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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 46 (32 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 ...
Call by Need Computations to RootStable Form
 In Proc. 24th ACM Symposium on Principles of Programming Languages
, 1997
"... The following theorem of Huet and L'evy forms the basis of all results on optimal reduction strategies for orthogonal term rewriting systems: every term not in normal form contains a needed redex, and repeated contraction of needed redexes results in the normal form, if the term under considera ..."
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Cited by 44 (5 self)
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The following theorem of Huet and L'evy forms the basis of all results on optimal reduction strategies for orthogonal term rewriting systems: every term not in normal form contains a needed redex, and repeated contraction of needed redexes results in the normal form, if the term under consideration has one. We generalize this theorem to computations to rootstable form and we argue that the resulting notion of rootneededness is more fundamental than (other variants of) neededness when it comes to infinitary normalization. 1 Introduction In this paper we are concerned with reduction strategies for term rewriting systems. A reduction strategy is called normalizing if repeated contraction of the redexes selected by the strategy leads to normal form. O'Donnell [13] showed that the paralleloutermost strategy, which contracts all outermost redexes in parallel, is normalizing for orthogonal term rewriting systems. Paralleloutermost is not an optimal reduction strategy since many of the r...
A Provably TimeEfficient Parallel Implementation of Full Speculation
 In Proceedings of the 23rd ACM Symposium on Principles of Programming Languages
, 1996
"... Speculative evaluation, including leniency and futures, is often used to produce high degrees of parallelism. Existing speculative implementations, however, may serialize computation because of their implementation of queues of suspended threads. We give a provably efficient parallel implementation ..."
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Cited by 18 (6 self)
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Speculative evaluation, including leniency and futures, is often used to produce high degrees of parallelism. Existing speculative implementations, however, may serialize computation because of their implementation of queues of suspended threads. We give a provably efficient parallel implementation of a speculative functional language on various machine models. The implementation includes proper parallelization of the necessary queuing operations on suspended threads. Our target machine models are a butterfly network, hypercube, and PRAM. To prove the efficiency of our implementation, we provide a cost model using a profiling semantics and relate the cost model to implementations on the parallel machine models. 1 Introduction Futures, lenient languages, and several implementations of graph reduction for lazy languages all use speculative evaluation (callbyspeculation [15]) to expose parallelism. The basic idea of speculative evaluation, in this context, is that the evaluation of a...
Relative Normalization in Orthogonal Expression Reduction Systems
 In: Proc. of the 4 th International workshop on Conditional (and Typed) Term Rewriting Systems, CTRS'94, Springer LNCS
, 1994
"... . We study reductions in orthogonal (leftlinear and nonambiguous) Expression Reduction Systems, a formalism for Term Rewriting Systems with bound variables and substitutions. To generalise the normalization theory of Huet and L'evy, we introduce the notion of neededness with respect to a set ..."
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Cited by 13 (10 self)
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. We study reductions in orthogonal (leftlinear and nonambiguous) Expression Reduction Systems, a formalism for Term Rewriting Systems with bound variables and substitutions. To generalise the normalization theory of Huet and L'evy, we introduce the notion of neededness with respect to a set of reductions \Pi or a set of terms S so that each existing notion of neededness can be given by specifying \Pi or S. We imposed natural conditions on S, called stability, that are sufficient and necessary for each term not in Snormal form (i.e., not in S) to have at least one Sneeded redex, and repeated contraction of Sneeded redexes in a term t to lead to an Snormal form of t whenever there is one. Our relative neededness notion is based on tracing (open) components, which are occurrences of contexts not containing any bound variable, rather than tracing redexes or subterms. 1 Introduction Since a normalizable term, in a rewriting system, may have an infinite reduction, it is important to...
Sequentiality, Second Order Monadic Logic and Tree Automata
 IN `PROCEEDINGS 10TH IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE, LICS'95', IEEE COMPUTER
, 1995
"... Given a term rewriting system R and a normalizable term t, a redex is needed if in any reduction sequence of t to a normal form, this redex will be contracted. Roughly, R is sequential if there is an optimal reduction strategy in which only needed redexes are contracted. More generally, G. Huet and ..."
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Cited by 7 (0 self)
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Given a term rewriting system R and a normalizable term t, a redex is needed if in any reduction sequence of t to a normal form, this redex will be contracted. Roughly, R is sequential if there is an optimal reduction strategy in which only needed redexes are contracted. More generally, G. Huet and J.J. Levy define in [8] the sequentiality of a predicate P on partially evaluated terms. We show here that the sequentiality of P is definable in SkS, the secondorder monadic logic with k successors, provided P is definable in SkS. We derive several known and new consequences of this remark: 1strong sequentiality, as defined in [8], of a left linear (possibly overlapping) rewrite system is decidable, 2NVsequentiality, as defined in [15] is decidable, even in the case of overlapping rewrite systems 3 sequentiality of any linear shallow rewrite system is decidable. Then we describe a direct construction of a tree automaton recognizing the set of terms that do have needed redexes, w...
Needed Reductions with ContextSensitive Rewriting
"... . Computing with functional programs involves reduction of terms to normal form. When considering nonterminating programs, this is achieved by using some special, normalizing strategy which obtains the normal form whenever it exists. Contextsensitive rewriting can improve termination and also ..."
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Cited by 5 (4 self)
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. Computing with functional programs involves reduction of terms to normal form. When considering nonterminating programs, this is achieved by using some special, normalizing strategy which obtains the normal form whenever it exists. Contextsensitive rewriting can improve termination and also avoid useless reductions by imposing fixed, syntactic restrictions on the replacements. In this paper, we analyze the efficiency of contextsensitive computations with respect to the notion of needed reduction. As contextsensitive rewriting is complete in performing reductions to a rootstable form, we base our investigation on Middeldorp's theory of rootnecessary reductions which is a generalization of Huet and L'evy's theory of (sequential) needed reductions to reductions leading to rootstable form both in sequential and parallel executions. Keywords: functional programming, needed reductions, replacement restrictions, strategies, term rewriting systems. 1 Introduction In con...
Minimal and Optimal relative normalization in orthogonal expression reduction systems
 J. Logic & Comput
, 1996
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Parallel Functional Programming: An Introduction
 INTERNATIONAL SYMPOSIUM ON PARALLEL SYMBOLIC COMPUTATION
, 1994
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