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Unravelings and Ultraproperties
 In Proceedings of the Fifth International Conference on Algebraic and Logic Programming (ALP'96), volume 1139 of LNCS
, 1996
"... Conditional rewriting is universally recognized as being much more complicated than unconditional rewriting. In this paper we study how much of conditional rewriting can be automatically inferred from the simpler theory of unconditional rewriting. We introduce a new tool, called unraveling, to autom ..."
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Cited by 26 (3 self)
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Conditional rewriting is universally recognized as being much more complicated than unconditional rewriting. In this paper we study how much of conditional rewriting can be automatically inferred from the simpler theory of unconditional rewriting. We introduce a new tool, called unraveling, to automatically translate a conditional term rewriting system (CTRS) into a term rewriting system (TRS). An unraveling enables to infer properties of a CTRS by studying the corresponding ultraproperty on the corresponding TRS. We show how to rediscover properties like decreasingness, and to give easy proofs of some existing results on CTRSs. Moreover, we show how unravelings provide a valuable tool to study modularity of CTRSs, automatically giving a multitude of new results.
LevelConfluence of Conditional Rewrite Systems with Extra Variables in RightHand Sides
 In Proceedings of the 6th International Conference on Rewriting Techniques and Applications
, 1995
"... Levelconfluence is an important property of conditional term rewriting systems that allow extra variables in the rewrite rules because it guarantees the completeness of narrowing for such systems. In this paper we present a syntactic condition ensuring levelconfluence for orthogonal, not necessari ..."
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Cited by 24 (3 self)
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Levelconfluence is an important property of conditional term rewriting systems that allow extra variables in the rewrite rules because it guarantees the completeness of narrowing for such systems. In this paper we present a syntactic condition ensuring levelconfluence for orthogonal, not necessarily terminating, conditional term rewriting systems that have extra variables in the righthand sides of the rewrite rules. To this end we generalize the parallel moves lemma. Our result bears practical significance since the class of systems that fall within its scope can be viewed as a computational model for functional logic programming languages with local definitions, such as letexpressions and whereconstructs. 1. Introduction There is a growing interest in combining the functional and logic programming paradigms in a single language, see Hanus [12] for a recent overview of the field. The underlying computational mechanism of most of these integrated languages is (conditional) narrowi...
A Sequential Reduction Strategy
 Theoretical Computer Science
, 1996
"... Kennaway proved the remarkable result that every (almost) orthogonal term rewriting system admits a computable sequential normalizing reduction strategy. In this paper we present a computable sequential reduction strategy similar in scope, but simpler and more general. Our strategy can be thought of ..."
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Cited by 22 (2 self)
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Kennaway proved the remarkable result that every (almost) orthogonal term rewriting system admits a computable sequential normalizing reduction strategy. In this paper we present a computable sequential reduction strategy similar in scope, but simpler and more general. Our strategy can be thought of as an outermostfairlike strategy that is allowed to be unfair to some redex of a term when contracting the redex is useless for the normalization of the term. Unlike the strategy of Kennaway, our strategy does not rely on syntactic restrictions that imply conuence. 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 systems. Our strategy is more versatile; in case of (almost) orthogonal term rewriting systems, it can be used to detect certain cases of nontermination. Our normalization proof is more accessible than Kennaway's. W...
Term Rewriting for Sale
, 1998
"... 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. We give a brief overview of the gene ..."
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Cited by 21 (15 self)
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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. We give a brief overview of the generation of termrewritingbased tools as done in the Asf+Sdf MetaEnvironment and then we sketch two major applications of term rewriting: transformation of legacy COBOL systems and compilation of Asf+Sdf to C. 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. 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.
On Extra Variables in (Equational) Logic Programming
, 1994
"... Extra variables in a clause are variables which occur in the body but not in the head. It has been argued that extra variables are necessary and contribute to the expressive power of logic languages. In the first part of this paper, we show that this is not true in general. For this purpose, we p ..."
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Cited by 21 (2 self)
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Extra variables in a clause are variables which occur in the body but not in the head. It has been argued that extra variables are necessary and contribute to the expressive power of logic languages. In the first part of this paper, we show that this is not true in general. For this purpose, we provide a simple syntactic transformation of each logic program into a logic program without extra variables. Moreover, we show a strong correspondence between the original and the transformed program with respect to the declarative and the operational semantics. In the second part of this paper, we use a similar technique to provide new completeness results for equational logic programs with extra variables. In equational logic programming it is well known that extra variables cause problems since narrowing, the standard operational semantics for equational logic programming, may become incomplete in the presence of extra variables. Since extra variables are useful from a programmin...
HigherOrder Rewriting
 12th Int. Conf. on Rewriting Techniques and Applications, LNCS 2051
, 1999
"... This paper will appear in the proceedings of the 10th international conference on rewriting techniques and applications (RTA'99). c flSpringer Verlag. ..."
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Cited by 20 (1 self)
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This paper will appear in the proceedings of the 10th international conference on rewriting techniques and applications (RTA'99). c flSpringer Verlag.
Open Problems in Rewriting
 Proceeding of the Fifth International Conference on Rewriting Techniques and Application (Montreal, Canada), LNCS 690
, 1991
"... Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27 ..."
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Cited by 19 (2 self)
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Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27, 28, 44, 56,57,76, 82, 81#; one edited collection of papers #1#; four monographs #3, 12,55,65#; and seven books #four of them still in progress# #8,9, 35, 54, 60,75, 84#. To encourage and stimulate continued progress in this area, wehave collected #with the help of colleagues# a number of problems that appear to us to be of interest and regarding whichwe do not know the answer. Questions on rewriting and other equational paradigms have been included; manyhave not aged su#ciently to be accorded the appellation #open problem". Wehave limited ourselves to theoretical questions, though there are certainly many additional interesting questions relating to applications and implementation
Nominal rewriting
 Information and Computation
"... Nominal rewriting is based on the observation that if we add support for alphaequivalence to firstorder syntax using the nominalset approach, then systems with binding, including higherorder reduction schemes such as lambdacalculus betareduction, can be smoothly represented. Nominal rewriting ma ..."
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Cited by 19 (7 self)
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Nominal rewriting is based on the observation that if we add support for alphaequivalence to firstorder syntax using the nominalset approach, then systems with binding, including higherorder reduction schemes such as lambdacalculus betareduction, can be smoothly represented. Nominal rewriting maintains a strict distinction between variables of the objectlanguage (atoms) and of the metalanguage (variables or unknowns). Atoms may be bound by a special abstraction operation, but variables cannot be bound, giving the framework a pronounced firstorder character, since substitution of terms for variables is not captureavoiding. We show how good properties of firstorder rewriting survive the extension, by giving an efficient rewriting algorithm, a critical pair lemma, and a confluence theorem
A ConstructorBased Approach for Positive/NegativeConditional Equational Specifications
 3 rd CTRS 1992, LNCS 656
, 1992
"... : We study algebraic specifications given by finite sets R of positive/negativeconditional equations (i. e. universally quantified firstorder implications with a single equation in the succedent and a conjunction of positive and negative (i. e. negated) equations in the antecedent). The class of m ..."
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Cited by 14 (10 self)
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: We study algebraic specifications given by finite sets R of positive/negativeconditional equations (i. e. universally quantified firstorder implications with a single equation in the succedent and a conjunction of positive and negative (i. e. negated) equations in the antecedent). The class of models of such a specification R does not contain in general a minimum model in the sense that it can be mapped to any other model by some homomorphism. We present a constructorbased approach for assigning appropriate semantics to such specifications. We introduce two syntactic restrictions: firstly, for a condition to be fulfilled we require the evaluation values of the terms of the negative equations to be in the set of evaluation values of constructor ground terms; secondly, we restrict the constructor rules to have "Horn" form and to be "constructorpreserving". A reduction relation for R is defined, which allows to generalize the fundamental results for positiveconditional rewrite sys...
Conditional Equational Specifications of Data Types with Partial Operations for Inductive Theorem Proving
 PROVING. 8 TH RTA 1997, LNCS 1232
, 1996
"... We propose a specification language for the formalization of data types with partial or nonterminating operations as part of a rewritebased logical framework for inductive theorem proving. The language requires constructors for designating data items and admits positive/negative conditional equati ..."
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Cited by 13 (9 self)
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We propose a specification language for the formalization of data types with partial or nonterminating operations as part of a rewritebased logical framework for inductive theorem proving. The language requires constructors for designating data items and admits positive/negative conditional equations as axioms in specifications. The (total algebra) semantics for such specifications is based on socalled data models. We present admissibility conditions that guarantee the unique existence of a distinguished data model with properties similar to those of the initial model of a usual equational specification. Since admissibility of a specification requires confluence of the induced rewrite relation, we provide an effectively testable confluence criterion which does not presuppose termination.