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A unique termination theorem for a theory with generalised commutative axioms

  • Hans-Josef Jeanrond
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 71)

Abstract

The procedures for deciding the unique termination property of rewriting systems by Knuth and Bendix [1], and Lankford and Ballantyne [2] are generalised to allow for permutative axioms of the form
$$F(F(t,e_1 ),e_2 ) = F(F(t,e_2 ),e_1 )$$
(t,e1,e2 are variable symbols).

These can be thought of as many sorted commutative axioms as they might appear in axiomatic specifications of abstract data types.

A method is presented for deciding the unique termination property of a set of "permutative rewrite rules" having the finite termination property. It relies on "confluence" results of Gerard Huet [4].

Keywords

Function Symbol Critical Pair Variable Symbol Abstract Data Type Term Rewrite System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    D.E.Knuth & P.B.Bendix: Simple Word Problems in Universal Algebras in Computational Problems in Abstract Algebra Ed. J.Leech, Pergamon Press 1970, pp.263–297Google Scholar
  2. [2]
    D.S.Lankford & A.M.Ballantyne: Decision Procedures for Simple Equational Theories with a Commutative Axiom: Complete Sets of Commutative Reductions Automatic Theorem Proving Project, Depts. Math. and Comp. Science, University of Texas at Austin; Report #ATP-35Google Scholar
  3. [3]
    D.S.Lankford & A.M.Ballantyne: Decision Procedures for Simple Equational Theories with Commutative-Associative Axioms: Complete Sets of Commutative-Associative Reductions As [2], Report #ATP-39Google Scholar
  4. [4]
    G.Huet: Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems IRIA-LABORIA, Domaine de Voluceau, F-78150 Rocquencourt France. Preliminary version in 18th IEEE Symposium on Foundations of Computer Science, Oct 1977Google Scholar
  5. [5]
    J.A. Robinson: A Machine-Oriented Logic Based on the Resolution Principle. JACM Vol.12, No.1; January 1965; pp.23–41Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Hans-Josef Jeanrond
    • 1
  1. 1.Computer Science DepartmentUniversity of EdinburghUK

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