Both command sourcing (CS) and event sourcing (ES) rely on determinism for correctness.
The correctness condition for ES is the determinism (purity) of the function
State -> Event -> State. Given that this function is deterministic, aka it always maps the same inputs to the same ouputs, we can rely on it to reconstitute state at any point in time. Determinism is typically achieved by ensuring that the
Event has all required information to make the state transition, ie no side effects. The
Event then is a sort of "closure" of all pertinent information about the event.
The correctness condition for CS is the determinism of the function
State -> Command -> Event. Herein lies one of the distinctions between command sourcing and event sourcing - a program can control its output, but it not its input. Since one can't control the input, aka command, one can't in general, enrich it with all required information to make the above function deterministic. A consequence of this is that you can't simply replay a