An Automata-Theoretic Model of Idealized Algol

(Extended Abstract)
  • Uday S. Reddy
  • Brian P. Dunphy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)

Abstract

In this paper, we present a new model of class-based Algol-like programming languages inspired by automata-theoretic concepts. The model may be seen as a variant of the ”object-based” model previously proposed by Reddy, where objects are described by their observable behaviour in terms of events. At the same time, it also reflects the intuitions behind state-based models studied by Reynolds, Oles, Tennent and O’Hearn where the effect of commands is described by state transformations. The idea is to view stores as automata, capturing not only their states but also the allowed state transformations. In this fashion, we are able to combine both the state-based and event-based views of objects. We illustrate the efficacy of the model by proving several test equivalences and discuss its connections to the previous models.

Keywords

State Transformation Simulation Relation Parametricity Graph Separation Logic Counter Object 
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.
This is a preview of subscription content, log in to check access

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abramsky, S., Honda, K., McCusker, G.: A fully abstract game semantics for general references. In: LICS 1998, pp. 334–344 (1998)Google Scholar
  2. 2.
    Abramsky, S., McCusker, G.: Linearity, sharing and state. In: Algol-like Languages [16], ch. 20Google Scholar
  3. 3.
    Barnett, M., Naumann, D.A.: Friends Need a Bit More: Maintaining Invariants Over Shared State. In: Kozen, D. (ed.) MPC 2004. LNCS, vol. 3125, pp. 54–84. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Dodds, M., Feng, X., Parkinson, M., Vafeiadis, V.: Deny-Guarantee Reasoning. In: Castagna, G. (ed.) ESOP 2009. LNCS, vol. 5502, pp. 363–377. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Dreyer, D., Neis, G., Birkedal, L.: The impact of higher-order state and control effects on local relational reasoning. In: ICFP (2010)Google Scholar
  6. 6.
    Dunphy, B.P., Reddy, U.S.: Parametric limits. In: LICS, pp. 242–253. IEEE (July 2004)Google Scholar
  7. 7.
    Eilenberg, S.: Automata, Languages, and Machines, vol. A and B. Academic Press (1974)Google Scholar
  8. 8.
    Fiore, M.P., Jung, A., Moggi, E., O’Hearn, P.W., Riecke, J., Rosolini, G., Stark, I.: Domains and denotational semantics: History, accomplishments and open problems. EATCS 59, 227–256 (1996)Google Scholar
  9. 9.
    Rustan, K., Leino, M., Schulte, W.: Using History Invariants to Verify Observers. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 80–94. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Meyer, A.R., Sieber, K.: Towards fully abstract semantics for local variables. In: POPL, pp. 191–203. ACM (1988); Reprinted as Chapter 7 of [16]Google Scholar
  11. 11.
    Mitchell, J.C., Plotkin, G.D.: Abstract types have existential types. TOPLAS 10(3), 470–502 (1988)CrossRefGoogle Scholar
  12. 12.
    O’Hearn, P.W., Reddy, U.S.: Objects, interference and the Yoneda embedding. Theoretical Computer Science 228(1), 211–252 (1999)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    O’Hearn, P.W., Reynolds, J.C.: From Algol to polymorphic linear lambda-calculus. JACM 47(1), 167–223 (2000)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    O’Hearn, P.W., Tennent, R.D.: Semantical analysis of specification logic, Part 2. Inf. Comput. 107(1), 25–57 (1993); Reprinted as Chapter 14 of [16]MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    O’Hearn, P.W., Tennent, R.D.: Parametricity and local variables. JACM 42(3), 658–709 (1995); Reprinted as Chapter 16 of [16]MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    O’Hearn, P.W., Tennent, R.D.: Algol-like Languages, vol. 2. Birkhäuser, Boston (1997)Google Scholar
  17. 17.
    Oles, F.J.: Type algebras, functor categories and block structure. In: Nivat, M., Reynolds, J.C. (eds.) Algebraic Methods in Semantics, pp. 543–573. Cambridge Univ. Press (1985)Google Scholar
  18. 18.
    Pitts, A.M., Stark, I.D.B.: Operational reasoning for functions with local state. In: Gordon, A.M., Pitts, A.M. (eds.) Higher Order Operational Techniques in Semantics, pp. 227–274. Cambridge Univ. Press, Cambridge (1998)Google Scholar
  19. 19.
    Reddy, U.S.: Global state considered unnecessary: An introduction to object-based semantics. J. Lisp and Symbolic Computation 9, 7–76 (1996); Reprinted as Chapter 19 of [16]CrossRefGoogle Scholar
  20. 20.
    Reddy, U.S.: Parametricity and naturality in the semantics of Algol-like languages. Electronic manuscript, University of Birmingham (December 1998), http://www.cs.bham.ac.uk/~udr/
  21. 21.
    Reddy, U.S.: Objects and classes in Algol-like languages. Inf. Comput. 172, 63–97 (2002)MATHCrossRefGoogle Scholar
  22. 22.
    Reddy, U.S., Yang, H.: Correctness of data representations involving heap data structures. Sci. of Comput. Prog. 50(1-3), 129–160 (2004)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Reynolds, J.C.: The essence of Algol. In: de Bakker, J.W., van Vliet, J.C. (eds.) Algorithmic Languages, pp. 345–372. North-Holland (1981); Reprinted as Chapter 3 of [16]Google Scholar
  24. 24.
    Reynolds, J.C.: Types, abstraction and parametric polymorphism. In: Mason, R.E.A. (ed.) Information Processing 1983, pp. 513–523. North-Holland, Amsterdam (1983)Google Scholar
  25. 25.
    Tennent, R.D.: Denotational semantics. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. 3, pp. 169–322. Oxford University Press (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Uday S. Reddy
    • 1
  • Brian P. Dunphy
    • 2
  1. 1.University of BirminghamUK
  2. 2.University of Illinois at Urbana-ChampaignUSA

Personalised recommendations