Verification of the Completeness of Unification Algorithms à la Robinson

Abstract

AbstractThis work presents a general methodology for verification of the completeness of first-order unification algorithms à la Robinson developed in the higher-order proof assistant PVS. The methodology is based on a previously developed formalization of the theorem of existence of most general unifiers for unifiable terms over first-order signatures. Termination and soundness proofs of any unification algorithm are proved by reusing the formalization of this theorem and completeness should be proved according to the specific way in that non unifiable inputs are treated by the algorithm.KeywordsPropositional CalculusFunction SymbolGeneral MethodologyUnification AlgorithmProof AssistantThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.