This has been simmering for a few months now, but there's a really weird phenomenon that Victoria and I noticed about ordering constraints in distributed IVM that deserves to be mentioned somewhere (whilst we plot a full publication). In a distributed IVM maintenance system, "happens before" constraints are not transitive. A slightly less bombastic way of phrasing this might be that in a distributed IVM system, all transitive "happens before" constraints are exposed as pairwise constraints.

Transactions#

Let's start by being a bit clearer about what problem we're talking about. When reasoning about distributed transaction processing, it's customary to abstract away the precise nature of the data. Instead of talking about tables, rows, variables, etc..., you simply think of abstract values ($A$, $B$, $C$, etc...). Similarly, each transaction $T$ represents some abstract computation; all we know about it is the set of values it reads (the "read set" $R(T)$) and the set of values it writes (the "write set" $W(T)$). Values are versioned, typically with some timestamp assigned to the transaction. So if $A$ is in $T_{42}$s write set, after $T_{42}$ finishes, we have $A$ version 42, or $A_{42}$. If $A$ isn't in $T_{42}$s write set, then it inherits its value from the prior version (i.e., $A_{42} = A_{41}$).

Typically, we think of transactions as running sequentially. Given some collection of transactions $T_1, \ldots, T_N$, we execute them one at a time. I'll write this as $$(A_{i+1}, B_{i+1}, \ldots) = T_{i+1}(A_i, B_i, \ldots)$$ Of course this is boring, and not very distributed... but it gives us a baseline for correctness that we call a serial ordering. We have the flexibility to execute the transactions however we want, as long as we can guarantee that we'll end up with the same final state $A_N, B_N, \ldots$.