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Making PVS Accessible to Generic Services by Interpretation in a Universal Format

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Interactive Theorem Proving (ITP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10499))

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Abstract

PVS is one of the most powerful proof assistant systems and its libraries of formalized mathematics are among the most comprehensive albeit under-appreciated ones. A characteristic feature of PVS is the use of a very rich mathematical and logical foundation, including e.g., record types, undecidable subtyping, and a deep integration of decision procedures. That makes it particularly difficult to develop integrations of PVS with other systems such as other reasoning tools or library management periphery.

This paper presents a translation of PVS and its libraries to the OMDoc/MMT framework that preserves the logical semantics and notations but makes further processing easy for third-party tools. OMDoc/MMT is a framework for formal knowledge that abstracts from logical foundations and concrete syntax to provide a universal representation format for formal libraries and interface layer for machine support. Our translation allows instantiating generic OMDoc/MMT-level tool support for the PVS library and enables future translations to libraries of other systems.

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Notes

  1. 1.

    Contrary to typical dependently-typed languages, PVS does not allow declaring dependent base types, but predicate subtyping can be used to introduce types that depend on terms. Interestingly, this is neither weaker nor stronger than the dependent types in typical \(\lambda \varPi \) calculi.

  2. 2.

    All numbers measured on standard laptops.

References

  1. 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 

  2. Gauthier, T., Kaliszyk, C.: Matching concepts across HOL libraries. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS, vol. 8543, pp. 267–281. Springer, Cham (2014). doi:10.1007/978-3-319-08434-3_20

    Chapter  Google Scholar 

  3. MathHub PVS Git Repository. http://gl.mathhub.info/PVS. Accessed 11 Apr 2017

  4. Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. J. Assoc. Comput. Mach. 40(1), 143–184 (1993)

    Article  MathSciNet  Google Scholar 

  5. Iancu, M., et al.: The Mizar mathematical library in OMDoc: translation and applications. J. Automated Reason. 50(2), 191–202 (2013). doi:10.1007/s10817-012-9271-4

  6. Iancu, M., Jucovschi, C., Kohlhase, M., Wiesing, T.: System description: MathHub.info. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS, vol. 8543, pp. 431–434. Springer, Cham (2014). doi:10.1007/978-3-319-08434-3_33. http://kwarc.info/kohlhase/papers/cicm14-mathhub.pdf. ISBN 978-3-319-08433-6

    Chapter  Google Scholar 

  7. Iancu, M.: Towards flexiformal mathematics. Ph.D. thesis. Jacobs University, Bremen (2017)

    Google Scholar 

  8. Kaliszyk, C., et al.: A standard for aligning mathematical concepts. In: Kohlhase, M. et al. (eds.) Intelligent Computer Mathematics – Work in Progress Papers (2016). http://kwarc.info/kohlhase/papers/cicmwip16-alignments.pdf

  9. Kohlhase, M.: OMDoc: An Open Markup Format for Mathematical Documents (Version 1.2). Lecture Notes in Artificial Intelligence, vol. 4180. Springer, Heidelberg (2006)

    Google Scholar 

  10. Kaliszyk, C., Rabe, F.: Towards knowledge management for HOL light. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS, vol. 8543, pp. 357–372. Springer, Cham (2014). doi:10.1007/978-3-319-08434-3_26. http://kwarc.info/frabe/Research/KR_hollight_14.pdf. ISBN 978-3-319-08433-6

  11. Kohlhase, M., Rabe, F.: QED reloaded: towards a pluralistic formal library of mathematical knowledge. J. Formalized Reason. 9(1), 201–234 (2016)

    MathSciNet  MATH  Google Scholar 

  12. Krauss, A., Schropp, A.: A mechanized translation from higher-order logic to set theory. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 323–338. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14052-5_23

    Chapter  Google Scholar 

  13. Kaliszyk, C., Urban, J.: HOL(y)Hammer: online ATP service for HOL light. Math. Comput. Sci. 9(1), 5–22 (2015)

    Article  Google Scholar 

  14. Keller, C., Werner, B.: Importing HOL light into Coq. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 307–322. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14052-5_22

    Chapter  Google Scholar 

  15. Kohlhase, M., Sucan, I.: A search engine for mathematical formulae. In: Calmet, J., Ida, T., Wang, D. (eds.) AISC 2006. LNCS, vol. 4120, pp. 241–253. Springer, Heidelberg (2006). doi:10.1007/11856290_21

    Chapter  Google Scholar 

  16. NASA Langley. Hypatheon: A Database Capability for PVS Theories (2016). https://shemesh.larc.nasa.gov/people/bld/hypatheon.html

  17. NASA Langley. NASA PVS Library (2016). http://shemesh.larc.nasa.gov/fm/ftp/larc/PVS-library/pvslib.html

  18. MathHub.info: Active Mathematics. http://mathhub.info. Accessed 28 Jan 2014

  19. Miller, D.A., Nadathur, G.: Higher-order logic programming. In: Shapiro, E. (ed.) ICLP 1986. LNCS, vol. 225, pp. 448–462. Springer, Heidelberg (1986). doi:10.1007/3-540-16492-8_94

    Chapter  Google Scholar 

  20. Meng, J., Paulson, L.: Translating higher-order clauses to first-order clauses. J. Automated Reason. 40(1), 35–60 (2008)

    Article  MathSciNet  Google Scholar 

  21. Owre, S., Rushby, J.M., Shankar, N.: PVS: a prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992). doi:10.1007/3-540-55602-8_217

    Chapter  Google Scholar 

  22. Obua, S., Skalberg, S.: Importing HOL into Isabelle/HOL. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS, vol. 4130, pp. 298–302. Springer, Heidelberg (2006). doi:10.1007/11814771_27

    Chapter  Google Scholar 

  23. Pfenning, F., et al.: The Logosphere Project (2003). http://www.logosphere.org/

  24. The PVS libraries in OMDoc/MMT format. https://gl.mathhub.info/PVS. Accessed 29 May 2017

  25. Rabe, F.: A logic-independent IDE. In: Benzmüller, C., Woltzenlogel Paleo, B. (eds.) Workshop on User Interfaces for Theorem Provers, pp. 48–60 (2014). Elsevier

    Google Scholar 

  26. Rabe, F.: How to identify, translate, and combine logics? J. Logic Comput. (2014). doi:10.1093/logcom/exu079

  27. Rabe, F.: Generic literals. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds.) CICM 2015. LNCS, vol. 9150, pp. 102–117. Springer, Cham (2015). doi:10.1007/978-3-319-20615-8_7

    Chapter  Google Scholar 

  28. Rabe, F.: A Modular Type Reconstruction Algorithm (2017). http://kwarc.info/frabe/Research/rabe_recon_17.pdf

  29. Rabe, F., Kohlhase, M.: A scalable module system. Inf. Comput. 230(1), 1–54 (2013)

    Article  MathSciNet  Google Scholar 

  30. vis.js - A dynamic, browser based visualization library. http://visjs.org. Accessed 04 May 2017

  31. Watt, S.M., et al. (eds.) Intelligent Computer Mathematics. LNCS, vol. 8543. Springer, Heidelberg (2014). doi:10.1007/978-3-319-08434-3. ISBN 978-3-319-08433-6

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Acknowledgements

This work has been partially funded by DFG under Grants KO 2428/13-1 and RA-18723-1. The authors gratefully acknowledge the contribution of Marcel Rupprecht, who has extended the graph viewer for this paper.

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Authors and Affiliations

  1. Computer Science, FAU Erlangen-Nürnberg, Erlangen, Germany

    Michael Kohlhase & Dennis Müller

  2. SRI Palo Alto, Menlo Park, USA

    Sam Owre

  3. Computer Science, Jacobs University Bremen, Bremen, Germany

    Florian Rabe

Authors
  1. Michael Kohlhase
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  2. Dennis Müller
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  3. Sam Owre
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  4. Florian Rabe
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Corresponding author

Correspondence to Dennis Müller .

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Editors and Affiliations

  1. University of Brasília, Brasília D.F., Brazil

    Mauricio Ayala-Rincón

  2. NASA, Hampton, VA, USA

    César A. Muñoz

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Kohlhase, M., Müller, D., Owre, S., Rabe, F. (2017). Making PVS Accessible to Generic Services by Interpretation in a Universal Format. In: Ayala-Rincón, M., Muñoz, C.A. (eds) Interactive Theorem Proving. ITP 2017. Lecture Notes in Computer Science(), vol 10499. Springer, Cham. https://doi.org/10.1007/978-3-319-66107-0_21

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  • DOI: https://doi.org/10.1007/978-3-319-66107-0_21

  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-66107-0

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