ocaml: phase 5.1 bowling.ml baseline (10-pin bowling score, sample game = 167)

Walks the pin-knockdown list applying strike/spare bonuses through
a 10-frame counter:

  strike (10):           score 10 + next 2 throws,  advance i+1
  spare  (a + b = 10):   score 10 + next 1 throw,   advance i+2
  open  (a + b < 10):    score a + b,                advance i+2

Frame ten special-cases are handled implicitly: the input includes
bonus throws naturally and the while-loop terminates after frame 10.

  bowling_score [10; 7; 3; 9; 0; 10; 0; 8; 8; 2; 0; 6;
                 10; 10; 10; 8; 1]
  = 20+19+9+18+8+10+6+30+28+19
  = 167

131 baseline programs total.

lib/ocaml/baseline/bowling.ml

@@ -0,0 +1,24 @@
+let bowling_score frames =
+  let arr = Array.of_list frames in
+  let n = Array.length arr in
+  let total = ref 0 in
+  let i = ref 0 in
+  let frame = ref 1 in
+  while !frame <= 10 && !i < n do
+    if arr.(!i) = 10 then begin
+      total := !total + 10 + arr.(!i + 1) + arr.(!i + 2);
+      i := !i + 1
+    end else if !i + 1 < n && arr.(!i) + arr.(!i + 1) = 10 then begin
+      total := !total + 10 + arr.(!i + 2);
+      i := !i + 2
+    end else begin
+      total := !total + arr.(!i) + arr.(!i + 1);
+      i := !i + 2
+    end;
+    frame := !frame + 1
+  done;
+  !total
+
+;;
+
+bowling_score [10; 7; 3; 9; 0; 10; 0; 8; 8; 2; 0; 6; 10; 10; 10; 8; 1]

lib/ocaml/baseline/expected.json

@@ -7,6 +7,7 @@
   "anagrams.ml": 3,
   "atm.ml": 120,
   "bag.ml": 3,
+  "bowling.ml": 167,
   "bf_full.ml": 6,
   "bisect.ml": 141,
   "bigint_add.ml": 28,

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 — bowling.ml baseline (10-pin bowling score
+  for canonical "167" PBA-style game). Walks pin-knockdown list
+  applying strike/spare bonuses through a 10-frame counter. Strike
+  consumes 1 throw + 2 bonus; spare consumes 2 throws + 1 bonus;
+  open frame is just the two pin counts. Frame ten special-cases
+  ignored (input includes the bonus throws naturally). 131 baseline
+  programs total.
 - 2026-05-10 Phase 5.1 — tail_factorial.ml baseline (12! via tail
   recursion = 479001600). Single-helper tail-recursive loop
   threading an accumulator. Companion to factorial.ml (10! via