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On Probabilistic Applicative Bisimulation and Call-by-Value λ-Calculi

  • Raphaëlle Crubillé
  • Ugo Dal Lago
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8410)

Abstract

Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is applied to a typed, call-by-value, lambda-calculus. Surprisingly, the obtained relation coincides with context equivalence, contrary to what happens when call-by-name evaluation is considered. Even more surprisingly, full-abstraction only holds in a symmetric setting.

Keywords

lambda calculus probabilistic computation bisimulation coinduction 

References

  1. 1.
    Abramsky, S.: The Lazy λ-Calculus. In: Turner, D. (ed.) Research Topics in Functional Programming, pp. 65–117. Addison Wesley (1990)Google Scholar
  2. 2.
    Berry, G., Curien, P.-L.: Sequential algorithms on concrete data structures. Theor. Comput. Sci. 20, 265–321 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Comaniciu, D., Ramesh, V., Meer, P.: Kernel-based object tracking. IEEE Trans. on Pattern Analysis and Machine Intelligence 25(5), 564–577 (2003)CrossRefGoogle Scholar
  4. 4.
    Crubille, R., Dal Lago, U.: On Probabilistic applicative bisimulation for call-by-value lambda calculi (long version) (2014), http://arxiv.org/abs/1401.3766
  5. 5.
    Dal Lago, U., Sangiorgi, D., Alberti, M.: On coinductive equivalences for higher-order probabilistic functional programs. In: POPL, pp. 297–308 (2014)Google Scholar
  6. 6.
    Dal Lago, U., Zorzi, M.: Probabilistic operational semantics for the lambda calculus. RAIRO - Theor. Inf. and Applic. 46(3), 413–450 (2012)CrossRefzbMATHGoogle Scholar
  7. 7.
    Danos, V., Harmer, R.: Probabilistic game semantics. ACM Trans. Comput. Log. 3(3), 359–382 (2002)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Desharnais, J., Edalat, A., Panangaden, P.: Bisimulation for labelled markov processes. Inf. Comput. 179(2), 163–193 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Ehrhard, T., Tasson, C., Pagani, M.: Probabilistic coherence spaces are fully abstract for probabilistic PCF. In: POPL, pp. 309–320 (2014)Google Scholar
  10. 10.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Goodman, N.D.: The principles and practice of probabilistic programming. In: POPL, pp. 399–402 (2013)Google Scholar
  12. 12.
    Gordon, A.D., Aizatulin, M., Borgström, J., Claret, G., Graepel, T., Nori, A.V., Rajamani, S.K., Russo, C.V.: A model-learner pattern for bayesian reasoning. In: POPL, pp. 403–416 (2013)Google Scholar
  13. 13.
    Goubault-Larrecq, J., Lasota, S., Nowak, D.: Logical relations for monadic types. Mathematical Structures in Computer Science 18(6), 1169–1217 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Howe, D.J.: Proving congruence of bisimulation in functional programming languages. Inf. Comput. 124(2), 103–112 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Jones, C., Plotkin, G.D.: A probabilistic powerdomain of evaluations. In: LICS, pp. 186–195 (1989)Google Scholar
  16. 16.
    Katz, J., Lindell, Y.: Introduction to Modern Cryptography. Chapman & Hall Cryptography and Network Security Series. Chapman & Hall (2007)Google Scholar
  17. 17.
    Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94(1), 1–28 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Lassen, S.B.: Relational Reasoning about Functions and Nondeterminism. PhD thesis, University of Aarhus (1998)Google Scholar
  19. 19.
    Manning, C.D., Schütze, H.: Foundations of statistical natural language processing, vol. 999. MIT Press (1999)Google Scholar
  20. 20.
    Ong, C.-H.L.: Non-determinism in a functional setting. In: LICS, pp. 275–286 (1993)Google Scholar
  21. 21.
    Park, S., Pfenning, F., Thrun, S.: A probabilistic language based on sampling functions. ACM Trans. Program. Lang. Syst. 31(1) (2008)Google Scholar
  22. 22.
    Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann (1988)Google Scholar
  23. 23.
    Pfeffer, A.: IBAL: A probabilistic rational programming language. In: IJCAI, pp. 733–740. Morgan Kaufmann (2001)Google Scholar
  24. 24.
    Pitts, A.: Operationally-based theories of program equivalence. In: Semantics and Logics of Computation, pp. 241–298. Cambridge University Press (1997)Google Scholar
  25. 25.
    Plotkin, G.D.: LCF considered as a programming language. Theor. Comput. Sci. 5(3), 223–255 (1977)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Ramsey, N., Pfeffer, A.: Stochastic lambda calculus and monads of probability distributions. In: POPL, pp. 154–165 (2002)Google Scholar
  27. 27.
    Shannon, C.: Communication theory of secrecy systems. Bell System Technical Journal 28, 656–715 (1949)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Thrun, S.: Robotic mapping: A survey. Exploring artificial intelligence in the new millennium, 1–35 (2002)Google Scholar
  29. 29.
    van Breugel, F., Mislove, M.W., Ouaknine, J., Worrell, J.: Domain theory, testing and simulation for labelled markov processes. Theor. Comput. Sci. 333(1-2), 171–197 (2005)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Raphaëlle Crubillé
    • 1
  • Ugo Dal Lago
    • 2
  1. 1.ENS-LyonFrance
  2. 2.INRIAUniversità di BolognaItaly

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