Coinductive Foundations of Infinitary Rewriting and Infinitary Equational Logic

Abstract

We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform way. We define ∞ =, the infinitary extension of a given equational theory =R, and → ∞ , the standard notion of infinitary rewriting associated to a reduction relation →R, as follows:Here µ and ν are the least and greatest fixed-point operators, respectively, andThe 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.