Correctness of Data Representations Involving Heap Data Structures

  • Uday S. Reddy
  • Hongseok Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2618)


While the semantics of local variables in programming languages is by now well-understood, the semantics of pointer-addressed heap variables is still an outstanding issue. In particular, the commonly assumed relational reasoning principles for data representations have not been validated in a semantic model of heap variables. In this paper, we define a parametricity semantics for a Pascal-like language with pointers and heap variables which gives such reasoning principles. It is found that the correspondences between data representations are not simply relations between states, but more intricate correspondences that also need to keep track of visible locations whose pointers can be stored and leaked.


Information Hiding Information Leakage Procedure Call Visible Location Simulation Relation 
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.


  1. 1.
    Abramsky, S., Honda, K., and McCusker, G. A fully abstract game semantics for general references. In LICS 1998 (1998), pp. 334–344.Google Scholar
  2. 2.
    Banerjee, A., and Naumann, D. A. Representation independence, confinement and access control. In POPL 2002 (2002), ACM.Google Scholar
  3. 3.
    Dunphy, B. P. Parametricity as a Notion of Uniformity in Reflexive Graphs. PhD thesis, University of Illinois, Dep. of Mathematics, 2002.Google Scholar
  4. 4.
    Ghica, D. R. Semantics of dynamic variables in Algol-like languages. Master’s thesis, Queen’s University, Kingston, Canada, Mar 1997. (available electronically from ).Google Scholar
  5. 5.
    Ghica, D. R. Parameters and linked structures in algol-like languages. In Report of the Dagstuhl Seminar 98261: The Semantic Challenge of Object-oriented Programming (1998), Schloss Dagstuhl.Google Scholar
  6. 6.
    Launchbury, J., and Peyton Jones, S. L. State in Haskell. J. Lisp and Symbolic Comput. 8, 4 (1995), 293–341.CrossRefGoogle Scholar
  7. 7.
    Levy, P. B. Call-by-Push-Value. PhD thesis, Queen Mary, University of London, March 2001.Google Scholar
  8. 8.
    Levy, P. B. Possible world semantics for general storage in call-by-value. In CSL 2002 (2002), pp. 232–246.Google Scholar
  9. 9.
    Meyer, A. R., and Sieber, K. Towards fully abstract semantics for local variables. In Fifteenth Ann. ACM Symp. on Princ. of Program. Lang. (1988), ACM, pp. 191–203. (Reprinted as Chapter 7 of [15]).Google Scholar
  10. 10.
    Mitchell, J. C., and Plotkin, G. D. Abstract types have existential types. ACM Trans. Program. Lang. Syst. 10, 3 (1988), 470–502.CrossRefGoogle Scholar
  11. 11.
    O’Hearn, P., Reynolds, J., and Yang, H. Local reasoning about programs that alter data structures. In CSL 2001 (Berlin, 2001), L. Fribourg, Ed., vol. 2142 of LNCS, Springer-Verlag, pp. 1–19.Google Scholar
  12. 12.
    O’Hearn, P. W., and Reynolds, J. C. From Algol to polymorphic linear lambda-calculus. J. ACM 47, 1 (2000), 167–223.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    O’Hearn, P. W., and Tennent, R. D. Semantics of local variables. In Applications of Categories in Computer Science, M. P. Fourman, P. T. Johnstone, and A. M. Pitts, Eds. Cambridge Univ. Press, 1992, pp. 217–238.Google Scholar
  14. 14.
    O’Hearn, P. W., and Tennent, R. D. Parametricity and local variables. J. ACM 42, 3 (1995), 658–709. (Reprinted as Chapter 16 of [15]).zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    O’Hearn, P. W., and Tennent, R. D. Algol-like Languages (Two volumes). Birkhäuser, Boston, 1997.Google Scholar
  16. 16.
    Oles, F. J. A Category-Theoretic Approach to the Semantics of Programming Languages. PhD thesis, Syracuse University, 1982.Google Scholar
  17. 17.
    Reddy, U. S. When parametricity implies naturality. Electronic manuscript, July 1997. URL
  18. 18.
    Reddy, U. S. Objects and classes in Algol-like languages. In Fifth Intern. Workshop on Foundations of Object-oriented Languages (Jan 1998), electronic proceedings at
  19. 19.
    Reddy, U. S. Objects and classes in Algol-like languages. Information and Computation 172 (2002), 63–97.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Reynolds, J. C. Towards a theory of type structure. In Coll. sur la Programmation, vol. 19 of LNCS. Springer-Verlag, 1974, pp. 408–425.Google Scholar
  21. 21.
    Reynolds, J. C. The essence of Algol. In Algorithmic Languages, J. W. de Bakker and J. C. van Vliet, Eds. North-Holland, 1981, pp. 345–372. (Reprinted as Chapter 3 of [15]).Google Scholar
  22. 22.
    Reynolds, J. C. Intuitionistic reasoning about shared mutable data structure. In Millenial Perspectives in Computer Science. Palgrave, 2000.Google Scholar
  23. 23.
    Robinson, E., and Rosolini, G. Reflexive graphs and parametric polymorphism. In Proceedings, Ninth Annual IEEE Symposium on Logic in Computer Science (July 1994), IEEE Computer Society Press.Google Scholar
  24. 24.
    Stark, I. Names and higher-order functions. Technical Report 363, University of Cambridge Computer Laboratory, April 1995.Google Scholar
  25. 25.
    Stark, I. Categorical models for local names. Lisp and Symbolic Computation 9, 1 (Feb. 1996), 77–107.CrossRefGoogle Scholar
  26. 26.
    Tennent, R. D. Correctness of data representations in Algol-like languages. In A Classical Mind: Essays in Honor of C. A. R. Hoare, A. W. Roscoe, Ed. Prentice-Hall International, 1994, pp. 405–417.Google Scholar
  27. 27.
    Wirth, N., and Hoare, C. A. R. A contribution to the development of Algol. Comm. ACM 9, 6 (June 1966), 413–432.zbMATHCrossRefGoogle Scholar
  28. 28.
    Yang, H. Local reasoning for stateful programs. Tech. Rep. UIUCDCS-R-2001-2227, University of Illinois, Dep. of Computer Science, July 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Uday S. Reddy
    • 1
  • Hongseok Yang
    • 2
  1. 1.School of Computer ScienceUniversity of BirminghamJapan
  2. 2.ROPASKorean Advanced Inst. of Science and TechnologyJapan

Personalised recommendations