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

TL;DR

This paper formalizes the theorem of existence of most general unifiers in first-order logic within the PVS proof assistant, closely following textbook proofs and enabling verification of unification algorithms.

Contribution

It provides a formalization aligned with textbook proofs in PVS, supporting verification of unification algorithms and applications in rewriting systems.

Findings

Formalization remains close to textbook proofs

Verified correctness of unification algorithms

Applied in a PVS development for term rewriting

Abstract

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.