Skip to main content
SpringerLink
Log in

Combination of unification algorithms

  • Unification Theory
  • 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

Unification in equational theories, i.e. solving equations in varieties, is a basic operation in many applications of Computer Science, particularly in Automated Deduction [Si 84]. A combination of unification algorithms for regular finitary collapse free equational theories with disjoint function symbols is presented. The idea is first to replace certain subterms by constants and to unify this constant abstraction and then to handle the replaced subterms in a recursive step. Total correctness is shown, i.e. the algorithm terminates and yields a correct and complete set of unifiers provided the special algorithms do.

...!seismo!mcvax!unido!uklirb!herold

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. Birkhoff, G., ‘On the Structure of Abstract Algebra', Proc. Cambridge Phil. Soc., Vol. 31, 433–454, (1935)

    Google Scholar 

  2. Burris, S. and Sankappanavar, H.P., ‘A Course in Universal Algebra', Springer-Verlag, (1981)

    Google Scholar 

  3. Fages, F., ‘Associative-Commutative Unification', in Proc. of 7th CADE (ed. R.E.Shostak). Springer-Verlag, LNCS 170, 194–208, (1984)

    Google Scholar 

  4. Fages, F. and Huet, G., ‘Unification and Matching in Equational Theories', Proc. of CAAP'83 (ed. G. Ausiello and M. Protasi), Springer-Verlag, LNCS 159, 205–220, (1983)

    Google Scholar 

  5. Goguen, J. A., Thatcher, J.W. and Wagner, E. G., ‘An Initial Algebra Approach to the Specification, Correctness and Implementation of Abstract Data Types', in ‘Current Trends in Programming Methodology, Vol.4, Data Structuring’ (ed. R. T. Yeh), Prentice Hall, (1978)

    Google Scholar 

  6. Grätzer, G., ‘Universal Algebra', Springer-Verlag, (1979)

    Google Scholar 

  7. Herold, A., ‘A Combination of Unification Algorithms', MEMO SEKI-85-VIII-KL, Universität Kaiserslautern, (1985)

    Google Scholar 

  8. Huet, G. and Oppen, D. C., ‘Equations and Rewrite Rules: A Survey', in ‘Formal Languages: Perspectives and Open Problems (ed R. Book), Academic Press, (1980)

    Google Scholar 

  9. Herold, A. and Siekmann, J., ‘Unification in Abelian Semigroups', MEMO SEKI-85-III-KL, Universität Kaiserslautern, (1985)

    Google Scholar 

  10. Huet, G., ‘Résolution d'équations dans des langages d'ordre 1, 2... ω'. Thèse de doctorat d'état. Université Paris VII, (1976)

    Google Scholar 

  11. Kirchner, C., ‘Methodes et outils de conception systematique d'algorithmes d'unification dans les théories équationelles', Thèse de doctorat d'état, Université de Nancy 1, (1985)

    Google Scholar 

  12. Loveland, D., ‘Automated Theorem Proving', North-Holland, (1978)

    Google Scholar 

  13. Livesey, M. and Siekmann, J., ‘Unification of Sets and Multisets', Universität Karisruhe, Techn. Report, (1976)

    Google Scholar 

  14. McNulty, G., ‘The Decision Problem for Equational Bases of Algebras', Annals of Mathematical Logic 10, 193–259, (1976)

    Article  Google Scholar 

  15. Robinson, J. A., ‘A Machine-Oriented Logic Based on the Resolution Principle', JACM, 12, No. 1, 23–41, (1965)

    Article  Google Scholar 

  16. Schmidt-Schauß, M., ‘Unification under Associativity and Idempotence is of Type Nullary', MEMO SEKI, Universität Kaiserslautern, (1986), (submitted to JAR)

    Google Scholar 

  17. Siekmann, J., ‘Universal Unification', in Proc. of 7th CADE (ed R.E. Shostak), Springer-Verlag, LNCS 170, 1–42, (1984)

    Google Scholar 

  18. Stickel, M.E., ‘A Unification Algorithm for Associative-Commutative Functions', JACM 28, No. 3, 423–434, (1981)

    Article  Google Scholar 

  19. Taylor, W., ‘Equational Logic', Houston Journal of Mathematics 5, (1979)

    Google Scholar 

  20. Tidén, E., ‘Unification in Combinations of Theories with Disjoint Sets of Function Symbols', Royal Institute of Technology, Department of Computing Science, S-100 44 Stockholm, Sweden, (1985)

    Google Scholar 

  21. Yelick, K., ‘Combining Unification Algorithms for Confined Regular Equational Theories', in Proc. of ‘Rewriting Techniques and Applications’ (ed J.-P. Jouannaud), Springer-Verlag, LNCS 202, 365–380, (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Informatik, Universität Kaiserslautern, Postfach 3049, D-6750, Kaiserslautern, F.R.Germany

    Alexander Herold

Authors
  1. Alexander Herold
    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

Herold, A. (1986). Combination of unification algorithms. 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_111

Download citation

  • DOI: https://doi.org/10.1007/3-540-16780-3_111

  • 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