ocaml: phase 5.1 next_permutation.ml baseline (5! - 1 = 119 successors)

Standard in-place next-permutation (Narayana's algorithm):

  let next_perm a =
    let n = Array.length a in
    let i = ref (n - 2) in
    while !i >= 0 && a.(!i) >= a.(!i + 1) do i := !i - 1 done;
    if !i < 0 then false
    else begin
      let j = ref (n - 1) in
      while a.(!j) <= a.(!i) do j := !j - 1 done;
      swap a.(!i) a.(!j);
      reverse a (!i + 1) (n - 1);
      true
    end

Starting from [1;2;3;4;5], next_perm returns true 119 times then
false (when reverse-sorted). 5! - 1 = 119.

Tests guarded `while … && a.(!i) … do` loops that rely on the
iter-242 short-circuit fix.

156 baseline programs total.

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 — next_permutation.ml baseline (count
+  permutations of [1;2;3;4;5] via Narayana's algorithm = 119).
+  Standard in-place algorithm: find largest i with a.(i) < a.(i+1),
+  largest j > i with a.(j) > a.(i), swap, reverse suffix from i+1.
+  Returns false when array is the reverse-sorted (final)
+  permutation. 5! = 120, minus the initial = 119 successful calls.
+  Tests guarded `while … >= 0 && a.(!i) >= a.(!i + 1) do …`
+  pattern using the new short-circuit semantics (would loop or
+  crash without iter-242 fix). 156 baseline programs total.
 - 2026-05-10 Phase 5.1 — `&&` / `||` short-circuit fix + bfs_grid.ml
   baseline (BFS shortest path on 5×5 grid with walls, dist 8). The
   evaluator's `:op` handler was evaluating BOTH sides of `&&`/`||`