Abstract
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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References
N. Dershowitz, Termination of rewriting, J. Symbolic Computation, 3, 69–116 (1987)
D.E. Knuth, P. B. Bendix, Simple word problems, In: J. Leech (ed.), Computational Problems in Abstract Algebra, 263–297, Pergamon Press (1970)
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© 1991 Springer-Verlag Berlin Heidelberg
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Cohen, D., Watson, P. (1991). An efficient representation of arithmetic for term rewriting. In: Book, R.V. (eds) Rewriting Techniques and Applications. RTA 1991. Lecture Notes in Computer Science, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53904-2_100
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DOI: https://doi.org/10.1007/3-540-53904-2_100
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Online ISBN: 978-3-540-46383-2
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