Section: New Results

Certified Concurrent Garbage Collector

Participants : David Cachera, Delphine Demange, David Pichardie, Yannick Zakowski.

Concurrent garbage collection algorithms are an emblematic challenge in the area of concurrent program verification. We addressed this problem by proposing a mechanized proof methodology based on the popular Rely-Guarantee (RG) proof technique. We designed a specific compiler intermediate representation (IR) with strong type guarantees, dedicated support for abstract concurrent data structures, and high-level iterators on runtime internals (objects, roots, fields, thread identifiers...). In addition, we defined an RG program logic supporting an incremental proof methodology where annotations and invariants can be progressively enriched. We have formalized the IR, the proof system, and proved the soundness of the methodology in the Coq proof assistant. Equipped with this IR, we have proved the correctness of a fully concurrent garbage collector where mutators never have to wait for the collector. This work has been published in [6] as an extended version of  [22].

In this work, reasoning simultaneously about the garbage collection algorithm and the concrete implementation of the concurrent data-structures it uses would have entailed an undesired and unnecessary complexity. The above proof is therefore conducted with respect to abstract operations which execute atomically. In practice, however, concurrent data-structures uses fine-grained concurrency, for performance reasons. One must therefore prove an observational refinement between the abstract concurrent data-structures and their fined-grained, “linearisable” implementation. To adress this issue, we introduce a methodology inspired by the work of Vafeiadis, and provide the approach with solid semantic foundations. Assuming that fine-grained implementations are proved correct with respect to an RG specification encompassing linearization conditions, we prove, once and for all, that this entails a semantic refinement of their abstraction. This methodology is instantiated to prove correct the main data-structure used in our garbage collector. This work has been published in [20].