Tactics for hierarchical proof

Mathematics in Computer Science

Volumn 3, Issue 3, 2010, Pages 309-330

  Aspinall, David ^a   Denney, Ewen ^b   Lüth, Christoph ^c  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b NASA AMES RESEARCH CENTER   (United States)

^c GERMAN RESEARCH CENTER FOR ARTIFICIAL INTELLIGENCE DFKI   (Germany)

Author keywords

Hierarchical proof; Hiproof; Tactical theorem proving

Indexed keywords

EID: 84905124838     PISSN: 16618270     EISSN: 16618289     Source Type: Journal    
DOI: 10.1007/s11786-010-0025-6     Document Type: Article

References (30)

1. Aboul-Hosn, K.: A proof-theoretic approach to tactics. In: Borwein, J.M., Farmer, W.M. (eds.) Mathematical Knowledge Management, 5th International Conference, MKM 2006. Lecture Notes in Computer Science, vol. 4108, pp. 54-66. Springer, Berlin (2006)
2. Allen, S.F., Bickford, M., Constable, R.L., Eaton, R., Kreitz, C., Lorigo, L., Moran, E.: Innovations in computational type theory using Nuprl. J. Appl. Logic 4(4), 428-469 (2006)
3. Appel, A.W., Felty, A.P.: Dependent types ensure partial correctness of theorem provers. J. Funct. Program. 14, 3-19 (2004)
4. Asperti, A., Coen, C.S., Tassi, E., Zacchiroli, S.: User interaction with the matita proof assistant. J. Autom. Reason. 39(2), 109-139 (2007)
5. Aspinall, D.: Proof general: a generic tool for proof development. In: Graf, S., Schwartzbach, M. (eds.) Tools and Algorithms for the Construction and Analysis of Systems, LNCS 1785, pp. 38-42. Springer, Berlin (2000)
6. Delahaye, D.: A tactic language for the system Coq. In: Logic for Programming and Automated Reasoning: 7th International Conference, LPAR 2000, Reunion Island, France, November 6-10, 2000. Lecture Notes in Computer Science, vol. 1955, pp. 85-95 (2000)
7. Denney, E., Power, J., Tourlas, K.: Hiproofs: a hierarchical notion of proof tree. In: Proceedings of Mathematical Foundations of Programing Semantics (MFPS). Electronic Notes in Theoretical Computer Science (ENTCS). Elsevier, Amsterdam (2005)
8. Felty, A.P.: Implementing tactics and tacticals in a higher-order logic programming language. J.Autom.Reason. 11(1), 41-81 (1993)
9. Felty, A.P., Howe, D.: Generalization and reuse of tactic proofs. In: Fifth International Conference on Logic Programming and Automated Reasoning LPAR. Lecture Notes in Computer Science, vol. 822. Springer, Berlin (1994)
10. Gordon, M.J.C., Milner, R., Wadsworth, C.P.: Edinburgh LCF. Lecture Notes in Computer Science, vol. 78, Springer, Berlin (1979)
11. Harrison, J.: Towards self-verification of HOL Light. In: Proceeding of the IJCAR 2006, the Third International Joint Conference on Automated Reasoning. Lecture Notes in Computer Science, vol. 4130, pp. 177-191. Springer, Berlin (2006)
12. Heneveld, A.: Using features in interactive theorem proving. PhD thesis, School of Informatics, University of Edinburgh (2006)
13. Jojgov, G.I., Geuvers, H.: A calculus of tactics and its operational semantics. Electr. Notes Theor. Comput. Sci. 93, 118-137 (2004)
14. Kirchner, F.: Coq tacticals and PVS strategies: a small-step semantics. In: Archer, M., Di Vito, B., Muñoz, C. (eds.) Design and Application of Strategies/Tactics in Higher Order Logics, pp. 69-83. NASA/CP-2003-212448 (2003)
15. Kirchner, F., Muñoz, C.: PVS#: streamlined tacticals for PVS. In: Proceedings of STRATEGIES'06 (2006)
16. Kohlhase, M.: OMDoc-an open markup format for mathematical documents. Lecture Notes in Computer Science, vol. 4180. Springer, Berlin (2006)
17. Kolbe, T., Walther, C.: Reusing proofs. In: Cohn, A.G. (ed.) Proceedings of the Eleventh European Conference on Artificial Intelligence, pp. 80-84, Chichester, Wiley, New York (1994)
18. Kreitz, C.: The nuprl proof development system, version 5-reference manual and user's guide. Department of Computer Science, Cornell-University, Ithaca 14853-7501 (2002)
19. Martin, A.P., Gardiner, P.H.B., Woodcock, J.C.P.: A tactic calculus-full version. Formal Aspects Comput. 8(E), 224-285 (1996)
20. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL-a proof assistant for higher-order logic. LectureNotes in Computer Science, vol. 2283, Springer, Berlin (2002)
21. Oliveira, M.V.M., Cavalcanti, A.L.C., Woodcock, J.C.P.: ArcAngel: a tactic language for refinement. Formal Aspects Comput. 15(1), 28-47 (2003)
22. Paulson, L.C.: Isabelle: the next 700 theorem provers. In: Odifreddi, P. (ed.) Logic and Computer Science, pp. 361-386. Academic Press, London (1990)
23. Pollack, R.: On extensibility of proof checkers. In: Dybjer, P., Nordström, B., Smith, J.M. (eds.) TYPES. Lecture Notes in Computer Science, vol. 996, pp. 140-161. Springer, Berlin (1994)
24. Sacerdoti Coen, C., Tassi, E., Zacchiroli, S.: Tinycals: Step by step tacticals. Electr. Notes Theor. Comput. Sci. 174(2), 125-142 (2007)
25. Schairer, A., Autexier, S., Hutter, D.: A pragmatic approach to reuse in tactical theorem proving. In: Proceedings of the 4th International Workshop on Strategies in Automated Deduction (STRATEGIES 2001). Electronic Notes in Computer Science, vol. 58, pp. 203-216. Elsevier, Amsterdam (2001)
26. Siekmann, J., Benzmüller, C., Autexier, S.: Computer supported mathematics with OMEGA. J. Appl. Logic 4(4), 533-559 (2006)
27. Siekmann, J., Hess, S., Benzmüller, C., Cheikhrouhou, L., Fiedler, A., Horacek, H., Kohlhase, M., Konrad, K., Meier, A., Melis, E., Pollet, M., Sorge, V.: LOUI: lovely omega user interface. Formal Aspects Comput. 11, 326-342 (1999)
28. Slind, K., Norrish,M.: Abrief overviewof HOL4. In: Mohamed, O.A., Muñoz,C., Tahar, S. (eds.) Theorem Proving in Higher-Order Logics TPHOLs 2008. Lecture Notes in Computer Science, vol. 5170, pp. 28-32. Springer, Berlin (2008)
29. Wagner, M., Autexier, S., Benzmüller, C.: PLATO: A mediator between text-editors and proof assistance systems. In: Autexier, S., Benzmüller, C. (eds.) 7thWorkshop on User Interfaces for Theorem Provers (UITP'06). Electronic Notes on Theoretical Computer Science, vol. 174(2), pp. 87-107. Elsevier (2006)
30. Wenzel, M.: Isar-ageneric interpretative approach to readable formal proof documents. In: Bertot,Y., Dowek, G.,Hirschowitz, A., Paulin, C., Théry, L. (eds.) Theorem Proving in Higher Order Logics TPHOLs'99. Lecture Notes in Computer Science, vol. 1690, pp. 167-184. Springer, Berlin (1999)