A Formally Verified Solver for Homogeneous Linear Diophantine Equations

Abstract

Abstract. In this work we are interested in minimal complete sets of solutions for homogeneous linear diophantine equations. Such equations naturally arise during AC-unification-that is, unification in the presence of associative and commutative symbols. Minimal complete sets of solutions are for example required to compute AC-critical pairs. We present a verified solver for homogeneous linear diophantine equations that we formalized in Isabelle/HOL. Our work provides the basis for formalizing AC-unification and will eventually enable the certification of automated AC-confluence and AC-completion tools.