Massimo Marchiori. Modularity of completeness revisited. In Jieh Hsiang, editor, Proc. 6th Int. Conf. on Rewriting Techniques and Applications (RTA'95), LNCS 914, pages 2--10, Kaiserslautern, Germany, April 1995. Springer-Verlag.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and pairwise constructorsharing CTRSs. Finally, it is shown that the related simplifying property is modular, even for composable CTRSs. Since very manynew modularity results have been published recently, we cannot render a detailed account of those here. Instead, the reader is referred to Marchiori (1995), Ohlebusch (1993,1995a, b) and Gramlich (1994c) for recent results on disjoint (conditional) TRSs, to Dershowitz (1994) Gramlich (1994a, b) and Ohlebusch (1994a) which deal with constructor sharing TRSs, and to Kurihara and Ohuchi (1995) as well as Middeldorp (1994a) which contain results for ....

Marchiori, M. (1995). Modularity of completeness revisited. In Proceedings of the 6th International Conference on Rewriting Techniques and Applications, 2--10. Lecture Notes in Computer Science 914, Berlin: Springer Verlag.

....In particular, we are interested in asymmetric preservation conditions which have only partially been explored up to now. This analysis naturally leads to a thorough investigation of collapsing reductions and the role of (non )left linearity partially refining the existing analyses of [25] and [13, 14, 22]. Besides the implications for the preservation of termination under (disjoint) combinations this analysis of collapsing reduction and (non )left linearity may have other potential applications, too. The rest of the paper is organized as follows. In Section 2 we recall some basic terminology about ....

.... equivalence of innermost termination and general termination are combined with the modularity of innermost termination ( 8] and (3) a syntactic approach via left linearity which in essence is based on commutation and uniqueness properties of (collapsing) reduction in left linear systems ( 25] [14, 22]) Due to lack of space we cannot give a more detailed account of the (numerous) papers on the subject and the above classification. We only mention some results to which we refer later on. Virtually all proofs for showing preservation results for termination under disjoint unions (and more ....

[Article contains additional citation context not shown here]

M. Marchiori. Modularity of Completeness Revisited . In J. Hsiang, ed., Proc. 6th Int. Conf. on Rewriting Techniques and Applications (RTA'95), LNCS 914, pp. 2--10. Springer, 1995.

....to find a transformation of the alien terms (subterms below the cap) such that a rewrite in the cap can be mirrored by a rewrite of transformed terms and such that a rewrite below the cap does not affect the transformation. Variations on this approach lead to the above results. Using the idea of [ Marchiori, 1995 ] for proving (b) one can extend the modularity of confluence to some constructor sharing unions of left linear systems. ....

Massimo Marchiori. Modularity of completeness revisited. In Proceedings of the Sixth International Conference on Rewriting Techniques and Applications (Kaiserslautern, Germany), volume 914 of Lecture Notes in Computer Science, pages 2--10, Berlin, April 1995. Springer-Verlag.

....In particular, we are interested in asymmetric preservation conditions which have only partially been explored up to now. This analysis naturally leads to a thorough investigation of collapsing reductions and the role of (non )left linearity partially refining the existing analyses of [25] and [13, 14, 22]. Besides the implications for the preservation of termination under (disjoint) combinations this analysis of collapsing reduction and (non )left linearity may have other potential applications, too. The rest of the paper is organized as follows. In Section 2 we recall some basic terminology about ....

.... equivalence of innermost termination and general termination are combined with the modularity of innermost termination ( 8] and (3) a syntactic approach via left linearity which in essence is based on commutation and uniqueness properties of (collapsing) reduction in left linear systems ( 25] [14, 22]) Due to lack of space we cannot give a more detailed account of the (numerous) papers on the subject and the above classification. We only mention some results to which we refer later on. Virtually all proofs for showing preservation results for termination under disjoint unions (and more ....

[Article contains additional citation context not shown here]

M. Marchiori. Modularity of Completeness Revisited . In J. Hsiang, ed., Proc. 6th RTA, LNCS 914, pp. 2--10. Springer, 1995.

....simple proof for analogous results for constructor sharing CTRSs. Furthermore, a simple counterexample disproves a conjecture of Middeldorp [Mid93] which is related to the above mentioned results. More sufficient conditions for the modularity of termination of TRSs can for instance be found in [TKB89, KO92, Gra94a, Gra94b, Ohl94c, Mar95]. The reader is referred to [Mid90, Mid93, Mid94, Ohl93, Gra93] for modularity results of CTRSs. In recent investigations, one tries to weaken the constructorsharing requirement. On the one hand, MT93, Mid94, Ohl94a, KO94] consider composable systems systems which have to contain all rewrite ....

M. Marchiori. Modularity of Completeness Revisited. In Proceedings of the 6th International Conference on Rewriting Techniques and Applications. Lecture Notes in Computer Science , Springer Verlag, 1995. To appear.

....P =Termination (Termination will be also indicated with the acronym SN, after Strong Normalization) Lemma 9.1 (TRSs; Phi) is SN acid. Among the many results on the modularity of termination (see e.g. 20, 13, 22, 24] for a panoramic) the best results so far obtained are the ones in [21] and [14]. We will come back to the result of [14] in the next subsection. In [21] Ohlebusch, generalizing a previous result of Gramlich for finitely branching TRSs ( 10] proved that C E termination is modular. It is straightforward to see that the class of C E terminating TRSs coincides with the ....

....indicated with the acronym SN, after Strong Normalization) Lemma 9.1 (TRSs; Phi) is SN acid. Among the many results on the modularity of termination (see e.g. 20, 13, 22, 24] for a panoramic) the best results so far obtained are the ones in [21] and [14] We will come back to the result of [14] in the next subsection. In [21] Ohlebusch, generalizing a previous result of Gramlich for finitely branching TRSs ( 10] proved that C E termination is modular. It is straightforward to see that the class of C E terminating TRSs coincides with the class of TRSs vaccinated via for(X; Y ) X; ....

[Article contains additional citation context not shown here]

M. Marchiori. Modularity of completeness revisited. In J. Hsiang, editor, Proceedings of the Sixth International Conference on Rewriting Techniques and Applications, volume 914 of LNCS, pages 2--10. Springer--Verlag, 1995.

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Massimo Marchiori. Modularity of completeness revisited. In Jieh Hsiang, editor, Proc. 6th Int. Conf. on Rewriting Techniques and Applications (RTA'95), LNCS 914, pages 2--10, Kaiserslautern, Germany, April 1995. Springer-Verlag.

No context found.

M. Marchiori. Modularity of completeness revisited. In J. Hsiang, editor, International Conference on Rewriting Techniques and Applications, number 914 in Lecture Notes in Computer Science, pages 2-- 10, Kaiserslautern, Apr. 1995. Springer Verlag.

No context found.

Massimo Marchiori. Modularity of completeness revisited. In Jieh Hsiang, editor, Proc. 6th Int. Conf. on Rewriting Techniques and Applications (RTA'95), LNCS 914, pages 2--10, Kaiserslautern, Germany, April 1995. Springer-Verlag.

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