Z. Khasidashvili, M. Ogawa, V. van Oostrom, Perpetuality and uniform normalization in orthogonal rewrite systems, Inform. & Comput. 164 (1) (2001) 118151. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Uniform Normalisation beyond Orthogonality - Khasidashvili, Ogawa, van Oostrom (2001) (1 citation) Self-citation (Khasidashvili Ogawa Van oostrom) (Correct)
....classical results in the study of uniform normalisation are: the I calculus is uniformly normalising [7, p. 20, 7 XXV] and non erasing steps are perpetual in orthogonal TRSs [14, Thm. II.5.9. 6] In previous work we have put these results and many variations on them in a unifying framework [13]. At the heart of that paper is the result (Thm. 3.16) that a term s not in normal form contains a redex which is external for any rewrite sequence from s. 1 The method presented here, is based instead on the existence of external redexes for a given sequence. This allows for generalisation of ....
....For ERSs and CRSs these results can be found as [12, Thm. 60] and [14, Cor. II.5.9.4] respectively. In this section the reader is assumed to be familiar with second order term rewrite systems be it in the form of combinatory reduction systems (CRSs [14] expression reduction systems (ERSs [13]) or higher order pattern rewrite systems (PRSs [17] We employ PRSs as de ned in op.cit. but will write x:s instead of x:s, thereby freeing the for usage as a function symbol. De nition 10. The order of a rewrite rule is the maximal order of the free variables in it. The order of a PRS ....
Z. Khasidashvili, M. Ogawa, and V. van Oostrom. Perpetuality and uniform normalization in orthogonal rewrite systems. I&C, To appear. http://www.phil.uu.nl/~oostrom/publication/ps/pun-icv2.ps.
Stable Results and Relative Normalization - Glauert, Kennaway, Khasidashvili Self-citation (Khasidashvili) (Correct)
....think that contracting only the S needed redexes of S needed families could yield S optimal reductions that are S minimal at the same time. We show however that this is not the case either in the # calculus or in OTRSs. Overview In the next section, we review Expression Reduction Systems [23, 24, 27]. In Section 3, we introduce the relative notion of neededness. In Section 4, we sketch some properties of our labelling system for OERSs needed to define a family relation among redexes. We prove correctness of the S needed strategy for computing terms of S, for all stable S, in Section 5, ....
....[42] and Aczel [1] Several interesting formalisms have been introduced later [24, 51, 36, 48] We refer to van Raamsdonk [49] for a survey. Expression Reduction Systems Here we use Expression Reduction Systems (ERSs) defined in [24] under the name of CRSs) The present formulation follows [27] and is simpler. Definition 1 Let # be an alphabet comprising variables x, y, z, function symbols, also called simple operators ; and operator signs or quantifier signs. Each function symbol has an arity k # N , and each operator sign # has an arity (m, n) with m,n #= 0 such that, for ....
[Article contains additional citation context not shown here]
Z. Khasidashvili, M. Ogawa, and V. van Oostrom. Perpetuality and uniform normalization in orthogonal rewrite systems. Information and Computation, To appear. Available from http://www.brl.ntt.co.jp/people/mizuhito/papers/ TRS.html.
On the Longest Perpetual Reductions in Orthogonal Expression.. - Khasidashvili (2000) (11 citations) Self-citation (Khasidashvili) (Correct)
....CERSs. In ERSs, orthogonality is defined as in CRSs [38,40] For conditional ERSs, we need also to require that descendants of redexes are redexes weakly similar to their ancestors, so that the admissible assignments are such that contraction of a redex cannot break down another redex [37] (for OERSs, this can easily be proven) To define descendants for CERS steps, we need to combine the descendant concepts for TRSs and for the calculus (or for S reduction rules) There are several different definitions of descendants both for TRSs and the calculus. For TRS steps, our definition ....
....contracted redex (x:s)t, its function part x:s, and the body s all have the contractum as the descendant, and the free occurrences of x in s descend to the corresponding substituted occurrences of t. This induces a descendant concept for S steps. For a precise definition of descendants we refer to [37]. Definition 4 A rewrite rule t s in a CERS R is left linear if t is linear (i.e. no metavariable occurs more than once in it) R is left linear if each rule in R is left linear. R is non ambiguous, or non overlapping, if an R redex u can properly contain an R redex v only in an argument, and ....
[Article contains additional citation context not shown here]
Z. Khasidashvili, M. Ogawa and V. van Oostrom, Perpetuality and uniform normalization in orthogonal rewrite systems, Information and Computation, in press. 38
Conservation and Uniform Normalization in Lambda Calculi.. - Neergaard, Sørensen (2002) (2 citations) (Correct)
No context found.
Z. Khasidashvili, M. Ogawa, V. van Oostrom, Perpetuality and uniform normalization in orthogonal rewrite systems, Inform. & Comput. 164 (1) (2001) 118151.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC