A Coinductive Treatment of Infinitary Rewriting release_tm3d63fkerbejerce2fdj5x3l4

by Joerg Endrullis, Helle Hvid Hansen, Dimitri Hendriks, Andrew Polonsky, Alexandra Silva

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2013  

Abstract

We introduce a coinductive definition of infinitary term rewriting. The setup is surprisingly simple, and has in contrast to the usual definitions of infinitary rewriting, neither need for ordinals nor for metric convergence. While the idea of a coinductive treatment of infinitary rewriting is not new, all previous approaches were limited to reductions of length at most omega. The approach presented in this paper is the first to capture the full infinitary term rewriting with reductions of arbitrary ordinal length. Apart from an elegant reformulation of known concepts, our approach gives rise, in a very natural way, to a novel notion of infinitary equational reasoning.
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Date   2013-06-26
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arXiv  1306.6224v1
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