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Article Dans Une Revue Journal of Automated Reasoning Année : 2023

A Proof Procedure For Separation Logic With Inductive Definitions and Data

Résumé

A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory reasoning. The calculus is sound and complete, in the sense that a sequent is valid iff it admits a (possibly infinite) proof tree. We show that the procedure terminates in the two following cases: (i) When the inductive rules that define the predicates occurring on the left-hand side of the entailment terminate, in which case the proof tree is always finite. (ii) When the theory is empty, in which case every valid sequent admits a rational proof tree, where the total number of pairwise distinct sequents occurring in the proof tree is doubly exponential w.r.t.\ the size of the end-sequent. We also show that the validity problem is undecidable for a wide class of theories, even with a very low expressive power.

Dates et versions

hal-03562664 , version 1 (09-02-2022)

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Mnacho Echenim, Nicolas Peltier. A Proof Procedure For Separation Logic With Inductive Definitions and Data. Journal of Automated Reasoning, 2023, 67 (3), pp.30. ⟨10.1007/s10817-023-09680-4⟩. ⟨hal-03562664⟩
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