We present a general theory of serializability, unifying a wide range of transactional algorithms, including some that are yet to come. To this end, we provide a compact semantics in which concurrent transactions push their effects into the shared view (or unpush to recall effects) and pull the effects of potentially uncommitted concurrent transactions into their local view (or unpull to detangle). Each operation comes with simple side-conditions given in terms of commutativity (Lipton’s left-movers and right-movers).

The benefit of this model is that most of the elaborate reasoning (coinduction, simulation, subtle invariants, etc.) necessary for proving the serializability of a transactional algorithm is already proved within the semantic model. Thus, proving serializability (or opacity) amounts simply to mapping the algorithm on to our rules, and showing that it satisfies the rules’ side-conditions.