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A Coinductive Framework for Infinitary Rewriting and Equational Reasoning (Extended Version)
[article]

2015
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arXiv
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pre-print

We present a coinductive framework for defining infinitary analogues of equational reasoning and rewriting in a uniform way. We define the relation =^infty, notion of infinitary equational reasoning, and ->^infty, the standard notion of infinitary rewriting as follows: =^infty := nu R. ( <-_root + ->_root + lift(R) )^* ->^infty := mu R. nu S. ( ->_root + lift(R) )^* ; lift(S) where lift(R) := (f(s_1,...,s_n), f(t_1,...,t_n)) | s_1 R t_1,...,s_n R t_n + id , and where mu is the least fixed point

arXiv:1505.01128v1
fatcat:mdhz2sza7bfd7ctbvmkc7lcvxi