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Faster Proof Checking in the Edinburgh Logical Framework

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Automated Deduction—CADE-18 (CADE 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2392))

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Abstract

This paper describes optimizations for checking proofs represented in the Edinburgh Logical Framework (LF). The optimizations allow large proofs to be checked efficiently which cannot feasibly be checked using the standard algorithm for LF. The crucial optimization is a form of result caching. To formalize this optimization, a path calculus for LF is developed and shown equivalent to a standard calculus.

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References

  1. S. Abramsky, D. Gabbay, and T. Maibaum, editors. Handbook of Logic in Computer Science. Oxford University Press, 1992.

    Google Scholar 

  2. A. Appel and E. Felten. Proof-carrying authentication. In 6th ACM Conference on Computer and Communication Security, 1999.

    Google Scholar 

  3. H. Barendregt. Lambda Calculi with Types, pages 117–309. Volume 2 of D. Gabbay, and T. Maibaum, editors. Handbook of Logic in Computer Science. Oxford University Press Abramsky et al. [1], 1992.

    Google Scholar 

  4. S. Berghofer and T. Nipkow. Proof terms for simply typed higher order logic. In Theorem Proving in Higher Order Logics, 13th International Conference, volume 1869 of LNCS, 2000.

    Chapter  Google Scholar 

  5. H. Cirstea, C. Kirchner, and L. Liquori. The Rho Cube. In F. Honsell, editor, Foundations of Software Science and Computation Structures (FOSSACS), 2001.

    Google Scholar 

  6. H. Comon, M. Dauchet, R. Gilleron, F. Jacquemard, D. Lugiez, S. Tison, and M. Tommasi. Tree automata techniques and applications. Available at http://www.grappa.univ-lille3.fr/tata, 1997.

  7. T. Coquand. An algorithm for testing conversion in Type Theory, pages 255–79. In A. Voronkov, editors. Handbook of Automated Reasoning. Elsevier and MIT Press Huet and Plotkin [12], 1991.

    Google Scholar 

  8. A. Degtyarev and A. Voronkov. The Inverse Method, chapter IV. In A. Voronkov, editors. Handbook of Automated Reasoning. Elsevier and MIT Press Robinson and Voronkov [19], 2001.

    Google Scholar 

  9. W. Farmer and J. Guttman. A Set Theory with Support for Partial Functions. Logica Studia, 66(1):59–78, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. Harper, F. Honsell, and G. Plotkin. A Framework for Defining Logics. Journal of the Association for Computing Machinery, 40(1):143–184, January 1993.

    Google Scholar 

  11. R. Harper and F. Pfenning. On Equivalence and Canonical Forms in the LF Type Theory. Technical Report CMU-CS-00-148, Carnegie Mellon University, July 2000.

    Google Scholar 

  12. G. Huet and G. Plotkin, editors. Logical Frameworks. Cambridge University Press, 1991.

    Google Scholar 

  13. F. Kamareddine. Reviewing the classical and the de Bruijn notation for λ-calculus and pure type systems. Logic and Computation, 11(3):363–394.

    Google Scholar 

  14. Z. Luo and R. Pollack. LEGO Proof Development System: User’s Manual. Technical Report ECS-LFCS-92-211, Edinburgh LFCS, 1992.

    Google Scholar 

  15. G. Necula. Proof-Carrying Code. In 24th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 106–119, January 1997.

    Google Scholar 

  16. G. Necula and P. Lee. Efficient representation and validation of proofs. In 13th Annual IEEE Symposium on Logic in Computer Science, pages 93–104, 1998.

    Google Scholar 

  17. F. Pfenning. Logical Frameworks, chapter XXI. In A. Voronkov, editors. Handbook of Automated Reasoning. Elsevier and MIT Press Robinson and Voronkov [19], 2001.

    Google Scholar 

  18. F. Pfenning and Carsten Schürmann. System Description: Twelf — A Meta-Logical Framework for Deductive Systems. In 16th International Conference on Automated Deduction, 1999.

    Google Scholar 

  19. A. Robinson and A. Voronkov, editors. Handbook of Automated Reasoning. Elsevier and MIT Press, 2001.

    Google Scholar 

  20. A. Stump. Checking Validities and Proofs with CVC and flea. PhD thesis, Stanford University, 2002. In preparation: check http://verify.stanford.edu/~stump/ for a draft.

  21. A. Stump, C. Barrett, and D. Dill. CVC: a Cooperating Validity Checker. In 14th International Conference on Computer-Aided Verification, 2002.

    Google Scholar 

  22. R. Virga. Higher-Order Rewriting with Dependent Types. PhD thesis, Carnegie Mellon University, October 1999.

    Google Scholar 

  23. W. Wong. Validation of HOL Proofs by Proof Checking. Formal Methods in System Design, 14(2):193–212, 1999.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Systems Laboratory, Stanford University, Stanford, CA, 94305, USA

    Aaron Stump & David L. Dill

Authors
  1. Aaron Stump
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  2. David L. Dill
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Manchester, Oxford Rd, Manchester, M13 9PL, UK

    Andrei Voronkov

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© 2002 Springer-Verlag Berlin Heidelberg

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Stump, A., Dill, D.L. (2002). Faster Proof Checking in the Edinburgh Logical Framework. In: Voronkov, A. (eds) Automated Deduction—CADE-18. CADE 2002. Lecture Notes in Computer Science(), vol 2392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45620-1_32

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  • DOI: https://doi.org/10.1007/3-540-45620-1_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43931-8

  • Online ISBN: 978-3-540-45620-9

  • eBook Packages: Springer Book Archive

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