Readable automated proofs of ruler and compass constructions

Abstract

Although there are several systems that successfully generate construction steps for ruler and compass construction problems, none of them provides readable synthetic correctness proofs for generated constructions. In this paper, we demonstrate how our triangle construction solver ArgoTriCS can cooperate with automated theorem provers for first-order logic and coherent logic so that it generates construction correctness proofs, that are both human-readable and formal (can be checked by interactive theorem provers such as Isabelle/HOL or Coq). For this purpose we identified a set of relevant lemmas and developed a coherent logic prover GCProver customized for geometry construction problems. Our experiments show that results are much better than with general purpose theorem provers.