skip to main content
research-article

Probabilistic coherence spaces are fully abstract for probabilistic PCF

Authors Info & Claims
Published:08 January 2014Publication History
Skip Abstract Section

Abstract

Probabilistic coherence spaces (PCoh) yield a semantics of higher-order probabilistic computation, interpreting types as convex sets and programs as power series. We prove that the equality of interpretations in Pcoh characterizes the operational indistinguishability of programs in PCF with a random primitive.

This is the first result of full abstraction for a semantics of probabilistic PCF. The key ingredient relies on the regularity of power series.

Along the way to the theorem, we design a weighted intersection type assignment system giving a logical presentation of PCoh.

Skip Supplemental Material Section

Supplemental Material

d2_left_t5.mp4

References

  1. S. Abramsky, R. Jagadeesan, and P. Malacaria. Full abstraction for PCF. Information and Computation, 163(2):409--470, Dec. 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. G. Boudol, P.-L. Curien, and C. Lavatelli. A semantics for lambda calculi with resources. Math. Struct. Comp. Sci., 9(4):437--482, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. A. Bucciarelli, A. Carraro, T. Ehrhard, G. Manzonetto, et al. Full abstraction for resource calculus with tests. In CSL11 -- Annual Conference of the EACSL, volume 12, pages 97--111, 2011.Google ScholarGoogle Scholar
  4. V. Danos and T. Ehrhard. Probabilistic coherence spaces as a model of higher-order probabilistic computation. Inf. Comput., 209(6):966--991, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. V. Danos and R. Harmer. Probabilistic game semantics. ACM Transactions on Computational Logic, 3(3):359--382, July 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. D. de Carvalho. Execution Time of λ-Terms via Denotational Semantics and Intersection Types. Preprint, 2009.Google ScholarGoogle Scholar
  7. T. Ehrhard. On Köthe sequence spaces and linear logic. Math. Struct. Comput. Sci., 12:579--623, 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. T. Ehrhard. Finiteness spaces. Math. Struct. Comput. Sci., 1 (4):615--646, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. T. Ehrhard and L. Regnier. The Differential Lambda-Calculus. Theor. Comput. Sci., 309(1):1--41, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. J.-Y. Girard. The system F of variable types, fifteen years later. Theor. Comput. Sci., 45:159--192, 1986. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. J.-Y. Girard. Linear logic. Theor. Comput. Sci., 50:1--102, 1987. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. J.-Y. Girard. Normal functors, power series and lambda-calculus. Ann. Pure Appl. Logic, 37(2):129--177, 1988.Google ScholarGoogle ScholarCross RefCross Ref
  13. J.-Y. Girard. Coherent banach spaces: a continuous denotational semantics. Theor. Comput. Sci., 227:297, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. J.-Y. Girard. Between logic and quantic: a tract. In T. Ehrhard, J.-Y. Girard, P. Ruet, and P. Scott, editors, Linear Logic in Computer Science, volume 316 of London Math. Soc. Lect. Notes Ser. CUP, 2004.Google ScholarGoogle Scholar
  15. J. Goubault-Larrecq and D. Varacca. Continuous random variables. In LICS, pages 97--106. IEEE Computer Society, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. É. Goursat. Cours d'analyse mathématique. Tome I. Gauthier-Villars, 1918.Google ScholarGoogle Scholar
  17. R. Hasegawa. Two applications of analytic functors. Theor. Comput. Sci., 272(1-2):113--175, 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. M. Hyland and L. Ong. On full abstraction for PCF. Information and Computation, 163(2):285--408, Dec. 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. C. Jones and G. Plotkin. A probabilistic powerdomains of evaluation. In LICS. IEEE Computer Society, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. A. J. Kfoury and J. B.Wells. Principality and decidable type inference for finite-rank intersection types. In POPL, pages 161--174, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. U. D. Lago and M. Zorzi. Probabilistic operational semantics for the lambda calculus. RAIRO - Theor. Inf. and Applic., 46(3):413--450, 2012.Google ScholarGoogle ScholarCross RefCross Ref
  22. J. Laird, G. Manzonetto, G. McCusker, and M. Pagani. Weighted relational models of typed lambda-calculi. In LICS 2013. IEEE Press, June 2013.Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. R. Milner. Fully abstract models of typed lambda-calculi. Theor. Comput. Sci., 4:1--22, 1977.Google ScholarGoogle ScholarCross RefCross Ref
  24. R. Milner and C. Strachey. A Theory of Programming Language Semantics. Chapman and Hall, London, 1976.Google ScholarGoogle Scholar
  25. E. Moggi. Computational lambda-calculus and monads. In LICS, pages 14--23. IEEE Computer Society, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. A. D. Pierro, C. Hankin, and H. Wiklicky. Probabilistic lambdacalculus and quantitative program analysis. J. Log. Comput., 15(2): 159--179, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. G. D. Plotkin. A powerdomain construction. SIAM J. Comput., 5(3): 452--487, 1976.Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. G. D. Plotkin. LCF considered as a programming language. Theor. Comput. Sci., 5(3):225--255, 1977.Google ScholarGoogle ScholarCross RefCross Ref
  29. N. Saheb-Djahromi. Cpo's of measures for nondeterminism. Theor. Comput. Sci., 12:19--37, 1980.Google ScholarGoogle ScholarCross RefCross Ref
  30. D. Scott. Continuous lattices. In Lawvere, editor, Toposes, Algebraic Geometry and Logic, volume 274 of Lecture Notes in Math., pages 97--136. Springer, 1972.Google ScholarGoogle Scholar

Index Terms

  1. Probabilistic coherence spaces are fully abstract for probabilistic PCF

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      • Published in

        cover image ACM SIGPLAN Notices
        ACM SIGPLAN Notices  Volume 49, Issue 1
        POPL '14
        January 2014
        661 pages
        ISSN:0362-1340
        EISSN:1558-1160
        DOI:10.1145/2578855
        Issue’s Table of Contents
        • cover image ACM Conferences
          POPL '14: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
          January 2014
          702 pages
          ISBN:9781450325448
          DOI:10.1145/2535838

        Copyright © 2014 ACM

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 8 January 2014

        Check for updates

        Qualifiers

        • research-article

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader
      About Cookies On This Site

      We use cookies to ensure that we give you the best experience on our website.

      Learn more

      Got it!