On Completeness of Logical Relations for Monadic Types

  • Sławomir Lasota
  • David Nowak
  • Yu Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4435)


Software security can be ensured by specifying and verifying security properties of software using formal methods with strong theoretical bases. In particular, programs can be modeled in the framework of lambda-calculi, and interesting properties can be expressed formally by contextual equivalence (a.k.a. observational equivalence). Furthermore, imperative features, which exist in most real-life software, can be nicely expressed in the so-called computational lambda-calculus. Contextual equivalence is difficult to prove directly, but we can often use logical relations as a tool to establish it in lambda-calculi. We have already defined logical relations for the computational lambda-calculus in previous work. We devote this paper to the study of their completeness w.r.t. contextual equivalence in the computational lambda-calculus.


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  1. 1.
    Benton, P.N., Bierman, G.M., de Paiva, V.C.V.: Computational types from a logical perspective. J. Functional Programming 8(2), 177–193 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Goubault-Larrecq, J., Lasota, S., Nowak, D.: Logical relations for monadic types. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 553–568. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Goubault-Larrecq, J., Lasota, S., Nowak, D., Zhang, Y.: Complete lax logical relations for cryptographic lambda-calculi. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 400–414. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Lasota, S., Nowak, D., Zhang, Y.: On completeness of logical relations for monadic types. Research Report cs.LO/0612106, arXiv (2006)Google Scholar
  5. 5.
    Lazić, R., Nowak, D.: A unifying approach to data-independence. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 581–595. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  6. 6.
    Mitchell, J.C.: Foundations of Programming Languages. MIT Press, Cambridge (1996)Google Scholar
  7. 7.
    Mitchell, J.C., Scedrov, A.: Notes on sconing and relators. In: Martini, S., Börger, E., Kleine Büning, H., Jäger, G., Richter, M.M. (eds.) CSL 1992. LNCS, vol. 702, pp. 352–378. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  8. 8.
    Moggi, E.: Notions of computation and monads. Information and Computation 93(1), 55–92 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    O’Hearn, P.W., Tennent, R.D.: Parametricity and local variables. J. ACM 42(3), 658–709 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Pitts, A., Stark, I.: Operational reasoning for functions with local state. In: Higher Order Operational Techniques in Semantics, pp. 227–273. Cambridge University Press, Cambridge (1998)Google Scholar
  11. 11.
    Plotkin, G.D.: Lambda-definability in the full type hierarchy. In: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pp. 363–373. Academic Press, London (1980)Google Scholar
  12. 12.
    Sieber, K.: Full abstraction for the second order subset of an algol-like language. Theoretical Computer Science 168(1), 155–212 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Sumii, E., Pierce, B.C.: Logical relations for encryption. J. Computer Security 11(4), 521–554 (2003)CrossRefGoogle Scholar
  14. 14.
    Zhang, Y.: Cryptographic logical relations. Ph. d. dissertation, ENS Cachan, France (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sławomir Lasota
    • 1
  • David Nowak
    • 2
  • Yu Zhang
    • 3
  1. 1.Institute of InformaticsWarsaw UniversityWarszawaPoland
  2. 2.RCISNational Institute of Advanced Industrial Science and TechnologyTokyoJapan
  3. 3.Project EverestINRIA Sophia-AntipolisFrance

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