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ContextSensitive Computations in Functional and Functional Logic Programs
 JOURNAL OF FUNCTIONAL AND LOGIC PROGRAMMING
, 1998
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ContextSensitive Rewriting Strategies
, 1997
"... Contextsensitive rewriting is a simple restriction of rewriting which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is (explicitly or automatically) specified on the arguments of symbols of the signature and inductively ..."
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Cited by 43 (30 self)
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Contextsensitive rewriting is a simple restriction of rewriting which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is (explicitly or automatically) specified on the arguments of symbols of the signature and inductively extended to arbitrary positions of terms built from those symbols. Termination is not only preserved but usually improved and several methods have been developed to formally prove it. In this paper, we investigate the definition, properties, and use of contextsensitive rewriting strategies, i.e., particular, fixed sequences of contextsensitive rewriting steps. We study how to define them in order to obtain efficient computations and to ensure that contextsensitive computations terminate whenever possible. We give conditions enabling the use of these strategies for rootnormalization, normalization, and infinitary normalization. We show that this theory is suitable for formalizing ...
Strongly Sequential and Inductively Sequential Term Rewriting Systems
, 1998
"... 1 Introduction Michael Hanus Salvador Lucas Aart Middeldorp Strongly sequential and inductively sequential term rewriting systems hanus@informatik.rwthaachen.de slucas@dsic.upv.es ami@score.is.tsukuba.ac.jp first(0,x) [] first(s(x),y::z) y::first(x,z) first x 1 0 s(x) x 2 first x 1 x 2 first 0 x ..."
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Cited by 29 (14 self)
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1 Introduction Michael Hanus Salvador Lucas Aart Middeldorp Strongly sequential and inductively sequential term rewriting systems hanus@informatik.rwthaachen.de slucas@dsic.upv.es ami@score.is.tsukuba.ac.jp first(0,x) [] first(s(x),y::z) y::first(x,z) first x 1 0 s(x) x 2 first x 1 x 2 first 0 x 2 first s x x 2 [] first s x y z y first x z first inductively sequential outermostneeded strategy needed rewriting needed Definitional trees inductively sequential inductively sequential index trees forwardbranching index trees matching dags outermostneeded strategy index reduction Informatik II, RWTH Aachen, D52056 Aachen, Germany, . Work partially supported by DFG (under grant Ha 2457/11) and Acci'on Integrada. DSIC, U.P. de Valencia, Camino de la Vera s/n, Apdo. 22012, E46071 Valencia, Spain, . Work partially supported by EECHCM grant ERBCHRXCT940624, Bancaixa (BancajaEuropa grant), Acci'on Integrada (HA19970073) and CICYT (under grant TIC 950433C0303). Institute of Informa...
Lazy rewriting on eager machinery
 ACM Transactions on Programming Languages and Systems
, 2000
"... The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives a ..."
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Cited by 23 (1 self)
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The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting. 1
Specialization of Inductively Sequential Functional Logic Programs
, 1999
"... Functional logic languages combine the operational principles of the most important declarative programming paradigms, namely functional and logic programming. Inductively sequential programs admit the definition of optimal computation strategies and are the basis of several recent (lazy) functional ..."
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Cited by 21 (11 self)
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Functional logic languages combine the operational principles of the most important declarative programming paradigms, namely functional and logic programming. Inductively sequential programs admit the definition of optimal computation strategies and are the basis of several recent (lazy) functional logic languages. In this paper, we define a partial evaluator for inductively sequential functional logic programs. We prove strong correctness of this partial evaluator and show that the nice properties of inductively sequential programs carry over to the specialization process and the specialized programs. In particular, the structure of the programs is preserved by the specialization process. This is in contrast to other partial evaluation methods for functional logic programs which can destroy the original program structure. Finally, we present some experiments which highlight the practical advantages of our approach. 1 Introduction Functional logic languages combine the operational p...
Constructor Equivalent Term Rewriting Systems are Strongly Sequential: a direct proof
 Information Processing Letters
, 1993
"... In [8], Thatte demonstrated the possibility of simulating an orthogonal TRS with a leftlinear constructor system obtained from the original system via a simple transformation. The class of strongly sequential systems (SS) was defined in [3]. In [2], we have defined the class of constructor equivale ..."
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Cited by 7 (3 self)
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In [8], Thatte demonstrated the possibility of simulating an orthogonal TRS with a leftlinear constructor system obtained from the original system via a simple transformation. The class of strongly sequential systems (SS) was defined in [3]. In [2], we have defined the class of constructor equivalent systems (CE) for which Thatte's transformation preserves strong sequentiality; in that same article, we prove that CE ae SS by showing that CE is a strict subset of the forwardbranching class [7] which is itself a strict subset of SS [1]. In this article, we give a direct proof (i.e. a proof which does not involve the forwardbranching class) of the inclusion CE ae SS. It uses parts of the proof given in [6] for deciding strong sequentiality.
Simulating ForwardBranching Systems with Constructor Systems
 Journal of Symbolic Computation
, 1997
"... Strongly sequential constructor systems admit a very efficient algorithm to compute normal forms. The class of forwardbranching systems contains the class of strongly sequential constructor systems, and admits a similar reduction algorithm, but less efficient on the entire class of forwardbranchin ..."
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Cited by 4 (0 self)
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Strongly sequential constructor systems admit a very efficient algorithm to compute normal forms. The class of forwardbranching systems contains the class of strongly sequential constructor systems, and admits a similar reduction algorithm, but less efficient on the entire class of forwardbranching systems. In this article, we present a new transformation which transforms any forwardbranching system into a strongly sequential constructor one. We prove the correctness and completeness of the transformation algorithm, then that the new system is equivalent to the input system, with respect to the behavior and the semantics. As a programming language, it permits us to have a less restrictive syntax without compromise of semantics and efficiency.
Deciding Strong Sequentiality for orthogonal term rewriting systems is in CoNP
, 1995
"... In [KM91], Klop and Middeldorp conjectured that deciding strong sequentiality for orthogonal term rewriting systems is NPComplete. This problem appeared as "Problem 8" in the list of open problems in rewriting published in [DJK91]. In this article we show that the problem is in coNP. If, as we con ..."
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Cited by 3 (0 self)
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In [KM91], Klop and Middeldorp conjectured that deciding strong sequentiality for orthogonal term rewriting systems is NPComplete. This problem appeared as "Problem 8" in the list of open problems in rewriting published in [DJK91]. In this article we show that the problem is in coNP. If, as we conjecture, the problem is also in NP , this reduces its chances of being NPComplete.
Separability and Translatability of Sequential Term Rewrite Systems Into the Lambda Calculus
, 2001
"... Orthogonal term rewrite systems do not currently have any semantics other than syntacticallybased ones such as term models and event structures. For a functional language which combines lambda calculus with term rewriting, a semantics is most easily given by translating the rewrite rules into lambd ..."
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Cited by 2 (0 self)
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Orthogonal term rewrite systems do not currently have any semantics other than syntacticallybased ones such as term models and event structures. For a functional language which combines lambda calculus with term rewriting, a semantics is most easily given by translating the rewrite rules into lambda calculus and then using wellunderstood semantics for the lambda calculus. We therefore study in this paper the question of which classes of TRS do or do not have such translations. We demonstrate by construction that forward branching orthogonal term rewrite systems are translatable into the lambda calculus. The translation satis es some strong properties concerning preservation of equality and of some inequalities. We prove that the forward branching systems are exactly the systems permitting such a translation which is, in a precise sense, uniform in the righthand sides. Connections are drawn between translatability, sequentiality and separability properties. Simple syntactic proofs are given of the nontranslatability of a class of TRSs, including Berry's F and several variants of it.
Decidable CallbyNeed Computations in Term Rewriting
, 2004
"... The theorem of Huet and Lévy stating that for orthogonal rewrite systems (i) every reducible term contains a needed redex and (ii) repeated contraction of needed redexes results in a normal form if the term under consideration has a normal form, forms the basis of all results on optimal normalizing ..."
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Cited by 2 (2 self)
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The theorem of Huet and Lévy stating that for orthogonal rewrite systems (i) every reducible term contains a needed redex and (ii) repeated contraction of needed redexes results in a normal form if the term under consideration has a normal form, forms the basis of all results on optimal normalizing strategies for orthogonal rewrite systems. However, needed redexes are not computable in general. In the paper we show how the use of approximations and elementary tree automata techniques allows one to obtain decidable conditions in a simple and elegant way. Surprisingly, by avoiding complicated concepts like index and sequentiality we are able to cover much larger classes of rewrite systems. We also study modularity aspects of the classes in our hierarchy. It turns out that none of the classes is preserved under signature extension. By imposing various conditions we recover the preservation under signature extension. By imposing some more conditions we are able to strengthen the signature extension results to modularity for disjoint and constructorsharing combinations.