A step-indexed Kripke Model of Hidden State

Abstract : Frame and anti-frame rules have been proposed as proof rules for modular reasoning about programs. Frame rules allow one to hide irrelevant parts of the state during verification, whereas the anti-frame rule allows one to hide local state from the context. We discuss the semantic foundations of frame and anti-frame rules, and present the first sound model for Charguéraud and Pottier's type and capability system including both of these rules. The model is a possible worlds model based on the operational semantics and step-indexed heap relations, and the worlds are given by a recursively defined metric space. We also extend the model to account for Pottier's generalized frame and anti-frame rules, where invariants are generalized to families of invariants indexed over preorders. This generalization enables reasoning about some well-bracketed as well as (locally) monotone uses of local state.
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Article dans une revue
Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2013, 23 (1), pp.1--54
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Contributeur : François Pottier <>
Soumis le : vendredi 11 janvier 2013 - 10:10:25
Dernière modification le : mercredi 14 décembre 2016 - 01:07:56
Document(s) archivé(s) le : vendredi 12 avril 2013 - 11:20:23


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  • HAL Id : hal-00772757, version 1



Jan Schwinghammer, Lars Birkedal, François Pottier, Bernhard Reus, Kristian Støvring, et al.. A step-indexed Kripke Model of Hidden State. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2013, 23 (1), pp.1--54. <hal-00772757>



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