ocaml: phase 5.1 euler40_small.ml baseline (Champernowne digit product = 15)

Build the Champernowne string '12345678910111213...' until at
least 1500 chars; product of digits at positions 1, 10, 100, 1000
is 1 * 1 * 5 * 3 = 15.

Initial implementation timed out: 'String.length (Buffer.contents
buf) < 1500' rebuilt the full string each iteration (O(n^2) in our
spec-level evaluator). Fixed by tracking length separately from
the Buffer:

  let len = ref 0 in
  while !len < 1500 do
    let s = string_of_int !i in
    Buffer.add_string buf s;
    len := !len + String.length s;
    i := !i + 1
  done

Real PE40 uses positions up to 10^6 (answer 210); 1000 keeps under
budget while exercising the same string-build + char-pick pattern.

122 baseline programs total.

lib/ocaml/baseline/euler40_small.ml

@@ -0,0 +1,22 @@
+let euler40 () =
+  let buf = Buffer.create 4096 in
+  let len = ref 0 in
+  let i = ref 1 in
+  while !len < 1500 do
+    let s = string_of_int !i in
+    Buffer.add_string buf s;
+    len := !len + String.length s;
+    i := !i + 1
+  done;
+  let s = Buffer.contents buf in
+  let prod = ref 1 in
+  let positions = [1; 10; 100; 1000] in
+  List.iter (fun p ->
+    let c = s.[p - 1] in
+    prod := !prod * (Char.code c - Char.code '0')
+  ) positions;
+  !prod
+
+;;
+
+euler40 ()

lib/ocaml/baseline/expected.json

@@ -36,6 +36,7 @@
   "euler29_small.ml": 15,
   "euler30_cube.ml": 1301,
   "euler34_small.ml": 145,
+  "euler40_small.ml": 15,
   "euler3.ml": 29,
   "euler4_small.ml": 9009,
   "euler5.ml": 232792560,

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.
+- 2026-05-10 Phase 5.1 — euler40_small.ml baseline (Champernowne
+  digit-product at 1, 10, 100, 1000 = 1*1*5*3 = 15). Builds the
+  Champernowne string until ≥1500 chars; tracks length separately
+  from the Buffer to avoid O(n²) `String.length (Buffer.contents
+  buf)` reallocation. Real PE40 uses positions up to 10^6 (answer
+  210). 122 baseline programs total.
 - 2026-05-09 Phase 5.1 — euler34_small.ml baseline (numbers equal
   to sum of factorials of digits, ≤2000 = 145). 145 = 1!+4!+5! =
   1+24+120. The other "factorion" 40585 is the only number above