What is a lattice? A partially ordered set where every pair of elements has a meet (greatest lower bound) and a join (least upper bound). What three levels form KindScript's containment lattice? Directory ⊒ File ⊒ Declaration. Higher = more general (contains more). Lower = more specific. Why does KindScript need canonicalization but Oxide doesn't? KindScript's CodeLocs have internal containment (directories subsume files), so sets can contain redundant elements. Oxide's loans are flat/atomic — no loan subsumes another. What is a powerset lattice? The set of all subsets of S, ordered by ⊆. Meet = intersection, join = union. Always a complete Boolean algebra. What does meet(dir, file) return? The file (if the file is under the directory). The file is the greatest lower bound — the most specific location contained by both.