A refinement hierarchy for free list memory allocators

Abstract

Existing implementations of dynamic memory allocators (DMA) employ a large spectrum of policies and techniques. The formal specifications of these techniques are quite complicated in isolation and very complex when combined. Therefore, the formal reasoning on a specific DMA implementation is difficult for automatic tools and mostly single-use. This paper proposes a solution to this problem by providing formal models for a full class of DMA, the free list class. To obtain manageable formal reasoning and reusable formal models, we organize these models in a hierarchy ranked by refinement relations. We prove the soundness of models and refinement relations using an off-the-shelf theorem prover. We demonstrate that our hierarchy is a basis for an algorithm theory for the class of free list DMA: it abstracts various existing implementations of DMA and leads to new DMA implementations. We illustrate its application to model-based code generation, testing, run-time verification, and static analysis.