Skip to main content
SpringerLink
Log in

Stateless Higher-Order Logic with Quantified Types

  • Conference paper
Interactive Theorem Proving (ITP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7998))

Included in the following conference series:

  • 1294 Accesses

Abstract

There have been numerous extensions to classical higher-order logic, but not all of them interact non-trivially. Two such extensions, stateless HOL and HOL extended with quantified types, generate an interesting conflict in the way that type operator variables are implemented and handled. This paper details a proposed solution to that conflict and explores the key impacts to the logical kernel. A prototype system, implemented in GHC Haskell, is discussed and compared to related systems.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Austin, E., Alexander, P.: HaskHOL: A Haskell Hosted Domain Specific Language Representation of HOL Light. In: Trends in Functional Programming Draft Proceedings (2010)

    Google Scholar 

  2. Bove, A., Dybjer, P., Norell, U.: A Brief Overview of Agda – A Functional Language with Dependent Types. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 73–78. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Coquand, T.: A New Paradox in Type Theory. In: Logic, Methodology and Philosophy of Science IX: Proceedings of the Ninth International Congress of Logic, Methodology, and Philosophy of Science, pp. 7–14. Elsevier (1994)

    Google Scholar 

  4. Gordon, M.: Why Higher-Order Logic is a Good Formalism for Specifying and Verifying Hardware, North-Holland (1986)

    Google Scholar 

  5. Haftmann, F.: From Higher-Order Logic to Haskell: There and Back Again. In: Gallagher, J.P., Voigtländer, J. (eds.) Proceedings of the 2010 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation, PEPM 2010, Madrid, Spain, January 18-19. ACM (2010)

    Google Scholar 

  6. 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 

  7. Homeier, P.V.: The HOL-Omega Logic. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 244–259. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Huffman, B.: Formal Verification of Monad Transformers. In: Thiemann, P., Findler, R.B. (eds.) ACM SIGPLAN International Conference on Functional Programming, ICFP 2012, Copenhagen, Denmark, September 9-15, pp. 15–16. ACM (2012)

    Google Scholar 

  9. Klein, G., Derrin, P., Elphinstone, K.: Experience Report: SEL4: Formally Verifying a High-Performance Microkernel. In: Proceedings of the 14th ACM SIGPLAN International Conference on Functional Programming, ICFP 2009, pp. 91–96. ACM, New York (2009)

    Chapter  Google Scholar 

  10. Melham, T.: Higher Order Logic and Hardware Verification. Cambridge University Press, New York (1993)

    Book  MATH  Google Scholar 

  11. Nipkow, T., Wenzel, M., Paulson, L.C. (eds.): Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)

    Google Scholar 

  12. Procter, A., Harrison, W.L., Stump, A.: The Design of a Practical Proof Checker for a Lazy Functional Language. In: Trends in Functional Programming Draft Proceedings (2012)

    Google Scholar 

  13. Slind, K., Norrish, M.: A Brief Overview of HOL4. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 28–32. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Völker, N.: HOL2P - A System of Classical Higher Order Logic with Second Order Polymorphism. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 334–351. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  15. Wiedijk, F.: Stateless HOL. In: Hirschowitz, T. (ed.) Proceedings Types for Proofs and Programs, Revised Selected Papers. EPTCS, vol. 53, pp. 47–61 (2009)

    Google Scholar 

  16. Yorgey, B.A., Weirich, S., Cretin, J., Jones, S.L.P., Vytiniotis, D., Magalhães, J.P.: Giving Haskell a Promotion. In: Pierce, B.C. (ed.) Proceedings of TLDI 2012: The Seventh ACM SIGPLAN Workshop on Types in Languages Design and Implementation, Philadelphia, PA, USA, January 28, pp. 53–66. ACM (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Information and Telecommunication Technology Center, The University of Kansas, 2335 Irving Hill Rd, Lawrence, KS, 66045, USA

    Evan Austin & Perry Alexander

Authors
  1. Evan Austin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Perry Alexander
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IRISA, Université Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France

    Sandrine Blazy

  2. Université Paris-Sud, LRI, Bat 650, Univ. Paris Sud, 91405, Orsay Cedex, France

    Christine Paulin-Mohring

  3. Inria Rennes-Bretagne Atlantique, Campus de Beaulieu, 35042, Rennes Cedex, France

    David Pichardie

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Austin, E., Alexander, P. (2013). Stateless Higher-Order Logic with Quantified Types. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds) Interactive Theorem Proving. ITP 2013. Lecture Notes in Computer Science, vol 7998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39634-2_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39634-2_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39633-5

  • Online ISBN: 978-3-642-39634-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation