artdag: Phase 7 optimisation laws as confluent maude module + 11 tests

lib/artdag/optimize-rules.sx — the effect-pipeline optimisation passes (identity
elim, no-op/zero-radius elim, adjacent fusion, idempotent over dedup) as a maude
module. Radius algebra is _+_ [assoc comm id: 0] (NOT Peano successor rules, which
are non-confluent here); mau/confluent? certifies 0 non-joinable critical pairs, so
the optimised pipeline's normal form / content id is rewrite-order stable. Consumes
lib/maude/confluence.sx. maude-optimize 25/25, total 183/183.

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

lib/artdag/conformance.sh

@@ -35,13 +35,15 @@ run_suite() {
 (load "lib/maude/matching.sx")
 (load "lib/maude/conditional.sx")
 (load "lib/maude/fire.sx")
+(load "lib/maude/confluence.sx")
 (load "lib/maude/rewrite.sx")
 (load "lib/maude/searchpath.sx")
 (load "lib/maude/strategy.sx")
 (load "lib/maude/meta.sx")
 (load "lib/maude/pretty.sx")
 (load "lib/maude/run.sx")'
-    BRIDGE_LOAD='(load "lib/artdag/maude-bridge.sx")'
+    BRIDGE_LOAD='(load "lib/artdag/maude-bridge.sx")
+(load "lib/artdag/optimize-rules.sx")'
   fi
   cat > "$TMP" << EPOCHS
 (epoch 1)

lib/artdag/optimize-rules.sx

@@ -0,0 +1,69 @@
+; lib/artdag/optimize-rules.sx — Phase 7: optimisation laws as a confluent maude module.
+; The optimised effect pipeline IS the normal form of the rule set, so confluence
+; (mau/confluent?) is exactly content-id stability: every rewrite order reaches the
+; same normal form. Media ops (blur/bright/id/over) are the opaque-op model from
+; lib/maude/tests/effects.sx — the engine reasons about the pipeline algebra, never
+; pixels. The radius algebra is an AC operator with identity 0 (unary 1s): Peano
+; successor rules (s M + N = s(M+N), 0 + N = N) are NOT confluent here (the symbolic
+; critical pairs M + 0 and (A+B)+C vs A+(B+C) stick), whereas [assoc comm id: 0]
+; joins them via canonical form. maude (lib/maude) is a READ-ONLY consumed substrate:
+; mau/parse-module, mau/creduce-term, mau/creduce->str, mau/ccanon, mau/confluent?,
+; mau/non-joinable-pairs, mau/cp->str.
+
+(define
+  artdag/opt-module-src
+  (str
+    "fmod ARTDAGOPT is\n"
+    "  sorts Img Num .\n"
+    "  op 0 : -> Num .\n"
+    "  op 1 : -> Num .\n"
+    "  op _+_ : Num Num -> Num [assoc comm id: 0] .\n"
+    "  op blur : Img Num -> Img .\n"
+    "  op bright : Img Num -> Img .\n"
+    "  op id : Img -> Img .\n"
+    "  op over : Img Img -> Img [comm] .\n"
+    "  vars I J : Img .\n"
+    "  vars M N : Num .\n"
+    "  eq id(I) = I .\n"
+    "  eq blur(I, 0) = I .\n"
+    "  eq bright(I, 0) = I .\n"
+    "  eq blur(blur(I, M), N) = blur(I, M + N) .\n"
+    "  eq bright(bright(I, M), N) = bright(I, M + N) .\n"
+    "  eq over(I, I) = I .\n"
+    "endfm"))
+
+(define artdag/opt-module (mau/parse-module artdag/opt-module-src))
+
+; ---- reduce a surface pipeline to its optimised normal form ----
+
+(define
+  artdag/opt-reduce-term
+  (fn (src) (mau/creduce-term artdag/opt-module src)))
+
+(define
+  artdag/opt-normal-form
+  (fn (src) (mau/creduce->str artdag/opt-module src)))
+
+(define artdag/opt-canon (fn (src) (mau/ccanon artdag/opt-module src)))
+
+; two surface pipelines optimise to the same pipeline (=> same content id) iff
+; their normal forms coincide.
+(define
+  artdag/opt-same-form?
+  (fn (a b) (= (artdag/opt-normal-form a) (artdag/opt-normal-form b))))
+
+; ---- confluence / content-id stability (consume lib/maude/confluence.sx) ----
+
+(define artdag/opt-confluent? (fn () (mau/confluent? artdag/opt-module)))
+
+(define
+  artdag/opt-non-joinable
+  (fn () (mau/non-joinable-pairs artdag/opt-module)))
+
+(define
+  artdag/opt-non-joinable->strs
+  (fn
+    ()
+    (map
+      (fn (cp) (mau/cp->str artdag/opt-module cp))
+      (artdag/opt-non-joinable))))

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": 14, "fail": 0}
+    "maude-optimize": {"pass": 25, "fail": 0}
   },
-  "total_pass": 172,
+  "total_pass": 183,
   "total_fail": 0,
-  "total": 172
+  "total": 183
 }

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 | 14 | 0 | 14 |
-| **Total** | **172** | **0** | **172** |
+| maude-optimize | 25 | 0 | 25 |
+| **Total** | **183** | **0** | **183** |

lib/artdag/tests/maude-optimize.sx

@@ -110,3 +110,60 @@
     (artdag/dag-id mo-diamond "a")
     (keys (artdag/dag-nodes mo-diamond-rt)))
   true)
+
+; ---- optimisation laws as a confluent maude module (optimize-rules.sx) ----
+; The optimised pipeline is the normal form; confluence => stable content id.
+
+(artdag-test "opt module is confluent" (artdag/opt-confluent?) true)
+
+(artdag-test
+  "opt module has no non-joinable critical pairs"
+  (len (artdag/opt-non-joinable))
+  0)
+
+(artdag-test
+  "law: identity elimination"
+  (artdag/opt-normal-form "id(src)")
+  "src")
+
+(artdag-test
+  "law: zero-radius blur is a no-op"
+  (artdag/opt-normal-form "blur(src, 0)")
+  "src")
+
+(artdag-test
+  "law: zero-radius bright is a no-op"
+  (artdag/opt-normal-form "bright(src, 0)")
+  "src")
+
+(artdag-test
+  "law: adjacent blur fusion adds radii"
+  (artdag/opt-normal-form "blur(blur(src, 1), 1)")
+  "blur(src, _+_(1, 1))")
+
+(artdag-test
+  "fusion normal form is rewrite-order stable"
+  (artdag/opt-same-form?
+    "blur(blur(blur(src, 1), 1), 1)"
+    "blur(blur(src, 1 + 1), 1)")
+  true)
+
+(artdag-test
+  "laws compose: id + no-op + fusion"
+  (artdag/opt-normal-form "bright(id(blur(blur(src, 1), 1)), 0)")
+  "blur(src, _+_(1, 1))")
+
+(artdag-test
+  "law: idempotent over dedup (CSE)"
+  (artdag/opt-normal-form "over(blur(src, 1), blur(src, 1))")
+  "blur(src, 1)")
+
+(artdag-test
+  "distinct over operands do not dedup"
+  (artdag/opt-same-form? "over(blur(src, 1), blur(src, 1 + 1))" "blur(src, 1)")
+  false)
+
+(artdag-test
+  "distinct pipelines stay distinct"
+  (artdag/opt-same-form? "blur(src, 1)" "bright(src, 1)")
+  false)