Modularity in term rewriting revisited
نویسندگان
چکیده
منابع مشابه
On modularity in infinitary term rewriting
We study modular properties in strongly convergent infinitary term rewriting. In particular, we show that: • Confluence is not preserved across direct sum of a finite number of systems, even when these are non-collapsing. • Confluence modulo equality of hypercollapsing subterms is not preserved across direct sum of a finite number of systems. • Normalization is not preserved across direct sum o...
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We introduce a modular property of equational proofs called modularity of normalization for the union of term rewrite systems with shared symbols The idea is that every normalization with R R R may be obtained by rst normalizing with R followed by an R normalization We develop criteria for this that cover non convergent TRS R where as the main restriction R is required to be left linear and con...
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Term rewriting systems are widely used throughout computer science as they provide an abstract model of computation while retaining a comparatively simple syntax and semantics. In order to reason within large term rewriting systems, structuring operations are used to build large term rewriting systems from smaller ones. Of particular interest is whether key properties are modular, that is, if t...
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We show that, unlike the case in finitary term rewriting, confluence is not a modular property of infinitary term rewriting systems, even when these are non-collapsing. We also give a positive result: two sufficient conditions for the modularity of confluence in the infinitary setting.
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We consider a variant of rational term rewriting as first introduced by Corradini et al., i.e., we consider rewriting of (infinite) terms with a finite number of different subterms. Motivated by computability theory, we show a number of decidability results related to the rewrite relation and prove an effective version of a confluence theorem for orthogonal systems.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2012
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2012.09.008