Topological Sorting

[Code--Topological Sorting]
Before creating a subsumption matrix for a type hierarchy, ALE needs to topologically sort the types. The topological sorting of the types in a type hierarchy ensures the placement of more general types before more specific ones. This is performed through a depth-first traversal of the hierarchy. For example, to topologically sort the type hierarchy presented in Figure 3.1, we start at $\bot$. Once we have added $\bot$ to our list of topologically sorted types, we continue to a, then b. Since b does not have any subtypes, we go back to a and move to c. Carrying on in the same fashion and adding new types to the list will result in [$\bot$, a, b, c, e, d]. Building a subsumption matrix based on this sorting results in an upper-triangular sparse matrix meaning that the lower left quadrant of the matrix consists only of zeros as in figures 3.2 and 3.3.