 
Summary: Submitted to:
LSFA 2011
c A.B. Avelar, A.L. Galdino, F.L.C. de Moura and M. AyalaRinc´on
A Formalization of the Theorem of Existence of FirstOrder
Most General Unifiers
Departamentos de 1Matem´atica e 2Ci^encia da Computac¸~ao, Universidade de Bras´ilia, Bras´ilia, Brazil
3Departamento de Matem´atica, Universidade Federal de Goi´as, Catal~ao, Brazil
{andreia@mat., flaviomoura@, galdino@, ayala@}unb.br
Andr´eia B Avelar1, Andr´e L Galdino3 , Fl´avio LC de Moura2and Mauricio AyalaRinc´on1,2§
This work presents a formalization of the theorem of existence of most general unifiers in firstorder
signatures in the higherorder proof assistant PVS. The distinguishing feature of this formalization
is that it remains close to the textbook proofs that are based on proving the correctness of the well
known Robinson's firstorder unification algorithm. The formalization was applied inside a PVS
development for term rewriting systems that provides a complete formalization of the KnuthBendix
Critical Pair theorem, among other relevant theorems of the theory of rewriting. In addition, the
formalization methodology has been proved of practical use in order to verify the correctness of
unification algorithms in the style of the original Robinson's unification algorithm.
1 Introduction
A formalization in the proof assistant PVS of the theorem of existence of most general unifiers (mgu's)
in firstorder theories is presented. There are several applications of this theorem on computational logic,
