Proving Negative Conjectures on Equational Theories using Induction and Abstract Interpretation
Résumé
In this paper we present a method to prove automatically initial negative properties on equational specifications. This method tends to combine induction and abstract interpretation. Induction is performed in a classical way using cover sets and rewriting. Abstract interpretation is done using an additional set of equations used to approximate the initial model into an abstract one. Like in the methods dedicated to the proof by induction of positive properties, the equational specification is supposed to be oriented into a terminating, confluent and complete term rewriting system.