choose: the set of all subsets of specified size

src/Data/Set.purs

@@ -24,6 +24,7 @@ module Data.Set
   , subset
   , properSubset
   , intersection
+  , choose
   ) where
 
 import Prelude hiding (map)
@@ -176,3 +177,11 @@ intersection s1 s2 = fromFoldable $ runPure (runSTArray (emptySTArray >>= inters
         LT -> pure $ Loop {a: l + 1, b: r}
         GT -> pure $ Loop {a: l, b: r + 1}
       else pure $ Done acc
+
+-- | The set of all subsets of specified size
+choose :: forall a. Ord a => Set a -> Int -> Set (Set a)
+choose = go (singleton empty)
+  where
+  go acc _ 0 = acc
+  go acc s n =
+    unions $ map (\e -> go (map (insert e) acc) (delete e s) (n - 1)) s

test/Test/Main.purs

@@ -26,3 +26,11 @@ main = do
          s2 = S.fromFoldable [2,4,6,8,10]
          s3 = S.fromFoldable [2,4]
      assert $ S.intersection s1 s2 == s3
+
+  log "choose"
+  do let set = S.fromFoldable [0, 1, 2]
+     assert $ S.choose set 2 == S.fromFoldable `S.map` S.fromFoldable [
+                                  [0, 1]
+                                , [1, 2]
+                                , [0, 2]
+                                ]