Mooly Sagiv
Thomas Reps
Reinhard Wilhelm
Abstract
This article concerns the static analysis of programs that perform destructive updating on heap-allocated storage. We give an algorithm that uses finite shape graphs to approximate conservatively the possible “shapes” that heap-allocated structures in a program can take on. For certain programs, our technique is able to determine such properties as (1) when the input to the program is a list, the output is also a list and (2) when the input to the program is a tree, the output is also a tree. For example, the method can determine that “listness” is preserved by (1) a program that performs list reversal via destructive updating of the input list and (2) a program that searches a list and splices a new element into the list. None of the previously known methods that use graphs to model the program's store are capable of determining that “listness” is preserved on these examples (or examples of similar complexity). In contrast with most previous work, our shape analysis algorithm is even accurate for certain programs that update cyclic data structures; that is, it is sometimes able to show that when the input to the program is a circular list, the output is also a circular list. For example, the shape-analysis algorithm can determine that an insertion into a circular list preserves “circular listness.”
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Index Terms
Solving shape-analysis problems in languages with destructive updating
Reviews
Max Hailperin
An abstract interpretation of imperative programs mutating pointer-based structures is presented. This interpretation can reach conclusions such as that inserting into a circular list yields a circular list, while inserting into an acyclic list yields an acyclic list. Each program point is assigned an abstract store resulting from three forms of abstraction: joining information from all program paths leading to the point, generalizing over program inputs, and bounding the number of objects. The last of these embodies the biggest innovation: the manner in which the unboundedly large collection of run-time objects is mapped to an analysis-time collection that is at worst exponentially large in the program size. One abstract object is used per alias configuration, that is, per possible set of aliased pointer variables, including one abstract object to represent all concrete objects that are not directly referenced by any variable. The authors also associate an is-shared bit with each abstract object. This bit shows whether sharing in the abstract store reflects sharing in the concrete store or is an artifact of abstraction. The main empirical result of the paper is that synergism between these is-shared bits and the per-alias-configuration allocation of abstract objects produces precise analysis results for a number of example programs. The authors skillfully use a running example to open up what would otherwise be a difficult paper to a potential audience of empirical investigators and practical adapters, who will find plenty of fertile ground for their work.
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