diff --git a/DDF/Bool.hs b/DDF/Bool.hs
--- a/DDF/Bool.hs
+++ b/DDF/Bool.hs
@@ -6,6 +6,10 @@
 
 class DBI r => Bool r where
   bool :: M.Bool -> r h M.Bool
+  true :: r h M.Bool
+  true = bool M.True
+  false :: r h M.Bool
+  false = bool M.False
   ite :: r h (a -> a -> M.Bool -> a)
 
 ite1 = app ite
diff --git a/DDF/Diff.hs b/DDF/Diff.hs
--- a/DDF/Diff.hs
+++ b/DDF/Diff.hs
@@ -209,3 +209,8 @@
 
 instance Map.Ord M.Float where
   diffOrd _ = Dict
+
+type instance DiffType v M.Ordering = M.Ordering
+instance (Vector r v, Ordering r) => Ordering (Diff r v) where
+  ordering = Diff . ordering
+  sel = Diff sel
diff --git a/DDF/Eval.hs b/DDF/Eval.hs
--- a/DDF/Eval.hs
+++ b/DDF/Eval.hs
@@ -26,6 +26,8 @@
 import qualified DDF.Meta.FreeVector as M
 import DDF.Lang
 
+newtype Eval h x = Eval {runEval :: h -> x}
+
 comb = Eval . M.const
 
 instance DBI Eval where
@@ -166,4 +168,9 @@
   state = comb M.state
   runState = comb M.runState
 
-newtype Eval h x = Eval {runEval :: h -> x}
+instance Ordering Eval where
+  ordering = comb
+  sel = comb f where
+    f x _ _ M.LT = x
+    f _ x _ M.EQ = x
+    f _ _ x M.GT = x
diff --git a/DDF/ImpW.hs b/DDF/ImpW.hs
--- a/DDF/ImpW.hs
+++ b/DDF/ImpW.hs
@@ -187,6 +187,10 @@
   freeVector = NoImpW freeVector
   runFreeVector = NoImpW runFreeVector
 
+instance (Prod r, Ordering r) => Ordering (ImpW r) where
+  sel = NoImpW sel
+  ordering = NoImpW . ordering
+
 instance Lang r => Lang (ImpW r) where
   exfalso = NoImpW exfalso
   writer = NoImpW writer
diff --git a/DDF/ImportMeta.hs b/DDF/ImportMeta.hs
--- a/DDF/ImportMeta.hs
+++ b/DDF/ImportMeta.hs
@@ -10,7 +10,8 @@
   module Data.Proxy,
   module DDF.Util) where
 
-import Prelude (($), show, (+), (-), (*), (/), (.), (++), (>>=), (<=), (<), (==), compare, print, Maybe(Just, Nothing), String, (||), Either(Left, Right))
+import Prelude (
+  ($), show, (+), (-), (*), (/), (.), (++), (>>=), (<=), (<), (==), compare, print, Maybe(Just, Nothing), String, (||), Either(Left, Right))
 import Data.Void (Void, absurd)
 import Control.Monad.Writer (Writer)
 import Control.Monad.State (State)
diff --git a/DDF/Lang.hs b/DDF/Lang.hs
--- a/DDF/Lang.hs
+++ b/DDF/Lang.hs
@@ -9,13 +9,14 @@
 
 module DDF.Lang (
   module DDF.Lang,
+  module DDF.Bimap,
   module DDF.Bool,
   module DDF.Char,
   module DDF.Double,
-  module DDF.Float,
-  module DDF.Bimap,
   module DDF.Dual,
+  module DDF.Float,
   module DDF.Meta.Diff,
+  module DDF.Ordering,
   module DDF.Unit,
   module DDF.Sum,
   module DDF.Int,
@@ -40,6 +41,7 @@
 import DDF.DiffWrapper
 import DDF.Fix
 import DDF.FreeVector
+import DDF.Ordering
 
 import qualified DDF.VectorTF as VTF
 import qualified DDF.Meta.VectorTF as M.VTF
@@ -56,7 +58,7 @@
 
 type FreeVectorBuilder b = M.Map.Map b M.Double
 type SVTFBuilder b = State (M.Bimap.Bimap (M.VTF.VectorTF b M.Int) M.Int) M.Int
-class (Bool r, Char r, Double r, Float r, Bimap r, Dual r, Unit r, Sum r, Int r, IO r, VTF.VectorTF r, DiffWrapper r, Fix r, FreeVector r) => Lang r where
+class (Ordering r, Char r, Double r, Float r, Bimap r, Dual r, Unit r, Sum r, Int r, IO r, VTF.VectorTF r, DiffWrapper r, Fix r, FreeVector r) => Lang r where
   exfalso :: r h (Void -> a)
   writer :: r h ((a, w) -> M.Writer w a)
   runWriter :: r h (M.Writer w a -> (a, w))
diff --git a/DDF/Ordering.hs b/DDF/Ordering.hs
new file mode 100644
--- /dev/null
+++ b/DDF/Ordering.hs
@@ -0,0 +1,26 @@
+{-# Language NoImplicitPrelude, NoMonomorphismRestriction #-}
+
+module DDF.Ordering (module DDF.Ordering, module DDF.DBI) where
+
+import DDF.DBI
+import DDF.Bool
+import qualified Prelude as M
+
+class DBI repr => Ordering repr where
+  sel :: repr h (a -> a -> a -> M.Ordering -> a)
+  ordering :: M.Ordering -> repr h M.Ordering
+  ltOrd :: repr h M.Ordering
+  ltOrd = ordering M.LT
+  eqOrd :: repr h M.Ordering
+  eqOrd = ordering M.EQ
+  gtOrd :: repr h M.Ordering
+  gtOrd = ordering M.GT
+
+sel1 = app1 sel
+sel2 = app2 sel
+sel3 = app3 sel
+sel4 = app4 sel
+
+isLT = sel3 true  false false
+isEQ = sel3 false true  false
+isGT = sel3 false false true
diff --git a/DDF/PE.hs b/DDF/PE.hs
--- a/DDF/PE.hs
+++ b/DDF/PE.hs
@@ -20,6 +20,8 @@
 import DDF.Lang
 import qualified Prelude as M
 import qualified DDF.Meta.Dual as M
+--import qualified DDF.Map as Map
+--import qualified Data.Map as M
 
 data P repr h a where
   Open   :: (forall hout. EnvT repr h hout -> P repr hout a) -> P repr h a
@@ -372,6 +374,27 @@
 
 instance IO repr => IO (P repr) where
   putStrLn = Unk putStrLn
+
+data MapPE (repr :: * -> * -> *) h k a :: * where
+  EmptyMap :: MapPE repr h k a
+  SingletonMap :: P repr h k -> P repr h a -> MapPE repr h k a
+
+{-
+type instance K repr h (M.Map k a) = MapPE repr h k a
+instance Map.Map repr => Map.Map (P repr) where
+  empty = static (EmptyMap, Map.empty)
+  singleton = abs $ abs $ f (s z) z where
+    f :: P repr h k -> P repr h a -> P repr h (M.Map k a)
+    f k a =
+      know (SingletonMap k a)
+        (Map.singleton2 (dynamic k) (dynamic a))
+        (\h -> f (app_open k h) (app_open a h))
+        (f (s k) (s a))
+  lookup = abs $ abs $ f (s z) z where
+    f :: P repr h (M.Map k a) -> P repr h k -> P repr h (Maybe a)
+    f (Known EmptyMap _ _ _ _) _ = nothing
+    f (Known (SingletonMap k a) _ _ _ _) r = ite3 (just1 a) nothing _
+-}
 
 pe :: DBI repr => P repr () a -> repr () a
 pe = dynamic
diff --git a/DDF/Show.hs b/DDF/Show.hs
--- a/DDF/Show.hs
+++ b/DDF/Show.hs
@@ -172,3 +172,7 @@
   double2Float = name "double2Float"
   state = name "state"
   runState = name "runState"
+
+instance Ordering Show where
+  ordering = name . show
+  sel = name "sel"
diff --git a/DDF/Size.hs b/DDF/Size.hs
--- a/DDF/Size.hs
+++ b/DDF/Size.hs
@@ -137,3 +137,7 @@
   double2Float = one
   state = one
   runState = one
+
+instance Ordering Size where
+  sel = one
+  ordering _ = one
diff --git a/DDF/TermGen.hs b/DDF/TermGen.hs
--- a/DDF/TermGen.hs
+++ b/DDF/TermGen.hs
@@ -69,28 +69,6 @@
   fix = mkT @Fix fix
   runFix = mkT @Fix runFix
 
-type instance SubLC c Lang = (
-  SubL c Fix,
-  SubL c Int,
-  SubL c Float,
-  SubL c Double,
-  SubL c Bimap,
-  SubL c IO,
-  SubL c Sum,
-  SubL c Dual,
-  SubL c DiffWrapper,
-  SubL c FreeVector,
-  SubL c VTF.VectorTF)
-
-instance SubL c Lang => Lang (Term c) where
-  state = mkT @Lang state
-  writer = mkT @Lang writer
-  exfalso = mkT @Lang exfalso
-  runState = mkT @Lang runState
-  runWriter = mkT @Lang runWriter
-  float2Double = mkT @Lang float2Double
-  double2Float = mkT @Lang double2Float
-
 type instance SubLC c FreeVector = SubL c DBI
 
 instance SubL c FreeVector => FreeVector (Term c) where
@@ -109,7 +87,6 @@
   char x = mkT @Char (char x)
 
 type instance SubLC c Bimap = (SubL c Int, SubL c Map.Map)
-
 instance SubL c Bimap => Bimap (Term c) where
   size = mkT @Bimap size
   empty = mkT @Bimap empty
@@ -123,7 +100,6 @@
   singleton = mkT @Bimap singleton
 
 type instance SubLC c Float = SubL c DBI
-
 instance SubL c Float => Float (Term c) where
   float x = mkT @Float (float x) 
   floatExp = mkT @Float floatExp
@@ -133,7 +109,6 @@
   floatDivide = mkT @Float floatDivide
 
 type instance SubLC c Double = SubL c Bool
-
 instance SubL c Double => Double (Term c) where
   doubleEq = mkT @Double doubleEq
   double x = mkT @Double (double x)
@@ -178,14 +153,12 @@
   bind = mkT @IO bind
 
 type instance SubLC c List = SubL c Y
-
 instance SubL c List => List (Term c) where
   nil = mkT @List nil
   cons = mkT @List cons
   listMatch = mkT @List listMatch
 
 type instance SubLC c Prod = SubL c DBI
-
 instance SubL c Prod => Prod (Term c) where
   zro = mkT @Prod zro
   fst = mkT @Prod fst
@@ -197,7 +170,6 @@
   y = mkT @Y y
 
 type instance SubLC c Map.Map = (SubL c Prod, SubL c Option)
-
 instance SubL c Map.Map => Map.Map (Term c) where
   empty = mkT @Map.Map Map.empty
   alter = mkT @Map.Map Map.alter
@@ -207,7 +179,6 @@
   unionWith = mkT @Map.Map Map.unionWith
 
 type instance SubLC c VTF.VectorTF = SubL c Double
-
 instance SubL c VTF.VectorTF => VTF.VectorTF (Term c) where
   zero = mkT @VTF.VectorTF VTF.zero
   plus = mkT @VTF.VectorTF VTF.plus
@@ -216,12 +187,16 @@
   vtfMatch = mkT @VTF.VectorTF VTF.vtfMatch
 
 type instance SubLC c Option = SubL c DBI
-
 instance SubL c Option => Option (Term c) where
   just = mkT @Option just
   nothing = mkT @Option nothing
   optionMatch = mkT @Option optionMatch
 
+type instance SubLC c Ordering = SubL c DBI
+instance SubL c Ordering => Ordering (Term c) where
+  sel = mkT @Ordering sel
+  ordering x = mkT @Ordering (ordering x)
+
 genInstance :: Q [Dec]
 genInstance =
   M.mapM gen [
@@ -245,7 +220,8 @@
     ''Y,
     ''Dual,
     ''DiffWrapper,
-    ''FreeVector]
+    ''FreeVector,
+    ''Ordering]
     where
       gen n = M.return $
         InstanceD
@@ -253,3 +229,26 @@
           []
           (AppT (AppT (ConT ''SubL) (ConT ''Lang)) (ConT n))
           [ValD (VarP 'sub) (NormalB (AppE (ConE 'Sub) (ConE 'Dict))) []]
+
+type instance SubLC c Lang = (
+  SubL c Fix,
+  SubL c Int,
+  SubL c Float,
+  SubL c Double,
+  SubL c Bimap,
+  SubL c IO,
+  SubL c Sum,
+  SubL c Dual,
+  SubL c DiffWrapper,
+  SubL c FreeVector,
+  SubL c VTF.VectorTF,
+  SubL c Ordering)
+
+instance SubL c Lang => Lang (Term c) where
+  state = mkT @Lang state
+  writer = mkT @Lang writer
+  exfalso = mkT @Lang exfalso
+  runState = mkT @Lang runState
+  runWriter = mkT @Lang runWriter
+  float2Double = mkT @Lang float2Double
+  double2Float = mkT @Lang double2Float
diff --git a/DDF/UnHOAS.hs b/DDF/UnHOAS.hs
--- a/DDF/UnHOAS.hs
+++ b/DDF/UnHOAS.hs
@@ -141,3 +141,7 @@
   double2Float = UnHOAS double2Float
   state = UnHOAS state
   runState = UnHOAS runState
+
+instance Ordering r => Ordering (UnHOAS r) where
+  sel = UnHOAS sel
+  ordering = UnHOAS . ordering
diff --git a/DDF/UnLiftEnv.hs b/DDF/UnLiftEnv.hs
--- a/DDF/UnLiftEnv.hs
+++ b/DDF/UnLiftEnv.hs
@@ -141,3 +141,7 @@
   runState = unLiftEnv runState
   float2Double = unLiftEnv float2Double
   double2Float = unLiftEnv double2Float
+
+instance (Prod r, Ordering r) => Ordering (UnLiftEnv r) where
+  sel = unLiftEnv sel
+  ordering = unLiftEnv . ordering
diff --git a/DeepDarkFantasy.cabal b/DeepDarkFantasy.cabal
--- a/DeepDarkFantasy.cabal
+++ b/DeepDarkFantasy.cabal
@@ -1,5 +1,5 @@
 name: DeepDarkFantasy
-version: 0.2017.8.17
+version: 0.2017.8.18
 cabal-version: 1.12
 build-type: Simple
 license: Apache
@@ -45,6 +45,7 @@
                    DDF.Meta.FreeVector
                    DDF.Meta.VectorTF
                    DDF.Option
+                   DDF.Ordering
                    DDF.PE
                    DDF.Prod
                    DDF.Sam.Hello