ocaml: phase 5.1 combinations.ml baseline (C(9, 4) = 126)

Pascal-recursion combination enumerator:

  let rec choose k xs =
    if k = 0 then [[]]
    else match xs with
      | [] -> []
      | h :: rest ->
        List.map (fun c -> h :: c) (choose (k - 1) rest)
        @ choose k rest

  C(9, 4) = |choose 4 [1; ...; 9]| = 126

Tests pure-functional enumeration with List.map + closure over h,
@ append, [] | h :: rest pattern match on shrinking input.

200 baseline programs total -- milestone.

lib/ocaml/baseline/combinations.ml

@@ -0,0 +1,12 @@
+let rec choose k xs =
+  if k = 0 then [[]]
+  else
+    match xs with
+    | [] -> []
+    | h :: rest ->
+      List.map (fun c -> h :: c) (choose (k - 1) rest)
+      @ choose k rest
+
+;;
+
+List.length (choose 4 [1; 2; 3; 4; 5; 6; 7; 8; 9])

lib/ocaml/baseline/expected.json

@@ -29,6 +29,7 @@
   "calc.ml": 13,
   "catalan.ml": 42,
   "closures.ml": 315,
+  "combinations.ml": 126,
   "convex_hull.ml": 5,
   "coin_change.ml": 6,
   "coin_min.ml": 6,

plans/ocaml-on-sx.md

@@ -407,6 +407,14 @@ _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.
+- 2026-05-11 Phase 5.1 — combinations.ml baseline (C(9, 4) = 126
+  enumerated). Pascal-style recursive split: with first element h,
+  combinations either include h (recurse with k−1 on rest) or
+  exclude h (recurse with k on rest); identity choose k [] = [].
+  C(9, 4) = 126 = 9!/(4!·5!). Tests pure-functional combination
+  enumeration with `List.map` + closure over `h`, `@` append,
+  and `[] | h :: rest` pattern match on shrinking input.
+  200 baseline programs total.
 - 2026-05-11 Phase 5.1 — unique_paths_obs.ml baseline (count
   monotone paths in 4×4 grid with obstacles at (1,1),(2,3),(3,0)
   = 3). Standard 2D DP with obstacle gating: dp[i][j] = dp[i-1][j]