Opacity proof for CaPR+ algorithm

In this paper, we describe an enhanced Automatic Checkpointing and Partial Rollback algorithm(CaPR+) to realize Software Transactional Memory(STM) that is based on continuous conflict detection, lazy versioning with automatic checkpointing, and partial rollback. Further, we provide a proof of correctness of CaPR+ algorithm, in particular, Opacity, a STM correctness criterion, that precisely captures the intuitive correctness guarantees required of transactional memories. The algorithm provides a natural way to realize a hybrid system of pure aborts and partial rollbacks. We have also implemented the algorithm, and shown its effectiveness with reference to the Red-black tree micro-benchmark and STAMP benchmarks. The results obtained demonstrate the effectiveness of the Partial Rollback mechanism over pure abort mechanisms, particularly in applications consisting of large transaction lengths.