The Anatomy of Innocence

  • Vincent Danos
  • Russell Harmer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2142)

Abstract

We reveal a symmetric structure in the ho/n games model of innocent strategies, introducing rigid strategies, a concept dual to bracketed strategies. We prove a direct definability theorem of general innocent strategies with respect to a simply typed language of extended Böhm trees, which gives an operational meaning to rigidity in call-by-name. A corresponding factorization of innocent strategies into rigid ones with some form of conditional as an oracle is constructed.

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References

  1. [AHM98]
    Samson Abramsky, Kohei Honda, and Guy McCusker. A fully abstract game semantics for general references. In Proceedings, Thirteenth Annual IEEE Symposium on Logic in Computer Science, pages 334–344, 1998.Google Scholar
  2. [AM97]
    Samson Abramsky and Guy McCusker. Linearity, sharing and state: a fully abstract game semantics for Idealized Algol with active expressions. In P. W. O’Hearn and R. D. Tennent, editors, Algol-like languages. Birkhaüser, 1997.Google Scholar
  3. [DH00]
    Vincent Danos and Russell Harmer. Probabilistic games semantics. In Proceedings of the 15 th Symposium on Logic in Computer Science, Santa Barbara, 2000. IEEE.Google Scholar
  4. [DHR96]
    Vincent Danos, Hugo Herbelin, and Laurent Regnier. Games semantics and abstract machines. In Proceedings of the 11 th Symposium on Logic in Computer Science, pages 394–405, New Brunswick, 1996. IEEE.Google Scholar
  5. [Her97]
    Hugo Herbelin. Games and weak head reduction for classical PCF. In ?, editor, Proceedings of TLCA’97, number 1210 in Lecture Notes in Computer Science, pages ?-?, ?, 1997. Springer Verlag.Google Scholar
  6. [HM99]
    R. S. Harmer and G. A. McCusker. A fully abstract game semantics for finite nondeterminism. In Proceedings, Fourteenth Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, 1999.Google Scholar
  7. [HO94]
    J. M. E. Hyland and C.-H. L. Ong. On full abstraction for PCF: I, II and III. To appear in Information and Computation, 200?, 1994.Google Scholar
  8. [Lai97]
    J. Laird. Full abstraction for functional languages with control. In Proceedings, Twelfth Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, 1997.Google Scholar
  9. [Lau99]
    Olivier Laurent. Polarized proof nets and λμ-calculus. Submitted to Theoretical Computer Science, 1999.Google Scholar
  10. [Lev98]
    P. B. Levy. Game semantics as continuation passing (extended abstract). unpublished, 1998.Google Scholar
  11. [McC96]
    Guy McCusker. Games and full abstraction for FPC. In Proceedings, Eleventh Annual IEEE Symposium on Logic in Computer Science, pages 174–183. IEEE Computer Society Press, 1996.Google Scholar
  12. [McC98]
    Guy McCusker. Games and Full Abstraction for a Functional Metalanguage with Recursive Types. Distinguished Dissertations in Computer Science. Springer-Verlag, 1998.Google Scholar
  13. [MH99]
    P. Malacaria and C. Hankin. Non-deterministic games and program analysis: An application to security. In Proceedings, Fourteenth Annual IEEE Symposium on Logic in Computer Science IEEE Computer Society Press, 1999.Google Scholar
  14. [Nic94]
    Hanno Nickau. Hereditarily sequential functionals. In Proceedings, Logical Foundations of Computer Science, volume 813 of Lecture Notes in Computer Science. Springer-Verlag, 1994.Google Scholar
  15. [Sel99]
    Peter Selinger. Control categories and duality: on the categorical semantics of the λμ-calculus. To appear, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Vincent Danos
    • 1
  • Russell Harmer
    • 2
  1. 1.Equipe Preuves, Programmes, SystèmesUniversité ParisParis Cedex 05France
  2. 2.School of Cognitive and Computing SciencesUniversity of SussexBrightonUK

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