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**1 - 2**of**2**### Verification of the Completeness of Unification Algorithms à la

"... Abstract. This work presents a general methodology for verification of the completeness of firstorder unification algorithms à 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 u ..."

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Abstract. This work presents a general methodology for verification of the completeness of firstorder unification algorithms à 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

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"... This work presents a formalization of the theorem of existence of most general unifiers in firstorder signatures on the higher-order proof assistant PVS. The proof is close to the textbook proofs that are based on proving the correctness of the well-known Robinson’s first-order unification algorithm ..."

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This work presents a formalization of the theorem of existence of most general unifiers in firstorder signatures on the higher-order proof assistant PVS. The proof is close to the textbook proofs that are based on proving the correctness of the well-known Robinson’s first-order unification algorithm and it was applied inside a complete PVS development for term rewriting systems that provides a complete formalization of the Knuth-Bendix Critical Pair theorem. The formalization methodology can be directly applied to verify unification algorithms in the style of the original Robinson’s one as it is illustrated. 1