On Applicative Similarity, Sequentiality, and Full Abstraction

  • Raphaëlle Crubillé
  • Ugo Dal Lago
  • Davide SangiorgiEmail author
  • Valeria Vignudelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9360)


We study how applicative bisimilarity behaves when instantiated on a call-by-value probabilistic \(\lambda \)-calculus, endowed with Plotkin’s parallel disjunction operator. We prove that congruence and coincidence with the corresponding context relation hold for both bisimilarity and similarity, the latter known to be impossible in sequential languages.


Probabilistic lambda calculus Bisimulation Coinduction Sequentiality 


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  1. 1.
    Abramsky, S.: The lazy \(\lambda \)-Calculus. In: Turner, D. (ed.) Research Topics in Functional Programming, pp. 65–117. Addison Wesley (1990)Google Scholar
  2. 2.
    Abramsky, S., Ong, C.-H.L.: Full abstraction in the lazy lambda calculus. Inf. Comput. 105(2), 159–267 (1993)MathSciNetCrossRefzbMATHGoogle 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.
    Crubillé, R., Dal Lago, U.: On probabilistic applicative bisimulation and call-by-value \(\lambda \)-calculi (long version). CoRR, abs/1401.3766 (2014)Google Scholar
  5. 5.
    Dal Lago, U., Sangiorgi, D., Alberti, M.: On coinductive equivalences for higher-order probabilistic functional programs (long version). CoRR, abs/1311.1722 (2013)Google Scholar
  6. 6.
    Dal Lago, U., Sangiorgi, D., Alberti, M.: On coinductive equivalences for higher-order probabilistic functional programs. In: POPL, pp. 297–308 (2014)Google Scholar
  7. 7.
    Dal Lago, U., Zorzi, M.: Probabilistic operational semantics for the lambda calculus. RAIRO - Theor. Inf. and Applic. 46(3), 413–450 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Danos, V., Harmer, R.: Probabilistic game semantics. ACM Trans. Comput. Log. 3(3), 359–382 (2002)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Desharnais, J., Edalat, A., Panangaden, P.: Bisimulation for labelled Markov processes. Inf. Comput. 179(2), 163–193 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ehrhard, T., Tasson, C., Pagani, M.: Probabilistic coherence spaces are fully abstract for probabilistic PCF. In: POPL, pp 309–320 (2014)Google Scholar
  11. 11.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Goodman, N.D.: The principles and practice of probabilistic programming. In: POPL, pp. 399–402 (2013)Google Scholar
  13. 13.
    Jones, C., Plotkin, G.D.: A probabilistic powerdomain of evaluations. In: LICS, pp. 186–195 (1989)Google Scholar
  14. 14.
    Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94(1), 1–28 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lassen, S.B.: Relational Reasoning about Functions and Nondeterminism. PhD thesis, University of Aarhus (1998)Google Scholar
  16. 16.
    Manning, C.D., Schütze, H.: Foundations of statistical natural language processing, vol. 999. MIT Press (1999)Google Scholar
  17. 17.
    Ong, C.-H.L.: Non-determinism in a functional setting. In: LICS, pp. 275–286 (1993)Google Scholar
  18. 18.
    Park, S., Pfenning, F., Thrun, S.: A probabilistic language based on sampling functions. ACM Trans. Program. Lang. Syst. 31(1) (2008)Google Scholar
  19. 19.
    Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann (1988)Google Scholar
  20. 20.
    Pfeffer, A.: IBAL: A probabilistic rational programming language. In: IJCAI, pp. 733–740. Morgan Kaufmann (2001)Google Scholar
  21. 21.
    Plotkin, G.D.: LCF considered as a programming language. Theor. Comput. Sci. 5(3), 223–255 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Ramsey, N., Pfeffer, A.: Stochastic lambda calculus and monads of probability distributions. In: POPL, pp. 154–165 (2002)Google Scholar
  23. 23.
    Thrun, S.: Robotic mapping: A survey. Exploring Artificial Intelligence in the New Millennium, pp. 1–35 (2002)Google Scholar
  24. 24.
    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)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Raphaëlle Crubillé
    • 1
  • Ugo Dal Lago
    • 2
  • Davide Sangiorgi
    • 2
    Email author
  • Valeria Vignudelli
    • 2
  1. 1.ENS-LyonLyonFrance
  2. 2.Universitá di Bologna and INRIABolognaItaly

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