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## Filters

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Primitive Rewriting
[chapter]

2005
*
Lecture Notes in Computer Science
*

It comes as no surprise that

doi:10.1007/11601548_10
fatcat:ndwwizgbe5gzzj2quk743cq3yy
*rewrite**systems*have the same*computational*power as the other basic models. 2 Moreover,*rewrite**systems*may be restricted*in*various ways, including left-linearity,*orthogonality*... Kleene's*computation*predicate-which is central to the undecidability results-is coded as a primitive*rewrite**system**in*the Appendix, and its properties are discussed*in*Sect. 5. ... Acknowledgement*I*thank the referees for their critical reading and constructive suggestions. ...##
###
Formalizing the Confluence of Orthogonal Rewriting Systems

2013
*
Electronic Proceedings in Theoretical Computer Science
*

*In*the theory of term

*rewriting*

*systems*(TRSs) determinism is captured by the well-known property of confluence, that basically states that whenever different

*computations*or simplifications from a term ... are possible, the

*computed*answers should coincide. ... parallel

*rewriting*reduction and

*orthogonal*

*rewriting*

*systems*. ...

##
###
Page 4349 of Mathematical Reviews Vol. , Issue 96g
[page]

1996
*
Mathematical Reviews
*

R.] (4-EANG-

*I*; Norwich); de Vries, Fer-Jan (NL-MATH-ST; Amsterdam) Transfinite reductions*in**orthogonal*term*rewriting**systems*. (English summary) Inform. and*Comput*. 119 (1995), no. 1, 18-38. ... For*orthogonal**rewrite**systems*, some fundamental properties known*in*the finite case are extended to the transfinite case. ...##
###
Open problems in rewriting
[chapter]

1991
*
Lecture Notes in Computer Science
*

*In*55

*i*t

*i*s p r o ved that for

*orthogonal*termrewriting

*systems*and combinatory reduction

*systems*, decreasing redexes implies termination strong normalization. ...

*In*51 it is shown that the con uence property almost" holds for

*in*nite

*rewriting*with

*orthogonal*term-

*rewriting*

*systems*. ...

##
###
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*higherorder*rewriting**systems*the structures are*i*-terms, i.e. containing functional abstraction. ...##
###
From term rewriting to generalised interaction nets
[chapter]

1996
*
Lecture Notes in Computer Science
*

*In*this paper we present a

*system*of interaction that generalises Lafont's interaction nets by allowing

*computation*

*in*several nets

*in*parallel and communication through a state. ... This framework allows us to represent large classes of term

*rewriting*

*systems*, genuine parallel functions, non-determinism, communication, sharing, and hence can be used to code features from Standard ... A term

*rewriting*

*system*is a set of

*rewrite*rules R = fl

*i*! r

*i*g

*i*, where l

*i*6 2 X and Var(r

*i*) Var(l

*i*). A term t

*rewrites*to a term u at position p with the rule l ! ...

##
###
Conditional narrowing without conditions

2003
*
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming - PPDP '03
*

We present a new evaluation strategy for functional logic programs described by weakly

doi:10.1145/888251.888255
dblp:conf/ppdp/AntoyBH03
fatcat:n3734tg5rjeh5cq7pnfnjo4h6a
*orthogonal*conditional term*rewriting**systems*. ... Our notion of weakly*orthogonal*conditional*rewrite**system*extends a notion of Bergstra and Klop and covers a large part of programs de£ned by conditional equations. ... The source*systems*of our transformation are the constructor-based conditional weakly*orthogonal*term*rewriting**systems*. ...##
###
Page 1159 of Mathematical Reviews Vol. , Issue 98B
[page]

1998
*
Mathematical Reviews
*

The class of

*orthogonal**rewrit*- ing*systems*is the main class of not-necessarily-terminating, but confluent*rewriting**systems*. ... The reason that confluence holds*in**orthogonal**rewriting**systems*is the absence of so-called critical pairs, meaning that*rewrite*steps never interfere (*in*a destruc- tive way) with one another. ...##
###
A sequential reduction strategy
[chapter]

1994
*
Lecture Notes in Computer Science
*

Kennaway proved the remarkable result that every (almost)

doi:10.1007/3-540-58431-5_13
fatcat:4ioi3xpshvcmdeg7ea63cf6n64
*orthogonal*term*rewriting**system*admits a*computable*sequential normalizing reduction strategy. ... Our strategy is more versatile;*in*case of (almost)*orthogonal*term*rewriting**systems*, it can be used to detect certain cases of nontermination. ... for weakly*orthogonal*higher-order*rewriting**systems*. ...##
###
A sequential reduction strategy

1996
*
Theoretical Computer Science
*

Kennaway proved the remarkable result that every (almost)

doi:10.1016/0304-3975(96)00041-2
fatcat:ix5bpww7avhihbh42x25prib6a
*orthogonal*term*rewriting**system*admits a*computable*sequential normalizing reduction strategy. ... Our strategy is more versatile;*in*case of (almost)*orthogonal*term*rewriting**systems*, it can be used to detect certain cases of nontermination. ... for weakly*orthogonal*higher-order*rewriting**systems*. ...##
###
Derivational Complexity Is an Invariant Cost Model
[chapter]

2010
*
Lecture Notes in Computer Science
*

We show that

doi:10.1007/978-3-642-15331-0_7
fatcat:z2ycl4f5gbgundcmao3c47fghq
*in*the context of*orthogonal*term*rewriting**systems*, derivational complexity is an invariant cost model, both*in*innermost and*in*outermost reduction. ... Acknowledgments We owe to Guillaume Bonfante the observation that our results, previously formulated for constructor*orthogonal**rewriting**systems*, hold indeed for any*orthogonal**system*, as it is now stated ...*in*the paper. ...##
###
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. ...##
###
Page 5981 of Mathematical Reviews Vol. , Issue 94j
[page]

1994
*
Mathematical Reviews
*

(F-INRIA; Le Chesnay) Optimal normalization

*in**orthogonal*term*rewriting**systems*. (English summary)*Rewriting*techniques and applications (Montreal, PQ, 1993), 243-258, Lecture Notes*in**Comput*. ... (English summary) Conditional term*rewriting**systems*(Pont-a-Mousson, 1992), 287-301, Lecture Notes*in**Comput*. Sci., 656, Springer, Berlin, 1993. ...##
###
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*. ...##
###
Page 6686 of Mathematical Reviews Vol. , Issue 94k
[page]

1994
*
Mathematical Reviews
*

Bound variables are also present

*in*many other*rewrite**systems*, such as*systems*with simplification rules for proof normalization. ... (F-PARIS1 1-RI; Orsay) Modularity of termination and confluence*in*combinations of*rewrite**systems*with /,,. ...
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