Exercises & discussion prompts

The vault service is re-mounted with a new path while a node-agent plugin that injects it is mid-activation. Which rules fire, in what order, and what does Thm 71 promise about the agent plugin's half-installed effects?

Take the sibling roster. Write its operations 𝒜ₖ (add, drop, list?) with their outcomes. Check Def 44 informally: do any two commute, outcomes included? If list returns an ordered array, does that change the answer? What if it returns a set?

List what an Olai plugin touches: context services, files under the vault, git, the browser, the doorbell. Mark each inside / acquisition / emission. For each emission decide withhold vs compensate, and name the compensation.

What does Cordis owning the Scope buy that Layer / ManagedRuntime alone don't? Is there anything the reactive coeffects need from Effect that Context.Tag can't express? Where does a FAILED fiber's error surface on the Effect side?

Why must the inverse be returned at the point of application (Def 8) rather than paired up front (Def 3)? Find an Olai effect whose correct inverse depends on the state it was applied at.

It is a page. Reconstruct claim (1) — gⱼ(δᵤ) = δ′ᵤ — with three effects and one of them removed; then say in one sentence what clause (2) of Def 42 is needed for.