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

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

2012-03-28

arxiv.org/abs/1203.6160v1

EPTCS 81, 2012, pp. 63-78

Computer Science

Logic in Computer Science

In Proceedings LSFA 2011, arXiv:1203.5423

Scientific paper

10.4204/EPTCS.81.5

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.

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