Context-sensitive 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 context-sensitive rewriting strategies, i.e., particular, fixed sequences of context-sensitive rewriting steps. We study how to define them in order to obtain efficient computations and to ensure that context-sensitive computations terminate whenever possible. We give conditions enabling the use of these strategies for root-normalization, normalization, and infinitary normalization. We show that this theory is suitable for formalizing ...

Innermost strategies are usually used in compiling term rewriting systems (TRSs) since they allow to eciently build result terms in a bottom-up fashion. However, innermost strategies do not always give the shortest normalising derivation. In many cases, using an appropriate laziness annotation on the arguments of function symbols, we evaluate lazy arguments only if it is necessary and hence, get a shorter derivation to normal forms while avoiding non-terminating reductions. We provide in this work a transformation of annotated TRSs, that allows to compute normal forms using an innermost strategy and to extract lazy derivations in the original TRS from normalising derivations in the transformed TRS. We apply our result to improve the eciency of equational reasoning in the Coq proof assistant using ELAN as an external rewriting engine.

. Constraint solving has been successfully employed in diverse areas such as Operation Research, Planning, Logic Programming, and Automated Deduction. This has led to the development of a number of specialised approaches as well as to the adoption of different integration schemes and methodologies. In this paper we introduce an approach to incorporate constraint solving in term rewriting and we compare it with the Constraint Logic Programming scheme. We compare the two approaches both at the theoretical and at the implementational level and discuss potentials for cross-fertilisation. 1 Introduction Constraint solving aims at the development of efficient procedures tailored to restricted domains as well as to the integration of such procedures into general purpose reasoners. Constraint solving has been successfully employed in diverse areas such as Operation Research, Planning, Logic Programming, and Automated Deduction. This has led to the development of a number of specialised approa...

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 pre-eminent 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.