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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 44 (31 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 ...
Explicit Cyclic Substitutions
, 1993
"... In this paper we consider rewrite systems that describe the lambdacalculus enriched with recursive and nonrecursive local definitions by generalizing the `explicit substitutions' used by Abadi, Cardelli, Curien, and Lévy [1] to describe sharing in lambdaterms. This leads to `explicit cyclic ..."
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Cited by 25 (2 self)
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In this paper we consider rewrite systems that describe the lambdacalculus enriched with recursive and nonrecursive local definitions by generalizing the `explicit substitutions' used by Abadi, Cardelli, Curien, and Lévy [1] to describe sharing in lambdaterms. This leads to `explicit cyclic substitutions' that can describe the mutual sharing of local recursive definitions. We demonstrate how this may be used to describe standard binding constructions (let and letrec)  directly using substitution and fixed point induction as well as using `smallstep' rewriting semantics where substitution is interleaved with the mechanics of the following betareductions. With this we hope to contribute to the synthesis of denotational and operational specifications of sharing and recursion.
A Conflict Between CallbyNeed Computation and Parallelism
, 1994
"... . In functional language implementation, there is a folklore belief that there is a conflict between implementing callbyneed semantics and parallel evaluation. In this note we illustrate this by proving that reduction algorithms of a certain general and commonly used form which give callbyneed ..."
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Cited by 15 (0 self)
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. In functional language implementation, there is a folklore belief that there is a conflict between implementing callbyneed semantics and parallel evaluation. In this note we illustrate this by proving that reduction algorithms of a certain general and commonly used form which give callbyneed semantics offer very little parallelism. The analysis of lazy patternmatching which leads to the above result also suggests an efficient sequential algorithm for the evaluation of a class functional programs satisfying certain constraints, an algorithm which respects the mathematical semantics of the program considered as a term rewrite system. 1 Introduction Huet and L'evy [Huet and L'evy, 1979, Huet and L'evy, 1991] have considered the problem of call by need computation of normal forms in orthogonal term rewrite systems. Call by need here means that no redex is ever reduced unless it must be reduced in order to compute the normal form. In general, such a redex cannot be effectiv...
CLEAN: a programming environment based on term graph rewriting
 Proc. of Joint COMPUGRAPH/SEMAGRAPH Workshop on Graph Rewriting and Computation (SEGRAGRA’95
, 1995
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Semantics and Strong Sequentiality of Priority Term Rewriting Systems
 LNCS
, 1996
"... Abstract. This paper gives an operational semantics of priority term rewriting systems (PRS) by using conditional systems, whose reduction is decidable and stable under substitution. We also de ne the class of strong sequential PRSs and show that this class is decidable. Moreover, we show that the i ..."
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Cited by 4 (1 self)
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Abstract. This paper gives an operational semantics of priority term rewriting systems (PRS) by using conditional systems, whose reduction is decidable and stable under substitution. We also de ne the class of strong sequential PRSs and show that this class is decidable. Moreover, we show that the index rewriting of strong sequential PRSs gives a normalizing strategy. 1
Incremental Needed Narrowing
 In Proc. of the Int’l Workshop on Implementation of Declarative Languages (IDL’99
, 1999
"... Needed narrowing is currently the best complete strategy for executing inductively sequential functional logic programs. Its optimality properties and the fact that inductively sequential programs are a subclass of strongly sequential programs support the claim that needed narrowing must be consider ..."
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Cited by 1 (1 self)
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Needed narrowing is currently the best complete strategy for executing inductively sequential functional logic programs. Its optimality properties and the fact that inductively sequential programs are a subclass of strongly sequential programs support the claim that needed narrowing must be considered the functional logic couterpart of Huet and Lévy's strongly needed reduction. In this paper, we show how a preeminent property of reduction in (a distinguished subclass of) strongly sequential programs, namely the incrementality of the evaluation, can be inherited by needed narrowing. We give an incremental definition of needed narrowing and show that the original optimality properties are kept. Moreover, we experimentally demonstrate that the incremental refinement can lead to substantial improvements in the overall evaluation process.
Efficient Strong Sequentiality Using Replacement Restrictions
, 1997
"... . Huet and L'evy defined the (orthogonal) strongly sequential term rewriting systems, for which index reduction, i.e., reduction of redexes placed at special positions called (strong) indices, is optimal and normalizing. Despite the fact that Huet and L'evy give an algorithm to compute in ..."
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Cited by 1 (1 self)
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. Huet and L'evy defined the (orthogonal) strongly sequential term rewriting systems, for which index reduction, i.e., reduction of redexes placed at special positions called (strong) indices, is optimal and normalizing. Despite the fact that Huet and L'evy give an algorithm to compute indices for the general case, there are many proposals to define subclasses of strongly sequential rewrite systems for which this can be done more efficiently. In this paper, we show that sometimes it is possible to enlarge such classes by only introducing fixed replacement restrictions, without forcing any sensible modification of the corresponding index reduction strategy. Keywords: functional programming, neededness, replacement restrictions, term rewriting. 1 Introduction For orthogonal term rewriting systems (TRSs), Huet and L'evy gave a formal basis for the definition of efficient sequential strategies, i.e., reduction sequences in which only one needed redex is reduced in each step [2, 4]. The ...
On the Complexity of Deciding CallbyNeed
 in: Proc. FoSSaCS, LNCS 2030, 2001
"... . In a recent paper we introduced a new framework for the study of call by need computations to normal form and rootstable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple decidability proofs for classes of rewrite systems that are muc ..."
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. In a recent paper we introduced a new framework for the study of call by need computations to normal form and rootstable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple decidability proofs for classes of rewrite systems that are much larger than earlier classes defined using the complicated sequentiality concept. In this paper we show that we can do without ground tree transducers in order to arrive at decidability proofs that are phrased in direct tree automata constructions. This allows us to derive better complexity bounds. 1 Introduction The seminal work of Huet and L'evy [11] on optimal normalizing reduction strategies for orthogonal rewrite systems marks the beginning of the quest for decidable subclasses of (orthogonal) rewrite systems that admit a computable call by need strategy for deriving normal forms. Call by need means that the strategy may only contract needed redexes, i.e., redexes that are contracted ...
Leftincompatible Term Rewriting Systems and Functional Strategy
"... This paper extends leftincompatible term rewriting systems defined by Toyama et.al.[17]. It is also shown that the functional strategy is normalizing in the class, where the functional strategy is the reduction strategy that finds index by some rule selection method and topdown and lefttoright l ..."
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This paper extends leftincompatible term rewriting systems defined by Toyama et.al.[17]. It is also shown that the functional strategy is normalizing in the class, where the functional strategy is the reduction strategy that finds index by some rule selection method and topdown and lefttoright lazy pattern matching method. 1