A Realizability Model for Impredicative Hoare Type Theory

  • Rasmus Lerchedahl Petersen
  • Lars Birkedal
  • Aleksandar Nanevski
  • Greg Morrisett
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4960)


We present a denotational model of impredicative Hoare Type Theory, a very expressive dependent type theory in which one can specify and reason about mutable abstract data types.

The model ensures soundness of the extension of Hoare Type Theory with impredicative polymorphism; makes the connections to separation logic clear, and provides a basis for investigation of further sound extensions of the theory, in particular equations between computations and types.


Type Theory Computation Type Dependent Type Separation Logic Recursive Type 
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  1. 1.
    Appel, A., Mellièes, P.-A., Richards, C., Vouillon, J.: A very modal model of a modern, major, general type system. In: POPL 2007 (2007)Google Scholar
  2. 2.
    Barnett, M., Leino, K.R.M., Schulte, W.: The Spec# programming system: An overview. In: Barthe, G., Burdy, L., Huisman, M., Lanet, J.-L., Muntean, T. (eds.) CASSIS 2004. LNCS, vol. 3362, Springer, Heidelberg (2005)Google Scholar
  3. 3.
    Benton, N., Leperchey, B.: Relational reasoning in a nominal semantics for storage. In: Urzyczyn, P. (ed.) TLCA 2005. LNCS, vol. 3461, pp. 88–101. Springer, Heidelberg (2005)Google Scholar
  4. 4.
    Berger, M., Honda, K., Yoshida, N.: A logical analysis of aliasing in imperative higher-order functions. In: Danvy, O., Pierce, B.C. (eds.) ICFP 2005, Tallinn, Estonia, September 2005, pp. 280–293 (2005)Google Scholar
  5. 5.
    Biering, B., Birkedal, L., Torp-Smith, N.: Bi hyperdoctrines and higher-order separation logic. In: Sagiv, M. (ed.) ESOP 2005. LNCS, vol. 3444, pp. 233–247. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    Biering, B., Birkedal, L., Torp-Smith, N.: BI hyperdoctrines, Higher-Order Separation Logic, and Abstraction. In: TOPLAS 2007 (to appear, 2007)Google Scholar
  7. 7.
    Birkedal, L., Møgelberg, R., Petersen, R.: Domain-theoretic models of parametric polymorphism. In: TCS (to appear, 2007)Google Scholar
  8. 8.
    Birkedal, L., Torp-Smith, N., Yang, H.: Semantics of separation-logic typing and higher-order frame rules for algol-like languages. LMCS 2(5:1), 1–33 (2006)MathSciNetGoogle Scholar
  9. 9.
    Birkedal, L., Yang, H.: Relational parametricity and separation logic. In: Seidl, H. (ed.) FOSSACS 2007. LNCS, vol. 4423, Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Burdy, L., Cheon, Y., Cok, D., Ernst, M., Kiniry, J., Leavens, G.T., Leino, K.R.M., Poll, E.: An overview of JML tools and applications. International Journal on Software Tools for Technology Transfer 7(3), 212–232 (2005)CrossRefGoogle Scholar
  11. 11.
    Detlefs, D.L., Leino, K.R.M., Nelson, G., Saxe, J.B.: Extended static checking. Compaq Systems Research Center, Research Report 159 (December 1998)Google Scholar
  12. 12.
    Evans, D., Larochelle, D.: Improving security using extensible lightweight static analysis. IEEE Software 19(1), 42–51 (2002)CrossRefGoogle Scholar
  13. 13.
    Jacobs, B.: Categorical Logic and Type Theory. Studies in Logic and the Foundations of Mathematics, vol. 141. Elsevier, Amsterdam (1999)zbMATHGoogle Scholar
  14. 14.
    Krishnaswami, N.: Separation logic for a higher-order typed language. In: SPACE 2006, pp. 73–82 (2006)Google Scholar
  15. 15.
    Krishnaswami, N., Aldrich, J., Birkedal, L.: Modular verification of the subject-observer pattern via higher-order separation logic. In: FTfJP (2007)Google Scholar
  16. 16.
    Morrisett, G., Walker, D., Crary, K., Glew, N.: From System F to typed assembly language. ACM TPLS 21(3), 527–568 (1999)CrossRefGoogle Scholar
  17. 17.
    Nanevski, A., Ahmed, A., Morrisett, G., Birkedal, L.: Abstract Predicates and Mutable ADTs in Hoare Type Theory. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 189–204. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    Nanevski, A., Morrisett, G., Birkedal, L.: Polymorphism and separation in Hoare Type Theory. In: ICFP 2006, Portland, Oregon, pp. 62–73 (2006)Google Scholar
  19. 19.
    O’Hearn, P.W., Yang, H., Reynolds, J.C.: Separation and information hiding. In: POPL 2004, pp. 268–280 (2004)Google Scholar
  20. 20.
    Petersen, R., Birkedal, L., Nanevski, A., Morrisett, G.: A realizability model of impredicative hoare type theory. Technical report, IT University of Copenhagen (2007),
  21. 21.
    Pym, D.: The Semantics and Proof Theory of the Logic of Bunched Implications. Applied Logics Series, vol. 26. Kluwer, Dordrecht (2002)zbMATHGoogle Scholar
  22. 22.
    Reus, B., Schwinghammer, J.: Separation Logic for Higher-Order Store. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 575–590. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  23. 23.
    Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS 2002, pp. 55–74 (2002)Google Scholar
  24. 24.
    Shinwell, M.: The Fresh Approach: Functional Programming with Names and Binders. PhD thesis, Computer Laboratory, Cambridge University (December 2004)Google Scholar
  25. 25.
    Shinwell, M.R., Pitts, A.M.: On a monadic semantics for freshness. TCS 342, 28–55 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Watkins, K., Cervesato, I., Pfenning, F., Walker, D.: A concurrent logical framework: The propositional fragment. In: Filliâtre, J.-C., Paulin-Mohring, C., Werner, B. (eds.) TYPES 2004. LNCS, vol. 3839, pp. 355–377. Springer, Heidelberg (2006)Google Scholar
  27. 27.
    Xi, H., Pfenning, F.: Dependent types in practical programming. In: POPL 1999, San Antonio, pp. 214–227 (1999)Google Scholar
  28. 28.
    Yoshida, N., Honda, K., Berger, M.: Local state in hoare logic for imperative higher-order functions. In: Seidl, H. (ed.) FOSSACS 2007. LNCS, vol. 4423, Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rasmus Lerchedahl Petersen
    • 1
  • Lars Birkedal
    • 1
  • Aleksandar Nanevski
    • 2
  • Greg Morrisett
    • 2
  1. 1.IT University of Copenhagen 
  2. 2.Harvard University 

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