### A Verified Ground Confluence Tool for Linear Variable-Separated Rewrite Systems in Isabelle/HOL

Bertram Felgenhauer, Aart Middeldorp, T. V. H. Prathamesh, and Franziska Rapp8th ACM SIGPLAN International Conference on Certified Programs and Proofs, pp. 132 – 143, 2019.

### Abstract

It is well known that (ground) confluence is a decidable property of ground term rewrite systems, and that this extends to larger classes. Here we present a formally verified ground confluence checker for linear, variable-separated rewrite systems. To this end, we formalize procedures for ground tree transducers and so-called RRn relations. The ground confluence checker is an important milestone on the way to formalizing the decidability of the first-order theory of ground rewriting for linear, variable-separated rewrite systems. It forms the basis for a formalized confluence checker for left-linear, right-ground systems.

### BibTeX

@inproceedings{BFAMPRFR-CPP19, author = "Bertram Felgenhauer and Aart Middeldorp and T.V.H. Prathamesh and Franziska Rapp", title = "A Verified Ground Confluence Tool for Linear Variable-Separated Rewrite Systems in {Isabelle/HOL}", booktitle = "Proceedings of the 8th International {ACM SIGPLAN} International Conference on Certified Programs and Proofs", pages = "132--143", publisher = "ACM", doi = "10.1145/3293880.3294098", year = 2019 }