ocaml: phase 5.1 euler6.ml baseline (Project Euler #6, sum^2 - sum_sq for 1..100 = 25164150)

Project Euler #6: difference between square of sum and sum of squares
for 1..100.

  let euler6 n =
    let sum = ref 0 in
    let sum_sq = ref 0 in
    for i = 1 to n do
      sum := !sum + i;
      sum_sq := !sum_sq + i * i
    done;
    !sum * !sum - !sum_sq

  euler6 100 = 5050^2 - 338350 = 25502500 - 338350 = 25164150

102 baseline programs total.

lib/ocaml/baseline/euler6.ml

@@ -0,0 +1,12 @@
+let euler6 n =
+  let sum = ref 0 in
+  let sum_sq = ref 0 in
+  for i = 1 to n do
+    sum := !sum + i;
+    sum_sq := !sum_sq + i * i
+  done;
+  !sum * !sum - !sum_sq
+
+;;
+
+euler6 100

lib/ocaml/baseline/expected.json

@@ -26,6 +26,7 @@
   "exception_user.ml": 26,
   "euler1.ml": 233168,
   "euler2.ml": 4613732,
+  "euler6.ml": 25164150,
   "expr_eval.ml": 16,
   "expr_simp.ml": 22,
   "factorial.ml": 3628800,

plans/ocaml-on-sx.md

@@ -407,6 +407,10 @@ _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 — euler6.ml baseline (Project Euler #6, square
+  of sum minus sum of squares for 1..100 = 25164150). Single for-loop
+  threading two refs; (sum 1..100)^2 - sum(i^2 for 1..100) = 5050^2
+  - 338350 = 25502500 - 338350 = 25164150. 102 baseline programs total.
 - 2026-05-09 Phase 5.1 — euler2.ml baseline (Project Euler #2, sum
   of even Fibonacci ≤ 4M = 4613732). Iterative two-ref Fibonacci,
   accumulating only even terms. Sequence: 1, 2, 3, 5, 8, 13, 21,