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.

This paper presents the formal development of the memory management module of a real time operating system. The interesting feature of this type of memory manager is that its dynamic memory allocation/reallocation mechanism behaves in O(1) (no loops). This brings a serious challenge on the "correct by construction" approach used to build this kind of system. This is due to the necessity to elaborate some delicate algorithms associated with complex data structures. To overcome this challenge, we follow the refinement principles of Event-B: we construct the proved executable code from some initial requirements. This development is interesting because some of the encountered problems are rather necessary to be studied in formal proved developments, among which are a modular encapsulation development, the design pattern of a linked list, and the usage of guarded events to develop pre-conditioned operations. It also gives us the opportunity to study a complex program construction in some general terms going beyond this specific example.

Runtime verification is a dynamic verification technique widely used in practice. In this paper we revisit the runtime verification technique with formula progression, which verifies the execution trace step by step by progressing the desired property written in temporal logic. The previous work did not discuss explicitly the bound for the sizes of expanded formulas, while the successive invoking of formula progression is likely to cause divergence. In this paper, we present the convergent formula progression by introducing a novel fix-point reduction technique, and prove it guarantees the sizes of expanded formulas be always convergent. To the best of our knowledge, this is the first work discussing the convergence of formula progression. Furthermore, we implement the new runtime verification framework, and experiments show the efficiency of our proposed strategy.