A Coq Tactic for Equality Learning in Linear Arithmetic

Sylvain Boulmé (1) , Alexandre Maréchal (1)

1 VERIMAG - IMAG - VERIMAG

Coq provides linear arithmetic tactics like omega or lia. Currently, these tactics let the current goal unchanged when they can not prove it. 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. The paper describes how we have implemented this idea in a new Coq tactic, dealing with linear arithmetic over rationals. It also illustrates that equality learning allows our tactic to interact with other Coq tactics.

Mots clés: Linear Programming; Clause Learning; Skeptical Approach

Domaines: Logique en informatique [cs.LO]

Sylvain Boulmé, Alexandre Maréchal. A Coq Tactic for Equality Learning in Linear Arithmetic. 2017. ⟨hal-01505598v1⟩