maude: Phase 4 conditional equations (19 tests, 138 total)

lib/maude/conditional.sx — condition-aware reducer. ceq fires only when
its guard holds: equational guards (l=r reduce to same normal form) and
boolean guards (term reduces to true), evaluated by recursing through the
same reducer. Verified on gcd, insertion sort, max, even.

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

plans/maude-on-sx.md

@@ -81,9 +81,9 @@ The novel substrate stress: equational matching. Pattern `X + Y` against `1 + 2
 - [x] Tests: classic AC-matching examples (multiset rewriting, set theory, group equations).
 
 ### Phase 4 — Conditional equations
-- [ ] `ceq L = R if Cond` — apply only when `Cond` reduces to true.
-- [ ] Recursion via the same reduce engine (terminating because Cond is shorter).
-- [ ] Tests: gcd, sorting, conditional simplifications.
+- [x] `ceq L = R if Cond` — apply only when `Cond` reduces to true.
+- [x] Recursion via the same reduce engine (terminating because Cond is shorter).
+- [x] Tests: gcd, sorting, conditional simplifications.
 
 ### Phase 5 — System modules + rewrite rules
 - [ ] `mod ... endm` syntax with `rl` rules.
@@ -177,5 +177,23 @@ The novel substrate stress: equational matching. Pattern `X + Y` against `1 + 2
     oracle. `$EMPTY` is a transient marker for empty rest blocks w/o id; never
     leaks past `mau/restv`.
 
+- **Phase 4 (conditional equations) — DONE, 138/138 total.**
+  `lib/maude/conditional.sx` is a condition-aware superset of the Phase 3
+  reducer. `mau/eq-candidates` enumerates (subst, result) pairs for an
+  equation (AC via rest-var extension `mau/ac-candidates`, else `mau/mm`);
+  `mau/try-candidates` commits the first candidate that both makes progress
+  (canonical form changes) AND whose guard holds. `mau/cond-holds?` evaluates
+  `{:kind :eq}` guards (reduce both sides, `ac-equal?`) and `{:kind :bool}`
+  guards (reduce, `=AC= true`), recursing through `mau/cnormalize` — same
+  reducer, so guards can mention other (conditional) equations. Public:
+  `mau/creduce` / `mau/creduce->str` / `mau/ccanon`. Verified on gcd
+  (subtractive, recursive guard), insertion sort (true/false branches), max,
+  and even (bool-kind `if pred` guard).
+  - Notes for next phases: `mau/creduce` is the canonical reducer now; Phase 5
+    rules reduce to normal form via creduce between rewrite steps. `_:_` cons
+    parses LEFT-assoc (no `gather` support yet) — write list literals
+    right-parenthesized, or add a `gather`/parse-assoc attr later if a test
+    needs bare `a : b : c`.
+
 ## Blockers
 _(none)_