ocaml: phase 5.1 max_path_tree.ml baseline (max root-to-leaf sum, 1+3+7 = 11)

Recursive ADT for binary trees:

  type tree = Leaf | Node of int * tree * tree

  let rec max_path t =
    match t with
    | Leaf -> 0
    | Node (v, l, r) ->
      let lp = max_path l in
      let rp = max_path r in
      v + (if lp > rp then lp else rp)

For the test tree:
       1
      /      2   3
    / \   \
   4   5   7

paths sum:    1+2+4=7, 1+2+5=8, 1+3+7=11.  max = 11.

Tests 3-arg Node constructor with positional arg destructuring, two
nested let-bindings, and if-then-else as an inline expression.

73 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -36,6 +36,7 @@
   "flatten_tree.ml": 28,
   "list_ops.ml": 30,
   "mat_mul.ml": 621,
+  "max_path_tree.ml": 11,
   "mod_inverse.ml": 27,
   "json_pretty.ml": 24,
   "kadane.ml": 6,

lib/ocaml/baseline/max_path_tree.ml

@@ -0,0 +1,21 @@
+type tree = Leaf | Node of int * tree * tree
+
+let rec max_path t =
+  match t with
+  | Leaf -> 0
+  | Node (v, l, r) ->
+    let lp = max_path l in
+    let rp = max_path r in
+    v + (if lp > rp then lp else rp)
+
+;;
+
+let t = Node (1,
+  Node (2,
+    Node (4, Leaf, Leaf),
+    Node (5, Leaf, Leaf)),
+  Node (3,
+    Leaf,
+    Node (7, Leaf, Leaf)))
+in
+max_path t

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 — max_path_tree.ml baseline (max root-to-leaf
+  sum in a binary tree, 1+3+7 = 11). Recursive ADT `tree = Leaf |
+  Node of int * tree * tree`. max_path returns 0 at Leaf, else
+  v + max(left subtree, right subtree). Tree has 6 nodes; the
+  rightmost path 1→3→7 maximises at 11. Tests 3-arg `Node`
+  constructor with positional arg destructuring + nested let-binding
+  + if-then-else as expression. 73 baseline programs total.
 - 2026-05-09 Phase 5.1 — mod_inverse.ml baseline (extended Euclidean
   + modular inverse, sum 4+21+2 = 27). ext_gcd returns a triple
   (gcd, x, y) such that ax + by = gcd. mod_inverse extracts x and