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Testing and debugging networks /in situ/ is notoriously difficult. Many vital correctness properties involve histories over multiple packets (e.g., prior established connections). Checking such properties requires /cross-packet state/, which cannot be fully captured on stateless switch hardware.Recent SDN work is enabling limited switch operations on persistent state. We present runtime checking of cross-packet correctness properties as a unique and instructive use case for developing stateful switch primitives. In this paper, we examine a set of cross-packet properties and distill from them switch features needed to monitor their correctness. We then contrast these against features provided by current approaches to switch state in SDNs and identify semantic gaps with an eye toward informing future switch instruction sets.