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Primitive Rewriting [chapter]

Nachum Dershowitz
2005 Lecture Notes in Computer Science  
It comes as no surprise that 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.  ... 
doi:10.1007/11601548_10 fatcat:ndwwizgbe5gzzj2quk743cq3yy

Formalizing the Confluence of Orthogonal Rewriting Systems

Ana Cristina Rocha Oliveira, Mauricio Ayala-Rincón
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.  ... 
doi:10.4204/eptcs.113.14 fatcat:bhnj7xoanzarrgfezdf6gnqwve

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]

Nachum Dershowitz, Jean-Pierre Jouannaud, Jan Willem Klop
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.  ... 
doi:10.1007/3-540-53904-2_120 fatcat:bsnbx2vghrc2tmv6xcywwijbjq

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 higherorder rewriting systems the structures are i-terms, i.e. containing functional abstraction.  ... 
doi:10.1016/s0304-3975(96)00173-9 fatcat:dmhrwtsgyvel5gogpybpihkccq

From term rewriting to generalised interaction nets [chapter]

Maribel Fernández, Ian Mackie
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 !  ... 
doi:10.1007/3-540-61756-6_94 fatcat:ox7kiwui4vgtpggom7v4da4wzu

Conditional narrowing without conditions

Sergio Antoy, Bernd Brassel, Michael Hanus
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 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.  ... 
doi:10.1145/888251.888255 dblp:conf/ppdp/AntoyBH03 fatcat:n3734tg5rjeh5cq7pnfnjo4h6a

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]

Sergio Antoy, Aart Middeldorp
1994 Lecture Notes in Computer Science  
Kennaway proved the remarkable result that every (almost) 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.  ... 
doi:10.1007/3-540-58431-5_13 fatcat:4ioi3xpshvcmdeg7ea63cf6n64

A sequential reduction strategy

Sergio Antoy, Aart Middeldorp
1996 Theoretical Computer Science  
Kennaway proved the remarkable result that every (almost) 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.  ... 
doi:10.1016/0304-3975(96)00041-2 fatcat:ix5bpww7avhihbh42x25prib6a

Derivational Complexity Is an Invariant Cost Model [chapter]

Ugo Dal Lago, Simone Martini
2010 Lecture Notes in Computer Science  
We show that 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.  ... 
doi:10.1007/978-3-642-15331-0_7 fatcat:z2ycl4f5gbgundcmao3c47fghq

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]

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

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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