Decidable Call-by-Need Computations in Term Rewriting
DURAND, Irène
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
DURAND, Irène
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
< Reduce
Linguistic signs, grammar and meaning: computational logic for natural language [SIGNES]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Language
en
Article de revue
This item was published in
Information and Computation. 2005, vol. 2, n° 196, p. 95-126
Elsevier
English Abstract
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 ...Read more >
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 constructor-sharing combinations.Read less <
English Keywords
Term Rewriting
Strategies
Call-by-Need
Tree Automata
Origin
Hal imported