ocaml: phase 5.1 polygon_area.ml baseline (pentagon 2x area = 32)

Shoelace formula on a pentagon with integer vertices:

  pts = [(0,0); (4,0); (4,3); (2,5); (0,3)]

  2 * area = | Σ (x_i * y_{i+1} - x_{i+1} * y_i) |
           = | 0*0 - 4*0 + 4*3 - 4*0 + 4*5 - 2*3 + 2*3 - 0*5
                + 0*0 - 0*3 |
           = 32

Returns the doubled form (32) to stay integral.

Tests:
  - let (x1, y1) = arr.(i) in   -- tuple destructure from array
  - arr.((i + 1) mod n)         -- modular wrap-around index
  - if a < 0 then - a else a    -- prefix - negation

162 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -122,6 +122,7 @@
   "prefix_sum.ml": 66,
   "pretty_table.ml": 64,
   "poly_stack.ml": 5,
+  "polygon_area.ml": 32,
   "pow_mod.ml": 738639,
   "prime_factors.ml": 17,
   "pythagorean.ml": 16,

lib/ocaml/baseline/polygon_area.ml

@@ -0,0 +1,17 @@
+let pts = [(0, 0); (4, 0); (4, 3); (2, 5); (0, 3)]
+
+let polygon_2area pts =
+  let arr = Array.of_list pts in
+  let n = Array.length arr in
+  let acc = ref 0 in
+  for i = 0 to n - 1 do
+    let (x1, y1) = arr.(i) in
+    let (x2, y2) = arr.((i + 1) mod n) in
+    acc := !acc + x1 * y2 - x2 * y1
+  done;
+  let a = !acc in
+  if a < 0 then - a else a
+
+;;
+
+polygon_2area pts

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.
+- 2026-05-10 Phase 5.1 — polygon_area.ml baseline (shoelace formula
+  on pentagon, returns 2× area = 32). Vertices (0,0), (4,0), (4,3),
+  (2,5), (0,3); shoelace sum |Σ(x_i·y_{i+1} − x_{i+1}·y_i)| = 32 so
+  the area is 16, and we return the doubled form to stay integral.
+  Tests `let (x1, y1) = arr.(i) in` tuple destructuring from array
+  access (previously suspected broken in bfs_grid but works here —
+  the iter-242 bug was actually `&&` short-circuit, not destructure),
+  modular wrap-around `arr.((i+1) mod n)`, prefix-`-` negation.
+  162 baseline programs total.
 - 2026-05-10 Phase 5.1 — min_cost_path.ml baseline (min-cost path
   through 4×4 cost grid, top-left to bottom-right with moves
   right/down only, optimal = 12). Standard 2D DP: dp[i][j] = min