ocaml: phase 5.1 sieve.ml baseline (Sieve of Eratosthenes)

Counts primes <= 50, expected 15.

Stresses the recently-added Array module + the new array-indexing
syntax together with nested control flow:

  let sieve = Array.make (n + 1) true in
  sieve.(0) <- false;
  sieve.(1) <- false;
  for i = 2 to n do
    if sieve.(i) then begin
      let j = ref (i * i) in
      while !j <= n do
        sieve.(!j) <- false;
        j := !j + i
      done
    end
  done;
  ...

Exercises: Array.make, arr.(i), arr.(i) <- v, nested for/while,
begin..end blocks, ref/!/:=, integer arithmetic. 24 baseline
programs total.

lib/ocaml/baseline/expected.json

@@ -22,6 +22,7 @@
   "queens.ml": 2,
   "quicksort.ml": 44,
   "roman.ml": 44,
+  "sieve.ml": 15,
   "sum_squares.ml": 385,
   "word_count.ml": 3
 }

lib/ocaml/baseline/sieve.ml

@@ -0,0 +1,22 @@
+let count_primes n =
+  let sieve = Array.make (n + 1) true in
+  sieve.(0) <- false;
+  sieve.(1) <- false;
+  for i = 2 to n do
+    if sieve.(i) then begin
+      let j = ref (i * i) in
+      while !j <= n do
+        sieve.(!j) <- false;
+        j := !j + i
+      done
+    end
+  done;
+  let count = ref 0 in
+  for i = 2 to n do
+    if sieve.(i) then count := !count + 1
+  done;
+  !count
+
+;;
+
+count_primes 50

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 — sieve.ml baseline (Sieve of Eratosthenes,
+  count of primes ≤ 50 = 15). Stresses Array.make + arr.(i) +
+  arr.(i) <- v + nested for/while loops + `begin..end` block. 24
+  baseline programs total.
 - 2026-05-09 Phase 4 — `arr.(i)` and `arr.(i) <- v` array indexing
   syntax (+3 tests, 515 total). parse-atom-postfix's `.(...)` branch
   now disambiguates between let-open and array-get based on whether