Skip to main content
SpringerLink
Log in

Generic Literals

  • Conference paper
  • First Online:
Intelligent Computer Mathematics (CICM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9150))

Included in the following conference series:

Abstract

Mmt is a formal framework that combines the flexibility of knowledge representation languages like OpenMath with the formal rigor of logical frameworks like LF. It systematically abstracts from theoretical and practical aspects of individual formal languages and tries to develop as many solutions as possible generically.

In this work, we allow Mmt theories to declare user-defined literals, which makes literals as user-extensible as operators, axioms, and notations. This is particularly important for framework languages, which must be able to represent any choice of literals. Theoretically, our literals are introduced by importing a model that defines the denotations of some types and function symbols. Practically, Mmt is coupled with a programming language, in which these models are defined.

Our results are implemented in the Mmt system. In particular, literals and computation on them are integrated with the parser and type checker.

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

References

  1. Asperti, A., Ricciotti, W., Sacerdoti Coen, C., Tassi, E.: Hints in unification. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 84–98. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  2. Buswell, S., Caprotti, O., Carlisle, D., Dewar, M., Gaetano, M., Kohlhase, M.: The Open Math Standard, Version 2.0. Technical report, The Open Math Society (2004). http://www.openmath.org/standard/om20

  3. Berger, U., Schwichtenberg, H.: An inverse of the evaluation functional for typed \(\lambda \)-Calculus. In: Kahn, G. (ed.) Logic in Computer Science, pp. 203–211. IEEE Computer Society Press, Los Alamitos (1991)

    Chapter  Google Scholar 

  4. Constable, R., Allen, S., Bromley, H., Cleaveland, W., Cremer, J., Harper, R., Howe, D., Knoblock, T., Mendler, N., Panangaden, P., Sasaki, J., Smith, S.: Implementing Mathematics with the Nuprl Development System. Prentice-Hall, Upper Saddle River (1986)

    Google Scholar 

  5. Farmer, W.M.: Biform theories in chiron. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573, pp. 66–79. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Farmer, W.M.: The formalization of syntax-based mathematical algorithms using quotation and evaluation. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS, vol. 7961, pp. 35–50. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Farmer, W., von Mohrenschildt, M.: An overview of a formal framework for managing mathematics. Ann. Math. Artif. Intell. 38(1–3), 165–191 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Harrison, J.: HOL light: a tutorial introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Kohlhase, M., Mance, F., Rabe, F.: A universal machine for biform theory graphs. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS, vol. 7961, pp. 82–97. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Kop, C., Nishida, N.: Term rewriting with logical constraints. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS, vol. 8152, pp. 343–358. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  12. Martin-Löf, P.: An intuitionistic theory of types: predicative part. In: Proceedings of the 1973 Logic Colloquium, pp. 73–118. North-Holland (1974)

    Google Scholar 

  13. Odersky, M., Spoon, L., Venners, B.: Programming in Scala. Artima (2007)

    Google Scholar 

  14. Pfenning, F., Schürmann, C.: System description: twelf - a meta-logical framework for deductive systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 202–206. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  15. Rabe, F.: The MMT API: a generic MKM system. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS, vol. 7961, pp. 339–343. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Sutcliffe, G., Schulz, S., Claessen, K., Baumgartner, P.: The TPTP typed first-order form with arithmetic. In: Bjørner, N., Voronkov, A. (eds.) LPAR-18 2012. LNCS, vol. 7180, pp. 406–419. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  19. Trybulec, A., Blair, H.: Computer assisted reasoning with MIZAR. In: Joshi, A. (ed.) Proceedings of the 9th International Joint Conference on Artificial Intelligence, pp. 26–28. Morgan Kaufmann, Los Angeles (1985)

    Google Scholar 

  20. Wolfram. Mathematica (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Jacobs University, Bremen, Germany

    Florian Rabe

Authors
  1. Florian Rabe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Florian Rabe .

Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham, United Kingdom

    Manfred Kerber

  2. McMaster University, Hamilton, Ontario, Canada

    Jacques Carette

  3. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  4. Jacobs University Bremen, Bremen, Germany

    Florian Rabe

  5. University of Birmingham, Birmingham, United Kingdom

    Volker Sorge

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Rabe, F. (2015). Generic Literals. In: Kerber, M., Carette, J., Kaliszyk, C., Rabe, F., Sorge, V. (eds) Intelligent Computer Mathematics. CICM 2015. Lecture Notes in Computer Science(), vol 9150. Springer, Cham. https://doi.org/10.1007/978-3-319-20615-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-20615-8_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20614-1

  • Online ISBN: 978-3-319-20615-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation