Faster Proof Checking in the Edinburgh Logical Framework
- 279 Downloads
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.
KeywordsDirected Acyclic Graph Free Variable Hash Table Logical Framework High Order Logic
Unable to display preview. Download preview PDF.
- 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. , 1992.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 , 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 , 2001.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 , 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