Skip to main content
SpringerLink
Log in

A new formula for the execution of categorical combinators

  • Term Rewriting Systems
  • Conference paper
  • First Online:
8th International Conference on Automated Deduction (CADE 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 230))

Included in the following conference series:

Abstract

Categorical Combinators form a formal system similar to Curry's Combinatory Logic. It was developed by Curien [2] inspired by the equivalence of the theories of typed λ-calculus and Cartesian Closed Categories as shown by Lambek [3] and Scott [8]. In this paper we show how to “execute” Categorical Combinators in an efficient way using a rewriting system. This efficiency is achieved by cutting down the number of laws, by introducing constants in a different way and choosing a more compact notation for the code.

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. N.G. DeBruijn, Lambda Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, Indag.Math. 34, 381–392 (1972).

    Google Scholar 

  2. P-L.Curien, Categorical Combinators, Sequential Algorithms and Functional Programming, Draft version of a monograph submitted to publication, Université Paris VII, LITP (1985).

    Google Scholar 

  3. J.Lambek, From Lambda-calculus to Cartesian Closed Categories, in To H.B.Curry: Essays on Combinatory Logic, Lambda-Calculus and Formalism, ed J.P.Seldin and J.R.Hindley, Academic Press (1980).

    Google Scholar 

  4. R.D.Lins, The Complexity of a translation of λ-calculus to Categorical Combinators, Computing Lab. Report N. 27 — The University of Kent at Canterbury (1985).

    Google Scholar 

  5. R.D.Lins, A New Way of Introducing Constants in Categorical Combinators, privately circulated, The University of Kent at Canterbury (1985).

    Google Scholar 

  6. R.D.Lins, On The Efficiency of Categorical Combinators as a Rewriting System, Computing Lab.Report N.34 — The University of Kent at Canterbury (1985).

    Google Scholar 

  7. R.D.Lins, Constants and Higher-Order Data Types in Categorical Combinators, in preparation.

    Google Scholar 

  8. D.Scott, Relating Theories of the Lambda-Calculus, in To H.B.Curry: Essays on Combinatory Logic, Lambda-Calculus and Formalism, ed. J.P.Seldin and J.R.Hindley, Academic Press (1980).

    Google Scholar 

  9. D.A. Turner, A New Implementation Technique for Applicative Languages, Software Practice and Experience, Vol 9, 31–49 (1979).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computing Laboratory - Unikent - Canterbury, CT2 7NF, England

    R. D. Lins

  2. Chesf - Comp. Hidro Elétrica do São Francisco, Brazil

    R. D. Lins

Authors
  1. R. D. Lins
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jörg H. Siekmann

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lins, R.D. (1986). A new formula for the execution of categorical combinators. In: Siekmann, J.H. (eds) 8th International Conference on Automated Deduction. CADE 1986. Lecture Notes in Computer Science, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16780-3_82

Download citation

  • DOI: https://doi.org/10.1007/3-540-16780-3_82

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16780-8

  • Online ISBN: 978-3-540-39861-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation