Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

A Terminating and Confluent Linear Lambda Calculus

  • Conference paper
Term Rewriting and Applications (RTA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4098))

Included in the following conference series:

Abstract

We present a rewriting system for the linear lambda calculus corresponding to the {!, \(\multimap\)}-fragment of intuitionistic linear logic. This rewriting system is shown to be strongly normalizing, and Church-Rosser modulo the trivial commuting conversion. Thus it provides a simple decision method for the equational theory of the linear lambda calculus. As an application we prove the strong normalization of the simply typed computational lambda calculus by giving a reduction-preserving translation into the linear lambda calculus.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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.

Similar content being viewed by others

References

  1. Barber, A.: Linear Type Theories, Semantics and Action Calculi. PhD Thesis ECS-LFCS-97-371, University of Edinburgh (1997)

    Google Scholar 

  2. Barber, A., Plotkin, G.: Dual intuitionistic linear logic. Manuscript. An earlier version available as Technical Report ECS-LFCS-96-347, LFCS, University of Edinburgh (1997)

    Google Scholar 

  3. Barr, M.: *-autonomous categories and linear logic. Math. Struct. Comp. Sci. 1, 159–178 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bierman, G.M.: What is a categorical model of intuitionistic linear logic? In: Dezani-Ciancaglini, M., Plotkin, G. (eds.) TLCA 1995. LNCS, vol. 902, pp. 78–93. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  5. Crole, R.: Categories for Types. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  6. Ghani, N.: Adjoint rewriting and the!-type constructor (manuscript) (1996)

    Google Scholar 

  7. Girard, J.-Y.: Linear logic. Theoret. Comp. Sci. 50, 1–102 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hasegawa, M.: Girard translation and logical predicates. J. Funct. Programming 10(1), 77–89 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hasegawa, M.: Linearly used effects: monadic and CPS transformations into the linear lambda calculus. In: Hu, Z., Rodríguez-Artalejo, M. (eds.) FLOPS 2002. LNCS, vol. 2441, pp. 67–182. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Hasegawa, M.: Semantics of linear continuation-passing in call-by-name. In: Kameyama, Y., Stuckey, P.J. (eds.) FLOPS 2004. LNCS, vol. 2998, pp. 229–243. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Hasegawa, M.: Classical linear logic of implications. Math. Struct. Comput. Sci. 15(2), 323–342 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Huet, G.: Confluent reductions: Abstract properties and applications to term rewriting systems. J. ACM 27(4), 797–821 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lambek, J., Scott, P.: Introduction to Higher-order Categorical Logic. Cambridge University Press, Cambridge (1986)

    MATH  Google Scholar 

  14. Stark, I., Lindley, S.: Reducibility and ⊤ ⊤-lifting for computation types. In: Urzyczyn, P. (ed.) TLCA 2005. LNCS, vol. 3461, pp. 262–277. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. Maraist, J., Odersky, M., Turner, D.N., Wadler, P.: Call-by-name, call-by-value, call-by-need and the linear lambda calculus. In: Proc. 11th Mathematical Foundations of Programming Semantics. ENTCS. Electr. Notes Theor. Comput. Sci., vol. 1, pp. 370–392 (1995)

    Google Scholar 

  16. Mellies, P.-A.: Categorical models of linear logic revisited. Theoret. Comp. Sci. (to appear, 2003)

    Google Scholar 

  17. Moggi, E.: Computational lambda-calculus and monads. In: Proc. 4th Annual Symposium on Logic in Computer Science pp. 14–23 (1989); a different version available as Technical Report ECS-LFCS-88-86, University of Edinburgh (1988)

    Google Scholar 

  18. Sabry, A., Wadler, P.: A reflection on call-by-value. ACM Transactions on Programming Languages and Systems 19(6), 916–941 (1997)

    Article  Google Scholar 

  19. Seely, R.A.G.: Linear logic, *-autonomous categories and cofree coalgebras. Categories in Computer Science, AMS Contemp. Math. 92, 371–389 (1989)

    MathSciNet  Google Scholar 

  20. Terese.: Term Rewriting Systems. Cambridge University Press, Cambridge (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Yo Ohta & Masahito Hasegawa

Authors
  1. Yo Ohta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masahito Hasegawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Carnegie Mellon University,  

    Frank Pfenning

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ohta, Y., Hasegawa, M. (2006). A Terminating and Confluent Linear Lambda Calculus. In: Pfenning, F. (eds) Term Rewriting and Applications. RTA 2006. Lecture Notes in Computer Science, vol 4098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11805618_13

Download citation

  • DOI: https://doi.org/10.1007/11805618_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36834-2

  • Online ISBN: 978-3-540-36835-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation