A Logical Mix of Approximation and Separation

  • Aquinas Hobor
  • Robert Dockins
  • Andrew W. Appel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6461)


We extract techniques developed in the Concurrent C minor project to build a framework for constructing logics that contain approximation and/or separation. Approximation occurs when the naïve semantic definitions contain a contravariant circularity (e.g., invariants of first-class locks), while separation occurs when one wishes to track resource accounting. We show how these two features can be mixed together in a modular way. Our work is machine checked in Coq and available as part of the Mechanized Semantic Library.


Program Logic Intuitionistic Logic Kripke Model Separation Structure Separation Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [ADH10]
    Appel, A., Dockins, R., Hobor, A.: Mechanized Semantic Library (2009-2010),
  2. [Ahm04]
    Ahmed, A.J.: Semantics of Types for Mutable State. PhD thesis, Princeton University, Princeton, NJ, Tech Report TR-713-04 (November 2004)Google Scholar
  3. [AMRV07]
    Appel, A.W., Melliès, P.-A., Richards, C.D., Vouillon, J.: A very modal model of a modern, major, general type system. In: Proc. 34th Annual Symposium on Principles of Programming Languages (POPL 2007), pp. 109–122 (January 2007)Google Scholar
  4. [COY07]
    Calcagno, C., O’Hearn, P.W., Yang, H.: Local action and abstract separation logic. In: LICS 2007: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science, pp. 366–378 (2007)Google Scholar
  5. [DAB09]
    Dreyer, D., Ahmed, A., Birkedal, L.: Logical step-indexed logical relations. In: Proceedings 24th Annual IEEE Symposium on Logic in Computer Science, LICS 2009 (2009)Google Scholar
  6. [DAH08]
    Dockins, R., Appel, A.W., Hobor, A.: Multimodal separation logic for reasoning about operational semantics. In: 24th Conference on the Mathematical Foundations of Programming Semantics (MFPS XXIV). Springer Electronic Notes in Theoretical Computer Science (ENTCS), pp. 5–20 (2008)Google Scholar
  7. [DH10]
    Dockins, R., Hobor, A.: A theory of termination via indirection (July 2010) (under submission)Google Scholar
  8. [DHA09]
    Dockins, R., Hobor, A., Appel, A.W.: A fresh look at separation algebras and share accounting. In: Hu, Z. (ed.) APLAS 2009. LNCS, vol. 5904, pp. 161–177. Springer, Heidelberg (2009) (to appear)CrossRefGoogle Scholar
  9. [HAZ08]
    Hobor, A., Appel, A.W., Nardelli, F.Z.: Oracle semantics for concurrent separation logic. In: Drossopoulou, S. (ed.) ESOP 2008. LNCS, vol. 4960, pp. 353–367. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. [HDA10]
    Hobor, A., Dockins, R., Appel, A.W.: A theory of indirection via approximation. In: Proc. 37th Annual ACM Symposium on Principles of Programming Languages (POPL 2010), pp. 171–185 (January 2010)Google Scholar
  11. [Hob08]
    Hobor, A.: Oracle Semanatics. PhD thesis, Princeton University, Princeton, NJ (November 2008)Google Scholar
  12. [Ler06]
    Leroy, X.: Formal certification of a compiler back-end, or: programming a compiler with a proof assistant. In: POPL 2006, pp. 42–54 (2006)Google Scholar
  13. [Nip02]
    Nipkow, T.: Hoare logics for recursive procedures and unbounded nondeterminism. In: Bradfield, J.C. (ed.) CSL 2002 and EACSL 2002. LNCS, vol. 2471, pp. 155–182. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. [Res00]
    Restall, G.: An Introduction to Substructural Logics. Routledge, London (2000)Google Scholar
  15. [Rey02]
    Reynolds, J.: Separation logic: A logic for shared mutable data structures. In: LICS 2002: IEEE Symposium on Logic in Computer Science, pp. 55–74 (July 2002)Google Scholar
  16. [Ric10]
    Richards, C.D.: The Approximation Modality in Models of Higher-Order Types. PhD thesis, Princeton University, Princeton, NJ (June 2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Aquinas Hobor
    • 1
  • Robert Dockins
    • 2
  • Andrew W. Appel
    • 2
  1. 1.National University of SingaporeSingapore
  2. 2.Princeton UniversityUSA

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