An efficient representation of arithmetic for term rewriting

  • Dave Cohen
  • Phil Watson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 488)


We give a locally confluent set of rewrite rules for integer (positive and negative) arithmetic using the familiar system of place notation. We are unable to prove its termination at present, but we strongly conjecture that rewriting with this system terminates and give our reasons. We show that every term has a normal form and so the rewrite system is normalising.

We justify our choice of representation in terms of both space efficiency and speed of rewriting.

Finally we give several examples of the use of our system.


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    N. Dershowitz, Termination of rewriting, J. Symbolic Computation, 3, 69–116 (1987)Google Scholar
  2. [KB70]
    D.E. Knuth, P. B. Bendix, Simple word problems, In: J. Leech (ed.), Computational Problems in Abstract Algebra, 263–297, Pergamon Press (1970)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Dave Cohen
    • 1
  • Phil Watson
    • 2
  1. 1.Department of Computer Science Royal Holloway and Bedford New CollegeUniversity of LondonUK
  2. 2.Department of Computing ScienceUniversity of GlasgowUK

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