Connecting a logical framework to a first-order logic prover

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3717 LNAI, Issue , 2005, Pages 285-301

  Abel, Andreas ^a   Coquand, Thierry ^a   Norell, Ulf ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

LOGIC PROVER; META-THEORETIC RESULT; RESOLUTION PROVER;

INTERFACES (COMPUTER); METADATA; THEOREM PROVING; TRANSLATION (LANGUAGES);

FORMAL LOGIC;

EID: 33646183688     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11559306_17     Document Type: Conference Paper

References (28)

1. Andreas Abel and Thierry Coquand. Untyped algorithmic equality for Martin-Lofs logical framework with surjective pairs. In Pawel Urzyczyn, editor, TLCA '05, volume 3461 of LNCS, pages 23-38. Springer, April 2005.
2. Andreas Abel, Thierry Coquand, and Ulf Norell. Connecting a logical framework to a first-order logic prover (extended version). Technical report, Department of Computing Science, Chalmers University of Technology, Gothenburg, Sweden, 2005. Available under http://www.cs.chalmers.se/~ulfn/papers/fol.html.
3. Thorsten Altenkirch, Conor McBride, and James McKinna. Why dependent types matter. Manuscript, available online, April 2005.
4. Michael Beeson. Otter-λ home page, 2005. URL: http://mh215a.cs. sjsu.edu/.
5. Yves Beitot and Pierre Castéran. Interactive Theorem Proving and Program Development. Coq'Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science. An EATCS Series. Springer, 2004.
6. Marc Bezem and Thierry Coquand. Newman's lemma - a case study in proof automation and geometric logic. Bulletin of the EATCS, 79:86-100, 2003. Logic in Computer Science Column.
7. Marc Bezem, Dimitri Hendriks, and Hans de Nivelle. Automated proof construction in type theory using resolution. JAR, 29(3-4):253-275, 2002.
8. Special Issue Mechanizing and Automating Mathematics: In honour of N.G. de Bruijn.
9. Koen Claessen and John Hughes. QuickCheck: a lightweight tool for random testing of Haskell programs. ACM SIGPLAN Notices, 35(9):268-279, 2000.
10. Catarina Coquand and Thierry Coquand. Structured type theory. In Workshop on Logical Frameworks and Meta-languages (LFM'99), Paris, France, September 1999.
11. Michel Coste, Henri Lombardi, and Marie-Françoise Roy. Dynamical methods in algebra: Effective Nullstellensätze. APAL, 111(3):203-256, 2001.
12. Niklas G. de Bruijn. A survey of the project Automath. In J. P. Seldin and J. R. Hindley, editors, To H. B. Curry: Essays in combinatory logic, lambda calculus and formalism, pages 579-606, London-New York, 1980. Academic Press.
13. Gerhard Gentzen. Untersuchungen über das logische Schließen. Mathematische Zeitschrift, 39:176-210, 405-431, 1935.
14. Xiaorong Huang, Manfred Kerber, Michael Kohlhase, Erica Melis, Dan Nesmith, Jörn Richts, and Jörg H. Siekmann. Omega-MKRP: A proof development environment. In Alan Bundy, editor, CADE'94, volume 814 of LNCS, pages 788-792. Springer, 1994.
15. Joe Hurd. Integrating Gandalf and HOL. In Yves Bertot, Gilles Dowek, André Hirschowitz, Christine Paulin, and Laurent Théry, editors, TPHOLS'99, volume 1690 of LNCS, pages 311-321. Springer, September 1999.
16. Joe Hurd. An LCF-style interface between HOL and first-order logic. In Andrei Voronkov, editor, CADE'02, volume 2392 of LNAI, pages 134-138. Springer, 2002.
17. Joe Hurd. First-order proof tactics in higher-order logic theorem provers. In Myla Archer, Ben Di Vito, and César Muñoz, editors, STRATA'03, number CP-2003-212448 in NASA Technical Reports, pages 56-68, September 2003.
18. Leslie Lamport. How to write a proof. In Global Analysis in Modern Mathematics, pages 311-321. Publish or Perish, Houston, Texas, U.S.A., February 1993.
19. Also appeared as SRC Research Report 94.
20. Jia Meng and Lawrence C. Paulson. Experiments on supporting interactive proof using resolution. In David A. Basin and Michael Rusinowitch, editors, IJCAR'04, volume 3097 of LNCS, pages 372-384. Springer, 2004.
21. Dale Miller. Unification under a mixed prefix. J. Symb. Comput., 14(4):321-358, 1992.
22. Bengt Nordström, Kent Petersson, and Jan Smith. Martin-Löf's type theory. In Handbook of Logic in Computer Science, volume 5. OUP, October 2000.
23. Bengt Nordström, Kent Petersson, and Jan M. Smith. Programming in Martin Löf's Type Theory: An Introduction. Clarendon Press, Oxford, 1990.
24. John Alan Robinson. A machine-oriented logic based on the resolution principle. JACM, 12(1):23-41, January 1965.
25. Stephan Schmitt, Lori Lorigo, Christoph Kreitz, and Aleksey Nogin. JProver: Integrating connection-based theorem proving into interactive proof assistants. In R. Gore, A. Leitsch, and T. Nipkow, editors, IJCAR'01, volume 2083 of LNAI, pages 421-426. Springer, 2001.
26. Jan M. Smith and Tanel Tammet. Optimized encodings of fragments of type theory in first-order logic. In Stefano Berardi and Mario Coppo, editors, TYPES'95, volume 1158 of LNCS, pages 265-287. Springer, 1995.
27. Tanel Tammet. Gandalf. JAR, 18(2): 199-204, 1997.
28. Cynthia A. Wick and William McCune. Automated reasoning about elementary point-set topology. JAR, 5(2):239-255, 1989.