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Verification of the Completeness of Unification Algorithms `a la Andreia B. Avelar1

Summary: Verification of the Completeness of Unification Algorithms `a la
Andr´eia B. Avelar1
, Fl´avio L. C. de Moura2
, Andr´e Luiz Galdino3
and Mauricio Ayala-Rinc´on1,2
Departamentos de 1
Matem´atica e 2
Ci^encia da Computa¸c~ao
Universidade de Bras´ilia, Bras´ilia, Brazil
Departamento de Matem´atica, Universidade Federal de Goi´as, Catal~ao, Brazil
{andreia@mat, ayala@, flaviomoura@, galdino@}.unb.br
Abstract. This work presents a general methodology for verification of the completeness of first-
order unification algorithms `a 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.
1 Introduction


Source: Ayala-Rincón, Mauricio - Departamento de Matemática, Universidade de Brasília


Collections: Mathematics