ocaml: phase 5.1 paren_depth.ml baseline (max nesting depth, 3+3+1 = 7)

One-pass walk tracking current depth and a high-water mark:

  let max_depth s =
    let d = ref 0 in
    let m = ref 0 in
    for i = 0 to String.length s - 1 do
      if s.[i] = '(' then begin
        d := !d + 1;
        if !d > !m then m := !d
      end
      else if s.[i] = ')' then d := !d - 1
    done;
    !m

Three inputs:
  '((1+2)*(3-(4+5)))'   3   (innermost (4+5) at depth 3)
  '(((deep)))'           3
  '()()()'               1   (no nesting)
  sum                    7

Tests for-loop char comparison s.[i] = '(' and the high-water-mark
idiom with two refs.

78 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -52,6 +52,7 @@
   "mutable_record.ml": 10,
   "option_match.ml": 5,
   "palindrome.ml": 4,
+  "paren_depth.ml": 7,
   "pancake_sort.ml": 910,
   "pascal.ml": 252,
   "pi_leibniz.ml": 314,

lib/ocaml/baseline/paren_depth.ml

@@ -0,0 +1,15 @@
+let max_depth s =
+  let d = ref 0 in
+  let m = ref 0 in
+  for i = 0 to String.length s - 1 do
+    if s.[i] = '(' then begin
+      d := !d + 1;
+      if !d > !m then m := !d
+    end
+    else if s.[i] = ')' then d := !d - 1
+  done;
+  !m
+
+;;
+
+max_depth "((1+2)*(3-(4+5)))" + max_depth "(((deep)))" + max_depth "()()()"

plans/ocaml-on-sx.md

@@ -407,6 +407,14 @@ _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.
+- 2026-05-09 Phase 5.1 — paren_depth.ml baseline (max paren nesting
+  depth, 3+3+1 = 7). One-pass walk tracking current depth and a
+  high-water mark. Tests three inputs:
+    "((1+2)*(3-(4+5)))" → 3
+    "(((deep)))"        → 3
+    "()()()"            → 1
+  Sum = 7. Tests for-loop char comparison `s.[i] = '('` and
+  high-water-mark idiom with two refs. 78 baseline programs total.
 - 2026-05-09 Phase 5.1 — pancake_sort.ml baseline (in-place pancake
   sort, 9 flips → 910). Each pass finds the max in [0..size-1],
   flips it to position 0 (if needed), then flips the size-prefix to