The Area Method : a Recapitulation

Predrag Janicic (1) , Julien Narboux (2) , Pedro Quaresma (3)

1 Faculty of Mathematics
2 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection
3 Departamento de Matematica

The area method for Euclidean constructive geometry was proposed by Chou et al. in the early 1990's. The method produces human-readable proofs and can efficiently prove many non-trivial geometry theorems. It is one of the most interesting and most successful methods for automated theorem proving in geometry and probably the most successful in the domain of automated production of readable proofs in geometry. In this paper, we provide a first complete presentation of the method. We provide both algorithmic and implementation details that were omitted in the original presentations. We also give a variant of Chou, Gao and Zhang's axiom system. Based on this axiom system, we proved formally all the lemmas needed by the method and its soundness using the Coq proof assistant.

Mots clés: automatic reasoning; geometry; Coq; area method; formalization

Domaines: Logique en informatique [cs.LO]

Predrag Janicic, Julien Narboux, Pedro Quaresma. The Area Method : a Recapitulation. Journal of Automated Reasoning, 2012, 48 (4), pp.489-532. ⟨10.1007/s10817-010-9209-7⟩. ⟨hal-00426563v2⟩