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 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 proofs – one 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.

Keywords: Linear Programming; Clause Learning; Skeptical Approach

Domains: Logic in Computer Science [cs.LO]

Sylvain Boulmé, Alexandre Maréchal. A Coq Tactic for Equality Learning in Linear Arithmetic. Interactive Theorem Proving - 9th International Conference, (ITP 2018), Jul 2018, Oxford, United Kingdom. ⟨10.1007/978-3-319-94821-8_7⟩. ⟨hal-01505598v2⟩