From fad81e0b0c89896f2aa222081ecadbadbd243649 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Mon, 11 May 2026 05:25:03 +0000
Subject: [PATCH] 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 | 12 ++++++++++++
 lib/ocaml/baseline/expected.json   |  1 +
 plans/ocaml-on-sx.md               |  8 ++++++++
 3 files changed, 21 insertions(+)
 create mode 100644 lib/ocaml/baseline/combinations.ml

diff --git a/lib/ocaml/baseline/combinations.ml b/lib/ocaml/baseline/combinations.ml
new file mode 100644
index 00000000..25a096d9
--- /dev/null
+++ b/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])
diff --git a/lib/ocaml/baseline/expected.json b/lib/ocaml/baseline/expected.json
index 025653bd..ed41cf21 100644
--- a/lib/ocaml/baseline/expected.json
+++ b/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,
diff --git a/plans/ocaml-on-sx.md b/plans/ocaml-on-sx.md
index 50b4dedc..5a5fe298 100644
--- a/plans/ocaml-on-sx.md
+++ b/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]