Goal-Oriented Conjecturing for Isabelle/HOL

  • Yutaka Nagashima
  • Julian ParsertEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11006)


We present PGT, a Proof Goal Transformer for Isabelle/HOL. Given a proof goal and its background context, PGT attempts to generate conjectures from the original goal by transforming the original proof goal. These conjectures should be weak enough to be provable by automation but sufficiently strong to identify and prove the original goal. By incorporating PGT into the pre-existing PSL framework, we exploit Isabelle’s strong automation to identify and prove such conjectures.


Proof Goal Original Goal Strong Automation QuickCheck Isabelle Theory File 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Blanchette, J.C.: Nitpick: a counterexample generator for Isabelle/HOL based on the relational model finder Kodkod. In: LPAR-17, pp. 20–25 (2010)Google Scholar
  2. 2.
    Buchberger, B.: Theory exploration with theorema (2000)Google Scholar
  3. 3.
    Bulwahn, L.: The new quickcheck for Isabelle. In: Hawblitzel, C., Miller, D. (eds.) CPP 2012. LNCS, vol. 7679, pp. 92–108. Springer, Heidelberg (2012). Scholar
  4. 4.
    Gauthier, T., Kaliszyk, C.: Sharing HOL4 and HOL light proof knowledge. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds.) LPAR 2015. LNCS, vol. 9450, pp. 372–386. Springer, Heidelberg (2015). Scholar
  5. 5.
    Gauthier, T., Kaliszyk, C., Urban, J.: Initial experiments with statistical conjecturing over large formal corpora, pp. 219–228 (2016).
  6. 6.
    Johansson, M., Dixon, L., Bundy, A.: Conjecture synthesis for inductive theories. J. Autom. Reason. 47(3), 251–289 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Johansson, M., Rosén, D., Smallbone, N., Claessen, K.: Hipster: integrating theory exploration in a proof assistant. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS (LNAI), vol. 8543, pp. 108–122. Springer, Cham (2014). Scholar
  8. 8.
    Nagashima, Y., Kumar, R.: A proof strategy language and proof script generation for Isabelle/HOL. In: de Moura, L. (ed.) CADE 2017. LNCS (LNAI), vol. 10395, pp. 528–545. Springer, Cham (2017). Scholar
  9. 9.
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL - A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002).

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CIIRC, Czech Technical University in PraguePragueCzech Republic
  2. 2.Department of Computer ScienceUniversity of InnsbruckInnsbruckAustria

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