An Application of CLP: Checking the Correctness of Theorems in Geometry

Denis Bouhineau (1) , Laurent Trilling (2) , Jacques Cohen (3)

1 IRIN
2 LSR - IMAG - Laboratoire Logiciels Systèmes Réseaux
3 Brandeis University

Constraint Logic Programming can be advantageously used to deal with quadratic constraints stemming from the verification of planar geometry theorems. A hybrid symbolic--numeric representation involving radicals and multiple precision rationals is used to denote the results of quadratic equations. A unification--like algorithm tests for the equality of two expressions using that representation. The proposed approach also utilizes geometric transformations to reduce the number of quadratic equations defining geometric constructions involving circles and straight lines. A large number (512) of geometry theorems has been verified using the proposed approach. Those theorems had been proven correct using a significantly more complex (exponential) approach in a treatise authored by Chou in 1988. Even though the proposed approach is based on verification -rather than strict correctness utilized by Chou- the efficiency attained is polynomial thus making the approach useful in classroom situations where a construction attempted by student has to be quickly validated or refuted.

Domaines: Environnements Informatiques pour l'Apprentissage Humain; Education

Denis Bouhineau, Laurent Trilling, Jacques Cohen. An Application of CLP: Checking the Correctness of Theorems in Geometry. Constraints, 1999, 4 (4), pp.383--405. ⟨hal-00961981⟩