A coinductive treatment of infinitary term rewriting and equational reasoning
Jörg Endrullis, Helle Hvid Hansen, Dimitri Hendriks, Andrew Polonsky, Alexandra Silva · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2015
We present a coinductive framework for defining infinitary analogues of equational reasoning and rewriting in a uniform way. We define the relation 1=, a hitherto unknown notion of infinitary equational reasoning, and !1, the standard notion of infinitary rewriting as follows: 1= := R. (=E [ 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.