A Coinductive Treatment of Infinitary Term Rewriting and Equational Reasoning (Extended Version).
Jörg Endrullis, Helle Hvid Hansen, Dimitri Hendriks, Andrew Polonsky, Alexandra Silva · Data Archiving and Networked Services (DANS) · 2015
rewriting in a uniform way. We define the relation 1=, a notion of infinitary equational reasoning, and !1, the standard notion of infinitary rewriting as follows: 1= := R. (=R [ R) !1 := μR. S. (!R [ R) S where μ and are the least and greatest fixed-point operators, respectively, and where R := { hf(s1, . . . , sn), f(t1, . . . , tn)i | f 2 , s1 R t1, . . . , sn R tn } [ Id . 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.