Skip to main content

A Modular Hierarchy of Logical Frameworks

  • Conference paper
Types for Proofs and Programs (TYPES 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3085))

Included in the following conference series:

Abstract

We present a method for defining logical frameworks as a collection of features which are defined and behave independently of one another. Each feature is a set of grammar clauses and rules of deduction such that the result of adding the feature to a framework is a conservative extension of the framework itself. We show how several existing logical frameworks can be so built, and how several much weaker frameworks defined in this manner are adequate for expressing a wide variety of object logics.

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

Access this chapter

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. Pientka, B., Pfenning, F.: Optimizing higher-order pattern unification (2003)

    Google Scholar 

  2. Jojgov, G.I.: Holes with binding power. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646, pp. 162–181. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. In: Proceedings 2nd Annual IEEE Symp. on Logic in Computer Science, LICS 1987, Ithaca, NY, USA, June 22-25, pp. 194–204. IEEE Computer Society Press, New York (1987)

    Google Scholar 

  4. Nordström, B., Petersson, K., Smith, J.: Programming in Martin-Löf’s Type Theory: an Introduction. Oxford University Press, Oxford (1990)

    MATH  Google Scholar 

  5. Nederpelt, R.P., Geuvers, J.H., Vrijer, R.C.D. (eds.): Selected Papers on AUTOMATH. Studies in Logic and the Foundations of Mathematics, vol. 133. North-Holland, Amsterdam (1994)

    MATH  Google Scholar 

  6. Klop, J.W., van Oostrom, V., van Raamsdonk, F.: Combinatory reduction systems:introduction and survey. Theoretical Computer Science 121, 279–308 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ghani, N.: Eta-expansions in dependent type theory — the calculus of constructions. In: de Groote, P., Hindley, J.R. (eds.) TLCA 1997. LNCS, vol. 1210, pp. 164–180. Springer, Heidelberg (1997)

    Google Scholar 

  8. Luo, Z.: Computation and Reasoning: A Type Theory for Computer Science. International Series of Monographs on Computer Science, vol. 11. Oxford University Press, Oxford (1994)

    MATH  Google Scholar 

  9. Luo, Z.: PAL+: a lambda-free logical framework. Journal of Functional Programming 13, 317–338 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Levin, M.Y., Pierce, B.C.: Tinkertype: A language for playing with formal systems. Technical report (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Adams, R. (2004). A Modular Hierarchy of Logical Frameworks. In: Berardi, S., Coppo, M., Damiani, F. (eds) Types for Proofs and Programs. TYPES 2003. Lecture Notes in Computer Science, vol 3085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24849-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24849-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22164-7

  • Online ISBN: 978-3-540-24849-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics