Verification of the completeness of unification algorithms à la Robinson

Authors:
Andréia B. Avelar;Flávio L. C. de Moura;André Luiz Galdino;Mauricio Ayala-Rincón
Affiliations:
Departamentos de Matemática e;Ciência da Computação, Universidade de Brasília, Brasília, Brazil;Departamento de Matemática, Universidade Federal de Goiás, Catalão, Brazil;Departamentos de Matemática e and Ciência da Computação, Universidade de Brasília, Brasília, Brazil
Venue:
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
Year:
2010

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Abstract

This 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.