Submitted to CADE-17
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Abstract:
Abstract. Shostak's decision procedure [Sho84] for equality in the combination of solvable and canonizable theories has been around for nearly two decades. Variations of this decision procedure have been implemented in a number of systems including STP [SSMS82], EHDM [EHD93], PVS [ORS92], STeP [MT96], and SVC [BDL96]. The algorithm is extremely subtle and a correctness argument for it has remained elusive. A previous paper by Cyrluk, Lincoln, and Shankar [CLS96] gave a rigorous presentation of the algorithm but only outlined its proof. Shostak's algorithm and all previously published variants of it are in fact incomplete. We describe a variation of Shostak's algorithm as a system of transformations on sets of equalities, along with straightforward proofs of soundness and completeness. 1
Citations
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