Skip to main content

Theory Presentation Combinators

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7362))

Abstract

We motivate and give semantics to theory presentation combinators as the foundational building blocks for a scalable library of theories. The key observation is that the category of contexts and fibered categories are the ideal theoretical tools for this purpose.

This research was supported by NSERC.

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

Buying options

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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Asperti, A., Sacerdoti Coen, C.: Some Considerations on the Usability of Interactive Provers. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.) AISC 2010. LNCS, vol. 6167, pp. 147–156. Springer, Heidelberg (2010), http://dl.acm.org/citation.cfm?id=1894483.1894498

    Chapter  Google Scholar 

  2. Burstall, R.M., Goguen, J.A.: Putting theories together to make specifications. In: IJCAI, pp. 1045–1058 (1977)

    Google Scholar 

  3. Burstall, R.M., Goguen, J.A.: The Semantics of Clear, a Specification Language. In: Bjorner, D. (ed.) Abstract Software Specifications. LNCS, vol. 86, pp. 292–332. Springer, Heidelberg (1980)

    Chapter  Google Scholar 

  4. Carette, J., Farmer, W.M.: High-Level Theories. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds.) AISC 2008, Calculemus 2008, and MKM 2008. LNCS (LNAI), vol. 5144, pp. 232–245. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Carette, J., Farmer, W.M., Jeremic, F., Maccio, V., O’Connor, R., Tran, Q.: The mathscheme library: Some preliminary experiments. Tech. rep., University of Bologna, Italy (2011), uBLCS-2011-04

    Google Scholar 

  6. Carette, J., Kiselyov, O.: Multi-stage programming with functors and monads: Eliminating abstraction overhead from generic code. Sci. Comput. Program. 76(5), 349–375 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Carette, J., O’Connor, R.: Theory Presentation Combinators (2012), http://arxiv.org/abs/1204.0053v2

  8. Cartmell, J.: Generalised algebraic theories and contextual categories. Annals of Pure and Applied Logic 32, 209–243 (1986), http://www.sciencedirect.com/science/article/pii/0168007286900539

    Article  MathSciNet  MATH  Google Scholar 

  9. CoFI (The Common Framework Initiative): Casl Reference Manual. LNCS, IFIP Series, vol. 2960. Springer (2004)

    Google Scholar 

  10. Farmer, W.M., Guttman, J.D., Thayer, F.J.: Little Theories. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 567–581. Springer, Heidelberg (1992)

    Google Scholar 

  11. Garillot, F., Gonthier, G., Mahboubi, A., Rideau, L.: Packaging Mathematical Structures. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 327–342. Springer, Heidelberg (2009), http://dx.doi.org/10.1007/978-3-642-03359-9_23

    Chapter  Google Scholar 

  12. Geuvers, H., Wiedijk, F., Zwanenburg, J.: A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals. In: Callaghan, P., Luo, Z., McKinna, J., Pollack, R. (eds.) TYPES 2000. LNCS, vol. 2277, pp. 96–111. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Grabowski, A., Schwarzweller, C.: On Duplication in Mathematical Repositories. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P., Rideau, L., Rioboo, R., Sexton, A. (eds.) AISC 2010. LNCS, vol. 6167, pp. 300–314. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Jacobs, B.: Categorical Logic and Type Theory. Studies in Logic and the Foundations of Mathematics, vol. 141. North Holland, Amsterdam (1999)

    MATH  Google Scholar 

  15. Oriat, C.: Detecting equivalence of modular specifications with categorical diagrams. Theor. Comput. Sci. 247(1-2), 141–190 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rabe, F., Kohlhase, M.: A Scalable Module System, http://kwarc.info/frabe/Research/mmt.pdf

  17. Sacerdoti Coen, C., Tassi, E.: Nonuniform coercions via unification hints. In: Hirschowitz, T. (ed.) TYPES. EPTCS, vol. 53, pp. 16–29 (2009)

    Google Scholar 

  18. Smith, D.R.: Constructing specification morphisms. Journal of Symbolic Computation 15, 5–6 (1993)

    Article  Google Scholar 

  19. Smith, D.R.: Mechanizing the development of software. In: Broy, M., Steinbrueggen, R. (eds.) Calculational System Design, Proceedings of the NATO Advanced Study Institute, pp. 251–292. IOS Press, Amsterdam (1999)

    Google Scholar 

  20. Spitters, B., van der Weegen, E.: Type classes for mathematics in type theory. Mathematical Structures in Computer Science 21(4), 795–825 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Wiedijk, F.: Estimating the cost of a standard library for a mathematical proof checker (2001), http://www.cs.ru.nl/~freek/notes/mathstdlib2.pdf

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Carette, J., O’Connor, R. (2012). Theory Presentation Combinators. In: Jeuring, J., et al. Intelligent Computer Mathematics. CICM 2012. Lecture Notes in Computer Science(), vol 7362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31374-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31374-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31373-8

  • Online ISBN: 978-3-642-31374-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics