Advertisement

Comodels and Effects in Mathematical Operational Semantics

  • Faris Abou-Saleh
  • Dirk Pattinson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7794)

Abstract

In the mid-nineties, Turi and Plotkin gave an elegant categorical treatment of denotational and operational semantics for process algebra-like languages, proving compositionality and adequacy by defining operational semantics as a distributive law of syntax over behaviour. However, its applications to stateful or effectful languages, incorporating (co)models of a countable Lawvere theory, have been elusive so far. We make some progress towards a coalgebraic treatment of such languages, proposing a congruence format related to the evaluation-in-context paradigm. We formalise the denotational semantics in suitable Kleisli categories, and prove adequacy and compositionality of the semantic theory under this congruence format.

Keywords

Transition System Natural Transformation Operational Semantic Denotational Semantic Semantic Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abou-Saleh, F., Pattinson, D.: Towards effects in mathematical operational semantics. Electr. Notes Theor. Comput. Sci. 276, 81–104 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Adamek, J.: Recursive data types in algebraically w-complete categories. Information and Computation 118(2), 181–190 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Adámek, J., Rosický, J.: Locally Presentable and Accessible Categories. Cambridge University Press (1994)Google Scholar
  4. 4.
    Hasuo, I., Jacobs, B., Sokolova, A.: Generic trace semantics via coinduction. Logical Methods in Computer Science 3(4) (2007)Google Scholar
  5. 5.
    Hyland, M., Plotkin, G., Power, J.: Combining effects: sum and tensor. Theor. Comput. Sci. 357, 70–99 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Hyland, M., Power, J.: Discrete lawvere theories and computational effects. Theor. Comput. Sci. 366(1-2), 144–162 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Johann, P., Simpson, A., Voigtländer, J.: A generic operational metatheory for algebraic effects. In: Proc. LICS 2010, pp. 209–218. IEEE Computer Society (2010)Google Scholar
  8. 8.
    Kelly, G.M.: Basic concepts of enriched category theory. Reprints in Theory and Applications of Categories (10), 1–136 (2005)Google Scholar
  9. 9.
    Klin, B.: Bialgebraic methods in structural operational semantics. Electron. Notes Theor. Comput. Sci. 175(1), 33–43 (2007)CrossRefGoogle Scholar
  10. 10.
    Kock, A.: Strong functors and monoidal monads. Archiv der Mathematik 23 (1972)Google Scholar
  11. 11.
    Lenisa, M., Power, J., Watanabe, H.: Category theory for operational semantics. Theor. Comput. Sci. 327(1-2), 135–154 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Moggi, E.: Notions of computation and monads. Inf. Comput. 93(1), 55–92 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Monteiro, L.: A Coalgebraic Characterization of Behaviours in the Linear Time – Branching Time Spectrum. In: Corradini, A., Montanari, U. (eds.) WADT 2008. LNCS, vol. 5486, pp. 251–265. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  14. 14.
    Plotkin, G., Power, J.: Tensors of comodels and models for operational semantics. Electron. Notes Theor. Comput. Sci. 218, 295–311 (2008)CrossRefGoogle Scholar
  15. 15.
    Plotkin, G.D., Power, J.: Adequacy for Algebraic Effects. In: Honsell, F., Miculan, M. (eds.) FOSSACS 2001. LNCS, vol. 2030, pp. 1–24. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Plotkin, G., Power, J.: Notions of Computation Determine Monads. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, pp. 342–356. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    Power, J.: Countable lawvere theories and computational effects. Electr. Notes Theor. Comput. Sci. 161, 59–71 (2006)CrossRefGoogle Scholar
  18. 18.
    Power, J.: Semantics for local computational effects. Electr. Notes Theor. Comput. Sci. 158, 355–371 (2006)CrossRefGoogle Scholar
  19. 19.
    Power, J., Shkaravska, O.: From comodels to coalgebras: State and arrays. Electron. Notes Theor. Comput. Sci. 106 (2004)Google Scholar
  20. 20.
    Power, J., Turi, D.: A coalgebraic foundation for linear time semantics. In: Category Theory and Computer Science. Elsevier (1999)Google Scholar
  21. 21.
    Staton, S.: Completeness for Algebraic Theories of Local State. In: Ong, L. (ed.) FOSSACS 2010. LNCS, vol. 6014, pp. 48–63. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  22. 22.
    Turi, D.: Functorial Operational Semantics and its Denotational Dual. PhD thesis, Free University, Amsterdam (June 1996)Google Scholar
  23. 23.
    Turi, D.: Categorical modelling of structural operational rules: Case studies. In: Category Theory and Computer Science, pp. 127–146 (1997)Google Scholar
  24. 24.
    Turi, D., Plotkin, G.D.: Towards a mathematical operational semantics. In: LICS, pp. 280–291 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Faris Abou-Saleh
    • 1
  • Dirk Pattinson
    • 2
  1. 1.Department of ComputingImperial College LondonUK
  2. 2.Research School of Computer ScienceAustralian National UniversityAustralia

Personalised recommendations