Interactive Proving, Higher-Order Rewriting, and Theory Analysis in Theorema 2.0

  • Alexander Maletzky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9725)


In this talk we will report on three useful tools recently implemented in the frame of the Theorema project: a graphical user interface for interactive proof development, a higher-order rewriting mechanism, and a tool for automatically analyzing the logical structure of Theorema-theories. Each of these three tools already proved extremely useful in the extensive formal exploration of a non-trivial mathematical theory, namely the theory of Gröbner bases and reduction rings, in Theorema 2.0.


Computer-assisted mathematical theory exploration Interactive theorem proving Theorema 


  1. 1.
    Buchberger, B., Jebelean, T., Kutsia, T., Maletzky, A., Windsteiger, W.: Theorema 2.0: computer-assisted natural-style mathematics. J. Formaliz. Reason. 9(1), 149–185 (2016)MathSciNetGoogle Scholar
  2. 2.
    Maletzky, A.: Computer-Assisted Exploration of Gröbner Bases Theory in Theorema. Ph.D. thesis, Research Institute for Symbolic Computation, Johannes Kepler University Linz, Austria (2016, to appear)Google Scholar
  3. 3.
    Maletzky, A.: Mathematical Theory Exploration in Theorema: Reduction Rings. In: CICM 2016 (2016). Preprint on
  4. 4.
    Padovani, V.: Filtrage d’ordre supérieure. Ph.D. thesis, Université Paris 7, Paris, France (1996)Google Scholar
  5. 5.
    Piroi, F., Kutsia, T.: The theorema environment for interactive proof development. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 261–275. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Stirling, C.: Decidability of higher-order matching. Log. Methods Comput. Sci. 5(3), 1–52 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Wenzel, M.: The Isabelle/Isar Reference Manual (2016), part of the Isabelle documentation.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Doctoral Program “Computational Mathematics” and RISCJohannes Kepler UniversityLinzAustria

Personalised recommendations