ocaml: phase 5.1 hanoi.ml baseline (Tower of Hanoi move count, n=10 -> 1023)

Classic doubly-recursive solution returning the move count:

  hanoi n from to via =
    if n = 0 then 0
    else hanoi (n-1) from via to + 1 + hanoi (n-1) via to from

For n = 10, returns 2^10 - 1 = 1023.

Exercises 4-arg recursion, conditional base case, and tail-position
addition. Uses 'to_' instead of 'to' for the destination param to
avoid collision with the 'to' keyword in for-loops — the OCaml
conventional workaround.

37 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -14,6 +14,7 @@
   "factorial.ml": 3628800,
   "fraction.ml": 7,
   "frequency.ml": 5,
+  "hanoi.ml": 1023,
   "fizzbuzz.ml": 57,
   "list_ops.ml": 30,
   "json_pretty.ml": 24,

lib/ocaml/baseline/hanoi.ml

@@ -0,0 +1,11 @@
+let rec hanoi n from to_ via =
+  if n = 0 then 0
+  else
+    let a = hanoi (n - 1) from via to_ in
+    let b = 1 in
+    let c = hanoi (n - 1) via to_ from in
+    a + b + c
+
+;;
+
+hanoi 10 1 3 2

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 — hanoi.ml baseline (Tower of Hanoi move
+  count, n=10 → 1023). Classic doubly-recursive solution returning
+  the number of moves: `hanoi n from to via = hanoi (n-1) from via
+  to + 1 + hanoi (n-1) via to from`. Counts to 2^10 - 1 = 1023 for
+  n=10, exercising tail-position addition + 4-arg recursion +
+  conditional base case. (Uses `to_` instead of `to` to avoid
+  collision with the `to` keyword in for-loops — OCaml conventional
+  workaround.) 37 baseline programs total.
 - 2026-05-09 Phase 5.1 — validate.ml baseline (Either-based input
   validation, 3 errors × 100 + 117 sum = 417). validate_int returns
   `Left msg` on empty / non-digit, `Right (int_of_string s)` on a