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Goal-Oriented Conjecturing for Isabelle/HOL

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Intelligent Computer Mathematics (CICM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11006))

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Abstract

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.

Y. Nagashima—Supported by the European Regional Development Fund under the project AI & Reasoning (reg. no.CZ.02.1.01/0.0/0.0/15_003/0000466)

J. Parsert—Supported by the European Research Council (ERC) grant no 714034 SMART.

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Notes

  1. 1.

    Available at Github https://github.com/data61/PSL/releases/tag/v0.1.1. The example of this paper appears in PSL/PGT/Example.thy.

  2. 2.

    Note that Nil is a universally quantified variable here.

References

  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. Buchberger, B.: Theory exploration with theorema (2000)

    Google Scholar 

  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). https://doi.org/10.1007/978-3-642-35308-6_10

    Chapter  MATH  Google Scholar 

  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). https://doi.org/10.1007/978-3-662-48899-7_26

    Chapter  MATH  Google Scholar 

  5. Gauthier, T., Kaliszyk, C., Urban, J.: Initial experiments with statistical conjecturing over large formal corpora, pp. 219–228 (2016). http://ceur-ws.org/Vol-1785/W23.pdf

  6. Johansson, M., Dixon, L., Bundy, A.: Conjecture synthesis for inductive theories. J. Autom. Reason. 47(3), 251–289 (2011)

    Article  MathSciNet  Google Scholar 

  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). https://doi.org/10.1007/978-3-319-08434-3_9

    Chapter  Google Scholar 

  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). https://doi.org/10.1007/978-3-319-63046-5_32

    Chapter  Google Scholar 

  9. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL - A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45949-9

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Authors and Affiliations

  1. CIIRC, Czech Technical University in Prague, Prague, Czech Republic

    Yutaka Nagashima

  2. Department of Computer Science, University of Innsbruck, Innsbruck, Austria

    Yutaka Nagashima & Julian Parsert

Authors
  1. Yutaka Nagashima
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  2. Julian Parsert
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Corresponding author

Correspondence to Julian Parsert .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Bayern, Germany

    Florian Rabe

  2. Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada

    William M. Farmer

  3. University of Cambridge, Cambridge, United Kingdom

    Grant O. Passmore

  4. Department of Computer Science, The George Washington University, Washington, District of Columbia, USA

    Abdou Youssef

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Nagashima, Y., Parsert, J. (2018). Goal-Oriented Conjecturing for Isabelle/HOL. In: Rabe, F., Farmer, W., Passmore, G., Youssef, A. (eds) Intelligent Computer Mathematics. CICM 2018. Lecture Notes in Computer Science(), vol 11006. Springer, Cham. https://doi.org/10.1007/978-3-319-96812-4_19

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  • DOI: https://doi.org/10.1007/978-3-319-96812-4_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96811-7

  • Online ISBN: 978-3-319-96812-4

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