Etude X

Category Optics

Lenses, prisms, and traversals for controlled focus.

Core Notes

Optics formalize focus: lenses read/write a part, prisms select variants, traversals sweep many.

lens = (get : S→A, set : S×A→S)
CRDTs map cleanly: focus on replica state, merge through a lens, lift back.

Applied Thread

Applied: use a lens to isolate a field, apply a delta, and prove the reconstruction preserves invariants.

trace: Def → Check(lens laws) → Counterexample(bad set) → Repair(fix)