Results 1 
7 of
7
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 ..."
Abstract

Cited by 43 (30 self)
 Add to MetaCart
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 ...
muterm: A Tool for Proving Termination of ContextSensitive Rewriting
 Proc. of 15h International Conference on Rewriting Techniques and Applications, RTA’04, LNCS 3091:200209
, 2004
"... Restrictions of rewriting can eventually achieve termination by pruning all in nite rewrite sequences issued from every term. Contextsensitive rewriting (CSR) is an example of such a restriction. In CSR, the replacements in some arguments of the function symbols are permanently forbidden. This ..."
Abstract

Cited by 21 (20 self)
 Add to MetaCart
Restrictions of rewriting can eventually achieve termination by pruning all in nite rewrite sequences issued from every term. Contextsensitive rewriting (CSR) is an example of such a restriction. In CSR, the replacements in some arguments of the function symbols are permanently forbidden. This paper describes muterm, a tool which can be used to automatically prove termination of CSR. The tool implements the generation of the appropriate orderings for proving termination of CSR by means of polynomial interpretations over the rational numbers.
Demandness in Rewriting and Narrowing
 Proc. of the 11th Int’l Workshop on Functional and (Constraint) Logic Programming WFLP’02, volume 76 of Electronic Notes in Theoretical Computer Science. Elsevier Sciences Publisher
, 2002
"... The traditional investigation of rewriting and narrowing strategies aims at establishing fundamental properties, such as soundness, completeness and/or optimality, of a strategy. In this work, we analyze and compare rewriting and narrowing strategies from the point of view of the information tak ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
The traditional investigation of rewriting and narrowing strategies aims at establishing fundamental properties, such as soundness, completeness and/or optimality, of a strategy. In this work, we analyze and compare rewriting and narrowing strategies from the point of view of the information taken into account by a strategy to compute a step. The notion of demandness provides a suitable framework for presenting and comparing wellknown strategies. We find the existence of an almost linear sequence of strategies that take into account more and more information. We show on examples that, as we progress on this sequence, a strategy becomes more focused and avoids some useless steps computed by strategies preceding it in this sequence. Our work, which is still in progress, clarifies the behavior of similar or related strategies and it promises to simplify the transfer of some results from one strategy to another. It also suggests that the notion of demandness is both atomic and fundamental to the study of strategies.
Termination of Lazy Rewriting Revisited
, 2007
"... Lazy rewriting is a proper restriction of term rewriting that dynamically restricts the reduction of certain arguments of functions in order to obtain termination. In contrast to contextsensitive rewriting, reductions at such argument positions are not completely forbidden but delayed. Based on the ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Lazy rewriting is a proper restriction of term rewriting that dynamically restricts the reduction of certain arguments of functions in order to obtain termination. In contrast to contextsensitive rewriting, reductions at such argument positions are not completely forbidden but delayed. Based on the observation that the only existing (nontrivial) approach to prove termination of such lazy rewrite systems is flawed, we develop a modified approach for transforming lazy rewrite systems into contextsensitive ones that is sound and complete with respect to termination. First experimental results with this transformation based technique are encouraging.
muterm: a tool for proving termination of rewriting with replacement restrictions
"... Abstract. This paper describes muterm, a tool which can be used to automatically prove termination of computational restrictions of rewriting such as contextsensitive rewriting and lazy rewriting. The tool can also be used to prove termination of rewriting. In this sense, muterm provides the firs ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. This paper describes muterm, a tool which can be used to automatically prove termination of computational restrictions of rewriting such as contextsensitive rewriting and lazy rewriting. The tool can also be used to prove termination of rewriting. In this sense, muterm provides the first implementation of reduction orderings based on polynomial interpretations over the rational numbers. 1
www.elsevier.com/locate/entcs Termination of Lazy Rewriting Revisited
"... Lazy rewriting is a proper restriction of term rewriting that dynamically restricts the reduction of certain arguments of functions in order to obtain termination. In contrast to contextsensitive rewriting, reductions at such argument positions are not completely forbidden but delayed. Based on the ..."
Abstract
 Add to MetaCart
Lazy rewriting is a proper restriction of term rewriting that dynamically restricts the reduction of certain arguments of functions in order to obtain termination. In contrast to contextsensitive rewriting, reductions at such argument positions are not completely forbidden but delayed. Based on the observation that the only existing (nontrivial) approach to prove termination of such lazy rewrite systems is flawed, we develop a modified approach for transforming lazy rewrite systems into contextsensitive ones that is sound and complete with respect to termination. First experimental results with this transformation based technique are encouraging. Keywords: term rewriting, lazy rewriting, termination, contextsensitive system
Termination of ContextSensitive Rewriting with BuiltIn Numbers and Collection Data Structures ⋆
"... Abstract. Contextsensitive rewriting is a restriction of rewriting that can be used to elegantly model declarative specification and programming languages such as Maude. Furthermore, it can be used to model lazy evaluation in functional languages such as Haskell. Building upon our previous work on ..."
Abstract
 Add to MetaCart
Abstract. Contextsensitive rewriting is a restriction of rewriting that can be used to elegantly model declarative specification and programming languages such as Maude. Furthermore, it can be used to model lazy evaluation in functional languages such as Haskell. Building upon our previous work on an expressive and elegant class of rewrite systems (called CERSs) that contains builtin numbers and supports the use of collection data structures such as sets or multisets, we consider contextsensitive rewriting with CERSs in this paper. This integration results in a natural way for specifying algorithms in the rewriting framework. In order to prove termination of this kind of rewriting automatically, we develop a dependency pair framework for contextsensitive rewriting with CERSs, resulting in a flexible termination method that can be automated effectively. Several powerful termination techniques are developed within this framework. An implementation in the termination prover AProVE has been successfully evaluated on a large collection of examples. 1