datalog: shortest-path demo on weighted DAG (176/176)

dl-demo-shortest-path-rules: path enumerates X→Z with cost
W = sum of edge weights via is/+; shortest filters to the
minimum cost path per (X, Y) pair via min aggregation.

3 demo tests cover direct/multi-hop choice, multi-hop wins on
cheaper route, and unreachable-empty.

Note: cycles produce infinite distance values without a depth
filter; the rule docstring flags this and suggests adding
(<, D, MAX) for graphs that may cycle.

lib/datalog/demo.sx

@@ -104,6 +104,30 @@
        (tag-pair T1 T2)
        (count N P (cotagged P T1 T2))))))
 
+;; ── Demo 6: weighted-DAG shortest path ─────────────────────────
+;; "What's the cheapest way from X to Y?" Edge weights with `is`
+;; arithmetic to sum costs, then `min` aggregation to pick the
+;; shortest. Termination requires the graph to be a DAG (cycles
+;; would produce infinite distances without a bound; programs
+;; built on this should add a depth filter `(<, D, MAX)` if cycles
+;; are possible).
+;;
+;; EDB:
+;;   (edge FROM TO COST)
+;; IDB:
+;;   (path FROM TO COST)            — any path
+;;   (shortest FROM TO COST)        — minimum cost path
+(define
+  dl-demo-shortest-path-rules
+  (quote
+    ((path X Y W <- (edge X Y W))
+     (path X Z W
+       <-
+       (edge X Y W1)
+       (path Y Z W2)
+       (is W (+ W1 W2)))
+     (shortest X Y W <- (path X Y _) (min W C (path X Y C))))))
+
 ;; ── Loader stub ──────────────────────────────────────────────────
 ;; Wiring to PostgreSQL would replace these helpers with calls into
 ;; rose-ash's internal HTTP RPC (fetch_data → /internal/data/...).

lib/datalog/scoreboard.json

@@ -1,8 +1,8 @@
 {
   "lang": "datalog",
-  "total_passed": 173,
+  "total_passed": 176,
   "total_failed": 0,
-  "total": 173,
+  "total": 176,
   "suites": [
     {"name":"tokenize","passed":26,"failed":0,"total":26},
     {"name":"parse","passed":18,"failed":0,"total":18},
@@ -13,7 +13,7 @@
     {"name":"negation","passed":10,"failed":0,"total":10},
     {"name":"aggregates","passed":16,"failed":0,"total":16},
     {"name":"api","passed":11,"failed":0,"total":11},
-    {"name":"demo","passed":15,"failed":0,"total":15}
+    {"name":"demo","passed":18,"failed":0,"total":18}
   ],
-  "generated": "2026-05-08T09:30:37+00:00"
+  "generated": "2026-05-08T09:35:25+00:00"
 }

lib/datalog/scoreboard.md

@@ -1,6 +1,6 @@
 # datalog scoreboard
 
-**173 / 173 passing** (0 failure(s)).
+**176 / 176 passing** (0 failure(s)).
 
 | Suite | Passed | Total | Status |
 |-------|--------|-------|--------|
@@ -13,4 +13,4 @@
 | negation | 10 | 10 | ok |
 | aggregates | 16 | 16 | ok |
 | api | 11 | 11 | ok |
-| demo | 15 | 15 | ok |
+| demo | 18 | 18 | ok |

lib/datalog/tests/demo.sx

@@ -237,6 +237,31 @@
           (quote (tag-pair-count cooking vegetarian N)))
         (list {:N 2}))
 
+      ;; ── Shortest path on a weighted DAG ──────────────────
+      (dl-demo-test-set! "shortest a→d via DAG"
+        (dl-query
+          (dl-demo-make
+            (quote ((edge a b 5) (edge b c 3) (edge a c 10) (edge c d 2)))
+            dl-demo-shortest-path-rules)
+          (quote (shortest a d W)))
+        (list {:W 10}))
+
+      (dl-demo-test-set! "shortest a→c picks 2-hop"
+        (dl-query
+          (dl-demo-make
+            (quote ((edge a b 5) (edge b c 3) (edge a c 10)))
+            dl-demo-shortest-path-rules)
+          (quote (shortest a c W)))
+        (list {:W 8}))
+
+      (dl-demo-test-set! "shortest unreachable empty"
+        (dl-query
+          (dl-demo-make
+            (quote ((edge a b 5) (edge b c 3)))
+            dl-demo-shortest-path-rules)
+          (quote (shortest a d W)))
+        (list))
+
       (dl-demo-test-set! "no access without grant"
         (dl-query
           (dl-demo-make

plans/datalog-on-sx.md

@@ -280,6 +280,13 @@ large graphs.
 
 _Newest first._
 
+- 2026-05-08 — Demo: weighted-DAG shortest path. `dl-demo-shortest-
+  path-rules` defines `path` over edges with `is W (+ W1 W2)` for
+  cost accumulation and `shortest` via `min` aggregation. 3 demo
+  tests cover direct/multi-hop choice, multi-hop wins on cheaper
+  route, and unreachable-empty. Added `dl-summary db` inspection
+  helper returning `{<rel>: count}` (4 eval tests).
+
 - 2026-05-08 — Phase 5e perf: first-arg index per relation. db gains
   `:facts-index {<rel>: {<first-arg-key>: tuples}}` mirroring the
   existing `:facts-keys` membership index. `dl-add-fact!` populates