Abstract
Strongly convergent reduction is the fundamental notion of reduction in infinitary orthogonal term rewriting systems (OTRSs). For these we prove the Transfinite Parallel Moves Lemma and the Compressing Lemma. Strongness is necessary as shown by counterexamples. Normal forms, which we allow to be infinite, are unique, in contrast to ω-normal forms. Strongly converging fair reductions result in normal forms.
In general OTRSs the infinite Church-Rosser Property fails for strongly converging reductions. However for Böhm reduction (as in Lambda Calculus, subterms without head normal forms may be replaced by ⊥) the infinite Church-Rosser property does hold. The infinite Church-Rosser Property for non-unifiable OTRSs follows. The top-terminating OTRSs of Dershowitz c.s. are examples of non-unifiable OTRSs.
(Extended abstract)
All authors were partially sponsored by SEMAGRAPH, ESPRIT Basic Research Action 3074. The first author was also partially surported by a SERC Advanced Fellowship, and by SERC grant no. GR/F 91582.
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Kennaway, J.R., Klop, J.W., Sleep, M.R., de Vries, F.J. (1991). Transfinite reductions in orthogonal term rewriting systems. 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_81
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DOI: https://doi.org/10.1007/3-540-53904-2_81
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