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A step-indexed Kripke model of hidden state

Published online by Cambridge University Press:  31 August 2012

JAN SCHWINGHAMMER ,
LARS BIRKEDAL ,
FRANÇOIS POTTIER ,
BERNHARD REUS ,
KRISTIAN STØVRING  and
HONGSEOK YANG
JAN SCHWINGHAMMER
Affiliation:
Saarland University, Saarbrücken, Germany
LARS BIRKEDAL
Affiliation:
IT University of Copenhagen, Copenhagen, Denmark
FRANÇOIS POTTIER
Affiliation:
INRIA Paris – Rocquencourt, Le Chesnay, France
BERNHARD REUS
Affiliation:
University of Sussex, Brighton, United Kingdom
KRISTIAN STØVRING
Affiliation:
University of Copenhagen, Copenhagen, Denmark
HONGSEOK YANG
Affiliation:
University of Oxford, Oxford, United Kingdom
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Abstract

Frame and anti-frame rules have been proposed as proof rules for modular reasoning about programs. Frame rules allow the hiding of irrelevant parts of the state during verification, whereas the anti-frame rule allows the hiding of 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 generalised frame and anti-frame rules, where invariants are generalised to families of invariants indexed over preorders. This generalisation enables reasoning about some well-bracketed as well as (locally) monotone uses of local state.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Issue 1 , February 2013 , pp. 1 - 54
Copyright
Copyright © Cambridge University Press 2012

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