We introduce an interleaving operational semantics for describing the client-observable behaviour of atomic transactions on distributed key-value stores. Our semantics builds on abstract states comprising centralised, global key-value stores and partial client views. Using our abstract states, we present operational definitions of well-known consistency models in the literature, and prove them to be equivalent to their existing declarative definitions using abstract executions. We explore two applications of our operational framework: 1) verifying that the COPS replicated database and the Clock-SI partitioned database satisfy their consistency models using trace refinement, and 2) proving invariant properties of client programs.
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