maude: Phase 2 syntactic equational reduction (26 tests, 91 total)

lib/maude/reduce.sx — one-sided syntactic matching (non-linear patterns
via bound-var equality), immutable substitutions, innermost fixpoint
normalisation. Tested on Peano arithmetic, list ops, a propositional
logic simplifier, and non-linear matching.

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

plans/maude-on-sx.md

@@ -68,9 +68,9 @@ The novel substrate stress: equational matching. Pattern `X + Y` against `1 + 2
 - [x] Tests: parse classic examples (peano nat, list of naturals).
 
 ### Phase 2 — Syntactic equational reduction
-- [ ] Apply equations left-to-right until no equation matches.
-- [ ] Standard pattern matching (no equational theories yet — strict syntactic match).
-- [ ] Tests: peano arithmetic, list manipulation, propositional logic simplifier.
+- [x] Apply equations left-to-right until no equation matches.
+- [x] Standard pattern matching (no equational theories yet — strict syntactic match).
+- [x] Tests: peano arithmetic, list manipulation, propositional logic simplifier.
 
 ### Phase 3 — Equational matching (assoc / comm / id)
 - [ ] Extend matching to handle `assoc` operators (flatten then match across permutations of subterm groups).
@@ -142,5 +142,16 @@ The novel substrate stress: equational matching. Pattern `X + Y` against `1 + 2
     `mau/parse-term-in` can parse term strings against its op table. Overloading
     is recorded but NOT resolved at parse time (resolve at reduce time).
 
+- **Phase 2 (syntactic reduction) — DONE, 91/91 total.** `lib/maude/reduce.sx`:
+  one-sided syntactic matching (`mau/match` — pattern vars only, non-linear
+  patterns checked by bound-var equality), immutable substitutions via `assoc`,
+  `mau/subst-apply`, top rewrite `mau/rewrite-top` (first unconditional eq whose
+  LHS matches; conditional eqs skipped until Phase 4), innermost normalisation
+  to a fixpoint `mau/normalize` (args normalised before the operator; fuel-
+  guarded). API: `mau/reduce` / `mau/reduce-term` / `mau/reduce->str`. Tested on
+  Peano (+,*), list ops (append/length/rev), a propositional simplifier, and
+  non-linear `same(X,X)`. Innermost is fine for confluent terminating eq sets;
+  Phase 3 will replace the matcher with AC-aware matching (multi-valued).
+
 ## Blockers
 _(none)_