Skip to main content
Springer Nature Link
Log in

Executable higher-order algebraic specifications

  • Invited Lectures
  • Conference paper
  • First Online:
STACS 91 (STACS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 480))

Included in the following conference series:

Abstract

Conventional algebraic specifications are first-order. Using higher-order equations in combination with first-order ones raises several fundamental model-theoretic and proof-theoretic questions. The model theory of higher-order equations is well understood (see [20] for a survey of algebraic specifications). The proof theory of higher-order equations is equally well understood, it requires higher- order matching, and higher-order rewriting therefore providing with a simple execution model. Higher-order variables may be instantiated by functions described by λ-expressions, bringing in λ-calculus, whose execution model is again rewriting (β-redexes). Hence rewriting is at the heart of all three execution models, which makes their combination quite simple on the operational side. The main question reviewed in this paper is whether the Church-Rosser and termination properties of these three execution models are preserved within their combination. We will see that the answer is to a large extent positive.

This work was parly supported by the “Greco de programmation du CNRS” and the ESPRIT working group COMPASS.

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. Henk Barendregt. Handbook of Theoretical Computer Science, volume B, chapter Functional Programming and Lambda Calculus, pages 321–364. North-Holland, 1990. J. van Leeuwen ed.

    Google Scholar 

  2. Val Breazu-Tannen. Combining algebra and higher-order types. In Proc. 3rd IEEE Symp. Logic in Computer Science, Edinburgh, July 1988.

    Google Scholar 

  3. Val Breazu-Tannen and Jean Gallier. Polymorphic rewriting conserves algebraic strong normalization. Theoretical Computer Science. to appear.

    Google Scholar 

  4. Hubert Comon. Completion of infinite rewrite systems. submitted, 1990.

    Google Scholar 

  5. Hubert Comon. Disunification: a survey. In Jean-Louis Lassez and Gordon Plötkin, editors, Computational Logic: Essays in Honor of Alan Robinson. MIT Press, 1990. to appear.

    Google Scholar 

  6. Hubert Comon, D. Lugiez, and Ph. Schnoebelen. Type inference in computer algebra. In Proc. EUROCAL 87, Leipzig, June 1987.

    Google Scholar 

  7. Nachum Dershowitz and Jean-Pierre Jouannaud. Handbook of Theoretical Computer Science, volume B, chapter Rewrite Systems, pages 243–309. North-Holland, 1990. J. van Leeuwen ed.

    Google Scholar 

  8. Daniel J. Dougherty. Adding algebraic rewriting to the untyped lambda calculus. Research report, Wesleyan University, USA, 1990. submitted.

    Google Scholar 

  9. K. Drosten. Termerssetzungssysteme. PhD thesis, University of Passau, Germany, 1989. In german.

    Google Scholar 

  10. K. Futatsugi, Joseph Goguen, Jean-Pierre Jouannaud, and J. Meseguer. Principles of OBJ2. In Proc. 12th ACM Symp. Principles of Programming Languages, New Orleans, 1985.

    Google Scholar 

  11. Jean Gallier. Logic and Computer Science, chapter On Girard's Candidats de Réductibilité. Academic Press, 1990. P. Odifreddi editor.

    Google Scholar 

  12. Jean-Pierre Jouannaud and Claude Kirchner. Solving equations in abstract algebras: A rule-based survey of unification. In Jean-Louis Lassez and Gordon Plötkin, editors, Computational Logic: Essays in Honor of Alan Robinson. MIT-Press, 1990. to appear.

    Google Scholar 

  13. Jean-Pierre Jouannaud and Mitsuhiro Okada. Embedding first-order and higher-order rewriting into lambda-calculus. Research report, University Paris Sud, 1990. submitted.

    Google Scholar 

  14. Aart Middeldorp. Modular Properties of Term Rewriting Systems. PhD thesis, Free University of Amsterdam, Netherland, 1990.

    Google Scholar 

  15. Mitsuhiro Okada. Strong normalizability for the combined system of the types lambda calculus and an arbitrary convergent term rewrite system. In Proc. ISSAC 89, Portland, Oregon, 1989.

    Google Scholar 

  16. Mitsuhiro Okada and X Grogono. Research report, Concordia University, 1990.

    Google Scholar 

  17. J. Tiuryn. Type inference problems: a survey. In Proc. MFCS 90, Banskà Bystrica, LNCS 452. Springer-Verlag, 1990.

    Google Scholar 

  18. Y. Toyama. Counterexamples to termination for the direct sum of term rewriting systems. Information Processing Letters, 25:141–143, April 1987.

    Article  Google Scholar 

  19. Y. Toyama. On the church-rosser property for the direct sum of term rewriting systems. Journal of the ACM, 34(1):128–143, April 1987.

    Article  Google Scholar 

  20. Martin Wirsing. Handbook of Theoretical Computer Science, volume B, chapter Algebraic Specification, pages 675–780. North-Holland, 1990. J. van Leeuwen ed.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Recherche en Informatique Bat. 490, 91405, Orsay Cedex, France

    Jean-Pierre Jouannaud

Authors
  1. Jean-Pierre Jouannaud
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Christian Choffrut Matthias Jantzen

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jouannaud, JP. (1991). Executable higher-order algebraic specifications. In: Choffrut, C., Jantzen, M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020784

Download citation

  • DOI: https://doi.org/10.1007/BFb0020784

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53709-0

  • Online ISBN: 978-3-540-47002-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics