artdag: Phase 7 cost-directed opt-improvement/opt-cheaper? + 5 tests

artdag/opt-improvement compares the original output cone (dce to id) vs the
maude-reduced DAG under an injected cost-fn, returning before/after total-work and
critical-path. opt-cheaper? asserts optimisation never increases cost: the 5-node
chain drops to 2 (work 5->2, path 5->2) and stays cheaper under radius-weighted cost
(5->3); over dedup and untouched DAGs are never pessimised. Consumes cost.sx. Phase 7
base + (later) cost box done. maude-optimize 38/38, total 196/196.

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

lib/artdag/optimize-rules.sx

@@ -186,3 +186,28 @@
     (let
       ((o (artdag/opt-reduce dag id)))
       (artdag/opt-last (artdag/dag-order o)))))
+
+; ---- cost-directed: the maude-optimised cone never costs more than the original ----
+; compares the original output cone (dce to id) against the maude-reduced DAG under an
+; injected cost-fn (op params). Monotone per-node costs => optimisation is never a
+; pessimisation: fewer nodes (DCE/dedup) and fused ops (one blur(M+N) for two blurs).
+
+(define
+  artdag/opt-improvement
+  (fn
+    (dag id cost-fn)
+    (let
+      ((orig (artdag/dce dag (list id))) (opt (artdag/opt-reduce dag id)))
+      {:before (artdag/total-work orig cost-fn)
+        :after (artdag/total-work opt cost-fn)
+        :before-path (artdag/critical-path orig cost-fn)
+        :after-path (artdag/critical-path opt cost-fn)
+        :optimized opt})))
+
+(define
+  artdag/opt-cheaper?
+  (fn
+    (dag id cost-fn)
+    (let
+      ((imp (artdag/opt-improvement dag id cost-fn)))
+      (<= (get imp :after) (get imp :before)))))

lib/artdag/scoreboard.json

@@ -10,9 +10,9 @@
     "serialize": {"pass": 13, "fail": 0},
     "stats": {"pass": 12, "fail": 0},
     "fault": {"pass": 14, "fail": 0},
-    "maude-optimize": {"pass": 33, "fail": 0}
+    "maude-optimize": {"pass": 38, "fail": 0}
   },
-  "total_pass": 191,
+  "total_pass": 196,
   "total_fail": 0,
-  "total": 191
+  "total": 196
 }

lib/artdag/scoreboard.md

@@ -14,5 +14,5 @@ _Generated by `lib/artdag/conformance.sh`_
 | serialize | 13 | 0 | 13 |
 | stats | 12 | 0 | 12 |
 | fault | 14 | 0 | 14 |
-| maude-optimize | 33 | 0 | 33 |
-| **Total** | **191** | **0** | **191** |
+| maude-optimize | 38 | 0 | 38 |
+| **Total** | **196** | **0** | **196** |

lib/artdag/tests/maude-optimize.sx

@@ -268,3 +268,36 @@
   (artdag/node-params
     (artdag/dag-get mo-plain-opt (artdag/opt-last (artdag/dag-order mo-plain-opt))))
   {:radius 3})
+
+; ---- cost-directed: optimisation never increases cost ----
+
+(define
+  mo-rcost
+  (fn (op params) (if (= op "blur") (max 1 (get params :radius)) 1)))
+
+(artdag-test
+  "opt-improvement: const-cost total work drops on fused chain"
+  (let ((imp (artdag/opt-improvement mo-chain5 mo-chain5-id artdag/const-cost)))
+    (list (get imp :before) (get imp :after)))
+  (list 5 2))
+
+(artdag-test
+  "opt-improvement: critical path shrinks under const cost"
+  (let ((imp (artdag/opt-improvement mo-chain5 mo-chain5-id artdag/const-cost)))
+    (< (get imp :after-path) (get imp :before-path)))
+  true)
+
+(artdag-test
+  "opt-cheaper?: fused chain is cheaper under radius-weighted cost"
+  (artdag/opt-cheaper? mo-chain5 mo-chain5-id mo-rcost)
+  true)
+
+(artdag-test
+  "opt-cheaper?: over dedup is cheaper"
+  (artdag/opt-cheaper? mo-dedup mo-dedup-id artdag/const-cost)
+  true)
+
+(artdag-test
+  "opt-cheaper?: untouched DAG keeps equal cost (never a pessimisation)"
+  (artdag/opt-cheaper? mo-plain mo-plain-id artdag/const-cost)
+  true)