Verifying Concurrent Memory Reclamation Algorithms with Grace

Memory management is one of the most complex aspects of modern concurrent algorithms, and various techniques proposed for it--such as hazard pointers, read-copy-update and epoch-based reclamation--have proved very challenging for formal reasoning. In this paper, we show that different memory reclamation techniques actually rely on the same implicit synchronisation pattern, not clearly reflected in the code, but only in the form of assertions used to argue its correctness. The pattern is based on the key concept of a grace period, during which a thread can access certain shared memory cells without fear that they get deallocated. We propose a modular reasoning method, motivated by the pattern, that handles all three of the above memory reclamation techniques in a uniform way. By explicating their fundamental core, our method achieves clean and simple proofs, scaling even to realistic implementations of the algorithms without a significant increase in proof complexity. We formalise the method using a combination of separation logic and temporal logic and use it to verify example instantiations of the three approaches to memory reclamation.