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/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))))