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Delimiting diagrams

By V. van Oostrom


We introduce the unifying notion of delimiting diagram. Hitherto unrelated results such as:\ud Minimality of the internal needed strategy for orthogonal first-order term rewriting systems,\ud maximality of the limit strategy for orthogonal higher-order pattern rewrite systems (with\ud maximality of the strategy Foo for the λ-calculus as a special case), and uniform normalisation\ud of balanced weak Church–Rosser abstract rewriting systems, all are seen to follow from the\ud property that any pair of diverging steps can be completed into a delimiting diagram. Apart\ud from yielding simple uniform proofs of those results, the same methodology yields a proof of\ud maximality of the strategy Foo for the λx--calculus. As far was we know, this is the first time\ud that a strategy has been proven maximal for a λ-calculus with explicit substitutions

Topics: Wijsbegeerte
Year: 2004
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