ocaml: phase 5.1 pascal.ml baseline (Pascal triangle row 10 middle = C(10,5) = 252)

next_row prepends 1, walks adjacent pairs (x, y) emitting x+y,
appends a final 1:

  let rec next_row prev =
    let rec aux a =
      match a with
      | [_] -> [1]
      | x :: y :: rest -> (x + y) :: aux (y :: rest)
      | [] -> []
    in
    1 :: aux prev

row n iterates next_row n times starting from [1] using a ref +
'for _ = 1 to n do r := next_row !r done'.

  row 10 = [1;10;45;120;210;252;210;120;45;10;1]
  List.nth (row 10) 5 = 252 = C(10, 5)

Exercises three-arm match including [_] singleton wildcard, x :: y
:: rest binding, and the for-loop with wildcard counter. 45 baseline
programs total.

lib/ocaml/baseline/expected.json

@@ -29,6 +29,7 @@
   "newton_sqrt.ml": 1414,
   "mutable_record.ml": 10,
   "option_match.ml": 5,
+  "pascal.ml": 252,
   "pi_leibniz.ml": 314,
   "pretty_table.ml": 64,
   "poly_stack.ml": 5,

lib/ocaml/baseline/pascal.ml

@@ -0,0 +1,19 @@
+let rec next_row prev =
+  let rec aux a =
+    match a with
+    | [_] -> [1]
+    | x :: y :: rest -> (x + y) :: aux (y :: rest)
+    | [] -> []
+  in
+  1 :: aux prev
+
+let row n =
+  let r = ref [1] in
+  for _ = 1 to n do
+    r := next_row !r
+  done;
+  !r
+
+;;
+
+List.nth (row 10) 5

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 — pascal.ml baseline (Pascal's triangle row
+  10 middle = C(10, 5) = 252). next_row prepends 1, walks adjacent
+  pairs (x, y) emitting x+y, appends a final 1. row n iterates
+  next_row n times starting from [1]. Three-arm match including
+  `[_]` (singleton wildcard) and `x :: y :: rest`. Iteration via
+  `for _ = 1 to n do r := next_row !r done`. 45 baseline programs
+  total.
 - 2026-05-09 Phase 5.1 — run_length.ml baseline (run-length encoding,
   sum of counts = 11). RLE encodes [1;1;1;2;2;3;3;3;3;1;1] as
   [(1,3);(2,2);(3,4);(1,2)]. Sum-of-counts = 11 verifies that the