Towards Automated Readable Proofs of Ruler and Compass Constructions
This work addresses the need for verifiable and understandable proofs in automated geometry construction, which is incremental as it builds on existing solvers but adds proof generation.
The paper tackles the problem of generating human-readable and formal correctness proofs for ruler and compass constructions, which existing systems lack, by demonstrating that their triangle construction solver ArgoTriCS can cooperate with automated theorem provers to produce such proofs, though they currently rely on high-level lemmas.
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 the present work, 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 Coq or Isabelle/HOL). These proofs currently rely on many high-level lemmas and our goal is to have them all formally shown from the basic axioms of geometry.