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Local Reasoning about Programs that Alter Data Structures
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
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LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
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Permission accounting in separation logic
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Separation logic, abstraction and inheritance
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Separation Logic Contracts for a Java-Like Language with Fork/Join
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Implicit Dynamic Frames: Combining Dynamic Frames and Separation Logic
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Verification of Concurrent Programs with Chalice
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SAS'03 Proceedings of the 10th international conference on Static analysis
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The relationship between separation logic and implicit dynamic frames
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ACM Transactions on Programming Languages and Systems (TOPLAS)
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Methodologies for static program verification and analysis often support recursive predicates in specifications, in order to reason about recursive data structures. Intuitively, a predicate instance represents the complete unrolling of its definition; this is the equirecursive interpretation. However, this semantics is unsuitable for static verification, when the recursion becomes unbounded. For this reason, most static verifiers differentiate between, e.g., a predicate instance and its corresponding body, while providing a facility to map between the two; this is the isorecursive semantics. While this latter interpretation is usually implemented in practice, only the equirecursive semantics is typically treated in theoretical work. In this paper, we provide both an isorecursive and an equirecursive formal semantics for recursive definitions in the context of Chalice, a verification methodology based on implicit dynamic frames. We show that development of such formalisations requires addressing several subtle issues, such as the possibility of infinitely-recursive definitions and the need for the isorecursive semantics to correctly reflect the restrictions that make it readily implementable. These questions are made more challenging still in the context of implicit dynamic frames, where the use of heap-dependent expressions provides further pitfalls for a correct formal treatment.