Unification in conditional-equational theories

  • Heinrich Hussmann
Automatic Programming II
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)


A complete unification procedure for confluent conditional term rewriting systems is presented which is a generalization of the narrowing process described by Fay and Hullot. Neither the finite termination property nor syntactical restrictions on conditions are needed. The algorithm can be seen as a new functional logic programming technique, too. The unification procedure has been built into the RAP system, a system supporting rapid prototyping for algebraic specifications.


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  1. [Bergstra, Klop 82]
    J. Bergstra, J. Klop, Conditional rewrite rules: confluence and termination. Report IW 198/82 Mathematical Centre, Amsterdam 1982Google Scholar
  2. [Broy et al. 82]
    M. Broy, P. Pepper, M. Wirsing, On the algebraic definition of programming languages. Report TUM-18204 Technical University, Munich 1982Google Scholar
  3. [Deransart 83]
    P.Deransart, An operational algebraic semantics of PROLOG programs. Internal Report INRIA 1983Google Scholar
  4. [Drosten 83]
    K. Drosten, Toward executable specifications using conditional axioms. Report 83-01 Technical University, Braunschweig 1983Google Scholar
  5. [Fay 79]
    M.Fay, First order unification in an equational theory. In: W.H. Joyner (ed.), Proc. 4th Workshop on Automated Deduction, Academic Press 1979Google Scholar
  6. [Fribourg 84]
    L. Fribourg, Oriented equational clauses as a programming language. Report 84002 Laboratoires de Marcoussis 1984 Short version in: Proc. 11th ICALP, LNCS 172, 162–173, Springer 1984Google Scholar
  7. [Fribourg 85]
    L.Fribourg, Handling function definitions through innermost superposition and rewriting. Report LITP 84-69. Also to appear in: Proc. RTA 85Google Scholar
  8. [Goguen, Meseguer 84]
    J.A. Goguen, J. Meseguer, Equality, types, modules and generics for logic programming. Report CSLI-84-5 Center for the Study of Language and Information, Stanford 1984Google Scholar
  9. [Huet, Oppen 80]
    G. Huet, D.C.Oppen, Equations and rewrite rules: a survey. In: R.V. Book (ed.), Formal language theory — perspectives and open problems. Academic Press 1980Google Scholar
  10. [Hullot 80]
    J.M. Hullot, Canonical forms and unification. Proc. 5th CADE, LNCS 87, 318–334, Springer 1980Google Scholar
  11. [Hussmann 85a]
    H.Hussmann, Unification in conditional-equational theories. Report MIP-8502 Universitaet Passau 1985Google Scholar
  12. [Hussmann 85b]
    H.Hussmann, Rapid prototyping for algebraic specifications — RAP system user's manual. Report MIP-8504 Universitaet Passau 1985Google Scholar
  13. [Kaplan 84]
    S. Kaplan, Fair conditional term rewriting systems: unification, termination and confluence. Report 194 LRI Orsay, Paris 1984Google Scholar
  14. [Remy, Zhang 84]
    J.-L.Remy, H.Zhang, REVEUR4: A system for validating algebraic specifications of parameterized abstract data types. Proc. 2nd ECAI Conf. 1984Google Scholar
  15. [Rety et al. 85]
    P.Rety, C.Kirchner, H.Kirchner, NARROWER: a new algorithm for unification and its application to logic programing. To appear in: Proc. RTA 85Google Scholar
  16. [Wirsing et al. 83]
    M. Wirsing, P. Pepper, H. Partsch, W. Dosch, M. Broy, On hierarchies of abstract data types. Acta Informatica 20(1983), 1–33.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Heinrich Hussmann
    • 1
  1. 1.Fakultät für InformatikUniversität PassauPassau

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