System Description: GAPT 2.0

  • Gabriel Ebner
  • Stefan Hetzl
  • Giselle Reis
  • Martin Riener
  • Simon Wolfsteiner
  • Sebastian Zivota
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9706)

Abstract

GAPT (General Architecture for Proof Theory) is a proof theory framework containing data structures, algorithms, parsers and other components common in proof theory and automated deduction. In contrast to automated and interactive theorem provers whose focus is the construction of proofs, GAPT concentrates on the transformation and further processing of proofs. In this paper, we describe the current 2.0 release of GAPT.

References

  1. 1.
    Andrews, P.B.: Resolution in type theory. J. Symbolic Log. 36(3), 414–432 (1971). doi:10.2307/2269949 MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Baaz, M., Hetzl, S., Leitsch, A., Richter, C., Spohr, H.: CERES: an analysis of fürstenberg’s proof of the infinity of primes. Theoret. Comput. Sci. 403(2–3), 160–175 (2008)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Baaz, M., Leitsch, A.: Cut-elimination and redundancy-elimination by resolution. J. Symbolic Comput. 29(2), 149–176 (2000)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Boespflug, M., Carbonneaux, Q., Hermant, O.: The \(\lambda {\Pi }\)-calculus modulo as a universal proof language. In: Pichardie, D., Weber, T. (eds.) Proceedings of PxTP2012: Proof Exchange for Theorem Proving, pp. 28–43 (2012)Google Scholar
  5. 5.
    Dunchev, C., Leitsch, A., Libal, T., Riener, M., Rukhaia, M., Weller, D., Paleo, B.W.: PROOFTOOL: a GUI for the GAPT framework. In: Kaliszyk, C., Lüth, C. (eds.) Proceedings 10th International Workshop on User Interfaces for Theorem Provers (UITP) 2012, EPTCS, vol. 118, pp. 1–14 (2012)Google Scholar
  6. 6.
    Eberhard, S., Hetzl, S.: Inductive theorem proving based on tree grammars. Ann. Pure Appl. Log. 166(6), 665–700 (2015)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Hetzl, S.: Project presentation: algorithmic structuring and compression of proofs (ASCOP). In: Jeuring, J., Campbell, J.A., Carette, J., Dos Reis, G., Sojka, P., Wenzel, M., Sorge, V. (eds.) CICM 2012. LNCS, vol. 7362, pp. 438–442. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Hetzl, S., Leitsch, A., Reis, G., Tapolczai, J., Weller, D.: Introducing quantified cuts in logic with equality. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 240–254. Springer, Heidelberg (2014)Google Scholar
  9. 9.
    Hetzl, S., Leitsch, A., Reis, G., Weller, D.: Algorithmic introduction of quantified cuts. Theoret. Comput. Sci. 549, 1–16 (2014)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Hetzl, S., Leitsch, A., Weller, D.: CERES in higher-order logic. Ann. Pure Appl. Log. 162(12), 1001–1034 (2011)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Hetzl, S., Leitsch, A., Weller, D.: Towards algorithmic cut-introduction. In: Bjørner, N., Voronkov, A. (eds.) LPAR-18 2012. LNCS, vol. 7180, pp. 228–242. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    Hetzl, S., Libal, T., Riener, M., Rukhaia, M.: Understanding resolution proofs through Herbrand’s theorem. In: Galmiche, D., Larchey-Wendling, D. (eds.) TABLEAUX 2013. LNCS, vol. 8123, pp. 157–171. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  13. 13.
    Hurd, J.: The OpenTheory standard theory library. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 177–191. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Libal, T., Riener, M., Rukhaia, M.: Advanced Proof Viewing in ProofTool. In: Benzmüller, C., Paleo, B.W. (eds.) Proceedings of the 11th Workshop on User Interfaces for Theorem Provers (UITP) 2014, EPTCS, vol. 167, pp. 35–47 (2014)Google Scholar
  15. 15.
    Miller, D.: A compact representation of proofs. Stud. Logica 46(4), 347–370 (1987)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Miller, D.: ProofCert: broad spectrum proof certificates. An ERC Advanced Grant funded for the five years 2012–2016. http://www.lix.polytechnique.fr/Labo/Dale.Miller/ProofCert.pdf
  17. 17.
    Reis, G.: Importing SMT and connection proofs as expansion trees. In: Kaliszyk, C., Paskevich, A. (eds.) Proceedings Fourth Workshop on Proof eXchange for Theorem Proving (PxTP), EPTCS, vol. 186, pp. 3–10 (2015)Google Scholar
  18. 18.
    Stasko, J., Zhang, E.: Focus+context display and navigation techniques for enhancing radial, space-filling hierarchy visualizations. In: IEEE Symposium on Information Visualization, 2000, InfoVis 2000, pp. 57–65 (2000)Google Scholar
  19. 19.
    Sutcliffe, G.: The TPTP world – infrastructure for automated reasoning. In: Clarke, E.M., Voronkov, A. (eds.) LPAR-16 2010. LNCS, vol. 6355, pp. 1–12. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  20. 20.
    Sutcliffe, G., Suttner, C.: The State of CASC. AI Commun. 19(1), 35–48 (2006)MathSciNetMATHGoogle Scholar
  21. 21.
    Sutcliffe, G., Schulz, S., Claessen, K., Van Gelder, A.: Using the TPTP language for writing derivations and finite interpretations. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 67–81. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Gabriel Ebner
    • 1
  • Stefan Hetzl
    • 1
  • Giselle Reis
    • 2
  • Martin Riener
    • 3
  • Simon Wolfsteiner
    • 1
  • Sebastian Zivota
    • 1
  1. 1.Vienna University of TechnologyViennaAustria
  2. 2.Inria & LIX/École PolytechniquePalaiseauFrance
  3. 3.Inria Nancy & MSR-Inria Joint CentrePalaiseauFrance

Personalised recommendations