To expand on this, the first level of equivalence between two data models is to show that there's a one-to-one correspondence between their value spaces. That's tricky to achieve, but feasible. To do a perfect one-to-one correspondence, you tend to find that the representation in one of the models is rather contorted and unnatural, and in practice people tend to prefer mappings that are imperfect but more natural - we see that all the time with XML-to-JSON mappings.
The second level of equivalence is to show that there's a one-to-one correspondence between the state transitions (updates) supported by the two models. That's very much harder.
Michael Kay
Saxonica
