Skip to main content
SpringerLink
Log in

Properties of Substitutions and Unifications

  • Chapter
Book cover GWAI-83

Part of the book series: Informatik-Fachberichte ((INFORMATIK,volume 76))

Abstract

In this paper the set of first order substitutions with a partial ordering “more general than” is investigated. It is proved that the set of equivalence classes of idempotent substitutions together with an added greatest element is a complete lattice. A simultaneous unification of finitely many finite sets of terms can be reduced to unifying each of the sets of terms separately and then building the supremum of the most general unifiers in this lattice. This saves time in an automatic proof procedure when combined with the concept of weak unification also introduced in this paper.

Work supported by the Deutsche Forschungsgemeinschaft

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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.

References

  1. Bibel, W.: Automated theorem proving. Vieweg Verlag, Wiesbaden (1982)

    MATH  Google Scholar 

  2. Huet, G.: Resolution d’équations dans des langages d’ordre 1,2,…, ω. Thése d’Etat, Univ. Paris VII (1976)

    Google Scholar 

  3. Huet, G.: Confluent Reductions, Abstract Properties and Applications to Term Rewriting Systems. JACM, 27, 797–821 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  4. Martelli, A., Montanari, U.: An Efficient Unification Algorithm. ACM Transactions on Programming Languages and Systems, 4, 258–281 (1982)

    Article  MATH  Google Scholar 

  5. Paterson, M.S., Wegman, M.N.: Linear Unification. J. of Computer and Systems Sci. 16, 158–167 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  6. Stillman, R.: The Concept of Weak Substitution in Theorem-Proving. JACM, 20 (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut fuer Infomatik, Technische Universitaet Muenchen, Postfach 202420, D-8000, Muenchen 2, Germany

    Elmar Eder

Authors
  1. Elmar Eder
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fachbereich Informatik, Universität Hamburg, Schlüterstraße 70, 2000, Hamburg 13, Germany

    Bernd Neumann

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Eder, E. (1983). Properties of Substitutions and Unifications. In: Neumann, B. (eds) GWAI-83. Informatik-Fachberichte, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69391-5_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-69391-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12871-7

  • Online ISBN: 978-3-642-69391-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation