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Developing developments

Vincent van Oostrom
1997 Theoretical Computer Science  
The reason why confluence holds in orthogonal rewriting systems is the absence of the so-called critical pairs, making that rewrite steps never interfere (in a destructive way) with one another.  ...  The class of orthogonal rewriting systems is the main class of not-necessarily-terminating, but confluent rewriting systems.  ...  In an orthogonal PRS, sets of redexes are simultaneous. Beta-Eta-Omega In this section we present a first adaptation of the confluence by orthogonality method, to the rewriting system &?  ... 
doi:10.1016/s0304-3975(96)00173-9 fatcat:dmhrwtsgyvel5gogpybpihkccq

Page 5263 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
Using Bohm trees we also show that orthogonal term graph rewriting systems are a correct implementation of orthogonal term rewrit- ing systems.  ...  We introduce the notion of Béhm tree, and show that for orthogonal term graph rewriting systems, BGhm tree equivalence defines a congru- ence.  ... 

Reduction Strategies and Acyclicity [chapter]

Jan Willem Klop, Vincent van Oostrom, Femke van Raamsdonk
2007 Lecture Notes in Computer Science  
We exploit a recently (re)discovered fact that there are no reduction cycles in orthogonal rewrite systems when each term has a normal form, in order to enhance some of the theorems on strategies, both  ...  In this paper we review some well-known theory about reduction strategies of various kinds: normalizing, outermost-fair, cofinal, Church-Rosser.  ...  This theorem generalizes to a wide class of rewrite systems, namely the weakly orthogonal fully extended higher-order rewriting systems.  ... 
doi:10.1007/978-3-540-73147-4_5 fatcat:ccjowy7k6bgtvbjle3jogvj4za

Book reports

Ervin Y. Rodin
1993 Computers and Mathematics with Applications  
A lattice for the abstract interpretation of term graph rewriting systems. 11. Event structures and orthogonal term graph rewriting. 12.  ...  nitary church-rosser property for non-collapsing orthogonal term rewriting systems. 5. The functional strategy and transitive term rewriting sys- tems. 6.  ... 
doi:10.1016/0898-1221(93)90008-j fatcat:zk4j7psgrncyletmai4mmdscba

Equational specifications, complete term rewriting systems, and computable and semicomputable algebras

J. A. Bergstra, J. V. Tucker
1995 Journal of the ACM  
We classify the computable and semicomputable algebras in terms of finite equational initial algebra specifications and their properties as term term rewriting systems, such as completeness.  ...  Equational specifications, complete term rewriting systems, and computable and semicomputable algebras Bergstra, J.A.; Tucker, J.V. Abstract.  ...  In particular, Dauchet [1989] indicates that a Turing machine computation can be encoded in a single orthogonal rewrite rule that gives rise to a terminating TRS.  ... 
doi:10.1145/227683.227687 fatcat:7tk5kkawmnagdecsvdxmg62hju

Some Properties of Non-Orthogonal Term Graph Rewriting

David Clark, Richard Kennaway
1995 Electronical Notes in Theoretical Computer Science  
This paper examines left-linear non-orthogonal term graph rewriting systems that allow asymmetric con icts between redexes.  ...  systems.  ...  Introduction What properties of rewrite systems associated with functional languages carry over to non-orthogonal term graph rewrite systems?  ... 
doi:10.1016/s1571-0661(05)80179-3 fatcat:3kvkhqf27ndwditic5miyzimhi

Strong sequentiality of left-linear overlapping rewrite systems [chapter]

Jean-Pierre Jouannaud, Walid Sadfi
1995 Lecture Notes in Computer Science  
Con uent term rewriting systems can be seen as a model for functional computations, in which redexes corresponding to instances of left hand sides of rules are repeatedly replaced by their corresponding  ...  In a landmark paper, Huet and Levy showed that such a strategy always exists for left linear nonoverlapping rewrite systems that are strongly sequential, a property that they proved decidable for such  ...  For orthogonal rewrite systems, every proper preredex is in R-normal form, but this is not true for the case of overlapping rules, as exampli ed by the rewrite system ff(g(b; h(a)); x) ?!  ... 
doi:10.1007/3-540-60381-6_14 fatcat:mhfzli3aonfafje5nt2lijx22e

Page 2950 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
orthogonal term rewriting systems.  ...  II. (English summary) J. Symbolic Comput. 16 (1993), no. 3, 227-241. Introduction: “In Part I [J.  ... 

Extended term rewriting systems [chapter]

Jan Willem Klop, Roel Vrijer
1991 Lecture Notes in Computer Science  
In this paper we will consider some extensions of the usual term rewrite format, namely: term rewriting with conditions, infmi~y term rewriting and term rewriting with bound variables.  ...  Discussions with Fer-Jan de Vries, who pointed out some shortcomings in an earlier version concerning Section 1, are gratefully acknowledged.  ...  (ii) The CTRS R is called left-linear if R u is so; likewise for ambiguous and orthogonal. (ii) Let R be a CTRS with rewrite relation -->.  ... 
doi:10.1007/3-540-54317-1_79 fatcat:g7vqrgyaafabtgesdd2mvgihnq

Transfinite reductions in orthogonal term rewriting systems [chapter]

J. R. Kennaway, J. W. Klop, M. R. Sleep, F. J. Vries
1991 Lecture Notes in Computer Science  
Strongly convergent reduction is the fundamental notion of reduction in infinitary orthogonal term rewriting systems (OTRSs).  ...  Normal forms, ,which we allow to be infinite, are unique, in contrast to co-normal forms. Strongly converging fair reductions result in normal forms.  ...  In Section 3 we prove the fundamental results for infinitary orthogonal rewrite systems, as summarized in Table 1 .1.  ... 
doi:10.1007/3-540-53904-2_81 fatcat:u6pxjbvrird7hcy6h7dmveso2q

Transfinite Reductions in Orthogonal Term Rewriting Systems

R. Kennaway, J.W. Klop, R. Sleep, F.J. Devries
1995 Information and Computation  
We establish some fundamental facts for infinitary orthogonal term rewriting systems (OTRSs): for strongly convergent reductions we prove the Transfinite Parallel Moves Lemma and the Compressing Lemma.  ...  Fair reductions result in ω-normal forms if they are converging, and in normal forms in case of strong convergence.  ...  INTRODUCTION The theory of Orthogonal Term Rewrite Systems (TRS) is now well established within theoretical computer science. Comprehensive surveys have appeared recently in [Der90a, Klo91] .  ... 
doi:10.1006/inco.1995.1075 fatcat:jk3dwz2eafga3e5qa3kfbaxu6e

Contents and abstracts of the electronic notes in Theoretical Computer Science vol. 2

Andrea Corradini, Ugo Montanari
1998 Theoretical Computer Science  
We survey the fundamental properties of infinitary rewriting in orthogonal term rewrite systems, and its relation to cyclic graph rewriting.  ...  These were grouped into sessions on Graph Rewriting I and II, Term Graph Rewriting I and 11, Computing University of East Anglia.  ...  Use relationships between export interfaces and import interfaces are our means to construct system architectures and to allow reuse of modules in different environments.  ... 
doi:10.1016/s0304-3975(97)83719-x fatcat:r47zmpkxhfehtaenl2crpu6sk4

Weak orthogonality implies confluence: The higher-order case [chapter]

Vincent Oostrom, Femke Raamsdonk
1994 Lecture Notes in Computer Science  
In ~his pape~ we prove confluence for weakly orthogonal Higher-Order Rewriting Systems. This generalises all the known 'confluence by orthogonality' results.  ...  If a rewriting system is orthogonal, then any set of redexes present in a term is simultaneous. Orthogonality in fact consists of three parts.  ...  By weak orthogonality, Eo[d'J!sc = Do(dJ!sc• We have Eo(dJ!scMi = C"(IJ!sc C'[rJ!sc = P II ' ~~ II ~ ;o[dJ!scMi ! N = D0[d]!  ... 
doi:10.1007/3-540-58140-5_35 fatcat:5m2mn4ktezfuvcoxfdkl5uyy4e

Page 7112 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
Our strategy is more versatile; in the case of (almost) orthogonal term rewriting systems, it can be used to detect certain cases of nontermination.  ...  On the contrary, it can easily be applied to any term rewriting system, and we show that the class of term rewriting systems for which our strategy is normalizing properly includes all (almost) orthogonal  ... 

Reduction Strategies for Left-Linear Term Rewriting Systems [chapter]

Yoshihito Toyama
2005 Lecture Notes in Computer Science  
We prove that approximated external reduction is a computable normalizing strategy for the class of left-linear term rewriting systems in which every critical pair can be joined with root balanced reductions  ...  Huet and Lévy (1979) showed that needed reduction is a normalizing strategy for orthogonal (i.e., left-linear and non-overlapping) term rewriting systems.  ...  Acknowledgments The first idea of the balanced weak Church-Rosser property was obtained in 1991 during my stay at the CWI, Amsterdam.  ... 
doi:10.1007/11601548_13 fatcat:zhejvqtolrdcrcs72xobfnhjs4
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