ocaml: phase 5.1 prefix_sum.ml baseline (precomputed sums + range queries, 14+25+27 = 66)

Two utility functions:

  prefix_sums xs   builds Array of len n+1 such that
                   arr.(i) = sum of xs[0..i-1]
  range_sum p lo hi = p.(hi+1) - p.(lo)

For [3;1;4;1;5;9;2;6;5;3]:
  range_sum 0 4   = 14   (3+1+4+1+5)
  range_sum 5 9   = 25   (9+2+6+5+3)
  range_sum 2 7   = 27   (4+1+5+9+2+6)
  sum             = 66

Tests List.iter mutating Array indexed by a ref counter, plus the
classic prefix-sum technique for O(1) range queries.

67 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -47,6 +47,7 @@
   "palindrome.ml": 4,
   "pascal.ml": 252,
   "pi_leibniz.ml": 314,
+  "prefix_sum.ml": 66,
   "pretty_table.ml": 64,
   "poly_stack.ml": 5,
   "prime_factors.ml": 17,

lib/ocaml/baseline/prefix_sum.ml

@@ -0,0 +1,16 @@
+let prefix_sums xs =
+  let n = List.length xs in
+  let arr = Array.make (n + 1) 0 in
+  let i = ref 0 in
+  List.iter (fun x ->
+    arr.(!i + 1) <- arr.(!i) + x;
+    i := !i + 1
+  ) xs;
+  arr
+
+let range_sum prefixes lo hi = prefixes.(hi + 1) - prefixes.(lo)
+
+;;
+
+let p = prefix_sums [3; 1; 4; 1; 5; 9; 2; 6; 5; 3] in
+range_sum p 0 4 + range_sum p 5 9 + range_sum p 2 7

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 — prefix_sum.ml baseline (precomputed prefix
+  sums for O(1) range queries, sum of three queries = 66).
+  prefix_sums xs returns an Array of len n+1 such that
+  `arr.(i) = sum of xs[0..i-1]`. range_sum computes any contiguous
+  subarray sum in O(1) via subtraction. Tests List.iter mutating
+  Array indexed by ref counter, plus the classic prefix-sum
+  technique. 67 baseline programs total.
 - 2026-05-09 Phase 5.1 — tic_tac_toe.ml baseline (3x3 winner check,
   X wins top row → 1). Board encoded as 9-element flat int array
   with 0=empty, 1=X, 2=O. Three predicate functions check row,