803:, 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
1042:
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
964:
as the core mathematical formalism. 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
935:. 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
1026:
To prove that a particular operational semantics for a language satisfies the logical formulas of an axiomatic semantics for that language. Such a proof demonstrates that it is "sound" to reason about a particular (operational)
882:
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
1446:
633:
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
865:
Apart from the choice between denotational, operational, or axiomatic approaches, most variations in formal semantic systems arise from the choice of supporting mathematical formalism.
1751:
811:. Denotational semantic descriptions can also serve as compositional translations from a programming language into the denotational metalanguage and used as a basis for designing
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1850:
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2012:
17:
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is a catch-all term for any formal semantics that describes concurrent computations. Historically important concurrent formalisms have included the
1854:
1811:
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that apply to them. Axiomatic semantics makes no distinction between a phrase's meaning and the logical formulas that describe it; its meaning
827:, although again the "implementation language" of the interpreter is generally a mathematical formalism. Operational semantics may define an
1950:
823:, whereby the execution of the language is described directly (rather than by translation). Operational semantics loosely corresponds to
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835:), and give meaning to phrases by describing the transitions they induce on states of the machine. Alternatively, as with the pure
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1326:(1981). A structural approach to operational semantics (Report). Technical Report DAIMI FN-19. Computer Science Department,
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For a variety of reasons, one might wish to describe the relationships between different formal semantics. For example:
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1690:. Proceedings of Symposium on Applied Mathematics. Vol. 19. American Mathematical Society. pp. 19–32.
1173:. Proceedings of Symposium on Applied Mathematics. Vol. 19. American Mathematical Society. pp. 19–32.
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50:
1583:(2009). "Semantics of interaction: An introduction to game semantics". In Andrew M. Pitts; P. Dybjer (eds.).
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2018:
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The semantics of programming languages: an elementary introduction using structural operational semantics
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839:, operational semantics can be defined via syntactic transformations on phrases of the language itself;
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exactly what can be proven about it in some logic. The canonical example of axiomatic semantics is
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Batty, Mark; Memarian, Kayvan; Nienhuis, Kyndylan; Pichon-Pharabod, Jean; Sewell, Peter (2015).
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The relation between computation and the underlying mathematical structures from fields such as
1511:"Some fundamental algebraic tools for the semantics of computation: Part 3. Indexed categories"
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definition. It must specify which of the phrases in a syntactically correct program represent
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658:; his chief aim was "a rigorous standard for proofs about computer programs, including
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There are many approaches to formal semantics; these belong to three major classes:
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A semantic definition of a programming language, in our approach, is founded on a
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Proceedings of the
National Academy of Sciences of the United States of America
1393:(1996). Theory and practice of action semantics (Report). BRICS Report RS9653.
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To prove that operational semantics over a high-level machine is related by a
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1005:, describes the meaning of a program fragment as the function transforming a
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Proceedings of the
European Symposium on Programming Languages and Systems
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must be imposed on an interpretation in the neighborhood of each command.
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1623:"Guarded commands, nondeterminacy and formal derivation of programs"
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The formal semantics of programming languages : an introduction
1079:
936:
924:
812:
765:
355:
896:
1347:; Thatcher, James W.; Wagner, Eric G.; Wright, Jesse B. (1977).
719:
The field of formal semantics encompasses all of the following:
1816:
The Formal
Semantics of Programming Languages: An Introduction
1300:
Denotational
Semantics: A Methodology for Language Development
849:
619:. It is closely related to, and often crosses over with, the
1546:"The problem of programming language concurrency semantics"
1408:
Deransart, Pierre; Jourdan, Martin; Lorho, Bernard (1988).
873:
Some variations of formal semantics include the following:
690:
seeded by Floyd's ideas, now sometimes collectively called
1410:"Attribute Grammars: Definitions, Systems and Bibliography
1343:
797:, whereby each phrase in the language is interpreted as a
34:
Mathematical study of the meaning of programming languages
1047:
It is also possible to relate multiple semantics through
847:, whereby one gives meaning to phrases by describing the
1977:"Programming Languages: Application and Interpretation"
662:, equivalence, and termination". Floyd further wrote:
1407:
729:
The relations between different approaches to meaning
603:
is the rigorous mathematical study of the meaning of
1860:
Formal Syntax and
Semantics of Programming Languages
1349:"Initial algebra semantics and continuous algebras"
1121:. Lecture Notes in Computer Science. Vol. 25.
1882:
1776:Semantics With Applications: A Formal Introduction
1198:"Memorial Resolution: Robert W. Floyd (1936–2001)"
1119:Category Theory Applied to Computation and Control
2028:
629:describes the processes a computer follows when
1910:Practical Foundations for Programming Languages
726:The relations between different semantic models
1928:
1849:
1772:
1971:
1589:. Cambridge University Press. pp. 1–32.
1223:"An axiomatic basis for computer programming"
576:
380:
1611:
1573:
1442:"Functorial semantics of algebraic theories"
923:define systems that systematically compute "
1430:
1017:
1929:Nielson, H. R.; Nielson, Flemming (2007).
1773:Nielson, H. R.; Nielson, Flemming (1992).
1339:
1337:
1316:
1291:
583:
569:
387:
373:
1932:Semantics with Applications: An Appetizer
1640:
1564:
1528:
1477:
1467:
1412:. Lecture Notes in Computer Science 323.
1383:
1366:
1262:
1260:
1240:
1877:
1832:
1704:
1687:Mathematical Aspects of Computer Science
1617:
1579:
1170:Mathematical Aspects of Computer Science
899:laws for describing and reasoning about
1810:
1726:
1436:
1334:
1322:
1297:
1273:. Cambridge, Mass.: MIT Press. p.
1266:
1152:
1150:
752:It has close links with other areas of
14:
2029:
1903:
1750:
1389:
1257:
1113:
2014:Introduction to Programming Languages
1949:
1839:Foundations for Programming Languages
1673:
1217:
1205:Stanford University Faculty Memorials
1156:
2010:
1211:
1147:
1117:(1975). "Semantics of computation".
1990:
1586:Semantics and Logics of Computation
24:
1756:Semantics of Programming Languages
1733:Semantics of Programming Languages
1661:
807:often translate the language into
25:
18:Semantics of programming languages
2063:
2004:
1885:Theories of Programming Languages
1193:
723:The definition of semantic models
450:Semantics (programming languages)
1955:Programming Language Foundations
1679:"Assigning Meanings to Programs"
1162:"Assigning Meanings to Programs"
621:semantics of mathematical proofs
1537:
1494:
1401:
1302:. William C. Brown Publishers.
1031:using a particular (axiomatic)
998:Predicate transformer semantics
2052:Programming language semantics
2047:Formal specification languages
1889:. Cambridge University Press.
1207:. Stanford Historical Society.
1187:
1107:
1085:Ontology (information science)
1075:Formal semantics (linguistics)
656:Assigning meanings to programs
13:
1:
1100:
868:
783:
1595:10.1017/CBO9780511526619.002
1566:10.1007/978-3-662-46669-8_12
1530:10.1016/0304-3975(91)90085-G
1516:Theoretical Computer Science
989:uses a metaphor inspired by
7:
1684:. In Schwartz, J.T. (ed.).
1167:. In Schwartz, J.T. (ed.).
1058:
958:(or "functorial") semantics
931:) for the various cases of
758:programming language design
714:
617:programming language syntax
597:programming language theory
535:Programming language theory
530:Natural language processing
10:
2068:
1998:. University of Cambridge.
1298:Schmidt, David A. (1986).
645:
319:Predicate transformational
26:
2042:Logic in computer science
1628:Communications of the ACM
1228:Communications of the ACM
907:manner. It also supports
555:Automated theorem proving
540:Computational linguistics
1993:"Denotational Semantics"
1131:10.1007/3-540-07142-3_75
1070:Formal semantics (logic)
1018:Describing relationships
699:In the 1970s, the terms
27:Not to be confused with
1267:Winskel, Glynn (1993).
1065:Computational semantics
1053:abstract interpretation
1029:interpretation strategy
1013:needed to establish it.
341:Abstract semantic graph
336:Abstract interpretation
29:Computational semantics
2011:Aaby, Anthony (2004).
1973:Krishnamurthi, Shriram
909:denotational semantics
794:Denotational semantics
708:denotational semantics
680:
515:Propositional calculus
160:Theory of descriptions
129:Context (language use)
1642:10.1145/360933.360975
1469:10.1073/pnas.50.5.869
1368:10.1145/321992.321997
1242:10.1145/363235.363259
970:Concurrency semantics
945:context-free grammars
933:the language's syntax
913:operational semantics
820:Operational semantics
702:operational semantics
686:published a paper on
664:
660:proofs of correctness
638:, thereby creating a
605:programming languages
525:Mathematical notation
260:programming languages
1559:. pp. 283–307.
1125:. pp. 151–163.
1090:Semantic equivalence
805:functional languages
774:program verification
654:published the paper
640:model of computation
607:. Semantics assigns
204:Semantic file system
1619:Dijkstra, Edsger W.
1460:1963PNAS...50..869L
1438:Lawvere, F. William
1095:Semantic technology
893:axiomatic semantics
888:Algebraic semantics
844:Axiomatic semantics
693:axiomatic semantics
550:Formal verification
465:Well-formed formula
224:Semantic similarity
1863:. Addison-Wesley.
1851:Slonneger, Kenneth
1728:Tennent, Robert D.
1501:Andrzej Tarlecki;
1354:Journal of the ACM
1324:Plotkin, Gordon D.
1051:via the theory of
1003:Edsger W. Dijkstra
920:Attribute grammars
475:Regular expression
1964:978-1-118-00747-1
1942:978-1-84628-692-6
1879:Reynolds, John C.
1834:Mitchell, John C.
1789:978-0-471-92980-2
1743:978-0-13-805599-8
1736:. Prentice Hall.
1719:978-0-471-92772-3
1395:Aarhus University
1345:Goguen, Joseph A.
1328:Aarhus University
1284:978-0-262-23169-5
1140:978-3-540-07142-6
1115:Goguen, Joseph A.
949:context-sensitive
939:, and to augment
901:program semantics
611:meaning to valid
593:
592:
485:Ground expression
445:Semantics (logic)
397:
396:
348:
347:
252:
251:
214:Semantic matching
16:(Redirected from
2059:
2022:
2017:. Archived from
1999:
1997:
1991:Winskel, Glynn.
1980:
1968:
1946:
1924:
1922:
1916:. Archived from
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1900:
1888:
1874:
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1844:
1829:
1807:
1805:
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1798:
1792:. Archived from
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1723:
1701:
1683:
1675:Floyd, Robert W.
1655:
1654:
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1581:Abramsky, Samson
1577:
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1221:(October 1969).
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1195:Knuth, Donald E.
1191:
1185:
1184:
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1158:Floyd, Robert W.
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879:Action semantics
829:abstract machine
754:computer science
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414:Formal languages
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219:Semantic parsing
209:Semantic desktop
187:Machine-learning
150:Semantic feature
137:Prototype theory
124:Compositionality
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1979:(2nd ed.).
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1855:Kurtz, Barry L.
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1235:(10): 576–580.
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1001:, developed by
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962:category theory
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837:lambda calculus
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746:category theory
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652:Robert W. Floyd
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2019:the original
2013:
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1951:Stump, Aaron
1935:. Springer.
1931:
1918:the original
1909:
1884:
1859:
1843:(Postscript)
1838:
1815:
1801:. Retrieved
1794:the original
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1752:Gunter, Carl
1732:
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1706:Hennessy, M.
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503:Applications
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423:Key concepts
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304:Denotational
258:Semantics of
257:
237:Semantic Web
196:Applications
155:Semantic gap
991:game theory
975:actor model
956:Categorical
951:conditions;
859:Hoare logic
762:type theory
688:Hoare logic
674:, and what
361:Linguistics
314:Operational
299:Concurrency
294:Categorical
97:Statistical
2031:Categories
2023:Semantics.
1803:2011-05-27
1697:0821867288
1180:0821867288
1101:References
1040:simulation
965:semantics;
929:attributes
927:" (called
869:Variations
800:denotation
784:Approaches
738:set theory
684:Tony Hoare
676:conditions
480:Production
102:Structural
91:lexicology
51:Linguistic
1957:. Wiley.
1782:. Wiley.
1712:. Wiley.
1667:Textbooks
1251:207726175
937:compilers
897:algebraic
895:based on
813:compilers
766:compilers
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682:In 1969,
668:syntactic
650:In 1967,
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627:Semantics
601:semantics
289:Axiomatic
284:Algebraic
69:Subfields
41:Semantics
1975:(2012).
1953:(2014).
1907:(2006).
1881:(1998).
1857:(1995).
1836:(1995).
1814:(1993).
1754:(1992).
1730:(1991).
1708:(1990).
1677:(1967).
1621:(1975).
1557:Springer
1509:(1991).
1488:16591125
1440:(1963).
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1123:Springer
1080:Ontology
1059:See also
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925:metadata
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715:Overview
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435:Alphabet
405:a series
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168:Analysis
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440:Syntax
328:Theory
279:Action
177:Latent
111:Topics
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1921:(PDF)
1914:(PDF)
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1780:(PDF)
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903:in a
734:logic
615:in a
270:Types
87:lexis
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1937:ISBN
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