2 research outputs found
Sound Automation of Magic Wands (extended version)
The magic wand (also called separating implication) is a
separation logic connective commonly used to specify properties of partial data
structures, for instance during iterative traversals. A footprint of a magic
wand formula is a state that, combined with any state in
which holds, yields a state in which holds. The key challenge of
proving a magic wand (also called packaging a wand) is to find such a
footprint. Existing package algorithms either have a high annotation overhead
or, as we show in this paper, are unsound. We present a formal framework that
precisely characterises a wide design space of possible package algorithms
applicable to a large class of separation logics. We prove in Isabelle/HOL that
our formal framework is sound and complete, and use it to develop a novel
package algorithm that offers competitive automation and is sound. Moreover, we
present a novel, restricted definition of wands and prove in Isabelle/HOL that
it is possible to soundly combine fractions of such wands, which is not the
case for arbitrary wands. We have implemented our techniques for the Viper
language, and demonstrate that they are effective in practice.Comment: Extended version of CAV 2022 publicatio
Sound Automation of Magic Wands (extended version)
The magic wand (also called separating implication) is a separation logic connective commonly used to specify properties of partial data structures, for instance during iterative traversals. A footprint of a magic wand formula is a state that, combined with any state in which holds, yields a state in which holds. The key challenge of proving a magic wand (also called packaging a wand) is to find such a footprint. Existing package algorithms either have a high annotation overhead or, as we show in this paper, are unsound. We present a formal framework that precisely characterises a wide design space of possible package algorithms applicable to a large class of separation logics. We prove in Isabelle/HOL that our formal framework is sound and complete, and use it to develop a novel package algorithm that offers competitive automation and is sound. Moreover, we present a novel, restricted definition of wands and prove in Isabelle/HOL that it is possible to soundly combine fractions of such wands, which is not the case for arbitrary wands. We have implemented our techniques for the Viper language, and demonstrate that they are effective in practice