A relational approach to interprocedural shape analysis

Originally published on dl.acm.org


Bertr, Jeannet, Alexey Loginov, Thomas W. Reps and Mooly Sagiv


This article addresses the verification of properties of imperative programs with recursive procedure calls, heap-allocated storage, and destructive updating of pointer-valued fields, that is, interprocedural shape analysis. The article makes three contributions.

— It introduces a new method for abstracting relations over memory configurations for use in abstract interpretation.

— It shows how this method furnishes the elements needed for a compositional approach to shape analysis. In particular, abstracted relations are used to represent the shape transformation performed by a sequence of operations, and an overapproximation to relational composition can be performed using the meet operation of the domain of abstracted relations.

— It applies these ideas in a new algorithm for context-sensitive interprocedural shape analysis. The algorithm creates procedure summaries using abstracted relations over memory configurations, and the meet-based composition operation provides a way to apply the summary transformer for a procedure P at each call site from which P is called.

The algorithm has been applied successfully to establish properties of both (i) recursive programs that manipulate lists and (ii) recursive programs that manipulate binary trees.

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