A Coq Tactic for Equality Learning in Linear Arithmetic

Abstract

Abstract. Coq provides linear arithmetic tactics like omega or lia. Currently, these tactics either fully prove the goal in progress, or fail. We propose to improve this behavior: when the goal is not provable in linear arithmetic, we inject in hypotheses new equalities discovered from the linear inequalities. These equalities may help other Coq tactics to discharge the goal. In other words, we apply -in interactive proofsone of the seminal idea of SMT-solving: combining tactics by exchanging equalities. The paper describes how we have implemented equality learning in a new Coq tactic, dealing with linear arithmetic over rationals. It also illustrates how this tactic interacts with other Coq tactics.

The Verified Polyhedron Library: an Overview

“…In particular, if the equalities and inequalities in the hypotheses form an empty polyhedron, that is, are contradictory, the goal is proved (ex falso quodlibet). See details in [6].…”