ocaml: phase 6 Array.sort/sub/append/exists/for_all/mem (+5 tests, 520 total)

Eight new Array functions, all in OCaml syntax inside runtime.sx,
delegating to the corresponding List operation on the cell's
underlying list:

  sort cmp a    -> a := List.sort cmp !a    (* mutates the cell *)
  stable_sort   = sort
  fast_sort     = sort
  append a b    -> ref (List.append !a !b)
  sub a pos n   -> ref (take n (drop pos !a))
  exists p      -> List.exists p !a
  for_all p     -> List.for_all p !a
  mem x a       -> List.mem x !a

Round-trip:
  let a = Array.of_list [3;1;4;1;5;9;2;6] in
  Array.sort compare a;
  Array.to_list a    = [1;1;2;3;4;5;6;9]

lib/ocaml/runtime.sx

@@ -560,6 +560,31 @@
      let to_list a = !a
      let of_list xs = ref xs
      let copy a = ref !a
+     let sort cmp a = a := List.sort cmp !a
+     let stable_sort = sort
+     let fast_sort = sort
+
+     let append a b = ref (List.append !a !b)
+
+     let sub a pos n =
+       let rec take xs k =
+         if k = 0 then []
+         else match xs with
+              | [] -> []
+              | h :: t -> h :: take t (k - 1)
+       in
+       let rec drop xs k =
+         if k = 0 then xs
+         else match xs with
+              | [] -> []
+              | _ :: t -> drop t (k - 1)
+       in
+       ref (take (drop !a pos) n)
+
+     let exists p a = List.exists p !a
+     let for_all p a = List.for_all p !a
+     let mem x a = List.mem x !a
+
      let blit src si dst di n =
        for k = 0 to n - 1 do
          set dst (di + k) (get src (si + k))

lib/ocaml/test.sh

@@ -1286,6 +1286,18 @@ cat > "$TMPFILE" << 'EPOCHS'
 (epoch 5032)
 (eval "(ocaml-run \"let a = Array.make 5 0 in for i = 0 to 4 do a.(i) <- i * i done; a.(3) + a.(4)\")")
 
+;; ── Array.sort / sub / append / exists / mem ─────────────────
+(epoch 5040)
+(eval "(ocaml-run \"let a = Array.of_list [3;1;4;1;5;9;2;6] in Array.sort compare a; Array.to_list a\")")
+(epoch 5041)
+(eval "(ocaml-run \"let a = Array.of_list [10;20;30;40;50] in let b = Array.sub a 1 3 in Array.fold_left (+) 0 b\")")
+(epoch 5042)
+(eval "(ocaml-run \"let a = Array.of_list [1;2;3] in let b = Array.of_list [4;5;6] in Array.fold_left (+) 0 (Array.append a b)\")")
+(epoch 5043)
+(eval "(ocaml-run \"let a = Array.init 5 (fun i -> i * 2) in Array.exists (fun x -> x = 6) a\")")
+(epoch 5044)
+(eval "(ocaml-run \"let a = Array.of_list [1;2;3;4;5] in Array.mem 3 a\")")
+
 EPOCHS
 
 OUTPUT=$(timeout 360 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
@@ -2043,6 +2055,13 @@ check 5030 "a.(2) <- 99; a.(2) + a.(0)"   '106'
 check 5031 "Array.init 4 + sum a.(0..3)"  '10'
 check 5032 "for + a.(i) <- i*i + sum"     '25'
 
+# ── Array.sort / sub / append / exists / mem ────────────────────
+check 5040 "Array.sort compare"           '(1 1 2 3 4 5 6 9)'
+check 5041 "Array.sub 1 3 sum"            '90'
+check 5042 "Array.append 6-len sum"       '21'
+check 5043 "Array.exists = 6"             'true'
+check 5044 "Array.mem 3 [1..5]"           'true'
+
 TOTAL=$((PASS + FAIL))
 if [ $FAIL -eq 0 ]; then
   echo "ok $PASS/$TOTAL OCaml-on-SX tests passed"

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _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 6 — Array.sort/stable_sort/fast_sort + sub +
+  append + exists + for_all + mem (+5 tests, 520 total). All
+  delegate to the corresponding List operation on the cell's
+  underlying list (sort mutates by replacing the cell, the rest are
+  pure observers). Array round-trip via of_list → sort → to_list
+  works as expected.
 - 2026-05-09 Phase 5.1 — brainfuck.ml baseline (subset interpreter,
   five `+++++.` groups → cumulative 5+10+15+20+25 = 75). No loop
   brackets — the interpreter only handles `> < + - .`, but that's