Title: 
Development Closed Critical Pairs -
Formalization and Certification


Abstract:

In this talk I present a recent formalization of the development closedness criterion for left-linear term rewrite systems (joint work with Aart Middeldorp). Since the paper proof by van Oostrom relies on graphical representations and intuition about overlapping redexes and descendants, it has previously eluded all formalization attempts. We employed proof terms as well as residual theory to obtain a formalized proof. We also present an extension of this result to almost development closed critical pairs. The formalizations were carried out  in the proof assistant Isabelle/HOL by extending the library IsaFoR (Isabelle Formalization of Rewriting). The results have been integrated into the certifier CeTA.