blockquote>
A semantic definition of a programming language, in our approach, is founded on a [[Syntax (programming languages)|syntactic]] definition. It must specify which of the phrases in a syntactically correct program represent [[Command (computing)|commands]], and what [[Conditional (computer programming)|conditions]] must be imposed on an interpretation in the neighborhood of each command.
</blockquote>
 
In 1969, [[Tony Hoare]] published a paper on [[Hoare logic]] seeded by Floyd's ideas, now sometimes collectively called ''[[axiomatic semantics]]''.<ref name="hoare">{{Cite journal
|last=Hoare
|first=C. A. R.
|authorlink=Tony Hoare
|title=An axiomatic basis for computer programming
|doi=10.1145/363235.363259
|journal=[[Communications of the ACM]]
|volume=12
|issue=10
|pages=576–580
|date=October 1969
|s2cid=207726175
|doi-access=free
}}</ref>{{r|winskel}}
 
In the 1970s, the terms ''[[operational semantics]]'' and ''[[denotational semantics]]'' emerged.<ref name=winskel>{{cite book |last1=Winskel |first1=Glynn |title=The formal semantics of programming languages : an introduction |date=1993 |publisher=MIT Press |location=Cambridge, Mass. |isbn=978-0-262-23169-5 |page=[https://archive.org/details/formalsemanticso0000wins/page/n17 xv] |url=https://archive.org/details/formalsemanticso0000wins}}</ref>
 
==Overview==
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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 paperreport |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 articlejournal |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=68-9568–95 |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==
Some variations of formal semantics include the following:
 
* '''[[Action semantics]]'''<ref name=Mosses1996>{{cite paperreport |author-link=Peter Mosses|author-first=[[Peter D. |author-last=Mosses]] |date=1996 |title=Theory and practice of action semantics |publisher=[[Aarhus University]] |series=BRICS Report RS9653}}</ref> is an approach that tries to modularize denotational semantics, splitting the formalization process in two layers (macro and microsemantics) and predefining three semantic entities (actions, data and yielders) to simplify the specification;
* '''[[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 articlejournal |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 |pagepages=869869–872 |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 categoricalCategorical 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 articlejournal |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=239-264239–264 |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=283-307283–307 |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=1-321–32 |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]];
* '''[[Predicate transformer semantics]]''',<ref name=Dijkstra1975>{{cite articlejournal |author-link=[[Edsger W. Dijkstra]]|author-first=Edsger W.|author-last=Dijkstra |date=1975 |title=Guarded commands, nondeterminacy and formal derivation of programs |journal=[[Communications of the ACM]] |volume=18 |issue=8 |pages=453–457 |doi=10.1145/360933.360975|s2cid=1679242 |doi-access=free }}</ref> developed by [[Edsger W. Dijkstra]], describes the meaning of a program fragment as the function transforming a [[postcondition]] to the [[precondition]] needed to establish it.
 
==Describing relationships==
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*To prove that operational semantics over a high-level machine is related by a [[simulation]] with the semantics over a low-level machine, whereby the low-level abstract machine contains more primitive operations than the high-level abstract machine definition of a given language. Such a proof demonstrates that the low-level machine "faithfully implements" the high-level machine.
 
It is also possible to relate multiple semantics through [[abstraction (computer science)#Semantics|abstractions]] via the theory of [[abstract interpretation]].{{cn|date=April 2024}}
 
▲== History ==
{{expand section|date=August 2013}}
[[Robert W. Floyd]] is credited with founding the field of programming language semantics in {{harvtxt|Floyd|1967}}.<ref>{{cite web |author=[[Donald Knuth|Donald E. Knuth]] |title=Memorial Resolution: Robert W. Floyd (1936–2001) |url=https://stacks.stanford.edu/file/druid:zy788sr3998/SC0193_MemorialResolution_Floyd_Robert.pdf |work=Stanford University Faculty Memorials |publisher=Stanford Historical Society |format=PDF}}</ref>
 
== See also ==
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*{{cite book |year=1991 |author-link=Robert D. Tennent |first=Robert D. |last=Tennent |title=Semantics of Programming Languages |url=https://books.google.com/books?id=K7N7QgAACAAJ |publisher=Prentice Hall |isbn=978-0-13-805599-8}}
*{{cite book |year=1992 |author-link=Carl Gunter (computer scientist) |first=Carl |last=Gunter |title=Semantics of Programming Languages |publisher=MIT Press |isbn=0-262-07143-6 }}
*{{cite book |year=1992 |firstfirst1=H. R. |lastlast1=Nielson |first2=Flemming |last2=Nielson |title=Semantics With Applications: A Formal Introduction |url=http://www.daimi.au.dk/~bra8130/Wiley_book/wiley.pdf |format=PDF |publisher=Wiley |isbn=978-0-471-92980-2 |access-date=2011-05-27 |archive-date=2012-04-17 |archive-url=https://web.archive.org/web/20120417112149/http://www.daimi.au.dk/~bra8130/Wiley_book/wiley.pdf |url-status=dead }}
*{{cite book |year=1993 |author-link=Glynn Winskel |first=Glynn |last=Winskel |title=The Formal Semantics of Programming Languages: An Introduction |publisher=MIT Press |isbn=0-262-73103-7 }}
*{{cite book |year=1995 |author-link=John C. Mitchell |last=Mitchell |first=John C. |url=http://www.lix.polytechnique.fr/~catuscia/teaching/cg520/papers_and_books/Mitchell_book.ps.gz |title=Foundations for Programming Languages |format=Postscript}}
*{{cite book |year=1995 |author-link=Kenneth Slonneger |firstfirst1=Kenneth |lastlast1=Slonneger |author-link2=Barry L. Kurtz |first2=Barry L. |last2=Kurtz |title=Formal Syntax and Semantics of Programming Languages |publisher=Addison-Wesley |isbn=0-201-65697-3 |url=http://www.cs.uiowa.edu/~slonnegr/plf/Book/}}
*{{cite book |year=1998 |author-link=John C. Reynolds |first=John C. |last=Reynolds |title=Theories of Programming Languages |url=https://archive.org/details/theoriesofprogra0000reyn |url-access=registration |publisher=Cambridge University Press |isbn=0-521-59414-6 }}
*{{cite book |year=2006 |author-link=Robert Harper (computer scientist) |first=Robert |last=Harper |title=Practical Foundations for Programming Languages |url=https://www.cs.cmu.edu/~rwh/plbook/book.pdf |format=PDF |url-status=dead |archive-url=https://web.archive.org/web/20070627041059/https://www.cs.cmu.edu/~rwh/plbook/book.pdf |archive-date=2007-06-27 }} (Working draft)
*{{cite book |firstfirst1=H. R. |lastlast1=Nielson |first2=Flemming |last2=Nielson |title=Semantics with Applications: An Appetizer |url=https://books.google.com/books?id=oPi0yERDUeYC |date=2007 |publisher=Springer |isbn=978-1-84628-692-6}}
*{{cite book |year=2014 |author-link=Aaron Stump |first=Aaron |last=Stump |title=Programming Language Foundations |publisher=Wiley |isbn=978-1-118-00747-1 }}
*{{cite web |author-link=Shriram Krishnamurthi |first=Shriram |last=Krishnamurthi |title=Programming Languages: Application and Interpretation |date=2012 |edition=2nd |url=http://cs.brown.edu/courses/cs173/2012/book/}}
; Lecture notes
*{{cite web |first=Glynn |last=Winskel |title=Denotational Semantics |publisher=University of Cambridge |url=http://www.cl.cam.ac.uk/~gw104/dens.pdf |format=PDF}}
{{refend}}
 
== External links ==
* {{cite book|last=Aaby|first=Anthony|title=Introduction to Programming Languages|year=2004|url=http://www.emu.edu.tr/aelci/Courses/D-318/D-318-Files/plbook/semantic.htm|url-status=bot: unknowndead|archive-url=https://web.archive.org/web/20150619164601/http://www.emu.edu.tr/aelci/Courses/D-318/D-318-Files/plbook/semantic.htm|archive-date=2015-06-19}} Semantics.
 
{{DEFAULTSORT:Semantics Of Programming Languages}}
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