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Topic: Term-rewriting

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Rewriting -- Facts, Info, and Encyclopedia article The non-deterministic nature of a rewriting system indicates that it is not an (A precise rule (or set of rules) specifying how to solve some problem) algorithm for changing one string to another, but a system of 'permissions'. The feature of this rewriting system that has some general application is that some unique result or normal form is obtainable; and naturally any serious (Click link for more info and facts about computer algebra) computer algebra system will have to perform this simplification automatically. in which P and Q are (A mathematical expression that is the sum of a number of terms) polynomials. www.absoluteastronomy.com /encyclopedia/r/re/rewriting.htm   (368 words)

Term Rewriting Systems - Cambridge University Press Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521391156   (235 words)

Term Rewriting for Sale Term rewriting has a large potential for industrial applications, but these applications are always larger than one could ever dream of: huge sets of rewrite rules and gigantic terms to rewrite pose interesting challenges for implementors and theoreticians alike. It will turn out that we have an ``alien'' view on research in term rewriting: properties like confluence and termination are of very limited use when selling term rewriting to industry. Based on these experiences we suggest the study of topics that could further advance the use of term rewriting in industrial applications: persistent term databases, generalized LR parsing versus parallel term rewriting, and coordination languages versus strategy languages. homepages.cwi.nl /~paulk/publications/WRLA98.html   (144 words)

term-rewriting.html This example illustrates clearly that not all rewrite systems terminate and hence that care should be taken in defining as well as implementing them. alpha.luc.ac.be /~gjb/maple/examples/term-rewriting1.html   (87 words)

Implementations of term rewriting systems In equational logic, rewriting is a correct and complete deduction inference rule as soon as the term rewriting system is confluent and terminating. By its elegant and simple formalism, term rewriting systems appear both as a powerful formal concept and as an efficient mechanism to deal with these problems. The notions necessary for understanding how rewriting is used in different implementations of theorem provers are presented in Section 2. www.lix.polytechnique.fr /~hermann/publications/trs-abs.html   (288 words)

MetaPRL Term Rewriting A term pattern matches a (regular) term if the operators are equal, the arities of the subterms are equal, and the subterm patterns match each of the subterms of the (regular) term. A redex pattern is either a second-order variable, or it is a term with redex patterns for its subterms. The variable syntax is extended to include variables that specify terms with bound variables, or substitutions. www.cs.cornell.edu /jyh/metaprl/system/mp-rewrite.html   (409 words)

Term Graph Rewriting - Plump (ResearchIndex) 331 Term Rewriting and All That (context) - Baader, Nipkow - 1998 ACM 10 Modularity in noncopying term rewriting (context) - Kurihara, Ohuchi - 1995 ACM DBLP Abstract: Term graph rewriting is concerned with the representation of functional expressions as graphs, and the evaluation of these expressions by rule-based graph transformation. citeseer.ist.psu.edu /plump98term.html   (1451 words)

Abstract of: Equational term graph rewriting We present an equational framework for term graph rewriting with cycles. The usual notion of homomorphism is phrased in terms of the notion of bisimulation, which is well-known in process algebra and concurrency theory. The general framework of term graphs with copying is compared with the more restricted copying facilities embodied in the μ-rule, and translations are given between term graphs and μ-expressions. db.cwi.nl /rapporten/abstract.php?abstractnr=525   (167 words)

Jakob Grue-Simonsen - Infinitary Term Rewriting Infinitary term rewriting is an extension of ordinary (first-order) term rewriting allowing for transfinite reduction sequences converging to limits. In the talk, we will review basic definitions and problems of infinitary term rewriting, sketch a proof of confluence by orthogonality, and briefly touch upon infinitary lambda calculus. The last 15 years have witnessed the slow development of the field, culminating in the general setting of so-called strongly convergent rewriting. www.pps.jussieu.fr /seminaire/sem2003/abstracts/grue.html   (88 words)

TERMGRAPH 2002 Term graph rewriting is concerned with the representation of functional expressions as graphs and the evaluation of these expressions by rule-based graph transformation. The aim of this workshop is to bring together researchers working in these different domains and to foster their interaction, to provide a forum for presenting new ideas and work in progress, and to enable newcomers to learn about current activities in term graph rewriting. Topics of interest include all aspects of term graphs and sharing of common subexpressions in rewriting, programming, automated reasoning and symbolic computation. www-users.cs.york.ac.uk /~det/Termgraph_2002/cfp.html   (240 words)

Categorical Term Rewriting: Monads and Modularity Term rewriting systems are widely used throughout computer science as they provide an abstract model of computation while retaining a comparatively simple syntax and semantics. As an application and demonstration of the usefulness of this approach, two modularity results for the disjoint union of two term rewriting systems are proven, the modularity of confluence (Toyama's theorem) and the modularity of strong normalization for a particular class of term rewriting systems (non-collapsing term rewriting systems). In order to reason within large term rewriting systems, structuring operations are used to build large term rewriting systems from smaller ones. www.lfcs.inf.ed.ac.uk /reports/98/ECS-LFCS-98-396   (277 words)

Term Rewriting Systems SS 2004 Term rewriting systems are used for computations and mechanized proofs with equations. Therefore, term rewriting systems are used in many areas like mechanized program verification, specification of programs and declarative programming. All functional programming languages are based on term rewriting systems, too. www-i2.informatik.rwth-aachen.de /lufgi2/tes04/index_e.html   (127 words)

Type Theory and Term Rewriting, Sept 1996 Unfortunately, collaboration between type theory and term rewriting systems is not as strong as it should be despite their common goals and extreme importance. Furthermore, the two notions of type theory and term rewriting are very general and cover various topics including termination, calculi of substitutions, subtyping, reduction, unification, interaction and process calculi, the logic of programs and theorem proving. The International School on Type Theory and Term Rewriting aims at bridging this gap and at bringing together leaders and active researchers in the various branches of type theory and term rewriting. www.cee.hw.ac.uk /~fairouz/school1996   (1996 words)

Abstract of: Term rewriting with traversal functions Term rewriting is an appealing technique for performing program analysis and program transformation. Tree (term) traversal is frequently used but is not supported by standard term rewriting. We extend many-sorted, first-order term rewriting with traversal functions that automate tree traversal in a simple and type safe way. db.cwi.nl /rapporten/abstract.php?abstractnr=1079   (91 words)

Term Rewriting and Unification We present a finite term rewriting system $R$ such that the DYADIC WORD CONCATENATION (= the concatenation of words in a two-letter alphabet) is expressible via the one-step rewriting relation in $R$. We construct a finite linear finitely terminating rewrite rule system with undecidable theory of one step rewriting. Since the full first-order theories of one-step rewriting turn out to be undecidable, in general, it is interesting to figure out decidable cases, both for specific classes of systems and particular single systems, as well as for restricted theories of bounded quantifier depth. www.mpi-sb.mpg.de /~sv/index-rew.html   (465 words)

Term Graph Rewriting In my dissertation [Kahl-1996], I presented a first algebraic approach to second-order term graph rewriting with the full expressiveness of Combinatory Reduction Systems, thus encompassing lambda calculus. Kinship of fibred rewriting steps with double-pushout rewriting steps is obvious; the main differences are that horizontal morphisms may belong to a different category than vertical morphisms, and that the host object is now the result of a universal construction, thus overcoming the traditional necessity of gluing conditions. Close inspection of the above rewriting step reveals that sharing is preserved as far as possible, and that the copying of what Wadsworth called ``non-abstractable parts'' already takes places in the construction of the host object, the middle graph of the lower row. www.cas.mcmaster.ca /~kahl/tgr.html   (273 words)

TeReSe The main implementation ingredients of the Meta-Environment are a generic term representation, a flexible software coordination architecture, a powerful parsing technology and efficient term rewriting engines. Finally, we will demonstrate the restructuring of COBOL sources to show the strength of term rewriting in industrial applications. We introduce a new framework for higher-order rewriting, which combines aspects of earlier defined frameworks with novel ones: function symbols and variables have both a type and an arity, and rules of functional type are admitted without compromising the relationship between equational reasoning and confluence. www.phil.uu.nl /~oostrom/TeReSe   (553 words)

Term Rewriting Systems and Applications Research Page J.W. Klop together with Detlef Plump, Univ. of York, England) is currently conduction an investigation to confluence of rewriting of first-order term graphs, both for the usual presentation of term graphs and for the equational presentation. Our note recasts the original definition in terms of rewriting, and shows that a partial recursive function is HG-computable iff it is TRS definable. The theory of rewriting systems has historical roots in the period when the fundamental notions of computation were discovered: recursion theory, lambda calculus, combinatory logic. www.cs.ru.nl /~jwk/researchpage.trs.html   (560 words)

Term rewriting Term rewriting is a special form of rewriting. I've always taken risks, and never worried what the world might really think of me. www.brainyencyclopedia.com /encyclopedia/t/te/term_rewriting.html   (59 words)

Term-Graph Rewriting Term-graph rewriting [13] is a practical technique derived from theoretical term rewriting. Where term rewriting assumes (computationally expensive) syntactic equality, term-graph rewriting relies instead on identity through shared graph nodes. Term-graph rewrite systems are exemplified by approaches such as the DACTL parallel intermediate language [49][41] or Lean [14]. www-fp.dcs.st-and.ac.uk /~kh/papers/pasco94/subsection3_5_3.html   (198 words)

Information and Computation Bibliography It turns out that conditional term rewriting is much more complicated than unconditional rewriting from a modularity point of view. A property of term rewriting systems is called modular if it is preserved under disjoint union. The aim of this paper is to analyze and extend these results to conditional term rewriting systems. theory.lcs.mit.edu /~iandc/References/middeldorp1993:110.html   (451 words)

Computer Science: Publication: Confluence of Curried Term-Rewriting Systems It is shown that currying preserves confluence of {\em arbitrary\/} term rewriting systems. Presenting such terms in curried form is usually regarded as a trivial change of notation. However, in the absence of a type-discipline, or in the presence of a more powerful type-discipline than simply typed $\lambda$-calculus, the change is not as trivial as one might first think. www.cs.kent.ac.uk /pubs/1995/567   (103 words)

Multiworld Augmented Term Rewriting --- Lawrence A. Crowl Augmented term rewriting (ATR) is a simple, uniform, and extensible computational model for constraint programming. We show that our extended ATR, multiworld augmented term rewriting (MATR), is capable of expressing CCSPs concisely and readably via examples and via our experience with a significant application. Masami Takikawa and Lawrence A. Crowl, "Multiworld Augmented Term Rewriting", Technical Report 94-60-06, Department of Computer Science, Oregon State University, Corvallis, Oregon, 97331-3202, November 1994 www.crowl.org /Lawrence/paper/reports/1994R-ORSTCS-94-60-06   (158 words)

On One-Pass Term Rewriting  Two restricted ways to apply a term rewriting system (TRS) to a tree are considered. When the one-pass root-started strategy is followed, rewriting starts from the root and continues stepwise towards the leaves without ever rewriting a part of the current tree produced in a previous rewrite step. One-pass leaf-started rewriting is defined similarly, but rewriting begins from the leaves. www.inf.u-szeged.hu /kutatas/actacybernetica/vol14n1/cikk7.xml   (167 words)

Orderal Term Rewriting Systems This article describes a generalization of term rewriting system technique used as a basis for decision algorithm for equational theories. The orderal term rewriting system technique is presented. @TechReport{Lifantsev95, author = "Maxim L. Lifantsev", title = "Orderal Term Rewriting Systems", type = "Unpublished Manuscript", institution = "Moscow State Engineering-Physics Institute (Technical University)", address = "Moscow, Russia" year = "1995", month = "September", } www.ecsl.cs.sunysb.edu /~maxim/Papers/OTRS   (152 words)

Using Term Rewriting to Verify Software Verifications are performed with the aid of a program that incorporates term rewriting, structural induction, and heuristics based on ideas used in the Boyer-Moore prover. Klop, "Term rewriting systems," in S. Abramsky, D. Gabby, and T. Maibaum, Eds., Handbook of Logic in Computer Science, ch. Index Terms- abstract data types; rewriting systems; program verification; theorem proving; software tools; term rewriting; verification tasks; while statements; representation functions; abstract data types; generic program units; abstract base classes; algebraic axioms; convergence; sufficient completeness; structural induction; Boyer-Moore prover; mechanical assistance csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/trans/ts/&toc=comp/trans/ts/1994/04/e4toc.xml&DOI=10.1109/32.277574   (567 words)

Term Rewriting Systems and P/T-Nets. Abstract: The aim of this paper is to establish some relationships between P/T-nets and a class of term rewriting systems. In the second section the authors recall the notion of term rewriting system with substitution closed balance. Keywords: term rewriting system; place/transition net; substitution closed balance. www.informatik.uni-hamburg.de /TGI/pnbib/t/tiplea_f1.html   (81 words)

Term Rewriting for Stack is now replaced by the right-hand side of the rewrite rule R, with all variables in the substitutions replaced by their corresponding terms. This term, which corresponds to a stack containing the single value scom.hud.ac.uk /scomtlm/book/node231.html   (163 words)

Simplification Orders in Term Rewriting The thesis presents various applications of proof theoretical methods to term rewriting. wwwmath.uni-muenster.de /logik/publ/diss/9.html   (22 words)

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