Data set identifiers

[knoepfel]

Data sets belong to data families. A given data set in family $A$ is then specified by the family element identifier $(A, i)$, where $i$ is the index of the data set within the family labeled $A$. Data sets, however, can be nested according to a hierarchy. For example, a data set residing in the family hierarchy $A \rightarrow B \rightarrow C$ is identified by an ordered tuple of family element identifiers:

$\left((A, 1), (B, 2), (C, 3)\right) = (A_1, B_2, C_3)$

which denotes that data set $A_1$ contains (in the mathematical sense) a nested data set $B_2$, which in turn contains a nested data set $C_3$. In addition, the identifier $(A_1, B_2, C_3)$ denotes a unique data set that is different from a data set identified by $(A_2, B_2, C_3)$, because each family element identifier is specified relative to the family element identifiers that precede it.

The set of data set identifiers are partially ordered and satisfy the following comparison operations:

• $(A_1, B_2, C_3) < (A_1, B_2) < (A_1) < ()$
• $(A_i, B_j, C_k) = (D_l, E_m, F_n)$ only if $A = D$, $B = E$, $C = F$, $i = l$, $j = m$, and $k = n$.

The length or depth of each identifier is its number of entries (e.g. the depth of $(A_7, B_9, C_5)$ is 3).

To determine whether two identifiers may be compared, the longer identifier is truncated to the same length as the shorter identifier. If the truncated identifier is equal to the shorter identifier, then the two identifiers may be compared.