NDLI: Analyzing Program Analyses

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Analyzing Program Analyses

Content Provider	ACM Digital Library
Author	Ranzato, Francesco Logozzo, Francesco Giacobazzi, Roberto
Abstract	We want to prove that a static analysis of a given program is complete, namely, no imprecision arises when asking some query on the program behavior in the concrete (ie, for its concrete semantics) or in the abstract (ie, for its abstract interpretation). Completeness proofs are therefore useful to assign confidence to alarms raised by static analyses. We introduce the completeness class of an abstraction as the set of all programs for which the abstraction is complete. Our first result shows that for any nontrivial abstraction, its completeness class is not recursively enumerable. We then introduce a stratified deductive system to prove the completeness of program analyses over an abstract domain A. We prove the soundness of the deductive system. We observe that the only sources of incompleteness are assignments and Boolean tests --- unlikely a common belief in static analysis, joins do not induce incompleteness. The first layer of this proof system is generic, abstraction-agnostic, and it deals with the standard constructs for program composition, that is, sequential composition, branching and guarded iteration. The second layer is instead abstraction-specific: the designer of an abstract domain A provides conditions for completeness in A of assignments and Boolean tests which have to be checked by a suitable static analysis or assumed in the completeness proof as hypotheses. We instantiate the second layer of this proof system first with a generic nonrelational abstraction in order to provide a sound rule for the completeness of assignments. Orthogonally, we instantiate it to the numerical abstract domains of Intervals and Octagons, providing necessary and sufficient conditions for the completeness of their Boolean tests and of assignments for Octagons.
Starting Page	261
Ending Page	273
Page Count	13
File Format	MPEG PDF
ISBN	9781450333009
DOI	10.1145/2676726.2676987
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2015-01-14
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Abstract interpretation Abstract domain
Content Type	Text Video
Resource Type	Article

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