ocaml: phase 5.1 interval_overlap.ml baseline (7 intervals, 6 overlapping pairs)

For each (i, j) pair with i < j, test whether intervals (s1, e1)
and (s2, e2) overlap via the standard `s1 <= e2 && s2 <= e1`.

  intervals: (1,4) (2,5) (7,9) (3,6) (8,10) (11,12) (0,2)

  overlapping pairs:
    (1,4) & (2,5)        (1,4) & (3,6)        (1,4) & (0,2)
    (2,5) & (3,6)        (2,5) & (0,2)
    (7,9) & (8,10)
                                                     = 6

Tests double for-loop with both-side tuple destructure via
`let (s1, e1) = arr.(i) in`, conjunctive comparison, list-to-
array conversion.

188 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -81,6 +81,7 @@
   "histogram_area.ml": 10,
   "huffman.ml": 224,
   "int_sqrt.ml": 1027,
+  "interval_overlap.ml": 6,
   "is_prime.ml": 25,
   "island_count.ml": 5,
   "fizz_classifier.ml": 540,

lib/ocaml/baseline/interval_overlap.ml

@@ -0,0 +1,16 @@
+let count_overlaps intervals =
+  let arr = Array.of_list intervals in
+  let n = Array.length arr in
+  let count = ref 0 in
+  for i = 0 to n - 1 do
+    let (s1, e1) = arr.(i) in
+    for j = i + 1 to n - 1 do
+      let (s2, e2) = arr.(j) in
+      if s1 <= e2 && s2 <= e1 then count := !count + 1
+    done
+  done;
+  !count
+
+;;
+
+count_overlaps [(1, 4); (2, 5); (7, 9); (3, 6); (8, 10); (11, 12); (0, 2)]

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.
+- 2026-05-11 Phase 5.1 — interval_overlap.ml baseline (count
+  overlapping interval pairs in 7-interval set = 6). For each pair
+  (i, j) test `s1 ≤ e2 && s2 ≤ e1`. Intervals: (1,4) (2,5) (7,9)
+  (3,6) (8,10) (11,12) (0,2). Overlapping pairs:
+    (1,4)&(2,5), (1,4)&(3,6), (1,4)&(0,2),
+    (2,5)&(3,6), (2,5)&(0,2), (7,9)&(8,10)
+  = 6 pairs. Tests double for-loop with both-side tuple destructure
+  via `let (s1, e1) = arr.(i) in`, conjunctive comparison, list-to-
+  array conversion. 188 baseline programs total.
 - 2026-05-11 Phase 5.1 — count_palindromes.ml baseline (count
   palindromic substrings of "aabaa" = 9). Expand-around-center
   with 2n−1 centers (n odd-length, n−1 even-length); for each,