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The Compiler Foundations Project

Shape Analysis with Inductive Recursion Synthesis [abstract] (ACM DL, PDF)
Bolei Guo, Neil Vachharajani, and David I. August
Proceedings of the ACM SIGPLAN 2007 Conference on Programming Language Design and Implementation (PLDI), June 2007.
Accept Rate: 25% (45/178).

Separation logic with recursively defined predicates allows for concise yet precise description of the shapes of data structures. However, most uses of separation logic for program analysis rely on pre-defined recursive predicates, limiting the class of programs analyzable to those that manipulate only a priori data structures. This paper describes a general algorithm based on \emph{inductive program synthesis} that automatically infers recursive shape invariants, yielding a shape analysis based on separation logic that can be applied to any program.

A key strength of separation logic is that it facilitates, via explicit expression of structural separation, local reasoning about heap where the effects of altering one part of a data structure are analyzed in isolation from the rest. The interaction between local reasoning and the global invariants given by recursive predicates is a difficult area, especially in the presence of complex internal sharing in the data structures. Existing approaches, using logic rules specifically designed for the list predicate to unfold and fold linked-lists, again require a priori knowledge about the shapes of the data structures and do not easily generalize to more complex data structures. We introduce a notion of ``truncation points" in a recursive predicate, which gives rise to generic algorithms for unfolding and folding arbitrary data structures.