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Extending ContextSensitivity in Term Rewriting
"... We propose a generalized version of contextsensitivity in term rewriting based on the notion of “forbidden patterns”. The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears in a certain context. This shape and context is expressed thr ..."
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We propose a generalized version of contextsensitivity in term rewriting based on the notion of “forbidden patterns”. The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears in a certain context. This shape and context is expressed through forbidden patterns. In particular we analyze the relationships among this novel approach and the commonly used notion of contextsensitivity in term rewriting, as well as the feasibility of rewriting with forbidden patterns from a computational point of view. The latter feasibility is characterized by demanding that restricting a rewrite relation yields an improved termination behaviour while still being powerful enough to compute meaningful results. Sufficient criteria for both kinds of properties in certain classes of rewrite systems with forbidden patterns are presented. 1
MUTERM version 1.0 User's manual
"... Introduction Restrictions of rewriting can eventually achieve termination by pruning all infinite rewrite sequences issued from every term. However, proving that such improvement is actually achieved can be difficult. Contextsensitive rewriting (CSR [Luc98]) is a restriction of rewriting which is ..."
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Introduction Restrictions of rewriting can eventually achieve termination by pruning all infinite rewrite sequences issued from every term. However, proving that such improvement is actually achieved can be difficult. Contextsensitive rewriting (CSR [Luc98]) is a restriction of rewriting which is useful for describing semantic aspects of programming languages (e.g., OBJ2, OBJ3, CafeOBJ, or Maude) and analyzing the computational properties (e.g., termination or completeness) of the corresponding programs (see [Luc98, Luc01a, Luc01b, Luc01c, NF01] for further details and motivations). In CSR, a mapping : \Sigma ! P(N) (called a replacement map) is used to discriminate the argument positions on which replacements are allowed; in this way, a restriction of rewriting is obtained. Example 1 Consider the following TRS R: first(0,x) ! [] from(x) ! x:from(s(x)) first(s(x),y:z) ! y:first(x,z) together with (s) = (:) = (from) = f1g and (first) = f1; 2g. Then, we have: from(0) ! 0:from(s(0
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 ..."
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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