We describe an abstract interpretation based framework for proving relationships between sizes of memory partitions. Instances of this framework can prove traditional properties such as memory safety and program termination but can also establish upper bounds on usage of dynamically allocated memory. Our framework also stands out in its ability to prove properties of programs manipulating both heap and arrays which is considered a difficult task. Technically, we define an abstract domain that is parameterized by an abstract domain for tracking memory partitions (sets of memory locations) and by a numerical abstract domain for tracking relationships between cardinalities of the partitions. We describe algorithms to construct the transfer functions for the abstract domain in terms of the corresponding transfer functions of the parameterized abstract domains. A prototype of the framework was implemented and used to prove interesting properties of realistic programs, including programs that could not have been automatically analyzed before.
We study how program analysis can be used to:• Automatically prove partial correctness of correct programs. • Discover, locate, and diagnose bugs in incorrect programs. Specifically, we present an algorithm that analyzes sorting programs that manipulate linked lists. A prototype of the algorithm has been implemented.We show that the algorithm is sufficiently precise to discover that (correct versions) of bubble-sort and insertion-sort procedures do, in fact, produce correctly sorted lists as outputs, and that the invariant "is-sorted" is maintained by listmanipulation operations such as element-insertion, elementdeletion, and even destructive list reversal and merging of two sorted lists. When we run the algorithm on erroneous versions of bubble-sort and insertion-sort procedures, it is able to discover and sometimes even locate and diagnose the error.
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