ocaml: phase 5.1 bsearch.ml baseline (binary search, position sum = 7)

Iterative binary search on a sorted int array:

  let bsearch arr target =
    let n = Array.length arr in
    let lo = ref 0 and hi = ref (n - 1) in
    let found = ref (-1) in
    while !lo <= !hi && !found = -1 do
      let mid = (!lo + !hi) / 2 in
      if arr.(mid) = target then found := mid
      else if arr.(mid) < target then lo := mid + 1
      else hi := mid - 1
    done;
    !found

For [1;3;5;7;9;11;13;15;17;19;21]:
  bsearch a 13   = 6
  bsearch a 5    = 2
  bsearch a 100  = -1
  sum            = 7

Exercises Array.of_list + arr.(i) + multi-let 'let lo = ... and
hi = ...' + while + multi-arm if/else if/else.

49 baseline programs total.

plans/ocaml-on-sx.md

@@ -407,6 +407,13 @@ _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 — bsearch.ml baseline (binary search,
+  position-sum 6 + 2 + (-1) = 7). Iterative bsearch on a sorted int
+  array using two index refs `lo`/`hi` and a sentinel `found = -1`.
+  while loop runs until `lo > hi` or found set. For [1;3;...;21]:
+  position of 13 = 6, 5 = 2, 100 = -1. Exercises Array.of_list +
+  arr.(i) + multi-let `let lo = ... and hi = ...` + while + multi-arm
+  if/else if. 49 baseline programs total.
 - 2026-05-09 Phase 5.1 — palindrome.ml baseline (two-pointer
   palindrome check, 4 of 6 inputs are palindromes). is_palindrome
   walks from both ends meeting in the middle, returning false on