Skip to main content
SpringerLink
Log in
Book cover

International Conference on Automated Deduction

CADE 1994: Automated Deduction — CADE-12 pp 650–664Cite as

Theory and practice of minimal modular higher-order E-unification

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 814))

Abstract

Modular higher-order E-unification, as described in [6], produces numerous redundant solutions in many practical cases. We present a refined algorithm for finitary theories with a finite number of non-free constants that avoids most redundant solutions, analyse it theoretically, and give first experimental results. In comparison to [6], the description of the E-unification algorithm is enriched by a definition of the translation process between first and higher-order terms and an explicit handling of new variables. This explicit handling gives deeper insight into the reasons for redundant solutions and thus provides a method for their avoidance. In order to study the efficiency of this method and the performance of the modular approach in general, some benchmark examples are presented and an interpretation of their empirical evaluation is given.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dougherty, D. and Johann, P.: A Combinatory Logic Approach to Higher-Order E-Unification. Proc. 11th Conf. Automated Deduction, LNCS 607 (1992), 79–93.

    Google Scholar 

  2. Gallier, J. and Snyder, W.: Complete Sets of Transformations for General E- Unification. Theoretical Computer Science, 67 (1988), 203–260.

    Google Scholar 

  3. Huet, G.: A Unification Algorithm for Typed λ-Calculus. Theoretical Computer Science 1 (1975), 27–57.

    Google Scholar 

  4. Müller, O.: Optimierung der modularen E-Unifikation höherer Stufe — Implementierung und Analyse, master thesis, Karlsruhe 1993.

    Google Scholar 

  5. Nipkow, T. and Qian, Z.: Modular Higher-Order E-Unification. Proc. 4th Int. Conf. Rewriting Techniques and Applications, LNCS 488 (1991), 200–214.

    Google Scholar 

  6. Qian, Z. and Wang, K.: Higher-Order E-Unification for Arbitrary Theories. Proc. of 1992 Int. Joint Conf. and Symp. on Logic Programming, MIT Press, 1992.

    Google Scholar 

  7. Snyder, W. and Gallier, J.: Higher-Order Unification Revisited: Complete Sets of Transformations. J. Symbolic Computation 8 (1989), 101–140.

    Google Scholar 

  8. Weber, F.: Softwareentwicklung mit Logik höherer Stufe — eine Anwendung von Theoriededuktion auf interaktives Beweisen, PhD thesis, Karlsruhe 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FZI, Haid-und-Neu-Str. 10-14, D-76131, Karlsruhe 1

    Olaf Müller

  2. Bertelsmann Distribution, An der Autobahn, D-33310, Gtersloh

    Franz Weber

Authors
  1. Olaf Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Franz Weber
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alan Bundy

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Müller, O., Weber, F. (1994). Theory and practice of minimal modular higher-order E-unification. In: Bundy, A. (eds) Automated Deduction — CADE-12. CADE 1994. Lecture Notes in Computer Science, vol 814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58156-1_47

Download citation

  • DOI: https://doi.org/10.1007/3-540-58156-1_47

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58156-7

  • Online ISBN: 978-3-540-48467-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation