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A Complete Gentzen-style Axiomatization for Set Constraints

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Set constraints are inclusion relations between expressions denoting sets of ground terms over a ranked alphabet. They are the main ingredient in set-based program analysis. In this paper we provide a Gentzen-style axiomatization for sequents Φ\forceΨ, where Φ and Ψ are finite sets of set constraints, based on the axioms of termset algebra. Sequents of the restricted form Φ\force\bottom correspond to positive set constraints, and those of the more general form Φ\forceΨ correspond to systems of mixed positive and negative set constraints. We show that the deductive system is (i) complete for the restricted sequents Φ\force\bottom over standard models, (ii) incomplete for general sequents Φ\forceΨ over standard models, but (iii) complete for general sequents over set-theoretic termset algebras.

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1995-05

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Cornell University

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computer science; technical report

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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR95-1518

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technical report

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