Data set identifiers

[knoepfel]

Data cells belong to data layers. A given data cell in data layer $A$ is then specified by the identifier $(A, i)$, where $i$ is the index of the data cell in data layer $A$. Data cells, however, can be nested according to a hierarchy. For example, a data cell residing in the data-layer hierarchy $A \rightarrow B \rightarrow C$ is identified by an ordered tuple of identifiers:

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

which denotes that data cell $A_1$ contains (in the mathematical sense) a nested data cell $B_2$, which in turn contains a nested data cell $C_3$. In addition, the identifier $(A_1, B_2, C_3)$ denotes a unique data cell that is different from a data cell identified by $(A_2, B_2, C_3)$.

The set of data-cell 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.