Transfinite reductions in orthogonal term rewriting systems [chapter]

J. R. Kennaway, J. W. Klop, M. R. Sleep, F. J. Vries
1991 Lecture Notes in Computer Science  
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 co-normal forms. Strongly converging fair reductions result in normal forms. In general OTRSs the infinite Church-Rosser Property fails for strongly converging
more » ... tions. However for B6hm reduction (as in Lambda Calculus, subterms without head normal forms may be replaced by _L) 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 nonunifiable OTRSs.
doi:10.1007/3-540-53904-2_81 fatcat:u6pxjbvrird7hcy6h7dmveso2q