A local shape analysis based on separation logic

Dino Distefano, Peter W. O'Hearn, Hongseok Yang
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Read: 26 April 2021

International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Pages 287-302
Topic(s): tools verification
Note(s): permission logic, separation logic, symbolic execution, abstract interpretation
Papers: berdine:aplas:2005, calcagno:sas:2006, calcagno:popl:2009

This paper moves beyond berdine:aplas:2005 to support reasoning about loops by augmenting symbolic execution with abstract interpretation. This allows them to reason about loops that reverse lists, deallocate entire lists, append lists, copy lists, insert/delete from the middle of a list, delete and filter circular lists, and deallocate ranges of values from sorted lists.

As in the slightly later paper with more authors calcagno:sas:2006, the idea is to use a fragment of separation logic as an abstract domain, to define an abstraction operator (“canonicalization rules”) and then to use least fixpoint to infer loop invariants.

Unlike their later work (calcagno:popl:2009), they restrict themselves to intra-procedural analyses although there is a slightly hard to follow sketch near the end which may be an early form of what the later paper called “biabduction”.

This is a rather strange paper: it does not feel quite finished. The paper says that their shape analysis is less powerful than the state of the art at the time, their canonicalization rewrite rules don’t produce a minimal result, they don’t know if the rewrite rules are confluent so they apply rules in a fixed order, the reporting on performance results is extremely vague, and some definitions are (in their words) “not exactly pretty”. The argument they make at the start of the paper (when comparing against the state of the art) is that their approach “is of interest because it suggests a genuinely different approach which has promise for the central problem of obtaining modular analyses.” (This promise was later kept in calcagno:popl:2009.)