Local Rely-Guarantee Conditions for Linearizability and Lock-Freedom

Rely-guarantee reasoning specifications typically consider all components of a concurrent system. For the important case where components operate on a shared data object, we derive a local instance of rely-guarantee reasoning, which permits specifications to examine a single pair of representative components only. Based on this instance, we define local proof obligations for linearizability and lock-freedom, which we then apply to a non-blocking concurrent stack with explicit memory reuse. Both the derivation of this local instance and its application are mechanized in the KIV interactive theorem prover.