ocaml: phase 5.1 count_inversions.ml baseline (12 inversions via merge sort)

Modified merge sort that counts inversions during the merge step:
when an element from the right half is selected, the remaining
elements of the left half (mid - i + 1) all form inversions with
that right element.

  count_inv [|8; 4; 2; 1; 3; 5; 7; 6|] = 12

Inversions of [8;4;2;1;3;5;7;6]:
  with 8: (8,4)(8,2)(8,1)(8,3)(8,5)(8,7)(8,6) = 7
  with 4: (4,2)(4,1)(4,3) = 3
  with 2: (2,1) = 1
  with 7: (7,6) = 1
                                        total = 12

Tests: let rec ... and ... mutual recursion, while + ref + array
mutation, in-place sort with auxiliary scratch array.

145 baseline programs total.

lib/ocaml/baseline/count_inversions.ml

@@ -0,0 +1,42 @@
+let count_inv arr =
+  let n = Array.length arr in
+  let temp = Array.make n 0 in
+  let count = ref 0 in
+  let rec merge lo mid hi =
+    let i = ref lo and j = ref (mid + 1) and k = ref lo in
+    while !i <= mid && !j <= hi do
+      if arr.(!i) <= arr.(!j) then begin
+        temp.(!k) <- arr.(!i);
+        i := !i + 1
+      end else begin
+        temp.(!k) <- arr.(!j);
+        count := !count + (mid - !i + 1);
+        j := !j + 1
+      end;
+      k := !k + 1
+    done;
+    while !i <= mid do
+      temp.(!k) <- arr.(!i);
+      i := !i + 1; k := !k + 1
+    done;
+    while !j <= hi do
+      temp.(!k) <- arr.(!j);
+      j := !j + 1; k := !k + 1
+    done;
+    for x = lo to hi do
+      arr.(x) <- temp.(x)
+    done
+  and sort lo hi =
+    if lo < hi then begin
+      let mid = (lo + hi) / 2 in
+      sort lo mid;
+      sort (mid + 1) hi;
+      merge lo mid hi
+    end
+  in
+  sort 0 (n - 1);
+  !count
+
+;;
+
+count_inv [|8; 4; 2; 1; 3; 5; 7; 6|]

lib/ocaml/baseline/expected.json

@@ -24,6 +24,7 @@
   "closures.ml": 315,
   "coin_change.ml": 6,
   "count_change.ml": 406,
+  "count_inversions.ml": 12,
   "csv.ml": 10,
   "dijkstra.ml": 7,
   "exception_handle.ml": 4,

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.
+- 2026-05-10 Phase 5.1 — count_inversions.ml baseline (count
+  inversions of [|8;4;2;1;3;5;7;6|] = 12, via merge-sort). Modified
+  merge sort: when right element is taken, accumulate `mid - i + 1`
+  inversions for the remaining left half. Tests `let rec merge ...
+  and sort ...` mutually recursive bindings, complex while + ref
+  + array mutation, in-place sort with auxiliary array.
+  145 baseline programs total.
 - 2026-05-10 Phase 5.1 — topo_sort.ml baseline (Kahn's algorithm
   topological sort of a 6-node DAG → all 6 vertices ordered).
   Standard BFS approach: compute in-degrees, seed queue with zero-