Advertisement

Point-and-Write – Documenting Formal Mathematics by Reference

  • Carst Tankink
  • Christoph Lange
  • Josef Urban
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7362)

Abstract

This paper describes the design and implementation of mechanisms for light-weight inclusion of formal mathematics in informal mathematical writings, particularly in a Web-based setting. This is conceptually done in three stages: (i) by choosing a suitable representation layer (based on RDF) for encoding the information about available resources of formal mathematics, (ii) by exporting this information from formal libraries, and (iii) by providing syntax and implementation for including formal mathematics in informal writings.

We describe the use case of an author referring to formal text from an informal narrative, and discuss design choices entailed by this use case. Furthermore, we describe an implementation of the use case within the Agora prototype: a Wiki for collaborating on formalized mathematics.

Keywords

Resource Description Framework Formal Text Source Text Resource Description Framework Data Resource Description Framework Graph 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Resource Description Framework (RDF): Concepts and abstract syntax. Recommendation, W3C (2004), http://www.w3.org/TR/rdf-concepts
  2. 2.
    RDFa in XHTML: Syntax and processing. Recommendation, W3C (October 2008), http://www.w3.org/TR/rdfa-syntax
  3. 3.
    Asperti, A., Geuvers, H., Loeb, I., Mamane, L.E., Coen, C.S.: An interactive algebra course with formalised proofs and definitions. In: Kohlhase [14], pp. 315–329Google Scholar
  4. 4.
    Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.): AISC 2010. LNCS, vol. 6167. Springer, Heidelberg (2010)zbMATHGoogle Scholar
  5. 5.
    Bancerek, G., Kohlhase, M.: Towards a Mizar Mathematical Library in OMDoc format. In: Matuszewski, R., Zalewska, A. (eds.) From Insight to Proof: Festschrift in Honour of Andrzej Trybulec. Studies in Logic, Grammar and Rhetoric, vol. 10(23), pp. 265–275. University of Białystok (2007)Google Scholar
  6. 6.
    Bancerek, G., Rudnicki, P.: A compendium of continuous lattices in MIZAR. J. Autom. Reasoning 29(3-4), 189–224 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Blackwell, A.F., Green, T.R.G.: Cognitive dimensions of information artefacts: a tutorial. Tutorial (1998), http://www.cl.cam.ac.uk/~afb21/CognitiveDimensions/CDtutorial.pdf
  8. 8.
    Cairns, P., Gow, J.: Literate proving: Presenting and documenting formal proofs. In: Kohlhase (ed.) [14], pp. 159–173Google Scholar
  9. 9.
    The Coq wiki, Browsable online at http://coq.inria.fr/cocorico
  10. 10.
    The Coq mailing list, coq-club@inria.frGoogle Scholar
  11. 11.
    Heath, T., Bizer, C.: Linked Data: Evolving the Web into a Global Data Space. Morgan & Claypool (2011)Google Scholar
  12. 12.
    Heinz, C., Moses, B.: The listings package. Technical report, CTAN (2007), http://www.ctan.org/tex-archive/macros/latex/contrib/listings
  13. 13.
    The Isabelle mailing list, cl-isabelle-users@lists.cam.ac.ukGoogle Scholar
  14. 14.
    Kohlhase, M. (ed.): MKM 2005. LNCS (LNAI), vol. 3863. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  15. 15.
    Kohlhase, M.: OMDoc – An Open Markup Format for Mathematical Documents [version 1.2]. LNCS (LNAI), vol. 4180. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Lange, C.: OMDoc ontology (2011), http://kwarc.info/projects/docOnto/omdoc.html
  17. 17.
    Lange, C.: Ontologies and languages for representing mathematical knowledge on the semantic web. Semantic Web Journal (in press, 2012)Google Scholar
  18. 18.
    Lange, C., Urban, J. (eds.): Proceedings of the ITP 2011 Workshop on Mathematical Wikis (MathWikis). CEUR-WS, vol. 767 (2011)Google Scholar
  19. 19.
    The Mizar mailing list, mizar-forum@mizar.uwb.edu.plGoogle Scholar
  20. 20.
    The Mizar wiki, Browsable online at http://wiki.mizar.org
  21. 21.
    Sauer, C., Smith, C., Benz, T.: Wikicreole: a common wiki markup. In: WikiSym 2007, pp. 131–142. ACM, New York (2007)CrossRefGoogle Scholar
  22. 22.
    The homotopy type theory blog, http://homotopytypetheory.org/
  23. 23.
    Urban, J.: XML-izing Mizar: making semantic processing and presentation of MML easy. In: Kohlhase (ed.) [14], pp. 346–360Google Scholar
  24. 24.
    Urban, J., Alama, J., Rudnicki, P., Geuvers, H.: A wiki for Mizar: Motivation, considerations, and initial prototype. In: Autexier, et al. (eds.) [4], pp. 455–469Google Scholar
  25. 25.
    Urban, J., Sutcliffe, G.: Automated reasoning and presentation support for formalizing mathematics in Mizar. In: Autexier, et al. (eds.) [4], pp. 132–146Google Scholar
  26. 26.
    van Eekelen, M.C.J.D., Geuvers, H., Schmaltz, J., Wiedijk, F.: ITP 2011. LNCS, vol. 6898. Springer, Heidelberg (2011)zbMATHCrossRefGoogle Scholar
  27. 27.
    Wenzel, M.: Isabelle as Document-Oriented Proof Assistant. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) Calculemus/MKM 2011. LNCS (LNAI), vol. 6824, pp. 244–259. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  28. 28.
    Wenzel, M.M.: Isabelle/Isar — a versatile environment for human-readable formal proof documents. PhD thesis, Technische Universität München (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Carst Tankink
    • 1
  • Christoph Lange
    • 2
    • 3
    • 4
  • Josef Urban
    • 1
  1. 1.Institute for Computing and Information ScienceRadboud UniversiteitNijmegenThe Netherlands
  2. 2.FB 3Universität BremenGermany
  3. 3.Computer ScienceJacobs University BremenGermany
  4. 4.School of Computer ScienceUniversity of BirminghamUK

Personalised recommendations