relations: Phase 2 reachability + roots/leaves + cycles (engine.sx, kind-parameterized closure) + 24 tests

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

plans/relations-on-sx.md

@@ -18,7 +18,7 @@ links. Reuses `lib/datalog/` — does not reimplement the engine.
 
 ## Status (rolling)
 
-`bash lib/relations/conformance.sh` → **22/22** (Phase 1 complete)
+`bash lib/relations/conformance.sh` → **46/46** (Phases 1–2 complete)
 
 ## Ground rules
 
@@ -72,11 +72,11 @@ lib/relations/federation.sx
 
 ## Phase 2 — Reachability + cycles
 
-- [ ] recursive reachability rules: `ancestors`, `descendants`, `reachable?(A,B)`
+- [x] recursive reachability rules: `ancestors`, `descendants`, `reachable?(A,B)`
   (transitive closure over a kind, the acl inheritance shape)
-- [ ] `roots` / `leaves` (no parents / no children) for a kind
-- [ ] cycle detection: `cycle?(X)` ⇔ `reachable(X, X)`; `acyclic?(db, kind)`
-- [ ] `lib/relations/tests/reach.sx` — deep chains, diamonds, disconnected nodes,
+- [x] `roots` / `leaves` (no parents / no children) for a kind
+- [x] cycle detection: `cycle?(X)` ⇔ `reachable(X, X)`; `acyclic?(db, kind)`
+- [x] `lib/relations/tests/reach.sx` — deep chains, diamonds, disconnected nodes,
   self-loops, multi-kind isolation
 
 ## Phase 3 — Typed relations + path explanation
@@ -100,6 +100,21 @@ lib/relations/federation.sx
 
 ## Progress log
 
+- **Phase 2 — reachability + cycles** (46/46). New `engine.sx` is one Datalog
+  ruleset. Reachability is kind-parameterised — `reach(K,X,Y)` carries the kind as
+  its first arg so a transitive walk over `parent` never leaks through `reply`
+  edges (the acl inheritance shape, but closures can't cross kinds). `rnode`
+  collects touched nodes; `root`/`leaf` use stratified negation over
+  `has_parent`/`has_child`. Cycles are data, not errors: `cycle?(node,kind)` ⇔
+  `reach(K,node,node)` holds, `acyclic?(kind)` ⇔ no `reach(K,X,X)`. Engine fns:
+  `relations-descendants/-ancestors/-reachable?/-roots/-leaves/-cycle?/-acyclic?`;
+  api.sx grew matching `relations/...` current-db wrappers. `relations-rules` and
+  `relations-pluck` moved from api.sx into engine.sx (engine now loads before api
+  in conformance.conf). reach.sx covers diamonds, deep chains, disconnected
+  components, self-loops, c1<->c2 cycles, and multi-kind isolation. acl
+  convergence: the `reach(X,Y):-edge(X,Y)` / `reach(X,Y):-edge(X,Z),reach(Z,Y)`
+  closure shape is shared with acl's eff_grant/eff_deny inheritance — flagged, not
+  extracted (per ground rules).
 - **Phase 1 — schema + direct relations** (22/22). `schema.sx`: `rel(Src,Dst,Kind)`
   fact constructor + accessors, open kind vocabulary (`parent member reply variant
   origin link`), `relations-fact-valid?`/`relations-known-kind?`. `api.sx`: db built