Skip to main content
SpringerLink
Log in

Second-Order Pre-logical Relations and Representation Independence

  • Conference paper
  • First Online:
Typed Lambda Calculi and Applications (TLCA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2044))

Included in the following conference series:

Abstract

We extend the notion of pre-logical relation between models of simply typed lambda-calculus, recently introduced by F. Honsell and D. Sannella, to models of second-order lambda calculus. With pre-logical relations, we obtain characterizations of the lambda-definable elements of and the observational equivalence between second-order models. These are are simpler than those using logical relations on extended models.

We also characterize representation independence for abstract data types and abstract data type constructors by the existence of a pre-logical relation between the representations, thereby varying and generalizing results of J.C. Mitchell to languages with higher-order constants.

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. Kim B. Bruce, Albert R. Meyer, and John C. Mitchell, The semantics of second-order lambda calculus, Information and Computation 85 (1990), 76–134.

    Article  MATH  MathSciNet  Google Scholar 

  2. Jo Erskine Hannay, Specification refinement with system F, In Proc. CSL’99, LNCS 1683, Springer Verlag, 1999, pp. 530–545.

    Google Scholar 

  3. Furio Honsell, John Longley, Donald Sannella, and Andrzej Tarlecki, Constructive data refinement in typed lambda calculus, 3rd Intl. Conf. on Foundations of Software Science and Computation Structures. European Joint Conferences on Theory and Practice of Software (ETAPS’2000), LNCS 1784, Springer Verlag, 2000, pp. 149–164.

    Google Scholar 

  4. Furio Honsell and Donald Sannella, Pre-logical relations, Proc. Computer Science Logic, CSL’99, LNCS 1683, Springer Verlag, 1999, pp. 546–561.

    Chapter  Google Scholar 

  5. Xavier Leroy, Applicative functors and fully transparent higher-order modules, Proc. of the 22nd Annual ACM Symposium on Principles of Programming Languages, ACM, 1995, pp. 142–153.

    Google Scholar 

  6. John C. Mitchell, Representation independence and data abstraction, Proceedings of the 13th ACM Symposium on Principles of Programming Languages, January 1986, pp. 263–276.

    Google Scholar 

  7. John C. Mitchell, On the equivalence of data representations, Artificial Intelligence and Mathematical Theory of Computation: Papers in Honour of John C. McCarthy (V. Lifschitz, ed.), Academic Press, 1991, pp. 305–330.

    Google Scholar 

  8. John C. Mitchell, Foundations for programming languages, The MIT Press, Cambridge, Mass., 1996.

    Google Scholar 

  9. John C. Mitchell and Albert Meyer, Second-order logical relations, Proc. Logics of Programs, LNCS 193, Springer Verlag, 1985, pp. 225–236.

    Google Scholar 

  10. John C. Mitchell and Gordon D. Plotkin, Abstract types have existential type, 12-th ACM Symposium on Principles of Programming Languages, 1985, pp. 37–51.

    Google Scholar 

  11. Robin Milner, Mads Tofte, Robert Harper, and David MacQueen, The definition of Standard ML (revised), The MIT Press, Cambridge, MA, 1997.

    Google Scholar 

  12. Gordon D. Plotkin, Lambda definability in the full type hierarchy, To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, 1980, pp. 363–373.

    Google Scholar 

  13. Gordon Plotkin, John Power, Don Sannella, and Robert Tennent, Lax logical relations, ICALP 2000, Springer LNCS 1853, 2000, pp. 85–102.

    Google Scholar 

  14. John Power and Edmund Robinson, Logical relations and data abstraction, Proc. Computer Science Logic, CSL 2000, LNCS 1862, Springer-Verlag, 2000, pp. 497–511.

    Google Scholar 

  15. R. Statman, Logical relations and the typed lambda calculus, Information and Control 65 (1985), 85–97.

    Article  MATH  MathSciNet  Google Scholar 

  16. W.W. Tait, Intensional interpretation of functionals of finite type, Journal of Symbolic Logic 32 (1967), 198–212.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centrum für Informations- und Sprachverarbeitung, Universität München, Oettingenstr. 67, D-80538, München, Germany

    Hans Leiβ

Authors
  1. Hans Leiβ
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, USA

    Samson Abramsky

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Leiβ, H. (2001). Second-Order Pre-logical Relations and Representation Independence. In: Abramsky, S. (eds) Typed Lambda Calculi and Applications. TLCA 2001. Lecture Notes in Computer Science, vol 2044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45413-6_24

Download citation

  • DOI: https://doi.org/10.1007/3-540-45413-6_24

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41960-0

  • Online ISBN: 978-3-540-45413-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation