Mller Neergaard, P. and Srensen, M. H. (1999), Conservation and uniform normalization in lambda calculi with erasing reductions, Submitted for publication. Home/Search Document Details and Download
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Perpetuality and Uniform Normalization in Orthogonal Rewrite .. - Khasidashvili, al. (1999) (1 citation) (Correct)
....where a rewrite system is said to be UN if each of its terms is so. Interest in the criteria for UN arises, for example, in the proofs of strong normalization of typed calculi, since these criteria are related to the work on reducing strong normalization proofs to proving weak normalization [50, 37, 23, 70, 17, 31, 24, 25, 65, 73, 49]. Furthermore, the question: Which classes of terms are UN is posed by Bohm and Intrigila [11] in connection with finding UN solutions to fixed point equations, and with the representability of partial recursive functions by UN PERPETUALITY AND UNIFORM NORMALIZATION 3 terms only, in the ....
....connection with finding UN solutions to fixed point equations, and with the representability of partial recursive functions by UN PERPETUALITY AND UNIFORM NORMALIZATION 3 terms only, in the calculus. 1 A useful UN subclass of terms has recently been identified by Mller Neergaard and Srensen [49]. Let us call a term t an 1 term if it has an infinite reduction. Furthermore, we call a reduction step t s and the corresponding contracted redex occurrence perpetual if s is an 1 term if t is so. A redex is called perpetual if its occurrence in every context (and the corresponding reduction ....
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Mller Neergaard, P. and Srensen, M. H. (1999), Conservation and uniform normalization in lambda calculi with erasing reductions, Submitted for publication.
Perpetuality and Uniform Normalization in Orthogonal.. - Khasidashvili, Ogawa, al. (1 citation) (Correct)
....is posed by Bohm and Intrigila [BI94] in connection with finding UN solutions to fixed point equations, and with the representability of partial recursive functions by UN terms only, in the calculus. 1 A useful UN subclass of terms has recently been identified by M ller Neergaard and S rensen [MNS99]. Let us call a term t an 1 term if it has an infinite reduction. Furthermore, we call a reduction step t s and the corresponding contracted redex occurrence perpetual if s is an 1 term if t is so. A redex is called perpetual if its occurrence in every context (and the corresponding reduction ....
....are also descendants of e 0 s l ) Hence 1(s l ) a contradiction. t 0 l w 0 t 1 l w 1 t 2 l w 2 t 3 l s l = s 0 l U (d) 0 s 1 l U (d) 1 s 2 l U (d) 2 s 3 l U (d) 3 M ller Neergaard and S rensen [MNS99] give a different proof of perpetuality of safe K redexes in the calculus (safe K redexes are called there good) The following example demonstrates that non erasing steps need not be perpetual in orthogonal CCERSs in general, that is, the restriction to fully extended CCERSs is necessary: ....
Møller Neergaard P. and Sørensen M.H., Conservation and uniform normalization in lambda calculi with erasing reductions. Submitted for publication, June 1999.
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