On the Compositionality of Round Abstraction

  • Dan R. Ghica
  • Mohamed N. Menaa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6269)


We revisit a technique called round abstraction as a solution to the problem of building low-latency synchronous systems from asynchronous specifications. We use a trace-semantic setting akin to Abramsky’s Interaction Categories, which is also a generalisation of pointer-free game semantic models. We define partial and total correctness for round abstraction relative to composition and note that in its most general case, round abstraction can lead to incorrect behaviour. We then identify sufficient properties to guarantee partially correct composition. Finally, we propose a framework for round abstraction that is totally correct when applied to asynchronous behaviours. We apply this procedure to the Geometry of Synthesis, a technique for compiling higher-order imperative programming languages into digital circuits using game semantics.


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  1. 1.
    Milner, R.: Calculi for synchrony and asynchrony. Theor. Comput. Sci. 25, 267–310 (1983)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)Google Scholar
  3. 3.
    Halbwachs, N., Mandel, L.: Simulation and verification of asynchronous systems by means of a synchronous model. In: ACSD, pp. 3–14. IEEE Computer Society, Los Alamitos (2006)Google Scholar
  4. 4.
    Benveniste, A., Caillaud, B., Guernic, P.L.: From synchrony to asynchrony. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 162–177. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Alur, R., Henzinger, T.A.: Reactive modules. Formal Methods in System Design 15(1), 7–48 (1999)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Ghica, D.R.: Geometry of Synthesis: a structured approach to VLSI design. In: POPL, pp. 363–375 (2007)Google Scholar
  7. 7.
    Ghica, D.R.: Function interface models for hardware compilation: Types, signatures, protocols. CoRR abs/0907.0749 (2009)Google Scholar
  8. 8.
    Ghica, D.R.: Applications of game semantics: From software analysis to hardware synthesis. In: LICS, pp. 17–26 (2009)Google Scholar
  9. 9.
    Abramsky, S., Melliès, P.A.: Concurrent games and full completeness. In: LICS, pp. 431–442 (1999)Google Scholar
  10. 10.
    Ghica, D.R., Murawski, A.: Angelic semantics of fine-grained concurrency. Annals of Pure and Applied Logic 151(2-3), 89–114 (2008)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ghica, D.R., Murawski, A.S., Ong, C.H.L.: Syntactic control of concurrency. Theor. Comput. Sci. 350(2-3), 234–251 (2006)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Berry, G., Gonthier, G.: The Esterel synchronous language: design, semantics and implementation. Technical Report 842, INRIA-Sophia Antiopolis (1988)Google Scholar
  13. 13.
    Chapiro, D.M.: Globally-asynchronous locally-synchronous systems. PhD thesis, Stanford Univ. (1984)Google Scholar
  14. 14.
    Gurd, J.R., Kirkham, C.C., Watson, I.: The Manchester prototype dataflow computer. Commun. ACM 28, 34–52 (1985)CrossRefGoogle Scholar
  15. 15.
    Ghica, D.R., McCusker, G.: The regular-language semantics of second-order Idealized Algol. Theor. Comput. Sci. 309(1-3), 469–502 (2003)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Jifeng, H., Josephs, M.B., Hoare, C.A.R.: A theory of synchrony and asynchrony. In: Programming Concepts and Methods. Elsevier, Amsterdam (1990)Google Scholar
  17. 17.
    Abramsky, S.: Interaction categories. In: Theory and Formal Methods, pp. 57–69 (1993)Google Scholar
  18. 18.
    Abramsky, S.: Abstract interpretation, logical relations and Kan extensions. J. Log. Comput. 1(1), 5–40 (1990)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Nain, S., Vardi, M.Y.: Trace semantics is fully abstract. In: LICS, pp. 59–68 (2009)Google Scholar
  20. 20.
    Ghica, D.R., Smith, A.: Geometry of Synthesis II: From games to delay-insensitive circuits. In: MFPS XXVI (forthcoming, 2010) Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

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

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