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/...).