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,