Hierarchical Shape Abstraction for Analysis of Free List Memory Allocators

We propose a hierarchical abstract domain for the analysis of free-list memory allocators that tracks shape and numerical properties about both the heap and the free lists. Our domain is based on Separation Logic extended with predicates that capture the pointer arithmetics constraints for the heap-list and the shape of the free-list. These predicates are combined using a hierarchical composition operator to specify the overlapping of the heap-list by the free-list. In addition to expressiveness, this operator leads to a compositional and compact representation of abstract values and simplifies the implementation of the abstract domain. The shape constraints are combined with numerical constraints over integer arrays to track properties about the allocation policies (best-fit, first-fit, etc). Such properties are out of the scope of the existing analyzers. We implemented this domain and we show its effectiveness on several implementations of free-list allocators.