Synchronous Game Semantics via Round Abstraction

  • Dan R. Ghica
  • Mohamed N. Menaa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6604)

Abstract

A synchronous game semantics—one in which several moves may occur simultaneously—is derived from a conventional (sequential) game semantics using a round abstraction algorithm. We choose the programming language Syntactic Control of Interference and McCusker’s fully abstract relational model as a convenient starting point and derive a synchronous game model first by refining the relational semantics into a trace semantics, then applying a round abstraction to it. We show that the resulting model is sound but not fully abstract. This work is practically motivated by applications to hardware synthesis via game semantics.

References

  1. 1.
    Abramsky, S., Jagadeesan, R., Malacaria, P.: Full abstraction for PCF. Inf. Comput. 163(2), 409–470 (2000)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Alur, R., Henzinger, T.A.: Reactive Modules. Formal Methods in System Design 15(1), 7–48 (1999)CrossRefGoogle Scholar
  3. 3.
    Berry, G., Gonthier, G.: The Esterel synchronous programming language: design, semantics and implementation. Sci. Comput. Program. 19(2), 87–152 (1992)CrossRefMATHGoogle Scholar
  4. 4.
    Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252 (1977)Google Scholar
  5. 5.
    Ghica, D.R.: Geometry of Synthesis: a structured approach to VLSI design. In: POPL, pp. 363–375 (2007)Google Scholar
  6. 6.
    Ghica, D.R., Menaa, M.N.: On the compositionality of round abstraction. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 417–431. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Ghica, D.R., Murawski, A.S.: Compositional model extraction for higher-order concurrent programs. In: Hermanns, H. (ed.) TACAS 2006. LNCS, vol. 3920, pp. 303–317. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Ghica, D.R., Murawski, A.S.: Angelic semantics of fine-grained concurrency. Ann. Pure Appl. Logic 151(2-3), 89–114 (2008)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Ghica, D.R., Murawski, A.S., Ong, C.-H.L.: Syntactic control of concurrency. Theor. Comput. Sci. 350(2-3), 234–251 (2006)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Ghica, D.R., Smith, A.: Geometry of Synthesis II: From games to delay-insensitive circuits. In: MFPS XXVI (2010)Google Scholar
  11. 11.
    Ghica, D.R., Smith, A.: Geometry of Synthesis III: Resource management through type inference. In: POPL (2011)(forthcoming)Google Scholar
  12. 12.
    Hyland, J.M.E., Ong, C.-H.L.: On full abstraction for PCF: I, II, and III. Inf. Comput. 163(2), 285–408 (2000)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    McCusker, G.: A Fully Abstract Relational Model of Syntactic Control of Interference. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 247–261. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    McCusker, G.: A graph model for imperative computation. Logical Methods in Computer Science 6(1) (2010), doi:10.2168/LMCS-6(1:2)2010Google Scholar
  15. 15.
    O’Hearn, P.W., Power, J., Takeyama, M., Tennent, R.D.: Syntactic control of interference revisited. Theor. Comput. Sci. 228(1-2), 211–252 (1999)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Reddy, U.S.: Global state considered unnecessary: An introduction to object-based semantics. Lisp and Symbolic Computation 9(1), 7–76 (1996)CrossRefGoogle Scholar
  17. 17.
    Reynolds, J.C.: Syntactic control of interference. In: POPL, pp. 39–46 (1978)Google Scholar
  18. 18.
    Reynolds, J.C.: The essence of Algol. In: Proceedings of the 1981 International Symposium on Algorithmic Languages, pp. 345–372. North-Holland, Amsterdam (1981)Google Scholar
  19. 19.
    Wall, M.: Games for Syntactic Control of Interference. PhD thesis, University of Sussex (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dan R. Ghica
    • 1
  • Mohamed N. Menaa
    • 1
  1. 1.University of BirminghamU.K.

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