A Coinductive Framework for Infinitary Rewriting and Equational Reasoning (Extended Version)
Year: 2015
Type: preprint
Abstract: 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 + 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 operator and nu is the greatest fixed point operator. The setup captures rewrite sequences of arbitrary ordinal length, but it has neither the need for ordinals nor for metric convergence. This makes the framework especially suitable for formalizations in theorem provers.
Source: arXiv (Cornell University)
Authors: Endrullis, Jörg, Hansen, Helle Hvid, Hendriks, Dimitri, Polonsky, Andrew, Silva, Alexandra
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2109660563