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We propose a hierarchical abstract domain for the analysis of free-listmemory allocators that tracks shape and numerical properties about both theheap and the free lists. Our domain is based on Separation Logic extended withpredicates that capture the pointer arithmetics constraints for the heap-listand the shape of the free-list. These predicates are combined using ahierarchical composition operator to specify the overlapping of the heap-listby the free-list. In addition to expressiveness, this operator leads to acompositional and compact representation of abstract values and simplifies theimplementation of the abstract domain. The shape constraints are combined withnumerical constraints over integer arrays to track properties about theallocation policies (best-fit, first-fit, etc). Such properties are out of thescope of the existing analyzers. We implemented this domain and we show itseffectiveness on several implementations of free-list allocators.

Hierarchical Shape Abstraction for Analysis of Free-List Memory Allocators