A Formalization of the Theorem of Existence of First-Order Most General Unifiers

Andréia B Avelar
(Universidade de Brasília)
André L Galdino
(Universidade Federal de Goiás)
Flávio LC de Moura
(Universidade de Brasília)
Mauricio Ayala-Rincón
(Universidade de Brasília)

This work presents a formalization of the theorem of existence of most general unifiers in first-order signatures in the higher-order 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 first-order unification algorithm. The formalization was applied inside a PVS development for term rewriting systems that provides a complete formalization of the Knuth-Bendix 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.

In Simona Ronchi della Rocca and Elaine Pimentel: Proceedings 6th Workshop on Logical and Semantic Frameworks with Applications (LSFA 2011), Belo Horizonte, Brazil, 27 August 2011, Electronic Proceedings in Theoretical Computer Science 81, pp. 63–78.
Published: 24th March 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.81.5 bibtex PDF
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