Projecting Games on Hypercoherences

  • Pierre Boudes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)


We compare two interpretations of programming languages: game semantics (a dynamic semantics dealing with computational traces) and hypercoherences (a static semantics dealing with results of computation). We consider polarized bordered games which are Laurent’s polarized games endowed with a notion of terminated computation (the border) allowing for a projection on hypercoherences. The main result is that the projection commutes to the interpretation of linear terms (exponential-free proofs of polarized linear logic). We discuss the extension to general terms.


Game Model Sequential Algorithm Linear Logic Central Strategy Dynamic Semantic 
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  1. 1.
    Abramsky, S., Jagadeesan, R., Malacaria, P.: Full abstraction for PCF. In: Theoretical Aspects of Computer Software, pp. 1–15 (1994)Google Scholar
  2. 2.
    Baillot, P., Danos, V., Ehrhard, T., Regnier, L.: Timeless games. In: Nielsen, M. (ed.) CSL 1997. LNCS, vol. 1414, pp. 56–77. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  3. 3.
    Berry, G., Curien, P.-L.: Sequential algorithms on concrete data structures. Theoretical Computer Science 20, 265–321 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bierman, G.M.: What is a categorical model of intuitionistic linear logic? In: Dezani-Ciancaglini, M., Plotkin, G. (eds.) TLCA 1995. LNCS, vol. 902, Springer, Heidelberg (1995)CrossRefGoogle Scholar
  5. 5.
    Boudes, P.: Non uniform hypercoherences. In: Blute, R., Selinger, P. (eds.) Electronic Notes in Theoretical Computer Science, vol. 69, Elsevier, Amsterdam (2003)Google Scholar
  6. 6.
    Bucciarelli, A., Ehrhard, T.: Sequentiality in an extensional framework. Information and Computation 110(2) (1994)Google Scholar
  7. 7.
    Ehrhard, T.: Hypercoherences: a strongly stable model of linear logic. Mathematical Structures in Computer Science 3 (1993)Google Scholar
  8. 8.
    Ehrhard, T.: A relative definability result for strongly stable functions and some corollaries. Information and Computation 152 (1999)Google Scholar
  9. 9.
    Ehrhard, T.: Parallel and serial hypercoherences. Theoretical computer science 247, 39–81 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Girard, J.-Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hyland, M., Ong, L.: On full abstraction for PCF: I, II and III. Information and Computation 163(2), 285–408 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Laird, J.: Games and sequential algorithms. Available by http (2001)Google Scholar
  13. 13.
    Lamarche, F.: Sequentiality, games and linear logic (announcement). In: Workshop on Categorical Logic in Computer Science. Publications of the Computer Science Department of Aarhus University, DAIMI PB-397-II (1992)Google Scholar
  14. 14.
    Laurent, O.: Étude de la polarisation en logique. Thèse de doctorat, Université Aix-Marseille II (March 2002)Google Scholar
  15. 15.
    Laurent, O.: Polarized games (extended abstract). In: Proceedings of the seventeenth annual IEEE symposium on Logic In Computer Science, July 2002, pp. 265–274. IEEE Computer Society Press, Los Alamitos (2002)Google Scholar
  16. 16.
    Longley, J.R.: The sequentially realizable functionals. Annals of Pure and Applied Logic 117(1-3), 1–93 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Melliès, P.-A.: Sequential algorithms and strongly stable functions. To appear in the special issue of TCS: Game Theory Meets Theoretical Computer Science (2003)Google Scholar
  18. 18.
    Melliès, P.-A.: Comparing hierarchies of types in models of linear logic. Information and Computation 189(2), 202–234 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Selinger, P.: Control categories and duality: on the categorical semantics of the lambda-mu calculus. Mathematical Structures in Computer Science 11, 207–260 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    van Oosten, J.: A combinatory algebra for sequential functionals of finite type. Technical Report 996, University of Utrecht (1997)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Pierre Boudes
    • 1
  1. 1.Institut de mathématiques de Luminy UMR 6206Marseille cedex 9France

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