In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages.[1] Semantics assigns computational meaning to valid strings in a programming language syntax. It is closely related to, and often crosses over with, the semantics of mathematical proofs.

Semantics describes the processes a computer follows when 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 platform, thereby creating a model of computation.


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 proofs of correctness, equivalence, and termination".[2][3] Floyd further wrote:[2]

A semantic definition of a programming language, in our approach, is founded on a syntactic definition. It must specify which of the phrases in a syntactically correct program represent commands, and what conditions must be imposed on an interpretation in the neighborhood of each command.

In 1969, Tony Hoare published a paper on Hoare logic seeded by Floyd's ideas, now sometimes collectively called axiomatic semantics.[4][5]

In the 1970s, the terms operational semantics and denotational semantics emerged.[5]


The field of formal semantics encompasses all of the following:

It has close links with other areas of computer science such as programming language design, type theory, compilers and interpreters, program verification and model checking.


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

Apart from the choice between denotational, operational, or axiomatic approaches, most variations in formal semantic systems arise from the choice of supporting mathematical formalism.[citation needed]


Some variations of formal semantics include the following:

Describing relationships

For a variety of reasons, one might wish to describe the relationships between different formal semantics. For example:

It is also possible to relate multiple semantics through abstractions via the theory of abstract interpretation.[citation needed]

See also


  1. ^ Goguen, Joseph A. (1975). "Semantics of computation". Category Theory Applied to Computation and Control. Lecture Notes in Computer Science. Vol. 25. Springer. pp. 151–163. doi:10.1007/3-540-07142-3_75. ISBN 978-3-540-07142-6.
  2. ^ a b Floyd, Robert W. (1967). "Assigning Meanings to Programs" (PDF). In Schwartz, J.T. (ed.). Mathematical Aspects of Computer Science. Proceedings of Symposium on Applied Mathematics. Vol. 19. American Mathematical Society. pp. 19–32. ISBN 0821867288.
  3. ^ Knuth, Donald E. "Memorial Resolution: Robert W. Floyd (1936–2001)" (PDF). Stanford University Faculty Memorials. Stanford Historical Society.
  4. ^ Hoare, C. A. R. (October 1969). "An axiomatic basis for computer programming". Communications of the ACM. 12 (10): 576–580. doi:10.1145/363235.363259. S2CID 207726175.
  5. ^ a b Winskel, Glynn (1993). The formal semantics of programming languages : an introduction. Cambridge, Mass.: MIT Press. p. xv. ISBN 978-0-262-23169-5.
  6. ^ Schmidt, David A. (1986). Denotational Semantics: A Methodology for Language Development. William C. Brown Publishers. ISBN 9780205104505.
  7. ^ Plotkin, Gordon D. (1981). A structural approach to operational semantics (Report). Technical Report DAIMI FN-19. Computer Science Department, Aarhus University.
  8. ^ a b Goguen, Joseph A.; Thatcher, James W.; Wagner, Eric G.; Wright, Jesse B. (1977). "Initial algebra semantics and continuous algebras". Journal of the ACM. 24 (1): 68–95. doi:10.1145/321992.321997. S2CID 11060837.
  9. ^ Mosses, Peter D. (1996). Theory and practice of action semantics (Report). BRICS Report RS9653. Aarhus University.
  10. ^ Deransart, Pierre; Jourdan, Martin; Lorho, Bernard (1988). "Attribute Grammars: Definitions, Systems and Bibliography. Lecture Notes in Computer Science 323. Springer-Verlag. ISBN 9780387500560.
  11. ^ Lawvere, F. William (1963). "Functorial semantics of algebraic theories". Proceedings of the National Academy of Sciences of the United States of America. 50 (5): 869–872. Bibcode:1963PNAS...50..869L. doi:10.1073/pnas.50.5.869. PMC 221940. PMID 16591125.
  12. ^ Andrzej Tarlecki; Rod M. Burstall; Joseph A. Goguen (1991). "Some fundamental algebraic tools for the semantics of computation: Part 3. Indexed categories". Theoretical Computer Science. 91 (2): 239–264. doi:10.1016/0304-3975(91)90085-G.
  13. ^ Batty, Mark; Memarian, Kayvan; Nienhuis, Kyndylan; Pichon-Pharabod, Jean; Sewell, Peter (2015). "The problem of programming language concurrency semantics" (PDF). Proceedings of the European Symposium on Programming Languages and Systems. Springer. pp. 283–307. doi:10.1007/978-3-662-46669-8_12.
  14. ^ Abramsky, Samson (2009). "Semantics of interaction: An introduction to game semantics". In Andrew M. Pitts; P. Dybjer (eds.). Semantics and Logics of Computation. Cambridge University Press. pp. 1–32. doi:10.1017/CBO9780511526619.002. ISBN 9780521580571.
  15. ^ Dijkstra, Edsger W. (1975). "Guarded commands, nondeterminacy and formal derivation of programs". Communications of the ACM. 18 (8): 453–457. doi:10.1145/360933.360975. S2CID 1679242.

Further reading

Lecture notes