relations: weakly-connected components (component, components partition, count) + 11 tests

tree.sx, reuses ureach-bfs. 158/158 across 9 suites.

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

lib/relations/conformance.conf

@@ -31,4 +31,5 @@ SUITES=(
   "tree:lib/relations/tests/tree.sx:(relations-tree-tests-run!)"
   "routes:lib/relations/tests/routes.sx:(relations-routes-tests-run!)"
   "bulk:lib/relations/tests/bulk.sx:(relations-bulk-tests-run!)"
+  "comp:lib/relations/tests/comp.sx:(relations-comp-tests-run!)"
 )

lib/relations/scoreboard.json

@@ -1,8 +1,8 @@
 {
   "lang": "relations",
-  "total_passed": 147,
+  "total_passed": 158,
   "total_failed": 0,
-  "total": 147,
+  "total": 158,
   "suites": [
     {"name":"direct","passed":22,"failed":0,"total":22},
     {"name":"reach","passed":24,"failed":0,"total":24},
@@ -11,7 +11,8 @@
     {"name":"shape","passed":18,"failed":0,"total":18},
     {"name":"tree","passed":16,"failed":0,"total":16},
     {"name":"routes","passed":9,"failed":0,"total":9},
-    {"name":"bulk","passed":12,"failed":0,"total":12}
+    {"name":"bulk","passed":12,"failed":0,"total":12},
+    {"name":"comp","passed":11,"failed":0,"total":11}
   ],
-  "generated": "2026-06-07T13:26:23+00:00"
+  "generated": "2026-06-07T13:42:22+00:00"
 }

lib/relations/scoreboard.md

@@ -1,6 +1,6 @@
 # relations scoreboard
 
-**147 / 147 passing** (0 failure(s)).
+**158 / 158 passing** (0 failure(s)).
 
 | Suite | Passed | Total | Status |
 |-------|--------|-------|--------|
@@ -12,3 +12,4 @@
 | tree | 16 | 16 | ok |
 | routes | 9 | 9 | ok |
 | bulk | 12 | 12 | ok |
+| comp | 11 | 11 | ok |

lib/relations/tests/comp.sx

@@ -0,0 +1,144 @@
+;; lib/relations/tests/comp.sx — extension: weakly-connected components.
+
+(define relations-cp-pass 0)
+(define relations-cp-fail 0)
+(define relations-cp-failures (list))
+
+(define
+  relations-cp-check!
+  (fn
+    (name got expected)
+    (if
+      (= got expected)
+      (set! relations-cp-pass (+ relations-cp-pass 1))
+      (do
+        (set! relations-cp-fail (+ relations-cp-fail 1))
+        (append!
+          relations-cp-failures
+          (str name "\n    expected: " expected "\n    got:      " got))))))
+
+(define
+  relations-cp-subset?
+  (fn
+    (xs ys)
+    (cond
+      ((= (len xs) 0) true)
+      ((relations-member? (first xs) ys)
+        (relations-cp-subset? (rest xs) ys))
+      (else false))))
+
+(define
+  relations-cp-set=?
+  (fn
+    (xs ys)
+    (and
+      (= (len xs) (len ys))
+      (relations-cp-subset? xs ys)
+      (relations-cp-subset? ys xs))))
+
+;; Does `comps` (a list of node-lists) contain a component set-equal to `want`?
+(define
+  relations-cp-has-comp?
+  (fn
+    (comps want)
+    (cond
+      ((= (len comps) 0) false)
+      ((relations-cp-set=? (first comps) want) true)
+      (else (relations-cp-has-comp? (rest comps) want)))))
+
+;; Three parent components + a separate member graph.
+;;   parent: a->b, b->c ; x->y ; z->z (self-loop, its own component)
+;;   member: m->n
+(define
+  relations-cp-fixture
+  (fn
+    ()
+    (relations-build-db
+      (list
+        (relations-rel (quote a) (quote b) (quote parent))
+        (relations-rel (quote b) (quote c) (quote parent))
+        (relations-rel (quote x) (quote y) (quote parent))
+        (relations-rel (quote z) (quote z) (quote parent))
+        (relations-rel (quote m) (quote n) (quote member))))))
+
+(define
+  relations-cp-run-all!
+  (fn
+    ()
+    (let
+      ((db (relations-cp-fixture)))
+      (do
+        (relations-cp-check!
+          "component of a"
+          (relations-cp-set=?
+            (relations-component db (quote a) (quote parent))
+            (list (quote a) (quote b) (quote c)))
+          true)
+        (relations-cp-check!
+          "component of c (same as a, undirected)"
+          (relations-cp-set=?
+            (relations-component db (quote c) (quote parent))
+            (list (quote a) (quote b) (quote c)))
+          true)
+        (relations-cp-check!
+          "self-loop node is its own component"
+          (relations-cp-set=?
+            (relations-component db (quote z) (quote parent))
+            (list (quote z)))
+          true)
+        (relations-cp-check!
+          "three parent components"
+          (relations-component-count db (quote parent))
+          3)
+        (relations-cp-check!
+          "one member component"
+          (relations-component-count db (quote member))
+          1)
+        (let
+          ((comps (relations-components db (quote parent))))
+          (do
+            (relations-cp-check!
+              "partition includes a-b-c"
+              (relations-cp-has-comp?
+                comps
+                (list (quote a) (quote b) (quote c)))
+              true)
+            (relations-cp-check!
+              "partition includes x-y"
+              (relations-cp-has-comp? comps (list (quote x) (quote y)))
+              true)
+            (relations-cp-check!
+              "partition includes z"
+              (relations-cp-has-comp? comps (list (quote z)))
+              true)))
+        (relations-cp-check!
+          "kind isolation: member component count is 1"
+          (relations-component-count db (quote member))
+          1)
+        (do
+          (relations/load!
+            (list
+              (relations-rel (quote p) (quote q) (quote parent))
+              (relations-rel (quote r) (quote s) (quote parent))))
+          (relations-cp-check!
+            "api component"
+            (relations-cp-set=?
+              (relations/component (quote p) (quote parent))
+              (list (quote p) (quote q)))
+            true)
+          (relations-cp-check!
+            "api component-count"
+            (relations/component-count (quote parent))
+            2)
+          (relations/load! (list)))))))
+
+(define
+  relations-comp-tests-run!
+  (fn
+    ()
+    (do
+      (set! relations-cp-pass 0)
+      (set! relations-cp-fail 0)
+      (set! relations-cp-failures (list))
+      (relations-cp-run-all!)
+      {:failures relations-cp-failures :total (+ relations-cp-pass relations-cp-fail) :passed relations-cp-pass :failed relations-cp-fail})))

lib/relations/tree.sx

@@ -103,6 +103,37 @@
 
 ;; --- current-db convenience layer ---
 
+(define
+  relations-component
+  (fn
+    (db node kind)
+    (relations-ureach-bfs db kind (list node) (list node))))
+
+(define
+  relations-components-loop
+  (fn
+    (db kind remaining acc)
+    (if
+      (= (len remaining) 0)
+      acc
+      (let
+        ((comp (relations-component db (first remaining) kind)))
+        (relations-components-loop
+          db
+          kind
+          (filter (fn (n) (not (relations-eng-member? n comp))) remaining)
+          (append acc (list comp)))))))
+
+(define
+  relations-component-count
+  (fn (db kind) (len (relations-components db kind))))
+
+(define
+  relations-components
+  (fn
+    (db kind)
+    (relations-components-loop db kind (relations-nodes db kind) (list))))
+
 (define
   relations/common-ancestors
   (fn
@@ -116,3 +147,15 @@
 (define
   relations/topo-order
   (fn (kind) (relations-topo-order (relations-ensure-db!) kind)))
+
+(define
+  relations/component
+  (fn (node kind) (relations-component (relations-ensure-db!) node kind)))
+
+(define
+  relations/components
+  (fn (kind) (relations-components (relations-ensure-db!) kind)))
+
+(define
+  relations/component-count
+  (fn (kind) (relations-component-count (relations-ensure-db!) kind)))

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` → **147/147** (Phases 1–4 complete + extensions)
+`bash lib/relations/conformance.sh` → **158/158** (Phases 1–4 complete + extensions)
 
 ## Ground rules
 
@@ -114,9 +114,22 @@ lib/relations/federation.sx
   cleanup: retract every local edge touching a node, all kinds, both directions —
   for domain object deletion; leaves federated peer links alone). api.sx,
   `lib/relations/tests/bulk.sx`.
+- [x] **weakly-connected components** — `component` (the undirected cluster of a
+  node), `components` (partition of all nodes for a kind), `component-count`. In
+  tree.sx, reusing `ureach-bfs`. `lib/relations/tests/comp.sx`.
 
 ## Progress log
 
+- **Extension: weakly-connected components** (158/158). `relations-component`
+  (the undirected cluster containing a node = `ureach-bfs` from it),
+  `relations-components` (greedy partition: pop a remaining node, take its
+  component, repeat) and `relations-component-count`, in tree.sx, + `relations/...`
+  wrappers. `lib/relations/tests/comp.sx` (11 tests: cluster from either end, self-
+  loop as its own component, partition contents, count, kind isolation, api).
+  Engine surface now feels SATURATED — base roadmap + 5 graph-algorithm extensions
+  cover direct/transitive/undirected reach, paths (shortest + all routes), cycles,
+  roots/leaves, siblings/degree, ancestors/LCA/topo, components, federation, and
+  bulk lifecycle. Pacing down.
 - **Extension: bulk lifecycle** (147/147). `relations-relate-many!` (batch
   `dl-assert!` over a list of (src dst kind) triples) and `relations-unrelate-node!`
   (query `rel` for every edge with the node as src or dst, across all kinds, then