Skip to main content
SpringerLink
Log in

Translating the IMPS Theory Library to MMT/OMDoc

  • Conference paper
  • First Online:
Intelligent Computer Mathematics (CICM 2018)

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

Included in the following conference series:

Abstract

The IMPS system by Farmer, Guttman and Thayer was an influential automated reasoning system, pioneering mechanisations of features like theory morphisms, partial functions with subsorts, and the little theories approach to the axiomatic method. It comes with a large library of formalised mathematical knowledge covering a broad spectrum of different fields. Since IMPS is no longer under development, this library is in danger of being lost. In its present form, it is also not compatible for use with any other mathematical system.

To remedy that, we formalise the logic of IMPS (LUTINS), and draw on both the original theory library source files as well as the internal data structures of the system to generate a representation in a modern knowledge management format. Using this approach, we translate the library to OMDoc/MMT and verify the result using type-checking in the MMT system against our implementation of LUTINS .

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    [FGT98] gives the example of the algorithm for differentiating polynomials for this.

  2. 2.

    The meta-theory-relation connects theories that live on different meta-levels; e.g. domain knowledge to its logical foundation and conversely the logical foundation to the logical framework it is formalised in.

  3. 3.

    This formalisation is part of the LATIN foundations see https://gl.mathhub.info/MMT/LATIN/blob/master/source/foundations/imps/lutins.mmt.

  4. 4.

    Which – like the original IMPS system – are written in the T language – a dialect of Scheme – and are hence often referred to simply as “T-files” in the following sections.

  5. 5.

    Note that the theories shown here are all part of the library; they are not duplicates created by the process from Fig. 7.

References

  1. Betzendahl, J.: Translating the IMPS theory library to MMT/OMDoc. Master’s Thesis. Informatik, Universität Bielefeld, April 2018. https://gl.kwarc.info/supervision/MSc-archive/blob/master/2018/jbetzendahl/thesis_imps2omdoc.pdf

  2. Church, A.: A formulation of the simple theory of types. J. Symb. Log. 5, 56–68 (1940)

    Article  MathSciNet  Google Scholar 

  3. Codescu, M., Horozal, F., Kohlhase, M., Mossakowski, T., Rabe, F.: Project abstract: logic atlas and integrator (LATIN). In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) CICM 2011. LNCS (LNAI), vol. 6824, pp. 289–291. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22673-1_24. https://kwarc.info/people/frabe/Research/CHKMR_latinabs_11.pdf

    Google Scholar 

  4. Farmer, W.M.: A partial-function version of Church’s simple theory of types. J. Symb. Log. 55, 1269–1291 (1990)

    Article  MathSciNet  Google Scholar 

  5. Farmer, W.M.: Theory interpretation in simple type theory. In: Heering, J., Meinke, K., Möller, B., Nipkow, T. (eds.) HOA 1993. LNCS, vol. 816, pp. 96–123. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-58233-9_6

    Chapter  Google Scholar 

  6. Farmer, W.M., Guttman, J.D., Javier Thayer, F.: Little theories. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 567–581. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55602-8_192

    Chapter  Google Scholar 

  7. Farmer, W.M., Guttman, J.D., Javier Thayer, F.: The IMPS 2.0 Users Manual, 1st edn. The MITRE Corporation, Bedford (1998)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. Iancu, M., Kohlhase, M., Rabe, F., Urban, J.: The Mizar mathematical library in OMDoc: translation and applications. J. Autom. Reason. 50(2), 191–202 (2013). https://doi.org/10.1007/s10817-012-9271-4

    Article  MathSciNet  MATH  Google Scholar 

  10. Iancu, M.: Towards flexiformal mathematics. Ph.D. thesis. Bremen, Germany: Jacobs University (2017). https://opus.jacobs-university.de/frontdoor/index/index/docId/721

  11. Kohlhase, M., Müller, D., Owre, S., Rabe, F.: Making PVS accessible to generic services by interpretation in a universal format. In: Ayala-Rincón, M., Muñoz, C.A. (eds.) ITP 2017. LNCS, vol. 10499, pp. 319–335. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66107-0_21. http://kwarc.info/kohlhase/submit/itp17-pvs.pdf

    Chapter  Google Scholar 

  12. Kohlhase, M.: OMDoc – An Open Markup Format for Mathematical Documents [version 1.2]. LNCS (LNAI), vol. 4180. Springer, Heidelberg (2006). https://doi.org/10.1007/11826095. http://omdoc.org/pubs/omdoc1.2.pdf

    Book  Google Scholar 

  13. Kaliszyk, C., Pąk, K., Urban, J.: Towards a Mizar environment for Isabelle: foundations and language. In: Avigad, J., Chlipala, A. (eds.) Proceedings of the 5th Conference on Certified Programs and Proofs (CPP 2016), pp. 58–65. ACM (2016). https://doi.org/10.1145/2854065.2854070

  14. 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 (LNAI), vol. 8543, pp. 357–372. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08434-3_26. http://kwarc.info/frabe/Research/KR_hollight_14.pdf

    Google Scholar 

  15. 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). https://doi.org/10.1007/978-3-642-14052-5_23

    Chapter  Google Scholar 

  16. 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). https://doi.org/10.1007/978-3-642-14052-5_22

    Chapter  Google Scholar 

  17. The LATIN Logic Atlas. https://gl.mathhub.info/MMT/LATIN. Accessed 02 June 2017

  18. MathHub MMT/LFX Git Repository. http://gl.mathhub.info/MMT/LFX. Accessed 15 May 2015

  19. Li, Y.: IMPS to OMDoc translation. Bachelor’s Thesis. McMaster University, August 2002

    Google Scholar 

  20. Müller, D., Gauthier, T., Kaliszyk, C., Kohlhase, M., Rabe, F.: Classification of alignments between concepts of formal mathematical systems. In: Geuvers, H., England, M., Hasan, O., Rabe, F., Teschke, O. (eds.) CICM 2017. LNCS (LNAI), vol. 10383, pp. 83–98. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-62075-6_7

    Chapter  Google Scholar 

  21. The OAF Project & System. http://oaf.mathhub.info. Accessed 23 April 2015

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

    Chapter  Google Scholar 

  23. Rabe, F.: How to identify, translate, and combine logics? J. Log. Comput. 27(6), 1753–1798 (2014). https://doi.org/10.1093/logcom/exu079

    Article  MATH  Google Scholar 

  24. Rabe, F.: MMT: a foundation-independent logical framework (2018). https://kwarc.info/people/frabe/Research/rabe_mmtsys_18.pdf

  25. Rabe, F., Kohlhase, M.: A scalable module system. Inf. Comput. 230, 1–54 (2013). http://kwarc.info/frabe/Research/mmt.pdf

    Article  MathSciNet  Google Scholar 

  26. Rupprecht, M., Kohlhase, M., Müller, D.: A flexible, interactive theory-graph viewer. In: Kohlhase, A., Pollanen, M. (eds.) 12th Workshop on Mathematical User Interfaces, MathUI 2017 (2017). http://kwarc.info/kohlhase/papers/mathui17-tgview.pdf

  27. Theorem Prover Museum - IMPS. https://github.com/theoremprovermuseum/imps. Accessed 28 April 2018

Download references

Acknowledgments

The authors gratefully acknowledge financial support from DFG-funded project OAF: An Open Archive for Formalizations (KO 2428/13-1) and fruitful discussions and clarifications from Bill Farmer, Dennis Müller, and Florian Rabe.

Author information

Authors and Affiliations

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

    Jonas Betzendahl & Michael Kohlhase

Authors
  1. Jonas Betzendahl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Kohlhase
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Jonas Betzendahl or Michael Kohlhase .

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

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Betzendahl, J., Kohlhase, M. (2018). Translating the IMPS Theory Library to MMT/OMDoc. 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_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-96812-4_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96811-7

  • Online ISBN: 978-3-319-96812-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation