ocaml: phase 5.1 ackermann.ml baseline (ack(3, 4) = 125)

Classic Ackermann function:

  let rec ack m n =
    if m = 0 then n + 1
    else if n = 0 then ack (m - 1) 1
    else ack (m - 1) (ack m (n - 1))

ack(3, 4) = 125, expanding to ~6700 evaluator frames — a useful
stress test of the call stack and control transfer. Real OCaml
evaluates this in milliseconds; ours takes ~2 minutes on a
contended host but completes correctly.

40 baseline programs total.

lib/ocaml/baseline/ackermann.ml

@@ -0,0 +1,8 @@
+let rec ack m n =
+  if m = 0 then n + 1
+  else if n = 0 then ack (m - 1) 1
+  else ack (m - 1) (ack m (n - 1))
+
+;;
+
+ack 3 4

lib/ocaml/baseline/expected.json

@@ -1,4 +1,5 @@
 {
+  "ackermann.ml": 125,
   "anagrams.ml": 3,
   "bag.ml": 3,
   "balance.ml": 3,

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 — ackermann.ml baseline (Ackermann function,
+  ack(3, 4) = 125). Three-arm recursion: m=0 base, n=0 reduces m,
+  else doubly-nested recursion `ack (m-1) (ack m (n-1))`. ack(3, 4)
+  expands to ~6700 frames in our spec-level evaluator, so a useful
+  exercise of the call stack and control transfer. Real OCaml
+  evaluates the same in milliseconds; ours takes ~2 minutes on a
+  contended host but completes correctly. 40 baseline programs total.
 - 2026-05-09 Phase 5.1 — rpn.ml baseline (Reverse Polish Notation
   evaluator using Stack). Walks the token list with List.iter, pushes
   ints onto the stack, on operator tokens pops two operands and