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Developing developments

1997
*
Theoretical Computer Science
*

The reason why confluence holds

doi:10.1016/s0304-3975(96)00173-9
fatcat:dmhrwtsgyvel5gogpybpihkccq
*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*&? ...##
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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. ...##
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Reduction Strategies and Acyclicity
[chapter]

2007
*
Lecture Notes in Computer Science
*

We exploit a recently (re)discovered fact that there are no reduction cycles

doi:10.1007/978-3-540-73147-4_5
fatcat:ccjowy7k6bgtvbjle3jogvj4za
*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*. ...##
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Book reports

1993
*
Computers and Mathematics with Applications
*

A lattice for the abstract interpretation of term graph

doi:10.1016/0898-1221(93)90008-j
fatcat:zk4j7psgrncyletmai4mmdscba
*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. ...##
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Equational specifications, complete term rewriting systems, and computable and semicomputable algebras

1995
*
Journal of the ACM
*

We classify the

doi:10.1145/227683.227687
fatcat:7tk5kkawmnagdecsvdxmg62hju
*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. ...##
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Some Properties of Non-Orthogonal Term Graph Rewriting

1995
*
Electronical Notes in Theoretical Computer Science
*

This paper examines left-linear non-

doi:10.1016/s1571-0661(05)80179-3
fatcat:3kvkhqf27ndwditic5miyzimhi
*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*? ...##
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Strong sequentiality of left-linear overlapping rewrite systems
[chapter]

1995
*
Lecture Notes in Computer Science
*

Con uent term

doi:10.1007/3-540-60381-6_14
fatcat:mhfzli3aonfafje5nt2lijx22e
*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) ?! ...##
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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. ...

##
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Extended term rewriting systems
[chapter]

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 -->. ...

##
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Transfinite reductions in orthogonal term rewriting systems
[chapter]

1991
*
Lecture Notes in Computer Science
*

Strongly convergent reduction is the fundamental notion of reduction

doi:10.1007/3-540-53904-2_81
fatcat:u6pxjbvrird7hcy6h7dmveso2q
*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. ...##
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Transfinite Reductions in Orthogonal Term Rewriting Systems

1995
*
Information and Computation
*

We establish some fundamental facts for infinitary

doi:10.1006/inco.1995.1075
fatcat:jk3dwz2eafga3e5qa3kfbaxu6e
*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] . ...##
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Contents and abstracts of the electronic notes in Theoretical Computer Science vol. 2

1998
*
Theoretical Computer Science
*

We survey the fundamental properties of infinitary

doi:10.1016/s0304-3975(97)83719-x
fatcat:r47zmpkxhfehtaenl2crpu6sk4
*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. ...##
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Weak orthogonality implies confluence: The higher-order case
[chapter]

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]! ...

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

2005
*
Lecture Notes in Computer Science
*

We prove that approximated external reduction is a

doi:10.1007/11601548_13
fatcat:zhejvqtolrdcrcs72xobfnhjs4
*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. ...
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