diff --git a/LICENSE b/LICENSE
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--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,30 @@
+Copyright (c) 2015, Athan Clark
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of Athan Clark nor the names of other
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/Setup.hs b/Setup.hs
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--- /dev/null
+++ b/Setup.hs
@@ -0,0 +1,2 @@
+import Distribution.Simple
+main = defaultMain
diff --git a/set-with.cabal b/set-with.cabal
new file mode 100644
--- /dev/null
+++ b/set-with.cabal
@@ -0,0 +1,37 @@
+Name:                   set-with
+Version:                0.0.1
+Author:                 Athan Clark <athan.clark@gmail.com>
+Maintainer:             Athan Clark <athan.clark@gmail.com>
+License:                BSD3
+License-File:           LICENSE
+Synopsis:               Set of elements sorted by a different data type.
+-- Description:
+Cabal-Version:          >= 1.10
+Build-Type:             Simple
+
+Library
+  Default-Language:     Haskell2010
+  HS-Source-Dirs:       src
+  GHC-Options:          -Wall
+  Exposed-Modules:      Data.SetWith
+  Build-Depends:        base >= 4.6 && < 5
+                      , containers
+                      , invariant
+
+Test-Suite spec
+  Type:                 exitcode-stdio-1.0
+  Default-Language:     Haskell2010
+  Hs-Source-Dirs:       src
+                      , test
+  Ghc-Options:          -Wall
+  Main-Is:              Spec.hs
+  Build-Depends:        base
+                      , tasty
+                      , tasty-quickcheck
+                      , tasty-hunit
+                      , QuickCheck
+                      , quickcheck-instances
+
+Source-Repository head
+  Type:                 git
+  Location:             https://github.com/athanclark/set-with.git
diff --git a/src/Data/SetWith.hs b/src/Data/SetWith.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/SetWith.hs
@@ -0,0 +1,216 @@
+{-# LANGUAGE
+    GeneralizedNewtypeDeriving
+  , NoImplicitPrelude
+  #-}
+
+module Data.SetWith where
+
+import Prelude (Show, String, Eq, Ord, Bool, Int, Maybe, fmap, not, fst, snd, zip, (.), ($))
+import qualified Data.Map as Map
+import qualified Data.List as List
+import Data.Maybe (isJust)
+import qualified Data.Foldable as Fold
+import Data.Functor.Invariant
+import Control.Applicative ((<$>))
+import Data.Monoid (Monoid)
+
+
+newtype SetWith k a = SetWith {unSetWith :: (a -> k, Map.Map k a)}
+  deriving (Monoid)
+
+instance Invariant (SetWith k) where
+  invmap = map
+
+instance Fold.Foldable (SetWith k) where
+  foldr = Data.SetWith.foldr
+
+
+-- * Operators
+
+(\\) :: Ord k => SetWith k a -> SetWith k a -> SetWith k a
+(SetWith (f,xs)) \\ (SetWith (_,ys)) = SetWith (f, Map.difference xs ys)
+
+-- * Query
+
+null :: SetWith k a -> Bool
+null (SetWith (_,xs)) = Map.null xs
+
+size :: SetWith k a -> Int
+size (SetWith (_,xs)) = Map.size xs
+
+member :: Ord k => a -> SetWith k a -> Bool
+member x (SetWith (f,xs)) = Map.member (f x) xs
+
+notMember :: Ord k => a -> SetWith k a -> Bool
+notMember x = not . member x
+
+lookupLT :: Ord k => a -> SetWith k a -> Maybe a
+lookupLT x (SetWith (f,xs)) = snd <$> Map.lookupLT (f x) xs
+
+lookupGT :: Ord k => a -> SetWith k a -> Maybe a
+lookupGT x (SetWith (f,xs)) = snd <$> Map.lookupGT (f x) xs
+
+lookupLE :: Ord k => a -> SetWith k a -> Maybe a
+lookupLE x (SetWith (f,xs)) = snd <$> Map.lookupLE (f x) xs
+
+lookupGE :: Ord k => a -> SetWith k a -> Maybe a
+lookupGE x (SetWith (f,xs)) = snd <$> Map.lookupGE (f x) xs
+
+isSubsetOf :: (Eq a, Ord k) => SetWith k a -> SetWith k a -> Bool
+isSubsetOf (SetWith (_,xs)) (SetWith (_,ys)) = Map.isSubmapOf xs ys
+
+isProperSubsetOf :: (Eq a, Ord k) => SetWith k a -> SetWith k a -> Bool
+isProperSubsetOf (SetWith (_,xs)) (SetWith (_,ys)) = Map.isProperSubmapOf xs ys
+
+-- * Construction
+
+empty :: (a -> k) -> SetWith k a
+empty f = SetWith (f, Map.empty)
+
+singleton :: Ord k => (a -> k) -> a -> SetWith k a
+singleton f x = insert x (empty f)
+
+insert :: Ord k => a -> SetWith k a -> SetWith k a
+insert x (SetWith (f,xs)) = SetWith (f, Map.insert (f x) x xs)
+
+delete :: Ord k => a -> SetWith k a -> SetWith k a
+delete x (SetWith (f,xs)) = SetWith (f, Map.delete (f x) xs)
+
+-- * Combine
+
+union :: Ord k => SetWith k a -> SetWith k a -> SetWith k a
+union (SetWith (f,xs)) (SetWith (_,ys)) = SetWith (f, Map.union xs ys)
+
+unions :: Ord k => (a -> k) -> [SetWith k a] -> SetWith k a
+unions f = List.foldl' union $ empty f
+
+difference :: Ord k => SetWith k a -> SetWith k a -> SetWith k a
+difference (SetWith (f,xs)) (SetWith (_,ys)) = SetWith (f, Map.difference xs ys)
+
+intersection :: Ord k => SetWith k a -> SetWith k a -> SetWith k a
+intersection (SetWith (f,xs)) (SetWith (_,ys)) = SetWith (f, Map.intersection xs ys)
+
+-- * Filter
+
+filter :: (a -> Bool) -> SetWith k a -> SetWith k a
+filter p (SetWith (f,xs)) = SetWith (f, Map.filter p xs)
+
+partition :: (a -> Bool) -> SetWith k a -> (SetWith k a, SetWith k a)
+partition p (SetWith (f,xs)) = let zs = Map.partition p xs
+                               in (SetWith (f, fst zs), SetWith (f, snd zs))
+
+split :: Ord k => a -> SetWith k a -> (SetWith k a, SetWith k a)
+split x (SetWith (f,xs)) = let zs = Map.split (f x) xs
+                           in (SetWith (f, fst zs), SetWith (f, snd zs))
+
+splitMember :: Ord k => a -> SetWith k a -> (SetWith k a, Bool, SetWith k a)
+splitMember x (SetWith (f,xs)) = let (l,b,r) = Map.splitLookup (f x) xs
+                                 in (SetWith (f,l), isJust b, SetWith (f,r))
+
+splitRoot :: Ord k => SetWith k a -> [SetWith k a]
+splitRoot (SetWith (f,xs)) = let xss = Map.splitRoot xs
+                             in fmap (\a -> SetWith (f,a)) xss
+
+-- * Indexed
+
+lookupIndex :: Ord k => a -> SetWith k a -> Maybe Int
+lookupIndex x (SetWith (f,xs)) = Map.lookupIndex (f x) xs
+
+findIndex :: Ord k => a -> SetWith k a -> Int
+findIndex x (SetWith (f,xs)) = Map.findIndex (f x) xs
+
+elemAt :: Int -> SetWith k a -> a
+elemAt i (SetWith (_,xs)) = snd $ Map.elemAt i xs
+
+deleteAt :: Int -> SetWith k a -> SetWith k a
+deleteAt i (SetWith (f,xs)) = SetWith (f, Map.deleteAt i xs)
+
+-- * Map
+
+map :: (a -> b) -> (b -> a) -> SetWith k a -> SetWith k b
+map f g (SetWith (p,xs)) = SetWith (p . g, Map.map f xs)
+
+mapMaybe :: (a -> Maybe b) -> (b -> a) -> SetWith k a -> SetWith k b
+mapMaybe f g (SetWith (p,xs)) = SetWith (p . g, Map.mapMaybe f xs)
+
+-- * Folds
+
+foldr :: (a -> b -> b) -> b -> SetWith k a -> b
+foldr f acc (SetWith (_,xs)) = Map.foldr f acc xs
+
+foldl :: (b -> a -> b) -> b -> SetWith k a -> b
+foldl f acc (SetWith (_,xs)) = Map.foldl f acc xs
+
+-- ** Strict Folds
+
+foldr' :: (a -> b -> b) -> b -> SetWith k a -> b
+foldr' f acc (SetWith (_,xs)) = Map.foldr' f acc xs
+
+foldl' :: (b -> a -> b) -> b -> SetWith k a -> b
+foldl' f acc (SetWith (_,xs)) = Map.foldl' f acc xs
+
+-- ** Legacy Fold
+
+fold :: (a -> b -> b) -> b -> SetWith k a -> b
+fold f acc (SetWith (_,xs)) = Map.fold f acc xs
+
+-- * Min/Max
+
+findMin :: SetWith k a -> a
+findMin = snd . Map.findMin . snd . unSetWith
+
+findMax :: SetWith k a -> a
+findMax = snd . Map.findMax . snd . unSetWith
+
+deleteMin :: SetWith k a -> SetWith k a
+deleteMin (SetWith (f,xs)) = SetWith (f, Map.deleteMin xs)
+
+deleteMax :: SetWith k a -> SetWith k a
+deleteMax (SetWith (f,xs)) = SetWith (f, Map.deleteMax xs)
+
+deleteFindMin :: SetWith k a -> (a, SetWith k a)
+deleteFindMin (SetWith (f,xs)) = let ((_,l),zs) = Map.deleteFindMin xs
+                                 in (l, SetWith (f,zs))
+
+deleteFindMax :: SetWith k a -> (a, SetWith k a)
+deleteFindMax (SetWith (f,xs)) = let ((_,l),zs) = Map.deleteFindMax xs
+                                 in (l, SetWith (f,zs))
+
+minView :: SetWith k a -> Maybe (a, SetWith k a)
+minView (SetWith (f,xs)) = (\(l,a) -> (l, SetWith (f,a))) <$> Map.minView xs
+
+maxView :: SetWith k a -> Maybe (a, SetWith k a)
+maxView (SetWith (f,xs)) = (\(l,a) -> (l, SetWith (f,a))) <$> Map.maxView xs
+
+-- * Conversion
+
+elems :: SetWith k a -> [a]
+elems (SetWith (_,xs)) = Map.elems xs
+
+toList :: SetWith k a -> (a -> k, [a])
+toList (SetWith (f,xs)) = (f, Map.elems xs)
+
+fromList :: Ord k => (a -> k) -> [a] -> SetWith k a
+fromList f = List.foldr insert $ empty f
+
+-- * Ordered List
+
+toAscList :: SetWith k a -> [a]
+toAscList (SetWith (_,xs)) = snd <$> Map.toAscList xs
+
+toDescList :: SetWith k a -> [a]
+toDescList (SetWith (_,xs)) = snd <$> Map.toDescList xs
+
+fromAscList :: Eq k => (a -> k) -> [a] -> SetWith k a
+fromAscList f xs = SetWith (f, Map.fromAscList $ (f <$> xs) `zip` xs)
+
+fromDistinctAscList :: (a -> k) -> [a] -> SetWith k a
+fromDistinctAscList f xs = SetWith (f, Map.fromDistinctAscList $ (f <$> xs) `zip` xs)
+
+-- * Debugging
+
+showTree :: (Show k, Show a) => SetWith k a -> String
+showTree (SetWith (_,xs)) = Map.showTree xs
+
+showTreeWith :: (Show k, Show a) => (k -> a -> String) -> Bool -> Bool -> SetWith k a -> String
+showTreeWith f a b (SetWith (_,xs)) = Map.showTreeWith f a b xs
diff --git a/test/Spec.hs b/test/Spec.hs
new file mode 100644
--- /dev/null
+++ b/test/Spec.hs
@@ -0,0 +1,13 @@
+module Spec where
+
+import Data.SetWithSpec
+
+import Test.Tasty
+
+
+main :: IO ()
+main = defaultMain tests
+
+tests :: TestTree
+tests = testGroup "Testing..."
+  [spec]