ocaml: phase 5.1 bracket_match.ml baseline (5/9 balanced strings)

Stack-based multi-bracket parenthesis matching for ( [ { ) ] }.
Non-bracket chars are skipped (treated as content).

Tests:
  ()           yes
  [{()}]       yes
  ({[}])       no  (mismatched closer)
  ""           yes
  ((           no  (unclosed)
  ()[](){}     yes
  (a(b)c)      yes  (a/b/c skipped)
  (()          no
  ])           no
                 5 balanced

Body uses begin/end-wrapped match inside while:

  else if c = ')' || c = ']' || c = '}' then begin
    match !stack with
    | [] -> ok := false
    | top :: rest ->
      let pair =
        (c = ')' && top = '(') ||
        (c = ']' && top = '[') ||
        (c = '}' && top = '{')
      in
      if pair then stack := rest else ok := false
  end

Tests side-effecting match arms inside while body, ref-of-list as
stack, multi-char pairing dispatch.

174 baseline programs total.

lib/ocaml/baseline/bracket_match.ml

@@ -0,0 +1,32 @@
+let bracket_match s =
+  let n = String.length s in
+  let stack = ref [] in
+  let ok = ref true in
+  let i = ref 0 in
+  while !ok && !i < n do
+    let c = s.[!i] in
+    if c = '(' || c = '[' || c = '{' then
+      stack := c :: !stack
+    else if c = ')' || c = ']' || c = '}' then begin
+      match !stack with
+      | [] -> ok := false
+      | top :: rest ->
+        let pair =
+          (c = ')' && top = '(') ||
+          (c = ']' && top = '[') ||
+          (c = '}' && top = '{')
+        in
+        if pair then stack := rest else ok := false
+    end;
+    i := !i + 1
+  done;
+  if !ok && !stack = [] then 1 else 0
+
+;;
+
+let strings = ["()"; "[{()}]"; "({[}])"; ""; "(("; "()[](){}"; "(a(b)c)"; "(()"; "])"] in
+let count = ref 0 in
+List.iter (fun s ->
+  count := !count + bracket_match s
+) strings;
+!count

lib/ocaml/baseline/expected.json

@@ -15,6 +15,7 @@
   "bipartite.ml": 4,
   "bits.ml": 21,
   "balance.ml": 3,
+  "bracket_match.ml": 5,
   "base_n.ml": 17,
   "bfs.ml": 6,
   "bfs_grid.ml": 8,

plans/ocaml-on-sx.md

@@ -407,6 +407,15 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-11 Phase 5.1 — bracket_match.ml baseline (multi-bracket
+  parenthesis matching over 9 test strings, 5 balanced). Stack-
+  based scan: push openers `( [ {`, pop and pair-check closers.
+  Sequence: `() [{()}] ({[}]) "" (( ()[](){} (a(b)c) (() ])` →
+  yes/yes/no/yes/no/yes/yes/no/no = 5.
+  Tests `begin … match !stack with [] -> … | top :: rest -> … end`
+  with side-effecting match arms inside a `while` body, ref-of-list
+  used as a stack, three-way char dispatch via short-circuited
+  comparisons. 174 baseline programs total.
 - 2026-05-11 Phase 5.1 — wildcard_match.ml baseline (recursive `*`
   /`?` wildcard matcher; over 3×6 = 18 (pattern, text) combos,
   6 match). Cases: