ocaml: phase 5.1 subset_sum.ml baseline (count subsets of [1..8] summing to 10 = 8)

Pure recursion — at each element, take it or don't:

  let rec count_subsets xs target =
    match xs with
    | [] -> if target = 0 then 1 else 0
    | x :: rest ->
      count_subsets rest target
      + count_subsets rest (target - x)

For [1;2;3;4;5;6;7;8] target 10, the recursion tree has 2^8 = 256
leaves. Returns 8 — number of subsets summing to 10:

  1+2+3+4, 1+2+7, 1+3+6, 1+4+5, 2+3+5, 2+8, 3+7, 4+6 = 8

Tests doubly-recursive list traversal pattern with single-arg list
+ accumulator-via-target.

65 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -57,6 +57,7 @@
   "run_length.ml": 11,
   "safe_div.ml": 20,
   "shuffle.ml": 55,
+  "subset_sum.ml": 8,
   "word_freq.ml": 8,
   "zip_unzip.ml": 1000,
   "sieve.ml": 15,

lib/ocaml/baseline/subset_sum.ml

@@ -0,0 +1,10 @@
+let rec count_subsets xs target =
+  match xs with
+  | [] -> if target = 0 then 1 else 0
+  | x :: rest ->
+    count_subsets rest target
+    + count_subsets rest (target - x)
+
+;;
+
+count_subsets [1; 2; 3; 4; 5; 6; 7; 8] 10

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 — subset_sum.ml baseline (count subsets of
+  [1..8] summing to 10 = 8). Pure recursion: at each element, take
+  it or don't. Base case: target=0 → 1, target≠0 → 0. 2^8 = 256
+  recursive calls. The 8 subsets are: 1+2+3+4, 1+2+7, 1+3+6, 1+4+5,
+  1+9 (no), 2+3+5, 2+8, 3+7, 4+6, 1+2+3+4. Verified count = 8.
+  Tests doubly-recursive list traversal pattern. 65 baseline programs
+  total.
 - 2026-05-09 Phase 5.1 — hailstone.ml baseline (Collatz length,
   starting from 27 → 111 steps to reach 1). Iterative while-loop
   applies `n / 2` if even, `3n + 1` if odd, counting steps. 27 is