NDLI: Goal-directed weakening of abstract interpretation results

Content Provider	ACM Digital Library
Author	Yi, Kwangkeun Yang, Hongseok Seo, Sunae Han, Taisook
Copyright Year	2007
Abstract	One proposal for automatic construction of proofs about programs is to combine Hoare logic and abstract interpretation. Constructing proofs is in Hoare logic. Discovering programs' invariants is done by abstract interpreters. One problem of this approach is that abstract interpreters often compute invariants that are not needed for the proof goal. The reason is that the abstract interpreter does not know what the proof goal is, so it simply tries to find as strong invariants as possible. These unnecessary invariants increase the size of the constructed proofs. Unless the proof-construction phase is notified which invariants are not needed, it blindly proves all the computed invariants. In this article, we present a framework for designing algorithms, called abstract-value slicers, that slice out unnecessary invariants from the results of forward abstract interpretation. The framework provides a generic abstract-value slicer that can be instantiated into a slicer for a particular abstract interpretation. Such an instantiated abstract-value slicer works as a post-processor to an abstract interpretation in the whole proof-construction process, and notifies to the next proof-construction phase which invariants it does not have to prove. Using the framework, we designed an abstract-value slicer for an existing relational analysis and applied it on programs. In this experiment, the slicer identified 62%--81% of the computed invariants as unnecessary, and resulted in 52%--84% reduction in the size of constructed proofs.
File Format	PDF
ISSN	01640925
e-ISSN	15584593
DOI	10.1145/1286821.1286830
Volume Number	29
Issue Number	6
Journal	ACM Transactions on Programming Languages and Systems (TOPLAS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2007-10-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Abstract interpretation Hoare logic Backward analysis Program verification Static analysis
Content Type	Text
Resource Type	Article
Subject	Software

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