maude: owise (otherwise) equations (8 tests, 229 total)

Parser reads trailing eq attributes (eq L = R [owise] .) via mau/split-attrs.
mau/crewrite-top is two-pass: ordinary equations first, owise last — an owise
catch-all fires only when no ordinary equation applies, regardless of
declaration order. Verified a catch-all declared first still defers.

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

lib/maude/conditional.sx

@@ -1,4 +1,4 @@
-;; lib/maude/conditional.sx — conditional equations (Phase 4).
+;; lib/maude/conditional.sx — conditional equations (Phase 4) + owise.
 ;;
 ;; A condition-aware superset of the Phase 3 reducer. `ceq L = R if COND` fires
 ;; only when COND holds under the matching substitution. Conditions come from
@@ -10,10 +10,13 @@
 ;; — termination rests on the guard reducing on structurally smaller arguments
 ;; (and the global fuel guard).
 ;;
+;; `owise` (otherwise): an equation tagged [owise] fires at a redex only when
+;; NO ordinary equation applies there. crewrite-top is two-pass: ordinary
+;; equations first, owise equations last.
+;;
 ;; Single-step firing uses the short-circuiting matcher in fire.sx
-;; (mau/fire-eq) so reduction is not quadratic/exponential in AC argument size.
-;; The eager candidate enumeration (mau/eq-candidates) is retained for `search`
-;; (rewrite.sx), which genuinely needs every successor.
+;; (mau/fire-eq). The eager candidate enumeration (mau/eq-candidates) is
+;; retained for `search` (rewrite.sx), which genuinely needs every successor.
 
 (define
   mau/ac-candidates
@@ -86,6 +89,14 @@
           (get c :result)
           (mau/try-candidates theory all-eqs cond term (rest cands)))))))
 
+;; ---- owise partitioning ----
+
+(define mau/eq-owise? (fn (e) (= (get e :owise) true)))
+(define mau/filter-owise (fn (eqs) (filter mau/eq-owise? eqs)))
+(define
+  mau/filter-noowise
+  (fn (eqs) (filter (fn (e) (not (mau/eq-owise? e))) eqs)))
+
 (define
   mau/crewrite-loop
   (fn
@@ -99,7 +110,14 @@
 
 (define
   mau/crewrite-top
-  (fn (theory eqs term) (mau/crewrite-loop theory eqs eqs term)))
+  (fn
+    (theory eqs term)
+    (let
+      ((r (mau/crewrite-loop theory eqs (mau/filter-noowise eqs) term)))
+      (if
+        (= r nil)
+        (mau/crewrite-loop theory eqs (mau/filter-owise eqs) term)
+        r))))
 
 (define
   mau/cnormalize