Q.-H. Nguyen. Compact Normalisation Trace via Lazy Rewriting. Electronic Notes in Theoretical Computer Science, volume 57, Elsevier, 2001. 68 Home/Search Document Details and Download
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Context-Sensitive Rewriting Strategies - Lucas (2000) (2 citations) (Correct)
....the value of any expression of the sort Nat without entering into infinite computations. For instance, it is possible to evaluate sel(s(0) from(0) to s(0) i.e. s(0) 2 eval (sel(s(0) from(0) Similar kinds of annotations have been utilized in term (graph) rewriting [FKW00, KW95, Mar90, Ngu01, Pol01] They have mainly been used to define restrictions of rewriting that permit the implementation of lazy reductions via eager rewritings in a transformed TRS [FKW00, KW95, Ngu01] In [Luc98a, Luc01b, Luc02a] we have analyzed how these proposals relate to CSR. 11.3 Context sensitive ....
.... Similar kinds of annotations have been utilized in term (graph) rewriting [FKW00, KW95, Mar90, Ngu01, Pol01] They have mainly been used to define restrictions of rewriting that permit the implementation of lazy reductions via eager rewritings in a transformed TRS [FKW00, KW95, Ngu01] In [Luc98a, Luc01b, Luc02a] we have analyzed how these proposals relate to CSR. 11.3 Context sensitive rewriting and evaluation strategies of ELAN Most computational systems whose operational principle is based on reduction (e.g. functional, algebraic, and equational programming languages as ....
Q.-H. Nguyen. Compact Normalisation Trace via Lazy Rewriting. Electronic Notes in Theoretical Computer Science, volume 57, Elsevier, 2001. 68
Lazy Rewriting and Context-Sensitive Rewriting - Lucas (2002) (Correct)
....3.2) Corollary 5.5 proves Fokkink et al. s claim. 6 Proving termination of lazy rewriting Corollary 5.5 is quite limited regarding proofs of LR( termination. However, it provides the basis for proving LR( termination as termination of CSR for a transformed TRS (and replacement map ) In [Ngu01], a transformation of pairs hR; i of TRSs and replacement maps is proposed to force that non variable subterms of all left hand sides of rules in R be replacing, i.e. to achieve R v . The transformation is as follows (see Section 6.1 of [Ngu01] let R = F ; R) be a TRS and 2 MF . Let l ....
....transformed TRS (and replacement map ) In [Ngu01] a transformation of pairs hR; i of TRSs and replacement maps is proposed to force that non variable subterms of all left hand sides of rules in R be replacing, i.e. to achieve R v . The transformation is as follows (see Section 6. 1 of [Ngu01]) let R = F ; R) be a TRS and 2 MF . Let l r 2 R, p 2 PosF (l) root(lj p ) f , and i 62 (f) be such that p:i 2 PosF (l) Then we obtain R as follows: F = F [ ff g, where f is a new symbol of arity ar(f ) ar(f) and such that ) f) fig, and (g) g) ....
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Q.-H. Nguyen. Compact Normalisation Trace via Lazy Rewriting. In B. Gramlich and S. Lucas, editors, Proc. of International Workshop on Reduction Strategies in Rewriting and Programming, WRS'01, Electronic Notes in Theoretical Computer Science, volume 57, 2001.
Context-Sensitive Rewriting, Lazy Rewriting, and On-demand Rewriting - Lucas (2001) (Correct)
....We show that under some conditions (namely, that all non variable subterms of the left hand sides of rules are replacing) CSR, LR, and ODR coincide. In this case, it makes sense using CSR as it is the simplest one. This is interesting since, looking for better implementations of LR, [FKW00,Ngu01] pay some attention to develop transformation techniques for achieving this condition thus (silently) using CSR rather than LR. Section 6 concludes. 2 Preliminaries Given a set A, P(A) denotes the set of all subsets of A. Given a binary relation R on a set A, we denote its transitive closure by ....
....(M D Sigma ; v Theta ) where we write just v Theta rather than v Theta j M D Sigma . 5 Lazy rewriting In lazy graph rewriting [FKW00] reductions are issued on labelled graphs. We adapt the framework to lazy term rewriting on labelled terms. An alternative adaptation can be found in [Ngu01]. We believe that ours is simpler and closer to [FKW00] Terms are built from a lazy signature, i.e. a signature supplied with a laziness predicate on Sigma Theta N that holds for (f; i) if and only if 1 i ar(f) and the ith argument of f is lazy (Definition 3.1.1 of [FKW00] Laziness ....
[Article contains additional citation context not shown here]
Q.-H. Nguyen. Compact Normalisation Trace via Lazy Rewriting. In B. Gramlich and S. Lucas, editors, Proc. of 1st International Workshop on Reduction Strategies in Rewriting and Programming, WRS'01, pages 7996, volume 2359, Servicio de Publicaciones de la Universidad Polit'ecnica de Valencia, 2001.
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