C. Kirchner and H. Kirchner, Rewriting: Theory and Applications, NorthHolland, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....just informal. Detailed confluence results for simplification rules only are published in [FAM97] Recently, these results have been simplified and extended to all three kinds of CHR [Abd97, Abd98] The papers adopt and extend the terminology and techniques of conditional term rewriting systems [DOS88, KiKi91] about confluence. The extensions enable handling of global knowledge (the built in constraint store) local variables and propagation rules. In [Abd98] it was also possible to adapt to CHR the idea of Knuth Bendix completion, an algorithm that makes a set of rules confluent by introducing ....

C. Kirchner and H. Kirchner, Rewriting: Theory and Applications, NorthHolland, 1991.

....simplified. When combining constraint solvers that share constraints, nonterminating simplification steps may arise even if each solver is terminating. e.g. one solver defines less than in terms of greater than and the other defines greater than in terms of less than. The notion of confluence [Kir89] is important for combining constraint solvers as well as for concurrent applications of CHRs. Concurrent CHRs are not applied in a fixed order. As correct CHRs are logical consequences of the program, any result of a simplification or propagation step will have the same meaning, however it is not ....

C. Kirchner and H. Kirchner, Rewriting: Theory and Applications, Working paper for a D.E.A. lecture at the University of Nancy I, France, 1989.

....set of SiRs both canonical and correct we can be sure that the SiRs indeed implement a well behaved constraint solver. As far as we know there is no other logic programming language that relies to such an extent on techniques developed for rewriting systems. An introduction to rewrite systems is [Kir89], to conditional rewriting systems [KR89, DO88] An introduction to automated theorem proving is [Gal86] For the relationship of automated theorem proving and logic programming we refer the reader to [WoMc91] Also note that completion of rewrite systems can serve as a theorem proving procedure ....

....Syntactically different constraint evaluations might also arise if combined solvers share constraints, depending on which solver comes first. To show that a set of SiRs is locally confluent, we employ a variant of the well known completion 2 procedure originally conceived by Knuth and Bendix [Kir89]. For some contrived examples, any completion procedure may not terminate. For each pair of SiRs whose head atoms overlap, so called critical pairs taking their bodies are produced. If we cannot show that the resolvents in the critical pair are identical by simplifying them, we orient them into a ....

[Article contains additional citation context not shown here]

C. Kirchner and H. Kirchner, Rewriting: Theory and Applications, Working paper for a D.E.A. lecture at the University of Nancy I, France, 1989.

.... this one) 15, 26, 41, 66] three workshop proceedings [33, 47, 77] five special journal issues [5, 88, 24, 40, 67] more than ten surveys [2, 7, 27, 28, 44, 56, 57, 76, 82, 81] one edited collection of papers [1] four monographs [3, 12, 55, 65] and seven books (four of them still in progress) [8, 9, 35, 54, 60, 75, 84]. To encourage and stimulate continued progress in this area, we have collected (with the help of colleagues) a number of problems that appear to us to be of interest and regarding which we do not know the answer. Questions on rewriting and other equational paradigms have been included; many have ....

C. Kirchner and H. Kirchner. Rewriting: Theory and Applications. North-Holland, 1991. In preparation.

....to distinguish between the declarative and non declarative parts of CC programs. By the way, very recent work in program analysis [2] starts from a subset of CCP that is confluent under a standard semantics. Our findings are the result of adapting work in conditional term rewrite systems (CTRS) [1, 5, 7] for CC languages. We will also detail the subtleties involved when transferring a theorem about confluence in CTRS to CC languages. In addition it turns out that our confluence test is also useful when combining program parts (libraries or modules) in which the same predicate is defined (totally ....

....test in combining systems. Section 6 concludes with a summary and directions for future work. 2 Preliminaries 2. 1 Conditional Rewriting We will give a quick introduction into the basic concepts of conditional term rewriting and confluence following [1] For surveys on the topic consider [5, 7]. Definition. A conditional (term) rewrite system (CTRS) is a set of conditional rewrite rules. A conditional rewrite rule is a (first order) formula of the form u 1 # v 1 : un # v n j l r; where l; r; u 1 ; un ; v 1 ; vn are (first order) terms built from a set F of ....

Claude Kirchner and H'el`ene Kirchner. Rewriting: Theory and Applications. North-Holland, 1991.

No context found.

C. Kirchner and H. Kirchner, Rewriting: Theory and Applications, NorthHolland, 1991.

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