Skip to main content
SpringerLink
Log in

On explicit substitutions and names (extended abstract)

  • Session 4: Semantics I
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

Included in the following conference series:

Abstract

Calculi with explicit substitutions have found widespread acceptance as a basis for abstract machines for functional languages. In this paper we investigate the relations between variants with de Bruijnnumbers, with variable names, with reduction based on raw expressions and calculi with equational judgements. We show the equivalence between these variants, which is crucial in establishing the correspondence between the semantics of the calculus and its implementations.

Research supported under the EPSRC project no. GR/L28296, x-SLAM: The Explicit Substitutions Linear Abstract Machine.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Abadi, L. Cardelli, P.-L. Curien, and J.-J. Lévy. Explicit substitutions. Journal of Functional Programming, 1(4):375–416, 1991.

    Google Scholar 

  2. R. Bloo and K.H. Rose. Preesrvation of strong normalisation in named lambda calculi with explicit substitution and garbage collection. In Proc. CSN'95 — Computer Science in the Netherlands, pages 62–72, 1995.

    Google Scholar 

  3. C. Coquand. From semantics to rules: A machine assisted analysis. In CSL'93, volume 832 of LNCS, 1994.

    Google Scholar 

  4. P.-L. Curien, Th. Hardin, and J.-J. Lévy. Confluence properties of weak and strong calculi of explicit substitutions. Journal of the ACM, 43:362–397, March 1996.

    Article  Google Scholar 

  5. Pierre-Louis Curien, An abstract framework for environment machines (Note). Theoretical Computer Science, 82(2):389–402, 1991.

    Article  Google Scholar 

  6. Herman Geuvers. Logics and Type Systems. PhD thesis, Univ. of Nijmegen, 1993.

    Google Scholar 

  7. Thérèse Hardin. Confluence results for the pure strong categorical logic CCL. λ-calculi as subsystems of CCL. Theoretical Computer Science, 65:291–342, 1989.

    Article  Google Scholar 

  8. F. Kamareddine and A. Rios. A lambda-calculus a la de bruijn with explicit substitutions. In PLILP'95, volume 982 of LNCS, 1995.

    Google Scholar 

  9. P. Lescanne. From λσ to λυ: a journey through calculi of explicit substitutions. POPL'94, pages 60–69, Portland, Oregon, 1994.

    Google Scholar 

  10. Per Martin-Löf. Intuitionistic Type Theory. Bibliopolis, Napoli, 1984.

    Google Scholar 

  11. P.-A. Mellies. Typed λ-calculi with explicit substitution may not terminate. TLCA'95, pages 328–334. LNCS No. 902, 1995.

    Google Scholar 

  12. E. Ritter and V. de Paiva. On explicit substitution and names. Technical report, Univ. of Birmingham, School of Computer Science, 1997.

    Google Scholar 

  13. Eike Ritter. Normalization for typed lambda calculi with explicit substitution. CSL'93, pages 295–304. LNCS No. 832, 1994.

    Google Scholar 

  14. Thomas Streicher. Correctness and Completeness of a Categorical Semantics of the Calculus of Constructions. PhD thesis, Universität Passau, June 1989.

    Google Scholar 

  15. A. Tasistro. Formulation of Martin-Löf's theory types with explicit substitutions. Licenciate Thesis, Chalmers University, Dept. of Computer Science, May 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, University of Birmingham, UK

    Eike Ritter & Valeria de Paiva

Authors
  1. Eike Ritter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Valeria de Paiva
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ritter, E., de Paiva, V. (1997). On explicit substitutions and names (extended abstract). In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_182

Download citation

  • DOI: https://doi.org/10.1007/3-540-63165-8_182

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation