Refinement verification of the lazy caching algorithm

The lazy caching algorithm of Afek et al. (ACM Trans. Program. Lang. Syst. 15, 182–206, 1993) is a protocol that allows the use of local caches with delayed updates. It results in a memory model that is not atomic (linearizable) but only sequentially consistent as defined by Lamport. In Distributed Computing 12 (1999), specifying and proving sequential consistency for the lazy caching algorithm was made into a benchmark for verification models. The present note contains such a specification and proof. It provides a simulation from the implementation to the abstract specification. The concrete verification only relies on the state space and the next-state relation. All behavioural aspects are treated in theories independent of the specific algorithm. The proofs of the underlying theories and of the concrete algorithm have been verified with the proof assistant PVS.