From c34ccfdfb5a18d35cd2a9d039b7e71dacc142b21 Mon Sep 17 00:00:00 2001
From: Matthew Leon <ml@matthewleon.com>
Date: Mon, 15 Jan 2018 17:17:43 -0500
Subject: [PATCH] powerSet function

---
 src/Data/Set.purs   |  7 +++++++
 test/Test/Main.purs | 16 ++++++++++++++--
 2 files changed, 21 insertions(+), 2 deletions(-)

diff --git a/src/Data/Set.purs b/src/Data/Set.purs
index 0269cd5..b794c04 100644
--- a/src/Data/Set.purs
+++ b/src/Data/Set.purs
@@ -24,6 +24,7 @@ module Data.Set
   , subset
   , properSubset
   , intersection
+  , powerSet
   ) where
 
 import Prelude hiding (map)
@@ -176,3 +177,9 @@ 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 the given set
+powerSet :: forall a. Ord a => Set a -> Set (Set a)
+powerSet =
+  foldl (\subPowerset a -> subPowerset `union` map (insert a) subPowerset)
+        (singleton empty)
diff --git a/test/Test/Main.purs b/test/Test/Main.purs
index 66c9e74..89e65b5 100644
--- a/test/Test/Main.purs
+++ b/test/Test/Main.purs
@@ -4,10 +4,9 @@ import Prelude
 
 import Control.Monad.Eff (Eff)
 import Control.Monad.Eff.Console (CONSOLE, log)
-import Test.Assert (ASSERT, assert)
-
 import Data.Set (Set)
 import Data.Set as S
+import Test.Assert (ASSERT, assert)
 
 main :: Eff (console :: CONSOLE, assert :: ASSERT) Unit
 main = do
@@ -26,3 +25,16 @@ main = do
          s2 = S.fromFoldable [2,4,6,8,10]
          s3 = S.fromFoldable [2,4]
      assert $ S.intersection s1 s2 == s3
+
+  log "powerSet"
+  do let set = S.fromFoldable [0, 1, 2]
+     assert $ S.powerSet set == (S.fromFoldable `S.map` S.fromFoldable [
+                                    []
+                                  , [0]
+                                  , [1]
+                                  , [2]
+                                  , [0,1]
+                                  , [0,2]
+                                  , [1,2]
+                                  , [0,1,2]
+                                ])