diff --git a/benchmarks/src/01.hs b/benchmarks/src/01.hs
--- a/benchmarks/src/01.hs
+++ b/benchmarks/src/01.hs
@@ -1,219 +1,340 @@
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE CPP   #-}
-
-module Main
-( main
-) where
-
-#define BENCH_SMALL
-#define BENCH_ESSENTIALS
-
---------------------------------------------------------------------------------
-import           Control.DeepSeq (NFData(..))
-import           Control.Exception.Base (evaluate)
-import           Control.Monad.Trans (liftIO)
---------------------------------------------------------------------------------
-import           Data.List
-import qualified Data.Map.Strict as Data.Map
---------------------------------------------------------------------------------
-import qualified Criterion.Config as C
-import qualified Criterion.Main   as C
---------------------------------------------------------------------------------
-import qualified DS.B01
-import qualified TS.B01
-import qualified IS.B01
---------------------------------------------------------------------------------
-import Common
---------------------------------------------------------------------------------
-
-data RNF where
-    RNF :: NFData a => a -> RNF
-
-instance NFData RNF where
-    rnf (RNF x) = rnf x
-
-main :: IO ()
-main = C.defaultMainWith C.defaultConfig (liftIO . evaluate $ rnf
-  [
-    RNF elems100000
-  , RNF elems200000
-  , RNF elems400000
-  , RNF elems800000
-
-  , RNF elems5000x5000
-  , RNF elems10000x5000
-
-  , RNF ds100000
-  , RNF ds200000
-
-  , RNF map100000
-  , RNF map200000
-  
-  , RNF is100000
-  , RNF is200000
- 
-  , RNF ts100000
-  , RNF ts200000
-
-  , RNF elem9999999
-  , RNF elem2500
-  ])
-  -- Insert 1 element into a store of size N. No collisions.
-  [
-    {-
-    C.bgroup "insert (Int) 01 100000"
-    [ C.bcompare
-      [ C.bench "DS" $ C.whnf (DS.B01.insert elem9999999) ds100000
-      , C.bench "DS (Unsafe)" $ C.whnf (DS.B01.insertUnsafe elem9999999) ds100000
-#ifndef BENCH_DS
-      , C.bench "Map" $ C.whnf (insertMap elem9999999) map10000
-      , C.bench "IS" $ C.whnf (IS.B01.force . IS.B01.insert elem9999999) is100000
-      , C.bench "TS" $ C.whnf (TS.B01.force . TS.B01.insert elem9999999) ts100000
-#endif
-      ]
-    ]
-  , C.bgroup "insert (Int) 01 200000"
-    [ C.bcompare
-      [ C.bench "DS" $ C.nf (DS.B01.insert elem9999999) ds200000
-      , C.bench "DS (Unsafe)" $ C.nf (DS.B01.insertUnsafe elem9999999) ds200000
-#ifndef BENCH_DS
-      , C.bench "Map" $ C.whnf (insertMap elem9999999) map20000
-      , C.bench "IS" $ C.whnf (IS.B01.force . IS.B01.insert elem9999999) is200000
-      , C.bench "TS" $ C.whnf (TS.B01.force . TS.B01.insert elem9999999) ts200000
-#endif
-      ]
-    ]
-  , C.bgroup "insert-collision (Int) 01 100000"
-    [ C.bcompare
-      [ C.bench "DS" $ C.whnf (DS.B01.insert elem2500) ds100000
-#ifndef BENCH_DS
-      , C.bench "Map" $ C.whnf (insertMap elem2500) map100000
-      , C.bench "IS" $ C.whnf (IS.B01.force . IS.B01.insert elem2500) is100000
-      , C.bench "TS" $ C.whnf (TS.B01.force . TS.B01.insert elem2500) ts100000
-#endif
-      ]
-    ]
-  , C.bgroup "insert-collision (Int) 01 200000"
-    [ C.bcompare
-      [ C.bench "DS" $ C.whnf (DS.B01.insert elem2500) ds200000
-#ifndef BENCH_DS
-      , C.bench "Map" $ C.whnf (insertMap elem2500) map200000
-      , C.bench "IS" $ C.whnf (IS.B01.force . IS.B01.insert elem2500) is200000
-      , C.bench "TS" $ C.whnf (TS.B01.force . TS.B01.insert elem2500) ts200000
-#endif
-      ]
-    ]
-    -}
-    C.bgroup "lookup OO EQ (Int) 01 200000"
-    [ C.bcompare
-      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOOEQ 10000) ds200000
-      , C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOOEQLens 10000) ds200000
-#ifndef BENCH_DS
-      , C.bench "Map" $ C.nf (Data.Map.lookup 10000) map200000
-      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOOEQ 10000) is200000
-      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOOEQ 10000) ts200000
-#endif
-      ]
-    ]
-  , C.bgroup "lookup OO GE (Int) 01 200000 (500)"
-    [ C.bcompare
-      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOOGE 199500) ds200000
-      , C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOOGELens 199500) ds200000
-#ifndef BENCH_DS
-      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOOGE 199500) is200000
-      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOOGE 199500) ts200000
-#endif
-      ]
-    ]
-  , C.bgroup "lookup OM EQ (Int) 01 200000"
-    [ C.bcompare
-      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOMEQ 200) ds200000
-      , C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOMEQLens 200) ds200000
-#ifndef BENCH_DS
-      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOMEQ 200) is200000
-      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOMEQ 200) ts200000
-#endif
-      ]
-    ]
-  , C.bgroup "lookup OM GE (Int) 01 200000 (500)"
-    [ C.bcompare
-      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOMGE 39900) ds200000
-      , C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOMGELens 39900) ds200000
-#ifndef BENCH_DS
-      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOMGE 39900) is200000
-      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOMGE 39900) ts200000
-#endif
-      ]
-    ]
-  , C.bgroup "lookup MM EQ (Int) 01 200000"
-    [ C.bcompare
-      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupMMEQ 200) ds200000
-      , C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupMMEQLens 200) ds200000
-#ifndef BENCH_DS
-      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupMMEQ 200) is200000
-      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupMMEQ 200) ts200000
-#endif
-      ]
-    ]
-  ]
-
-
----
-
-insertListDS :: [C01] -> DS.B01.DS -> DS.B01.DS
-insertListDS xs s0 = foldl' (flip DS.B01.insert) s0 xs
-
-insertListTS :: [C01] -> TS.B01.TS -> TS.B01.TS
-insertListTS xs s0 = snd $!
-  foldl' (\(n, acc) x -> if n == t
-                           then rnf acc `seq` (0, TS.B01.insert x acc)
-                           else (n + 1, TS.B01.insert x acc)
-         ) (0 :: Int, s0) xs
-  where t = 10000
-
-insertListIS :: [C01] -> IS.B01.IS -> IS.B01.IS
-insertListIS xs s0 = snd $! 
-  foldl' (\(n, acc) x -> if n == t
-                           then rnf acc `seq` (0, IS.B01.insert x acc)
-                           else (n + 1, IS.B01.insert x acc)
-         ) (0 :: Int, s0) xs
-  where t = 10000
-
-insertListMap :: [C01] -> Data.Map.Map Int C01 -> Data.Map.Map Int C01
-insertListMap xs s0 = foldl' (flip insertMap) s0 xs
-
-insertMap :: C01 -> Data.Map.Map Int C01 -> Data.Map.Map Int C01
-insertMap x@(C01 oo _ _) = Data.Map.insert oo x
-
--- MAP
-
-map100000 :: Data.Map.Map Int C01
-map100000 = insertListMap elems100000 Data.Map.empty
-
-map200000 :: Data.Map.Map Int C01
-map200000 = insertListMap elems200000 Data.Map.empty
-
--- IS
-
-is100000 :: IS.B01.IS
-is100000 = insertListIS elems100000 IS.B01.empty
-
-is200000 :: IS.B01.IS
-is200000 = insertListIS elems200000 IS.B01.empty
-
--- DS
-
-ds100000 :: DS.B01.DS
-ds100000 = insertListDS elems100000 DS.B01.empty
-
-ds200000 :: DS.B01.DS
-ds200000 = insertListDS elems200000 DS.B01.empty
-
--- TS
-
-ts100000 :: TS.B01.TS
-ts100000 = insertListTS elems100000 TS.B01.empty
-
-ts200000 :: TS.B01.TS
-ts200000 = insertListTS elems200000 TS.B01.empty
-
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE CPP   #-}
+
+module Main
+( main
+) where
+
+-- #define BENCH_SMALL
+-- #define BENCH_ESSENTIALS
+
+--------------------------------------------------------------------------------
+import           Control.DeepSeq (NFData(..))
+import           Control.Exception.Base (evaluate)
+import           Control.Monad.Trans (liftIO)
+--------------------------------------------------------------------------------
+import           Data.List
+import qualified Data.Map.Strict as Data.Map
+--------------------------------------------------------------------------------
+import qualified Criterion.Config as C
+import qualified Criterion.Main   as C
+--------------------------------------------------------------------------------
+import qualified DS.B01
+import qualified TS.B01
+import qualified IS.B01
+--------------------------------------------------------------------------------
+import Common
+--------------------------------------------------------------------------------
+
+data RNF where
+    RNF :: NFData a => a -> RNF
+
+instance NFData RNF where
+    rnf (RNF x) = rnf x
+
+main :: IO ()
+main = C.defaultMainWith C.defaultConfig (liftIO . evaluate $ rnf
+  [
+    RNF elems200000
+  , RNF map200000
+  , RNF ds200000
+  , RNF is200000
+  , RNF ts200000
+
+#ifdef BENCH_SMALL
+  , RNF elems50000
+  , RNF elems100000
+  
+  , RNF ds50000
+  , RNF ds100000
+
+  , RNF map50000
+  , RNF map100000
+  
+  , RNF is50000
+  , RNF is100000
+ 
+  , RNF ts50000
+  , RNF ts100000
+#endif
+
+  , RNF elem9999999
+  , RNF elem2500
+  ])
+  -- Insert 1 element into a store of size N. No collisions.
+  [
+#ifdef BENCH_SMALL
+    C.bgroup "insertLookup (Int) 01 100000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.insertLookup 9999999 9999999 9999999) ds100000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.insertLookup 9999999 9999999 9999999) is100000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.insertLookup 9999999 9999999 9999999) ts100000
+#endif
+      ]
+    ] ,
+#endif
+    C.bgroup "insertLookup (Int) 01 200000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.insertLookup 9999999 9999999 9999999) ds200000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.insertLookup 9999999 9999999 9999999) is200000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.insertLookup 9999999 9999999 9999999) ts200000
+#endif
+      ]
+    ]
+#ifdef BENCH_SMALL
+  , C.bgroup "insert (Int) 01 100000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (DS.B01.insert elem9999999) ds100000
+#ifndef BENCH_DS
+      , C.bench "Map" $ C.whnf (insertMap elem9999999) map100000
+#endif
+      ]
+    ]
+#endif
+  , C.bgroup "insert (Int) 01 200000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (DS.B01.insert elem9999999) ds200000
+#ifndef BENCH_DS
+      , C.bench "Map" $ C.whnf (insertMap elem9999999) map200000
+#endif
+      ]
+    ]
+#ifdef BENCH_SMALL
+  , C.bgroup "lookup OO EQ (Int) 01 50000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOOEQ 10000) ds50000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOOEQLens 10000) ds50000
+#ifndef BENCH_DS
+      , C.bench "Map" $ C.nf (Data.Map.lookup 10000) map50000
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOOEQ 10000) is50000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOOEQ 10000) ts50000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OO GE (Int) 01 50000 (500)"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOOGE 49500) ds50000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOOGELens 99500) ds50000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOOGE 49500) is50000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOOGE 49500) ts50000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OM EQ (Int) 01 50000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOMEQ 200) ds50000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOMEQLens 200) ds50000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOMEQ 200) is50000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOMEQ 200) ts50000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OM GE (Int) 01 50000 (500)"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOMGE 9900) ds50000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOMGELens 9900) ds50000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOMGE 9900) is50000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOMGE 9900) ts50000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup MM EQ (Int) 01 50000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupMMEQ 200) ds50000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupMMEQLens 200) ds50000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupMMEQ 200) is50000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupMMEQ 200) ts50000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OO EQ (Int) 01 100000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOOEQ 10000) ds100000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOOEQLens 10000) ds100000
+#ifndef BENCH_DS
+      , C.bench "Map" $ C.nf (Data.Map.lookup 10000) map100000
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOOEQ 10000) is100000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOOEQ 10000) ts100000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OO GE (Int) 01 100000 (500)"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOOGE 99500) ds100000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOOGELens 99500) ds100000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOOGE 99500) is100000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOOGE 99500) ts100000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OM EQ (Int) 01 100000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOMEQ 200) ds100000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOMEQLens 200) ds100000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOMEQ 200) is100000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOMEQ 200) ts100000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OM GE (Int) 01 100000 (500)"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOMGE 19900) ds100000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOMGELens 19900) ds100000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOMGE 19900) is100000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOMGE 19900) ts100000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup MM EQ (Int) 01 100000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupMMEQ 200) ds100000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupMMEQLens 200) ds100000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupMMEQ 200) is100000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupMMEQ 200) ts100000
+#endif
+      ]
+    ]
+#endif
+  , C.bgroup "lookup OO EQ (Int) 01 200000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOOEQ 10000) ds200000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOOEQLens 10000) ds200000
+#ifndef BENCH_DS
+      , C.bench "Map" $ C.nf (Data.Map.lookup 10000) map200000
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOOEQ 10000) is200000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOOEQ 10000) ts200000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OO GE (Int) 01 200000 (500)"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOOGE 199500) ds200000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOOGELens 199500) ds200000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOOGE 199500) is200000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOOGE 199500) ts200000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OM EQ (Int) 01 200000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOMEQ 200) ds200000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOMEQLens 200) ds200000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOMEQ 200) is200000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOMEQ 200) ts200000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup OM GE (Int) 01 200000 (500)"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupOMGE 39900) ds200000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupOMGELens 39900) ds200000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupOMGE 39900) is200000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupOMGE 39900) ts200000
+#endif
+      ]
+    ]
+  , C.bgroup "lookup MM EQ (Int) 01 200000"
+    [ C.bcompare
+      [ C.bench "DS" $ C.whnf (forceList . DS.B01.lookupMMEQ 200) ds200000
+      --, C.bench "DS (Lens)" $ C.whnf (forceList . DS.B01.lookupMMEQLens 200) ds200000
+#ifndef BENCH_DS
+      , C.bench "IS" $ C.whnf (forceList . IS.B01.lookupMMEQ 200) is200000
+      , C.bench "TS" $ C.whnf (forceList . TS.B01.lookupMMEQ 200) ts200000
+#endif
+      ]
+    ]
+  ]
+
+
+---
+
+insertListDS :: [C01] -> DS.B01.DS -> DS.B01.DS
+insertListDS xs s0 = foldl' (flip DS.B01.insert) s0 xs
+
+insertListTS :: [C01] -> TS.B01.TS -> TS.B01.TS
+insertListTS xs s0 = snd $!
+  foldl' (\(n, acc) x -> if n == t
+                           then rnf acc `seq` (0, TS.B01.insert x acc)
+                           else (n + 1, TS.B01.insert x acc)
+         ) (0 :: Int, s0) xs
+  where t = 10000
+
+insertListIS :: [C01] -> IS.B01.IS -> IS.B01.IS
+insertListIS xs s0 = snd $! 
+  foldl' (\(n, acc) x -> if n == t
+                           then rnf acc `seq` (0, IS.B01.insert x acc)
+                           else (n + 1, IS.B01.insert x acc)
+         ) (0 :: Int, s0) xs
+  where t = 10000
+
+insertListMap :: [C01] -> Data.Map.Map Int C01 -> Data.Map.Map Int C01
+insertListMap xs s0 = foldl' (flip insertMap) s0 xs
+
+insertMap :: C01 -> Data.Map.Map Int C01 -> Data.Map.Map Int C01
+insertMap x@(C01 oo _ _) = Data.Map.insert oo x
+
+-- MAP
+
+#ifdef BENCH_SMALL
+map50000 :: Data.Map.Map Int C01
+map50000 = insertListMap elems50000 Data.Map.empty
+
+map100000 :: Data.Map.Map Int C01
+map100000 = insertListMap elems100000 Data.Map.empty
+#endif
+
+map200000 :: Data.Map.Map Int C01
+map200000 = insertListMap elems200000 Data.Map.empty
+
+-- IS
+
+#ifdef BENCH_SMALL
+is50000 :: IS.B01.IS
+is50000 = insertListIS elems50000 IS.B01.empty
+
+is100000 :: IS.B01.IS
+is100000 = insertListIS elems100000 IS.B01.empty
+#endif
+
+is200000 :: IS.B01.IS
+is200000 = insertListIS elems200000 IS.B01.empty
+
+-- DS
+
+#ifdef BENCH_SMALL
+ds50000 :: DS.B01.DS
+ds50000 = insertListDS elems50000 DS.B01.empty
+
+ds100000 :: DS.B01.DS
+ds100000 = insertListDS elems100000 DS.B01.empty
+#endif
+
+ds200000 :: DS.B01.DS
+ds200000 = insertListDS elems200000 DS.B01.empty
+
+-- TS
+
+#ifdef BENCH_SMALL
+ts50000 :: TS.B01.TS
+ts50000 = insertListTS elems50000 TS.B01.empty
+
+ts100000 :: TS.B01.TS
+ts100000 = insertListTS elems100000 TS.B01.empty
+#endif
+
+ts200000 :: TS.B01.TS
+ts200000 = insertListTS elems200000 TS.B01.empty
+
diff --git a/benchmarks/src/Common.hs b/benchmarks/src/Common.hs
--- a/benchmarks/src/Common.hs
+++ b/benchmarks/src/Common.hs
@@ -1,73 +1,76 @@
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE UndecidableInstances #-}
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE DeriveDataTypeable #-}
-{-# LANGUAGE CPP #-}
-{-# OPTIONS_GHC -fno-warn-orphans #-} 
-
-#define BENCH_ESSENTIALS
-
-module Common
-where
-
---------------------------------------------------------------------------------
-import           Control.DeepSeq (NFData(..))
-import           Data.Data
---------------------------------------------------------------------------------
-
-data C01 = C01 
-    {-# UNPACK #-} !Int
-    {-# UNPACK #-} !Int
-                   ![Int]
-    deriving (Eq, Ord, Show, Typeable)
-
-instance NFData C01 where
-    rnf (C01 x y z) = rnf x `seq` rnf y `seq` rnf z
-
-elem9999999 :: C01
-elem9999999 = head $! generate 9999999 1 
-
-elem2500 :: C01
-elem2500 = head $! generate 2500 1 
-
-elems5000x5000 :: [C01]
-elems5000x5000 = generate 5000 5000
-
-elems10000x5000 :: [C01]
-elems10000x5000 = generate 10000 5000
-
-#ifdef BENCH_SMALL
-elems10000 :: [C01]
-elems10000 = generate 0 10000
-
-elems20000 :: [C01]
-elems20000 = generate 0 20000
-
-#else
-elems100000 :: [C01]
-elems100000 = generate 0 100000
-
-elems200000 :: [C01]
-elems200000 = generate 0 200000
-
-elems400000 :: [C01]
-elems400000 = generate 0 400000
-
-elems800000 :: [C01]
-elems800000 = generate 0 800000
-#endif
-
-generate :: Int -> Int -> [C01]
-generate o n = map (\x -> C01 x (x `div` s) [x .. x + s]) [o .. (n + o) - 1]
-  where
-    s = 5
-
-forceList :: [a] -> ()
-forceList ll = seq (go ll) ()
-  where
-    go [] = ()
-    go (_:xs) = go xs
-
-
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE UndecidableInstances #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE DeriveDataTypeable #-}
+{-# LANGUAGE CPP #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-} 
+
+-- #define BENCH_ESSENTIALS
+
+module Common
+where
+
+--------------------------------------------------------------------------------
+import           Control.DeepSeq (NFData(..))
+import           Data.Data
+--------------------------------------------------------------------------------
+
+data C01 = C01 
+    {-# UNPACK #-} !Int
+    {-# UNPACK #-} !Int
+                   ![Int]
+    deriving (Eq, Ord, Show, Typeable)
+
+instance NFData C01 where
+    rnf (C01 x y z) = rnf x `seq` rnf y `seq` rnf z
+
+elem9999999 :: C01
+elem9999999 = head $! generate 9999999 1 
+
+elem2500 :: C01
+elem2500 = head $! generate 2500 1 
+
+elems5000x5000 :: [C01]
+elems5000x5000 = generate 5000 5000
+
+elems10000x5000 :: [C01]
+elems10000x5000 = generate 10000 5000
+
+-- #ifdef BENCH_SMALL
+elems10000 :: [C01]
+elems10000 = generate 0 10000
+
+elems20000 :: [C01]
+elems20000 = generate 0 20000
+
+-- #else
+elems50000 :: [C01]
+elems50000 = generate 0 50000
+
+elems100000 :: [C01]
+elems100000 = generate 0 100000
+
+elems200000 :: [C01]
+elems200000 = generate 0 200000
+
+elems400000 :: [C01]
+elems400000 = generate 0 400000
+
+elems800000 :: [C01]
+elems800000 = generate 0 800000
+-- #endif
+
+generate :: Int -> Int -> [C01]
+generate o n = map (\x -> C01 x (x `div` s) [x .. x + s]) [o .. (n + o) - 1]
+  where
+    s = 5
+
+forceList :: [a] -> ()
+forceList ll = seq (go ll) ()
+  where
+    go [] = ()
+    go (_:xs) = go xs
+
+
diff --git a/benchmarks/src/DS/B01.hs b/benchmarks/src/DS/B01.hs
--- a/benchmarks/src/DS/B01.hs
+++ b/benchmarks/src/DS/B01.hs
@@ -1,91 +1,99 @@
-{-# LANGUAGE TypeOperators #-}
-
-module DS.B01
-where
-
---------------------------------------------------------------------------------
-import Control.Lens
---------------------------------------------------------------------------------
-import Common (C01(..))
---------------------------------------------------------------------------------
-import qualified Data.Store as S
-import           Data.Store (M, O, (.:), (.:.), (:.)(..), (.>=), (.==))
-import           Data.Store.Lens
---------------------------------------------------------------------------------
-
-size :: DS -> Int
-size = S.size
-
-data DSTag = DSTag
-
-type DSTS  = Int :. Int :. Int
-type DSKRS = O   :. O   :. M
-type DSIRS = O   :. M   :. M
-
-type DS    = S.Store DSTag DSKRS DSIRS DSTS C01
-type DSKey = S.Key DSKRS DSTS
-type DSRawKey = S.RawKey DSKRS DSTS
-type DSSel = S.Selection DSTag DSKRS DSIRS DSTS
-
-key :: C01 -> DSKey
-key (C01 d1 d2 d3) = S.dimO d1 .: S.dimO d2 .:. S.dimM d3
-{-# INLINE key #-}
-
-sD1 :: (DSTag, S.N0)
-sD1 = (DSTag, S.n0)
-{-# INLINE sD1 #-}
-
-sD2 :: (DSTag, S.N1)
-sD2 = (DSTag, S.n1)
-{-# INLINE sD2 #-}
-
-sD3 :: (DSTag, S.N2)
-sD3 = (DSTag, S.n2)
-{-# INLINE sD3 #-}
-
-insert :: C01 -> DS -> DS
-insert e s = snd $! S.insert' (key e) e s
-
-insertUnsafe :: C01 -> DS -> DS
-insertUnsafe e s = snd $! S.unsafeInsert (key e) e s
-
-lookupOOEQ :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
-lookupOOEQ x = S.lookup (sD1 .== x)
-
-lookupOOEQLens :: Int -> DS -> [C01]
-lookupOOEQLens x o = S.elements (o ^. with (sD1 .== x))
-
-lookupOOGE :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
-lookupOOGE x = S.lookup (sD1 .>= x)
-
-lookupOOGELens :: Int -> DS -> [C01]
-lookupOOGELens x o = S.elements (o ^. with (sD1 .>= x))
-
-lookupOMEQ :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
-lookupOMEQ x = S.lookup (sD2 .== x)
-
-lookupOMEQLens :: Int -> DS -> [C01]
-lookupOMEQLens x o = S.elements (o ^. with (sD2 .== x))
-
-lookupOMGE :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
-lookupOMGE x = S.lookup (sD2 .>= x)
-
-lookupOMGELens :: Int -> DS -> [C01]
-lookupOMGELens x o = S.elements (o ^. with (sD2 .>= x))
-
-lookupMMEQ :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
-lookupMMEQ x = S.lookup (sD3 .== x)
-
-lookupMMEQLens :: Int -> DS -> [C01] 
-lookupMMEQLens x o = S.elements (o ^. with (sD3 .== x))
-
-empty :: DS
-empty = S.empty
-
-{-
-gen  n = map (\x -> C01 x (x `div` 5) [x .. x + 5]) [0 .. (n - 1)]
-gen' n = map (\x -> C01 (x `div` 2) (x `div` 5) [x .. x + 5]) [0 .. (n - 1)]
-store = foldl' (flip DS.B01.insert) empty $! gen 8
-newKey (C01 _ d2 d3) = key $ C01 0 d2 d3
-storeU = S.updateWithKey' (\_ e -> Just (e, Just $ newKey e)) (sD1 .>= 0) store
--}
+{-# LANGUAGE TypeOperators #-}
+
+module DS.B01
+where
+
+--------------------------------------------------------------------------------
+import Control.Lens
+--------------------------------------------------------------------------------
+import Common (C01(..))
+--------------------------------------------------------------------------------
+import qualified Data.Store as S
+import           Data.Store (M, O, (.:), (.:.), (:.)(..), (.>=), (.==))
+import           Data.Store.Lens
+--------------------------------------------------------------------------------
+
+size :: DS -> Int
+size = S.size
+
+data DSTag = DSTag
+
+type DSTS  = Int :. Int :. Int
+type DSKRS = O   :. O   :. M
+type DSIRS = O   :. M   :. M
+
+type DS    = S.Store DSTag DSKRS DSIRS DSTS C01
+type DSKey = S.Key DSKRS DSTS
+type DSRawKey = S.RawKey DSKRS DSTS
+type DSSel = S.Selection DSTag DSKRS DSIRS DSTS
+
+key :: C01 -> DSKey
+key (C01 d1 d2 d3) = S.dimO d1 .: S.dimO d2 .:. S.dimM d3
+{-# INLINE key #-}
+
+sD1 :: (DSTag, S.N0)
+sD1 = (DSTag, S.n0)
+{-# INLINE sD1 #-}
+
+sD2 :: (DSTag, S.N1)
+sD2 = (DSTag, S.n1)
+{-# INLINE sD2 #-}
+
+sD3 :: (DSTag, S.N2)
+sD3 = (DSTag, S.n2)
+{-# INLINE sD3 #-}
+
+insert :: C01 -> DS -> DS
+insert e s = snd $! S.insert' (key e) e s
+
+insertLookup :: Int -> Int -> Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
+insertLookup d1 d2 d3 s =
+  S.lookup (sD1 .== d1) new ++
+  S.lookup (sD2 .== d2) new ++
+  S.lookup (sD3 .== d3) new
+  where new = snd $! S.insert' (key e) e s
+        e   = C01 d1 d2 [d3]
+
+insertUnsafe :: C01 -> DS -> DS
+insertUnsafe e s = snd $! S.unsafeInsert (key e) e s
+
+lookupOOEQ :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
+lookupOOEQ x = S.lookup (sD1 .== x)
+
+lookupOOEQLens :: Int -> DS -> [C01]
+lookupOOEQLens x o = S.elements (o ^. with (sD1 .== x))
+
+lookupOOGE :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
+lookupOOGE x = S.lookup (sD1 .>= x)
+
+lookupOOGELens :: Int -> DS -> [C01]
+lookupOOGELens x o = S.elements (o ^. with (sD1 .>= x))
+
+lookupOMEQ :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
+lookupOMEQ x = S.lookup (sD2 .== x)
+
+lookupOMEQLens :: Int -> DS -> [C01]
+lookupOMEQLens x o = S.elements (o ^. with (sD2 .== x))
+
+lookupOMGE :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
+lookupOMGE x = S.lookup (sD2 .>= x)
+
+lookupOMGELens :: Int -> DS -> [C01]
+lookupOMGELens x o = S.elements (o ^. with (sD2 .>= x))
+
+lookupMMEQ :: Int -> DS -> [(S.RawKey DSKRS DSTS, C01)]
+lookupMMEQ x = S.lookup (sD3 .== x)
+
+lookupMMEQLens :: Int -> DS -> [C01] 
+lookupMMEQLens x o = S.elements (o ^. with (sD3 .== x))
+
+empty :: DS
+empty = S.empty
+
+{-
+gen  n = map (\x -> C01 x (x `div` 5) [x .. x + 5]) [0 .. (n - 1)]
+gen' n = map (\x -> C01 (x `div` 2) (x `div` 5) [x .. x + 5]) [0 .. (n - 1)]
+store = foldl' (flip DS.B01.insert) empty $! gen 8
+newKey (C01 _ d2 d3) = key $ C01 0 d2 d3
+storeU = S.updateWithKey' (\_ e -> Just (e, Just $ newKey e)) (sD1 .>= 0) store
+-}
diff --git a/benchmarks/src/TS/B01.hs b/benchmarks/src/TS/B01.hs
--- a/benchmarks/src/TS/B01.hs
+++ b/benchmarks/src/TS/B01.hs
@@ -1,103 +1,114 @@
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE DeriveDataTypeable #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# OPTIONS_GHC -fno-warn-orphans #-} 
-
-module TS.B01
-where
-
---------------------------------------------------------------------------------
-import Control.Applicative
-import Control.DeepSeq (NFData(..))
-import Control.Lens
---------------------------------------------------------------------------------
-import qualified Data.IntSet
-import           Data.Foldable (toList)
-import           Data.Functor.Identity
---------------------------------------------------------------------------------
-import Common (C01(..))
---------------------------------------------------------------------------------
-import qualified Data.Table as T
---------------------------------------------------------------------------------
-
-size :: T.Table t -> Int
-size = T.count
-
-instance T.Tabular C01 where
-  type PKT C01 = Int
-  data Key k C01 b where
-    D1 :: T.Key T.Primary         C01 Int
-    D2 :: T.Key T.SupplementalInt C01 Int
-    D3 :: T.Key T.InvertedInt     C01 Data.IntSet.IntSet
-  data Tab C01 i = C01IX
-    { ixd1 :: i T.Primary         Int
-    , ixd2 :: i T.SupplementalInt Int
-    , ixd3 :: i T.InvertedInt     Data.IntSet.IntSet
-    }
-
-  fetch D1 (C01 x _ _) = x
-  fetch D2 (C01 _ x _) = x
-  fetch D3 (C01 _ _ x) = Data.IntSet.fromList x
-
-  primary = D1
-  primarily D1 r = r
-
-  mkTab f =
-    C01IX <$> f D1
-          <*> f D2
-          <*> f D3
-  
-  forTab (C01IX d1 d2 d3) f =
-    C01IX <$> f D1 d1
-          <*> f D2 d2
-          <*> f D3 d3
-
-  ixTab (C01IX x _ _) D1 = x
-  ixTab (C01IX _ x _) D2 = x
-  ixTab (C01IX _ _ x) D3 = x
-
-instance NFData (T.Tab C01 (T.AnIndex C01)) where
-    rnf (C01IX x1 x2 x3) = rnf x1 `seq` rnf x2 `seq` rnf x3
-
-type TS = T.Table C01
-
-insert :: C01 -> TS -> TS
-insert = T.insert
-
-lookupOOEQ :: Int -> TS -> [C01]
-lookupOOEQ x o = toList (o ^. T.with D1 (==) x)
-
-lookupOOGE :: Int -> TS -> [C01]
-lookupOOGE x o = toList (o ^. T.with D1 (>=) x)
-
-lookupOMEQ :: Int -> TS -> [C01]
-lookupOMEQ x o = toList (o ^. T.with D2 (==) x)
-
-lookupOMGE :: Int -> TS -> [C01]
-lookupOMGE x o = toList (o ^. T.with D2 (>=) x)
-
-lookupMMEQ :: Int -> TS -> [C01]
-lookupMMEQ x o = toList (o ^. T.withAny D3 [x])
-
-empty :: TS
-empty = T.empty
-
-force :: TS -> ()
-force T.EmptyTable = ()
-force (T.Table tab) = seq go ()
-  where
-    go :: T.Tab C01 (T.AnIndex C01)
-    go = runIdentity $! T.forTab tab (\_ i -> Identity $! case i of
-      T.PrimaryMap m -> m `seq` T.PrimaryMap m
-      T.CandidateMap m -> m `seq` T.CandidateMap m
-      T.CandidateIntMap m -> m `seq` T.CandidateIntMap m
-      T.CandidateHashMap m -> m `seq` T.CandidateHashMap m
-      T.SupplementalMap m -> m `seq` T.SupplementalMap m
-      T.SupplementalIntMap m -> m `seq` T.SupplementalIntMap m
-      T.SupplementalHashMap m -> m `seq` T.SupplementalHashMap m
-      T.InvertedMap m -> m `seq` T.InvertedMap m
-      T.InvertedIntMap m -> m `seq` T.InvertedIntMap m
-      T.InvertedHashMap m -> m `seq` T.InvertedHashMap m)
-
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE DeriveDataTypeable #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-} 
+
+module TS.B01
+where
+
+--------------------------------------------------------------------------------
+import Control.Applicative
+import Control.DeepSeq (NFData(..))
+import Control.Lens
+--------------------------------------------------------------------------------
+import qualified Data.IntSet
+import           Data.Foldable (toList)
+import           Data.Functor.Identity
+--------------------------------------------------------------------------------
+import Common (C01(..))
+--------------------------------------------------------------------------------
+import qualified Data.Table as T
+--------------------------------------------------------------------------------
+
+size :: T.Table t -> Int
+size = T.count
+
+instance T.Tabular C01 where
+  type PKT C01 = Int
+  data Key k C01 b where
+    D1 :: T.Key T.Primary         C01 Int
+    D2 :: T.Key T.SupplementalInt C01 Int
+    D3 :: T.Key T.InvertedInt     C01 Data.IntSet.IntSet
+  data Tab C01 i = C01IX
+    { ixd1 :: i T.Primary         Int
+    , ixd2 :: i T.SupplementalInt Int
+    , ixd3 :: i T.InvertedInt     Data.IntSet.IntSet
+    }
+
+  fetch D1 (C01 x _ _) = x
+  fetch D2 (C01 _ x _) = x
+  fetch D3 (C01 _ _ x) = Data.IntSet.fromList x
+
+  primary = D1
+  primarily D1 r = r
+
+  mkTab f =
+    C01IX <$> f D1
+          <*> f D2
+          <*> f D3
+  
+  forTab (C01IX d1 d2 d3) f =
+    let x1 = f D1 d1
+        x2 = f D2 d2
+        x3 = f D3 d3
+    in
+    C01IX <$> seq x1 x1 
+          <*> seq x2 x2
+          <*> seq x3 x3
+
+  ixTab (C01IX x _ _) D1 = x
+  ixTab (C01IX _ x _) D2 = x
+  ixTab (C01IX _ _ x) D3 = x
+
+instance NFData (T.Tab C01 (T.AnIndex C01)) where
+    rnf (C01IX x1 x2 x3) = rnf x1 `seq` rnf x2 `seq` rnf x3
+
+type TS = T.Table C01
+
+insert :: C01 -> TS -> TS
+insert = T.insert
+
+insertLookup :: Int -> Int -> Int -> TS -> [C01]
+insertLookup d1 d2 d3 s = 
+  toList (new ^. T.with D1 (==) d1) ++
+  toList (new ^. T.with D2 (==) d2) ++
+  toList (new ^. T.withAny D3 [d3])
+  where new = T.insert (C01 d1 d2 [d3]) s
+
+lookupOOEQ :: Int -> TS -> [C01]
+lookupOOEQ x o = toList (o ^. T.with D1 (==) x)
+
+lookupOOGE :: Int -> TS -> [C01]
+lookupOOGE x o = toList (o ^. T.with D1 (>=) x)
+
+lookupOMEQ :: Int -> TS -> [C01]
+lookupOMEQ x o = toList (o ^. T.with D2 (==) x)
+
+lookupOMGE :: Int -> TS -> [C01]
+lookupOMGE x o = toList (o ^. T.with D2 (>=) x)
+
+lookupMMEQ :: Int -> TS -> [C01]
+lookupMMEQ x o = toList (o ^. T.withAny D3 [x])
+
+empty :: TS
+empty = T.empty
+
+force :: TS -> ()
+force T.EmptyTable = ()
+force (T.Table tab) = seq go ()
+  where
+    go :: T.Tab C01 (T.AnIndex C01)
+    go = runIdentity $! T.forTab tab (\_ i -> Identity $! case i of
+      T.PrimaryMap m -> m `seq` T.PrimaryMap m
+      T.CandidateMap m -> m `seq` T.CandidateMap m
+      T.CandidateIntMap m -> m `seq` T.CandidateIntMap m
+      T.CandidateHashMap m -> m `seq` T.CandidateHashMap m
+      T.SupplementalMap m -> m `seq` T.SupplementalMap m
+      T.SupplementalIntMap m -> m `seq` T.SupplementalIntMap m
+      T.SupplementalHashMap m -> m `seq` T.SupplementalHashMap m
+      T.InvertedMap m -> m `seq` T.InvertedMap m
+      T.InvertedIntMap m -> m `seq` T.InvertedIntMap m
+      T.InvertedHashMap m -> m `seq` T.InvertedHashMap m)
+
diff --git a/data-store.cabal b/data-store.cabal
--- a/data-store.cabal
+++ b/data-store.cabal
@@ -1,115 +1,114 @@
-name:                data-store
-version:             0.3.0.4
-
-synopsis:    Type safe, in-memory dictionary with multidimensional keys.
-description: Type safe, in-memory dictionary with multidimensional keys.
-  Similar to ixset, higgsset, tables. But offers: type safe interface,
-  auto-increment dimensions, specifying the relationships between the key dimension and the elements (one-one, one-many, many-one, many-many), performance. 
-
-homepage: https://github.com/Palmik/data-store           
-
-license:             BSD3
-license-file:        LICENSE
-
-author:              Petr Pilař
-maintainer:          the.palmik+maintainer@gmail.com
-
-category:            Data
-
-build-type:          Simple
-cabal-version:       >= 1.8
-
-source-repository head
-  type: git
-  location: git://github.com/Palmik/data-store.git
-  branch: master
-
-library
-  hs-source-dirs:      src
-  exposed-modules:
-      Data.Store
-    , Data.Store.Selection
-    , Data.Store.Storable
-    , Data.Store.Lens
-    
-    , Data.Store.Internal.Type
-    , Data.Store.Internal.Function
-  
-  other-modules:
-      Data.Map.Extra
-    , Data.IntSet.Extra
-
-  build-depends:
-      base         >= 4.5 && < 5
-    , containers   >= 0.4 && < 1
-    , lens         >= 3.9 && < 4
-    , transformers >= 0.2 && < 0.4
-    , vector       >= 0.10 && < 0.11
-
-    , cereal     >= 0.3.5 && < 0.4
-    , deepseq    >= 1.3.0 && < 1.4
-    , safecopy   >= 0.8 && < 0.9
-  ghc-options: -O2 -Wall
-
-test-suite data-store-tests
-  type:           exitcode-stdio-1.0
-  hs-source-dirs: tests, src
-  main-is:        Main.hs
-
-  other-modules:
-      Test.Data.Store01
-
-    , Data.Store    
-    , Data.Store.Lens    
-  
-  build-depends:
-      base         >= 4.5 && < 5
-    , containers   >= 0.4 && < 1
-    , lens         >= 3.9 && < 4
-    , transformers >= 0.2 && < 0.4
-    , vector       >= 0.10 && < 0.11
-
-    , cereal     >= 0.3.5 && < 0.4
-    , deepseq    >= 1.3.0 && < 1.4
-    , safecopy   >= 0.8 && < 0.9
-
-    , test-framework             >= 0.8
-    , test-framework-quickcheck2 >= 0.3
-    , QuickCheck                 >= 2.4 && < 2.6
-
-benchmark data-store-benchmark-01
-  type:           exitcode-stdio-1.0
-  hs-source-dirs: benchmarks/src, src
-  main-is:        01.hs
-
-  other-modules:
-      Common
-    , DS.B01
-    , TS.B01
-
-
-  build-depends:
-      base         >= 4.6 && < 5
-    , containers   >= 0.5 && < 1
-    , lens         >= 3.9 && < 4
-    , transformers >= 0.2 && < 0.4
-    , vector       >= 0.10 && < 0.11
-
-    , cereal     >= 0.3.5 && < 0.4
-    , deepseq    >= 1.3.0 && < 1.4
-    , safecopy   >= 0.8 && < 0.9
-
-    , unordered-containers >= 0.2
-    , tagged     >= 0.4
-    , mtl        >= 2.1
-
-    , ixset
-    , tables     >= 0.3.1.1
-    , lens       >= 3.8
-    , bytestring 
-    , criterion  >= 0.6.2
-    , deepseq    >= 1.3.0
-    , random     >= 1.0.1
-  
-  ghc-options: -Wall -O2
-
+name:                data-store
+version:             0.3.0.6
+
+synopsis:    Type safe, in-memory dictionary with multidimensional keys.
+description: Type safe, in-memory dictionary with multidimensional keys.
+  Similar to ixset, higgsset, tables. But offers: type safe interface,
+  auto-increment dimensions, specifying the relationships between the key dimension and the elements (one-one, one-many, many-one, many-many), performance. 
+
+homepage: https://github.com/Palmik/data-store           
+
+license:             BSD3
+license-file:        LICENSE
+
+author:              Petr Pilar
+maintainer:          the.palmik+maintainer@gmail.com
+
+category:            Data
+
+build-type:          Simple
+cabal-version:       >= 1.8
+
+source-repository head
+  type: git
+  location: git://github.com/Palmik/data-store.git
+  branch: master
+
+library
+  hs-source-dirs:      src
+  exposed-modules:
+      Data.Store
+    , Data.Store.Selection
+    , Data.Store.Storable
+    , Data.Store.Lens
+    
+    , Data.Store.Internal.Type
+    , Data.Store.Internal.Function
+  
+  other-modules:
+      Data.Map.Extra
+    , Data.IntSet.Extra
+
+  build-depends:
+      base         >= 4.5 && < 5
+    , containers   >= 0.4 && < 1
+    , lens         >= 3.9 && < 4
+    , transformers >= 0.2 && < 0.4
+
+    , cereal     >= 0.3.5 && < 0.4
+    , deepseq    >= 1.3.0 && < 1.4
+    , safecopy   >= 0.8 && < 0.9
+  ghc-options: -O2 -Wall
+
+test-suite data-store-tests
+  type:           exitcode-stdio-1.0
+  hs-source-dirs: tests, src
+  main-is:        Main.hs
+
+  other-modules:
+      Test.Data.Store01
+
+    , Data.Store    
+    , Data.Store.Lens    
+  
+  build-depends:
+      base         >= 4.5 && < 5
+    , containers   >= 0.4 && < 1
+    , lens         >= 3.9 && < 4
+    , transformers >= 0.2 && < 0.4
+    , vector       >= 0.10 && < 0.11
+
+    , cereal     >= 0.3.5 && < 0.4
+    , deepseq    >= 1.3.0 && < 1.4
+    , safecopy   >= 0.8 && < 0.9
+
+    , test-framework             >= 0.8
+    , test-framework-quickcheck2 >= 0.3
+    , QuickCheck                 >= 2.4 && < 2.6
+
+benchmark data-store-benchmark-01
+  type:           exitcode-stdio-1.0
+  hs-source-dirs: benchmarks/src, src
+  main-is:        01.hs
+
+  other-modules:
+      Common
+    , DS.B01
+    , TS.B01
+
+
+  build-depends:
+      base         >= 4.6 && < 5
+    , containers   >= 0.5 && < 1
+    , lens         >= 3.9 && < 4
+    , transformers >= 0.2 && < 0.4
+    , vector       >= 0.10 && < 0.11
+
+    , cereal     >= 0.3.5 && < 0.4
+    , deepseq    >= 1.3.0 && < 1.4
+    , safecopy   >= 0.8 && < 0.9
+
+    , unordered-containers >= 0.2
+    , tagged     >= 0.4
+    , mtl        >= 2.1
+
+    , ixset
+    , tables     >= 0.3.1.1
+    , lens       >= 3.8
+    , bytestring 
+    , criterion  >= 0.6.2
+    , deepseq    >= 1.3.0
+    , random     >= 1.0.1
+  
+  ghc-options: -Wall -O2
+
diff --git a/src/Data/IntSet/Extra.hs b/src/Data/IntSet/Extra.hs
--- a/src/Data/IntSet/Extra.hs
+++ b/src/Data/IntSet/Extra.hs
@@ -1,41 +1,41 @@
-module Data.IntSet.Extra
-( foldrM
-, foldrM'
-, foldlM
-, foldlM'
-) where
-
---------------------------------------------------------------------------------
-import qualified Data.IntSet
---------------------------------------------------------------------------------
-
--- TODO: Measure INLINE/SPECIALIZE tradeoff.
-
--- | Monadic fold over the elements of a `Data.IntSet.IntSet`,
--- associating to the right, i.e. from right to left. 
-foldrM :: Monad f => (Int -> b -> f b) -> b -> Data.IntSet.IntSet -> f b
-foldrM go start = Data.IntSet.foldr (\i acc -> acc >>= go i) (return start)
-{-# INLINE foldrM #-}
---{-# SPECIALIZE foldrM :: (Int -> b -> Maybe b) -> b -> Data.IntSet.IntSet -> Maybe b #-}
-
--- | Strict monadic fold over the elements of a `Data.IntSet.IntSet`,
--- associating to the right, i.e. from right to left. 
-foldrM' :: Monad f => (Int -> b -> f b) -> b -> Data.IntSet.IntSet -> f b
-foldrM' go start = Data.IntSet.foldr' (\i acc -> acc >>= go i) (return start)
-{-# INLINE foldrM' #-}
---{-# SPECIALIZE foldrM' :: (Int -> b -> Maybe b) -> b -> Data.IntSet.IntSet -> Maybe b #-}
-
--- | Monadic fold over the elements of a `Data.IntSet.IntSet`,
--- associating to the left, i.e. from left to right. 
-foldlM :: Monad f => (b -> Int -> f b) -> b -> Data.IntSet.IntSet -> f b
-foldlM go start = Data.IntSet.foldl (\acc i -> acc >>= flip go i) (return start)
-{-# INLINE foldlM #-}
---{-# SPECIALIZE foldlM :: (b -> Int -> Maybe b) -> b -> Data.IntSet.IntSet -> Maybe b #-}
-
--- | Monadic fold over the elements of a `Data.IntSet.IntSet`,
--- associating to the left, i.e. from left to right. 
-foldlM' :: Monad f => (b -> Int -> f b) -> b -> Data.IntSet.IntSet -> f b
-foldlM' go start = Data.IntSet.foldl' (\acc i -> acc >>= flip go i) (return start)
-{-# INLINE foldlM' #-}
---{-# SPECIALIZE foldlM' :: (b -> Int -> Maybe b) -> b -> Data.IntSet.IntSet -> Maybe b #-}
-
+module Data.IntSet.Extra
+( foldrM
+, foldrM'
+, foldlM
+, foldlM'
+) where
+
+--------------------------------------------------------------------------------
+import qualified Data.IntSet
+--------------------------------------------------------------------------------
+
+-- TODO: Measure INLINE/SPECIALIZE tradeoff.
+
+-- | Monadic fold over the elements of a `Data.IntSet.IntSet`,
+-- associating to the right, i.e. from right to left. 
+foldrM :: Monad f => (Int -> b -> f b) -> b -> Data.IntSet.IntSet -> f b
+foldrM go start = Data.IntSet.foldr (\i acc -> acc >>= go i) (return start)
+{-# INLINE foldrM #-}
+--{-# SPECIALIZE foldrM :: (Int -> b -> Maybe b) -> b -> Data.IntSet.IntSet -> Maybe b #-}
+
+-- | Strict monadic fold over the elements of a `Data.IntSet.IntSet`,
+-- associating to the right, i.e. from right to left. 
+foldrM' :: Monad f => (Int -> b -> f b) -> b -> Data.IntSet.IntSet -> f b
+foldrM' go start = Data.IntSet.foldr' (\i acc -> acc >>= go i) (return start)
+{-# INLINE foldrM' #-}
+--{-# SPECIALIZE foldrM' :: (Int -> b -> Maybe b) -> b -> Data.IntSet.IntSet -> Maybe b #-}
+
+-- | Monadic fold over the elements of a `Data.IntSet.IntSet`,
+-- associating to the left, i.e. from left to right. 
+foldlM :: Monad f => (b -> Int -> f b) -> b -> Data.IntSet.IntSet -> f b
+foldlM go start = Data.IntSet.foldl (\acc i -> acc >>= flip go i) (return start)
+{-# INLINE foldlM #-}
+--{-# SPECIALIZE foldlM :: (b -> Int -> Maybe b) -> b -> Data.IntSet.IntSet -> Maybe b #-}
+
+-- | Monadic fold over the elements of a `Data.IntSet.IntSet`,
+-- associating to the left, i.e. from left to right. 
+foldlM' :: Monad f => (b -> Int -> f b) -> b -> Data.IntSet.IntSet -> f b
+foldlM' go start = Data.IntSet.foldl' (\acc i -> acc >>= flip go i) (return start)
+{-# INLINE foldlM' #-}
+--{-# SPECIALIZE foldlM' :: (b -> Int -> Maybe b) -> b -> Data.IntSet.IntSet -> Maybe b #-}
+
diff --git a/src/Data/Map/Extra.hs b/src/Data/Map/Extra.hs
--- a/src/Data/Map/Extra.hs
+++ b/src/Data/Map/Extra.hs
@@ -1,24 +1,24 @@
-{-# LANGUAGE CPP #-}
-
-module Data.Map.Extra
-( insertUnique
-) where
-
---------------------------------------------------------------------------------
-#if MIN_VERSION_containers(0,5,0)
-import qualified Data.Map.Strict as Data.Map
-#else
-import qualified Data.Map
-#endif
---------------------------------------------------------------------------------
-
--- | The expression (@insertUnique k v old@)
--- returns (@Just (Data.Map.insert k v old)@) if the map @old@ did not contain
--- anything under the key @k@, otherwise returns @Nothing@.
-insertUnique :: Ord k => k -> a -> Data.Map.Map k a -> Maybe (Data.Map.Map k a)
-insertUnique k a m =
-    case Data.Map.insertLookupWithKey (\_ _ o' -> o') k a m of
-        (Nothing, res) -> Just res
-        (Just _,  _) -> Nothing
-{-# INLINE insertUnique #-}
-
+{-# LANGUAGE CPP #-}
+
+module Data.Map.Extra
+( insertUnique
+) where
+
+--------------------------------------------------------------------------------
+#if MIN_VERSION_containers(0,5,0)
+import qualified Data.Map.Strict as Data.Map
+#else
+import qualified Data.Map
+#endif
+--------------------------------------------------------------------------------
+
+-- | The expression (@insertUnique k v old@)
+-- returns (@Just (Data.Map.insert k v old)@) if the map @old@ did not contain
+-- anything under the key @k@, otherwise returns @Nothing@.
+insertUnique :: Ord k => k -> a -> Data.Map.Map k a -> Maybe (Data.Map.Map k a)
+insertUnique k a m =
+    case Data.Map.insertLookupWithKey (\_ _ o' -> o') k a m of
+        (Nothing, res) -> Just res
+        (Just _,  _) -> Nothing
+{-# INLINE insertUnique #-}
+
diff --git a/src/Data/Store.hs b/src/Data/Store.hs
--- a/src/Data/Store.hs
+++ b/src/Data/Store.hs
@@ -159,6 +159,9 @@
 , toList
 , elements
 , keys
+, insertList
+, insertList'
+, unsafeInsertList
 , fromList
 , fromList'
 , unsafeFromList
@@ -166,6 +169,8 @@
   -- * Querying
 , size
 , lookup
+, lookupOrderByA
+, lookupOrderByD
 
   -- ** Selection
   --
@@ -447,10 +452,60 @@
 -- list of (raw key)-element pairs that match the selection.
 -- 
 -- Complexity: /O(c + s * min(n, W))/
+--
+-- See also:
+--
+--   * 'Data.Store.lookupOrderByA'
+--
+--   * 'Data.Store.lookupOrderByD'
 lookup :: IsSelection sel => sel tag krs irs ts -> I.Store tag krs irs ts v -> [(I.RawKey krs ts, v)]
 lookup sel s = I.genericLookup (resolve sel s) s
 {-# INLINE lookup #-}
 
+-- | The expression (@'Data.Store.Selection.lookup' sel store@) is
+-- list of (raw key)-element pairs that match the selection.
+-- The list is sorted in ascending order with respect to the specified dimension.
+--
+-- NOTE: The function only works (this is ensured on the type level) with when
+-- the ordering is based on dimensions of type one-one and one-many.
+--
+-- Complexity: /O(c + (s * log(s)) + s * min(n, W))/
+--
+-- See also:
+--
+--   * 'Data.Store.lookupOrderByD'
+--
+--   * 'Data.Store.lookup'
+lookupOrderByA :: (I.DimensionRelation n krs ts ~ I.O, I.GetDimension n (I.IKey krs ts), IsSelection sel)
+               => sel tag krs irs ts
+               -> (tag, n)
+               -> I.Store tag krs irs ts v
+               -> [(I.RawKey krs ts, v)]
+lookupOrderByA sel (_, n) s = I.genericLookupAsc (resolve sel s) n s
+{-# INLINE lookupOrderByA #-}
+
+-- | The expression (@'Data.Store.Selection.lookup' sel store@) is
+-- list of (raw key)-element pairs that match the selection.
+-- The list is sorted in descending order with respect to the specified dimension.
+--
+-- NOTE: The function only works (this is ensured on the type level) with when
+-- the ordering is based on dimensions of type one-one and one-many.
+--
+-- Complexity: /O(c + (s * log(s)) + s * min(n, W))/
+--
+-- See also:
+--
+--   * 'Data.Store.lookupOrderByA'
+--
+--   * 'Data.Store.lookup'
+lookupOrderByD :: (I.DimensionRelation n krs ts ~ I.O, I.GetDimension n (I.IKey krs ts), IsSelection sel)
+               => sel tag krs irs ts
+               -> (tag, n)
+               -> I.Store tag krs irs ts v
+               -> [(I.RawKey krs ts, v)]
+lookupOrderByD sel (_, n) s = I.genericLookupDesc (resolve sel s) n s
+{-# INLINE lookupOrderByD #-}
+
 -- | The expression (@'Data.Store.size' store@) is the number of elements
 -- in @store@. 
 size :: I.Store tag krs irs ts v -> Int
@@ -630,7 +685,7 @@
 keys (I.Store vs _ _) = Data.List.map (I.keyInternalToRaw . fst) $ Data.IntMap.elems vs
 {-# INLINE keys #-}
 
--- | The expression (@'Data.Store.fromList' kvs@) is either
+-- | The expression (@'Data.Store.fromList' kes@) is either
 -- a) (@Just store@) where @store@ is a store containing exactly the given
 -- key-element pairs or;
 -- b) @Nothing@ if inserting any of the key-element pairs would
@@ -639,23 +694,63 @@
 -- See also:
 --
 -- * 'Data.Store.fromList''
+--
+-- * 'Data.Store.insertList'
+--
+-- * 'Data.Store.insertList''
 fromList :: I.Empty (I.Index irs ts) => [(I.Key krs ts, v)] -> Maybe (I.Store tag krs irs ts v)
-fromList = Data.Foldable.foldlM (\s (k, v) -> snd <$> insert k v s) I.empty 
+fromList = insertList I.empty
 {-# INLINE fromList #-}
 
--- | The expression (@'Data.Store.fromList'' kvs@) is @store@
+-- | The expression (@'Data.Store.fromList' old kes@) is either
+-- a) (@Just store@) where @store@ is a store containing exactly the key element pairs of @old@ plus the given
+-- key-element pairs @kes@ or;
+-- b) @Nothing@ if inserting any of the key-element pairs would
+-- cause a collision.
+--
+-- See also:
+--
+-- * 'Data.Store.insertList''
+--
+-- * 'Data.Store.fromList'
+--
+-- * 'Data.Store.fromList''
+insertList :: I.Empty (I.Index irs ts) => I.Store tag krs irs ts v -> [(I.Key krs ts, v)] -> Maybe (I.Store tag krs irs ts v)
+insertList = Data.Foldable.foldlM (\s (k, v) -> snd <$> insert k v s) 
+{-# INLINE insertList #-}
+
+-- | The expression (@'Data.Store.fromList'' kes@) is @store@
 -- containing the given key-element pairs (colliding pairs are not included).
 --
 -- See also:
 --
 -- * 'Data.Store.fromList'
+--
+-- * 'Data.Store.insertList''
+--
+-- * 'Data.Store.insertList'
 fromList' :: I.Empty (I.Index irs ts) => [(I.Key krs ts, v)] -> I.Store tag krs irs ts v
-fromList' = Data.List.foldl' (\s (k, v) -> snd $! insert' k v $! s) I.empty 
+fromList' = insertList' I.empty
 {-# INLINE fromList' #-}
 
+-- | The expression (@'Data.Store.insertList'' old kes@) is @store@
+-- containing the key-element pairs of @old@ plus the given key-element pairs @kvs@
+-- (colliding pairs are not included and the pairs from @kes@ take precedence).
+--
+-- See also:
+--
+-- * 'Data.Store.insertList'
+--
+-- * 'Data.Store.fromList''
+--
+-- * 'Data.Store.fromList'
+insertList' :: I.Empty (I.Index irs ts) => I.Store tag krs irs ts v -> [(I.Key krs ts, v)] -> I.Store tag krs irs ts v
+insertList' = Data.List.foldl' (\s (k, v) -> snd $! insert' k v $! s)
+{-# INLINE insertList' #-}
+
 -- | UNSAFE! This function can corrupt the store.
 -- 
--- The expression (@'Data.Store.fromList'' kvs@) is @store@
+-- The expression (@'Data.Store.unsafeFromList' kes@) is @store@
 -- containing the given key-element pairs (colliding pairs cause UNDEFINED BEHAVIOUR).
 --
 -- See also:
@@ -664,8 +759,27 @@
 --
 -- * 'Data.Store.fromList'
 unsafeFromList :: I.Empty (I.Index irs ts) => [(I.Key krs ts, v)] -> I.Store tag krs irs ts v
-unsafeFromList = Data.Foldable.foldl (\s (k, v) -> snd $ unsafeInsert k v s) I.empty 
+unsafeFromList = unsafeInsertList I.empty 
 {-# INLINE unsafeFromList #-}
+
+-- | UNSAFE! This function can corrupt the store.
+-- 
+-- The expression (@'Data.Store.unsafeInsertList' old kvs@) is @store@
+-- containing the key-element pairs of @old@ plus the given key-element pairs @kvs@
+-- (colliding pairs cause UNDEFINED BEHAVIOUR).
+--
+-- See also:
+--
+-- * 'Data.Store.insertList'
+--
+-- * 'Data.Store.insertList''
+--
+-- * 'Data.Store.fromList'
+--
+-- * 'Data.Store.fromList''
+unsafeInsertList :: I.Empty (I.Index irs ts) => I.Store tag krs irs ts v -> [(I.Key krs ts, v)] -> I.Store tag krs irs ts v
+unsafeInsertList = Data.Foldable.foldl (\s (k, v) -> snd $ unsafeInsert k v s)
+{-# INLINE unsafeInsertList #-}
 
 -- INSTANCES
 
diff --git a/src/Data/Store/Internal/Function.hs b/src/Data/Store/Internal/Function.hs
--- a/src/Data/Store/Internal/Function.hs
+++ b/src/Data/Store/Internal/Function.hs
@@ -1,293 +1,328 @@
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE RankNTypes #-}
-{-# LANGUAGE CPP #-}
-
-module Data.Store.Internal.Function
-where
-
---------------------------------------------------------------------------------
-import           Control.Applicative hiding (empty)
---------------------------------------------------------------------------------
-import           Data.Monoid ((<>))
-import           Data.Functor.Identity 
-import qualified Data.List
-#if MIN_VERSION_containers(0,5,0)
-import qualified Data.IntMap.Strict as Data.IntMap
-import qualified Data.Map.Strict as Data.Map
-#else
-import qualified Data.IntMap
-import qualified Data.Map
-#endif
-import qualified Data.IntSet
-import qualified Data.IntSet.Extra
---------------------------------------------------------------------------------
-import qualified Data.Store.Internal.Type as I
---------------------------------------------------------------------------------
-
-moduleName :: String
-moduleName = "Data.Store.Internal.Function"
-
-genericSubset :: I.Empty (I.Index irs ts)
-              => Data.IntSet.IntSet
-              -> I.Store tag krs irs ts v
-              -> I.Store tag krs irs ts v
-genericSubset ids (I.Store vs _ _) =
-  Data.IntSet.foldr (\i acc ->
-    case Data.IntMap.lookup i vs of
-      Just (ik, e) -> runIdentity $ genericInsert indexInsertID'' ik e acc
-      _ -> acc
-    ) I.empty ids
-{-# INLINE genericSubset #-}
-
-genericLookup :: Data.IntSet.IntSet
-              -> I.Store tag krs irs ts v
-              -> [(I.RawKey krs ts, v)]
-genericLookup ids (I.Store vs _ _) = {-# SCC "genericLookup" #-} 
-  Data.IntSet.foldr (\i acc ->
-    case Data.IntMap.lookup i vs of
-      Just (ik, v) -> (keyInternalToRaw ik, v) : acc
-      _ -> acc
-    ) [] ids
-{-# INLINE genericLookup #-}
-
-genericUpdateWithKey :: (Applicative f, Monad f)
-                     => (I.IKey krs ts -> Int -> I.Store tag krs irs ts e -> f (I.Store tag krs irs ts e))
-                     -> (I.RawKey krs ts -> e -> Maybe (e, Maybe (I.Key krs ts)))
-                     -> Data.IntSet.IntSet
-                     -> I.Store tag krs irs ts e
-                     -> f (I.Store tag krs irs ts e)
-genericUpdateWithKey ins tr ids old = Data.IntSet.Extra.foldlM' accum old ids
-    where
-      accum store@(I.Store vs ix nid) i =
-          case Data.IntMap.lookup i vs of
-            Just (ik, v) ->
-                case tr (keyInternalToRaw ik) v of
-                  -- User wants to update the element & key.
-                  Just (nv, Just nk) -> let nik = mergeKeys nk ik in 
-                    if nik /= ik
-                       -- The keys are different: update the element & key.
-                       then insertPair i nik nv <$> ins nik i (store { I.storeI = indexDeleteID ik i ix })
-                       -- The keys are identical: update the element.
-                       else pure $! insertPair i nik nv store
-
-                  -- Update the element.
-                  Just (nv, Nothing) -> pure $! insertPair i ik nv store
-
-                  -- Delete.
-                  Nothing -> pure I.Store
-                    { I.storeV = Data.IntMap.delete i vs
-                    , I.storeI = indexDeleteID ik i ix
-                    , I.storeNID = nid
-                    }
-            _ -> pure store
-      {-# INLINEABLE accum #-}
-      
-      insertPair i' ik' e' s'@(I.Store es' _ _) = s' 
-        { I.storeV = Data.IntMap.insert i' (ik', e') es'
-        }
-      {-# INLINE insertPair #-}
-{-# INLINE genericUpdateWithKey #-}
-
-
-mergeKeys :: I.Key krs ts -> I.IKey krs ts -> I.IKey krs ts
-mergeKeys (I.K1 I.KeyDimensionA) ik@(I.K1 _) = ik
-mergeKeys (I.K1 (I.KeyDimensionO d))   (I.K1 _)   = I.K1 (I.IKeyDimensionO d)
-mergeKeys (I.K1 (I.KeyDimensionM d))   (I.K1 _)   = I.K1 (I.IKeyDimensionM d)
-mergeKeys (I.KN I.KeyDimensionA s) (I.KN ik is) = I.KN ik $ mergeKeys s is
-mergeKeys (I.KN (I.KeyDimensionO d) s) (I.KN _ is) = I.KN (I.IKeyDimensionO d) $ mergeKeys s is
-mergeKeys (I.KN (I.KeyDimensionM d) s) (I.KN _ is) = I.KN (I.IKeyDimensionM d) $ mergeKeys s is
-mergeKeys _ _ = error $ moduleName <> ".genericUpdate.mergeKeys: The impossible happened."
-{-# INLINEABLE mergeKeys #-}
-
-keyInternalToRaw :: I.IKey krs ts -> I.RawKey krs ts
-keyInternalToRaw (I.K1 (I.IKeyDimensionO x)) = x
-keyInternalToRaw (I.K1 (I.IKeyDimensionM x)) = x
-keyInternalToRaw (I.KN (I.IKeyDimensionO x) s) = x I.:. keyInternalToRaw s
-keyInternalToRaw (I.KN (I.IKeyDimensionM x) s) = x I.:. keyInternalToRaw s
-{-# INLINE keyInternalToRaw #-}
-
-keyFromInternal :: I.IKey krs ts -> I.Key krs ts
-keyFromInternal (I.K1 (I.IKeyDimensionO x)) = I.K1 (I.KeyDimensionO x)
-keyFromInternal (I.K1 (I.IKeyDimensionM x)) = I.K1 (I.KeyDimensionM x)
-keyFromInternal (I.KN (I.IKeyDimensionO x) s) = I.KN (I.KeyDimensionO x) (keyFromInternal s)
-keyFromInternal (I.KN (I.IKeyDimensionM x) s) = I.KN (I.KeyDimensionM x) (keyFromInternal s)
-
-keyToInternal :: I.Index irs ts -> I.Key krs ts -> I.IKey krs ts
-keyToInternal (I.I1 ix) (I.K1 I.KeyDimensionA) = I.K1 (I.IKeyDimensionO $! nextKey ix) 
-keyToInternal (I.I1 _) (I.K1 (I.KeyDimensionO x)) = I.K1 (I.IKeyDimensionO x) 
-keyToInternal (I.I1 _) (I.K1 (I.KeyDimensionM x)) = I.K1 (I.IKeyDimensionM x) 
-keyToInternal (I.IN ix is) (I.KN I.KeyDimensionA s) = I.KN (I.IKeyDimensionO $! nextKey ix) $ keyToInternal is s
-keyToInternal (I.IN _ is) (I.KN (I.KeyDimensionO x) s) = I.KN (I.IKeyDimensionO x) $ keyToInternal is s
-keyToInternal (I.IN _ is) (I.KN (I.KeyDimensionM x) s) = I.KN (I.IKeyDimensionM x) $ keyToInternal is s 
-keyToInternal _ _ = error $ moduleName <> ".insert.keyToInternal: Impossible happened."
-{-# INLINE keyToInternal #-}
-      
-nextKey :: I.Auto t => I.IndexDimension r t -> t
-nextKey i =
-  case i of
-    (I.IndexDimensionM m) -> nextKey' m
-    (I.IndexDimensionO m) -> nextKey' m
-  where
-    nextKey' m = if Data.Map.null m
-                   then minBound
-                   else succ . fst $! Data.Map.findMax m
-    {-# INLINE nextKey' #-}
-{-# INLINE nextKey #-}
-
-genericInsert :: Applicative f 
-              => (I.IKey krs ts -> Int -> I.Store tag krs irs ts e -> f (I.Store tag krs irs ts e))
-              -> I.IKey krs ts
-              -> e
-              -> I.Store tag krs irs ts e
-              -> f (I.Store tag krs irs ts e)
-genericInsert ins ik e old@(I.Store _ _ nid) = go <$> ins ik nid old
-  where
-    go s'@(I.Store es' _ _) = s'
-      { I.storeV = Data.IntMap.insert nid (ik, e) es'
-      , I.storeNID = nid + 1
-      }
-    {-# INLINE go #-}
-{-# INLINE genericInsert #-}
-
--- | Inserts the given element identifier into the store's index under the given
--- internal key.
---
--- In case of collisions: returns 'Data.Maybe.Nothing'.
-indexInsertID :: I.IKey krs ts
-              -> Int
-              -> I.Store tag krs irs ts e
-              -> Maybe (I.Store tag krs irs ts e)
-indexInsertID ik eid old@(I.Store _ index _) =
-  if Data.List.null $ findCollisions ik index
-    then Just $! runIdentity $! indexInsertID'' ik eid old
-    else Nothing
-{-# INLINE indexInsertID #-}
-
--- | Inserts the given element identifier into the store's index under the given
--- internal key.
---
--- In case of collisions: deletes them.
-indexInsertID' :: I.IKey krs ts
-               -> Int
-               -> I.Store tag krs irs ts e
-               -> Identity (I.Store tag krs irs ts e)
-indexInsertID' ik eid old@(I.Store _ index _) = --{-# SCC "indexInsertID'" #-} 
-  indexInsertID'' ik eid $! Data.IntSet.foldl' go old collisions
-  where
-    go s'@(I.Store es' ix' _) i =
-      case Data.IntMap.updateLookupWithKey (\_ _ -> Nothing) i es' of
-        (Just (ik', _), v'') -> s'
-          { I.storeV = v''
-          , I.storeI = indexDeleteID ik' i ix'
-          } 
-        _ -> error $ moduleName <> ".insertInternal'.go: The impossible happened."
-    {-# INLINEABLE go #-}
-
-    collisions = Data.IntSet.delete eid $! Data.IntSet.fromList $! findCollisions ik index
-    {-# INLINE collisions #-}
-{-# INLINE indexInsertID' #-}
-
--- | UNSAFE. Inserts the given element identifier into the store's index under the given
--- internal key.
--- 
--- In case of collisions: ignores them.
-indexInsertID'' :: I.IKey krs ts
-                -> Int
-                -> I.Store tag krs irs ts e
-                -> Identity (I.Store tag krs irs ts e)
-indexInsertID'' ik eid old@(I.Store _ index _) = --{-# SCC "indexInsertID''" #-}
-  zipped `seq` Identity $! old { I.storeI = zipped }
-  where
-    zipped = zipD ik index
-
-    zipD :: I.IKey krs ts -> I.Index irs ts -> I.Index irs ts
-    zipD (I.KN kd kt) (I.IN ixd it) = I.IN (combine kd ixd) $! zipD kt it
-    zipD (I.K1 kd) (I.I1 ixd) = I.I1 $! combine kd ixd
-    zipD _ _ = error $ moduleName <> ".indexInsertID''.zipD: The impossible happened."
-    {-# INLINE zipD #-}
-
-    combine :: I.IKeyDimension krs ts -> I.IndexDimension irs ts -> I.IndexDimension irs ts
-    combine kd ixd =
-      case (ixd, kd) of
-        (I.IndexDimensionO m, I.IKeyDimensionO k)  ->
-          I.IndexDimensionO $! goO k eid m
-        
-        (I.IndexDimensionO m, I.IKeyDimensionM ks) ->
-          I.IndexDimensionO $! Data.List.foldl' (\acc k -> goO k eid acc) m ks 
-
-        (I.IndexDimensionM m, I.IKeyDimensionO k)  ->
-          I.IndexDimensionM $! goM k eid $! m
-
-        (I.IndexDimensionM m, I.IKeyDimensionM ks) ->
-          I.IndexDimensionM $! Data.List.foldl' (\acc k -> goM k eid acc) m ks
-    {-# INLINEABLE combine #-}
-
-    goO :: Ord k => k -> Int -> Data.Map.Map k Int -> Data.Map.Map k Int
-    goO = Data.Map.insert 
-    {-# INLINE goO #-}
-
-    goM :: Ord k => k -> Int -> Data.Map.Map k Data.IntSet.IntSet -> Data.Map.Map k Data.IntSet.IntSet
-    goM k e = Data.Map.insertWith (\_ s -> Data.IntSet.insert e s) k (Data.IntSet.singleton e)
-    {-# INLINE goM #-}
-{-# INLINE indexInsertID'' #-}
-
-findCollisions :: I.IKey krs ts -> I.Index irs ts -> [Int]
-findCollisions ik ix = {-# SCC "findCollisions" #-} zipD ik ix [] 
-  where
-    zipD :: I.IKey krs ts -> I.Index irs ts -> [Int] -> [Int]
-    zipD (I.KN kd kt) (I.IN ixd it) = combine kd ixd . zipD kt it
-    zipD (I.K1 kd) (I.I1 ixd) = combine kd ixd
-    zipD _ _ = error $ moduleName <> ".findCollisions.zipD: The impossible happened."
-
-    combine :: I.IKeyDimension krs ts -> I.IndexDimension irs ts -> [Int] -> [Int]
-    combine kd ixd = 
-      case (ixd, kd) of
-        (I.IndexDimensionO m, I.IKeyDimensionO k)  -> goO k m
-        (I.IndexDimensionO m, I.IKeyDimensionM ks) -> foldr (\k acc -> goO k m . acc) id ks
-        _ -> id
-    {-# INLINE combine #-}
-
-    goO :: Ord k => k -> Data.Map.Map k Int -> [Int] -> [Int]
-    goO k m =
-      case Data.Map.lookup k $! m of
-        Nothing -> id
-        Just  i -> (i:)
-    {-# INLINE goO #-}
-
--- | Deletes EID fron an index.
-indexDeleteID :: I.IKey krs ts
-              -> Int
-              -> I.Index irs ts
-              -> I.Index irs ts
-indexDeleteID ik eid = zipD ik
-  where
-    zipD :: I.IKey krs ts -> I.Index irs ts -> I.Index irs ts
-    zipD (I.KN kd kt) (I.IN ixd it) = I.IN (combine kd ixd) $! zipD kt it
-    zipD (I.K1 kd) (I.I1 ixd) = I.I1 $! combine kd ixd
-    zipD _ _ = error $ moduleName <> ".indexDeleteID.zipD: The impossible happened."
-    {-# INLINEABLE zipD #-}
-
-    combine :: Ord t => I.IKeyDimension kr t -> I.IndexDimension ir t -> I.IndexDimension ir t
-    combine key index =
-      case (index, key) of
-        (I.IndexDimensionO m, I.IKeyDimensionO k)  -> I.IndexDimensionO $! goO m k
-        (I.IndexDimensionO m, I.IKeyDimensionM ks) -> I.IndexDimensionO $! Data.List.foldl' goO m ks
-        (I.IndexDimensionM m, I.IKeyDimensionO k)  -> I.IndexDimensionM $! goM m k
-        (I.IndexDimensionM m, I.IKeyDimensionM ks) -> I.IndexDimensionM $! Data.List.foldl' goM m ks
-    {-# INLINEABLE combine #-}
-
-    goO :: Ord k => Data.Map.Map k Int -> k -> Data.Map.Map k Int
-    goO m k = Data.Map.update (\i' -> if i' == eid then Nothing else Just i') k m
-    {-# INLINE goO #-}
-
-    goM :: Ord k => Data.Map.Map k Data.IntSet.IntSet -> k -> Data.Map.Map k Data.IntSet.IntSet
-    goM m k = Data.Map.update
-      (\ids -> let nids = Data.IntSet.delete eid ids in
-        if Data.IntSet.null nids
-          then Nothing
-          else Just nids
-      ) k m
-    {-# INLINE goM #-}
-{-# INLINE indexDeleteID #-}
-
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE CPP #-}
+
+module Data.Store.Internal.Function
+where
+
+--------------------------------------------------------------------------------
+import           Control.Applicative hiding (empty)
+--------------------------------------------------------------------------------
+import           Data.Monoid ((<>))
+import           Data.Functor.Identity 
+import qualified Data.List
+#if MIN_VERSION_containers(0,5,0)
+import qualified Data.IntMap.Strict as Data.IntMap
+import qualified Data.Map.Strict as Data.Map
+#else
+import qualified Data.IntMap
+import qualified Data.Map
+#endif
+import qualified Data.IntSet
+import qualified Data.IntSet.Extra
+--------------------------------------------------------------------------------
+import qualified Data.Store.Internal.Type as I
+--------------------------------------------------------------------------------
+
+moduleName :: String
+moduleName = "Data.Store.Internal.Function"
+
+genericSubset :: I.Empty (I.Index irs ts)
+              => Data.IntSet.IntSet
+              -> I.Store tag krs irs ts v
+              -> I.Store tag krs irs ts v
+genericSubset ids (I.Store vs _ _) =
+  Data.IntSet.foldr (\i acc ->
+    case Data.IntMap.lookup i vs of
+      Just (ik, e) -> runIdentity $ genericInsert indexInsertID'' ik e acc
+      _ -> acc
+    ) I.empty ids
+{-# INLINE genericSubset #-}
+
+genericLookup :: Data.IntSet.IntSet
+              -> I.Store tag krs irs ts v
+              -> [(I.RawKey krs ts, v)]
+genericLookup ids (I.Store vs _ _) = {-# SCC "genericLookup" #-} 
+  Data.IntSet.foldr (\i acc ->
+    case Data.IntMap.lookup i vs of
+      Just (ik, v) -> (keyInternalToRaw ik, v) : acc
+      _ -> acc
+    ) [] ids
+{-# INLINE genericLookup #-}
+
+genericLookupAsc :: I.GetDimension n (I.IKey krs ts)
+                 => Data.IntSet.IntSet
+                 -> n
+                 -> I.Store tag krs irs ts v
+                 -> [(I.RawKey krs ts, v)]
+genericLookupAsc ids n (I.Store vs _ _) =
+  map (\(ik, v) -> (keyInternalToRaw ik, v)) . Data.List.sortBy (lookupSortComparator n) $
+  Data.IntSet.foldr (\i acc ->
+    case Data.IntMap.lookup i vs of
+      Just (ik, v) -> (ik, v) : acc
+      _ -> acc
+    ) [] ids
+{-# INLINE genericLookupAsc #-}
+
+genericLookupDesc :: I.GetDimension n (I.IKey krs ts)
+                  => Data.IntSet.IntSet
+                  -> n
+                  -> I.Store tag krs irs ts v
+                  -> [(I.RawKey krs ts, v)]
+genericLookupDesc ids n (I.Store vs _ _) =
+  map (\(ik, v) -> (keyInternalToRaw ik, v)) . Data.List.sortBy (flip $ lookupSortComparator n) $
+  Data.IntSet.foldr (\i acc ->
+    case Data.IntMap.lookup i vs of
+      Just (ik, v) -> (ik, v) : acc
+      _ -> acc
+    ) [] ids
+{-# INLINE genericLookupDesc #-}
+
+lookupSortComparator :: I.GetDimension n (I.IKey krs ts) => n -> (I.IKey krs ts, e) -> (I.IKey krs ts, e) -> Ordering
+lookupSortComparator n (k1, _) (k2, _) = case (I.getDimension n k1, I.getDimension n k2) of
+  (I.IKeyDimensionO d1, I.IKeyDimensionO d2) -> d1 `compare` d2
+  (I.IKeyDimensionM  _, I.IKeyDimensionM  _) -> error $
+    moduleName <> "lookupSortComparator: Comparing keys based on many-one or many-many dimensions is not supported."
+{-# INLINEABLE lookupSortComparator #-}
+
+genericUpdateWithKey :: (Applicative f, Monad f)
+                     => (I.IKey krs ts -> Int -> I.Store tag krs irs ts e -> f (I.Store tag krs irs ts e))
+                     -> (I.RawKey krs ts -> e -> Maybe (e, Maybe (I.Key krs ts)))
+                     -> Data.IntSet.IntSet
+                     -> I.Store tag krs irs ts e
+                     -> f (I.Store tag krs irs ts e)
+genericUpdateWithKey ins tr ids old = Data.IntSet.Extra.foldlM' accum old ids
+    where
+      accum store@(I.Store vs ix nid) i =
+          case Data.IntMap.lookup i vs of
+            Just (ik, v) ->
+                case tr (keyInternalToRaw ik) v of
+                  -- User wants to update the element & key.
+                  Just (nv, Just nk) -> let nik = mergeKeys nk ik in 
+                    if nik /= ik
+                       -- The keys are different: update the element & key.
+                       then insertPair i nik nv <$> ins nik i (store { I.storeI = indexDeleteID ik i ix })
+                       -- The keys are identical: update the element.
+                       else pure $! insertPair i nik nv store
+
+                  -- Update the element.
+                  Just (nv, Nothing) -> pure $! insertPair i ik nv store
+
+                  -- Delete.
+                  Nothing -> pure I.Store
+                    { I.storeV = Data.IntMap.delete i vs
+                    , I.storeI = indexDeleteID ik i ix
+                    , I.storeNID = nid
+                    }
+            _ -> pure store
+      {-# INLINEABLE accum #-}
+      
+      insertPair i' ik' e' s'@(I.Store es' _ _) = s' 
+        { I.storeV = Data.IntMap.insert i' (ik', e') es'
+        }
+      {-# INLINE insertPair #-}
+{-# INLINE genericUpdateWithKey #-}
+
+
+mergeKeys :: I.Key krs ts -> I.IKey krs ts -> I.IKey krs ts
+mergeKeys (I.K1 I.KeyDimensionA) ik@(I.K1 _) = ik
+mergeKeys (I.K1 (I.KeyDimensionO d))   (I.K1 _)   = I.K1 (I.IKeyDimensionO d)
+mergeKeys (I.K1 (I.KeyDimensionM d))   (I.K1 _)   = I.K1 (I.IKeyDimensionM d)
+mergeKeys (I.KN I.KeyDimensionA s) (I.KN ik is) = I.KN ik $ mergeKeys s is
+mergeKeys (I.KN (I.KeyDimensionO d) s) (I.KN _ is) = I.KN (I.IKeyDimensionO d) $ mergeKeys s is
+mergeKeys (I.KN (I.KeyDimensionM d) s) (I.KN _ is) = I.KN (I.IKeyDimensionM d) $ mergeKeys s is
+mergeKeys _ _ = error $ moduleName <> ".genericUpdate.mergeKeys: The impossible happened."
+{-# INLINEABLE mergeKeys #-}
+
+keyInternalToRaw :: I.IKey krs ts -> I.RawKey krs ts
+keyInternalToRaw (I.K1 (I.IKeyDimensionO x)) = x
+keyInternalToRaw (I.K1 (I.IKeyDimensionM x)) = x
+keyInternalToRaw (I.KN (I.IKeyDimensionO x) s) = x I.:. keyInternalToRaw s
+keyInternalToRaw (I.KN (I.IKeyDimensionM x) s) = x I.:. keyInternalToRaw s
+{-# INLINE keyInternalToRaw #-}
+
+keyFromInternal :: I.IKey krs ts -> I.Key krs ts
+keyFromInternal (I.K1 (I.IKeyDimensionO x)) = I.K1 (I.KeyDimensionO x)
+keyFromInternal (I.K1 (I.IKeyDimensionM x)) = I.K1 (I.KeyDimensionM x)
+keyFromInternal (I.KN (I.IKeyDimensionO x) s) = I.KN (I.KeyDimensionO x) (keyFromInternal s)
+keyFromInternal (I.KN (I.IKeyDimensionM x) s) = I.KN (I.KeyDimensionM x) (keyFromInternal s)
+
+keyToInternal :: I.Index irs ts -> I.Key krs ts -> I.IKey krs ts
+keyToInternal (I.I1 ix) (I.K1 I.KeyDimensionA) = I.K1 (I.IKeyDimensionO $! nextKey ix) 
+keyToInternal (I.I1 _) (I.K1 (I.KeyDimensionO x)) = I.K1 (I.IKeyDimensionO x) 
+keyToInternal (I.I1 _) (I.K1 (I.KeyDimensionM x)) = I.K1 (I.IKeyDimensionM x) 
+keyToInternal (I.IN ix is) (I.KN I.KeyDimensionA s) = I.KN (I.IKeyDimensionO $! nextKey ix) $ keyToInternal is s
+keyToInternal (I.IN _ is) (I.KN (I.KeyDimensionO x) s) = I.KN (I.IKeyDimensionO x) $ keyToInternal is s
+keyToInternal (I.IN _ is) (I.KN (I.KeyDimensionM x) s) = I.KN (I.IKeyDimensionM x) $ keyToInternal is s 
+keyToInternal _ _ = error $ moduleName <> ".insert.keyToInternal: Impossible happened."
+{-# INLINE keyToInternal #-}
+      
+nextKey :: I.Auto t => I.IndexDimension r t -> t
+nextKey i =
+  case i of
+    (I.IndexDimensionM m) -> nextKey' m
+    (I.IndexDimensionO m) -> nextKey' m
+  where
+    nextKey' m = if Data.Map.null m
+                   then minBound
+                   else succ . fst $! Data.Map.findMax m
+    {-# INLINE nextKey' #-}
+{-# INLINE nextKey #-}
+
+genericInsert :: Applicative f 
+              => (I.IKey krs ts -> Int -> I.Store tag krs irs ts e -> f (I.Store tag krs irs ts e))
+              -> I.IKey krs ts
+              -> e
+              -> I.Store tag krs irs ts e
+              -> f (I.Store tag krs irs ts e)
+genericInsert ins ik e old@(I.Store _ _ nid) = go <$> ins ik nid old
+  where
+    go s'@(I.Store es' _ _) = s'
+      { I.storeV = Data.IntMap.insert nid (ik, e) es'
+      , I.storeNID = nid + 1
+      }
+    {-# INLINE go #-}
+{-# INLINE genericInsert #-}
+
+-- | Inserts the given element identifier into the store's index under the given
+-- internal key.
+--
+-- In case of collisions: returns 'Data.Maybe.Nothing'.
+indexInsertID :: I.IKey krs ts
+              -> Int
+              -> I.Store tag krs irs ts e
+              -> Maybe (I.Store tag krs irs ts e)
+indexInsertID ik eid old@(I.Store _ index _) =
+  if Data.List.null $ findCollisions ik index
+    then Just $! runIdentity $! indexInsertID'' ik eid old
+    else Nothing
+{-# INLINE indexInsertID #-}
+
+-- | Inserts the given element identifier into the store's index under the given
+-- internal key.
+--
+-- In case of collisions: deletes them.
+indexInsertID' :: I.IKey krs ts
+               -> Int
+               -> I.Store tag krs irs ts e
+               -> Identity (I.Store tag krs irs ts e)
+indexInsertID' ik eid old@(I.Store _ index _) = --{-# SCC "indexInsertID'" #-} 
+  indexInsertID'' ik eid $! Data.IntSet.foldl' go old collisions
+  where
+    go s'@(I.Store es' ix' _) i =
+      case Data.IntMap.updateLookupWithKey (\_ _ -> Nothing) i es' of
+        (Just (ik', _), v'') -> s'
+          { I.storeV = v''
+          , I.storeI = indexDeleteID ik' i ix'
+          } 
+        _ -> error $ moduleName <> ".insertInternal'.go: The impossible happened."
+    {-# INLINEABLE go #-}
+
+    collisions = Data.IntSet.delete eid $! Data.IntSet.fromList $! findCollisions ik index
+    {-# INLINE collisions #-}
+{-# INLINE indexInsertID' #-}
+
+-- | UNSAFE. Inserts the given element identifier into the store's index under the given
+-- internal key.
+-- 
+-- In case of collisions: ignores them.
+indexInsertID'' :: I.IKey krs ts
+                -> Int
+                -> I.Store tag krs irs ts e
+                -> Identity (I.Store tag krs irs ts e)
+indexInsertID'' ik eid old@(I.Store _ index _) = --{-# SCC "indexInsertID''" #-}
+  zipped `seq` Identity $! old { I.storeI = zipped }
+  where
+    zipped = zipD ik index
+
+    zipD :: I.IKey krs ts -> I.Index irs ts -> I.Index irs ts
+    zipD (I.KN kd kt) (I.IN ixd it) = I.IN (combine kd ixd) $! zipD kt it
+    zipD (I.K1 kd) (I.I1 ixd) = I.I1 $! combine kd ixd
+    zipD _ _ = error $ moduleName <> ".indexInsertID''.zipD: The impossible happened."
+    {-# INLINE zipD #-}
+
+    combine :: I.IKeyDimension krs ts -> I.IndexDimension irs ts -> I.IndexDimension irs ts
+    combine kd ixd =
+      case (ixd, kd) of
+        (I.IndexDimensionO m, I.IKeyDimensionO k)  ->
+          I.IndexDimensionO $! goO k eid m
+        
+        (I.IndexDimensionO m, I.IKeyDimensionM ks) ->
+          I.IndexDimensionO $! Data.List.foldl' (\acc k -> goO k eid acc) m ks 
+
+        (I.IndexDimensionM m, I.IKeyDimensionO k)  ->
+          I.IndexDimensionM $! goM k eid $! m
+
+        (I.IndexDimensionM m, I.IKeyDimensionM ks) ->
+          I.IndexDimensionM $! Data.List.foldl' (\acc k -> goM k eid acc) m ks
+    {-# INLINEABLE combine #-}
+
+    goO :: Ord k => k -> Int -> Data.Map.Map k Int -> Data.Map.Map k Int
+    goO = Data.Map.insert 
+    {-# INLINE goO #-}
+
+    goM :: Ord k => k -> Int -> Data.Map.Map k Data.IntSet.IntSet -> Data.Map.Map k Data.IntSet.IntSet
+    goM k e = Data.Map.insertWith (\_ s -> Data.IntSet.insert e s) k (Data.IntSet.singleton e)
+    {-# INLINE goM #-}
+{-# INLINE indexInsertID'' #-}
+
+findCollisions :: I.IKey krs ts -> I.Index irs ts -> [Int]
+findCollisions ik ix = {-# SCC "findCollisions" #-} zipD ik ix [] 
+  where
+    zipD :: I.IKey krs ts -> I.Index irs ts -> [Int] -> [Int]
+    zipD (I.KN kd kt) (I.IN ixd it) = combine kd ixd . zipD kt it
+    zipD (I.K1 kd) (I.I1 ixd) = combine kd ixd
+    zipD _ _ = error $ moduleName <> ".findCollisions.zipD: The impossible happened."
+
+    combine :: I.IKeyDimension krs ts -> I.IndexDimension irs ts -> [Int] -> [Int]
+    combine kd ixd = 
+      case (ixd, kd) of
+        (I.IndexDimensionO m, I.IKeyDimensionO k)  -> goO k m
+        (I.IndexDimensionO m, I.IKeyDimensionM ks) -> foldr (\k acc -> goO k m . acc) id ks
+        _ -> id
+    {-# INLINE combine #-}
+
+    goO :: Ord k => k -> Data.Map.Map k Int -> [Int] -> [Int]
+    goO k m =
+      case Data.Map.lookup k $! m of
+        Nothing -> id
+        Just  i -> (i:)
+    {-# INLINE goO #-}
+
+-- | Deletes EID fron an index.
+indexDeleteID :: I.IKey krs ts
+              -> Int
+              -> I.Index irs ts
+              -> I.Index irs ts
+indexDeleteID ik eid = zipD ik
+  where
+    zipD :: I.IKey krs ts -> I.Index irs ts -> I.Index irs ts
+    zipD (I.KN kd kt) (I.IN ixd it) = I.IN (combine kd ixd) $! zipD kt it
+    zipD (I.K1 kd) (I.I1 ixd) = I.I1 $! combine kd ixd
+    zipD _ _ = error $ moduleName <> ".indexDeleteID.zipD: The impossible happened."
+    {-# INLINEABLE zipD #-}
+
+    combine :: Ord t => I.IKeyDimension kr t -> I.IndexDimension ir t -> I.IndexDimension ir t
+    combine key index =
+      case (index, key) of
+        (I.IndexDimensionO m, I.IKeyDimensionO k)  -> I.IndexDimensionO $! goO m k
+        (I.IndexDimensionO m, I.IKeyDimensionM ks) -> I.IndexDimensionO $! Data.List.foldl' goO m ks
+        (I.IndexDimensionM m, I.IKeyDimensionO k)  -> I.IndexDimensionM $! goM m k
+        (I.IndexDimensionM m, I.IKeyDimensionM ks) -> I.IndexDimensionM $! Data.List.foldl' goM m ks
+    {-# INLINEABLE combine #-}
+
+    goO :: Ord k => Data.Map.Map k Int -> k -> Data.Map.Map k Int
+    goO m k = Data.Map.update (\i' -> if i' == eid then Nothing else Just i') k m
+    {-# INLINE goO #-}
+
+    goM :: Ord k => Data.Map.Map k Data.IntSet.IntSet -> k -> Data.Map.Map k Data.IntSet.IntSet
+    goM m k = Data.Map.update
+      (\ids -> let nids = Data.IntSet.delete eid ids in
+        if Data.IntSet.null nids
+          then Nothing
+          else Just nids
+      ) k m
+    {-# INLINE goM #-}
+{-# INLINE indexDeleteID #-}
+
diff --git a/src/Data/Store/Internal/Type.hs b/src/Data/Store/Internal/Type.hs
--- a/src/Data/Store/Internal/Type.hs
+++ b/src/Data/Store/Internal/Type.hs
@@ -1,560 +1,590 @@
-{-# LANGUAGE MultiParamTypeClasses #-}
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE EmptyDataDecls #-}
-{-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE KindSignatures #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE RankNTypes #-}
-{-# LANGUAGE UndecidableInstances #-}
-{-# LANGUAGE DeriveDataTypeable #-}
-{-# LANGUAGE StandaloneDeriving #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE CPP #-}
-
-module Data.Store.Internal.Type
-where
-
---------------------------------------------------------------------------------
-import           Control.Applicative ((<$>), (<*>))
-import           Control.DeepSeq (NFData(rnf))
---------------------------------------------------------------------------------
-import           Data.Data (Typeable, Typeable2)
-import qualified Data.Data
-import qualified Data.List
-import           Data.Monoid ((<>))
-#if MIN_VERSION_containers(0,5,0)
-import qualified Data.IntMap.Strict as Data.IntMap
-import qualified Data.Map.Strict    as Data.Map
-#else
-import qualified Data.IntMap
-import qualified Data.Map
-#endif
-import qualified Data.IntSet
-import qualified Data.Foldable as F
-
-import qualified Data.SafeCopy  as Ser
-import qualified Data.Serialize as Ser (Serialize, get, put)
---------------------------------------------------------------------------------
-
-moduleName :: String
-moduleName = "Data.Store.Internal.Type"
-
--- | This is type-level tag for tagging dimensions of key and the index of a store.
--- You can think of @'Data.Store.Internal.Type.M'@ as an abbreviation for
--- "many".
---
--- * When @'Data.Store.Internal.Type.Key'@ dimension is tagged with
--- @'Data.Store.Internal.Type.M'@, it means that a single element can be
--- indexed under multiple key dimension values. Example: @Content@ (element) has
--- many tags.
---
--- * When @'Data.Store.Internal.Type.Index'@ dimension is tagged with
--- @'Data.Store.Internal.Type.M'@, it means that a multiple elements can be
--- indexed under a single key dimension values. Example: One rating can be shared by
--- many @Content@s (elements).
---
--- See also:
---
--- * 'Data.Store.Internal.Type.O'
---
--- * 'Data.Store.Internal.Type.Key'
---
--- * 'Data.Store.Internal.Type.Store'
-data M 
-
--- | This is type-level tag for tagging dimensions of key and the index of a store.
--- You can think of @'Data.Store.Internal.Type.O'@ as an abbreviation for
--- "one".
---
--- * When @'Data.Store.Internal.Type.Key'@ dimension is tagged with
--- @'Data.Store.Internal.Type.O'@, it means that a single element is indexed
--- under exactly one key dimension value. Example: @Content@ (element) has exactly one title.
---
--- * When @'Data.Store.Internal.Type.Index'@ dimension is tagged with
--- @'Data.Store.Internal.Type.O'@, it means that at most one element can be
--- indexed under one key dimension value. Example: One @ContentID@ corresponds
--- to at most one @Content@ (element).
---
--- See also:
---
--- * 'Data.Store.Internal.Type.M'
---
--- * 'Data.Store.Internal.Type.Key'
---
--- * 'Data.Store.Internal.Type.Store'
-data O
-
--- | Type-level zero.
-data Z = Z
-
--- | Type-level successor of a number.
-data S n = S n
-
-type N0 = Z
-type N1 = S N0
-type N2 = S N1
-type N3 = S N2
-type N4 = S N3
-type N5 = S N4
-type N6 = S N5
-type N7 = S N6
-type N8 = S N7
-type N9 = S N8
-type N10 = S N9
-
-n0 :: N0
-n0 = Z
-n1 :: N1
-n1 = S n0
-n2 :: N2
-n2 = S n1
-n3 :: N3
-n3 = S n2
-n4 :: N4
-n4 = S n3
-n5 :: N5
-n5 = S n4
-n6 :: N6
-n6 = S n5
-n7 :: N7
-n7 = S n6
-n8 :: N8
-n8 = S n7
-n9 :: N9
-n9 = S n8
-n10 :: N10
-n10 = S n9
-
-type family   DimensionRelation n rs ts :: *
-type instance DimensionRelation Z O ts = O
-type instance DimensionRelation Z M ts = M
-type instance DimensionRelation Z (r :. rt) (t :. tt) = r
-type instance DimensionRelation (S n) (r :. rt) (t :. tt) = DimensionRelation n rt tt
-
-type family   DimensionType n rs ts :: *
-type instance DimensionType Z M t = t
-type instance DimensionType Z O t = t
-type instance DimensionType Z (r :. rt) (t :. tt) = t
-type instance DimensionType (S n) (r :. rt) (t :. tt) = DimensionType n rt tt
-
-type family   RawDimensionType n a :: *
-type instance RawDimensionType n (Index irs ts) = IndexDimension (DimensionRelation n irs ts) (DimensionType n irs ts)
-
--- | The pupose of the @'Data.Store.Internal.Type.RawKey'@ type family is
--- to derive a type of a \"raw key\" that is easier to pattern match against
--- than @'Data.Store.Internal.Key'@.
---
--- Example:
---
--- > RawKey (O :. O :. O :. M :. O) (ContentID :. String :. String :. String :. Double) ~ (ContentID :. String :. String :. [String] :. Double)
-type family   RawKey kspec tspec :: *
-type instance RawKey (O :. rt) (t :. tt) =  t  :. RawKey rt tt
-type instance RawKey (M :. rt) (t :. tt) = [t] :. RawKey rt tt
-type instance RawKey O t =  t
-type instance RawKey M t = [t]
-
-class (Ord k, Enum k, Bounded k) => Auto k where
-instance (Ord k, Enum k, Bounded k) => Auto k where
-
--- | The store data type has four type arguments that define what and how
--- things are stored.
---
--- The @krs@ (key relation specification) and @irs@ (index relation
--- specification) define the relations between the dimensions of the key
--- and the elements. To that end, we use @'Data.Store.Internal.Type.O'@ and
--- @'Data.Store.Internal.Type.M'@ type-level tags and
--- @'Data.Store.Type.Internal.(:.)'@ data type to create tuple of these
--- tags (to describe all the dimensions).
---
--- The possible relations are as follows:
---
--- * One-one: Every intem is indexed under exactly one key dimension value. One key dimension value
--- corresponds to at most one elements.
---
--- * One-many: Every element is indexed under exactly one key dimension value. One key dimension value can
--- correspond to many elements.
---
--- * Many-one: Every element can be indexed under multiple (zero or more) key dimension values. One key dimension value
--- corresponds to at most one elements.
---
--- * Many-many: Every element cab be indexed under multiple (zero or more) key dimension value. One key dimension value
--- can correspond to many elements.
---
--- The @ts@ (type specification) defines the type of the key's dimensions
--- and finally @v@ is the type of the elements stored.
---
--- In our example with @Content@, we have five dimensions: ID, name, body,
--- tags and rating. We would like our store to have these properties:
---
--- * @Content@ has one ID, only one content can have a given ID.
---
--- * @Content@ has one name, only one content can have a given name.
---
--- * @Content@ has one body, many contents can have the same content.
---
--- * @Content@ has many tags, many contents can have tte same tag.
---
--- * @Content@ has one rating, many contents can have the same rating.
---
--- So in our case, we define:
---
--- > type ContentStoreKRS = O         :. O      :. O      :. M      :. O
--- > type ContentStoreIRS = O         :. O      :. M      :. M      :. M
--- > type ContentStoreTS  = ContentID :. String :. String :. String :. Double
--- > type ContentStore = Store ContentStoreKRS ContentStoreIRS ContentStoreTS Content
---
--- See also:
---
--- * 'Data.Store.Internal.Type.O'
---
--- * 'Data.Store.Internal.Type.M'
---
--- * 'Data.Store.Internal.Type.(:.)'
---
--- * 'Data.Store.Internal.Type.Key'
---
-data Store tag krs irs ts v = Store
-    { storeV :: !(Data.IntMap.IntMap (IKey krs ts, v))
-    , storeI :: !(Index irs ts)
-    , storeNID :: {-# UNPACK #-} !Int
-    } deriving (Typeable)
-
-instance (Show h, Show t) => Show (h :. t) where
-    show (h :. t) = show h <> " :. " <> show t
-
-instance (Ser.Serialize (IKey krs ts), Ser.Serialize (Index irs ts), Ser.Serialize v) => Ser.Serialize (Store tag krs irs ts v) where
-    get = Store <$> Ser.get <*> Ser.get <*> Ser.get
-    put (Store vs ix nid) = Ser.put vs >> Ser.put ix >> Ser.put nid
-
-instance (Ser.SafeCopy (IKey krs ts), Ser.SafeCopy (Index irs ts), Ser.SafeCopy v) => Ser.SafeCopy (Store tag krs irs ts v) where
-    getCopy = Ser.contain $ Store <$> Ser.safeGet <*> Ser.safeGet <*> Ser.safeGet
-    putCopy (Store vs ix nid) = Ser.contain $ Ser.safePut vs >> Ser.safePut ix >> Ser.safePut nid
-
-instance (Show (IKey krs ts), Show v) => Show (Store tag krs irs ts v) where
-    show (Store vs _ _) = "[" <> go <> "]"
-      where
-        go = Data.List.intercalate "," $ map (\(ik, v) -> "((" <> show ik <> "), " <> show v <> ")")
-                                       $ F.toList vs
-
-data GenericKey dim rs ts where
-    KN :: !(dim r t) -> !(GenericKey dim rt tt) -> GenericKey dim (r :. rt) (t :. tt)
-    K1 :: !(dim r t) -> GenericKey dim r t
-
-instance Eq (GenericKey IKeyDimension rs ts) where
-    (K1 x) == (K1 y) = x == y
-    (KN x xt) == (KN y yt) = x == y && xt == yt
-    _ == _ = False    
-
-    (K1 x) /= (K1 y) = x /= y
-    (KN x xt) /= (KN y yt) = x /= y || xt /= yt
-    _ /= _ = True
-
-{-
-instance Eq (dim O t) => Eq (GenericKey dim O t) where
-    (K1 x) == (K1 y) = x == y
-    (K1 x) /= (K1 y) = x /= y
-
-instance Eq (dim M t) => Eq (GenericKey dim M t) where
-    (K1 x) == (K1 y) = x == y
-    (K1 x) /= (K1 y) = x /= y
-
-instance (Eq (dim r t), Eq (GenericKey dim rt tt)) => Eq (GenericKey dim (r :. rt) (t :. tt)) where
-    (KN x xt) == (KN y yt) = x == y && xt == yt
-    _ == _ = False
-
-    (KN x xt) /= (KN y yt) = x /= y || xt /= yt
-    _ /= _ = True
--}
-
-instance Ser.Serialize (dim O t) => Ser.Serialize (GenericKey dim O t) where
-    get = K1 <$> Ser.get
-    put (K1 d) = Ser.put d
-
-instance Ser.Serialize (dim M t) => Ser.Serialize (GenericKey dim M t) where
-    get = K1 <$> Ser.get
-    put (K1 d) = Ser.put d
-
-instance (Ser.Serialize (GenericKey dim rt tt), Ser.Serialize (dim r t)) => Ser.Serialize (GenericKey dim (r :. rt) (t :. tt)) where
-    get = KN <$> Ser.get <*> Ser.get
-    put (KN d dt) = Ser.put d >> Ser.put dt
-    put (K1 _) = error $ moduleName <> ".GenricKey.put: The impossible happened."
-
-instance Ser.SafeCopy (dim O t) => Ser.SafeCopy (GenericKey dim O t) where
-    getCopy = Ser.contain $ K1 <$> Ser.safeGet
-    putCopy (K1 d) = Ser.contain $ Ser.safePut d
-
-instance Ser.SafeCopy (dim M t) => Ser.SafeCopy (GenericKey dim M t) where
-    getCopy = Ser.contain $ K1 <$> Ser.safeGet
-    putCopy (K1 d) = Ser.contain $ Ser.safePut d
-
-instance (Ser.SafeCopy (GenericKey dim rt tt), Ser.SafeCopy (dim r t)) => Ser.SafeCopy (GenericKey dim (r :. rt) (t :. tt)) where
-    getCopy = Ser.contain $ KN <$> Ser.safeGet <*> Ser.safeGet
-    putCopy (KN d dt) = Ser.contain $ Ser.safePut d >> Ser.safePut dt
-    putCopy (K1 _) = error $ moduleName <> ".GenricKey.putCopy: The impossible happened."
-
-instance Typeable2 (GenericKey dim) where
-    typeOf2 (K1 _) = Data.Data.mkTyConApp (Data.Data.mkTyCon3 "data-store" moduleName "K1") []
-    typeOf2 (KN _ _) = Data.Data.mkTyConApp (Data.Data.mkTyCon3 "data-store" moduleName "KN") []
-
-type  Key = GenericKey  KeyDimension
-type IKey = GenericKey IKeyDimension
-
-instance Show t => Show (Key O t) where
-    show (K1 d) = show d 
-
-instance Show t => Show (Key M t) where
-    show (K1 d) = show d 
-
-instance (Show t, Show (Key rt tt)) => Show (Key (r :. rt) (t :. tt)) where
-    show (KN d k) = show d <> ", " <> show k
-    show (K1 _) = error $ moduleName <> ".Key.show: The impossible happened."
-
-instance Show t => Show (IKey O t) where
-    show (K1 d) = show d 
-
-instance Show t => Show (IKey M t) where
-    show (K1 d) = show d 
-
-instance (Show t, Show (IKey rt tt)) => Show (IKey (r :. rt) (t :. tt)) where
-    show (KN d k) = show d <> ", " <> show k
-    show (K1 _) = error $ moduleName <> ".IKey.show: The impossible happened."
-
-data Index rs ts where
-    IN :: Ord t => !(IndexDimension r t) -> !(Index rt tt) -> Index (r :. rt) (t :. tt)
-    I1 :: Ord t => !(IndexDimension r t) -> Index r t
-
-instance (Ord t, Ser.Serialize t) => Ser.Serialize (Index O t) where
-    get = I1 <$> Ser.get
-    put (I1 ixd) = Ser.put ixd
-
-instance (Ord t, Ser.Serialize t) => Ser.Serialize (Index M t) where
-    get = I1 <$> Ser.get
-    put (I1 ixd) = Ser.put ixd
-
-instance (Ord t, Ser.Serialize t, Ser.Serialize (Index rt tt)) => Ser.Serialize (Index (O :. rt) (t :. tt)) where
-    get = IN <$> Ser.get <*> Ser.get
-    put (IN ixd ixt) = Ser.put ixd >> Ser.put ixt
-    put (I1 _) = error $ moduleName <> ".Index.put: The impossible happened (#1)."
-
-instance (Ord t, Ser.Serialize t, Ser.Serialize (Index rt tt)) => Ser.Serialize (Index (M :. rt) (t :. tt)) where
-    get = IN <$> Ser.get <*> Ser.get
-    put (IN ixd ixt) = Ser.put ixd >> Ser.put ixt
-    put (I1 _) = error $ moduleName <> ".Index.put: The impossible happened (#2)."
-
-instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (Index O t) where
-    getCopy = Ser.contain $ I1 <$> Ser.safeGet
-    putCopy (I1 ixd) = Ser.contain $ Ser.safePut ixd
-
-instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (Index M t) where
-    getCopy = Ser.contain $ I1 <$> Ser.safeGet
-    putCopy (I1 ixd) = Ser.contain $ Ser.safePut ixd
-
-instance (Ord t, Ser.SafeCopy t, Ser.SafeCopy (Index rt tt)) => Ser.SafeCopy (Index (O :. rt) (t :. tt)) where
-    getCopy = Ser.contain $ IN <$> Ser.safeGet <*> Ser.safeGet
-    putCopy (IN ixd ixt) = Ser.contain $ Ser.safePut ixd >> Ser.safePut ixt
-    putCopy (I1 _) = error $ moduleName <> ".Index.putCopy: The impossible happened (#1)."
-
-instance (Ord t, Ser.SafeCopy t, Ser.SafeCopy (Index rt tt)) => Ser.SafeCopy (Index (M :. rt) (t :. tt)) where
-    getCopy = Ser.contain $ IN <$> Ser.safeGet <*> Ser.safeGet
-    putCopy (IN ixd ixt) = Ser.contain $ Ser.safePut ixd >> Ser.safePut ixt
-    putCopy (I1 _) = error $ moduleName <> ".Index.putCopy: The impossible happened (#2)."
-
-instance Typeable2 Index where
-    typeOf2 (I1 _) = Data.Data.mkTyConApp (Data.Data.mkTyCon3 "data-store" moduleName "I1") []
-    typeOf2 (IN _ _) = Data.Data.mkTyConApp (Data.Data.mkTyCon3 "data-store" moduleName "IN") []
-
-instance Show t => Show (Index O t) where
-    show (I1 d) = show d
-
-instance Show t => Show (Index M t) where
-    show (I1 d) = show d
-
-instance (Show t, Show (Index rt tt)) => Show (Index (r :. rt) (t :. tt)) where
-    show (IN d i) = show d <> "\n" <> show i
-    show (I1 _) = error $ moduleName <> ".Index.show: The impossible happened."
-
-data KeyDimension r t where
-    KeyDimensionO :: Ord t =>  t  -> KeyDimension O t
-    KeyDimensionM :: Ord t => [t] -> KeyDimension M t
-    KeyDimensionA :: Auto t => KeyDimension O t
-
-deriving instance Typeable2 KeyDimension
-
-instance Show t => Show (KeyDimension r t) where
-    show (KeyDimensionM ts) = show ts
-    show (KeyDimensionO t)  = show t
-    show  KeyDimensionA     = show "Auto"
-
-data IKeyDimension r t where
-    IKeyDimensionO :: Ord t => t  -> IKeyDimension O t
-    IKeyDimensionM :: Ord t => [t] -> IKeyDimension M t
-
-instance Eq (IKeyDimension r t) where
-    (IKeyDimensionM x) == (IKeyDimensionM y) = x == y
-    (IKeyDimensionO x) == (IKeyDimensionO y) = x == y
-    _ == _ = False
-
-    (IKeyDimensionM x) /= (IKeyDimensionM y) = x /= y
-    (IKeyDimensionO x) /= (IKeyDimensionO y) = x /= y
-    _ /= _ = True    
-
-deriving instance Typeable2 IKeyDimension
-
-instance (Ord t, Ser.Serialize t) => Ser.Serialize (IKeyDimension O t) where
-    get = IKeyDimensionO <$> Ser.get
-    put (IKeyDimensionO x) = Ser.put x
-
-instance (Ord t, Ser.Serialize t) => Ser.Serialize (IKeyDimension M t) where
-    get = IKeyDimensionM <$> Ser.get
-    put (IKeyDimensionM x) = Ser.put x
-
-instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (IKeyDimension O t) where
-    getCopy = Ser.contain $ IKeyDimensionO <$> Ser.safeGet
-    putCopy (IKeyDimensionO x)  = Ser.contain $ Ser.safePut x
-
-instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (IKeyDimension M t) where
-    getCopy = Ser.contain $ IKeyDimensionM <$> Ser.safeGet
-    putCopy (IKeyDimensionM x)  = Ser.contain $ Ser.safePut x
-
-instance Show t => Show (IKeyDimension r t) where
-    show (IKeyDimensionM ts) = show ts
-    show (IKeyDimensionO t)  = show t
-
-data IndexDimension r t where
-    IndexDimensionO :: Ord t
-                    => !(Data.Map.Map t Int)
-                    -> IndexDimension O t
-    
-    IndexDimensionM :: Ord t
-                    => !(Data.Map.Map t Data.IntSet.IntSet)
-                    -> IndexDimension M t
-
-instance (Ord t, Ser.Serialize t) => Ser.Serialize (IndexDimension O t) where
-    get = IndexDimensionO <$> Ser.get
-    put (IndexDimensionO x) = Ser.put x
-
-instance (Ord t, Ser.Serialize t) => Ser.Serialize (IndexDimension M t) where
-    get = IndexDimensionM <$> Ser.get
-    put (IndexDimensionM x) = Ser.put x
-
-instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (IndexDimension O t) where
-    getCopy = Ser.contain $ IndexDimensionO <$> Ser.safeGet
-    putCopy (IndexDimensionO x)  = Ser.contain $ Ser.safePut x
-
-instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (IndexDimension M t) where
-    getCopy = Ser.contain $ IndexDimensionM <$> Ser.safeGet
-    putCopy (IndexDimensionM x)  = Ser.contain $ Ser.safePut x
-
-instance Show t => Show (IndexDimension r t) where
-    show (IndexDimensionM m) = show $ map (\(k, vs) -> (k, Data.IntSet.toList vs)) $ Data.Map.toList m
-    show (IndexDimensionO m) = show $ Data.Map.toList m
-
-class GetDimension n a where
-    getDimension :: n -> a -> RawDimensionType n a
-
-instance GetDimension Z (Index O t) where
-    getDimension _ (I1 ixd) = ixd
-
-instance GetDimension Z (Index M t) where
-    getDimension _ (I1 ixd) = ixd
-
-instance GetDimension Z (Index (r :. rt) (t :. tt)) where
-    getDimension _ (IN ixd _) = ixd
-    getDimension _ (I1 _) = error $ moduleName <> ".Index.getDimension: The impossible happened."
-
-instance GetDimension n (Index rt tt) => GetDimension (S n) (Index (r :. rt) (t :. tt)) where
-    getDimension (S n) (IN _ ixt) = getDimension n ixt
-    getDimension _ (I1 _) = error $ moduleName <> ".Index.getDimension: The impossible happened."
-
-data TT
-data FF
-
-type family   EmptyProxyIsSpecial t :: *
-type instance EmptyProxyIsSpecial Int = TT
-
-class Empty a where
-    empty :: a
-
-class EmptyProxy flag a where
-    emptyProxy :: flag -> a
-
-instance Ord t => Empty (Index O t) where
-    empty = I1 (IndexDimensionO Data.Map.empty)
-
-instance Ord t => Empty (Index M t) where
-    empty = I1 (IndexDimensionM Data.Map.empty)
-
-instance (Ord t, Empty (Index rt tt)) => Empty (Index (O :. rt) (t :. tt)) where
-    empty = IN (IndexDimensionO Data.Map.empty) empty
-
-instance (Ord t, Empty (Index rt tt)) => Empty (Index (M :. rt) (t :. tt)) where
-    empty = IN (IndexDimensionM Data.Map.empty) empty
-
-instance Empty (Index irs ts) => Empty (Store tag krs irs ts e) where
-    empty = Store
-        { storeV = Data.IntMap.empty
-        , storeI = empty
-        , storeNID = 0
-        }
-    {-# INLINE empty #-}
-
--- | Data type for creating tuples, it is used to:
---
--- * Create type-level tuples of relation tags for relation specification of
--- the key and the index of the store.
---
--- > M :. O :. O :. M
---
--- * Create type-level tuples of types for type specification of the key
--- and index of the store.
---
--- > Int :. Double :. String :. String
---
--- * Create value-level tuples to return raw key (with resolved
--- auto-increment dimensions).
---
--- > [1, 2, 3] :. 3.5 :. "Foo" :. ["Bar1", "Bar2"]
-data h :. t = h :. t
-infixr 3 :.
-
-
--- NFDATA INSTANCES
-
-instance (NFData e, NFData (IKey krs ts), NFData (Index irs ts)) => NFData (Store tag krs irs ts e) where
-    rnf (Store ke ix nid) = rnf ke `seq` rnf ix `seq` rnf nid
-
-instance NFData t => NFData (IndexDimension r t) where
-    rnf (IndexDimensionO m) = rnf m
-    rnf (IndexDimensionM m) = rnf m
-
-instance NFData t => NFData (Index O t) where
-    rnf (I1 kd) = rnf kd
-     
-instance NFData t => NFData (Index M t) where
-    rnf (I1 kd) = rnf kd
-
-instance (NFData t, NFData (Index rt tt)) => NFData (Index (r :. rt) (t :. tt)) where
-    rnf (IN kd kt) = rnf kd `seq` rnf kt
-    rnf (I1 _) = error "Impossible! (Index NFData)"
-
-instance NFData t => NFData (IKeyDimension r t) where
-    rnf (IKeyDimensionO x) = rnf x
-    rnf (IKeyDimensionM x) = rnf x
-
-instance NFData t => NFData (IKey O t) where
-    rnf (K1 kd) = rnf kd
-     
-instance NFData t => NFData (IKey M t) where
-    rnf (K1 kd) = rnf kd
-
-instance (NFData t, NFData (IKey rt tt)) => NFData (IKey (r :. rt) (t :. tt)) where
-    rnf (KN kd kt) = rnf kd `seq` rnf kt
-    rnf (K1 _) = error "Impossible! (IKey NFData)"
-
-instance (NFData a, NFData b) => NFData (a :. b) where
-    rnf (a :. b) = rnf a `seq` rnf b
-
-
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE EmptyDataDecls #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE UndecidableInstances #-}
+{-# LANGUAGE DeriveDataTypeable #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE CPP #-}
+
+module Data.Store.Internal.Type
+where
+
+--------------------------------------------------------------------------------
+import           Control.Applicative ((<$>), (<*>))
+import           Control.DeepSeq (NFData(rnf))
+--------------------------------------------------------------------------------
+import           Data.Data (Typeable, Typeable2)
+import qualified Data.Data
+import qualified Data.List
+import           Data.Monoid ((<>))
+#if MIN_VERSION_containers(0,5,0)
+import qualified Data.IntMap.Strict as Data.IntMap
+import qualified Data.Map.Strict    as Data.Map
+#else
+import qualified Data.IntMap
+import qualified Data.Map
+#endif
+import qualified Data.IntSet
+import qualified Data.Foldable as F
+
+import qualified Data.SafeCopy  as Ser
+import qualified Data.Serialize as Ser (Serialize, get, put)
+--------------------------------------------------------------------------------
+
+moduleName :: String
+moduleName = "Data.Store.Internal.Type"
+
+-- | This is type-level tag for tagging dimensions of key and the index of a store.
+-- You can think of @'Data.Store.Internal.Type.M'@ as an abbreviation for
+-- "many".
+--
+-- * When @'Data.Store.Internal.Type.Key'@ dimension is tagged with
+-- @'Data.Store.Internal.Type.M'@, it means that a single element can be
+-- indexed under multiple key dimension values. Example: @Content@ (element) has
+-- many tags.
+--
+-- * When @'Data.Store.Internal.Type.Index'@ dimension is tagged with
+-- @'Data.Store.Internal.Type.M'@, it means that a multiple elements can be
+-- indexed under a single key dimension values. Example: One rating can be shared by
+-- many @Content@s (elements).
+--
+-- See also:
+--
+-- * 'Data.Store.Internal.Type.O'
+--
+-- * 'Data.Store.Internal.Type.Key'
+--
+-- * 'Data.Store.Internal.Type.Store'
+data M 
+
+-- | This is type-level tag for tagging dimensions of key and the index of a store.
+-- You can think of @'Data.Store.Internal.Type.O'@ as an abbreviation for
+-- "one".
+--
+-- * When @'Data.Store.Internal.Type.Key'@ dimension is tagged with
+-- @'Data.Store.Internal.Type.O'@, it means that a single element is indexed
+-- under exactly one key dimension value. Example: @Content@ (element) has exactly one title.
+--
+-- * When @'Data.Store.Internal.Type.Index'@ dimension is tagged with
+-- @'Data.Store.Internal.Type.O'@, it means that at most one element can be
+-- indexed under one key dimension value. Example: One @ContentID@ corresponds
+-- to at most one @Content@ (element).
+--
+-- See also:
+--
+-- * 'Data.Store.Internal.Type.M'
+--
+-- * 'Data.Store.Internal.Type.Key'
+--
+-- * 'Data.Store.Internal.Type.Store'
+data O
+
+-- | Type-level zero.
+data Z = Z
+
+-- | Type-level successor of a number.
+data S n = S n
+
+type N0 = Z
+type N1 = S N0
+type N2 = S N1
+type N3 = S N2
+type N4 = S N3
+type N5 = S N4
+type N6 = S N5
+type N7 = S N6
+type N8 = S N7
+type N9 = S N8
+type N10 = S N9
+
+n0 :: N0
+n0 = Z
+n1 :: N1
+n1 = S n0
+n2 :: N2
+n2 = S n1
+n3 :: N3
+n3 = S n2
+n4 :: N4
+n4 = S n3
+n5 :: N5
+n5 = S n4
+n6 :: N6
+n6 = S n5
+n7 :: N7
+n7 = S n6
+n8 :: N8
+n8 = S n7
+n9 :: N9
+n9 = S n8
+n10 :: N10
+n10 = S n9
+
+type family   DimensionRelation n rs ts :: *
+type instance DimensionRelation Z O ts = O
+type instance DimensionRelation Z M ts = M
+type instance DimensionRelation Z (r :. rt) (t :. tt) = r
+type instance DimensionRelation (S n) (r :. rt) (t :. tt) = DimensionRelation n rt tt
+
+type family   DimensionType n rs ts :: *
+type instance DimensionType Z M t = t
+type instance DimensionType Z O t = t
+type instance DimensionType Z (r :. rt) (t :. tt) = t
+type instance DimensionType (S n) (r :. rt) (t :. tt) = DimensionType n rt tt
+
+type family   RawDimensionType n a :: *
+type instance RawDimensionType n (Index irs ts) = IndexDimension (DimensionRelation n irs ts) (DimensionType n irs ts)
+type instance RawDimensionType n (IKey krs ts) = IKeyDimension (DimensionRelation n krs ts) (DimensionType n krs ts)
+
+type family   LookupMap n krs irs ts v :: *
+type instance LookupMap n krs irs ts v =
+  Data.Map.Map (DimensionType n krs ts) (LookupMapElement (DimensionRelation n krs ts) (RawKey krs ts, v))
+
+type family   LookupMapElement r e :: *
+type instance LookupMapElement O e = e
+type instance LookupMapElement M e = [e]
+
+-- | The pupose of the @'Data.Store.Internal.Type.RawKey'@ type family is
+-- to derive a type of a \"raw key\" that is easier to pattern match against
+-- than @'Data.Store.Internal.Key'@.
+--
+-- Example:
+--
+-- > RawKey (O :. O :. O :. M :. O) (ContentID :. String :. String :. String :. Double) ~ (ContentID :. String :. String :. [String] :. Double)
+type family   RawKey kspec tspec :: *
+type instance RawKey (O :. rt) (t :. tt) =  t  :. RawKey rt tt
+type instance RawKey (M :. rt) (t :. tt) = [t] :. RawKey rt tt
+type instance RawKey O t =  t
+type instance RawKey M t = [t]
+
+type family   RawKeyDimension n kspec tspec :: *
+type instance RawKeyDimension Z (O :. rt) (t :. tt) = t
+type instance RawKeyDimension Z (M :. rt) (t :. tt) = [t]
+type instance RawKeyDimension Z O t = t
+type instance RawKeyDimension Z M t = [t]
+type instance RawKeyDimension (S n) (r :. rt) (t :. tt) = RawKeyDimension n rt tt
+
+class (Ord k, Enum k, Bounded k) => Auto k where
+instance (Ord k, Enum k, Bounded k) => Auto k where
+
+-- | The store data type has four type arguments that define what and how
+-- things are stored.
+--
+-- The @krs@ (key relation specification) and @irs@ (index relation
+-- specification) define the relations between the dimensions of the key
+-- and the elements. To that end, we use @'Data.Store.Internal.Type.O'@ and
+-- @'Data.Store.Internal.Type.M'@ type-level tags and
+-- @'Data.Store.Type.Internal.(:.)'@ data type to create tuple of these
+-- tags (to describe all the dimensions).
+--
+-- The possible relations are as follows:
+--
+-- * One-one: Every intem is indexed under exactly one key dimension value. One key dimension value
+-- corresponds to at most one elements.
+--
+-- * One-many: Every element is indexed under exactly one key dimension value. One key dimension value can
+-- correspond to many elements.
+--
+-- * Many-one: Every element can be indexed under multiple (zero or more) key dimension values. One key dimension value
+-- corresponds to at most one elements.
+--
+-- * Many-many: Every element cab be indexed under multiple (zero or more) key dimension value. One key dimension value
+-- can correspond to many elements.
+--
+-- The @ts@ (type specification) defines the type of the key's dimensions
+-- and finally @v@ is the type of the elements stored.
+--
+-- In our example with @Content@, we have five dimensions: ID, name, body,
+-- tags and rating. We would like our store to have these properties:
+--
+-- * @Content@ has one ID, only one content can have a given ID.
+--
+-- * @Content@ has one name, only one content can have a given name.
+--
+-- * @Content@ has one body, many contents can have the same content.
+--
+-- * @Content@ has many tags, many contents can have tte same tag.
+--
+-- * @Content@ has one rating, many contents can have the same rating.
+--
+-- So in our case, we define:
+--
+-- > type ContentStoreKRS = O         :. O      :. O      :. M      :. O
+-- > type ContentStoreIRS = O         :. O      :. M      :. M      :. M
+-- > type ContentStoreTS  = ContentID :. String :. String :. String :. Double
+-- > type ContentStore = Store ContentStoreKRS ContentStoreIRS ContentStoreTS Content
+--
+-- See also:
+--
+-- * 'Data.Store.Internal.Type.O'
+--
+-- * 'Data.Store.Internal.Type.M'
+--
+-- * 'Data.Store.Internal.Type.(:.)'
+--
+-- * 'Data.Store.Internal.Type.Key'
+--
+data Store tag krs irs ts v = Store
+    { storeV :: !(Data.IntMap.IntMap (IKey krs ts, v))
+    , storeI :: !(Index irs ts)
+    , storeNID :: {-# UNPACK #-} !Int
+    } deriving (Typeable)
+
+instance (Show h, Show t) => Show (h :. t) where
+    show (h :. t) = show h <> " :. " <> show t
+
+instance (Ser.Serialize (IKey krs ts), Ser.Serialize (Index irs ts), Ser.Serialize v) => Ser.Serialize (Store tag krs irs ts v) where
+    get = Store <$> Ser.get <*> Ser.get <*> Ser.get
+    put (Store vs ix nid) = Ser.put vs >> Ser.put ix >> Ser.put nid
+
+instance (Ser.SafeCopy (IKey krs ts), Ser.SafeCopy (Index irs ts), Ser.SafeCopy v) => Ser.SafeCopy (Store tag krs irs ts v) where
+    getCopy = Ser.contain $ Store <$> Ser.safeGet <*> Ser.safeGet <*> Ser.safeGet
+    putCopy (Store vs ix nid) = Ser.contain $ Ser.safePut vs >> Ser.safePut ix >> Ser.safePut nid
+
+instance (Show (IKey krs ts), Show v) => Show (Store tag krs irs ts v) where
+    show (Store vs _ _) = "[" <> go <> "]"
+      where
+        go = Data.List.intercalate "," $ map (\(ik, v) -> "((" <> show ik <> "), " <> show v <> ")")
+                                       $ F.toList vs
+
+data GenericKey dim rs ts where
+    KN :: !(dim r t) -> !(GenericKey dim rt tt) -> GenericKey dim (r :. rt) (t :. tt)
+    K1 :: !(dim r t) -> GenericKey dim r t
+
+instance Eq (GenericKey IKeyDimension rs ts) where
+    (K1 x) == (K1 y) = x == y
+    (KN x xt) == (KN y yt) = x == y && xt == yt
+    _ == _ = False    
+
+    (K1 x) /= (K1 y) = x /= y
+    (KN x xt) /= (KN y yt) = x /= y || xt /= yt
+    _ /= _ = True
+
+{-
+instance Eq (dim O t) => Eq (GenericKey dim O t) where
+    (K1 x) == (K1 y) = x == y
+    (K1 x) /= (K1 y) = x /= y
+
+instance Eq (dim M t) => Eq (GenericKey dim M t) where
+    (K1 x) == (K1 y) = x == y
+    (K1 x) /= (K1 y) = x /= y
+
+instance (Eq (dim r t), Eq (GenericKey dim rt tt)) => Eq (GenericKey dim (r :. rt) (t :. tt)) where
+    (KN x xt) == (KN y yt) = x == y && xt == yt
+    _ == _ = False
+
+    (KN x xt) /= (KN y yt) = x /= y || xt /= yt
+    _ /= _ = True
+-}
+
+instance Ser.Serialize (dim O t) => Ser.Serialize (GenericKey dim O t) where
+    get = K1 <$> Ser.get
+    put (K1 d) = Ser.put d
+
+instance Ser.Serialize (dim M t) => Ser.Serialize (GenericKey dim M t) where
+    get = K1 <$> Ser.get
+    put (K1 d) = Ser.put d
+
+instance (Ser.Serialize (GenericKey dim rt tt), Ser.Serialize (dim r t)) => Ser.Serialize (GenericKey dim (r :. rt) (t :. tt)) where
+    get = KN <$> Ser.get <*> Ser.get
+    put (KN d dt) = Ser.put d >> Ser.put dt
+    put (K1 _) = error $ moduleName <> ".GenricKey.put: The impossible happened."
+
+instance Ser.SafeCopy (dim O t) => Ser.SafeCopy (GenericKey dim O t) where
+    getCopy = Ser.contain $ K1 <$> Ser.safeGet
+    putCopy (K1 d) = Ser.contain $ Ser.safePut d
+
+instance Ser.SafeCopy (dim M t) => Ser.SafeCopy (GenericKey dim M t) where
+    getCopy = Ser.contain $ K1 <$> Ser.safeGet
+    putCopy (K1 d) = Ser.contain $ Ser.safePut d
+
+instance (Ser.SafeCopy (GenericKey dim rt tt), Ser.SafeCopy (dim r t)) => Ser.SafeCopy (GenericKey dim (r :. rt) (t :. tt)) where
+    getCopy = Ser.contain $ KN <$> Ser.safeGet <*> Ser.safeGet
+    putCopy (KN d dt) = Ser.contain $ Ser.safePut d >> Ser.safePut dt
+    putCopy (K1 _) = error $ moduleName <> ".GenricKey.putCopy: The impossible happened."
+
+instance Typeable2 (GenericKey dim) where
+    typeOf2 (K1 _) = Data.Data.mkTyConApp (Data.Data.mkTyCon3 "data-store" moduleName "K1") []
+    typeOf2 (KN _ _) = Data.Data.mkTyConApp (Data.Data.mkTyCon3 "data-store" moduleName "KN") []
+
+type  Key = GenericKey  KeyDimension
+type IKey = GenericKey IKeyDimension
+
+instance Show t => Show (Key O t) where
+    show (K1 d) = show d 
+
+instance Show t => Show (Key M t) where
+    show (K1 d) = show d 
+
+instance (Show t, Show (Key rt tt)) => Show (Key (r :. rt) (t :. tt)) where
+    show (KN d k) = show d <> ", " <> show k
+    show (K1 _) = error $ moduleName <> ".Key.show: The impossible happened."
+
+instance Show t => Show (IKey O t) where
+    show (K1 d) = show d 
+
+instance Show t => Show (IKey M t) where
+    show (K1 d) = show d 
+
+instance (Show t, Show (IKey rt tt)) => Show (IKey (r :. rt) (t :. tt)) where
+    show (KN d k) = show d <> ", " <> show k
+    show (K1 _) = error $ moduleName <> ".IKey.show: The impossible happened."
+
+data Index rs ts where
+    IN :: Ord t => !(IndexDimension r t) -> !(Index rt tt) -> Index (r :. rt) (t :. tt)
+    I1 :: Ord t => !(IndexDimension r t) -> Index r t
+
+instance (Ord t, Ser.Serialize t) => Ser.Serialize (Index O t) where
+    get = I1 <$> Ser.get
+    put (I1 ixd) = Ser.put ixd
+
+instance (Ord t, Ser.Serialize t) => Ser.Serialize (Index M t) where
+    get = I1 <$> Ser.get
+    put (I1 ixd) = Ser.put ixd
+
+instance (Ord t, Ser.Serialize t, Ser.Serialize (Index rt tt)) => Ser.Serialize (Index (O :. rt) (t :. tt)) where
+    get = IN <$> Ser.get <*> Ser.get
+    put (IN ixd ixt) = Ser.put ixd >> Ser.put ixt
+    put (I1 _) = error $ moduleName <> ".Index.put: The impossible happened (#1)."
+
+instance (Ord t, Ser.Serialize t, Ser.Serialize (Index rt tt)) => Ser.Serialize (Index (M :. rt) (t :. tt)) where
+    get = IN <$> Ser.get <*> Ser.get
+    put (IN ixd ixt) = Ser.put ixd >> Ser.put ixt
+    put (I1 _) = error $ moduleName <> ".Index.put: The impossible happened (#2)."
+
+instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (Index O t) where
+    getCopy = Ser.contain $ I1 <$> Ser.safeGet
+    putCopy (I1 ixd) = Ser.contain $ Ser.safePut ixd
+
+instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (Index M t) where
+    getCopy = Ser.contain $ I1 <$> Ser.safeGet
+    putCopy (I1 ixd) = Ser.contain $ Ser.safePut ixd
+
+instance (Ord t, Ser.SafeCopy t, Ser.SafeCopy (Index rt tt)) => Ser.SafeCopy (Index (O :. rt) (t :. tt)) where
+    getCopy = Ser.contain $ IN <$> Ser.safeGet <*> Ser.safeGet
+    putCopy (IN ixd ixt) = Ser.contain $ Ser.safePut ixd >> Ser.safePut ixt
+    putCopy (I1 _) = error $ moduleName <> ".Index.putCopy: The impossible happened (#1)."
+
+instance (Ord t, Ser.SafeCopy t, Ser.SafeCopy (Index rt tt)) => Ser.SafeCopy (Index (M :. rt) (t :. tt)) where
+    getCopy = Ser.contain $ IN <$> Ser.safeGet <*> Ser.safeGet
+    putCopy (IN ixd ixt) = Ser.contain $ Ser.safePut ixd >> Ser.safePut ixt
+    putCopy (I1 _) = error $ moduleName <> ".Index.putCopy: The impossible happened (#2)."
+
+instance Typeable2 Index where
+    typeOf2 (I1 _) = Data.Data.mkTyConApp (Data.Data.mkTyCon3 "data-store" moduleName "I1") []
+    typeOf2 (IN _ _) = Data.Data.mkTyConApp (Data.Data.mkTyCon3 "data-store" moduleName "IN") []
+
+instance Show t => Show (Index O t) where
+    show (I1 d) = show d
+
+instance Show t => Show (Index M t) where
+    show (I1 d) = show d
+
+instance (Show t, Show (Index rt tt)) => Show (Index (r :. rt) (t :. tt)) where
+    show (IN d i) = show d <> "\n" <> show i
+    show (I1 _) = error $ moduleName <> ".Index.show: The impossible happened."
+
+data KeyDimension r t where
+    KeyDimensionO :: Ord t =>  t  -> KeyDimension O t
+    KeyDimensionM :: Ord t => [t] -> KeyDimension M t
+    KeyDimensionA :: Auto t => KeyDimension O t
+
+deriving instance Typeable2 KeyDimension
+
+instance Show t => Show (KeyDimension r t) where
+    show (KeyDimensionM ts) = show ts
+    show (KeyDimensionO t)  = show t
+    show  KeyDimensionA     = show "Auto"
+
+data IKeyDimension r t where
+    IKeyDimensionO :: Ord t => t  -> IKeyDimension O t
+    IKeyDimensionM :: Ord t => [t] -> IKeyDimension M t
+
+instance Eq (IKeyDimension r t) where
+    (IKeyDimensionM x) == (IKeyDimensionM y) = x == y
+    (IKeyDimensionO x) == (IKeyDimensionO y) = x == y
+    _ == _ = False
+
+    (IKeyDimensionM x) /= (IKeyDimensionM y) = x /= y
+    (IKeyDimensionO x) /= (IKeyDimensionO y) = x /= y
+    _ /= _ = True    
+
+deriving instance Typeable2 IKeyDimension
+
+instance (Ord t, Ser.Serialize t) => Ser.Serialize (IKeyDimension O t) where
+    get = IKeyDimensionO <$> Ser.get
+    put (IKeyDimensionO x) = Ser.put x
+
+instance (Ord t, Ser.Serialize t) => Ser.Serialize (IKeyDimension M t) where
+    get = IKeyDimensionM <$> Ser.get
+    put (IKeyDimensionM x) = Ser.put x
+
+instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (IKeyDimension O t) where
+    getCopy = Ser.contain $ IKeyDimensionO <$> Ser.safeGet
+    putCopy (IKeyDimensionO x)  = Ser.contain $ Ser.safePut x
+
+instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (IKeyDimension M t) where
+    getCopy = Ser.contain $ IKeyDimensionM <$> Ser.safeGet
+    putCopy (IKeyDimensionM x)  = Ser.contain $ Ser.safePut x
+
+instance Show t => Show (IKeyDimension r t) where
+    show (IKeyDimensionM ts) = show ts
+    show (IKeyDimensionO t)  = show t
+
+data IndexDimension r t where
+    IndexDimensionO :: Ord t
+                    => !(Data.Map.Map t Int)
+                    -> IndexDimension O t
+    
+    IndexDimensionM :: Ord t
+                    => !(Data.Map.Map t Data.IntSet.IntSet)
+                    -> IndexDimension M t
+
+instance (Ord t, Ser.Serialize t) => Ser.Serialize (IndexDimension O t) where
+    get = IndexDimensionO <$> Ser.get
+    put (IndexDimensionO x) = Ser.put x
+
+instance (Ord t, Ser.Serialize t) => Ser.Serialize (IndexDimension M t) where
+    get = IndexDimensionM <$> Ser.get
+    put (IndexDimensionM x) = Ser.put x
+
+instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (IndexDimension O t) where
+    getCopy = Ser.contain $ IndexDimensionO <$> Ser.safeGet
+    putCopy (IndexDimensionO x)  = Ser.contain $ Ser.safePut x
+
+instance (Ord t, Ser.SafeCopy t) => Ser.SafeCopy (IndexDimension M t) where
+    getCopy = Ser.contain $ IndexDimensionM <$> Ser.safeGet
+    putCopy (IndexDimensionM x)  = Ser.contain $ Ser.safePut x
+
+instance Show t => Show (IndexDimension r t) where
+    show (IndexDimensionM m) = show $ map (\(k, vs) -> (k, Data.IntSet.toList vs)) $ Data.Map.toList m
+    show (IndexDimensionO m) = show $ Data.Map.toList m
+
+class GetDimension n a where
+    getDimension :: n -> a -> RawDimensionType n a
+
+instance GetDimension Z (Index O t) where
+    getDimension _ (I1 ixd) = ixd
+
+instance GetDimension Z (Index M t) where
+    getDimension _ (I1 ixd) = ixd
+
+instance GetDimension Z (Index (r :. rt) (t :. tt)) where
+    getDimension _ (IN ixd _) = ixd
+    getDimension _ (I1 _) = error $ moduleName <> ".Index.getDimension: The impossible happened."
+
+instance GetDimension n (Index rt tt) => GetDimension (S n) (Index (r :. rt) (t :. tt)) where
+    getDimension (S n) (IN _ ixt) = getDimension n ixt
+    getDimension _ (I1 _) = error $ moduleName <> ".Index.getDimension: The impossible happened."
+
+instance GetDimension Z (IKey O t) where
+    getDimension _ (K1 kd) = kd
+
+instance GetDimension Z (IKey M t) where
+    getDimension _ (K1 kd) = kd
+
+instance GetDimension Z (IKey (r :. rt) (t :. tt)) where
+    getDimension _ (KN kd _) = kd
+    getDimension _ (K1 _) = error $ moduleName <> ".IKey.getDimension: The impossible happened."
+
+instance GetDimension n (IKey rt tt) => GetDimension (S n) (IKey (r :. rt) (t :. tt)) where
+    getDimension (S n) (KN _ kt) = getDimension n kt
+    getDimension _ (K1 _) = error $ moduleName <> ".IKey.getDimension: The impossible happened."
+
+data TT
+data FF
+
+type family   EmptyProxyIsSpecial t :: *
+type instance EmptyProxyIsSpecial Int = TT
+
+class Empty a where
+    empty :: a
+
+class EmptyProxy flag a where
+    emptyProxy :: flag -> a
+
+instance Ord t => Empty (Index O t) where
+    empty = I1 (IndexDimensionO Data.Map.empty)
+
+instance Ord t => Empty (Index M t) where
+    empty = I1 (IndexDimensionM Data.Map.empty)
+
+instance (Ord t, Empty (Index rt tt)) => Empty (Index (O :. rt) (t :. tt)) where
+    empty = IN (IndexDimensionO Data.Map.empty) empty
+
+instance (Ord t, Empty (Index rt tt)) => Empty (Index (M :. rt) (t :. tt)) where
+    empty = IN (IndexDimensionM Data.Map.empty) empty
+
+instance Empty (Index irs ts) => Empty (Store tag krs irs ts e) where
+    empty = Store
+        { storeV = Data.IntMap.empty
+        , storeI = empty
+        , storeNID = 0
+        }
+    {-# INLINE empty #-}
+
+-- | Data type for creating tuples, it is used to:
+--
+-- * Create type-level tuples of relation tags for relation specification of
+-- the key and the index of the store.
+--
+-- > M :. O :. O :. M
+--
+-- * Create type-level tuples of types for type specification of the key
+-- and index of the store.
+--
+-- > Int :. Double :. String :. String
+--
+-- * Create value-level tuples to return raw key (with resolved
+-- auto-increment dimensions).
+--
+-- > [1, 2, 3] :. 3.5 :. "Foo" :. ["Bar1", "Bar2"]
+data h :. t = h :. t
+infixr 3 :.
+
+
+-- NFDATA INSTANCES
+
+instance (NFData e, NFData (IKey krs ts), NFData (Index irs ts)) => NFData (Store tag krs irs ts e) where
+    rnf (Store ke ix nid) = rnf ke `seq` rnf ix `seq` rnf nid
+
+instance NFData t => NFData (IndexDimension r t) where
+    rnf (IndexDimensionO m) = rnf m
+    rnf (IndexDimensionM m) = rnf m
+
+instance NFData t => NFData (Index O t) where
+    rnf (I1 kd) = rnf kd
+     
+instance NFData t => NFData (Index M t) where
+    rnf (I1 kd) = rnf kd
+
+instance (NFData t, NFData (Index rt tt)) => NFData (Index (r :. rt) (t :. tt)) where
+    rnf (IN kd kt) = rnf kd `seq` rnf kt
+    rnf (I1 _) = error "Impossible! (Index NFData)"
+
+instance NFData t => NFData (IKeyDimension r t) where
+    rnf (IKeyDimensionO x) = rnf x
+    rnf (IKeyDimensionM x) = rnf x
+
+instance NFData t => NFData (IKey O t) where
+    rnf (K1 kd) = rnf kd
+     
+instance NFData t => NFData (IKey M t) where
+    rnf (K1 kd) = rnf kd
+
+instance (NFData t, NFData (IKey rt tt)) => NFData (IKey (r :. rt) (t :. tt)) where
+    rnf (KN kd kt) = rnf kd `seq` rnf kt
+    rnf (K1 _) = error "Impossible! (IKey NFData)"
+
+instance (NFData a, NFData b) => NFData (a :. b) where
+    rnf (a :. b) = rnf a `seq` rnf b
+
+
diff --git a/src/Data/Store/Lens.hs b/src/Data/Store/Lens.hs
--- a/src/Data/Store/Lens.hs
+++ b/src/Data/Store/Lens.hs
@@ -1,33 +1,33 @@
-{-# LANGUAGE Rank2Types #-}
-{-# LANGUAGE FlexibleInstances #-}
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE UndecidableInstances #-}
-
-module Data.Store.Lens
-( With(..)
-) where
-
---------------------------------------------------------------------------------
-import qualified Control.Lens
---------------------------------------------------------------------------------
-import           Data.Monoid 
-import           Data.Functor.Identity
---------------------------------------------------------------------------------
-import qualified Data.Store.Internal.Type     as I
-import qualified Data.Store.Internal.Function as I
-import qualified Data.Store.Selection         as I (IsSelection(resolve))
-import qualified Data.Store                   as I ()
---------------------------------------------------------------------------------
-
-class With sel where
-    with :: I.Empty (I.Index irs ts) 
-         => sel tag krs irs ts -> Control.Lens.Lens' (I.Store tag krs irs ts v)
-                                                     (I.Store tag krs irs ts v)
-
-instance I.IsSelection sel => With sel where
-    with sel tr old =
-      fmap (mappend (runIdentity $! I.genericUpdateWithKey I.indexInsertID'' (\_ _ -> Nothing) ids old))
-           (tr (I.genericSubset ids old))
-      where
-        ids = I.resolve sel old
-
+{-# LANGUAGE Rank2Types #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE UndecidableInstances #-}
+
+module Data.Store.Lens
+( With(..)
+) where
+
+--------------------------------------------------------------------------------
+import qualified Control.Lens
+--------------------------------------------------------------------------------
+import           Data.Monoid 
+import           Data.Functor.Identity
+--------------------------------------------------------------------------------
+import qualified Data.Store.Internal.Type     as I
+import qualified Data.Store.Internal.Function as I
+import qualified Data.Store.Selection         as I (IsSelection(resolve))
+import qualified Data.Store                   as I ()
+--------------------------------------------------------------------------------
+
+class With sel where
+    with :: I.Empty (I.Index irs ts) 
+         => sel tag krs irs ts -> Control.Lens.Lens' (I.Store tag krs irs ts v)
+                                                     (I.Store tag krs irs ts v)
+
+instance I.IsSelection sel => With sel where
+    with sel tr old =
+      fmap (mappend (runIdentity $! I.genericUpdateWithKey I.indexInsertID'' (\_ _ -> Nothing) ids old))
+           (tr (I.genericSubset ids old))
+      where
+        ids = I.resolve sel old
+
diff --git a/src/Data/Store/Selection.hs b/src/Data/Store/Selection.hs
--- a/src/Data/Store/Selection.hs
+++ b/src/Data/Store/Selection.hs
@@ -1,235 +1,235 @@
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE RankNTypes #-}
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE CPP #-}
-
-module Data.Store.Selection
-( (.<)
-, (.<=)
-, (.>)
-, (.>=)
-, (./=)
-, (.==)
-, (.&&)
-, (.||)
-, not
-, all
-, all1D
-, any
-, any1D
-, IsSelection(..)
-, Selection
-) where
-
---------------------------------------------------------------------------------
-import           Prelude hiding (not, all, any)
---------------------------------------------------------------------------------
-import           Data.Monoid ((<>))
-import qualified Data.IntSet
-import qualified Data.List
-#if MIN_VERSION_containers(0,5,0)
-import qualified Data.IntMap.Strict as Data.IntMap
-import qualified Data.Map.Strict    as Data.Map
-#else
-import qualified Data.IntMap
-import qualified Data.Map
-#endif
---------------------------------------------------------------------------------
-import qualified Data.Store.Internal.Type as I
---------------------------------------------------------------------------------
-
-moduleName :: String
-moduleName = "Data.Store.Selection"
-
--- INTERFACE
-
-infix  4  .==, ./=, .<, .<=, .>=, .>
-infixr 3  .&&
-infixr 2  .||
-
--- | The expression (@not' sel@) is a selection that includes all values
--- except those that match the selection @sel@. 
-not :: IsSelection sel => sel tag krs irs ts -> Selection tag krs irs ts
-not = SelectionNot
-{-# INLINE not #-}
-
--- | Selection that matches the intersection of all the selections in the
--- list or everything if the list is empty.
-all :: [Selection tag krs irs ts] -> Selection tag krs irs ts
-all []  = error $ moduleName <> ".all: empty list."
-all [s] = s
-all (s:rest) = Data.List.foldl' (.&&) s rest -- this way we do not have to intersect with "everything"
-{-# INLINE all #-}
-
--- | The expression (@'Data.Store.Selection.all1D' d ss@) is equivalent to (@'Data.Store.Selection.all'' $ map ($ d) ss@).
-all1D :: (tag, n) -> [(tag, n) -> Selection tag krs irs ts] -> Selection tag krs irs ts
-all1D _ [] = error $ moduleName <> ".all1D: empty list."
-all1D d [h] = h d
-all1D d (h:rest) = Data.List.foldl' (\acc f -> acc .&& f d) (h d) rest -- this way we do not have to intersect with "everything"
-{-# INLINE all1D #-}
-
--- | Selection that matches the union of all the selections in the
--- list or nothing if the list is empty.
-any :: [Selection tag krs irs ts] -> Selection tag krs irs ts
-any [] = error $ moduleName <> ".any: empty list."
-any (x:xs) = Data.List.foldl' (.||) x xs
-{-# INLINE any #-}
-
--- | The expression (@'Data.Store.Selection.any1D' d ss@) is equivalent to (@'Data.Store.Selection.any'' $ map ($ d) ss@).
-any1D :: (tag, n) -> [(tag, n) -> Selection tag krs irs ts] -> Selection tag krs irs ts
-any1D _ [] = error $ moduleName <> ".any1D: empty list."
-any1D d (x:xs) = Data.List.foldl' (\acc f -> acc .|| f d) (x d) xs
-{-# INLINE any1D #-}
-
--- | The expression (@sDim .< c@) is a selection that includes value
--- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
--- such that @k < c@.
---
--- Complexity of @'Data.Store.Selection.resolve'@: /O(log n + k)/
-(.<) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
-(.<) (_, n) = SelectionType . SelectionDimension n (Condition True False False)
-{-# INLINE (.<) #-}
-
--- | The expression (@sDim .<= c@) is a selection that includes value
--- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
--- such that @k <= c@.
---
--- Complexity of @'Data.Store.Selection.resolve'@: /O(log n + k)/
-(.<=) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
-(.<=) (_, n) = SelectionType . SelectionDimension n (Condition True True False)
-{-# INLINE (.<=) #-}
-
--- | The expression (@sDim .> c@) is a selection that includes value
--- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
--- such that @k > c@.
---
--- Complexity of @'Data.Store.Selection.resolve'@: /O(log n + k)/
-(.>) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
-(.>) (_, n) = SelectionType . SelectionDimension n (Condition False False True)
-{-# INLINE (.>) #-}
-
--- | The expression (@sDim .>= c@) is a selection that includes value
--- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
--- such that @k >= c@.
---
--- Complexity of @'Data.Store.Selection.resolve'@: /O(log n + k)/
-(.>=) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
-(.>=) (_, n) = SelectionType . SelectionDimension n (Condition False True True)
-{-# INLINE (.>=) #-}
-
--- | The expression (@sDim ./= c@) is a selection that includes value
--- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
--- such that @k /= c@.
---
--- Complexity of @'Data.Store.Selection.resolve'@: /O(n)/
-(./=) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
-(./=) (_, n) = SelectionType . SelectionDimension n (Condition True False True)
-{-# INLINE (./=) #-}
-
--- | The expression (@sDim .== c@) is a selection that includes value
--- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
--- such that @k == c@.
---
--- Complexity of @'Data.Store.Selection.resolve'@: /O(log n)/
-(.==) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
-(.==) (_, n) = SelectionType . SelectionDimension n (Condition False True False)
-{-# INLINE (.==) #-}
-
--- | The expression (@s1 .&& s2@) is a selection that includes the
--- intersection of the selections @s1@ and @s2@.
---
--- Complexity of @'Data.Store.Selection.resolve'@: /O(c(s1) + c(s2) + s(s1) + s(s2)/
-(.&&) :: (IsSelection s1, IsSelection s2)
-      => s1 tag krs irs ts -> s2 tag krs irs ts -> Selection tag krs irs ts
-(.&&) = SelectionA
-{-# INLINE (.&&) #-}
-
--- | The expression (@s1 .|| s2@) is a selection that includes the
--- union of the selections @s1@ and @s2@.
---
--- Complexity of @'Data.Store.Selection.resolve'@: /O(c(s1) + c(s2) + s(s1) + s(s2)/
-(.||) :: (IsSelection s1, IsSelection s2)
-      => s1 tag krs irs ts -> s2 tag krs irs ts -> Selection tag krs irs ts
-(.||) = SelectionO
-{-# INLINE (.||) #-}
-
--- IMPLEMENTATION
-
-instance IsSelection Selection where
-    resolve (SelectionType sel) s = resolve sel s
-    resolve (SelectionA s1 s2) s = Data.IntSet.intersection (resolve s1 s) (resolve s2 s)
-    resolve (SelectionO s1 s2) s = Data.IntSet.union (resolve s1 s) (resolve s2 s)
-    resolve (SelectionNot sel) s@(I.Store vs _ _) =
-        Data.IntSet.difference (Data.IntMap.keysSet vs) (resolve sel s)
-    {-# INLINE resolve #-}
-
-instance IsSelection (SelectionDimension n) where
-    resolve = resolveSD
-    {-# INLINE resolve #-}
-
-resolveSD :: forall tag n krs irs ts v . SelectionDimension n tag krs irs ts 
-          -> I.Store tag krs irs ts v
-          -> Data.IntSet.IntSet
-resolveSD (SelectionDimension _ (Condition False False False) _) _ = {-# SCC "resolveSD" #-} Data.IntSet.empty
-resolveSD (SelectionDimension _ (Condition True True True) _) (I.Store vs _ _) = {-# SCC "resolveSD" #-}  Data.IntSet.fromList $ Data.IntMap.keys vs
-resolveSD (SelectionDimension n (Condition lt eq gt) v) (I.Store _ ix _) = {-# SCC "resolveSD" #-} 
-    go $! I.getDimension n ix
-    where
-      go (I.IndexDimensionO m) = m `seq` case Data.Map.splitLookup v m of
-          (lk, ek, gk) -> (if lt then trO lk else Data.IntSet.empty) <>
-                          (if eq then trMaybeO ek else Data.IntSet.empty) <>
-                          (if gt then trO gk else Data.IntSet.empty)                         
-      go (I.IndexDimensionM m) = m `seq` case Data.Map.splitLookup v m of
-          (lk, ek, gk) -> (if lt then trM lk else Data.IntSet.empty) <>
-                          (if eq then trMaybeM ek else Data.IntSet.empty) <>
-                          (if gt then trM gk else Data.IntSet.empty)
-      {-# INLINEABLE go #-}
-
-      trO :: Data.Map.Map k Int -> Data.IntSet.IntSet
-      trO xs = {-# SCC "resolveSD.trO" #-} Data.Map.foldl' ins Data.IntSet.empty xs
-        where ins acc i = Data.IntSet.insert i acc
-      {-# INLINE trO #-}
-
-      trMaybeO :: Maybe Int -> Data.IntSet.IntSet
-      trMaybeO (Just x) = Data.IntSet.singleton x
-      trMaybeO _ = Data.IntSet.empty
-      {-# INLINE trMaybeO #-}
-
-      trM :: Data.Map.Map k Data.IntSet.IntSet -> Data.IntSet.IntSet
-      trM = Data.Map.foldl' Data.IntSet.union Data.IntSet.empty
-      {-# INLINE trM #-}
-
-      trMaybeM :: Maybe Data.IntSet.IntSet -> Data.IntSet.IntSet
-      trMaybeM (Just x) = x
-      trMaybeM _ = Data.IntSet.empty
-      {-# INLINE trMaybeM #-}
-{-# INLINE resolveSD #-}
-
--- | TYPE
-
-data SelectionDimension n tag krs irs ts where
-    SelectionDimension :: I.GetDimension n (I.Index irs ts)
-                       => n
-                       -> Condition
-                       -> I.DimensionType n irs ts
-                       -> SelectionDimension n tag krs irs ts
-
-data Selection tag krs irs ts where
-    SelectionType :: IsSelection sel => sel tag krs irs ts -> Selection tag krs irs ts    
-
-    SelectionA :: (IsSelection s1, IsSelection s2)
-               => s1 tag krs irs ts -> s2 tag krs irs ts -> Selection tag krs irs ts
-
-    SelectionO :: (IsSelection s1, IsSelection s2)
-               => s1 tag krs irs ts -> s2 tag krs irs ts -> Selection tag krs irs ts
-
-    SelectionNot :: IsSelection sel => sel tag krs irs ts -> Selection tag krs irs ts
-
-data Condition = Condition !Bool !Bool !Bool
-
-class IsSelection sel where
-    resolve :: sel tag krs irs ts -> I.Store tag krs irs ts v -> Data.IntSet.IntSet
-   
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE CPP #-}
+
+module Data.Store.Selection
+( (.<)
+, (.<=)
+, (.>)
+, (.>=)
+, (./=)
+, (.==)
+, (.&&)
+, (.||)
+, not
+, all
+, all1D
+, any
+, any1D
+, IsSelection(..)
+, Selection
+) where
+
+--------------------------------------------------------------------------------
+import           Prelude hiding (not, all, any)
+--------------------------------------------------------------------------------
+import           Data.Monoid ((<>))
+import qualified Data.IntSet
+import qualified Data.List
+#if MIN_VERSION_containers(0,5,0)
+import qualified Data.IntMap.Strict as Data.IntMap
+import qualified Data.Map.Strict    as Data.Map
+#else
+import qualified Data.IntMap
+import qualified Data.Map
+#endif
+--------------------------------------------------------------------------------
+import qualified Data.Store.Internal.Type as I
+--------------------------------------------------------------------------------
+
+moduleName :: String
+moduleName = "Data.Store.Selection"
+
+-- INTERFACE
+
+infix  4  .==, ./=, .<, .<=, .>=, .>
+infixr 3  .&&
+infixr 2  .||
+
+-- | The expression (@not' sel@) is a selection that includes all values
+-- except those that match the selection @sel@. 
+not :: IsSelection sel => sel tag krs irs ts -> Selection tag krs irs ts
+not = SelectionNot
+{-# INLINE not #-}
+
+-- | Selection that matches the intersection of all the selections in the
+-- list or everything if the list is empty.
+all :: [Selection tag krs irs ts] -> Selection tag krs irs ts
+all []  = error $ moduleName <> ".all: empty list."
+all [s] = s
+all (s:rest) = Data.List.foldl' (.&&) s rest -- this way we do not have to intersect with "everything"
+{-# INLINE all #-}
+
+-- | The expression (@'Data.Store.Selection.all1D' d ss@) is equivalent to (@'Data.Store.Selection.all'' $ map ($ d) ss@).
+all1D :: (tag, n) -> [(tag, n) -> Selection tag krs irs ts] -> Selection tag krs irs ts
+all1D _ [] = error $ moduleName <> ".all1D: empty list."
+all1D d [h] = h d
+all1D d (h:rest) = Data.List.foldl' (\acc f -> acc .&& f d) (h d) rest -- this way we do not have to intersect with "everything"
+{-# INLINE all1D #-}
+
+-- | Selection that matches the union of all the selections in the
+-- list or nothing if the list is empty.
+any :: [Selection tag krs irs ts] -> Selection tag krs irs ts
+any [] = error $ moduleName <> ".any: empty list."
+any (x:xs) = Data.List.foldl' (.||) x xs
+{-# INLINE any #-}
+
+-- | The expression (@'Data.Store.Selection.any1D' d ss@) is equivalent to (@'Data.Store.Selection.any'' $ map ($ d) ss@).
+any1D :: (tag, n) -> [(tag, n) -> Selection tag krs irs ts] -> Selection tag krs irs ts
+any1D _ [] = error $ moduleName <> ".any1D: empty list."
+any1D d (x:xs) = Data.List.foldl' (\acc f -> acc .|| f d) (x d) xs
+{-# INLINE any1D #-}
+
+-- | The expression (@sDim .< c@) is a selection that includes value
+-- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
+-- such that @k < c@.
+--
+-- Complexity of @'Data.Store.Selection.resolve'@: /O(log n + k)/
+(.<) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
+(.<) (_, n) = SelectionType . SelectionDimension n (Condition True False False)
+{-# INLINE (.<) #-}
+
+-- | The expression (@sDim .<= c@) is a selection that includes value
+-- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
+-- such that @k <= c@.
+--
+-- Complexity of @'Data.Store.Selection.resolve'@: /O(log n + k)/
+(.<=) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
+(.<=) (_, n) = SelectionType . SelectionDimension n (Condition True True False)
+{-# INLINE (.<=) #-}
+
+-- | The expression (@sDim .> c@) is a selection that includes value
+-- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
+-- such that @k > c@.
+--
+-- Complexity of @'Data.Store.Selection.resolve'@: /O(log n + k)/
+(.>) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
+(.>) (_, n) = SelectionType . SelectionDimension n (Condition False False True)
+{-# INLINE (.>) #-}
+
+-- | The expression (@sDim .>= c@) is a selection that includes value
+-- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
+-- such that @k >= c@.
+--
+-- Complexity of @'Data.Store.Selection.resolve'@: /O(log n + k)/
+(.>=) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
+(.>=) (_, n) = SelectionType . SelectionDimension n (Condition False True True)
+{-# INLINE (.>=) #-}
+
+-- | The expression (@sDim ./= c@) is a selection that includes value
+-- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
+-- such that @k /= c@.
+--
+-- Complexity of @'Data.Store.Selection.resolve'@: /O(n)/
+(./=) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
+(./=) (_, n) = SelectionType . SelectionDimension n (Condition True False True)
+{-# INLINE (./=) #-}
+
+-- | The expression (@sDim .== c@) is a selection that includes value
+-- @x@ if and only if it is indexed in the @sDim@ dimension with a key @k@
+-- such that @k == c@.
+--
+-- Complexity of @'Data.Store.Selection.resolve'@: /O(log n)/
+(.==) :: I.GetDimension n (I.Index irs ts) => (tag, n) -> I.DimensionType n irs ts -> Selection tag krs irs ts
+(.==) (_, n) = SelectionType . SelectionDimension n (Condition False True False)
+{-# INLINE (.==) #-}
+
+-- | The expression (@s1 .&& s2@) is a selection that includes the
+-- intersection of the selections @s1@ and @s2@.
+--
+-- Complexity of @'Data.Store.Selection.resolve'@: /O(c(s1) + c(s2) + s(s1) + s(s2)/
+(.&&) :: (IsSelection s1, IsSelection s2)
+      => s1 tag krs irs ts -> s2 tag krs irs ts -> Selection tag krs irs ts
+(.&&) = SelectionA
+{-# INLINE (.&&) #-}
+
+-- | The expression (@s1 .|| s2@) is a selection that includes the
+-- union of the selections @s1@ and @s2@.
+--
+-- Complexity of @'Data.Store.Selection.resolve'@: /O(c(s1) + c(s2) + s(s1) + s(s2)/
+(.||) :: (IsSelection s1, IsSelection s2)
+      => s1 tag krs irs ts -> s2 tag krs irs ts -> Selection tag krs irs ts
+(.||) = SelectionO
+{-# INLINE (.||) #-}
+
+-- IMPLEMENTATION
+
+instance IsSelection Selection where
+    resolve (SelectionType sel) s = resolve sel s
+    resolve (SelectionA s1 s2) s = Data.IntSet.intersection (resolve s1 s) (resolve s2 s)
+    resolve (SelectionO s1 s2) s = Data.IntSet.union (resolve s1 s) (resolve s2 s)
+    resolve (SelectionNot sel) s@(I.Store vs _ _) =
+        Data.IntSet.difference (Data.IntMap.keysSet vs) (resolve sel s)
+    {-# INLINE resolve #-}
+
+instance IsSelection (SelectionDimension n) where
+    resolve = resolveSD
+    {-# INLINE resolve #-}
+
+resolveSD :: forall tag n krs irs ts v . SelectionDimension n tag krs irs ts 
+          -> I.Store tag krs irs ts v
+          -> Data.IntSet.IntSet
+resolveSD (SelectionDimension _ (Condition False False False) _) _ = {-# SCC "resolveSD" #-} Data.IntSet.empty
+resolveSD (SelectionDimension _ (Condition True True True) _) (I.Store vs _ _) = {-# SCC "resolveSD" #-}  Data.IntSet.fromList $ Data.IntMap.keys vs
+resolveSD (SelectionDimension n (Condition lt eq gt) v) (I.Store _ ix _) = {-# SCC "resolveSD" #-} 
+    go $! I.getDimension n ix
+    where
+      go (I.IndexDimensionO m) = m `seq` case Data.Map.splitLookup v m of
+          (lk, ek, gk) -> (if lt then trO lk else Data.IntSet.empty) <>
+                          (if eq then trMaybeO ek else Data.IntSet.empty) <>
+                          (if gt then trO gk else Data.IntSet.empty)                         
+      go (I.IndexDimensionM m) = m `seq` case Data.Map.splitLookup v m of
+          (lk, ek, gk) -> (if lt then trM lk else Data.IntSet.empty) <>
+                          (if eq then trMaybeM ek else Data.IntSet.empty) <>
+                          (if gt then trM gk else Data.IntSet.empty)
+      {-# INLINEABLE go #-}
+
+      trO :: Data.Map.Map k Int -> Data.IntSet.IntSet
+      trO xs = {-# SCC "resolveSD.trO" #-} Data.Map.foldl' ins Data.IntSet.empty xs
+        where ins acc i = Data.IntSet.insert i acc
+      {-# INLINE trO #-}
+
+      trMaybeO :: Maybe Int -> Data.IntSet.IntSet
+      trMaybeO (Just x) = Data.IntSet.singleton x
+      trMaybeO _ = Data.IntSet.empty
+      {-# INLINE trMaybeO #-}
+
+      trM :: Data.Map.Map k Data.IntSet.IntSet -> Data.IntSet.IntSet
+      trM = Data.Map.foldl' Data.IntSet.union Data.IntSet.empty
+      {-# INLINE trM #-}
+
+      trMaybeM :: Maybe Data.IntSet.IntSet -> Data.IntSet.IntSet
+      trMaybeM (Just x) = x
+      trMaybeM _ = Data.IntSet.empty
+      {-# INLINE trMaybeM #-}
+{-# INLINE resolveSD #-}
+
+-- | TYPE
+
+data SelectionDimension n tag krs irs ts where
+    SelectionDimension :: I.GetDimension n (I.Index irs ts)
+                       => n
+                       -> Condition
+                       -> I.DimensionType n irs ts
+                       -> SelectionDimension n tag krs irs ts
+
+data Selection tag krs irs ts where
+    SelectionType :: IsSelection sel => sel tag krs irs ts -> Selection tag krs irs ts    
+
+    SelectionA :: (IsSelection s1, IsSelection s2)
+               => s1 tag krs irs ts -> s2 tag krs irs ts -> Selection tag krs irs ts
+
+    SelectionO :: (IsSelection s1, IsSelection s2)
+               => s1 tag krs irs ts -> s2 tag krs irs ts -> Selection tag krs irs ts
+
+    SelectionNot :: IsSelection sel => sel tag krs irs ts -> Selection tag krs irs ts
+
+data Condition = Condition !Bool !Bool !Bool
+
+class IsSelection sel where
+    resolve :: sel tag krs irs ts -> I.Store tag krs irs ts v -> Data.IntSet.IntSet
+   
diff --git a/src/Data/Store/Storable.hs b/src/Data/Store/Storable.hs
--- a/src/Data/Store/Storable.hs
+++ b/src/Data/Store/Storable.hs
@@ -1,110 +1,110 @@
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE FlexibleContexts #-}
-
-module Data.Store.Storable
-( Storable(..)
-
-, insert
-, insert'
-, updateWithKey
-, updateWithKey'
-, update
-, update'
-, fromList
-, fromList'
-) where
-
---------------------------------------------------------------------------------
-import qualified Data.Store.Internal.Type as I 
-import qualified Data.Store as S 
-import qualified Data.Store.Selection as S (IsSelection()) 
---------------------------------------------------------------------------------
-
--- | This type-class facilitates the common use case where the key under
--- which given values is to be indexed can be derived from the value.
---
--- Example:
---
--- The @Storable@ type-class instance for our @Content@ data type would look
--- like this:
---
--- > instance Storable Content where
--- >     type StoreKRS Content = O         :. O      :. O      :. M      :. O 
--- >     type StoreIRS Content = O         :. O      :. M      :. M      :. M
--- >     type StoreTS  Content = ContentID :. String :. String :. String :. Double
--- >
--- >     key (Content cn cb cts cr) = 
--- >         S.dimA .: S.dimO cn .: S.dimO cb .: S.dimM cts .:. S.dimO cr
-class Storable v where
-    type StoreKRS t :: *
-    type StoreIRS t :: *
-    type StoreTS  t :: *
-    
-    key :: v -> S.Key (StoreKRS v) (StoreTS v)
-
--- | See @'Data.Store.insert'@.
-insert :: Storable v
-       => v
-       -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
-       -> Maybe (S.RawKey (StoreKRS v) (StoreTS v), S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
-insert v = S.insert (key v) v
-{-# INLINE insert #-}
-
--- | See @'Data.Store.insert''@.
-insert' :: Storable v
-        => v
-        -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
-        -> (S.RawKey (StoreKRS v) (StoreTS v), S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
-insert' v = S.insert' (key v) v
-{-# INLINE insert' #-}
-
--- | See @'Data.Store.update'@.
-update :: (Storable v, S.IsSelection sel)
-       => (v -> Maybe v)
-       -> sel tag (StoreKRS v) (StoreIRS v) (StoreTS v)
-       -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
-       -> Maybe (S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
-update tr = S.update (maybe Nothing (\v -> Just (v, Just $! key v)) . tr)
-{-# INLINE update #-}
-
--- | See @'Data.Store.update''@.
-update' :: (Storable v, S.IsSelection sel)
-        => (v -> Maybe v)
-        -> sel tag (StoreKRS v) (StoreIRS v) (StoreTS v)
-        -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
-        -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
-update' tr = S.update' (maybe Nothing (\v -> Just (v, Just $! key v)) . tr)
-{-# INLINE update' #-}
-
--- | See @'Data.Store.updateWithKey'@.
-updateWithKey :: (Storable v, S.IsSelection sel)
-              => (S.RawKey (StoreKRS v) (StoreTS v) -> v -> Maybe v)
-              -> sel tag (StoreKRS v) (StoreIRS v) (StoreTS v)
-              -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
-              -> Maybe (S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
-updateWithKey tr = S.updateWithKey (\rk vv -> maybe Nothing (\v -> Just (v, Just $! key v)) $ tr rk vv)
-{-# INLINE updateWithKey #-}
-
--- | See @'Data.Store.updateWithKey''@.
-updateWithKey' :: (Storable v, S.IsSelection sel)
-               => (S.RawKey (StoreKRS v) (StoreTS v) -> v -> Maybe v)
-               -> sel tag (StoreKRS v) (StoreIRS v) (StoreTS v)
-               -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
-               -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
-updateWithKey' tr = S.updateWithKey' (\rk vv -> maybe Nothing (\v -> Just (v, Just $! key v)) $ tr rk vv)
-{-# INLINE updateWithKey' #-}
-
--- | See @'Data.Store.fromList'@.
-fromList :: (I.Empty (I.Index (StoreIRS v) (StoreTS v)), Storable v)
-         => [v]
-         -> Maybe (S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
-fromList = S.fromList . map (\v -> (key v, v))
-{-# INLINE fromList #-}
-
--- | See @'Data.Store.fromList''@.
-fromList' :: (I.Empty (I.Index (StoreIRS v) (StoreTS v)), Storable v)
-          => [v]
-          -> I.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
-fromList' = S.fromList' . map (\v -> (key v, v))
-{-# INLINE fromList' #-}
-
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE FlexibleContexts #-}
+
+module Data.Store.Storable
+( Storable(..)
+
+, insert
+, insert'
+, updateWithKey
+, updateWithKey'
+, update
+, update'
+, fromList
+, fromList'
+) where
+
+--------------------------------------------------------------------------------
+import qualified Data.Store.Internal.Type as I 
+import qualified Data.Store as S 
+import qualified Data.Store.Selection as S (IsSelection()) 
+--------------------------------------------------------------------------------
+
+-- | This type-class facilitates the common use case where the key under
+-- which given values is to be indexed can be derived from the value.
+--
+-- Example:
+--
+-- The @Storable@ type-class instance for our @Content@ data type would look
+-- like this:
+--
+-- > instance Storable Content where
+-- >     type StoreKRS Content = O         :. O      :. O      :. M      :. O 
+-- >     type StoreIRS Content = O         :. O      :. M      :. M      :. M
+-- >     type StoreTS  Content = ContentID :. String :. String :. String :. Double
+-- >
+-- >     key (Content cn cb cts cr) = 
+-- >         S.dimA .: S.dimO cn .: S.dimO cb .: S.dimM cts .:. S.dimO cr
+class Storable v where
+    type StoreKRS t :: *
+    type StoreIRS t :: *
+    type StoreTS  t :: *
+    
+    key :: v -> S.Key (StoreKRS v) (StoreTS v)
+
+-- | See @'Data.Store.insert'@.
+insert :: Storable v
+       => v
+       -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
+       -> Maybe (S.RawKey (StoreKRS v) (StoreTS v), S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
+insert v = S.insert (key v) v
+{-# INLINE insert #-}
+
+-- | See @'Data.Store.insert''@.
+insert' :: Storable v
+        => v
+        -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
+        -> (S.RawKey (StoreKRS v) (StoreTS v), S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
+insert' v = S.insert' (key v) v
+{-# INLINE insert' #-}
+
+-- | See @'Data.Store.update'@.
+update :: (Storable v, S.IsSelection sel)
+       => (v -> Maybe v)
+       -> sel tag (StoreKRS v) (StoreIRS v) (StoreTS v)
+       -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
+       -> Maybe (S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
+update tr = S.update (maybe Nothing (\v -> Just (v, Just $! key v)) . tr)
+{-# INLINE update #-}
+
+-- | See @'Data.Store.update''@.
+update' :: (Storable v, S.IsSelection sel)
+        => (v -> Maybe v)
+        -> sel tag (StoreKRS v) (StoreIRS v) (StoreTS v)
+        -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
+        -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
+update' tr = S.update' (maybe Nothing (\v -> Just (v, Just $! key v)) . tr)
+{-# INLINE update' #-}
+
+-- | See @'Data.Store.updateWithKey'@.
+updateWithKey :: (Storable v, S.IsSelection sel)
+              => (S.RawKey (StoreKRS v) (StoreTS v) -> v -> Maybe v)
+              -> sel tag (StoreKRS v) (StoreIRS v) (StoreTS v)
+              -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
+              -> Maybe (S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
+updateWithKey tr = S.updateWithKey (\rk vv -> maybe Nothing (\v -> Just (v, Just $! key v)) $ tr rk vv)
+{-# INLINE updateWithKey #-}
+
+-- | See @'Data.Store.updateWithKey''@.
+updateWithKey' :: (Storable v, S.IsSelection sel)
+               => (S.RawKey (StoreKRS v) (StoreTS v) -> v -> Maybe v)
+               -> sel tag (StoreKRS v) (StoreIRS v) (StoreTS v)
+               -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
+               -> S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
+updateWithKey' tr = S.updateWithKey' (\rk vv -> maybe Nothing (\v -> Just (v, Just $! key v)) $ tr rk vv)
+{-# INLINE updateWithKey' #-}
+
+-- | See @'Data.Store.fromList'@.
+fromList :: (I.Empty (I.Index (StoreIRS v) (StoreTS v)), Storable v)
+         => [v]
+         -> Maybe (S.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v)
+fromList = S.fromList . map (\v -> (key v, v))
+{-# INLINE fromList #-}
+
+-- | See @'Data.Store.fromList''@.
+fromList' :: (I.Empty (I.Index (StoreIRS v) (StoreTS v)), Storable v)
+          => [v]
+          -> I.Store tag (StoreKRS v) (StoreIRS v) (StoreTS v) v
+fromList' = S.fromList' . map (\v -> (key v, v))
+{-# INLINE fromList' #-}
+
diff --git a/tests/Main.hs b/tests/Main.hs
--- a/tests/Main.hs
+++ b/tests/Main.hs
@@ -1,14 +1,14 @@
-module Main
-( main
-) where
-
-------------------------------------------------------------------------------
-import Test.Framework (defaultMain, testGroup)
-------------------------------------------------------------------------------
-import qualified Test.Data.Store01
-------------------------------------------------------------------------------
-
-main :: IO ()
-main = defaultMain
-    [ testGroup "Data.Store01" Test.Data.Store01.tests
-    ]
+module Main
+( main
+) where
+
+------------------------------------------------------------------------------
+import Test.Framework (defaultMain, testGroup)
+------------------------------------------------------------------------------
+import qualified Test.Data.Store01
+------------------------------------------------------------------------------
+
+main :: IO ()
+main = defaultMain
+    [ testGroup "Data.Store01" Test.Data.Store01.tests
+    ]
diff --git a/tests/Test/Data/Store01.hs b/tests/Test/Data/Store01.hs
--- a/tests/Test/Data/Store01.hs
+++ b/tests/Test/Data/Store01.hs
@@ -1,323 +1,375 @@
-{-# LANGUAGE TypeOperators #-}
-
-module Test.Data.Store01
-( tests
-) where
-
---------------------------------------------------------------------------------
-import Control.Arrow
-import Control.Applicative
---------------------------------------------------------------------------------
-import Test.Framework
-import Test.Framework.Providers.QuickCheck2
-import Test.QuickCheck
---------------------------------------------------------------------------------
-import qualified Data.List as L
-import           Data.Maybe
-import qualified Data.Foldable
-import qualified Data.Set
-import qualified Data.IntSet
---------------------------------------------------------------------------------
-import qualified Data.Store as S
-import           Data.Store (M, O, (.:), (.:.), (:.)(..), (.<), (.<=), (.>), (.>=), (./=), (.==), (.&&), (.||))
---------------------------------------------------------------------------------
-
-data D = D
-    { dOM :: Int
-    , dMO :: [Int]
-    , dMM :: [Int]
-    } deriving (Eq, Ord, Show)
-
-type DID = Int
-
-data DStoreTag = DStoreTag
-
-type DSTS  = DID :. Int :. Int :. Int
-type DSKRS = O       :. O   :. M   :. M 
-type DSIRS = O       :. M   :. O   :. M 
-type DS = S.Store DStoreTag DSKRS DSIRS DSTS D
-type DSKey = S.Key DSKRS DSTS
-type DSSelection = S.Selection DStoreTag DSKRS DSIRS DSTS
-
-sOO :: (DStoreTag, S.N0)
-sOO = (DStoreTag, S.n0)
-
-sOM :: (DStoreTag, S.N1)
-sOM = (DStoreTag, S.n1)
-
-sMO :: (DStoreTag, S.N2)
-sMO = (DStoreTag, S.n2)
-
-sMM :: (DStoreTag, S.N3)
-sMM = (DStoreTag, S.n3)
-
-makeKey :: Int -> Int -> [Int] -> [Int] -> DSKey
-makeKey oo om mo mm = 
-    S.dimO oo .: S.dimO om .: S.dimM mo .:. S.dimM mm
-
-vkey :: D -> DSKey
-vkey (D om mo mm) =  
-    S.dimA .: S.dimO om .: S.dimM mo .:. S.dimM mm
-
-
-vkey' :: Int -> D -> DSKey
-vkey' i (D om mo mm) = 
-    S.dimO i .: S.dimO om .: S.dimM mo .:. S.dimM mm
-
-tests :: [Test]
-tests =
-    [ testProperty "insert1" prop_insert1
-    , testProperty "insert2" prop_insert2
-   
-    , testProperty "insert'1" prop_insert'1
-
-    , testProperty "lookup1" prop_lookup1
-    
-    , testProperty "update1" prop_update1
-    , testProperty "update2" prop_update2
-    , testProperty "update3" prop_update3
-    ]
-
--- | Tests insert (auto-incrementation) #1.
-prop_insert1 (D om mo mm) =
-    case S.insert (vkey v) v emptyS of
-      Just (i :. _, store) -> (i == minBound) && (S.size store == 1)
-      _ -> False
-
-    where
-      emptyS :: DS
-      emptyS = S.empty
-
-      v = D om (L.nub mo) (L.nub mm)
-
--- | Tests insert (auto-incrementation) #2.
-prop_insert2 = ids == map fst inserts
-    where
-      (i0 :. _, s0) = fromJust $ S.insert (vkey $ mval 0) (mval 0) S.empty
-
-      inserts :: [(Int, DS)]
-      inserts =
-        foldl (\acc@((_, s') : _) v -> let (i :. _, s) = fromJust $ S.insert (vkey v) v s'
-                                       in  (i, s) : acc
-              ) [(i0, s0)] ds
-
-      ids :: [Int]
-      ids = reverse . take 100 $ iterate succ minBound
-
-      ds :: [D]
-      ds = map mval [1..99]
-
-      mval :: Int -> D
-      mval i = D i [i] [i]
-
--- | Tests insert' (deleting collisions)
-prop_insert'1 xs =
-  (Data.Set.fromList (S.elements store1) == Data.Set.fromList (S.elements store2)) &&
-  checkLookup sOO oos &&
-  checkLookup sOM oms &&
-  checkLookup sMO mos &&
-  checkLookup sMM mms
-  where
-    lookupSet :: DSSelection -> DS -> Data.Set.Set D
-    lookupSet sel s = Data.Set.fromList $ map snd $ S.lookup sel s
-
-    checkLookup dim xs =
-      all (\x -> lookupSet (dim .== x) store1 == lookupSet (dim .== x) store2) xs
-
-    kes :: [(DSKey, D)]
-    kes = zipWith (\i x -> (vkey' i x, x)) [0 ..] xs
-
-    oos :: [Int]
-    oos = [ 0 .. 5000 ]
-
-    oms :: [Int]
-    oms = Data.IntSet.toList $
-      foldr (\(D om _ _) acc -> Data.IntSet.insert om acc) Data.IntSet.empty xs
-
-    mos :: [Int]
-    mos = Data.IntSet.toList $
-      foldr (\(D _ mo _) acc -> Data.IntSet.union (Data.IntSet.fromList mo) acc) Data.IntSet.empty xs
-
-    mms :: [Int]
-    mms = Data.IntSet.toList $
-      foldr (\(D _ _ mm) acc -> Data.IntSet.union (Data.IntSet.fromList mm) acc) Data.IntSet.empty xs
-
-    store1 :: DS
-    store1 = S.fromList' kes
-    
-    store2 :: DS
-    store2 = foldl (\acc (k, x) -> snd $ S.insert' k x acc) store1 kes
-
--- | Tests insert, lookup (EQ, LT, GT, NEQ) #1.
-prop_lookup1 = byOO_EQ  && byOM_EQ  && byMO_EQ  && byMM_EQ  &&
-               byOO_LT  && byOM_LT  && byMO_LT  && byMM_LT  &&
-               byOO_GT  && byOM_GT  && byMO_GT  && byMM_GT  &&
-               byOO_NEQ && byOM_NEQ && byMO_NEQ && byMM_NEQ
-    where
-      byOO_EQ :: Bool
-      byOO_EQ = all (\r -> length r == 1) $
-        map (\k -> S.lookup (sOO .== k) store) oos
-
-      byOM_EQ :: Bool
-      byOM_EQ = all (\r -> length r == 50) $
-        map (\k -> S.lookup (sOM .== k) store) oms
-
-      byMO_EQ :: Bool
-      byMO_EQ = all (\r -> length r == 1) $
-        map (\k -> S.lookup (sMO .== k) store) mos
-
-      byMM_EQ :: Bool
-      byMM_EQ = all (\(k, r) -> length r == (100 - k)) $
-        map (\k -> (k, S.lookup (sMM .== k) store)) mms
-
-      byOO_LT :: Bool
-      byOO_LT = all (\(k, r) -> length r == (k + minBound)) $
-        map (\k -> (k, S.lookup (sOO .< k) store)) oos
-
-      byOM_LT :: Bool
-      byOM_LT = all (\(k, r) -> length r == (k * 50)) $
-        map (\k -> (k, S.lookup (sOM .< k) store)) oms
-
-      byMO_LT :: Bool
-      byMO_LT = all (\(k, r) -> length r == k) $
-        map (\k -> (k, S.lookup (sMO .< k) store)) mos
-
-      byMM_LT :: Bool
-      byMM_LT = all (\(k, r) -> length r == (if k == 0 then 0 else 100)) $
-        map (\k -> (k, S.lookup (sMM .< k) store)) mms
-
-      byOO_GT :: Bool
-      byOO_GT = all (\(k, r) -> length r == (99 - k + minBound)) $
-        map (\k -> (k, S.lookup (sOO .> k) store)) oos
-
-      byOM_GT :: Bool
-      byOM_GT = all (\(k, r) -> length r == ((1 - k) * 50)) $
-        map (\k -> (k, S.lookup (sOM .> k) store)) oms
-
-      byMO_GT :: Bool
-      byMO_GT = all (\(k, r) -> length r == (99 - k)) $
-        map (\k -> (k, S.lookup (sMO .> k) store)) mos
-
-      byMM_GT :: Bool
-      byMM_GT = all (\(k, r) -> length r == (99 - k)) $
-        map (\k -> (k, S.lookup (sMM .> k) store)) mms
-      
-      byOO_NEQ :: Bool
-      byOO_NEQ = all (\(k, r) -> length r == 99) $
-        map (\k -> (k, S.lookup (sOO ./= k) store)) oos
-
-      byOM_NEQ :: Bool
-      byOM_NEQ = all (\(k, r) -> length r == 50) $
-        map (\k -> (k, S.lookup (sOM ./= k) store)) oms
-
-      byMO_NEQ :: Bool
-      byMO_NEQ = all (\(k, r) -> length r == 99) $
-        map (\k -> (k, S.lookup (sMO ./= k) store)) mos
-
-      byMM_NEQ :: Bool
-      byMM_NEQ = all (\(k, r) -> length r == (if k == 0 then 99 else 100)) $
-        map (\k -> (k, S.lookup (sMM ./= k) store)) mms
-      
-      store :: DS
-      store = foldl (\s v -> snd . fromJust $ S.insert (vkey v) v s) S.empty ds
-
-      ds :: [D]
-      ds = map mval [0..99]
-
-      mval :: Int -> D
-      mval i = D (i `mod` 2) [i] [0..i]
-
-      -- Every key in this list corresponds to exactly 1 d.
-      oos :: [Int]
-      oos = take 100 $ iterate succ minBound
-
-      -- Every key in this list corresponds to exactly 50 ds.
-      oms :: [Int]
-      oms = [0, 1]
-
-      -- Every key in this list corresponds to exactly 1 d.
-      mos :: [Int]
-      mos = [0..99]
-
-      -- Every key 'k' in this list corresponds to exactly '100 - k'
-      -- ds.
-      mms :: [Int]
-      mms = [0..99]
-
--- | Tests insert, delete #1
-prop_update1 = deleteMM
-    where
-      deleteMM :: Bool
-      deleteMM = all (\(k, s, l) -> S.size s == k && length l == 0) $
-        map (\k -> let res = S.delete (sMM .== k) store
-                   in  (k, res, S.lookup (sMM .== k) res)
-            ) mms  
-
-      store :: DS
-      store = foldl (\s v -> snd . fromJust $ S.insert (vkey v) v s) S.empty ds
-
-      ds :: [D]
-      ds = map mval [0..99]
-
-      mval :: Int -> D
-      mval i = D (i `mod` 2) [i] [0..i]
-      
-      mms :: [Int]
-      mms = [0..99]
-
--- | Tests insert, delete #2
-prop_update2 = test1
-    where
-      test1 :: Bool
-      test1 = lookupRes1 == [v2] &&
-              lookupRes2 == [v3] &&
-              S.size res == 2
-        where
-          res = S.delete ((sOM .== 1) .&& (sMM .== 1)) store
-          lookupRes1 = map snd $ S.lookup (sOM .== 1) res
-          lookupRes2 = map snd $ S.lookup (sMM .== 1) res
-
-      store :: DS
-      store = foldl (\s v -> snd . fromJust $ S.insert (vkey v) v s) S.empty ds
-
-      ds :: [D]
-      ds = [v1, v2, v3]
-
-      v1 = D 1 [1] [1]
-      v2 = D 1 [2] [2, 3]
-      v3 = D 2 [3] [1, 2]
-  
--- | Tests insert, update (changing key)
-prop_update3 = test1
-    where
-      test1 :: Bool
-      test1 = lookupRes1 == [v2] &&
-              lookupRes2 == [v3] &&
-              lookupRes3 == [v1] &&
-              lookupRes4 == [v1] &&
-              lookupRes5 == [v1] &&
-              S.size res == 3
-        where
-          res = fromJust $ S.update (\v -> Just (v, Just $ makeKey 0 0 [0] [0])) (sOO .== minBound) store
-          lookupRes1 = map snd $ S.lookup (sOM .== 1) res
-          lookupRes2 = map snd $ S.lookup (sMM .== 1) res
-          lookupRes3 = map snd $ S.lookup (sOM .== 0) res
-          lookupRes4 = map snd $ S.lookup (sMO .== 0) res
-          lookupRes5 = map snd $ S.lookup (sMM .== 0) res
-
-      store :: DS
-      store = foldl (\s v -> snd . fromJust $ S.insert (vkey v) v s) S.empty ds
-
-      ds :: [D]
-      ds = [v1, v2, v3]
-
-      v1 = D 1 [1] [1]
-      v2 = D 1 [2] [2, 3]
-      v3 = D 2 [3] [1, 2]
-
---------------------------------------------------------------------------------
--- | QuickCheck machinery.
-
-instance Arbitrary D where
-    arbitrary = (\(om, mo, mm) -> D om (L.nub mo) (L.nub mm)) <$> arbitrary
-
+{-# LANGUAGE TypeOperators #-}
+
+module Test.Data.Store01
+( tests
+) where
+
+--------------------------------------------------------------------------------
+import Control.Arrow
+import Control.Applicative
+--------------------------------------------------------------------------------
+import Test.Framework
+import Test.Framework.Providers.QuickCheck2
+import Test.QuickCheck
+--------------------------------------------------------------------------------
+import qualified Data.List as L
+import           Data.Maybe
+import qualified Data.Foldable
+import qualified Data.Set
+import qualified Data.IntSet
+--------------------------------------------------------------------------------
+import qualified Data.Store as S
+import           Data.Store (M, O, (.:), (.:.), (:.)(..), (.<), (.<=), (.>), (.>=), (./=), (.==), (.&&), (.||))
+--------------------------------------------------------------------------------
+
+data D = D
+    { dOM :: Int
+    , dMO :: [Int]
+    , dMM :: [Int]
+    } deriving (Eq, Ord, Show)
+
+type DID = Int
+
+data DStoreTag = DStoreTag
+
+type DSTS  = DID :. Int :. Int :. Int
+type DSKRS = O       :. O   :. M   :. M 
+type DSIRS = O       :. M   :. O   :. M 
+type DS = S.Store DStoreTag DSKRS DSIRS DSTS D
+type DSKey = S.Key DSKRS DSTS
+type DSSelection = S.Selection DStoreTag DSKRS DSIRS DSTS
+
+sOO :: (DStoreTag, S.N0)
+sOO = (DStoreTag, S.n0)
+
+sOM :: (DStoreTag, S.N1)
+sOM = (DStoreTag, S.n1)
+
+sMO :: (DStoreTag, S.N2)
+sMO = (DStoreTag, S.n2)
+
+sMM :: (DStoreTag, S.N3)
+sMM = (DStoreTag, S.n3)
+
+makeKey :: Int -> Int -> [Int] -> [Int] -> DSKey
+makeKey oo om mo mm = 
+    S.dimO oo .: S.dimO om .: S.dimM mo .:. S.dimM mm
+
+vkey :: D -> DSKey
+vkey (D om mo mm) =  
+    S.dimA .: S.dimO om .: S.dimM mo .:. S.dimM mm
+
+
+vkey' :: Int -> D -> DSKey
+vkey' i (D om mo mm) = 
+    S.dimO i .: S.dimO om .: S.dimM mo .:. S.dimM mm
+
+tests :: [Test]
+tests =
+    [ testProperty "insert1" prop_insert1
+    , testProperty "insert2" prop_insert2
+   
+    , testProperty "insert'1" prop_insert'1
+
+    , testProperty "lookup1" prop_lookup1
+    , testProperty "lookupOrderBy1" prop_lookupOrderBy1
+    
+    , testProperty "update1" prop_update1
+    , testProperty "update2" prop_update2
+    , testProperty "update3" prop_update3
+    ]
+
+-- | Tests insert (auto-incrementation) #1.
+prop_insert1 (D om mo mm) =
+    case S.insert (vkey v) v emptyS of
+      Just (i :. _, store) -> (i == minBound) && (S.size store == 1)
+      _ -> False
+
+    where
+      emptyS :: DS
+      emptyS = S.empty
+
+      v = D om (L.nub mo) (L.nub mm)
+
+-- | Tests insert (auto-incrementation) #2.
+prop_insert2 = ids == map fst inserts
+    where
+      (i0 :. _, s0) = fromJust $ S.insert (vkey $ mval 0) (mval 0) S.empty
+
+      inserts :: [(Int, DS)]
+      inserts =
+        foldl (\acc@((_, s') : _) v -> let (i :. _, s) = fromJust $ S.insert (vkey v) v s'
+                                       in  (i, s) : acc
+              ) [(i0, s0)] ds
+
+      ids :: [Int]
+      ids = reverse . take 100 $ iterate succ minBound
+
+      ds :: [D]
+      ds = map mval [1..99]
+
+      mval :: Int -> D
+      mval i = D i [i] [i]
+
+-- | Tests insert' (deleting collisions)
+prop_insert'1 xs =
+  (Data.Set.fromList (S.elements store1) == Data.Set.fromList (S.elements store2)) &&
+  checkLookup sOO oos &&
+  checkLookup sOM oms &&
+  checkLookup sMO mos &&
+  checkLookup sMM mms
+  where
+    lookupSet :: DSSelection -> DS -> Data.Set.Set D
+    lookupSet sel s = Data.Set.fromList $ map snd $ S.lookup sel s
+
+    checkLookup dim xs =
+      all (\x -> lookupSet (dim .== x) store1 == lookupSet (dim .== x) store2) xs
+
+    kes :: [(DSKey, D)]
+    kes = zipWith (\i x -> (vkey' i x, x)) [0 ..] xs
+
+    oos :: [Int]
+    oos = [ 0 .. 5000 ]
+
+    oms :: [Int]
+    oms = Data.IntSet.toList $
+      foldr (\(D om _ _) acc -> Data.IntSet.insert om acc) Data.IntSet.empty xs
+
+    mos :: [Int]
+    mos = Data.IntSet.toList $
+      foldr (\(D _ mo _) acc -> Data.IntSet.union (Data.IntSet.fromList mo) acc) Data.IntSet.empty xs
+
+    mms :: [Int]
+    mms = Data.IntSet.toList $
+      foldr (\(D _ _ mm) acc -> Data.IntSet.union (Data.IntSet.fromList mm) acc) Data.IntSet.empty xs
+
+    store1 :: DS
+    store1 = S.fromList' kes
+    
+    store2 :: DS
+    store2 = foldl (\acc (k, x) -> snd $ S.insert' k x acc) store1 kes
+
+-- | Tests insert, lookup (EQ, LT, GT, NEQ) #1.
+prop_lookup1 = byOO_EQ  && byOM_EQ  && byMO_EQ  && byMM_EQ  &&
+               byOO_LT  && byOM_LT  && byMO_LT  && byMM_LT  &&
+               byOO_GT  && byOM_GT  && byMO_GT  && byMM_GT  &&
+               byOO_NEQ && byOM_NEQ && byMO_NEQ && byMM_NEQ
+    where
+      byOO_EQ :: Bool
+      byOO_EQ = all (\r -> length r == 1) $
+        map (\k -> S.lookup (sOO .== k) store) oos
+
+      byOM_EQ :: Bool
+      byOM_EQ = all (\r -> length r == 50) $
+        map (\k -> S.lookup (sOM .== k) store) oms
+
+      byMO_EQ :: Bool
+      byMO_EQ = all (\r -> length r == 1) $
+        map (\k -> S.lookup (sMO .== k) store) mos
+
+      byMM_EQ :: Bool
+      byMM_EQ = all (\(k, r) -> length r == (100 - k)) $
+        map (\k -> (k, S.lookup (sMM .== k) store)) mms
+
+      byOO_LT :: Bool
+      byOO_LT = all (\(k, r) -> length r == (k + minBound)) $
+        map (\k -> (k, S.lookup (sOO .< k) store)) oos
+
+      byOM_LT :: Bool
+      byOM_LT = all (\(k, r) -> length r == (k * 50)) $
+        map (\k -> (k, S.lookup (sOM .< k) store)) oms
+
+      byMO_LT :: Bool
+      byMO_LT = all (\(k, r) -> length r == k) $
+        map (\k -> (k, S.lookup (sMO .< k) store)) mos
+
+      byMM_LT :: Bool
+      byMM_LT = all (\(k, r) -> length r == (if k == 0 then 0 else 100)) $
+        map (\k -> (k, S.lookup (sMM .< k) store)) mms
+
+      byOO_GT :: Bool
+      byOO_GT = all (\(k, r) -> length r == (99 - k + minBound)) $
+        map (\k -> (k, S.lookup (sOO .> k) store)) oos
+
+      byOM_GT :: Bool
+      byOM_GT = all (\(k, r) -> length r == ((1 - k) * 50)) $
+        map (\k -> (k, S.lookup (sOM .> k) store)) oms
+
+      byMO_GT :: Bool
+      byMO_GT = all (\(k, r) -> length r == (99 - k)) $
+        map (\k -> (k, S.lookup (sMO .> k) store)) mos
+
+      byMM_GT :: Bool
+      byMM_GT = all (\(k, r) -> length r == (99 - k)) $
+        map (\k -> (k, S.lookup (sMM .> k) store)) mms
+      
+      byOO_NEQ :: Bool
+      byOO_NEQ = all (\(k, r) -> length r == 99) $
+        map (\k -> (k, S.lookup (sOO ./= k) store)) oos
+
+      byOM_NEQ :: Bool
+      byOM_NEQ = all (\(k, r) -> length r == 50) $
+        map (\k -> (k, S.lookup (sOM ./= k) store)) oms
+
+      byMO_NEQ :: Bool
+      byMO_NEQ = all (\(k, r) -> length r == 99) $
+        map (\k -> (k, S.lookup (sMO ./= k) store)) mos
+
+      byMM_NEQ :: Bool
+      byMM_NEQ = all (\(k, r) -> length r == (if k == 0 then 99 else 100)) $
+        map (\k -> (k, S.lookup (sMM ./= k) store)) mms
+      
+      store :: DS
+      store = foldl (\s v -> snd . fromJust $ S.insert (vkey v) v s) S.empty ds
+
+      ds :: [D]
+      ds = map mval [0..99]
+
+      mval :: Int -> D
+      mval i = D (i `mod` 2) [i] [0..i]
+
+      -- Every key in this list corresponds to exactly 1 d.
+      oos :: [Int]
+      oos = take 100 $ iterate succ minBound
+
+      -- Every key in this list corresponds to exactly 50 ds.
+      oms :: [Int]
+      oms = [0, 1]
+
+      -- Every key in this list corresponds to exactly 1 d.
+      mos :: [Int]
+      mos = [0..99]
+
+      -- Every key 'k' in this list corresponds to exactly '100 - k'
+      -- ds.
+      mms :: [Int]
+      mms = [0..99]
+
+-- | Tests insert, lookupOrderByA #1.
+prop_lookupOrderBy1 = l1 && l2 
+    where
+      l1 :: Bool
+      l1 = isSortedOM (S.lookupOrderByA (sMM .>= 20) sOM store) &&
+           isSortedOM (S.lookupOrderByA (sMM .<= 50 .&& sOM .== 5) sOM store) &&
+           isSortedOM (S.lookupOrderByA (sOO .>= 20) sOM store) &&
+           isSortedOM (S.lookupOrderByA (sOM .>= 3) sOM store) 
+
+      isSortedOM :: [(S.RawKey DSKRS DSTS, D)] -> Bool
+      isSortedOM [] = True      
+      isSortedOM [_] = True
+      isSortedOM ((_ :. x1 :. _, _) : (_ :. x2 :. _, _) : t) = x1 <= x2 && isSortedOM t       
+      
+      l2 :: Bool
+      l2 = isSortedOO (S.lookupOrderByA (sMM .>= 20) sOO store) &&
+           isSortedOO (S.lookupOrderByA (sMM .<= 50 .&& sOM .== 1) sOO store) &&
+           isSortedOO (S.lookupOrderByA (sOO .>= 20) sOO store) &&
+           isSortedOO (S.lookupOrderByA (sOM .>= 3) sOO store)
+
+      isSortedOO :: [(S.RawKey DSKRS DSTS, D)] -> Bool
+      isSortedOO [] = True      
+      isSortedOO [_] = True
+      isSortedOO ((x1 :. _, _) : (x2 :. _, _) : t) = x1 <= x2 && isSortedOO t       
+
+      store :: DS
+      store = foldl (\s v -> snd . fromJust $ S.insert (vkey v) v s) S.empty ds
+
+      ds :: [D]
+      ds = map mval [0..99]
+
+      mval :: Int -> D
+      mval i = D (i `mod` 20) [i] [0..i]
+
+      -- Every key in this list corresponds to exactly 1 d.
+      oos :: [Int]
+      oos = take 100 $ iterate succ minBound
+
+      -- Every key in this list corresponds to exactly 50 ds.
+      oms :: [Int]
+      oms = [0..19]
+
+      -- Every key in this list corresponds to exactly 1 d.
+      mos :: [Int]
+      mos = [0..99]
+
+      -- Every key 'k' in this list corresponds to exactly '100 - k'
+      -- ds.
+      mms :: [Int]
+      mms = [0..99]
+
+-- | Tests insert, delete #1
+prop_update1 = deleteMM
+    where
+      deleteMM :: Bool
+      deleteMM = all (\(k, s, l) -> S.size s == k && length l == 0) $
+        map (\k -> let res = S.delete (sMM .== k) store
+                   in  (k, res, S.lookup (sMM .== k) res)
+            ) mms  
+
+      store :: DS
+      store = foldl (\s v -> snd . fromJust $ S.insert (vkey v) v s) S.empty ds
+
+      ds :: [D]
+      ds = map mval [0..99]
+
+      mval :: Int -> D
+      mval i = D (i `mod` 2) [i] [0..i]
+      
+      mms :: [Int]
+      mms = [0..99]
+
+-- | Tests insert, delete #2
+prop_update2 = test1
+    where
+      test1 :: Bool
+      test1 = lookupRes1 == [v2] &&
+              lookupRes2 == [v3] &&
+              S.size res == 2
+        where
+          res = S.delete ((sOM .== 1) .&& (sMM .== 1)) store
+          lookupRes1 = map snd $ S.lookup (sOM .== 1) res
+          lookupRes2 = map snd $ S.lookup (sMM .== 1) res
+
+      store :: DS
+      store = foldl (\s v -> snd . fromJust $ S.insert (vkey v) v s) S.empty ds
+
+      ds :: [D]
+      ds = [v1, v2, v3]
+
+      v1 = D 1 [1] [1]
+      v2 = D 1 [2] [2, 3]
+      v3 = D 2 [3] [1, 2]
+  
+-- | Tests insert, update (changing key)
+prop_update3 = test1
+    where
+      test1 :: Bool
+      test1 = lookupRes1 == [v2] &&
+              lookupRes2 == [v3] &&
+              lookupRes3 == [v1] &&
+              lookupRes4 == [v1] &&
+              lookupRes5 == [v1] &&
+              S.size res == 3
+        where
+          res = fromJust $ S.update (\v -> Just (v, Just $ makeKey 0 0 [0] [0])) (sOO .== minBound) store
+          lookupRes1 = map snd $ S.lookup (sOM .== 1) res
+          lookupRes2 = map snd $ S.lookup (sMM .== 1) res
+          lookupRes3 = map snd $ S.lookup (sOM .== 0) res
+          lookupRes4 = map snd $ S.lookup (sMO .== 0) res
+          lookupRes5 = map snd $ S.lookup (sMM .== 0) res
+
+      store :: DS
+      store = foldl (\s v -> snd . fromJust $ S.insert (vkey v) v s) S.empty ds
+
+      ds :: [D]
+      ds = [v1, v2, v3]
+
+      v1 = D 1 [1] [1]
+      v2 = D 1 [2] [2, 3]
+      v3 = D 2 [3] [1, 2]
+
+--------------------------------------------------------------------------------
+-- | QuickCheck machinery.
+
+instance Arbitrary D where
+    arbitrary = (\(om, mo, mm) -> D om (L.nub mo) (L.nub mm)) <$> arbitrary
+
