Solving disequations
Résumé
We present a general study of equations (objects of form s=t and disequations (objects of form s \ne t) solving. The problem is approached from its fully general mathematical definition clearly separating universally and existentially quantified variables. In addition it is showed to have many connections with unification in equational theories like associativity commutativity, in particular methods similar to those used to solve equational unification problem works in solving disequations. This abstract framework is then applied to study the sufficient completeness of a rewrite rule based definition of a function.