Theorem Reuse by Proof Term Transformation

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

Volumn 3223, Issue , 2004, Pages 152-167

  Johnsen, Einar Broch ^a   Lüth, Christoph ^b  

^a UNIVERSITY OF OSLO   (Norway)

^b UNIVERSITY OF BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACTING; FORMAL LOGIC;

ABSTRACTION PROCESS; AUTOMATED PROOFS; DATA TYPE; INFERENCE RULES; ISABELLE; LOGICAL FRAMEWORKS; THEOREM PROVERS;

THEOREM PROVING;

EID: 26844487743     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-30142-4_12     Document Type: Article

References (26)

1. P. Anderson and D. Basin. Program development schemata as derived rules. Journal of Symbolic Computation, 30(1):5-3G, July 2000.
2. E. Astesiano, M. Bidoit, H. Kirchner, B. Krieg-Brückner, P. D. Mosses, D. Sannella, and A. Tarlecki. CASL: The Common Algebraic Specification Language. Theoretical Computer Science, 286(2):153-196, 2002.
3. S. Autexier, D. Hutter, T. Mossakowski, and A. Schairer. The development graph manager MAYA. In H. Kirchner and C. Ringeissen, editors, Proc. 9th Int. Conf. Algebraic Methodology and Software Technology (AMAST'02), LNCS 2422, p. 495-501. Springer, 2002.
4. S. Berghofer and T. Nipkow. Proof terms for simply typed higher order logic. In J. Harrison and M. Aagaard, editors, 13th Intl. Conf. on Theorem Proving in Higher Order Logics (TPHOLs'00), LNCS 1869, p. 38-52. Springer, 2000.
5. Y. Bertot, O. Pons, and L. Rideau. Notions of dependency in proof assistants. In User Interfaces in Theorem Provers, Eindhoven Univ. of Technology, 1998.
6. A. Felty and D. Howe. Generalization and reuse of tactic proofs. In F. Pfenning, editor, 5th Intl. Conf. on Logic Programming and Automated Reasoning (LPAR'94), LNCS 822, pages 1-15. Springer, July 1994.
7. F. Giunchiglia, A. Villafiorita, and T. Walsh. Theories of abstraction. AI Communications, 10(3-4):167-176, 1997.
8. R. Harper, F. Honsell, and G. Plotkin. A framework for defining logics. Journal of the ACM, 40(1):143-184, Jan. 1993.
9. D. Hutter and M. Kohlhase. Managing structural information by higher-order colored unification. Journal of Automated Reasoning, 25:123-164, 2000.
10. E. B. Johnsen and C. Lüth. Abstracting refinements for transformation. Nordic Journal of Computing, 10(4):313-336, 2003.
11. C. Lüth and B. Wolfl. TAS - a generic window inference system. In J. Harrison and M. Aagaard, editors, 13th Intl. Conf. Theorem Proving in Higher Order Logics (TPHOLs'00), volume LNCS 1869, p. 405-422. Springer, 2000.
12. N. Magaud. Changing data representation within the Coq system. In 16th Intl. Conf. Theorem Proving in Higher Order Logics (TPHOLs'03), LNCS 2758, p. 87-102. Springer, 2003.
13. N. Magaud and Y. Bertot. Changing data structures in type theory: A study of natural numbers. In P. Callaghan, Z. Luo, J. McKinna, and R. Pollack, editors, Types for Proofs and Programs, Intl. Workshop (TYPES 2000), LNCS 2277, p. 181-196. Springer, 2002.
14. E. Melis and J. Whittle. Analogy in inductive theorem proving. Journal of Automated Reasoning, 22(2):117-147, 1999.
15. D. Miller, G. Nadathur, F. Pfenning, and A. Scedrov. Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic, 51:125-157, 1991.
16. T. Nipkow, L. C. Paulson, and M. Wenzel. Isabelle/HOL - A Proof Assistant for Higher-Order Logic, LNCS 2283. Springer, 2002.
17. L. C. Paulson. Isabelle: The next 700 theorem provers. In P. Odifreddi, editor, Logic and Computer Science, p. 361-386. Academic Press, 1990.
18. F. Pfenning. Logic programming in the LF logical framework. In G. Huet and G. Plotkin, editors, Logical Frameworks, p. 149-181. Cambridge Univ. Press, 1991.
19. F. Pfenning. Logical frameworks. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, p. 1063-1147. Elsevier Science Publishers, 2001.
20. O. Pons. Generalization in type theory based proof assistants. In P. Callaghan, Z. Luo, J. McKinna, and R. Pollack, editors, Types for Proofs and Programs, Intl. Workshop (TYPES 2000), LNCS 2277, p. 217-232. Springer, 2002.
21. D. Prawitz. Ideas and results in proof theory. In J. E. Fenstad, editor, Proceedings of the Second Scandinavian Logic Symposium, Studies in Logic and the Foundations of Mathematics 63, p. 235-307. North-Holland, Amsterdam, 1971.
22. W. Reif and K. Stenzel. Reuse of proofs in software verification. In R. K. Shyamasundar, editor, Proc. Foundations of Software Technology and Theoretical Computer Science, LNCS 761, p. 284-293. Springer, 1993.
23. D. Smith. Constructing specification morphisms. Journal of Symbolic Computation, 15:571-606, 1993.
24. D. R. Smith and M. R. Lowry. Algorithm theories and design tactics. Science of Computer Programming, 14:305-321, 1990.
25. Y. V. Srinivas and R. Jullig. Specware: Formal support for composing software. In Proc. Conf. Mathematics of Program Construction, LNCS 947. Springer, 1995.
26. C. Walther and T. Kolbe. Proving theorems by reuse. Artificial Intelligence, 116(1-2):17-66, 2000.