Characterizing Provability in BI's Pointer Logic through Resource Graphs
Didier Galmiche, Daniel Méry, Loria Université, Henri Poincaré · 2005
Abstract We propose a characterization of provability in BI's Pointer Logic (PL)that is based on semantic structures called resource graphs. This logic has been defined for reasoning about mutable data structures and results about models andverification have been already provided. Here, we define resource graphs that capture PL models by considering heaps as resources and by using a labellingprocess. We study provability in PL from a new calculus that builds such graphs from which proofs or countermodels can be generated. Properties of soundnessand completeness are proved and the countermodel generation is studied. 1 Introduction Separation logics are logics for reasoning about mutable data structures in which thepre- and postconditions are written in a logic enriched with specific forms of conjunction or implication. In this context, Reynolds has proposed an intuitionistic logic ex-tended with a separation connective \\Lambda [12] and Ishtiaq and O'Hearn have investigatedthe same approach from the point of view of the logic of Bunched Implications (BI)