Rely/Guarantee, Refinement and the ABA Problem: Part 1

Rely/guarantee reasoning provides a compositional way of reasoning about concurrency. The ABA problem occurs in many non-blocking concurrent data structures, where a change made by a concurrent process may be undetected by other processes. Guarantee conditions provide a useful mechanism for reasoning about such changes, as is demonstrated by two non-blocking examples, the Treiber stack and the Herlihy-Wing queue. The ABA problem can be identified by the program making a step where the before and after states do not correspond to a valid step at the sequential level. Therefore, such invalid behaviour relates to a failure of the guarantee condition. As such behaviour is non-linearisable, this suggests a strong relationship between refinement with rely/guarantee and linearisability.