ocaml: phase 5.1 tarjan_scc.ml baseline (8-node digraph, 4 SCCs)

Tarjan's strongly-connected components in a single DFS using
index/lowlink:

  graph (8 nodes, directed):
    0 -> 1 -> 2 -> 0   (3-cycle)
    2 -> 3
    3 -> 4
    4 -> 5 -> 6 -> 4   (3-cycle)
    4 -> 7

  SCCs: {0,1,2}, {3}, {4,5,6}, {7}  =  4 components

Module-level ref + array state (index_arr, lowlink, on_stack,
stack, scc_count). When lowlink(v) = index(v), pop from stack
until v is removed; that's a complete SCC.

Tests: recursive function with module-level mutable state,
nested begin/end branches inside List.iter closure, inner
`let rec pop ()` traversing a ref-of-list, pattern match on
[] / h :: rest cons-list shape.

154 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -135,6 +135,7 @@
   "stable_unique.ml": 46,
   "subseq_check.ml": 3,
   "tail_factorial.ml": 479001600,
+  "tarjan_scc.ml": 4,
   "subset_sum.ml": 8,
   "tic_tac_toe.ml": 1,
   "topo_sort.ml": 6,

lib/ocaml/baseline/tarjan_scc.ml

@@ -0,0 +1,53 @@
+let n = 8
+
+let adj = [|
+  [1];
+  [2];
+  [0; 3];
+  [4];
+  [5; 7];
+  [6];
+  [4];
+  []
+|]
+
+let index_counter = ref 0
+let stack = ref []
+let on_stack = Array.make n false
+let index_arr = Array.make n (-1)
+let lowlink = Array.make n 0
+let scc_count = ref 0
+
+let rec strongconnect v =
+  index_arr.(v) <- !index_counter;
+  lowlink.(v) <- !index_counter;
+  index_counter := !index_counter + 1;
+  stack := v :: !stack;
+  on_stack.(v) <- true;
+  List.iter (fun w ->
+    if index_arr.(w) = -1 then begin
+      strongconnect w;
+      if lowlink.(w) < lowlink.(v) then lowlink.(v) <- lowlink.(w)
+    end else if on_stack.(w) then begin
+      if index_arr.(w) < lowlink.(v) then lowlink.(v) <- index_arr.(w)
+    end
+  ) adj.(v);
+  if lowlink.(v) = index_arr.(v) then begin
+    let rec pop () =
+      match !stack with
+      | [] -> ()
+      | w :: rest ->
+        stack := rest;
+        on_stack.(w) <- false;
+        if w <> v then pop ()
+    in
+    pop ();
+    scc_count := !scc_count + 1
+  end
+
+;;
+
+for v = 0 to n - 1 do
+  if index_arr.(v) = -1 then strongconnect v
+done;
+!scc_count

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 — tarjan_scc.ml baseline (Tarjan's
+  strongly-connected components on 8-node digraph → 4 SCCs).
+  Graph: 0→1→2→0 (cycle) plus 2→3, 3→4, 4→5→6→4 (cycle), 4→7.
+  SCCs: {0,1,2}, {3}, {4,5,6}, {7} = 4 components. Single DFS
+  with index/lowlink, on-stack flag, pop until root when
+  lowlink = index. Tests recursive functions with module-level
+  ref + array state, nested begin/end branches inside List.iter
+  closure, inner `let rec pop ()` walking ref-of-list, pattern
+  match on `[] | h :: rest`. 154 baseline programs total.
 - 2026-05-10 Phase 5.1 — lev_iter.ml baseline (iterative
   Levenshtein DP, sum of 5 distances = 16). Rolling-array DP
   (O(min(m,n)) space). Distances: kitten→sitting=3, saturday→