From f315e93ce22df1fcddb5d34de8aed6dcf187e17e Mon Sep 17 00:00:00 2001
From: John Ericson <John.Ericson@Obsidian.Systems>
Date: Mon, 28 Jan 2019 17:42:58 -0500
Subject: [PATCH 01/10] Clean up whitespace

---
 src/Data/Dependent/Map.hs | 109 +++++++++++++++++++-------------------
 1 file changed, 54 insertions(+), 55 deletions(-)

diff --git a/src/Data/Dependent/Map.hs b/src/Data/Dependent/Map.hs
index 5160ae1..7ff73f5 100644
--- a/src/Data/Dependent/Map.hs
+++ b/src/Data/Dependent/Map.hs
@@ -13,7 +13,7 @@ module Data.Dependent.Map
     ( DMap
     , DSum(..), Some(..)
     , GCompare(..), GOrdering(..)
-    
+
     -- * Operators
     , (!), (\\)
 
@@ -24,7 +24,7 @@ module Data.Dependent.Map
     , notMember
     , lookup
     , findWithDefault
-    
+
     -- * Construction
     , empty
     , singleton
@@ -37,7 +37,7 @@ module Data.Dependent.Map
     , insertWithKey'
     , insertLookupWithKey
     , insertLookupWithKey'
-    
+
     -- ** Delete\/Update
     , delete
     , adjust
@@ -52,7 +52,7 @@ module Data.Dependent.Map
     -- * Combine
 
     -- ** Union
-    , union         
+    , union
     , unionWithKey
     , unions
     , unionsWithKey
@@ -60,9 +60,9 @@ module Data.Dependent.Map
     -- ** Difference
     , difference
     , differenceWithKey
-    
+
     -- ** Intersection
-    , intersection           
+    , intersection
     , intersectionWithKey
 
     -- * Traversal
@@ -84,7 +84,7 @@ module Data.Dependent.Map
     -- * Conversion
     , keys
     , assocs
-    
+
     -- ** Lists
     , toList
     , fromList
@@ -97,7 +97,7 @@ module Data.Dependent.Map
     , fromAscListWithKey
     , fromDistinctAscList
 
-    -- * Filter 
+    -- * Filter
     , filter
     , filterWithKey
     , partitionWithKey
@@ -106,14 +106,14 @@ module Data.Dependent.Map
     , mapMaybeWithKey
     , mapEitherWithKey
 
-    , split         
-    , splitLookup   
+    , split
+    , splitLookup
 
     -- * Submap
     , isSubmapOf, isSubmapOfBy
     , isProperSubmapOf, isProperSubmapOfBy
 
-    -- * Indexed 
+    -- * Indexed
     , lookupIndex
     , findIndex
     , elemAt
@@ -133,7 +133,7 @@ module Data.Dependent.Map
     , updateMaxWithKey
     , minViewWithKey
     , maxViewWithKey
-    
+
     -- * Debugging
     , showTree
     , showTreeWith
@@ -188,21 +188,21 @@ infixl 9 !,\\ --
 m1 \\ m2 = difference m1 m2
 
 -- #if __GLASGOW_HASKELL__
--- 
+--
 -- {--------------------------------------------------------------------
---   A Data instance  
+--   A Data instance
 -- --------------------------------------------------------------------}
--- 
+--
 -- -- This instance preserves data abstraction at the cost of inefficiency.
 -- -- We omit reflection services for the sake of data abstraction.
--- 
+--
 -- instance (Data k, Data a, GCompare k) => Data (DMap k) where
 --   gfoldl f z m   = z fromList `f` toList m
 --   toConstr _     = error "toConstr"
 --   gunfold _ _    = error "gunfold"
 --   dataTypeOf _   = mkNoRepType "Data.Map.Map"
 --   dataCast2 f    = gcast2 f
--- 
+--
 -- #endif
 
 {--------------------------------------------------------------------
@@ -279,7 +279,7 @@ insertR kx x = kx `seq` go
             GEQ -> t
 
 -- | /O(log n)/. Insert with a function, combining new value and old value.
--- @'insertWith' f key value mp@ 
+-- @'insertWith' f key value mp@
 -- will insert the entry @key :=> value@ into @mp@ if key does
 -- not exist in the map. If the key does exist, the function will
 -- insert the entry @key :=> f new_value old_value@.
@@ -292,7 +292,7 @@ insertWith' :: GCompare k => (f v -> f v -> f v) -> k v -> f v -> DMap k f -> DM
 insertWith' f = insertWithKey' (\_ x' y' -> f x' y')
 
 -- | /O(log n)/. Insert with a function, combining key, new value and old value.
--- @'insertWithKey' f key value mp@ 
+-- @'insertWithKey' f key value mp@
 -- will insert the entry @key :=> value@ into @mp@ if key does
 -- not exist in the map. If the key does exist, the function will
 -- insert the entry @key :=> f key new_value old_value@.
@@ -427,7 +427,7 @@ updateWithKey f k = k `seq` go
 
 -- | /O(log n)/. Lookup and update. See also 'updateWithKey'.
 -- The function returns changed value, if it is updated.
--- Returns the original key value if the map entry is deleted. 
+-- Returns the original key value if the map entry is deleted.
 updateLookupWithKey :: forall k f v. GCompare k => (k v -> f v -> Maybe (f v)) -> k v -> DMap k f -> (Maybe (f v), DMap k f)
 updateLookupWithKey f k = k `seq` go
  where
@@ -436,7 +436,7 @@ updateLookupWithKey f k = k `seq` go
    go (Bin sx kx x l r) =
           case gcompare k kx of
                GLT -> let (found,l') = go l in (found,balance kx x l' r)
-               GGT -> let (found,r') = go r in (found,balance kx x l r') 
+               GGT -> let (found,r') = go r in (found,balance kx x l r')
                GEQ -> case f kx x of
                        Just x' -> (Just x',Bin sx kx x' l r)
                        Nothing -> (Just x,glue l r)
@@ -495,7 +495,7 @@ lookupIndex k = k `seq` go 0
     go !idx (Bin _ kx _ l r)
       = case gcompare k kx of
           GLT -> go idx l
-          GGT -> go (idx + size l + 1) r 
+          GGT -> go (idx + size l + 1) r
           GEQ -> Just (idx + size l)
 
 -- | /O(log n)/. Retrieve an element by /index/. Calls 'error' when an
@@ -522,7 +522,7 @@ updateAt f i0 t = i0 `seq` go i0 t
       EQ -> case f kx x of
               Just x' -> Bin sx kx x' l r
               Nothing -> glue l r
-      where 
+      where
         sizeL = size l
 
 -- | /O(log n)/. Delete the element at /index/.
@@ -599,7 +599,7 @@ updateMaxWithKey f = go
     go Tip                 = Tip
 
 {--------------------------------------------------------------------
-  Union. 
+  Union.
 --------------------------------------------------------------------}
 
 -- | The union of a list of maps:
@@ -615,7 +615,7 @@ unionsWithKey f ts
   = foldlStrict (unionWithKey f) empty ts
 
 -- | /O(m*log(n\/m + 1)), m <= n/.
--- The expression (@'union' t1 t2@) takes the left-biased union of @t1@ and @t2@. 
+-- The expression (@'union' t1 t2@) takes the left-biased union of @t1@ and @t2@.
 -- It prefers @t1@ when duplicate keys are encountered,
 -- i.e. (@'union' == 'unionWith' 'const'@).
 union :: GCompare k => DMap k f -> DMap k f -> DMap k f
@@ -650,7 +650,7 @@ unionWithKey f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of
   Difference
 --------------------------------------------------------------------}
 
--- | /O(m * log (n\/m + 1)), m <= n/. Difference of two maps. 
+-- | /O(m * log (n\/m + 1)), m <= n/. Difference of two maps.
 -- Return elements of the first map not existing in the second map.
 difference :: GCompare k => DMap k f -> DMap k g -> DMap k f
 difference Tip _   = Tip
@@ -666,7 +666,7 @@ difference t1 (Bin _ k2 _x2 l2 r2) = case split k2 t1 of
 -- | /O(n+m)/. Difference with a combining function. When two equal keys are
 -- encountered, the combining function is applied to the key and both values.
 -- If it returns 'Nothing', the element is discarded (proper set difference). If
--- it returns (@'Just' y@), the element is updated with a new value @y@. 
+-- it returns (@'Just' y@), the element is updated with a new value @y@.
 differenceWithKey :: GCompare k => (forall v. k v -> f v -> g v -> Maybe (f v)) -> DMap k f -> DMap k g -> DMap k f
 differenceWithKey _ Tip _   = Tip
 differenceWithKey _ t1 Tip  = t1
@@ -739,7 +739,7 @@ submap' f (Bin _ kx x l r) t
   where
     (lt,found,gt) = splitLookupWithKey kx t
 
--- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal). 
+-- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' 'eqTagged'@).
 isProperSubmapOf :: (GCompare k, EqTag k f) => DMap k f -> DMap k f -> Bool
 isProperSubmapOf m1 m2
@@ -749,7 +749,7 @@ isProperSubmapOf m1 m2
  The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
  @m1@ and @m2@ are not equal,
  all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
- applied to their respective keys and values. 
+ applied to their respective keys and values.
 -}
 isProperSubmapOfBy :: GCompare k => (forall v. k v -> k v -> f v -> g v -> Bool) -> DMap k f -> DMap k g -> Bool
 isProperSubmapOfBy f t1 t2
@@ -871,7 +871,7 @@ mapAccumRWithKey f = go
 
 -- | /O(n*log n)/.
 -- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@.
--- 
+--
 -- The size of the result may be smaller if @f@ maps two or more distinct
 -- keys to the same new key.  In this case the associated values will be
 -- combined using @c@.
@@ -886,8 +886,8 @@ mapKeysWith c f = fromListWithKey c . Prelude.map fFirst . toList
 -- That is, for any values @x@ and @y@, if @x@ < @y@ then @f x@ < @f y@.
 -- /The precondition is not checked./
 -- Semi-formally, we have:
--- 
--- > and [x < y ==> f x < f y | x <- ls, y <- ls] 
+--
+-- > and [x < y ==> f x < f y | x <- ls, y <- ls]
 -- >                     ==> mapKeysMonotonic f s == mapKeys f s
 -- >     where ls = keys s
 --
@@ -899,7 +899,7 @@ mapKeysMonotonic f (Bin sz k x l r) =
     Bin sz (f k) x (mapKeysMonotonic f l) (mapKeysMonotonic f r)
 
 {--------------------------------------------------------------------
-  Folds  
+  Folds
 --------------------------------------------------------------------}
 
 -- | /O(n)/. Fold the keys and values in the map, such that
@@ -937,7 +937,7 @@ foldlWithKey' f = go
 -}
 
 {--------------------------------------------------------------------
-  List variations 
+  List variations
 --------------------------------------------------------------------}
 
 -- | /O(n)/. Return all keys of the map in ascending order.
@@ -955,7 +955,7 @@ assocs m
   = toList m
 
 {--------------------------------------------------------------------
-  Lists 
+  Lists
   use [foldlStrict] to reduce demand on the control-stack
 --------------------------------------------------------------------}
 
@@ -963,7 +963,7 @@ assocs m
 -- If the list contains more than one value for the same key, the last value
 -- for the key is retained.
 fromList :: GCompare k => [DSum k f] -> DMap k f
-fromList xs       
+fromList xs
   = foldlStrict ins empty xs
   where
     ins :: GCompare k => DMap k f -> DSum k f -> DMap k f
@@ -971,7 +971,7 @@ fromList xs
 
 -- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWithKey'.
 fromListWithKey :: GCompare k => (forall v. k v -> f v -> f v -> f v) -> [DSum k f] -> DMap k f
-fromListWithKey f xs 
+fromListWithKey f xs
   = foldlStrict (ins f) empty xs
   where
     ins :: GCompare k => (forall v. k v -> f v -> f v -> f v) -> DMap k f -> DSum k f -> DMap k f
@@ -991,8 +991,8 @@ toDescList t  = foldlWithKey (\xs k x -> (k :=> x):xs) [] t
 
 {--------------------------------------------------------------------
   Building trees from ascending/descending lists can be done in linear time.
-  
-  Note that if [xs] is ascending that: 
+
+  Note that if [xs] is ascending that:
     fromAscList xs       == fromList xs
     fromAscListWith f xs == fromListWith f xs
 --------------------------------------------------------------------}
@@ -1006,7 +1006,7 @@ fromAscList xs
 -- | /O(n)/. Build a map from an ascending list in linear time with a
 -- combining function for equal keys.
 -- /The precondition (input list is ascending) is not checked./
-fromAscListWithKey :: GEq k => (forall v. k v -> f v -> f v -> f v) -> [DSum k f] -> DMap k f 
+fromAscListWithKey :: GEq k => (forall v. k v -> f v -> f v -> f v) -> [DSum k f] -> DMap k f
 fromAscListWithKey f xs
   = fromDistinctAscList (combineEq f xs)
   where
@@ -1032,12 +1032,12 @@ fromDistinctAscList xs
   = build const (length xs) xs
   where
     -- 1) use continutations so that we use heap space instead of stack space.
-    -- 2) special case for n==5 to build bushier trees. 
-    
+    -- 2) special case for n==5 to build bushier trees.
+
     build :: (DMap k f -> [DSum k f] -> b) -> Int -> [DSum k f] -> b
     build c 0 xs'  = c Tip xs'
     build c 5 xs'  = case xs' of
-                       ((k1:=>x1):(k2:=>x2):(k3:=>x3):(k4:=>x4):(k5:=>x5):xx) 
+                       ((k1:=>x1):(k2:=>x2):(k3:=>x3):(k4:=>x4):(k5:=>x5):xx)
                             -> c (bin k4 x4 (bin k2 x2 (singleton k1 x1) (singleton k3 x3)) (singleton k5 x5)) xx
                        _ -> error "fromDistinctAscList build"
     build c n xs'  = seq nr $ build (buildR nr c) nl xs'
@@ -1048,10 +1048,10 @@ fromDistinctAscList xs
     buildR :: Int -> (DMap k f -> [DSum k f] -> b) -> DMap k f -> [DSum k f] -> b
     buildR n c l ((k:=>x):ys) = build (buildB l k x c) n ys
     buildR _ _ _ []           = error "fromDistinctAscList buildR []"
-    
+
     buildB :: DMap k f -> k v -> f v -> (DMap k f -> a -> b) -> DMap k f -> a -> b
     buildB l k x c r zs       = c (bin k x l r) zs
-                      
+
 {--------------------------------------------------------------------
   Split
 --------------------------------------------------------------------}
@@ -1106,15 +1106,15 @@ splitLookupWithKey k = toTriple . go
       GEQ -> Triple' l (Just (kx, x)) r
 
 {--------------------------------------------------------------------
-  Eq converts the tree to a list. In a lazy setting, this 
-  actually seems one of the faster methods to compare two trees 
+  Eq converts the tree to a list. In a lazy setting, this
+  actually seems one of the faster methods to compare two trees
   and it is certainly the simplest :-)
 --------------------------------------------------------------------}
 instance EqTag k f => Eq (DMap k f) where
   t1 == t2  = (size t1 == size t2) && (toAscList t1 == toAscList t2)
 
 {--------------------------------------------------------------------
-  Ord 
+  Ord
 --------------------------------------------------------------------}
 
 instance OrdTag k f => Ord (DMap k f) where
@@ -1166,7 +1166,7 @@ showsTree showelem wide lbars rbars t
   = case t of
       Tip -> showsBars lbars . showString "|\n"
       Bin _ kx x Tip Tip
-          -> showsBars lbars . showString (showelem kx x) . showString "\n" 
+          -> showsBars lbars . showString (showelem kx x) . showString "\n"
       Bin _ kx x l r
           -> showsTree showelem wide (withBar rbars) (withEmpty rbars) r .
              showWide wide rbars .
@@ -1177,19 +1177,19 @@ showsTree showelem wide lbars rbars t
 showsTreeHang :: (forall v. k v -> f v -> String) -> Bool -> [String] -> DMap k f -> ShowS
 showsTreeHang showelem wide bars t
   = case t of
-      Tip -> showsBars bars . showString "|\n" 
+      Tip -> showsBars bars . showString "|\n"
       Bin _ kx x Tip Tip
-          -> showsBars bars . showString (showelem kx x) . showString "\n" 
+          -> showsBars bars . showString (showelem kx x) . showString "\n"
       Bin _ kx x l r
-          -> showsBars bars . showString (showelem kx x) . showString "\n" . 
+          -> showsBars bars . showString (showelem kx x) . showString "\n" .
              showWide wide bars .
              showsTreeHang showelem wide (withBar bars) l .
              showWide wide bars .
              showsTreeHang showelem wide (withEmpty bars) r
 
 showWide :: Bool -> [String] -> String -> String
-showWide wide bars 
-  | wide      = showString (concat (reverse bars)) . showString "|\n" 
+showWide wide bars
+  | wide      = showString (concat (reverse bars)) . showString "|\n"
   | otherwise = id
 
 showsBars :: [String] -> ShowS
@@ -1250,4 +1250,3 @@ foldlStrict f = go
   where
     go z []     = z
     go z (x:xs) = z `seq` go (f z x) xs
-

From 53405ebd66da99476bdd416ce43d979dd7e02e6e Mon Sep 17 00:00:00 2001
From: John Ericson <John.Ericson@Obsidian.Systems>
Date: Mon, 28 Jan 2019 18:09:12 -0500
Subject: [PATCH 02/10] Get rid of *Tag classes

Depends on https://github.com/mokus0/dependent-sum/pull/23. Also should
depend on getting rid of GHC <8 support. In this repo.
---
 dependent-map.cabal       |  3 ++-
 src/Data/Dependent/Map.hs | 32 +++++++++++++++++++++-----------
 2 files changed, 23 insertions(+), 12 deletions(-)

diff --git a/dependent-map.cabal b/dependent-map.cabal
index 29f15fb..e274307 100644
--- a/dependent-map.cabal
+++ b/dependent-map.cabal
@@ -42,6 +42,7 @@ Library
     build-depends:      semigroups
   build-depends:        base >= 3 && < 5,
                         containers,
-                        dependent-sum >= 0.3.2
+                        dependent-sum >= 0.3.2,
+                        constraints-extras >= 0.2.3.0 && < 0.3
   if impl(ghc >= 7.2) && impl(ghc < 7.8)
     ghc-options:        -trust base -trust dependent-sum
diff --git a/src/Data/Dependent/Map.hs b/src/Data/Dependent/Map.hs
index 7ff73f5..40a6f76 100644
--- a/src/Data/Dependent/Map.hs
+++ b/src/Data/Dependent/Map.hs
@@ -8,6 +8,8 @@
 #endif
 #if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 708
 {-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE UndecidableInstances #-}
 #endif
 module Data.Dependent.Map
     ( DMap
@@ -151,7 +153,9 @@ import Data.Dependent.Map.Typeable ({- instance Typeable ... -})
 #endif
 
 import Data.Dependent.Sum
+import Data.Constraint.Extras
 import Data.GADT.Compare
+import Data.GADT.Show
 import Data.Maybe (isJust)
 #if !MIN_VERSION_base(4,8,0)
 import Data.Monoid
@@ -717,8 +721,11 @@ intersectionWithKey f (Bin s1 k1 x1 l1 r1) t2 =
 -- | /O(n+m)/.
 -- This function is defined as (@'isSubmapOf' = 'isSubmapOfBy' 'eqTagged')@).
 --
-isSubmapOf :: (GCompare k, EqTag k f) => DMap k f -> DMap k f -> Bool
-isSubmapOf m1 m2 = isSubmapOfBy eqTagged m1 m2
+isSubmapOf
+  :: forall k f
+  .  (GCompare k, Has (ComposeC Eq f) k)
+  => DMap k f -> DMap k f -> Bool
+isSubmapOf m1 m2 = isSubmapOfBy (\k _ x0 x1 -> has @(ComposeC Eq f) k (x0 == x1)) m1 m2
 
 {- | /O(n+m)/.
  The expression (@'isSubmapOfBy' f t1 t2@) returns 'True' if
@@ -741,9 +748,12 @@ submap' f (Bin _ kx x l r) t
 
 -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' 'eqTagged'@).
-isProperSubmapOf :: (GCompare k, EqTag k f) => DMap k f -> DMap k f -> Bool
+isProperSubmapOf
+  :: forall k f
+  .  (GCompare k, Has (ComposeC Eq f) k)
+  => DMap k f -> DMap k f -> Bool
 isProperSubmapOf m1 m2
-  = isProperSubmapOfBy eqTagged m1 m2
+  = isProperSubmapOfBy (\k _ x0 x1 -> has @(ComposeC Eq f) k (x0 == x1)) m1 m2
 
 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
  The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
@@ -1110,21 +1120,21 @@ splitLookupWithKey k = toTriple . go
   actually seems one of the faster methods to compare two trees
   and it is certainly the simplest :-)
 --------------------------------------------------------------------}
-instance EqTag k f => Eq (DMap k f) where
+instance (GEq k, Has (ComposeC Eq f) k) => Eq (DMap k f) where
   t1 == t2  = (size t1 == size t2) && (toAscList t1 == toAscList t2)
 
 {--------------------------------------------------------------------
   Ord
 --------------------------------------------------------------------}
 
-instance OrdTag k f => Ord (DMap k f) where
-    compare m1 m2 = compare (toAscList m1) (toAscList m2)
+instance (GCompare k, Has (ComposeC Eq f) k, Has (ComposeC Ord f) k) => Ord (DMap k f) where
+  compare m1 m2 = compare (toAscList m1) (toAscList m2)
 
 {--------------------------------------------------------------------
   Read
 --------------------------------------------------------------------}
 
-instance (GCompare k, ReadTag k f) => Read (DMap k f) where
+instance (GCompare k, GRead k, Has (ComposeC Read f) k) => Read (DMap k f) where
   readPrec = parens $ prec 10 $ do
     Ident "fromList" <- lexP
     xs <- readPrec
@@ -1135,7 +1145,7 @@ instance (GCompare k, ReadTag k f) => Read (DMap k f) where
 {--------------------------------------------------------------------
   Show
 --------------------------------------------------------------------}
-instance ShowTag k f => Show (DMap k f) where
+instance (GShow k, Has (ComposeC Show f) k) => Show (DMap k f) where
     showsPrec p m = showParen (p>10)
         ( showString "fromList "
         . showsPrec 11 (toList m)
@@ -1143,11 +1153,11 @@ instance ShowTag k f => Show (DMap k f) where
 
 -- | /O(n)/. Show the tree that implements the map. The tree is shown
 -- in a compressed, hanging format. See 'showTreeWith'.
-showTree :: ShowTag k f => DMap k f -> String
+showTree :: (GShow k, Has (ComposeC Show f) k) => DMap k f -> String
 showTree m
   = showTreeWith showElem True False m
   where
-    showElem :: ShowTag k f => k v -> f v -> String
+    showElem :: (GShow k, Has (ComposeC Show f) k) => k v -> f v -> String
     showElem k x  = show (k :=> x)
 
 

From 14c657e2ccfdcccbe33130bc3ed93056f1ac27df Mon Sep 17 00:00:00 2001
From: Ali Abrar <aliabrar@gmail.com>
Date: Fri, 8 Feb 2019 22:36:31 -0500
Subject: [PATCH 03/10] Use Has' instead of ComposeC

---
 src/Data/Dependent/Map.hs | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/src/Data/Dependent/Map.hs b/src/Data/Dependent/Map.hs
index 40a6f76..91250cb 100644
--- a/src/Data/Dependent/Map.hs
+++ b/src/Data/Dependent/Map.hs
@@ -723,9 +723,9 @@ intersectionWithKey f (Bin s1 k1 x1 l1 r1) t2 =
 --
 isSubmapOf
   :: forall k f
-  .  (GCompare k, Has (ComposeC Eq f) k)
+  .  (GCompare k, Has' Eq k f)
   => DMap k f -> DMap k f -> Bool
-isSubmapOf m1 m2 = isSubmapOfBy (\k _ x0 x1 -> has @(ComposeC Eq f) k (x0 == x1)) m1 m2
+isSubmapOf m1 m2 = isSubmapOfBy (\k _ x0 x1 -> has' @Eq @f k (x0 == x1)) m1 m2
 
 {- | /O(n+m)/.
  The expression (@'isSubmapOfBy' f t1 t2@) returns 'True' if
@@ -750,10 +750,10 @@ submap' f (Bin _ kx x l r) t
 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' 'eqTagged'@).
 isProperSubmapOf
   :: forall k f
-  .  (GCompare k, Has (ComposeC Eq f) k)
+  .  (GCompare k, Has' Eq k f)
   => DMap k f -> DMap k f -> Bool
 isProperSubmapOf m1 m2
-  = isProperSubmapOfBy (\k _ x0 x1 -> has @(ComposeC Eq f) k (x0 == x1)) m1 m2
+  = isProperSubmapOfBy (\k _ x0 x1 -> has' @Eq @f k (x0 == x1)) m1 m2
 
 {- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
  The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
@@ -1120,21 +1120,21 @@ splitLookupWithKey k = toTriple . go
   actually seems one of the faster methods to compare two trees
   and it is certainly the simplest :-)
 --------------------------------------------------------------------}
-instance (GEq k, Has (ComposeC Eq f) k) => Eq (DMap k f) where
+instance (GEq k, Has' Eq k f) => Eq (DMap k f) where
   t1 == t2  = (size t1 == size t2) && (toAscList t1 == toAscList t2)
 
 {--------------------------------------------------------------------
   Ord
 --------------------------------------------------------------------}
 
-instance (GCompare k, Has (ComposeC Eq f) k, Has (ComposeC Ord f) k) => Ord (DMap k f) where
+instance (GCompare k, Has' Eq k f, Has' Ord k f) => Ord (DMap k f) where
   compare m1 m2 = compare (toAscList m1) (toAscList m2)
 
 {--------------------------------------------------------------------
   Read
 --------------------------------------------------------------------}
 
-instance (GCompare k, GRead k, Has (ComposeC Read f) k) => Read (DMap k f) where
+instance (GCompare k, GRead k, Has' Read k f) => Read (DMap k f) where
   readPrec = parens $ prec 10 $ do
     Ident "fromList" <- lexP
     xs <- readPrec
@@ -1145,7 +1145,7 @@ instance (GCompare k, GRead k, Has (ComposeC Read f) k) => Read (DMap k f) where
 {--------------------------------------------------------------------
   Show
 --------------------------------------------------------------------}
-instance (GShow k, Has (ComposeC Show f) k) => Show (DMap k f) where
+instance (GShow k, Has' Show k f) => Show (DMap k f) where
     showsPrec p m = showParen (p>10)
         ( showString "fromList "
         . showsPrec 11 (toList m)
@@ -1153,11 +1153,11 @@ instance (GShow k, Has (ComposeC Show f) k) => Show (DMap k f) where
 
 -- | /O(n)/. Show the tree that implements the map. The tree is shown
 -- in a compressed, hanging format. See 'showTreeWith'.
-showTree :: (GShow k, Has (ComposeC Show f) k) => DMap k f -> String
+showTree :: (GShow k, Has' Show k f) => DMap k f -> String
 showTree m
   = showTreeWith showElem True False m
   where
-    showElem :: (GShow k, Has (ComposeC Show f) k) => k v -> f v -> String
+    showElem :: (GShow k, Has' Show k f) => k v -> f v -> String
     showElem k x  = show (k :=> x)
 
 

From 5985aad23ed339bc8ebda5164cb16a379b0a2b39 Mon Sep 17 00:00:00 2001
From: John Ericson <John.Ericson@Obsidian.Systems>
Date: Tue, 12 Feb 2019 01:17:54 -0500
Subject: [PATCH 04/10] Get the Internals module ready for NonEmptyDMap

---
 src/Data/Dependent/Map.hs          |  98 ++++-----
 src/Data/Dependent/Map/Internal.hs | 316 ++++++++++++++++++++---------
 2 files changed, 266 insertions(+), 148 deletions(-)

diff --git a/src/Data/Dependent/Map.hs b/src/Data/Dependent/Map.hs
index 91250cb..cf9a8e1 100644
--- a/src/Data/Dependent/Map.hs
+++ b/src/Data/Dependent/Map.hs
@@ -254,11 +254,11 @@ insert kx x = kx `seq` go
             GLT -> let !l' = go l
                    in if l' `ptrEq` l
                       then t
-                      else balance ky y l' r
+                      else Bin' $! balance ky y l' r
             GGT -> let !r' = go r
                    in if r' `ptrEq` r
                       then t
-                      else balance ky y l r'
+                      else Bin' $! balance ky y l r'
             GEQ
               | kx `ptrEq` ky && x `ptrEq` y -> t
               | otherwise -> Bin sz kx x l r
@@ -275,11 +275,11 @@ insertR kx x = kx `seq` go
             GLT -> let !l' = go l
                    in if l' `ptrEq` l
                       then t
-                      else balance ky y l' r
+                      else Bin' $! balance ky y l' r
             GGT -> let !r' = go r
                    in if r' `ptrEq` r
                    then t
-                   else balance ky y l r'
+                   else Bin' $! balance ky y l r'
             GEQ -> t
 
 -- | /O(log n)/. Insert with a function, combining new value and old value.
@@ -308,8 +308,8 @@ insertWithKey f kx x = kx `seq` go
     go Tip = singleton kx x
     go (Bin sy ky y l r) =
         case gcompare kx ky of
-            GLT -> balance ky y (go l) r
-            GGT -> balance ky y l (go r)
+            GLT -> Bin' $! balance ky y (go l) r
+            GGT -> Bin' $! balance ky y l (go r)
             GEQ -> Bin sy kx (f kx x y) l r
 
 -- | Same as 'insertWithKey', but the combining function is applied strictly.
@@ -320,8 +320,8 @@ insertWithKey' f kx x = kx `seq` go
     go Tip = singleton kx $! x
     go (Bin sy ky y l r) =
         case gcompare kx ky of
-            GLT -> balance ky y (go l) r
-            GGT -> balance ky y l (go r)
+            GLT -> Bin' $! balance ky y (go l) r
+            GGT -> Bin' $! balance ky y l (go r)
             GEQ -> let x' = f kx x y in seq x' (Bin sy kx x' l r)
 
 -- | /O(log n)/. Combines insert operation with old value retrieval.
@@ -337,9 +337,9 @@ insertLookupWithKey f kx x = kx `seq` go
     go (Bin sy ky y l r) =
         case gcompare kx ky of
             GLT -> let (found, l') = go l
-                  in (found, balance ky y l' r)
+                  in (found, Bin' $! balance ky y l' r)
             GGT -> let (found, r') = go r
-                  in (found, balance ky y l r')
+                  in (found, Bin' $! balance ky y l r')
             GEQ -> (Just y, Bin sy kx (f kx x y) l r)
 
 -- | /O(log n)/. A strict version of 'insertLookupWithKey'.
@@ -352,9 +352,9 @@ insertLookupWithKey' f kx x = kx `seq` go
     go (Bin sy ky y l r) =
         case gcompare kx ky of
             GLT -> let (found, l') = go l
-                  in (found, balance ky y l' r)
+                  in (found, Bin' $! balance ky y l' r)
             GGT -> let (found, r') = go r
-                  in (found, balance ky y l r')
+                  in (found, Bin' $! balance ky y l r')
             GEQ -> let x' = f kx x y in x' `seq` (Just y, Bin sy kx x' l r)
 
 {--------------------------------------------------------------------
@@ -371,8 +371,8 @@ delete k = k `seq` go
     go Tip = Tip
     go (Bin _ kx x l r) =
         case gcompare k kx of
-            GLT -> balance kx x (go l) r
-            GGT -> balance kx x l (go r)
+            GLT -> Bin' $! balance kx x (go l) r
+            GGT -> Bin' $! balance kx x l (go r)
             GEQ -> glue l r
 
 -- | /O(log n)/. Update a value at a specific key with the result of the provided function.
@@ -423,8 +423,8 @@ updateWithKey f k = k `seq` go
     go Tip = Tip
     go (Bin sx kx x l r) =
         case gcompare k kx of
-           GLT -> balance kx x (go l) r
-           GGT -> balance kx x l (go r)
+           GLT -> Bin' $! balance kx x (go l) r
+           GGT -> Bin' $! balance kx x l (go r)
            GEQ -> case f kx x of
                    Just x' -> Bin sx kx x' l r
                    Nothing -> glue l r
@@ -439,8 +439,8 @@ updateLookupWithKey f k = k `seq` go
    go Tip = (Nothing,Tip)
    go (Bin sx kx x l r) =
           case gcompare k kx of
-               GLT -> let (found,l') = go l in (found,balance kx x l' r)
-               GGT -> let (found,r') = go r in (found,balance kx x l r')
+               GLT -> let (found,l') = go l in (found,Bin' $! balance kx x l' r)
+               GGT -> let (found,r') = go r in (found,Bin' $! balance kx x l r')
                GEQ -> case f kx x of
                        Just x' -> (Just x',Bin sx kx x' l r)
                        Nothing -> (Just x,glue l r)
@@ -457,8 +457,8 @@ alter f k = k `seq` go
                Just x  -> singleton k x
 
     go (Bin sx kx x l r) = case gcompare k kx of
-               GLT -> balance kx x (go l) r
-               GGT -> balance kx x l (go r)
+               GLT -> Bin' $! balance kx x (go l) r
+               GGT -> Bin' $! balance kx x l (go r)
                GEQ -> case f (Just x) of
                        Just x' -> Bin sx kx x' l r
                        Nothing -> glue l r
@@ -472,8 +472,8 @@ alterF k f = go
     go Tip = maybe Tip (singleton k) <$> f Nothing
 
     go (Bin sx kx x l r) = case gcompare k kx of
-      GLT -> (\l' -> balance kx x l' r) <$> go l
-      GGT -> (\r' -> balance kx x l r') <$> go r
+      GLT -> (\l' -> Bin' $! balance kx x l' r) <$> go l
+      GGT -> (\r' -> Bin' $! balance kx x l r') <$> go r
       GEQ -> maybe (glue l r) (\x' -> Bin sx kx x' l r) <$> f (Just x)
 
 {--------------------------------------------------------------------
@@ -521,8 +521,8 @@ updateAt f i0 t = i0 `seq` go i0 t
  where
     go _ Tip  = Tip
     go i (Bin sx kx x l r) = case compare i sizeL of
-      LT -> balance kx x (go i l) r
-      GT -> balance kx x l (go (i-sizeL-1) r)
+      LT -> Bin' $! balance kx x (go i l) r
+      GT -> Bin' $! balance kx x l (go (i-sizeL-1) r)
       EQ -> case f kx x of
               Just x' -> Bin sx kx x' l r
               Nothing -> glue l r
@@ -573,13 +573,13 @@ lookupMax m = case m of
 -- | /O(log n)/. Delete the minimal key. Returns an empty map if the map is empty.
 deleteMin :: DMap k f -> DMap k f
 deleteMin (Bin _ _  _ Tip r)  = r
-deleteMin (Bin _ kx x l r)    = balance kx x (deleteMin l) r
+deleteMin (Bin _ kx x l r)    = Bin' $! balance kx x (deleteMin l) r
 deleteMin Tip                 = Tip
 
 -- | /O(log n)/. Delete the maximal key. Returns an empty map if the map is empty.
 deleteMax :: DMap k f -> DMap k f
 deleteMax (Bin _ _  _ l Tip)  = l
-deleteMax (Bin _ kx x l r)    = balance kx x l (deleteMax r)
+deleteMax (Bin _ kx x l r)    = Bin' $! balance kx x l (deleteMax r)
 deleteMax Tip                 = Tip
 
 -- | /O(log n)/. Update the value at the minimal key.
@@ -589,7 +589,7 @@ updateMinWithKey f = go
     go (Bin sx kx x Tip r) = case f kx x of
                                   Nothing -> r
                                   Just x' -> Bin sx kx x' Tip r
-    go (Bin _ kx x l r)    = balance kx x (go l) r
+    go (Bin _ kx x l r)    = Bin' $! balance kx x (go l) r
     go Tip                 = Tip
 
 -- | /O(log n)/. Update the value at the maximal key.
@@ -599,7 +599,7 @@ updateMaxWithKey f = go
     go (Bin sx kx x l Tip) = case f kx x of
                               Nothing -> l
                               Just x' -> Bin sx kx x' l Tip
-    go (Bin _ kx x l r)    = balance kx x l (go r)
+    go (Bin _ kx x l r)    = Bin' $! balance kx x l (go r)
     go Tip                 = Tip
 
 {--------------------------------------------------------------------
@@ -630,7 +630,7 @@ union (Bin _ kx x Tip Tip) t2 = insert kx x t2
 union t1@(Bin _ k1 x1 l1 r1) t2 = case split k1 t2 of
   (l2, r2)
     | l1 `ptrEq` l1l2 && r1 `ptrEq` r1r2 -> t1
-    | otherwise -> combine k1 x1 l1l2 r1r2
+    | otherwise -> Bin' $! combine k1 x1 l1l2 r1r2
     where !l1l2 = l1 `union` l2
           !r1r2 = r1 `union` r2
 
@@ -645,8 +645,8 @@ unionWithKey _ t1 Tip  = t1
 unionWithKey _ Tip t2  = t2
 unionWithKey f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of
   (l2, mx2, r2) -> case mx2 of
-      Nothing -> combine k1 x1 l1l2 r1r2
-      Just x2 -> combine k1 (f k1 x1 x2) l1l2 r1r2
+      Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
+      Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
     where !l1l2 = unionWithKey f l1 l2
           !r1r2 = unionWithKey f r1 r2
 
@@ -676,10 +676,10 @@ differenceWithKey _ Tip _   = Tip
 differenceWithKey _ t1 Tip  = t1
 differenceWithKey f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of
   (l2, mx2, r2) -> case mx2 of
-      Nothing -> combine k1 x1 l1l2 r1r2
+      Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
       Just x2 -> case f k1 x1 x2 of
         Nothing -> merge l1l2 r1r2
-        Just x1x2 -> combine k1 x1x2 l1l2 r1r2
+        Just x1x2 -> Bin' $! combine k1 x1x2 l1l2 r1r2
     where !l1l2 = differenceWithKey f l1 l2
           !r1r2 = differenceWithKey f r1 r2
 
@@ -700,7 +700,7 @@ intersection t1@(Bin s1 k1 x1 l1 r1) t2 =
   in if found
      then if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1
           then t1
-          else combine k1 x1 l1l2 r1r2
+          else Bin' $! combine k1 x1 l1l2 r1r2
      else merge l1l2 r1r2
 
 -- | /O(m * log (n\/m + 1), m <= n/. Intersection with a combining function.
@@ -713,7 +713,7 @@ intersectionWithKey f (Bin s1 k1 x1 l1 r1) t2 =
       !r1r2 = intersectionWithKey f r1 r2
   in case found of
        Nothing -> merge l1l2 r1r2
-       Just x2 -> combine k1 (f k1 x1 x2) l1l2 r1r2
+       Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
 
 {--------------------------------------------------------------------
   Submap
@@ -777,7 +777,7 @@ filterWithKey p = go
     go t@(Bin _ kx x l r)
       | p kx x    = if l' `ptrEq` l && r' `ptrEq` r
                     then t
-                    else combine kx x l' r'
+                    else Bin' $! combine kx x l' r'
       | otherwise = merge l' r'
       where !l' = go l
             !r' = go r
@@ -791,8 +791,8 @@ partitionWithKey p0 m0 = toPair (go p0 m0)
     go :: GCompare k => (forall v. k v -> f v -> Bool) -> DMap k f -> (DMap k f :*: DMap k f)
     go _ Tip = (Tip :*: Tip)
     go p (Bin _ kx x l r)
-      | p kx x    = (combine kx x l1 r1 :*: merge l2 r2)
-      | otherwise = (merge l1 r1 :*: combine kx x l2 r2)
+      | p kx x    = ((Bin' $! combine kx x l1 r1) :*: merge l2 r2)
+      | otherwise = (merge l1 r1 :*: (Bin' $! combine kx x l2 r2))
       where
         (l1 :*: l2) = go p l
         (r1 :*: r2) = go p r
@@ -807,7 +807,7 @@ mapMaybeWithKey f = go
   where
     go Tip = Tip
     go (Bin _ kx x l r) = case f kx x of
-        Just y  -> combine kx y (go l) (go r)
+        Just y  -> Bin' $! combine kx y (go l) (go r)
         Nothing -> merge (go l) (go r)
 
 -- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
@@ -820,8 +820,8 @@ mapEitherWithKey f0 = toPair . go f0
        -> DMap k f -> (DMap k g :*: DMap k h)
     go _ Tip = (Tip :*: Tip)
     go f (Bin _ kx x l r) = case f kx x of
-      Left y  -> (combine kx y l1 r1 :*: merge l2 r2)
-      Right z -> (merge l1 r1 :*: combine kx z l2 r2)
+      Left y  -> ((Bin' $! combine kx y l1 r1) :*: merge l2 r2)
+      Right z -> (merge l1 r1 :*: (Bin' $! combine kx z l2 r2))
       where
         (l1,l2) = mapEitherWithKey f l
         (r1,r2) = mapEitherWithKey f r
@@ -1075,8 +1075,8 @@ split k = toPair . go
     go :: DMap k f -> (DMap k f :*: DMap k f)
     go Tip              = (Tip :*: Tip)
     go (Bin _ kx x l r) = case gcompare k kx of
-          GLT -> let !(lt :*: gt) = go l in (lt :*: combine kx x gt r)
-          GGT -> let !(lt :*: gt) = go r in (combine kx x l lt :*: gt)
+          GLT -> let !(lt :*: gt) = go l in (lt :*: (Bin' $! combine kx x gt r))
+          GGT -> let !(lt :*: gt) = go r in ((Bin' $! combine kx x l lt) :*: gt)
           GEQ -> (l :*: r)
 {-# INLINABLE split #-}
 
@@ -1088,8 +1088,8 @@ splitLookup k = toTriple . go
     go :: DMap k f -> Triple' (DMap k f) (Maybe (f v)) (DMap k f)
     go Tip              = Triple' Tip Nothing Tip
     go (Bin _ kx x l r) = case gcompare k kx of
-      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (combine kx x gt r)
-      GGT -> let !(Triple' lt z gt) = go r in Triple' (combine kx x l lt) z gt
+      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
+      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
       GEQ -> Triple' l (Just x) r
 
 -- | /O(log n)/. The expression (@'splitMember' k map@) splits a map just
@@ -1100,8 +1100,8 @@ splitMember k = toTriple . go
     go :: DMap k f -> Triple' (DMap k f) Bool (DMap k f)
     go Tip              = Triple' Tip False Tip
     go (Bin _ kx x l r) = case gcompare k kx of
-      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (combine kx x gt r)
-      GGT -> let !(Triple' lt z gt) = go r in Triple' (combine kx x l lt) z gt
+      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
+      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
       GEQ -> Triple' l True r
 
 -- | /O(log n)/.
@@ -1111,8 +1111,8 @@ splitLookupWithKey k = toTriple . go
     go :: DMap k f -> Triple' (DMap k f) (Maybe (k v, f v)) (DMap k f)
     go Tip              = Triple' Tip Nothing Tip
     go (Bin _ kx x l r) = case gcompare k kx of
-      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (combine kx x gt r)
-      GGT -> let !(Triple' lt z gt) = go r in Triple' (combine kx x l lt) z gt
+      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
+      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
       GEQ -> Triple' l (Just (kx, x)) r
 
 {--------------------------------------------------------------------
diff --git a/src/Data/Dependent/Map/Internal.hs b/src/Data/Dependent/Map/Internal.hs
index 5596144..54f77cc 100644
--- a/src/Data/Dependent/Map/Internal.hs
+++ b/src/Data/Dependent/Map/Internal.hs
@@ -10,8 +10,12 @@
 #if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 708
 {-# LANGUAGE PolyKinds #-}
 #endif
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE PatternSynonyms #-}
 module Data.Dependent.Map.Internal where
 
+import Prelude hiding (lookup)
+
 import Data.Dependent.Sum
 import Data.GADT.Compare
 import Data.Some
@@ -31,14 +35,23 @@ import Data.Typeable (Typeable)
 -- More informally, 'DMap' is to dependent products as 'M.Map' is to @(->)@.
 -- Thus it could also be thought of as a partial (in the sense of \"partial
 -- function\") dependent product.
-data DMap k f where
-    Tip :: DMap k f
-    Bin :: {- sz    -} !Int
-        -> {- key   -} !(k v)
-        -> {- value -} f v
-        -> {- left  -} !(DMap k f)
-        -> {- right -} !(DMap k f)
-        -> DMap k f
+data DMap k f
+  = Tip
+  | Bin' {-# UNPACK #-} !(NonEmptyDMap k f)
+#if MIN_VERSION_base(4,7,0)
+    deriving Typeable
+#endif
+
+pattern Bin s k v l r = Bin' (NonEmptyDMap s k v l r)
+
+data NonEmptyDMap k f where
+    NonEmptyDMap
+         :: {- sz    -} !Int
+         -> {- key   -} !(k v)
+         -> {- value -} f v
+         -> {- left  -} !(DMap k f)
+         -> {- right -} !(DMap k f)
+         -> NonEmptyDMap k f
 #if MIN_VERSION_base(4,7,0)
     deriving Typeable
 #endif
@@ -54,12 +67,19 @@ data DMap k f where
 empty :: DMap k f
 empty = Tip
 
+-- | /O(1)/. A map with a single element.
+--
+-- > singleton 1 'a'        == fromList [(1, 'a')]
+-- > size (singleton 1 'a') == 1
+singletonNE :: k v -> f v -> NonEmptyDMap k f
+singletonNE k x = NonEmptyDMap 1 k x Tip Tip
+
 -- | /O(1)/. A map with a single element.
 --
 -- > singleton 1 'a'        == fromList [(1, 'a')]
 -- > size (singleton 1 'a') == 1
 singleton :: k v -> f v -> DMap k f
-singleton k x = Bin 1 k x Tip Tip
+singleton k x = Bin' $! singletonNE k x
 
 {--------------------------------------------------------------------
   Query
@@ -68,38 +88,51 @@ singleton k x = Bin 1 k x Tip Tip
 -- | /O(1)/. Is the map empty?
 null :: DMap k f -> Bool
 null Tip    = True
-null Bin{}  = False
+null Bin'{}  = False
+
+-- | /O(1)/. The number of elements in the map.
+sizeNE :: NonEmptyDMap k f -> Int
+sizeNE (NonEmptyDMap n _ _ _ _) = n
 
 -- | /O(1)/. The number of elements in the map.
 size :: DMap k f -> Int
-size Tip                = 0
-size (Bin n _ _ _ _)    = n
+size Tip      = 0
+size (Bin' ne) = sizeNE ne
+
+-- | /O(log n)/. Lookup the value at a key in the map.
+--
+-- The function will return the corresponding value as @('Just' value)@,
+-- or 'Nothing' if the key isn't in the map.
+lookupNE :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> Maybe (f v)
+lookupNE k ne = k `seq` lookupNE' k ne
+
+-- | Skips the seq
+{-# INLINE lookupNE' #-}
+lookupNE' :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> Maybe (f v)
+lookupNE' k (NonEmptyDMap _ kx x l r) = case gcompare k kx of
+    GLT -> lookup' k l
+    GGT -> lookup' k r
+    GEQ -> Just x
 
 -- | /O(log n)/. Lookup the value at a key in the map.
 --
 -- The function will return the corresponding value as @('Just' value)@,
 -- or 'Nothing' if the key isn't in the map.
 lookup :: forall k f v. GCompare k => k v -> DMap k f -> Maybe (f v)
-lookup k = k `seq` go
-    where
-        go :: DMap k f -> Maybe (f v)
-        go Tip = Nothing
-        go (Bin _ kx x l r) = 
-            case gcompare k kx of
-                GLT -> go l
-                GGT -> go r
-                GEQ -> Just x
+lookup k m = k `seq` lookup' k m
+
+-- | Skips the seq
+{-# INLINE lookup' #-}
+lookup' :: forall k f v. GCompare k => k v -> DMap k f -> Maybe (f v)
+lookup' k = \case
+    Tip -> Nothing
+    (Bin' ne) -> lookupNE' k ne
+
+lookupAssocNE :: forall k f v. GCompare k => Some k -> NonEmptyDMap k f -> Maybe (DSum k f)
+lookupAssocNE (This k) m = (k :=>) <$> lookupNE k m
 
 lookupAssoc :: forall k f v. GCompare k => Some k -> DMap k f -> Maybe (DSum k f)
-lookupAssoc (This k) = k `seq` go
-  where
-    go :: DMap k f -> Maybe (DSum k f)
-    go Tip = Nothing
-    go (Bin _ kx x l r) =
-        case gcompare k kx of
-            GLT -> go l
-            GGT -> go r
-            GEQ -> Just (kx :=> x)
+lookupAssoc (This k) m = (k :=>) <$> lookup k m
 
 {--------------------------------------------------------------------
   Utility functions that maintain the balance properties of the tree.
@@ -107,7 +140,7 @@ lookupAssoc (This k) = k `seq` go
   in [r] > [k], and that [l] and [r] are valid trees.
   
   In order of sophistication:
-    [Bin sz k x l r]  The type constructor.
+    [Bin' sz k x l r]  The type constructor.
     [bin k x l r]     Maintains the correct size, assumes that both [l]
                       and [r] are balanced with respect to each other.
     [balance k x l r] Restores the balance and size.
@@ -133,60 +166,85 @@ lookupAssoc (This k) = k `seq` go
 {--------------------------------------------------------------------
   Combine
 --------------------------------------------------------------------}
-combine :: GCompare k => k v -> f v -> DMap k f -> DMap k f -> DMap k f
+combineNE :: GCompare k => k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+combineNE kx x l@(NonEmptyDMap sizeL ky y ly ry) r@(NonEmptyDMap sizeR kz z lz rz)
+    | delta*sizeL <= sizeR  = balanceNEL kz z (combineNEL kx x l lz) rz
+    | delta*sizeR <= sizeL  = balanceNER ky y ly (combineNER kx x ry r)
+    | otherwise             = binNE kx x (Bin' l) (Bin' r)
+
+combineNEL :: GCompare k => k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
+combineNEL kx x l Tip = insertMaxNE kx x l
+combineNEL kx x l (Bin' r) = combineNE kx x l r
+
+combineNER :: GCompare k => k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+combineNER kx x Tip r = insertMinNE kx x r
+combineNER kx x (Bin' l) r = combineNE kx x l r
+
+combine :: GCompare k => k v -> f v -> DMap k f -> DMap k f -> NonEmptyDMap k f
 combine kx x Tip r  = insertMin kx x r
 combine kx x l Tip  = insertMax kx x l
-combine kx x l@(Bin sizeL ky y ly ry) r@(Bin sizeR kz z lz rz)
-  | delta*sizeL <= sizeR  = balance kz z (combine kx x l lz) rz
-  | delta*sizeR <= sizeL  = balance ky y ly (combine kx x ry r)
-  | otherwise             = bin kx x l r
-
+combine kx x (Bin' l) (Bin' r) = combineNE kx x l r
 
 -- insertMin and insertMax don't perform potentially expensive comparisons.
-insertMax,insertMin :: k v -> f v -> DMap k f -> DMap k f
-insertMax kx x t
-  = case t of
-      Tip -> singleton kx x
-      Bin _ ky y l r
-          -> balance ky y l (insertMax kx x r)
-             
-insertMin kx x t
-  = case t of
-      Tip -> singleton kx x
-      Bin _ ky y l r
-          -> balance ky y (insertMin kx x l) r
+
+insertMaxNE, insertMinNE :: k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f
+insertMaxNE kx x (NonEmptyDMap _ ky y l r) = balanceNER ky y l (insertMax kx x r)
+insertMinNE kx x (NonEmptyDMap _ ky y l r) = balanceNEL ky y (insertMin kx x l) r
+
+insertMax, insertMin :: k v -> f v -> DMap k f -> NonEmptyDMap k f
+insertMax kx x t  = case t of
+    Tip -> singletonNE kx x
+    Bin' ne -> insertMaxNE kx x ne
              
+insertMin kx x t = case t of
+    Tip -> singletonNE kx x
+    Bin' ne -> insertMinNE kx x ne
+
 {--------------------------------------------------------------------
   [merge l r]: merges two trees.
 --------------------------------------------------------------------}
+mergeNE :: NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+mergeNE l@(NonEmptyDMap sizeL kx x lx rx) r@(NonEmptyDMap sizeR ky y ly ry)
+    | delta*sizeL <= sizeR = balanceNEL ky y (mergeNEL l ly) ry
+    | delta*sizeR <= sizeL = balanceNER kx x lx (mergeNER rx r)
+    | otherwise            = glueNE l r
+
+mergeNEL :: NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
+mergeNEL l Tip = l
+mergeNEL l (Bin' r) = mergeNE l r
+
+mergeNER :: DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+mergeNER Tip r = r
+mergeNER (Bin' l) r = mergeNE l r
+
 merge :: DMap k f -> DMap k f -> DMap k f
 merge Tip r   = r
 merge l Tip   = l
-merge l@(Bin sizeL kx x lx rx) r@(Bin sizeR ky y ly ry)
-  | delta*sizeL <= sizeR = balance ky y (merge l ly) ry
-  | delta*sizeR <= sizeL = balance kx x lx (merge rx r)
-  | otherwise            = glue l r
+merge (Bin' l) (Bin' r) = Bin' $! mergeNE l r
 
 {--------------------------------------------------------------------
   [glue l r]: glues two trees together.
   Assumes that [l] and [r] are already balanced with respect to each other.
 --------------------------------------------------------------------}
+glueNE :: NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+glueNE l r 
+    | sizeNE l > sizeNE r = case deleteFindMax l of
+        (km :=> m, l') -> balanceNER km m l' r
+    | otherwise = case deleteFindMin r of
+        (km :=> m, r') -> balanceNEL km m l r'
+
 glue :: DMap k f -> DMap k f -> DMap k f
 glue Tip r = r
 glue l Tip = l
-glue l r   
-  | size l > size r = case deleteFindMax l of (km :=> m,l') -> balance km m l' r
-  | otherwise       = case deleteFindMin r of (km :=> m,r') -> balance km m l r'
+glue (Bin' l) (Bin' r) = Bin' $! glueNE l r
 
 -- | /O(log n)/. Delete and find the minimal element.
 --
 -- > deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")]) 
 -- > deleteFindMin                                            Error: can not return the minimal element of an empty map
 
-deleteFindMin :: DMap k f -> (DSum k f, DMap k f)
-deleteFindMin t = case minViewWithKey t of
-      Nothing -> (error "Map.deleteFindMin: can not return the minimal element of an empty map", Tip)
-      Just p -> p
+deleteFindMin :: NonEmptyDMap k f -> (DSum k f, DMap k f)
+deleteFindMin = minViewWithKeyNE
 
 -- | A strict pair.
 data (:*:) a b = !a :*: !b
@@ -205,40 +263,46 @@ toTriple (Triple' a b c) = (a, b, c)
 {-# INLINE toTriple #-}
 
 -- | /O(log n)/. Retrieves the minimal (key :=> value) entry of the map, and
--- the map stripped of that element, or 'Nothing' if passed an empty map.
-minViewWithKey :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
-minViewWithKey Tip = Nothing
-minViewWithKey (Bin _ k0 x0 l0 r0) = Just $! toPair $ go k0 x0 l0 r0
+-- the map stripped of that element
+minViewWithKeyNE :: forall k f . NonEmptyDMap k f -> (DSum k f, DMap k f)
+minViewWithKeyNE (NonEmptyDMap _ k0 x0 l0 r0) = toPair $ go k0 x0 l0 r0
   where
     go :: k v -> f v -> DMap k f -> DMap k f -> DSum k f :*: DMap k f
     go k x Tip r = (k :=> x) :*: r
     go k x (Bin _ kl xl ll lr) r =
       let !(km :*: l') = go kl xl ll lr
-      in (km :*: balance k x l' r)
+      in (km :*: (Bin' $! balance k x l' r))
+
+-- | /O(log n)/. Retrieves the minimal (key :=> value) entry of the map, and
+-- the map stripped of that element, or 'Nothing' if passed an empty map.
+minViewWithKey :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
+minViewWithKey Tip = Nothing
+minViewWithKey (Bin' ne) = Just $! minViewWithKeyNE ne
 
 -- | /O(log n)/. Retrieves the maximal (key :=> value) entry of the map, and
 -- the map stripped of that element, or 'Nothing' if passed an empty map.
-maxViewWithKey :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
-maxViewWithKey Tip = Nothing
-maxViewWithKey (Bin _ k0 x0 l0 r0) = Just $! toPair $ go k0 x0 l0 r0
+maxViewWithKeyNE :: forall k f . NonEmptyDMap k f -> (DSum k f, DMap k f)
+maxViewWithKeyNE (NonEmptyDMap _ k0 x0 l0 r0) = toPair $ go k0 x0 l0 r0
   where
     go :: k v -> f v -> DMap k f -> DMap k f -> DSum k f :*: DMap k f
     go k x l Tip = (k :=> x) :*: l
     go k x l (Bin _ kr xr rl rr) =
       let !(km :*: r') = go kr xr rl rr
-      in (km :*: balance k x l r')
+      in (km :*: (Bin' $! balance k x l r'))
+
+-- | /O(log n)/. Retrieves the maximal (key :=> value) entry of the map, and
+-- the map stripped of that element, or 'Nothing' if passed an empty map.
+maxViewWithKey :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
+maxViewWithKey Tip = Nothing
+maxViewWithKey (Bin' ne) = Just $! maxViewWithKeyNE ne
 
 -- | /O(log n)/. Delete and find the maximal element.
 --
 -- > deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")])
 -- > deleteFindMax empty                                      Error: can not return the maximal element of an empty map
 
-deleteFindMax :: DMap k f -> (DSum k f, DMap k f)
-deleteFindMax t
-  = case t of
-      Bin _ k x l Tip -> (k :=> x,l)
-      Bin _ k x l r   -> let (km,r') = deleteFindMax r in (km,balance k x l r')
-      Tip             -> (error "Map.deleteFindMax: can not return the maximal element of an empty map", Tip)
+deleteFindMax :: NonEmptyDMap k f -> (DSum k f, DMap k f)
+deleteFindMax = maxViewWithKeyNE
 
 
 {--------------------------------------------------------------------
@@ -275,49 +339,103 @@ delta,ratio :: Int
 delta = 4
 ratio = 2
 
-balance :: k v -> f v -> DMap k f -> DMap k f -> DMap k f
-balance k x l r
-  | sizeL + sizeR <= 1    = Bin sizeX k x l r
-  | sizeR >= delta*sizeL  = rotateL k x l r
+-- TODO delete these
+
+balanceNE :: k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+balanceNE k x l r
+  | sizeL + sizeR <= 1    = NonEmptyDMap sizeX k x (Bin' l) (Bin' r)
+  | sizeR >= delta*sizeL  = rotateL k x (Bin' l) r
+  | sizeL >= delta*sizeR  = rotateR k x l (Bin' r)
+  | otherwise             = NonEmptyDMap sizeX k x (Bin' l) (Bin' r)
+  where
+    sizeL = sizeNE l
+    sizeR = sizeNE r
+    sizeX = sizeL + sizeR + 1
+
+balanceNEL :: k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
+balanceNEL k x l r
+  | sizeL + sizeR <= 1    = NonEmptyDMap sizeX k x (Bin' l) r
+  | sizeR >= delta*sizeL  = let
+      r' = case r of
+          Tip -> error "balanceNEL: Declared size of 'r' is greater than 1, shouldn't be empty"
+          Bin' ne -> ne
+    in rotateL k x (Bin' l) r'
   | sizeL >= delta*sizeR  = rotateR k x l r
-  | otherwise             = Bin sizeX k x l r
+  | otherwise             = NonEmptyDMap sizeX k x (Bin' l) r
+  where
+    sizeL = sizeNE l
+    sizeR = size r
+    sizeX = sizeL + sizeR + 1
+
+balanceNER :: k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+balanceNER k x l r
+  | sizeL + sizeR <= 1    = NonEmptyDMap sizeX k x l (Bin' r)
+  | sizeR >= delta*sizeL  = rotateL k x l r
+  | sizeL >= delta*sizeR  = let
+      l' = case l of
+          Tip -> error "balanceNER: Declared size of 'l' is greater than 1, shouldn't be empty"
+          Bin' ne -> ne
+    in rotateR k x l' (Bin' r)
+  | otherwise             = NonEmptyDMap sizeX k x l (Bin' r)
+  where
+    sizeL = size l
+    sizeR = sizeNE r
+    sizeX = sizeL + sizeR + 1
+
+
+balance :: k v -> f v -> DMap k f -> DMap k f -> NonEmptyDMap k f
+balance k x l r
+  | sizeL + sizeR <= 1    = NonEmptyDMap sizeX k x l r
+  | sizeR >= delta*sizeL  = let
+      r' = case r of
+          Tip -> error "balance: Declared size of 'r' is greater than 1, shouldn't be empty"
+          Bin' ne -> ne
+    in rotateL k x l r'
+  | sizeL >= delta*sizeR  = let
+      l' = case l of
+          Tip -> error "balance: Declared size of 'l' is greater than 1, shouldn't be empty"
+          Bin' ne -> ne
+    in rotateR k x l' r
+  | otherwise             = NonEmptyDMap sizeX k x l r
   where
     sizeL = size l
     sizeR = size r
     sizeX = sizeL + sizeR + 1
 
 -- rotate
-rotateL :: k v -> f v -> DMap k f -> DMap k f -> DMap k f
-rotateL k x l r@(Bin _ _ _ ly ry)
+rotateL :: k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+rotateL k x l r@(NonEmptyDMap _ _ _ ly ry)
   | size ly < ratio*size ry = singleL k x l r
   | otherwise               = doubleL k x l r
-rotateL _ _ _ Tip = error "rotateL Tip"
 
-rotateR :: k v -> f v -> DMap k f -> DMap k f -> DMap k f
-rotateR k x l@(Bin _ _ _ ly ry) r
+rotateR :: k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
+rotateR k x l@(NonEmptyDMap _ _ _ ly ry) r
   | size ry < ratio*size ly = singleR k x l r
   | otherwise               = doubleR k x l r
-rotateR _ _ Tip _ = error "rotateR Tip"
 
 -- basic rotations
-singleL, singleR :: k v -> f v -> DMap k f -> DMap k f -> DMap k f
-singleL k1 x1 t1 (Bin _ k2 x2 t2 t3)  = bin k2 x2 (bin k1 x1 t1 t2) t3
-singleL _ _ _ Tip = error "singleL Tip"
-singleR k1 x1 (Bin _ k2 x2 t1 t2) t3  = bin k2 x2 t1 (bin k1 x1 t2 t3)
-singleR _ _ Tip _ = error "singleR Tip"
-
-doubleL, doubleR :: k v -> f v -> DMap k f -> DMap k f -> DMap k f
-doubleL k1 x1 t1 (Bin _ k2 x2 (Bin _ k3 x3 t2 t3) t4) = bin k3 x3 (bin k1 x1 t1 t2) (bin k2 x2 t3 t4)
+singleL :: k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+singleL k1 x1 t1 (NonEmptyDMap _ k2 x2 t2 t3)  = binNE k2 x2 (bin k1 x1 t1 t2) t3
+
+singleR :: k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
+singleR k1 x1 (NonEmptyDMap _ k2 x2 t1 t2) t3  = binNE k2 x2 t1 (bin k1 x1 t2 t3)
+
+doubleL :: k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+doubleL k1 x1 t1 (NonEmptyDMap _ k2 x2 (Bin _ k3 x3 t2 t3) t4) = binNE k3 x3 (bin k1 x1 t1 t2) (bin k2 x2 t3 t4)
 doubleL _ _ _ _ = error "doubleL"
-doubleR k1 x1 (Bin _ k2 x2 t1 (Bin _ k3 x3 t2 t3)) t4 = bin k3 x3 (bin k2 x2 t1 t2) (bin k1 x1 t3 t4)
+
+doubleR :: k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
+doubleR k1 x1 (NonEmptyDMap _ k2 x2 t1 (Bin _ k3 x3 t2 t3)) t4 = binNE k3 x3 (bin k2 x2 t1 t2) (bin k1 x1 t3 t4)
 doubleR _ _ _ _ = error "doubleR"
 
 {--------------------------------------------------------------------
   The bin constructor maintains the size of the tree
 --------------------------------------------------------------------}
+binNE :: k v -> f v -> DMap k f -> DMap k f -> NonEmptyDMap k f
+binNE k x l r = NonEmptyDMap (size l + size r + 1) k x l r
+
 bin :: k v -> f v -> DMap k f -> DMap k f -> DMap k f
-bin k x l r
-  = Bin (size l + size r + 1) k x l r
+bin k x l r = Bin' $! binNE k x l r
 
 {--------------------------------------------------------------------
   Utility functions that return sub-ranges of the original
@@ -370,7 +488,7 @@ filterGt cmp = go
   where
     go Tip              = Tip
     go (Bin _ kx x l r) = case cmp (This kx) of
-              LT -> combine kx x (go l) r
+              LT -> Bin' $! combine kx x (go l) r
               GT -> go r
               EQ -> r
 
@@ -380,5 +498,5 @@ filterLt cmp = go
     go Tip              = Tip
     go (Bin _ kx x l r) = case cmp (This kx) of
           LT -> go l
-          GT -> combine kx x l (go r)
+          GT -> Bin' $! combine kx x l (go r)
           EQ -> l

From 403b7e90eb271d61af037b2a09373ba032ac6f0d Mon Sep 17 00:00:00 2001
From: John Ericson <John.Ericson@Obsidian.Systems>
Date: Tue, 12 Feb 2019 01:17:13 -0500
Subject: [PATCH 05/10] Create NonEmptyDMap

Do this by factor out just about all explicity recursive DMap functions
into mutually recursive DMap and NonEmptyDMap functions. This largely
deduplicates the implementation of both, while ensuring that neither has
extra indirection/imbalances.
---
 dependent-map.cabal                 |    4 +-
 src/Data/Dependent/Map.hs           |  524 ++----------
 src/Data/Dependent/Map/Internal.hs  |   36 +-
 src/Data/Dependent/Map/Internal2.hs | 1169 +++++++++++++++++++++++++++
 src/Data/Dependent/Map/NonEmpty.hs  |  855 ++++++++++++++++++++
 5 files changed, 2102 insertions(+), 486 deletions(-)
 create mode 100644 src/Data/Dependent/Map/Internal2.hs
 create mode 100644 src/Data/Dependent/Map/NonEmpty.hs

diff --git a/dependent-map.cabal b/dependent-map.cabal
index e274307..9d1254c 100644
--- a/dependent-map.cabal
+++ b/dependent-map.cabal
@@ -34,7 +34,9 @@ Library
   ghc-options:          -fwarn-unused-imports -fwarn-unused-binds
   exposed-modules:      Data.Dependent.Map,
                         Data.Dependent.Map.Lens,
-                        Data.Dependent.Map.Internal
+                        Data.Dependent.Map.NonEmpty,
+                        Data.Dependent.Map.Internal,
+                        Data.Dependent.Map.Internal2
   other-modules:        Data.Dependent.Map.PtrEquality
   if impl(ghc < 7.8)
     other-modules:      Data.Dependent.Map.Typeable
diff --git a/src/Data/Dependent/Map.hs b/src/Data/Dependent/Map.hs
index cf9a8e1..ea72c9f 100644
--- a/src/Data/Dependent/Map.hs
+++ b/src/Data/Dependent/Map.hs
@@ -148,6 +148,7 @@ import qualified Prelude
 import Control.Applicative (Applicative(..), (<$>))
 #endif
 import Data.Dependent.Map.Internal
+import Data.Dependent.Map.Internal2
 #if !MIN_VERSION_base(4,7,0)
 import Data.Dependent.Map.Typeable ({- instance Typeable ... -})
 #endif
@@ -163,7 +164,6 @@ import Data.Monoid
 import Data.Semigroup
 import Data.Some
 import Text.Read
-import Data.Dependent.Map.PtrEquality
 
 instance (GCompare k) => Monoid (DMap k f) where
     mempty  = empty
@@ -246,41 +246,13 @@ findWithDefault def k m = case lookup k m of
 -- replaced with the supplied value. 'insert' is equivalent to
 -- @'insertWith' 'const'@.
 insert :: forall k f v. GCompare k => k v -> f v -> DMap k f -> DMap k f
-insert kx x = kx `seq` go
-    where
-        go :: DMap k f -> DMap k f
-        go Tip = singleton kx x
-        go t@(Bin sz ky y l r) = case gcompare kx ky of
-            GLT -> let !l' = go l
-                   in if l' `ptrEq` l
-                      then t
-                      else Bin' $! balance ky y l' r
-            GGT -> let !r' = go r
-                   in if r' `ptrEq` r
-                      then t
-                      else Bin' $! balance ky y l r'
-            GEQ
-              | kx `ptrEq` ky && x `ptrEq` y -> t
-              | otherwise -> Bin sz kx x l r
+insert kx x = Bin' . makeInsert kx x
 
 -- | /O(log n)/. Insert a new key and value in the map if the key
 -- is not already present. If the key is already present, @insertR@
 -- does nothing.
 insertR :: forall k f v. GCompare k => k v -> f v -> DMap k f -> DMap k f
-insertR kx x = kx `seq` go
-    where
-        go :: DMap k f -> DMap k f
-        go Tip = singleton kx x
-        go t@(Bin sz ky y l r) = case gcompare kx ky of
-            GLT -> let !l' = go l
-                   in if l' `ptrEq` l
-                      then t
-                      else Bin' $! balance ky y l' r
-            GGT -> let !r' = go r
-                   in if r' `ptrEq` r
-                   then t
-                   else Bin' $! balance ky y l r'
-            GEQ -> t
+insertR kx x = Bin' . makeInsertR kx x
 
 -- | /O(log n)/. Insert with a function, combining new value and old value.
 -- @'insertWith' f key value mp@
@@ -302,27 +274,11 @@ insertWith' f = insertWithKey' (\_ x' y' -> f x' y')
 -- insert the entry @key :=> f key new_value old_value@.
 -- Note that the key passed to f is the same key passed to 'insertWithKey'.
 insertWithKey :: forall k f v. GCompare k => (k v -> f v -> f v -> f v) -> k v -> f v -> DMap k f -> DMap k f
-insertWithKey f kx x = kx `seq` go
-  where
-    go :: DMap k f -> DMap k f
-    go Tip = singleton kx x
-    go (Bin sy ky y l r) =
-        case gcompare kx ky of
-            GLT -> Bin' $! balance ky y (go l) r
-            GGT -> Bin' $! balance ky y l (go r)
-            GEQ -> Bin sy kx (f kx x y) l r
+insertWithKey f kx x = Bin' . makeInsertWithKey f kx x
 
 -- | Same as 'insertWithKey', but the combining function is applied strictly.
 insertWithKey' :: forall k f v. GCompare k => (k v -> f v -> f v -> f v) -> k v -> f v -> DMap k f -> DMap k f
-insertWithKey' f kx x = kx `seq` go
-  where
-    go :: DMap k f -> DMap k f
-    go Tip = singleton kx $! x
-    go (Bin sy ky y l r) =
-        case gcompare kx ky of
-            GLT -> Bin' $! balance ky y (go l) r
-            GGT -> Bin' $! balance ky y l (go r)
-            GEQ -> let x' = f kx x y in seq x' (Bin sy kx x' l r)
+insertWithKey' f kx x = Bin' . makeInsertWithKey' f kx x
 
 -- | /O(log n)/. Combines insert operation with old value retrieval.
 -- The expression (@'insertLookupWithKey' f k x map@)
@@ -330,32 +286,12 @@ insertWithKey' f kx x = kx `seq` go
 -- and the second element equal to (@'insertWithKey' f k x map@).
 insertLookupWithKey :: forall k f v. GCompare k => (k v -> f v -> f v -> f v) -> k v -> f v -> DMap k f
                     -> (Maybe (f v), DMap k f)
-insertLookupWithKey f kx x = kx `seq` go
-  where
-    go :: DMap k f -> (Maybe (f v), DMap k f)
-    go Tip = (Nothing, singleton kx x)
-    go (Bin sy ky y l r) =
-        case gcompare kx ky of
-            GLT -> let (found, l') = go l
-                  in (found, Bin' $! balance ky y l' r)
-            GGT -> let (found, r') = go r
-                  in (found, Bin' $! balance ky y l r')
-            GEQ -> (Just y, Bin sy kx (f kx x y) l r)
+insertLookupWithKey f kx x = fmap Bin' . makeInsertLookupWithKey f kx x
 
 -- | /O(log n)/. A strict version of 'insertLookupWithKey'.
 insertLookupWithKey' :: forall k f v. GCompare k => (k v -> f v -> f v -> f v) -> k v -> f v -> DMap k f
                      -> (Maybe (f v), DMap k f)
-insertLookupWithKey' f kx x = kx `seq` go
-  where
-    go :: DMap k f -> (Maybe (f v), DMap k f)
-    go Tip = x `seq` (Nothing, singleton kx x)
-    go (Bin sy ky y l r) =
-        case gcompare kx ky of
-            GLT -> let (found, l') = go l
-                  in (found, Bin' $! balance ky y l' r)
-            GGT -> let (found, r') = go r
-                  in (found, Bin' $! balance ky y l r')
-            GEQ -> let x' = f kx x y in x' `seq` (Just y, Bin sy kx x' l r)
+insertLookupWithKey' f kx x = fmap Bin' . makeInsertLookupWithKey' f kx x
 
 {--------------------------------------------------------------------
   Deletion
@@ -365,15 +301,7 @@ insertLookupWithKey' f kx x = kx `seq` go
 -- | /O(log n)/. Delete a key and its value from the map. When the key is not
 -- a member of the map, the original map is returned.
 delete :: forall k f v. GCompare k => k v -> DMap k f -> DMap k f
-delete k = k `seq` go
-  where
-    go :: DMap k f -> DMap k f
-    go Tip = Tip
-    go (Bin _ kx x l r) =
-        case gcompare k kx of
-            GLT -> Bin' $! balance kx x (go l) r
-            GGT -> Bin' $! balance kx x l (go r)
-            GEQ -> glue l r
+delete k = fst $ makeDelete k
 
 -- | /O(log n)/. Update a value at a specific key with the result of the provided function.
 -- When the key is not
@@ -384,27 +312,11 @@ adjust f = adjustWithKey (\_ x -> f x)
 -- | /O(log n)/. Adjust a value at a specific key. When the key is not
 -- a member of the map, the original map is returned.
 adjustWithKey :: GCompare k => (k v -> f v -> f v) -> k v -> DMap k f -> DMap k f
-adjustWithKey f0 !k0 = go f0 k0
-  where
-    go :: GCompare k => (k v -> f v -> f v) -> k v -> DMap k f -> DMap k f
-    go _f _k Tip = Tip
-    go f k (Bin sx kx x l r) =
-      case gcompare k kx of
-        GLT -> Bin sx kx x (go f k l) r
-        GGT -> Bin sx kx x l (go f k r)
-        GEQ -> Bin sx kx (f kx x) l r
+adjustWithKey f k = fst $ makeAdjustWithKey f k
 
 -- | /O(log n)/. A strict version of 'adjustWithKey'.
 adjustWithKey' :: GCompare k => (k v -> f v -> f v) -> k v -> DMap k f -> DMap k f
-adjustWithKey' f0 !k0 = go f0 k0
-  where
-    go :: GCompare k => (k v -> f v -> f v) -> k v -> DMap k f -> DMap k f
-    go _f _k Tip = Tip
-    go f k (Bin sx kx x l r) =
-      case gcompare k kx of
-        GLT -> Bin sx kx x (go f k l) r
-        GGT -> Bin sx kx x l (go f k r)
-        GEQ -> let !x' = f kx x in Bin sx kx x' l r
+adjustWithKey' f k = fst $ makeAdjustWithKey' f k
 
 -- | /O(log n)/. The expression (@'update' f k map@) updates the value @x@
 -- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
@@ -417,64 +329,24 @@ update f = updateWithKey (\_ x -> f x)
 -- the element is deleted. If it is (@'Just' y@), the key @k@ is bound
 -- to the new value @y@.
 updateWithKey :: forall k f v. GCompare k => (k v -> f v -> Maybe (f v)) -> k v -> DMap k f -> DMap k f
-updateWithKey f k = k `seq` go
-  where
-    go :: DMap k f -> DMap k f
-    go Tip = Tip
-    go (Bin sx kx x l r) =
-        case gcompare k kx of
-           GLT -> Bin' $! balance kx x (go l) r
-           GGT -> Bin' $! balance kx x l (go r)
-           GEQ -> case f kx x of
-                   Just x' -> Bin sx kx x' l r
-                   Nothing -> glue l r
+updateWithKey f k = fst $ makeUpdateWithKey f k
 
 -- | /O(log n)/. Lookup and update. See also 'updateWithKey'.
 -- The function returns changed value, if it is updated.
 -- Returns the original key value if the map entry is deleted.
 updateLookupWithKey :: forall k f v. GCompare k => (k v -> f v -> Maybe (f v)) -> k v -> DMap k f -> (Maybe (f v), DMap k f)
-updateLookupWithKey f k = k `seq` go
- where
-   go :: DMap k f -> (Maybe (f v), DMap k f)
-   go Tip = (Nothing,Tip)
-   go (Bin sx kx x l r) =
-          case gcompare k kx of
-               GLT -> let (found,l') = go l in (found,Bin' $! balance kx x l' r)
-               GGT -> let (found,r') = go r in (found,Bin' $! balance kx x l r')
-               GEQ -> case f kx x of
-                       Just x' -> (Just x',Bin sx kx x' l r)
-                       Nothing -> (Just x,glue l r)
+updateLookupWithKey f k = fst $ makeUpdateLookupWithKey f k
 
 -- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
 -- 'alter' can be used to insert, delete, or update a value in a 'Map'.
 -- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@.
 alter :: forall k f v. GCompare k => (Maybe (f v) -> Maybe (f v)) -> k v -> DMap k f -> DMap k f
-alter f k = k `seq` go
-  where
-    go :: DMap k f -> DMap k f
-    go Tip = case f Nothing of
-               Nothing -> Tip
-               Just x  -> singleton k x
-
-    go (Bin sx kx x l r) = case gcompare k kx of
-               GLT -> Bin' $! balance kx x (go l) r
-               GGT -> Bin' $! balance kx x l (go r)
-               GEQ -> case f (Just x) of
-                       Just x' -> Bin sx kx x' l r
-                       Nothing -> glue l r
+alter k f = fst $ makeAlter k f
 
 -- | Works the same as 'alter' except the new value is return in some 'Functor' @f@.
 -- In short : @(\v' -> alter (const v') k dm) <$> f (lookup k dm)@
 alterF :: forall k f v g. (GCompare  k, Functor f) => k v -> (Maybe (g v) -> f (Maybe (g v))) -> DMap k g -> f (DMap k g)
-alterF k f = go
-  where
-    go :: DMap k g -> f (DMap k g)
-    go Tip = maybe Tip (singleton k) <$> f Nothing
-
-    go (Bin sx kx x l r) = case gcompare k kx of
-      GLT -> (\l' -> Bin' $! balance kx x l' r) <$> go l
-      GGT -> (\r' -> Bin' $! balance kx x l r') <$> go r
-      GEQ -> maybe (glue l r) (\x' -> Bin sx kx x' l r) <$> f (Just x)
+alterF k f = fst $ makeAlterF k f
 
 {--------------------------------------------------------------------
   Indexing
@@ -492,42 +364,17 @@ findIndex k t
 -- | /O(log n)/. Lookup the /index/ of a key. The index is a number from
 -- /0/ up to, but not including, the 'size' of the map.
 lookupIndex :: forall k f v. GCompare k => k v -> DMap k f -> Maybe Int
-lookupIndex k = k `seq` go 0
-  where
-    go :: Int -> DMap k f -> Maybe Int
-    go !idx Tip  = idx `seq` Nothing
-    go !idx (Bin _ kx _ l r)
-      = case gcompare k kx of
-          GLT -> go idx l
-          GGT -> go (idx + size l + 1) r
-          GEQ -> Just (idx + size l)
+lookupIndex k = fst $ makeLookupIndex k
 
 -- | /O(log n)/. Retrieve an element by /index/. Calls 'error' when an
 -- invalid index is used.
 elemAt :: Int -> DMap k f -> DSum k f
-elemAt _ Tip = error "Map.elemAt: index out of range"
-elemAt i (Bin _ kx x l r)
-  = case compare i sizeL of
-      LT -> elemAt i l
-      GT -> elemAt (i-sizeL-1) r
-      EQ -> kx :=> x
-  where
-    sizeL = size l
+elemAt = fst makElemAt
 
 -- | /O(log n)/. Update the element at /index/. Does nothing when an
 -- invalid index is used.
 updateAt :: (forall v. k v -> f v -> Maybe (f v)) -> Int -> DMap k f -> DMap k f
-updateAt f i0 t = i0 `seq` go i0 t
- where
-    go _ Tip  = Tip
-    go i (Bin sx kx x l r) = case compare i sizeL of
-      LT -> Bin' $! balance kx x (go i l) r
-      GT -> Bin' $! balance kx x l (go (i-sizeL-1) r)
-      EQ -> case f kx x of
-              Just x' -> Bin sx kx x' l r
-              Nothing -> glue l r
-      where
-        sizeL = size l
+updateAt f i0 = fst $ makeUpdateAt f i0
 
 -- | /O(log n)/. Delete the element at /index/.
 -- Defined as (@'deleteAt' i map = 'updateAt' (\k x -> 'Nothing') i map@).
@@ -547,13 +394,7 @@ findMin m = case lookupMin m of
   Nothing -> error "Map.findMin: empty map has no minimal element"
 
 lookupMin :: DMap k f -> Maybe (DSum k f)
-lookupMin m = case m of
-      Tip -> Nothing
-      Bin _ kx x l _ -> Just $! go kx x l
-  where
-    go :: k v -> f v -> DMap k f -> DSum k f
-    go kx x Tip = kx :=> x
-    go _  _ (Bin _ kx x l _) = go kx x l
+lookupMin = fst makeLookupMin
 
 -- | /O(log n)/. The maximal key of the map. Calls 'error' is the map is empty.
 findMax :: DMap k f -> DSum k f
@@ -562,45 +403,23 @@ findMax m = case lookupMax m of
   Nothing -> error "Map.findMax: empty map has no maximal element"
 
 lookupMax :: DMap k f -> Maybe (DSum k f)
-lookupMax m = case m of
-      Tip -> Nothing
-      Bin _ kx x _ r -> Just $! go kx x r
-  where
-    go :: k v -> f v -> DMap k f -> DSum k f
-    go kx x Tip = kx :=> x
-    go _  _ (Bin _ kx x _ r) = go kx x r
+lookupMax = fst makeLookupMax
 
 -- | /O(log n)/. Delete the minimal key. Returns an empty map if the map is empty.
 deleteMin :: DMap k f -> DMap k f
-deleteMin (Bin _ _  _ Tip r)  = r
-deleteMin (Bin _ kx x l r)    = Bin' $! balance kx x (deleteMin l) r
-deleteMin Tip                 = Tip
+deleteMin = fst makeDeleteMin
 
 -- | /O(log n)/. Delete the maximal key. Returns an empty map if the map is empty.
 deleteMax :: DMap k f -> DMap k f
-deleteMax (Bin _ _  _ l Tip)  = l
-deleteMax (Bin _ kx x l r)    = Bin' $! balance kx x l (deleteMax r)
-deleteMax Tip                 = Tip
+deleteMax = fst makeDeleteMax
 
 -- | /O(log n)/. Update the value at the minimal key.
 updateMinWithKey :: (forall v. k v -> f v -> Maybe (f v)) -> DMap k f -> DMap k f
-updateMinWithKey f = go
- where
-    go (Bin sx kx x Tip r) = case f kx x of
-                                  Nothing -> r
-                                  Just x' -> Bin sx kx x' Tip r
-    go (Bin _ kx x l r)    = Bin' $! balance kx x (go l) r
-    go Tip                 = Tip
+updateMinWithKey f = fst $ makeUpdateMinWithKey f
 
 -- | /O(log n)/. Update the value at the maximal key.
 updateMaxWithKey :: (forall v. k v -> f v -> Maybe (f v)) -> DMap k f -> DMap k f
-updateMaxWithKey f = go
- where
-    go (Bin sx kx x l Tip) = case f kx x of
-                              Nothing -> l
-                              Just x' -> Bin sx kx x' l Tip
-    go (Bin _ kx x l r)    = Bin' $! balance kx x l (go r)
-    go Tip                 = Tip
+updateMaxWithKey f = fst $ makeUpdateMaxWithKey f
 
 {--------------------------------------------------------------------
   Union.
@@ -623,16 +442,7 @@ unionsWithKey f ts
 -- It prefers @t1@ when duplicate keys are encountered,
 -- i.e. (@'union' == 'unionWith' 'const'@).
 union :: GCompare k => DMap k f -> DMap k f -> DMap k f
-union t1 Tip  = t1
-union t1 (Bin _ kx x Tip Tip) = insertR kx x t1
-union Tip t2  = t2
-union (Bin _ kx x Tip Tip) t2 = insert kx x t2
-union t1@(Bin _ k1 x1 l1 r1) t2 = case split k1 t2 of
-  (l2, r2)
-    | l1 `ptrEq` l1l2 && r1 `ptrEq` r1r2 -> t1
-    | otherwise -> Bin' $! combine k1 x1 l1l2 r1r2
-    where !l1l2 = l1 `union` l2
-          !r1r2 = r1 `union` r2
+union t1 t2 = fst makeUnion t1 t2
 
 {--------------------------------------------------------------------
   Union with a combining function
@@ -641,14 +451,7 @@ union t1@(Bin _ k1 x1 l1 r1) t2 = case split k1 t2 of
 -- | /O(n+m)/.
 -- Union with a combining function.
 unionWithKey :: GCompare k => (forall v. k v -> f v -> f v -> f v) -> DMap k f -> DMap k f -> DMap k f
-unionWithKey _ t1 Tip  = t1
-unionWithKey _ Tip t2  = t2
-unionWithKey f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of
-  (l2, mx2, r2) -> case mx2 of
-      Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
-      Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
-    where !l1l2 = unionWithKey f l1 l2
-          !r1r2 = unionWithKey f r1 r2
+unionWithKey f = fst $ makeUnionWithKey f
 
 {--------------------------------------------------------------------
   Difference
@@ -657,31 +460,14 @@ unionWithKey f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of
 -- | /O(m * log (n\/m + 1)), m <= n/. Difference of two maps.
 -- Return elements of the first map not existing in the second map.
 difference :: GCompare k => DMap k f -> DMap k g -> DMap k f
-difference Tip _   = Tip
-difference t1 Tip  = t1
-difference t1 (Bin _ k2 _x2 l2 r2) = case split k2 t1 of
-  (l1, r1)
-    | size t1 == size l1l2 + size r1r2 -> t1
-    | otherwise -> merge l1l2 r1r2
-    where
-      !l1l2 = l1 `difference` l2
-      !r1r2 = r1 `difference` r2
+difference = fst makeDifference
 
 -- | /O(n+m)/. Difference with a combining function. When two equal keys are
 -- encountered, the combining function is applied to the key and both values.
 -- If it returns 'Nothing', the element is discarded (proper set difference). If
 -- it returns (@'Just' y@), the element is updated with a new value @y@.
 differenceWithKey :: GCompare k => (forall v. k v -> f v -> g v -> Maybe (f v)) -> DMap k f -> DMap k g -> DMap k f
-differenceWithKey _ Tip _   = Tip
-differenceWithKey _ t1 Tip  = t1
-differenceWithKey f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of
-  (l2, mx2, r2) -> case mx2 of
-      Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
-      Just x2 -> case f k1 x1 x2 of
-        Nothing -> merge l1l2 r1r2
-        Just x1x2 -> Bin' $! combine k1 x1x2 l1l2 r1r2
-    where !l1l2 = differenceWithKey f l1 l2
-          !r1r2 = differenceWithKey f r1 r2
+differenceWithKey f = fst $ makeDifferenceWithKey f
 
 {--------------------------------------------------------------------
   Intersection
@@ -691,29 +477,11 @@ differenceWithKey f (Bin _ k1 x1 l1 r1) t2 = case splitLookup k1 t2 of
 -- Return data in the first map for the keys existing in both maps.
 -- (@'intersection' m1 m2 == 'intersectionWith' 'const' m1 m2@).
 intersection :: GCompare k => DMap k f -> DMap k f -> DMap k f
-intersection Tip _ = Tip
-intersection _ Tip = Tip
-intersection t1@(Bin s1 k1 x1 l1 r1) t2 =
-  let !(l2, found, r2) = splitMember k1 t2
-      !l1l2 = intersection l1 l2
-      !r1r2 = intersection r1 r2
-  in if found
-     then if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1
-          then t1
-          else Bin' $! combine k1 x1 l1l2 r1r2
-     else merge l1l2 r1r2
+intersection = fst makeIntersection
 
 -- | /O(m * log (n\/m + 1), m <= n/. Intersection with a combining function.
 intersectionWithKey :: GCompare k => (forall v. k v -> f v -> g v -> h v) -> DMap k f -> DMap k g -> DMap k h
-intersectionWithKey _ Tip _ = Tip
-intersectionWithKey _ _ Tip = Tip
-intersectionWithKey f (Bin s1 k1 x1 l1 r1) t2 =
-  let !(l2, found, r2) = splitLookup k1 t2
-      !l1l2 = intersectionWithKey f l1 l2
-      !r1r2 = intersectionWithKey f r1 r2
-  in case found of
-       Nothing -> merge l1l2 r1r2
-       Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
+intersectionWithKey f = fst $ makeIntersectionWithKey f
 
 {--------------------------------------------------------------------
   Submap
@@ -737,14 +505,7 @@ isSubmapOfBy f t1 t2
   = (size t1 <= size t2) && (submap' f t1 t2)
 
 submap' :: GCompare k => (forall v. k v -> k v -> f v -> g v -> Bool) -> DMap k f -> DMap k g -> Bool
-submap' _ Tip _ = True
-submap' _ _ Tip = False
-submap' f (Bin _ kx x l r) t
-  = case found of
-      Nothing -> False
-      Just (ky, y)  -> f kx ky x y && submap' f l lt && submap' f r gt
-  where
-    (lt,found,gt) = splitLookupWithKey kx t
+submap' f t1 t2 = fst (makeSubmap' f) t1 t2
 
 -- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
 -- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' 'eqTagged'@).
@@ -771,31 +532,13 @@ isProperSubmapOfBy f t1 t2
 
 -- | /O(n)/. Filter all keys\/values that satisfy the predicate.
 filterWithKey :: GCompare k => (forall v. k v -> f v -> Bool) -> DMap k f -> DMap k f
-filterWithKey p = go
-  where
-    go Tip = Tip
-    go t@(Bin _ kx x l r)
-      | p kx x    = if l' `ptrEq` l && r' `ptrEq` r
-                    then t
-                    else Bin' $! combine kx x l' r'
-      | otherwise = merge l' r'
-      where !l' = go l
-            !r' = go r
+filterWithKey = makeFilterWithKey
 
 -- | /O(n)/. Partition the map according to a predicate. The first
 -- map contains all elements that satisfy the predicate, the second all
 -- elements that fail the predicate. See also 'split'.
 partitionWithKey :: GCompare k => (forall v. k v -> f v -> Bool) -> DMap k f -> (DMap k f, DMap k f)
-partitionWithKey p0 m0 = toPair (go p0 m0)
-  where
-    go :: GCompare k => (forall v. k v -> f v -> Bool) -> DMap k f -> (DMap k f :*: DMap k f)
-    go _ Tip = (Tip :*: Tip)
-    go p (Bin _ kx x l r)
-      | p kx x    = ((Bin' $! combine kx x l1 r1) :*: merge l2 r2)
-      | otherwise = (merge l1 r1 :*: (Bin' $! combine kx x l2 r2))
-      where
-        (l1 :*: l2) = go p l
-        (r1 :*: r2) = go p r
+partitionWithKey = makePartitionWithKey
 
 -- | /O(n)/. Map values and collect the 'Just' results.
 mapMaybe :: GCompare k => (forall v. f v -> Maybe (g v)) -> DMap k f -> DMap k g
@@ -803,28 +546,12 @@ mapMaybe f = mapMaybeWithKey (const f)
 
 -- | /O(n)/. Map keys\/values and collect the 'Just' results.
 mapMaybeWithKey :: GCompare k => (forall v. k v -> f v -> Maybe (g v)) -> DMap k f -> DMap k g
-mapMaybeWithKey f = go
-  where
-    go Tip = Tip
-    go (Bin _ kx x l r) = case f kx x of
-        Just y  -> Bin' $! combine kx y (go l) (go r)
-        Nothing -> merge (go l) (go r)
+mapMaybeWithKey = makeMapMaybeWithKey
 
 -- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
 mapEitherWithKey :: GCompare k =>
   (forall v. k v -> f v -> Either (g v) (h v)) -> DMap k f -> (DMap k g, DMap k h)
-mapEitherWithKey f0 = toPair . go f0
-  where
-    go :: GCompare k
-       => (forall v. k v -> f v -> Either (g v) (h v))
-       -> DMap k f -> (DMap k g :*: DMap k h)
-    go _ Tip = (Tip :*: Tip)
-    go f (Bin _ kx x l r) = case f kx x of
-      Left y  -> ((Bin' $! combine kx y l1 r1) :*: merge l2 r2)
-      Right z -> (merge l1 r1 :*: (Bin' $! combine kx z l2 r2))
-      where
-        (l1,l2) = mapEitherWithKey f l
-        (r1,r2) = mapEitherWithKey f r
+mapEitherWithKey = makeMapEitherWithKey
 
 {--------------------------------------------------------------------
   Mapping
@@ -832,52 +559,28 @@ mapEitherWithKey f0 = toPair . go f0
 
 -- | /O(n)/. Map a function over all values in the map.
 map :: (forall v. f v -> g v) -> DMap k f -> DMap k g
-map f = go
-  where
-    go Tip = Tip
-    go (Bin sx kx x l r) = Bin sx kx (f x) (go l) (go r)
+map f = fst $ makeMap f
 
 -- | /O(n)/. Map a function over all values in the map.
 mapWithKey :: (forall v. k v -> f v -> g v) -> DMap k f -> DMap k g
-mapWithKey f = go
-  where
-    go Tip = Tip
-    go (Bin sx kx x l r) = Bin sx kx (f kx x) (go l) (go r)
+mapWithKey f = fst $ makeMapWithKey f
 
 -- | /O(n)/.
 -- @'traverseWithKey' f m == 'fromList' <$> 'traverse' (\(k, v) -> (,) k <$> f k v) ('toList' m)@
 -- That is, behaves exactly like a regular 'traverse' except that the traversing
 -- function also has access to the key associated with a value.
 traverseWithKey :: Applicative t => (forall v. k v -> f v -> t (g v)) -> DMap k f -> t (DMap k g)
-traverseWithKey f = go
-  where
-    go Tip = pure Tip
-    go (Bin 1 k v _ _) = (\v' -> Bin 1 k v' Tip Tip) <$> f k v
-    go (Bin s k v l r) = flip (Bin s k) <$> go l <*> f k v <*> go r
+traverseWithKey f = fst $ makeTraverseWithKey f
 
 -- | /O(n)/. The function 'mapAccumLWithKey' threads an accumulating
 -- argument throught the map in ascending order of keys.
 mapAccumLWithKey :: (forall v. a -> k v -> f v -> (a, g v)) -> a -> DMap k f -> (a, DMap k g)
-mapAccumLWithKey f = go
-  where
-    go a Tip               = (a,Tip)
-    go a (Bin sx kx x l r) =
-                 let (a1,l') = go a l
-                     (a2,x') = f a1 kx x
-                     (a3,r') = go a2 r
-                 in (a3,Bin sx kx x' l' r')
+mapAccumLWithKey f = fst $ makeMapAccumLWithKey f
 
 -- | /O(n)/. The function 'mapAccumRWithKey' threads an accumulating
 -- argument through the map in descending order of keys.
 mapAccumRWithKey :: (forall v. a -> k v -> f v -> (a, g v)) -> a -> DMap k f -> (a, DMap k g)
-mapAccumRWithKey f = go
-  where
-    go a Tip = (a,Tip)
-    go a (Bin sx kx x l r) =
-                 let (a1,r') = go a r
-                     (a2,x') = f a1 kx x
-                     (a3,l') = go a2 l
-                 in (a3,Bin sx kx x' l' r')
+mapAccumRWithKey f = fst $ makeMapAccumRWithKey f
 
 -- | /O(n*log n)/.
 -- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@.
@@ -904,9 +607,7 @@ mapKeysWith c f = fromListWithKey c . Prelude.map fFirst . toList
 -- This means that @f@ maps distinct original keys to distinct resulting keys.
 -- This function has better performance than 'mapKeys'.
 mapKeysMonotonic :: (forall v. k1 v -> k2 v) -> DMap k1 f -> DMap k2 f
-mapKeysMonotonic _ Tip = Tip
-mapKeysMonotonic f (Bin sz k x l r) =
-    Bin sz (f k) x (mapKeysMonotonic f l) (mapKeysMonotonic f r)
+mapKeysMonotonic f = fst $ makeMapKeysMonotonic f
 
 {--------------------------------------------------------------------
   Folds
@@ -924,18 +625,12 @@ foldWithKey = foldrWithKey
 -- | /O(n)/. Post-order fold.  The function will be applied from the lowest
 -- value to the highest.
 foldrWithKey :: (forall v. k v -> f v -> b -> b) -> b -> DMap k f -> b
-foldrWithKey f = go
-  where
-    go z Tip              = z
-    go z (Bin _ kx x l r) = go (f kx x (go z r)) l
+foldrWithKey = makeFoldrWithKey
 
 -- | /O(n)/. Pre-order fold.  The function will be applied from the highest
 -- value to the lowest.
 foldlWithKey :: (forall v. b -> k v -> f v -> b) -> b -> DMap k f -> b
-foldlWithKey f = go
-  where
-    go z Tip              = z
-    go z (Bin _ kx x l r) = go (f (go z l) kx x) r
+foldlWithKey = makeFoldlWithKey
 
 {-
 -- | /O(n)/. A strict version of 'foldlWithKey'.
@@ -1038,29 +733,7 @@ fromAscListWithKey f xs
 -- | /O(n)/. Build a map from an ascending list of distinct elements in linear time.
 -- /The precondition is not checked./
 fromDistinctAscList :: [DSum k f] -> DMap k f
-fromDistinctAscList xs
-  = build const (length xs) xs
-  where
-    -- 1) use continutations so that we use heap space instead of stack space.
-    -- 2) special case for n==5 to build bushier trees.
-
-    build :: (DMap k f -> [DSum k f] -> b) -> Int -> [DSum k f] -> b
-    build c 0 xs'  = c Tip xs'
-    build c 5 xs'  = case xs' of
-                       ((k1:=>x1):(k2:=>x2):(k3:=>x3):(k4:=>x4):(k5:=>x5):xx)
-                            -> c (bin k4 x4 (bin k2 x2 (singleton k1 x1) (singleton k3 x3)) (singleton k5 x5)) xx
-                       _ -> error "fromDistinctAscList build"
-    build c n xs'  = seq nr $ build (buildR nr c) nl xs'
-                   where
-                     nl = n `div` 2
-                     nr = n - nl - 1
-
-    buildR :: Int -> (DMap k f -> [DSum k f] -> b) -> DMap k f -> [DSum k f] -> b
-    buildR n c l ((k:=>x):ys) = build (buildB l k x c) n ys
-    buildR _ _ _ []           = error "fromDistinctAscList buildR []"
-
-    buildB :: DMap k f -> k v -> f v -> (DMap k f -> a -> b) -> DMap k f -> a -> b
-    buildB l k x c r zs       = c (bin k x l r) zs
+fromDistinctAscList = fst makeFromDistinctAscList
 
 {--------------------------------------------------------------------
   Split
@@ -1070,50 +743,22 @@ fromDistinctAscList xs
 -- the keys in @map1@ are smaller than @k@ and the keys in @map2@ larger than @k@.
 -- Any key equal to @k@ is found in neither @map1@ nor @map2@.
 split :: forall k f v. GCompare k => k v -> DMap k f -> (DMap k f, DMap k f)
-split k = toPair . go
-  where
-    go :: DMap k f -> (DMap k f :*: DMap k f)
-    go Tip              = (Tip :*: Tip)
-    go (Bin _ kx x l r) = case gcompare k kx of
-          GLT -> let !(lt :*: gt) = go l in (lt :*: (Bin' $! combine kx x gt r))
-          GGT -> let !(lt :*: gt) = go r in ((Bin' $! combine kx x l lt) :*: gt)
-          GEQ -> (l :*: r)
+split = fst . makeSplit
 {-# INLINABLE split #-}
 
 -- | /O(log n)/. The expression (@'splitLookup' k map@) splits a map just
 -- like 'split' but also returns @'lookup' k map@.
 splitLookup :: forall k f v. GCompare k => k v -> DMap k f -> (DMap k f, Maybe (f v), DMap k f)
-splitLookup k = toTriple . go
-  where
-    go :: DMap k f -> Triple' (DMap k f) (Maybe (f v)) (DMap k f)
-    go Tip              = Triple' Tip Nothing Tip
-    go (Bin _ kx x l r) = case gcompare k kx of
-      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
-      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
-      GEQ -> Triple' l (Just x) r
+splitLookup = fst . makeSplitLookup
 
 -- | /O(log n)/. The expression (@'splitMember' k map@) splits a map just
 -- like 'split' but also returns @'member' k map@.
 splitMember :: forall k f v. GCompare k => k v -> DMap k f -> (DMap k f, Bool, DMap k f)
-splitMember k = toTriple . go
-  where
-    go :: DMap k f -> Triple' (DMap k f) Bool (DMap k f)
-    go Tip              = Triple' Tip False Tip
-    go (Bin _ kx x l r) = case gcompare k kx of
-      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
-      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
-      GEQ -> Triple' l True r
+splitMember = fst . makeSplitMember
 
 -- | /O(log n)/.
 splitLookupWithKey :: forall k f v. GCompare k => k v -> DMap k f -> (DMap k f, Maybe (k v, f v), DMap k f)
-splitLookupWithKey k = toTriple . go
-  where
-    go :: DMap k f -> Triple' (DMap k f) (Maybe (k v, f v)) (DMap k f)
-    go Tip              = Triple' Tip Nothing Tip
-    go (Bin _ kx x l r) = case gcompare k kx of
-      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
-      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
-      GEQ -> Triple' l (Just (kx, x)) r
+splitLookupWithKey = fst . makeSplitLookupWithKey
 
 {--------------------------------------------------------------------
   Eq converts the tree to a list. In a lazy setting, this
@@ -1172,48 +817,10 @@ showTreeWith showelem hang wide t
   | otherwise = (showsTree showelem wide [] [] t) ""
 
 showsTree :: (forall v. k v -> f v -> String) -> Bool -> [String] -> [String] -> DMap k f -> ShowS
-showsTree showelem wide lbars rbars t
-  = case t of
-      Tip -> showsBars lbars . showString "|\n"
-      Bin _ kx x Tip Tip
-          -> showsBars lbars . showString (showelem kx x) . showString "\n"
-      Bin _ kx x l r
-          -> showsTree showelem wide (withBar rbars) (withEmpty rbars) r .
-             showWide wide rbars .
-             showsBars lbars . showString (showelem kx x) . showString "\n" .
-             showWide wide lbars .
-             showsTree showelem wide (withEmpty lbars) (withBar lbars) l
+showsTree showelem wide = fst $ makeShowsTree showelem wide
 
 showsTreeHang :: (forall v. k v -> f v -> String) -> Bool -> [String] -> DMap k f -> ShowS
-showsTreeHang showelem wide bars t
-  = case t of
-      Tip -> showsBars bars . showString "|\n"
-      Bin _ kx x Tip Tip
-          -> showsBars bars . showString (showelem kx x) . showString "\n"
-      Bin _ kx x l r
-          -> showsBars bars . showString (showelem kx x) . showString "\n" .
-             showWide wide bars .
-             showsTreeHang showelem wide (withBar bars) l .
-             showWide wide bars .
-             showsTreeHang showelem wide (withEmpty bars) r
-
-showWide :: Bool -> [String] -> String -> String
-showWide wide bars
-  | wide      = showString (concat (reverse bars)) . showString "|\n"
-  | otherwise = id
-
-showsBars :: [String] -> ShowS
-showsBars bars
-  = case bars of
-      [] -> id
-      _  -> showString (concat (reverse (tail bars))) . showString node
-
-node :: String
-node           = "+--"
-
-withBar, withEmpty :: [String] -> [String]
-withBar bars   = "|  ":bars
-withEmpty bars = "   ":bars
+showsTreeHang showelem wide = fst $ makeShowsTreeHang showelem wide
 
 {--------------------------------------------------------------------
   Assertions
@@ -1225,38 +832,11 @@ valid t
   = balanced t && ordered t && validsize t
 
 ordered :: GCompare k => DMap k f -> Bool
-ordered t
-  = bounded (const True) (const True) t
-  where
-    bounded :: GCompare k => (Some k -> Bool) -> (Some k -> Bool) -> DMap k f -> Bool
-    bounded lo hi t'
-      = case t' of
-          Tip              -> True
-          Bin _ kx _ l r  -> (lo (This kx)) && (hi (This kx)) && bounded lo (< This kx) l && bounded (> This kx) hi r
+ordered = fst makeOrdered
 
 -- | Exported only for "Debug.QuickCheck"
 balanced :: DMap k f -> Bool
-balanced t
-  = case t of
-      Tip            -> True
-      Bin _ _ _ l r  -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) &&
-                        balanced l && balanced r
+balanced = fst makeBalanced
 
 validsize :: DMap k f -> Bool
-validsize t
-  = (realsize t == Just (size t))
-  where
-    realsize t'
-      = case t' of
-          Tip            -> Just 0
-          Bin sz _ _ l r -> case (realsize l,realsize r) of
-                            (Just n,Just m)  | n+m+1 == sz  -> Just sz
-                            _                               -> Nothing
-{--------------------------------------------------------------------
-  Utilities
---------------------------------------------------------------------}
-foldlStrict :: (a -> b -> a) -> a -> [b] -> a
-foldlStrict f = go
-  where
-    go z []     = z
-    go z (x:xs) = z `seq` go (f z x) xs
+validsize = fst makeValidsize
diff --git a/src/Data/Dependent/Map/Internal.hs b/src/Data/Dependent/Map/Internal.hs
index 54f77cc..803d5fa 100644
--- a/src/Data/Dependent/Map/Internal.hs
+++ b/src/Data/Dependent/Map/Internal.hs
@@ -23,10 +23,10 @@ import Data.Some
 import Data.Typeable (Typeable)
 #endif
 
--- |Dependent maps: 'k' is a GADT-like thing with a facility for 
+-- |Dependent maps: 'k' is a GADT-like thing with a facility for
 -- rediscovering its type parameter, elements of which function as identifiers
 -- tagged with the type of the thing they identify.  Real GADTs are one
--- useful instantiation of @k@, as are 'Tag's from "Data.Unique.Tag" in the 
+-- useful instantiation of @k@, as are 'Tag's from "Data.Unique.Tag" in the
 -- 'prim-uniq' package.
 --
 -- Semantically, @'DMap' k f@ is equivalent to a set of @'DSum' k f@ where no two
@@ -56,6 +56,16 @@ data NonEmptyDMap k f where
     deriving Typeable
 #endif
 
+nonEmpty :: DMap k f -> Maybe (NonEmptyDMap k f)
+nonEmpty = \case
+    Tip -> Nothing
+    Bin' ne -> Just ne
+
+fromNonEmpty :: Maybe (NonEmptyDMap k f) -> DMap k f
+fromNonEmpty = \case
+    Nothing -> Tip
+    Just ne -> Bin' ne
+
 {--------------------------------------------------------------------
   Construction
 --------------------------------------------------------------------}
@@ -138,7 +148,7 @@ lookupAssoc (This k) m = (k :=>) <$> lookup k m
   Utility functions that maintain the balance properties of the tree.
   All constructors assume that all values in [l] < [k] and all values
   in [r] > [k], and that [l] and [r] are valid trees.
-  
+
   In order of sophistication:
     [Bin' sz k x l r]  The type constructor.
     [bin k x l r]     Maintains the correct size, assumes that both [l]
@@ -146,7 +156,7 @@ lookupAssoc (This k) m = (k :=>) <$> lookup k m
     [balance k x l r] Restores the balance and size.
                       Assumes that the original tree was balanced and
                       that [l] or [r] has changed by at most one element.
-    [combine k x l r] Restores balance and size. 
+    [combine k x l r] Restores balance and size.
 
   Furthermore, we can construct a new tree from two trees. Both operations
   assume that all values in [l] < all values in [r] and that [l] and [r]
@@ -156,10 +166,10 @@ lookupAssoc (This k) m = (k :=>) <$> lookup k m
     [merge l r]       Merges two trees and restores balance.
 
   Note: in contrast to Adam's paper, we use (<=) comparisons instead
-  of (<) comparisons in [combine], [merge] and [balance]. 
-  Quickcheck (on [difference]) showed that this was necessary in order 
-  to maintain the invariants. It is quite unsatisfactory that I haven't 
-  been able to find out why this is actually the case! Fortunately, it 
+  of (<) comparisons in [combine], [merge] and [balance].
+  Quickcheck (on [difference]) showed that this was necessary in order
+  to maintain the invariants. It is quite unsatisfactory that I haven't
+  been able to find out why this is actually the case! Fortunately, it
   doesn't hurt to be a bit more conservative.
 --------------------------------------------------------------------}
 
@@ -195,7 +205,7 @@ insertMax, insertMin :: k v -> f v -> DMap k f -> NonEmptyDMap k f
 insertMax kx x t  = case t of
     Tip -> singletonNE kx x
     Bin' ne -> insertMaxNE kx x ne
-             
+
 insertMin kx x t = case t of
     Tip -> singletonNE kx x
     Bin' ne -> insertMinNE kx x ne
@@ -227,7 +237,7 @@ merge (Bin' l) (Bin' r) = Bin' $! mergeNE l r
   Assumes that [l] and [r] are already balanced with respect to each other.
 --------------------------------------------------------------------}
 glueNE :: NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
-glueNE l r 
+glueNE l r
     | sizeNE l > sizeNE r = case deleteFindMax l of
         (km :=> m, l') -> balanceNER km m l' r
     | otherwise = case deleteFindMin r of
@@ -240,7 +250,7 @@ glue (Bin' l) (Bin' r) = Bin' $! glueNE l r
 
 -- | /O(log n)/. Delete and find the minimal element.
 --
--- > deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")]) 
+-- > deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")])
 -- > deleteFindMin                                            Error: can not return the minimal element of an empty map
 
 deleteFindMin :: NonEmptyDMap k f -> (DSum k f, DMap k f)
@@ -321,7 +331,7 @@ deleteFindMax = maxViewWithKeyNE
   Note that:
   - [delta] should be larger than 4.646 with a [ratio] of 2.
   - [delta] should be larger than 3.745 with a [ratio] of 1.534.
-  
+
   - A lower [delta] leads to a more 'perfectly' balanced tree.
   - A higher [delta] performs less rebalancing.
 
@@ -467,7 +477,7 @@ trim cmplo cmphi t@(Bin _ kx _ l r)
               GT -> t
               _  -> trim cmplo cmphi l
       _  -> trim cmplo cmphi r
-              
+
 trimLookupLo :: GCompare k => Some k -> (Some k -> Ordering) -> DMap k f -> (Maybe (DSum k f), DMap k f)
 trimLookupLo _  _     Tip = (Nothing,Tip)
 trimLookupLo lo cmphi t@(Bin _ kx x l r)
diff --git a/src/Data/Dependent/Map/Internal2.hs b/src/Data/Dependent/Map/Internal2.hs
new file mode 100644
index 0000000..7282e98
--- /dev/null
+++ b/src/Data/Dependent/Map/Internal2.hs
@@ -0,0 +1,1169 @@
+{-# LANGUAGE GADTs, RankNTypes #-}
+{-# LANGUAGE BangPatterns #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE CPP #-}
+#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
+{-# LANGUAGE Trustworthy #-}
+#endif
+#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 708
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE UndecidableInstances #-}
+#endif
+module Data.Dependent.Map.Internal2 where
+
+import Prelude hiding (null, lookup, map)
+#if !MIN_VERSION_base(4,8,0)
+import Control.Applicative (Applicative(..), (<$>))
+#endif
+import Data.Dependent.Map.Internal
+#if !MIN_VERSION_base(4,7,0)
+import Data.Dependent.Map.Typeable ({- instance Typeable ... -})
+#endif
+import Data.Dependent.Map.PtrEquality
+
+import Data.Dependent.Sum
+import Data.GADT.Compare
+import Data.List.NonEmpty (NonEmpty (..))
+import qualified Data.List.NonEmpty as NEL
+import Data.Some
+
+{--------------------------------------------------------------------
+  Insertion Worker Builders
+--------------------------------------------------------------------}
+
+makeInsert
+    :: forall k f v
+    .  GCompare k
+    => k v
+    -> f v
+    -> DMap k f
+    -> NonEmptyDMap k f
+makeInsert kx x = kx `seq` go
+    where
+        go :: DMap k f -> NonEmptyDMap k f
+        go Tip = singletonNE kx x
+        go (Bin' t@(NonEmptyDMap sz ky y l r)) = case gcompare kx ky of
+            GLT -> let !l' = go l
+                   in case l of
+                        Bin' nel | l' `ptrEq` nel -> t
+                        _ -> balanceNEL ky y l' r
+            GGT -> let !r' = go r
+                   in case r of
+                        Bin' ner | r' `ptrEq` ner -> t
+                        _ -> balanceNER ky y l r'
+            GEQ
+              | kx `ptrEq` ky && x `ptrEq` y -> t
+              | otherwise -> NonEmptyDMap sz kx x l r
+
+makeInsertR
+  :: forall k f v
+  . GCompare k
+  => k v
+  -> f v
+  -> DMap k f
+  -> NonEmptyDMap k f
+makeInsertR kx x = kx `seq` go
+    where
+        go :: DMap k f -> NonEmptyDMap k f
+        go Tip = singletonNE kx x
+        go (Bin' t@(NonEmptyDMap sz ky y l r)) = case gcompare kx ky of
+            GLT -> let !l' = go l
+                   in case l of
+                        Bin' nel | l' `ptrEq` nel -> t
+                        _ -> balanceNEL ky y l' r
+            GGT -> let !r' = go r
+                   in case r of
+                        Bin' ner | r' `ptrEq` ner -> t
+                        _ -> balanceNER ky y l r'
+            GEQ -> t
+
+makeInsertWithKey
+  :: forall k f v
+  .  GCompare k
+  => (k v -> f v -> f v -> f v)
+  -> k v
+  -> f v
+  -> DMap k f
+  -> NonEmptyDMap k f
+makeInsertWithKey f kx x = kx `seq` go
+  where
+    go :: DMap k f -> NonEmptyDMap k f
+    go Tip = singletonNE kx x
+    go (Bin sy ky y l r) =
+        case gcompare kx ky of
+            GLT -> balanceNEL ky y (go l) r
+            GGT -> balanceNER ky y l (go r)
+            GEQ -> NonEmptyDMap sy kx (f kx x y) l r
+
+makeInsertWithKey'
+  :: forall k f v
+  .  GCompare k
+  => (k v -> f v -> f v -> f v)
+  -> k v
+  -> f v
+  -> DMap k f
+  -> NonEmptyDMap k f
+makeInsertWithKey' f kx x = kx `seq` go
+  where
+    go :: DMap k f -> NonEmptyDMap k f
+    go Tip = singletonNE kx $! x
+    go (Bin sy ky y l r) =
+        case gcompare kx ky of
+            GLT -> balanceNEL ky y (go l) r
+            GGT -> balanceNER ky y l (go r)
+            GEQ -> let x' = f kx x y in seq x' (NonEmptyDMap sy kx x' l r)
+
+makeInsertLookupWithKey
+  :: forall k f v
+  .  GCompare k
+  => (k v -> f v -> f v -> f v)
+  -> k v
+  -> f v
+  -> DMap k f
+  -> (Maybe (f v), NonEmptyDMap k f)
+makeInsertLookupWithKey f kx x = kx `seq` go
+  where
+    go :: DMap k f -> (Maybe (f v), NonEmptyDMap k f)
+    go Tip = (Nothing, singletonNE kx x)
+    go (Bin sy ky y l r) =
+        case gcompare kx ky of
+            GLT -> let (found, l') = go l
+                  in (found, balanceNEL ky y l' r)
+            GGT -> let (found, r') = go r
+                  in (found, balanceNER ky y l r')
+            GEQ -> (Just y, NonEmptyDMap sy kx (f kx x y) l r)
+
+makeInsertLookupWithKey'
+  :: forall k f v
+  .  GCompare k
+  => (k v -> f v -> f v -> f v)
+  -> k v
+  -> f v
+  -> DMap k f
+  -> (Maybe (f v), NonEmptyDMap k f)
+makeInsertLookupWithKey' f kx x = kx `seq` go
+  where
+    go :: DMap k f -> (Maybe (f v), NonEmptyDMap k f)
+    go Tip = x `seq` (Nothing, singletonNE kx x)
+    go (Bin sy ky y l r) =
+        case gcompare kx ky of
+            GLT -> let (found, l') = go l
+                  in (found, balanceNEL ky y l' r)
+            GGT -> let (found, r') = go r
+                  in (found, balanceNER ky y l r')
+            GEQ -> let x' = f kx x y in x' `seq` (Just y, NonEmptyDMap sy kx x' l r)
+
+{--------------------------------------------------------------------
+  Deletion Worker Builders
+--------------------------------------------------------------------}
+
+makeDelete
+  :: forall k f v
+  .  GCompare k
+  => k v
+  -> ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+     )
+makeDelete k = (k `seq` go, k `seq` nonEmpty . go')
+  where
+    go :: DMap k f -> DMap k f
+    go Tip = Tip
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> DMap k f
+    go' (NonEmptyDMap _ kx x l r) =
+        case gcompare k kx of
+            GLT -> Bin' $! balance kx x (go l) r
+            GGT -> Bin' $! balance kx x l (go r)
+            GEQ -> glue l r
+
+makeAdjustWithKey
+  :: forall k f v
+  .  GCompare k
+  => (k v -> f v -> f v)
+  -> k v
+  -> ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> NonEmptyDMap k f
+     )
+makeAdjustWithKey f k = (k `seq` go, k `seq` go')
+  where
+    go :: DMap k f -> DMap k f
+    go Tip = Tip
+    go (Bin' ne) = Bin' $! go' ne
+
+    go' :: NonEmptyDMap k f -> NonEmptyDMap k f
+    go' (NonEmptyDMap sx kx x l r) =
+      case gcompare k kx of
+        GLT -> NonEmptyDMap sx kx x (go l) r
+        GGT -> NonEmptyDMap sx kx x l (go r)
+        GEQ -> NonEmptyDMap sx kx (f kx x) l r
+
+makeAdjustWithKey'
+  :: forall k f v
+  .  GCompare k
+  => (k v -> f v -> f v)
+  -> k v
+  -> ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> NonEmptyDMap k f
+     )
+makeAdjustWithKey' f k = (k `seq` go, k `seq` go')
+  where
+    go :: DMap k f -> DMap k f
+    go Tip = Tip
+    go (Bin' ne) = Bin' $! go' ne
+
+    go' :: NonEmptyDMap k f -> NonEmptyDMap k f
+    go' (NonEmptyDMap sx kx x l r) =
+      case gcompare k kx of
+        GLT -> NonEmptyDMap sx kx x (go l) r
+        GGT -> NonEmptyDMap sx kx x l (go r)
+        GEQ -> let !x' = f kx x in NonEmptyDMap sx kx x' l r
+
+makeUpdateWithKey
+  :: forall k f v
+  .  GCompare k
+  => (k v -> f v -> Maybe (f v))
+  -> k v
+  -> ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+     )
+makeUpdateWithKey f k = (k `seq` go, k `seq` nonEmpty . go')
+  where
+    go :: DMap k f -> DMap k f
+    go Tip = Tip
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> DMap k f
+    go' (NonEmptyDMap sx kx x l r) =
+        case gcompare k kx of
+           GLT -> Bin' $! balance kx x (go l) r
+           GGT -> Bin' $! balance kx x l (go r)
+           GEQ -> case f kx x of
+                   Just x' -> Bin sx kx x' l r
+                   Nothing -> glue l r
+
+makeUpdateLookupWithKey
+  :: forall k f v
+  .  GCompare k
+  => (k v -> f v -> Maybe (f v))
+  -> k v
+  -> ( DMap k f -> (Maybe (f v), DMap k f)
+     , NonEmptyDMap k f -> (Maybe (f v), Maybe (NonEmptyDMap k f))
+     )
+makeUpdateLookupWithKey f k = (k `seq` go, k `seq` fmap nonEmpty . go')
+  where
+    go :: DMap k f -> (Maybe (f v), DMap k f)
+    go Tip = (Nothing, Tip)
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> (Maybe (f v), DMap k f)
+    go' (NonEmptyDMap sx kx x l r) =
+           case gcompare k kx of
+                GLT -> let (found,l') = go l in (found,Bin' $! balance kx x l' r)
+                GGT -> let (found,r') = go r in (found,Bin' $! balance kx x l r')
+                GEQ -> case f kx x of
+                        Just x' -> (Just x',Bin sx kx x' l r)
+                        Nothing -> (Just x,glue l r)
+
+makeAlter
+  :: forall k f v
+  .  GCompare k
+  => (Maybe (f v) -> Maybe (f v))
+  -> k v
+  -> ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+     )
+makeAlter f k = (k `seq` go, k `seq` nonEmpty . go')
+  where
+    go :: DMap k f -> DMap k f
+    go Tip = case f Nothing of
+               Nothing -> Tip
+               Just x  -> singleton k x
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> DMap k f
+    go' (NonEmptyDMap sx kx x l r) = case gcompare k kx of
+               GLT -> Bin' $! balance kx x (go l) r
+               GGT -> Bin' $! balance kx x l (go r)
+               GEQ -> case f (Just x) of
+                       Just x' -> Bin sx kx x' l r
+                       Nothing -> glue l r
+
+{--------------------------------------------------------------------
+  Indexing Worker Builders
+--------------------------------------------------------------------}
+
+makeAlterF
+  :: forall k f v g
+  .  (GCompare  k, Functor f)
+  => k v
+  -> (Maybe (g v) -> f (Maybe (g v)))
+  -> ( DMap k g -> f (DMap k g)
+     , NonEmptyDMap k g -> f (Maybe (NonEmptyDMap k g))
+     )
+makeAlterF k f = (go, fmap nonEmpty . go')
+  where
+    go :: DMap k g -> f (DMap k g)
+    go Tip = maybe Tip (singleton k) <$> f Nothing
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k g -> f (DMap k g)
+    go' (NonEmptyDMap sx kx x l r) = case gcompare k kx of
+      GLT -> (\l' -> Bin' $! balance kx x l' r) <$> go l
+      GGT -> (\r' -> Bin' $! balance kx x l r') <$> go r
+      GEQ -> maybe (glue l r) (\x' -> Bin sx kx x' l r) <$> f (Just x)
+
+makeLookupIndex
+  :: forall k f v
+  .  GCompare k
+  => k v
+  -> ( DMap k f -> Maybe Int
+     , NonEmptyDMap k f -> Maybe Int
+     )
+makeLookupIndex k = (k `seq` go 0, k `seq` go' 0)
+  where
+    go :: Int -> DMap k f -> Maybe Int
+    go !idx Tip  = idx `seq` Nothing
+    go !idx (Bin' ne) = go' idx ne
+
+    go' :: Int -> NonEmptyDMap k f -> Maybe Int
+    go' !idx (NonEmptyDMap _ kx _ l r)
+      = case gcompare k kx of
+          GLT -> go idx l
+          GGT -> go (idx + size l + 1) r
+          GEQ -> Just (idx + size l)
+
+makElemAt
+  :: ( Int -> DMap k f -> DSum k f
+     , Int -> NonEmptyDMap k f -> DSum k f
+     )
+makElemAt = (go, go')
+  where
+    go _ Tip = error "Map.elemAt: index out of range"
+    go i (Bin' ne) = go' i ne
+
+    go' :: Int -> NonEmptyDMap k f -> DSum k f
+    go' i (NonEmptyDMap _ kx x l r)
+      = case compare i sizeL of
+          LT -> go i l
+          GT -> go (i-sizeL-1) r
+          EQ -> kx :=> x
+      where
+        sizeL = size l
+
+makeUpdateAt
+  :: forall k f v
+  .  (forall v. k v -> f v -> Maybe (f v))
+  -> Int
+  -> ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+     )
+makeUpdateAt f i0 = (i0 `seq` go i0, i0 `seq` nonEmpty . go' i0)
+  where
+    go :: Int -> DMap k f -> DMap k f
+    go _ Tip  = Tip
+    go i (Bin' ne) = go' i ne
+
+    go' :: Int -> NonEmptyDMap k f -> DMap k f
+    go' i (NonEmptyDMap sx kx x l r) = case compare i sizeL of
+      LT -> Bin' $! balance kx x (go i l) r
+      GT -> Bin' $! balance kx x l (go (i-sizeL-1) r)
+      EQ -> case f kx x of
+              Just x' -> Bin sx kx x' l r
+              Nothing -> glue l r
+      where
+        sizeL = size l
+
+{--------------------------------------------------------------------
+  Minimal, Maximal Worker Builders
+--------------------------------------------------------------------}
+
+makeLookupMin
+  :: ( DMap k f -> Maybe (DSum k f)
+     , NonEmptyDMap k f -> DSum k f
+     )
+makeLookupMin = (go, go')
+  where
+    go m = case m of
+      Tip -> Nothing
+      Bin _ kx x l _ -> Just $! goInner kx x l
+
+    go' (NonEmptyDMap _ kx x l _) = goInner kx x l
+
+    goInner :: k v -> f v -> DMap k f -> DSum k f
+    goInner kx x Tip = kx :=> x
+    goInner kx x (Bin' ne) = goInner' kx x ne
+
+    goInner' :: k v -> f v -> NonEmptyDMap k f -> DSum k f
+    goInner' _  _ (NonEmptyDMap _ kx x l _) = goInner kx x l
+
+makeLookupMax
+  :: ( DMap k f -> Maybe (DSum k f)
+     , NonEmptyDMap k f -> DSum k f
+     )
+makeLookupMax = (go, go')
+  where
+    go m = case m of
+      Tip -> Nothing
+      Bin _ kx x _ r -> Just $! goInner kx x r
+
+    go' (NonEmptyDMap _ kx x _ r) = goInner kx x r
+
+    goInner :: k v -> f v -> DMap k f -> DSum k f
+    goInner kx x Tip = kx :=> x
+    goInner kx x (Bin' ne) = goInner' kx x ne
+
+    goInner' :: k v -> f v -> NonEmptyDMap k f -> DSum k f
+    goInner' _  _ (NonEmptyDMap _ kx x _ r) = goInner kx x r
+
+makeDeleteMin
+  :: forall k f
+  .  ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+     )
+makeDeleteMin = (go, nonEmpty . go')
+  where
+    go :: DMap k f -> DMap k f
+    go Tip       = Tip
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> DMap k f
+    go' (NonEmptyDMap _ _  _ Tip r) = r
+    go' (NonEmptyDMap _ kx x l r)   = Bin' $! balance kx x (go l) r
+
+makeDeleteMax
+  :: forall k f
+  .  ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+     )
+makeDeleteMax = (go, nonEmpty . go')
+  where
+    go :: DMap k f -> DMap k f
+    go Tip       = Tip
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> DMap k f
+    go' (NonEmptyDMap _ _  _ l Tip) = l
+    go' (NonEmptyDMap _ kx x l r)   = Bin' $! balance kx x l (go r)
+
+
+-- | /O(log n)/. Update the value at the minimal key.
+makeUpdateMinWithKey
+  :: (forall v. k v -> f v -> Maybe (f v))
+  -> ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> Maybe (NonEmptyDMap k f))
+makeUpdateMinWithKey f = (go, nonEmpty . go')
+ where
+    go Tip       = Tip
+    go (Bin' ne) = go' ne
+
+    go' (NonEmptyDMap sx kx x Tip r) = case f kx x of
+                                  Nothing -> r
+                                  Just x' -> Bin sx kx x' Tip r
+    go' (NonEmptyDMap _ kx x l r)    = Bin' $! balance kx x (go l) r
+
+makeUpdateMaxWithKey
+  :: (forall v. k v -> f v -> Maybe (f v))
+  -> ( DMap k f -> DMap k f
+     , NonEmptyDMap k f -> Maybe (NonEmptyDMap k f))
+makeUpdateMaxWithKey f = (go, nonEmpty . go')
+ where
+    go Tip                 = Tip
+    go (Bin' ne) = go' ne
+
+    go' (NonEmptyDMap sx kx x l Tip) = case f kx x of
+                              Nothing -> l
+                              Just x' -> Bin sx kx x' l Tip
+    go' (NonEmptyDMap _ kx x l r)    = Bin' $! balance kx x l (go r)
+
+{--------------------------------------------------------------------
+  Union Worker Builders
+--------------------------------------------------------------------}
+
+makeUnion
+  :: GCompare k
+  => ( DMap k f -> DMap k f -> DMap k f
+     , NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f)
+makeUnion = (go, go')
+  where
+    go t1 Tip  = t1
+    go t1 (Bin _ kx x Tip Tip) = Bin' $! makeInsertR kx x t1
+    go Tip t2  = t2
+    go (Bin _ kx x Tip Tip) t2 = Bin' $! makeInsert kx x t2
+    go t1@(Bin _ k1 x1 l1 r1) t2 = case fst (makeSplit k1) t2 of
+      (l2, r2)
+        | l1 `ptrEq` l1l2 && r1 `ptrEq` r1r2 -> t1
+        | otherwise -> Bin' $! combine k1 x1 l1l2 r1r2
+        where !l1l2 = l1 `go` l2
+              !r1r2 = r1 `go` r2
+
+    go' t1 (NonEmptyDMap _ kx x Tip Tip) = makeInsertR kx x (Bin' t1)
+    go' (NonEmptyDMap _ kx x Tip Tip) t2 = makeInsert kx x (Bin' t2)
+    go' t1@(NonEmptyDMap _ k1 x1 l1 r1) t2 = case snd (makeSplit k1) t2 of
+      (l2, r2)
+        | l1 `ptrEq` l1l2 && r1 `ptrEq` r1r2 -> t1
+        | otherwise -> combine k1 x1 l1l2 r1r2
+        where !l1l2 = l1 `go` l2
+              !r1r2 = r1 `go` r2
+
+makeUnionWithKey
+  :: GCompare k
+  => (forall v. k v -> f v -> f v -> f v)
+  -> ( DMap k f -> DMap k f -> DMap k f
+     , NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f)
+makeUnionWithKey f = (go, go')
+  where
+    go t1 Tip  = t1
+    go Tip t2  = t2
+    go (Bin _ k1 x1 l1 r1) t2 = case fst (makeSplitLookup k1) t2 of
+      (l2, mx2, r2) -> case mx2 of
+          Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
+          Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
+        where !l1l2 = go l1 l2
+              !r1r2 = go r1 r2
+
+    go' (NonEmptyDMap _ k1 x1 l1 r1) t2 = case snd (makeSplitLookup k1) t2 of
+      (l2, mx2, r2) -> case mx2 of
+          Nothing -> combine k1 x1 l1l2 r1r2
+          Just x2 -> combine k1 (f k1 x1 x2) l1l2 r1r2
+        where !l1l2 = go l1 l2
+              !r1r2 = go r1 r2
+
+{--------------------------------------------------------------------
+  Difference Worker Builders
+--------------------------------------------------------------------}
+
+makeDifference
+  :: GCompare k
+  => ( DMap k f -> DMap k g -> DMap k f
+     , NonEmptyDMap k f -> NonEmptyDMap k g -> DMap k f
+     )
+makeDifference = (go, go')
+  where
+    go Tip _   = Tip
+    go t1 Tip  = t1
+    go t1 (Bin _ k2 _x2 l2 r2) = case fst (makeSplit k2) t1 of
+      (l1, r1)
+        | size t1 == size l1l2 + size r1r2 -> t1
+        | otherwise -> merge l1l2 r1r2
+        where
+          !l1l2 = l1 `go` l2
+          !r1r2 = r1 `go` r2
+
+    go' t1 (NonEmptyDMap _ k2 _x2 l2 r2) = case snd (makeSplit k2) t1 of
+      (l1, r1)
+        | sizeNE t1 == size l1l2 + size r1r2 -> Bin' t1
+        | otherwise -> merge l1l2 r1r2
+        where
+          !l1l2 = l1 `go` l2
+          !r1r2 = r1 `go` r2
+
+makeDifferenceWithKey
+  :: GCompare k
+  => (forall v. k v -> f v -> g v -> Maybe (f v))
+  -> ( DMap k f -> DMap k g -> DMap k f
+     , NonEmptyDMap k f -> NonEmptyDMap k g -> DMap k f
+     )
+makeDifferenceWithKey f = (go, go')
+  where
+    go Tip _   = Tip
+    go t1 Tip  = t1
+    go (Bin _ k1 x1 l1 r1) t2 = case fst (makeSplitLookup k1) t2 of
+      (l2, mx2, r2) -> case mx2 of
+          Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
+          Just x2 -> case f k1 x1 x2 of
+            Nothing -> merge l1l2 r1r2
+            Just x1x2 -> Bin' $! combine k1 x1x2 l1l2 r1r2
+        where !l1l2 = go l1 l2
+              !r1r2 = go r1 r2
+
+    go' (NonEmptyDMap _ k1 x1 l1 r1) t2 = case snd (makeSplitLookup k1) t2 of
+      (l2, mx2, r2) -> case mx2 of
+          Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
+          Just x2 -> case f k1 x1 x2 of
+            Nothing -> merge l1l2 r1r2
+            Just x1x2 -> Bin' $! combine k1 x1x2 l1l2 r1r2
+        where !l1l2 = go l1 l2
+              !r1r2 = go r1 r2
+
+{--------------------------------------------------------------------
+  Intersection Worker Builders
+--------------------------------------------------------------------}
+
+makeIntersection
+  :: GCompare k
+  => ( DMap k f -> DMap k f -> DMap k f
+     , NonEmptyDMap k f -> NonEmptyDMap k f -> DMap k f
+     )
+makeIntersection = (go, go')
+  where
+    go Tip _ = Tip
+    go _ Tip = Tip
+    go t1@(Bin s1 k1 x1 l1 r1) t2 =
+      let !(l2, found, r2) = fst (makeSplitMember k1) t2
+          !l1l2 = go l1 l2
+          !r1r2 = go r1 r2
+      in if found
+         then if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1
+              then t1
+              else Bin' $! combine k1 x1 l1l2 r1r2
+         else merge l1l2 r1r2
+
+    go' t1@(NonEmptyDMap s1 k1 x1 l1 r1) t2 =
+      let !(l2, found, r2) = snd (makeSplitMember k1) t2
+          !l1l2 = go l1 l2
+          !r1r2 = go r1 r2
+      in if found
+         then if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1
+              then Bin' t1
+              else Bin' $! combine k1 x1 l1l2 r1r2
+         else merge l1l2 r1r2
+
+makeIntersectionWithKey
+  :: forall k f g h
+  .  GCompare k
+  => (forall v. k v -> f v -> g v -> h v)
+  -> ( DMap k f -> DMap k g -> DMap k h
+     , NonEmptyDMap k f -> NonEmptyDMap k g -> DMap k h
+     )
+makeIntersectionWithKey f = (go, go')
+  where
+    go :: DMap k f -> DMap k g -> DMap k h
+    go Tip _ = Tip
+    go _ Tip = Tip
+    go (Bin s1 k1 x1 l1 r1) t2 =
+      let !(l2, found, r2) = fst (makeSplitLookup k1) t2
+          !l1l2 = go l1 l2
+          !r1r2 = go r1 r2
+      in case found of
+           Nothing -> merge l1l2 r1r2
+           Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
+
+    go' :: NonEmptyDMap k f -> NonEmptyDMap k g -> DMap k h
+    go' (NonEmptyDMap s1 k1 x1 l1 r1) t2 =
+      let !(l2, found, r2) = snd (makeSplitLookup k1) t2
+          !l1l2 = go l1 l2
+          !r1r2 = go r1 r2
+      in case found of
+           Nothing -> merge l1l2 r1r2
+           Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
+
+{--------------------------------------------------------------------
+  Submap Worker Builders
+--------------------------------------------------------------------}
+
+makeSubmap'
+  :: GCompare k
+  => (forall v. k v -> k v -> f v -> g v -> Bool)
+  -> ( DMap k f -> DMap k g -> Bool
+     , NonEmptyDMap k f -> NonEmptyDMap k g -> Bool
+     )
+makeSubmap' f = (go, go')
+  where
+    go Tip _ = True
+    go _ Tip = False
+    go (Bin _ kx x l r) t
+      = case found of
+          Nothing -> False
+          Just (ky, y)  -> f kx ky x y && go l lt && go r gt
+      where
+        (lt, found, gt) = fst (makeSplitLookupWithKey kx) t
+
+    go' (NonEmptyDMap _ kx x l r) t
+      = case found of
+          Nothing -> False
+          Just (ky, y)  -> f kx ky x y && go l lt && go r gt
+      where
+        (lt, found, gt) = snd (makeSplitLookupWithKey kx) t
+
+{--------------------------------------------------------------------
+  Filter and partition
+--------------------------------------------------------------------}
+
+makeFilterWithKey
+  :: GCompare k
+  => (forall v. k v -> f v -> Bool)
+  -> DMap k f -> DMap k f
+makeFilterWithKey p = go
+  where
+    go Tip = Tip
+    go t@(Bin _ kx x l r)
+      | p kx x    = if l' `ptrEq` l && r' `ptrEq` r
+                    then t
+                    else Bin' $! combine kx x l' r'
+      | otherwise = merge l' r'
+      where !l' = go l
+            !r' = go r
+
+makePartitionWithKey
+  :: forall k f g h
+  .  GCompare k
+  => (forall v. k v -> f v -> Bool)
+  -> DMap k f
+  -> (DMap k f, DMap k f)
+makePartitionWithKey p m0 = toPair (go m0)
+  where
+    go :: DMap k f -> (DMap k f :*: DMap k f)
+    go Tip = (Tip :*: Tip)
+    go (Bin _ kx x l r)
+      | p kx x    = ((Bin' $! combine kx x l1 r1) :*: merge l2 r2)
+      | otherwise = (merge l1 r1 :*: (Bin' $! combine kx x l2 r2))
+      where
+        (l1 :*: l2) = go l
+        (r1 :*: r2) = go r
+
+makeMapMaybeWithKey
+  :: GCompare k
+  => (forall v. k v -> f v -> Maybe (g v))
+  -> DMap k f
+  -> DMap k g
+makeMapMaybeWithKey f = go
+  where
+    go Tip = Tip
+    go (Bin _ kx x l r) = case f kx x of
+        Just y  -> Bin' $! combine kx y (go l) (go r)
+        Nothing -> merge (go l) (go r)
+
+makeMapEitherWithKey
+  :: forall k f g h
+  .  GCompare k
+  => (forall v. k v -> f v -> Either (g v) (h v))
+  -> DMap k f
+  -> (DMap k g, DMap k h)
+makeMapEitherWithKey f = toPair . go
+  where
+    go :: GCompare k
+       => DMap k f -> (DMap k g :*: DMap k h)
+    go Tip = (Tip :*: Tip)
+    go (Bin _ kx x l r) = case f kx x of
+      Left y  -> ((Bin' $! combine kx y l1 r1) :*: merge l2 r2)
+      Right z -> (merge l1 r1 :*: (Bin' $! combine kx z l2 r2))
+      where
+        (l1 :*: l2) = go l
+        (r1 :*: r2) = go r
+
+{--------------------------------------------------------------------
+  Mapping Worker Builders
+--------------------------------------------------------------------}
+
+makeMap
+  :: (forall v. f v -> g v)
+  -> ( DMap k f -> DMap k g
+     , NonEmptyDMap k f -> NonEmptyDMap k g
+     )
+makeMap f = (go, go')
+  where
+    go Tip = Tip
+    go (Bin' ne) = Bin' $! go' ne
+
+    go' (NonEmptyDMap sx kx x l r) = NonEmptyDMap sx kx (f x) (go l) (go r)
+
+makeMapWithKey
+  :: (forall v. k v -> f v -> g v)
+  -> ( DMap k f -> DMap k g
+     , NonEmptyDMap k f -> NonEmptyDMap k g
+     )
+makeMapWithKey f = (go, go')
+  where
+    go Tip = Tip
+    go (Bin' ne) = Bin' $! go' ne
+
+    go' (NonEmptyDMap sx kx x l r) = NonEmptyDMap sx kx (f kx x) (go l) (go r)
+
+makeTraverseWithKey
+  :: Applicative t
+  => (forall v. k v -> f v -> t (g v))
+  -> ( DMap k f -> t (DMap k g)
+     , NonEmptyDMap k f -> t (NonEmptyDMap k g)
+     )
+makeTraverseWithKey f = (go, go')
+  where
+    go Tip = pure Tip
+    go (Bin' ne) = Bin' <$> go' ne
+
+    go' (NonEmptyDMap 1 k v _ _) = (\v' -> NonEmptyDMap 1 k v' Tip Tip) <$> f k v
+    go' (NonEmptyDMap s k v l r) = flip (NonEmptyDMap s k) <$> go l <*> f k v <*> go r
+
+makeMapAccumLWithKey
+  :: (forall v. a -> k v -> f v -> (a, g v))
+  -> ( a -> DMap k f -> (a, DMap k g)
+     , a -> NonEmptyDMap k f -> (a, NonEmptyDMap k g)
+     )
+makeMapAccumLWithKey f = (go, go')
+  where
+    go a Tip       = (a,Tip)
+    go a (Bin' ne) = Bin' <$> go' a ne
+
+    go' a (NonEmptyDMap sx kx x l r) =
+                 let (a1,l') = go a l
+                     (a2,x') = f a1 kx x
+                     (a3,r') = go a2 r
+                 in (a3, NonEmptyDMap sx kx x' l' r')
+
+makeMapAccumRWithKey
+  :: (forall v. a -> k v -> f v -> (a, g v))
+  -> ( a -> DMap k f -> (a, DMap k g)
+     , a -> NonEmptyDMap k f -> (a, NonEmptyDMap k g)
+     )
+makeMapAccumRWithKey f = (go, go')
+  where
+    go a Tip = (a,Tip)
+    go a (Bin' ne) = Bin' <$> go' a ne
+
+    go' a (NonEmptyDMap sx kx x l r) =
+                 let (a1,r') = go a r
+                     (a2,x') = f a1 kx x
+                     (a3,l') = go a2 l
+                 in (a3, NonEmptyDMap sx kx x' l' r')
+
+makeMapKeysMonotonic
+  :: (forall v. k1 v -> k2 v)
+  -> ( DMap k1 f -> DMap k2 f
+     , NonEmptyDMap k1 f -> NonEmptyDMap k2 f
+     )
+makeMapKeysMonotonic f = (go, go')
+  where
+    go Tip = Tip
+    go (Bin' ne) = Bin' $! go' ne
+
+    go' (NonEmptyDMap sz k x l r) = NonEmptyDMap sz (f k) x (go l) (go r)
+
+{--------------------------------------------------------------------
+  Folds
+--------------------------------------------------------------------}
+
+makeFoldrWithKey
+  :: (forall v. k v -> f v -> b -> b)
+  -> b
+  -> DMap k f
+  -> b
+makeFoldrWithKey f = go
+  where
+    go z Tip              = z
+    go z (Bin _ kx x l r) = go (f kx x (go z r)) l
+
+makeFoldr1WithKey
+  :: (forall v. k v -> f v -> b -> b)
+  -> (forall v. k v -> f v -> b)
+  -> NonEmptyDMap k f -> b
+makeFoldr1WithKey f g = go
+  where
+    go (NonEmptyDMap _ kx x l Tip) = makeFoldrWithKey f (g kx x) l
+    go (NonEmptyDMap _ kx x l (Bin' r)) = makeFoldrWithKey f (f kx x (go r)) l
+
+makeFoldlWithKey
+  :: (forall v. b -> k v -> f v -> b)
+  -> b
+  -> DMap k f
+  -> b
+makeFoldlWithKey f = go
+  where
+    go z Tip              = z
+    go z (Bin _ kx x l r) = go (f (go z l) kx x) r
+
+makeFoldl1WithKey
+  :: (forall v. b -> k v -> f v -> b)
+  -> (forall v. k v -> f v -> b)
+  -> NonEmptyDMap k f -> b
+makeFoldl1WithKey f g = go
+  where
+    go (NonEmptyDMap _ kx x Tip r) = makeFoldlWithKey f (g kx x) r
+    go (NonEmptyDMap _ kx x (Bin' l) r) = makeFoldlWithKey f (f (go l) kx x) r
+
+{--------------------------------------------------------------------
+  Building trees from ascending/descending lists worker builders
+--------------------------------------------------------------------}
+
+makeFromDistinctAscList
+  :: ( [DSum k f] -> DMap k f
+     , NonEmpty (DSum k f) -> NonEmptyDMap k f
+     )
+makeFromDistinctAscList
+  = ( \xs -> build const (length xs) xs
+    , \xs -> build' const (length xs) xs
+    )
+  where
+    -- 1) use continutations so that we use heap space instead of stack space.
+    -- 2) special case for n==5 to build bushier trees.
+
+    build
+      :: (DMap k f -> [DSum k f] -> b)
+      -> Int
+      -> [DSum k f]
+      -> b
+    build c 0 xs'  = c Tip xs'
+    build c 5 xs'  = case xs' of
+                       ((k1:=>x1):(k2:=>x2):(k3:=>x3):(k4:=>x4):(k5:=>x5):xx)
+                            -> c (bin k4 x4 (bin k2 x2 (singleton k1 x1) (singleton k3 x3)) (singleton k5 x5)) xx
+                       _ -> error "fromDistinctAscList build"
+    build c n xs'  = seq nr $ build (buildR nr c) nl xs'
+                   where
+                     nl = n `div` 2
+                     nr = n - nl - 1
+
+    build'
+      :: (NonEmptyDMap k f -> [DSum k f] -> b)
+      -> Int
+      -> NonEmpty (DSum k f)
+      -> b
+    build' c 5 xs'  = case xs' of
+                       (k1:=>x1) :| ((k2:=>x2):(k3:=>x3):(k4:=>x4):(k5:=>x5):xx)
+                            -> c (binNE k4 x4 (bin k2 x2 (singleton k1 x1) (singleton k3 x3)) (singleton k5 x5)) xx
+                       _ -> error "fromDistinctAscList build'"
+    build' c n xs'  = seq nr $ build' (build'R nr c) nl xs'
+                   where
+                     nl = n `div` 2
+                     nr = n - nl - 1
+
+    -- TODO use 'NonEmpty' to hoist partiality to caller
+    buildR
+      :: Int
+      -> (DMap k f -> [DSum k f] -> b)
+      -> DMap k f -> [DSum k f] -> b
+    buildR n c l ((k:=>x):ys) = build (buildB l k x c) n ys
+    buildR _ _ _ []           = error "fromDistinctAscList buildR []"
+
+    build'R
+      :: Int
+      -> (NonEmptyDMap k f -> [DSum k f] -> b)
+      -> NonEmptyDMap k f -> [DSum k f] -> b
+    build'R n c l ((k:=>x):ys) = build (build'B l k x c) n ys
+    build'R _ _ _ []           = error "fromDistinctAscList build'R []"
+
+    buildB
+      :: DMap k f -> k v -> f v
+      -> (DMap k f -> a -> b)
+      -> DMap k f -> a -> b
+    buildB l k x c r zs = c (bin k x l r) zs
+
+    build'B
+      :: NonEmptyDMap k f -> k v -> f v
+      -> (NonEmptyDMap k f -> a -> b)
+      -> DMap k f -> a -> b
+    build'B l k x c r zs = c (binNE k x (Bin' l) r) zs
+
+{--------------------------------------------------------------------
+  Split Worker Builders
+--------------------------------------------------------------------}
+
+makeSplit
+  :: forall k f v. GCompare k
+  => k v
+  -> ( DMap k f -> (DMap k f, DMap k f)
+     , NonEmptyDMap k f -> (DMap k f, DMap k f)
+     )
+makeSplit k = (toPair . go, toPair . go')
+  where
+    go :: DMap k f -> (DMap k f :*: DMap k f)
+    go Tip       = (Tip :*: Tip)
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> (DMap k f :*: DMap k f)
+    go' (NonEmptyDMap _ kx x l r) = case gcompare k kx of
+          GLT -> let !(lt :*: gt) = go l in (lt :*: (Bin' $! combine kx x gt r))
+          GGT -> let !(lt :*: gt) = go r in ((Bin' $! combine kx x l lt) :*: gt)
+          GEQ -> (l :*: r)
+{-# INLINABLE makeSplit #-}
+
+makeSplitLookup
+  :: forall k f v
+  .  GCompare k
+  => k v
+  -> ( DMap k f -> (DMap k f, Maybe (f v), DMap k f)
+     , NonEmptyDMap k f -> (DMap k f, Maybe (f v), DMap k f)
+     )
+makeSplitLookup k = (toTriple . go, toTriple . go')
+  where
+    go :: DMap k f -> Triple' (DMap k f) (Maybe (f v)) (DMap k f)
+    go Tip       = Triple' Tip Nothing Tip
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> Triple' (DMap k f) (Maybe (f v)) (DMap k f)
+    go' (NonEmptyDMap _ kx x l r) = case gcompare k kx of
+      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
+      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
+      GEQ -> Triple' l (Just x) r
+
+makeSplitMember
+  :: forall k f v
+  .  GCompare k
+  => k v
+  -> ( DMap k f -> (DMap k f, Bool, DMap k f)
+     , NonEmptyDMap k f -> (DMap k f, Bool, DMap k f)
+     )
+makeSplitMember k = (toTriple . go, toTriple . go')
+  where
+    go :: DMap k f -> Triple' (DMap k f) Bool (DMap k f)
+    go Tip       = Triple' Tip False Tip
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> Triple' (DMap k f) Bool (DMap k f)
+    go' (NonEmptyDMap _ kx x l r) = case gcompare k kx of
+      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
+      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
+      GEQ -> Triple' l True r
+
+makeSplitLookupWithKey
+  :: forall k f v
+  .  GCompare k
+  => k v
+  -> ( DMap k f -> (DMap k f, Maybe (k v, f v), DMap k f)
+     , NonEmptyDMap k f -> (DMap k f, Maybe (k v, f v), DMap k f)
+     )
+makeSplitLookupWithKey k = (toTriple . go, toTriple . go')
+  where
+    go :: DMap k f -> Triple' (DMap k f) (Maybe (k v, f v)) (DMap k f)
+    go Tip       = Triple' Tip Nothing Tip
+    go (Bin' ne) = go' ne
+
+    go' :: NonEmptyDMap k f -> Triple' (DMap k f) (Maybe (k v, f v)) (DMap k f)
+    go' (NonEmptyDMap _ kx x l r) = case gcompare k kx of
+      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
+      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
+      GEQ -> Triple' l (Just (kx, x)) r
+
+{--------------------------------------------------------------------
+  Show
+--------------------------------------------------------------------}
+
+makeShowsTree
+  :: (forall v. k v -> f v -> String)
+  -> Bool
+  -> ( [String] -> [String] -> DMap k f -> ShowS
+     , [String] -> [String] -> NonEmptyDMap k f -> ShowS
+     )
+makeShowsTree showelem wide = (go, go')
+  where
+    go lbars rbars t = case t of
+        Tip -> showsBars lbars . showString "|\n"
+        Bin' ne -> go' lbars rbars ne
+
+    go' lbars rbars t = case t of
+        NonEmptyDMap _ kx x Tip Tip
+            -> showsBars lbars . showString (showelem kx x) . showString "\n"
+        NonEmptyDMap _ kx x l r
+            -> go (withBar rbars) (withEmpty rbars) r .
+               showWide wide rbars .
+               showsBars lbars . showString (showelem kx x) . showString "\n" .
+               showWide wide lbars .
+               go (withEmpty lbars) (withBar lbars) l
+
+makeShowsTreeHang
+  :: (forall v. k v -> f v -> String)
+  -> Bool
+  -> ( [String] -> DMap k f -> ShowS
+     , [String] -> NonEmptyDMap k f -> ShowS
+     )
+makeShowsTreeHang showelem wide = (go, go')
+  where
+    go bars t = case t of
+        Tip -> showsBars bars . showString "|\n"
+        Bin' ne -> go' bars ne
+
+    go' bars t = case t of
+        NonEmptyDMap _ kx x Tip Tip
+            -> showsBars bars . showString (showelem kx x) . showString "\n"
+        NonEmptyDMap _ kx x l r
+            -> showsBars bars . showString (showelem kx x) . showString "\n" .
+               showWide wide bars .
+               go (withBar bars) l .
+               showWide wide bars .
+               go (withEmpty bars) r
+
+showWide :: Bool -> [String] -> String -> String
+showWide wide bars
+  | wide      = showString (concat (reverse bars)) . showString "|\n"
+  | otherwise = id
+
+showsBars :: [String] -> ShowS
+showsBars bars
+  = case bars of
+      [] -> id
+      _  -> showString (concat (reverse (tail bars))) . showString node
+
+node :: String
+node           = "+--"
+
+withBar, withEmpty :: [String] -> [String]
+withBar bars   = "|  ":bars
+withEmpty bars = "   ":bars
+
+{--------------------------------------------------------------------
+  Assertions
+--------------------------------------------------------------------}
+
+makeOrdered
+  :: forall k f
+  .  GCompare k
+  => ( DMap k f -> Bool
+     , NonEmptyDMap k f -> Bool
+     )
+makeOrdered
+  = ( bounded (const True) (const True)
+    , bounded' (const True) (const True)
+    )
+  where
+    bounded
+      :: (Some k -> Bool)
+      -> (Some k -> Bool)
+      -> DMap k f-> Bool
+    bounded lo hi t' = case t' of
+        Tip     -> True
+        Bin' ne -> bounded' lo hi ne
+
+    bounded'
+      :: (Some k -> Bool)
+      -> (Some k -> Bool)
+      -> NonEmptyDMap k f-> Bool
+    bounded' lo hi t'
+      = case t' of
+          NonEmptyDMap _ kx _ l r  -> (lo (This kx)) && (hi (This kx)) && bounded lo (< This kx) l && bounded (> This kx) hi r
+
+-- | Exported only for "Debug.QuickCheck"
+makeBalanced
+  :: ( DMap k f -> Bool
+     , NonEmptyDMap k f -> Bool
+     )
+makeBalanced = (go, go')
+  where
+    go t = case t of
+        Tip     -> True
+        Bin' ne -> go' ne
+
+    go' t = case t of
+        NonEmptyDMap _ _ _ l r  -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) &&
+                        go l && go r
+
+makeValidsize
+  :: ( DMap k f -> Bool
+     , NonEmptyDMap k f -> Bool
+     )
+makeValidsize =
+  ( \t -> realsize t == Just (size t)
+  , \t -> realsize' t == Just (sizeNE t)
+  )
+  where
+    realsize t = case t of
+        Tip -> Just 0
+        Bin' ne -> realsize' ne
+    realsize' t = case t of
+        NonEmptyDMap sz _ _ l r -> case (realsize l,realsize r) of
+                            (Just n,Just m)  | n+m+1 == sz  -> Just sz
+                            _                               -> Nothing
+
+{--------------------------------------------------------------------
+  Utilities
+--------------------------------------------------------------------}
+
+foldlStrict :: (a -> b -> a) -> a -> [b] -> a
+foldlStrict f = go
+  where
+    go z []     = z
+    go z (x:xs) = z `seq` go (f z x) xs
+
+foldl1Strict
+  :: (a -> a -> a)
+  -> NonEmpty a -> a
+foldl1Strict f (x NEL.:| xs) = foldlStrict f x xs
diff --git a/src/Data/Dependent/Map/NonEmpty.hs b/src/Data/Dependent/Map/NonEmpty.hs
new file mode 100644
index 0000000..575346b
--- /dev/null
+++ b/src/Data/Dependent/Map/NonEmpty.hs
@@ -0,0 +1,855 @@
+{-# LANGUAGE GADTs, RankNTypes #-}
+{-# LANGUAGE BangPatterns #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE CPP #-}
+#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 702
+{-# LANGUAGE Trustworthy #-}
+#endif
+#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 708
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE UndecidableInstances #-}
+#endif
+module Data.Dependent.Map.NonEmpty
+    ( NonEmptyDMap
+    , DSum(..), Some(..)
+    , GCompare(..), GOrdering(..)
+
+    -- * Operators
+    , (!), (\\)
+
+    -- * Query
+    , null
+    , size
+    , member
+    , notMember
+    , lookup
+    , findWithDefault
+
+    -- * Construction
+    , empty
+    , singleton
+
+    -- ** Insertion
+    , insert
+    , insertWith
+    , insertWith'
+    , insertWithKey
+    , insertWithKey'
+    , insertLookupWithKey
+    , insertLookupWithKey'
+
+    -- ** Delete\/Update
+    , delete
+    , adjust
+    , adjustWithKey
+    , adjustWithKey'
+    , update
+    , updateWithKey
+    , updateLookupWithKey
+    , alter
+    , alterF
+
+    -- * Combine
+
+    -- ** Union
+    , union
+    , unionWithKey
+    , unions
+    , unionsWithKey
+
+    -- ** Difference
+    , difference
+    , differenceWithKey
+
+    -- ** Intersection
+    , intersection
+    , intersectionWithKey
+
+    -- * Traversal
+    -- ** Map
+    , map
+    , mapWithKey
+    , traverseWithKey
+    , mapAccumLWithKey
+    , mapAccumRWithKey
+    , mapKeysWith
+    , mapKeysMonotonic
+
+    -- ** Fold
+    , foldWithKey
+    , foldrWithKey
+    , foldlWithKey
+    -- , foldlWithKey'
+
+    -- * Conversion
+    , keys
+    , assocs
+
+    -- ** Lists
+    , toList
+    , fromList
+    , fromListWithKey
+
+    -- ** Ordered lists
+    , toAscList
+    , toDescList
+    , fromAscList
+    , fromAscListWithKey
+    , fromDistinctAscList
+
+    -- * Filter
+    , filter
+    , filterWithKey
+    , partitionWithKey
+
+    , mapMaybe
+    , mapMaybeWithKey
+    , mapEitherWithKey
+
+    , split
+    , splitLookup
+
+    -- * Submap
+    , isSubmapOf, isSubmapOfBy
+    , isProperSubmapOf, isProperSubmapOfBy
+
+    -- * Indexed
+    , lookupIndex
+    , findIndex
+    , elemAt
+    , updateAt
+    , deleteAt
+
+    -- * Min\/Max
+    , findMin
+    , findMax
+    , lookupMin
+    , lookupMax
+    , deleteMin
+    , deleteMax
+    , deleteFindMin
+    , deleteFindMax
+    , updateMinWithKey
+    , updateMaxWithKey
+    , minViewWithKey
+    , maxViewWithKey
+
+    -- * Debugging
+    , showTree
+    , showTreeWith
+    , valid
+    ) where
+
+import Prelude hiding (null, lookup, map)
+#if !MIN_VERSION_base(4,8,0)
+import Control.Applicative (Applicative(..), (<$>))
+#endif
+import Data.Dependent.Map.Internal
+import Data.Dependent.Map.Internal2
+#if !MIN_VERSION_base(4,7,0)
+import Data.Dependent.Map.Typeable ({- instance Typeable ... -})
+#endif
+
+import Data.Bifunctor (bimap)
+import Data.Dependent.Sum
+import Data.Constraint.Extras
+import Data.GADT.Compare
+import Data.GADT.Show
+import Data.Maybe (isJust)
+import Data.List.NonEmpty (NonEmpty (..))
+import qualified Data.List.NonEmpty as NEL
+#if !MIN_VERSION_base(4,8,0)
+import Data.Monoid
+#endif
+import Data.Semigroup
+import Data.Some
+import Text.Read
+
+instance (GCompare k) => Semigroup (NonEmptyDMap k f) where
+  (<>) = union
+
+{--------------------------------------------------------------------
+  Operators
+--------------------------------------------------------------------}
+infixl 9 !,\\ --
+
+-- | /O(log n)/. Find the value at a key.
+-- Calls 'error' when the element can not be found.
+--
+-- > fromList [(5,'a'), (3,'b')] ! 1    Error: element not in the map
+-- > fromList [(5,'a'), (3,'b')] ! 5 == 'a'
+
+(!) :: GCompare k => NonEmptyDMap k f -> k v -> f v
+(!) m k    = find k m
+
+-- | Same as 'difference'.
+(\\) :: GCompare k => NonEmptyDMap k f -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+m1 \\ m2 = difference m1 m2
+
+-- #if __GLASGOW_HASKELL__
+--
+-- {--------------------------------------------------------------------
+--   A Data instance
+-- --------------------------------------------------------------------}
+--
+-- -- This instance preserves data abstraction at the cost of inefficiency.
+-- -- We omit reflection services for the sake of data abstraction.
+--
+-- instance (Data k, Data a, GCompare k) => Data (NonEmptyDMap k) where
+--   gfoldl f z m   = z fromList `f` toList m
+--   toConstr _     = error "toConstr"
+--   gunfold _ _    = error "gunfold"
+--   dataTypeOf _   = mkNoRepType "Data.Map.Map"
+--   dataCast2 f    = gcast2 f
+--
+-- #endif
+
+{--------------------------------------------------------------------
+  Query
+--------------------------------------------------------------------}
+
+-- | /O(log n)/. Is the key a member of the map? See also 'notMember'.
+member :: GCompare k => k a -> NonEmptyDMap k f -> Bool
+member k = isJust . lookupNE k
+
+-- | /O(log n)/. Is the key not a member of the map? See also 'member'.
+notMember :: GCompare k => k v -> NonEmptyDMap k f -> Bool
+notMember k m = not (member k m)
+
+-- | /O(log n)/. Find the value at a key.
+-- Calls 'error' when the element can not be found.
+-- Consider using 'lookup' when elements may not be present.
+find :: GCompare k => k v -> NonEmptyDMap k f -> f v
+find k m = case lookupNE k m of
+    Nothing -> error "NonEmptyDMap.find: element not in the map"
+    Just v  -> v
+
+-- | /O(log n)/. The expression @('findWithDefault' def k map)@ returns
+-- the value at key @k@ or returns default value @def@
+-- when the key is not in the map.
+findWithDefault :: GCompare k => f v -> k v -> NonEmptyDMap k f -> f v
+findWithDefault def k m = case lookupNE k m of
+    Nothing -> def
+    Just v  -> v
+
+{--------------------------------------------------------------------
+  Insertion
+--------------------------------------------------------------------}
+
+-- | /O(log n)/. Insert a new key and value in the map.
+-- If the key is already present in the map, the associated value is
+-- replaced with the supplied value. 'insert' is equivalent to
+-- @'insertWith' 'const'@.
+insert :: forall k f v. GCompare k => k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f
+insert kx x = makeInsert kx x . Bin'
+
+-- | /O(log n)/. Insert a new key and value in the map if the key
+-- is not already present. If the key is already present, @insertR@
+-- does nothing.
+insertR :: forall k f v. GCompare k => k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f
+insertR kx x = makeInsertR kx x . Bin'
+
+-- | /O(log n)/. Insert with a function, combining new value and old value.
+-- @'insertWith' f key value mp@
+-- will insert the entry @key :=> value@ into @mp@ if key does
+-- not exist in the map. If the key does exist, the function will
+-- insert the entry @key :=> f new_value old_value@.
+insertWith :: GCompare k => (f v -> f v -> f v) -> k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f
+insertWith f = insertWithKey (\_ x' y' -> f x' y')
+
+-- | Same as 'insertWith', but the combining function is applied strictly.
+-- This is often the most desirable behavior.
+insertWith' :: GCompare k => (f v -> f v -> f v) -> k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f
+insertWith' f = insertWithKey' (\_ x' y' -> f x' y')
+
+-- | /O(log n)/. Insert with a function, combining key, new value and old value.
+-- @'insertWithKey' f key value mp@
+-- will insert the entry @key :=> value@ into @mp@ if key does
+-- not exist in the map. If the key does exist, the function will
+-- insert the entry @key :=> f key new_value old_value@.
+-- Note that the key passed to f is the same key passed to 'insertWithKey'.
+insertWithKey :: forall k f v. GCompare k => (k v -> f v -> f v -> f v) -> k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f
+insertWithKey f kx x = makeInsertWithKey f kx x . Bin'
+
+-- | Same as 'insertWithKey', but the combining function is applied strictly.
+insertWithKey' :: forall k f v. GCompare k => (k v -> f v -> f v -> f v) -> k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f
+insertWithKey' f kx x = makeInsertWithKey' f kx x . Bin'
+
+-- | /O(log n)/. Combines insert operation with old value retrieval.
+-- The expression (@'insertLookupWithKey' f k x map@)
+-- is a pair where the first element is equal to (@'lookup' k map@)
+-- and the second element equal to (@'insertWithKey' f k x map@).
+insertLookupWithKey :: forall k f v. GCompare k => (k v -> f v -> f v -> f v) -> k v -> f v -> NonEmptyDMap k f
+                    -> (Maybe (f v), NonEmptyDMap k f)
+insertLookupWithKey f kx x = makeInsertLookupWithKey f kx x . Bin'
+
+-- | /O(log n)/. A strict version of 'insertLookupWithKey'.
+insertLookupWithKey' :: forall k f v. GCompare k => (k v -> f v -> f v -> f v) -> k v -> f v -> NonEmptyDMap k f
+                     -> (Maybe (f v), NonEmptyDMap k f)
+insertLookupWithKey' f kx x = makeInsertLookupWithKey' f kx x . Bin'
+
+{--------------------------------------------------------------------
+  Deletion
+  [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
+--------------------------------------------------------------------}
+
+-- | /O(log n)/. Delete a key and its value from the map. When the key is not
+-- a member of the map, the original map is returned.
+delete :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+delete k = snd $ makeDelete k
+
+-- | /O(log n)/. Update a value at a specific key with the result of the provided function.
+-- When the key is not
+-- a member of the map, the original map is returned.
+adjust :: GCompare k => (f v -> f v) -> k v -> NonEmptyDMap k f -> NonEmptyDMap k f
+adjust f = adjustWithKey (\_ x -> f x)
+
+-- | /O(log n)/. Adjust a value at a specific key. When the key is not
+-- a member of the map, the original map is returned.
+adjustWithKey :: GCompare k => (k v -> f v -> f v) -> k v -> NonEmptyDMap k f -> NonEmptyDMap k f
+adjustWithKey f k = snd $ makeAdjustWithKey f k
+
+-- | /O(log n)/. A strict version of 'adjustWithKey'.
+adjustWithKey' :: GCompare k => (k v -> f v -> f v) -> k v -> NonEmptyDMap k f -> NonEmptyDMap k f
+adjustWithKey' f k = snd $ makeAdjustWithKey' f k
+
+-- | /O(log n)/. The expression (@'update' f k map@) updates the value @x@
+-- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
+-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
+update :: GCompare k => (f v -> Maybe (f v)) -> k v -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+update f = updateWithKey (\_ x -> f x)
+
+-- | /O(log n)/. The expression (@'updateWithKey' f k map@) updates the
+-- value @x@ at @k@ (if it is in the map). If (@f k x@) is 'Nothing',
+-- the element is deleted. If it is (@'Just' y@), the key @k@ is bound
+-- to the new value @y@.
+updateWithKey :: forall k f v. GCompare k => (k v -> f v -> Maybe (f v)) -> k v -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+updateWithKey f k = snd $ makeUpdateWithKey f k
+
+-- | /O(log n)/. Lookup and update. See also 'updateWithKey'.
+-- The function returns changed value, if it is updated.
+-- Returns the original key value if the map entry is deleted.
+updateLookupWithKey :: forall k f v. GCompare k => (k v -> f v -> Maybe (f v)) -> k v -> NonEmptyDMap k f -> (Maybe (f v), Maybe (NonEmptyDMap k f))
+updateLookupWithKey f k = snd $ makeUpdateLookupWithKey f k
+
+-- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
+-- 'alter' can be used to insert, delete, or update a value in a 'Map'.
+-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@.
+alter :: forall k f v. GCompare k => (Maybe (f v) -> Maybe (f v)) -> k v -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+alter k f = snd $ makeAlter k f
+
+-- | Works the same as 'alter' except the new value is return in some 'Functor' @f@.
+-- In short : @(\v' -> alter (const v') k dm) <$> f (lookup k dm)@
+alterF :: forall k f v g. (GCompare  k, Functor f) => k v -> (Maybe (g v) -> f (Maybe (g v))) -> NonEmptyDMap k g -> f (Maybe (NonEmptyDMap k g))
+alterF k f = snd $ makeAlterF k f
+
+{--------------------------------------------------------------------
+  Indexing
+--------------------------------------------------------------------}
+
+-- | /O(log n)/. Return the /index/ of a key. The index is a number from
+-- /0/ up to, but not including, the 'size' of the map. Calls 'error' when
+-- the key is not a 'member' of the map.
+findIndex :: GCompare k => k v -> NonEmptyDMap k f -> Int
+findIndex k t
+  = case lookupIndex k t of
+      Nothing  -> error "Map.findIndex: element is not in the map"
+      Just idx -> idx
+
+-- | /O(log n)/. Lookup the /index/ of a key. The index is a number from
+-- /0/ up to, but not including, the 'size' of the map.
+lookupIndex :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> Maybe Int
+lookupIndex k = snd $ makeLookupIndex k
+
+-- | /O(log n)/. Retrieve an element by /index/. Calls 'error' when an
+-- invalid index is used.
+elemAt :: Int -> NonEmptyDMap k f -> DSum k f
+elemAt = snd makElemAt
+
+-- | /O(log n)/. Update the element at /index/. Does nothing when an
+-- invalid index is used.
+updateAt :: (forall v. k v -> f v -> Maybe (f v)) -> Int -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+updateAt f i0 = snd $ makeUpdateAt f i0
+
+-- | /O(log n)/. Delete the element at /index/.
+-- Defined as (@'deleteAt' i map = 'updateAt' (\k x -> 'Nothing') i map@).
+deleteAt :: Int -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+deleteAt i m
+  = updateAt (\_ _ -> Nothing) i m
+
+
+{--------------------------------------------------------------------
+  Minimal, Maximal
+--------------------------------------------------------------------}
+
+-- | /O(log n)/. The minimal key of the map. Calls 'error' is the map is empty.
+findMin :: NonEmptyDMap k f -> DSum k f
+findMin m = lookupMin m
+
+lookupMin :: NonEmptyDMap k f -> DSum k f
+lookupMin = snd makeLookupMin
+
+-- | /O(log n)/. The maximal key of the map. Calls 'error' is the map is empty.
+findMax :: NonEmptyDMap k f -> DSum k f
+findMax m = lookupMax m
+
+lookupMax :: NonEmptyDMap k f -> DSum k f
+lookupMax = snd makeLookupMax
+
+-- | /O(log n)/. Delete the minimal key. Returns an empty map if the map is empty.
+deleteMin :: NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+deleteMin = snd makeDeleteMin
+
+-- | /O(log n)/. Delete the maximal key. Returns an empty map if the map is empty.
+deleteMax :: NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+deleteMax = snd makeDeleteMax
+
+-- | /O(log n)/. Update the value at the minimal key.
+updateMinWithKey :: (forall v. k v -> f v -> Maybe (f v)) -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+updateMinWithKey f = snd $ makeUpdateMinWithKey f
+
+-- | /O(log n)/. Update the value at the maximal key.
+updateMaxWithKey :: (forall v. k v -> f v -> Maybe (f v)) -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+updateMaxWithKey f = snd $ makeUpdateMaxWithKey f
+
+{--------------------------------------------------------------------
+  Union.
+--------------------------------------------------------------------}
+
+-- | The union of a non-empty list of maps:
+--   (@'unions' == 'Prelude.foldl1' 'union'@).
+unions :: GCompare k => NonEmpty (NonEmptyDMap k f) -> NonEmptyDMap k f
+unions ts
+  = foldl1Strict union ts
+
+-- | The union of a list of maps, with a combining operation:
+--   (@'unionsWithKey' f == 'Prelude.foldl' ('unionWithKey' f) 'empty'@).
+unionsWithKey :: GCompare k => (forall v. k v -> f v -> f v -> f v) -> NonEmpty (NonEmptyDMap k f) -> NonEmptyDMap k f
+unionsWithKey f ts
+  = foldl1Strict (unionWithKey f) ts
+
+-- | /O(m*log(n\/m + 1)), m <= n/.
+-- The expression (@'union' t1 t2@) takes the left-biased union of @t1@ and @t2@.
+-- It prefers @t1@ when duplicate keys are encountered,
+-- i.e. (@'union' == 'unionWith' 'const'@).
+union :: GCompare k => NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+union t1 t2 = snd makeUnion t1 t2
+
+{--------------------------------------------------------------------
+  Union with a combining function
+--------------------------------------------------------------------}
+
+-- | /O(n+m)/.
+-- Union with a combining function.
+unionWithKey :: GCompare k => (forall v. k v -> f v -> f v -> f v) -> NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
+unionWithKey f t1 t2 = snd (makeUnionWithKey f) t1 t2
+
+{--------------------------------------------------------------------
+  Difference
+--------------------------------------------------------------------}
+
+-- | /O(m * log (n\/m + 1)), m <= n/. Difference of two maps.
+-- Return elements of the first map not existing in the second map.
+difference :: GCompare k => NonEmptyDMap k f -> NonEmptyDMap k g -> Maybe (NonEmptyDMap k f)
+difference t1 t2 = nonEmpty $ snd makeDifference t1 t2
+
+-- | /O(n+m)/. Difference with a combining function. When two equal keys are
+-- encountered, the combining function is applied to the key and both values.
+-- If it returns 'Nothing', the element is discarded (proper set difference). If
+-- it returns (@'Just' y@), the element is updated with a new value @y@.
+differenceWithKey :: GCompare k => (forall v. k v -> f v -> g v -> Maybe (f v)) -> NonEmptyDMap k f -> NonEmptyDMap k g -> Maybe (NonEmptyDMap k f)
+differenceWithKey f t1 t2 = nonEmpty $ snd (makeDifferenceWithKey f) t1 t2
+
+{--------------------------------------------------------------------
+  Intersection
+--------------------------------------------------------------------}
+
+-- | /O(m * log (n\/m + 1), m <= n/. Intersection of two maps.
+-- Return data in the first map for the keys existing in both maps.
+-- (@'intersection' m1 m2 == 'intersectionWith' 'const' m1 m2@).
+intersection :: GCompare k => NonEmptyDMap k f -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+intersection t1 t2 = nonEmpty $ snd makeIntersection t1 t2
+
+-- | /O(m * log (n\/m + 1), m <= n/. Intersection with a combining function.
+intersectionWithKey :: GCompare k => (forall v. k v -> f v -> g v -> h v) -> NonEmptyDMap k f -> NonEmptyDMap k g -> Maybe (NonEmptyDMap k h)
+intersectionWithKey f t1 t2 = nonEmpty $ snd (makeIntersectionWithKey f) t1 t2
+
+{--------------------------------------------------------------------
+  Submap
+--------------------------------------------------------------------}
+-- | /O(n+m)/.
+-- This function is defined as (@'isSubmapOf' = 'isSubmapOfBy' 'eqTagged')@).
+--
+isSubmapOf
+  :: forall k f
+  .  (GCompare k, Has' Eq k f)
+  => NonEmptyDMap k f -> NonEmptyDMap k f -> Bool
+isSubmapOf m1 m2 = isSubmapOfBy (\k _ x0 x1 -> has' @Eq @f k (x0 == x1)) m1 m2
+
+{- | /O(n+m)/.
+ The expression (@'isSubmapOfBy' f t1 t2@) returns 'True' if
+ all keys in @t1@ are in tree @t2@, and when @f@ returns 'True' when
+ applied to their respective keys and values.
+-}
+isSubmapOfBy :: GCompare k => (forall v. k v -> k v -> f v -> g v -> Bool) -> NonEmptyDMap k f -> NonEmptyDMap k g -> Bool
+isSubmapOfBy f t1 t2
+  = (sizeNE t1 <= sizeNE t2) && (submap' f t1 t2)
+
+submap' :: GCompare k => (forall v. k v -> k v -> f v -> g v -> Bool) -> NonEmptyDMap k f -> NonEmptyDMap k g -> Bool
+submap' f t1 t2 = snd (makeSubmap' f) t1 t2
+
+-- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
+-- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' 'eqTagged'@).
+isProperSubmapOf
+  :: forall k f
+  .  (GCompare k, Has' Eq k f)
+  => NonEmptyDMap k f -> NonEmptyDMap k f -> Bool
+isProperSubmapOf m1 m2
+  = isProperSubmapOfBy (\k _ x0 x1 -> has' @Eq @f k (x0 == x1)) m1 m2
+
+{- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
+ The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
+ @m1@ and @m2@ are not equal,
+ all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
+ applied to their respective keys and values.
+-}
+isProperSubmapOfBy :: GCompare k => (forall v. k v -> k v -> f v -> g v -> Bool) -> NonEmptyDMap k f -> NonEmptyDMap k g -> Bool
+isProperSubmapOfBy f t1 t2
+  = (sizeNE t1 < sizeNE t2) && (submap' f t1 t2)
+
+{--------------------------------------------------------------------
+  Filter and partition
+--------------------------------------------------------------------}
+
+-- | /O(n)/. Filter all keys\/values that satisfy the predicate.
+filterWithKey :: GCompare k => (forall v. k v -> f v -> Bool) -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
+filterWithKey p = nonEmpty . makeFilterWithKey p . Bin'
+
+-- | /O(n)/. Partition the map according to a predicate. The first
+-- map contains all elements that satisfy the predicate, the second all
+-- elements that fail the predicate. See also 'split'.
+partitionWithKey :: GCompare k => (forall v. k v -> f v -> Bool) -> NonEmptyDMap k f -> (Maybe (NonEmptyDMap k f), Maybe (NonEmptyDMap k f))
+partitionWithKey p t = (nonEmpty t1, nonEmpty t2)
+  where (t1, t2) = makePartitionWithKey p $ Bin' t
+
+-- | /O(n)/. Map values and collect the 'Just' results.
+mapMaybe :: GCompare k => (forall v. f v -> Maybe (g v)) -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k g)
+mapMaybe f = mapMaybeWithKey (const f)
+
+-- | /O(n)/. Map keys\/values and collect the 'Just' results.
+mapMaybeWithKey :: GCompare k => (forall v. k v -> f v -> Maybe (g v)) -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k g)
+mapMaybeWithKey f = nonEmpty . makeMapMaybeWithKey f . Bin'
+
+-- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
+mapEitherWithKey :: GCompare k =>
+  (forall v. k v -> f v -> Either (g v) (h v)) -> NonEmptyDMap k f -> (Maybe (NonEmptyDMap k g), Maybe (NonEmptyDMap k h))
+mapEitherWithKey f t = (nonEmpty t1, nonEmpty t2)
+  where (t1, t2) = makeMapEitherWithKey f $ Bin' t
+
+{--------------------------------------------------------------------
+  Mapping
+--------------------------------------------------------------------}
+
+-- | /O(n)/. Map a function over all values in the map.
+map :: (forall v. f v -> g v) -> NonEmptyDMap k f -> NonEmptyDMap k g
+map f = snd $ makeMap f
+
+-- | /O(n)/. Map a function over all values in the map.
+mapWithKey :: (forall v. k v -> f v -> g v) -> NonEmptyDMap k f -> NonEmptyDMap k g
+mapWithKey f = snd $ makeMapWithKey f
+
+-- | /O(n)/.
+-- @'traverseWithKey' f m == 'fromList' <$> 'traverse' (\(k, v) -> (,) k <$> f k v) ('toList' m)@
+-- That is, behaves exactly like a regular 'traverse' except that the traversing
+-- function also has access to the key associated with a value.
+traverseWithKey :: Applicative t => (forall v. k v -> f v -> t (g v)) -> NonEmptyDMap k f -> t (NonEmptyDMap k g)
+traverseWithKey f = snd $ makeTraverseWithKey f
+
+-- | /O(n)/. The function 'mapAccumLWithKey' threads an accumulating
+-- argument throught the map in ascending order of keys.
+mapAccumLWithKey :: (forall v. a -> k v -> f v -> (a, g v)) -> a -> NonEmptyDMap k f -> (a, NonEmptyDMap k g)
+mapAccumLWithKey f = snd $ makeMapAccumLWithKey f
+
+-- | /O(n)/. The function 'mapAccumRWithKey' threads an accumulating
+-- argument through the map in descending order of keys.
+mapAccumRWithKey :: (forall v. a -> k v -> f v -> (a, g v)) -> a -> NonEmptyDMap k f -> (a, NonEmptyDMap k g)
+mapAccumRWithKey f = snd $ makeMapAccumRWithKey f
+
+-- | /O(n*log n)/.
+-- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@.
+--
+-- The size of the result may be smaller if @f@ maps two or more distinct
+-- keys to the same new key.  In this case the associated values will be
+-- combined using @c@.
+mapKeysWith :: GCompare k2 => (forall v. k2 v -> f v -> f v -> f v) -> (forall v. k1 v -> k2 v) -> NonEmptyDMap k1 f -> NonEmptyDMap k2 f
+mapKeysWith c f = fromListWithKey c . NEL.map fFirst . toList
+    where fFirst (x :=> y) = (f x :=> y)
+
+
+-- | /O(n)/.
+-- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@
+-- is strictly monotonic.
+-- That is, for any values @x@ and @y@, if @x@ < @y@ then @f x@ < @f y@.
+-- /The precondition is not checked./
+-- Semi-formally, we have:
+--
+-- > and [x < y ==> f x < f y | x <- ls, y <- ls]
+-- >                     ==> mapKeysMonotonic f s == mapKeys f s
+-- >     where ls = keys s
+--
+-- This means that @f@ maps distinct original keys to distinct resulting keys.
+-- This function has better performance than 'mapKeys'.
+mapKeysMonotonic :: (forall v. k1 v -> k2 v) -> NonEmptyDMap k1 f -> NonEmptyDMap k2 f
+mapKeysMonotonic f = snd $ makeMapKeysMonotonic f
+
+{--------------------------------------------------------------------
+  Folds
+--------------------------------------------------------------------}
+
+-- | /O(n)/. Fold the keys and values in the map, such that
+-- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
+--
+-- This is identical to 'foldrWithKey', and you should use that one instead of
+-- this one.  This name is kept for backward compatibility.
+foldWithKey :: (forall v. k v -> f v -> b -> b) -> b -> NonEmptyDMap k f -> b
+foldWithKey = foldrWithKey
+{-# DEPRECATED foldWithKey "Use foldrWithKey instead" #-}
+
+-- | /O(n)/. Post-order fold.  The function will be applied from the lowest
+-- value to the highest.
+foldrWithKey :: (forall v. k v -> f v -> b -> b) -> b -> NonEmptyDMap k f -> b
+foldrWithKey f b = makeFoldrWithKey f b . Bin'
+
+-- | /O(n)/. Pre-order fold.  The function will be applied from the highest
+-- value to the lowest.
+foldlWithKey :: (forall v. b -> k v -> f v -> b) -> b -> NonEmptyDMap k f -> b
+foldlWithKey f b = makeFoldlWithKey f b . Bin'
+
+foldr1WithKey
+  :: (forall v. k v -> f v -> b -> b)
+  -> (forall v. k v -> f v -> b)
+  -> NonEmptyDMap k f -> b
+foldr1WithKey = makeFoldr1WithKey
+
+foldl1WithKey
+  :: (forall v. b -> k v -> f v -> b)
+  -> (forall v. k v -> f v -> b)
+  -> NonEmptyDMap k f -> b
+foldl1WithKey = makeFoldl1WithKey
+
+{-
+-- | /O(n)/. A strict version of 'foldlWithKey'.
+foldlWithKey' :: (b -> k -> a -> b) -> b -> NonEmptyDMap k -> b
+foldlWithKey' f = go
+  where
+    go z Tip              = z
+    go z (NonEmptyDMap _ kx x l r) = z `seq` go (f (go z l) kx x) r
+-}
+
+{--------------------------------------------------------------------
+  List variations
+--------------------------------------------------------------------}
+
+-- | /O(n)/. Return all keys of the map in ascending order.
+--
+-- > keys (fromList [(5,"a"), (3,"b")]) == [3,5]
+-- > keys empty == []
+
+keys  :: NonEmptyDMap k f -> NonEmpty (Some k)
+keys m = (\(k :=> _) -> This k) <$> assocs m
+
+-- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
+assocs :: NonEmptyDMap k f -> NonEmpty (DSum k f)
+assocs m = toList m
+
+{--------------------------------------------------------------------
+  Lists
+  use [foldlStrict] to reduce demand on the control-stack
+--------------------------------------------------------------------}
+
+-- | /O(n*log n)/. Build a map from a list of key\/value pairs. See also 'fromAscList'.
+-- If the list contains more than one value for the same key, the last value
+-- for the key is retained.
+fromList :: GCompare k => NonEmpty (DSum k f) -> NonEmptyDMap k f
+fromList xs
+  = unions $ ins <$> xs
+  where
+    ins :: GCompare k => DSum k f -> NonEmptyDMap k f
+    ins (k :=> x) = singletonNE k x
+
+-- | /O(n*log n)/. Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWithKey'.
+fromListWithKey :: GCompare k => (forall v. k v -> f v -> f v -> f v) -> NonEmpty (DSum k f) -> NonEmptyDMap k f
+fromListWithKey f xs
+  = unionsWithKey f $ ins <$> xs
+  where
+    ins :: GCompare k => DSum k f -> NonEmptyDMap k f
+    ins (k :=> x) = singletonNE k x
+
+-- | /O(n)/. Convert to a list of key\/value pairs.
+toList :: NonEmptyDMap k f -> NonEmpty (DSum k f)
+toList t      = toAscList t
+
+-- | /O(n)/. Convert to an ascending list.
+toAscList :: NonEmptyDMap k f -> NonEmpty (DSum k f)
+toAscList t   = foldr1WithKey
+  (\k x xs -> NEL.cons (k :=> x) xs)
+  (\k x -> pure $ k :=> x)
+  t
+
+-- | /O(n)/. Convert to a descending list.
+toDescList :: NonEmptyDMap k f -> NonEmpty (DSum k f)
+toDescList t  = foldl1WithKey
+  (\xs k x1 -> NEL.cons (k :=> x1) xs)
+  (\k x -> pure $ k :=> x)
+  t
+
+{--------------------------------------------------------------------
+  Building trees from ascending/descending lists can be done in linear time.
+
+  Note that if [xs] is ascending that:
+    fromAscList xs       == fromList xs
+    fromAscListWith f xs == fromListWith f xs
+--------------------------------------------------------------------}
+
+-- | /O(n)/. Build a map from an ascending list in linear time.
+-- /The precondition (input list is ascending) is not checked./
+fromAscList :: GEq k => NonEmpty (DSum k f) -> NonEmptyDMap k f
+fromAscList xs
+  = fromAscListWithKey (\_ x _ -> x) xs
+
+-- | /O(n)/. Build a map from an ascending list in linear time with a
+-- combining function for equal keys.
+-- /The precondition (input list is ascending) is not checked./
+fromAscListWithKey
+  :: forall k f
+  .  GEq k
+  => (forall v. k v -> f v -> f v -> f v)
+  -> NonEmpty (DSum k f)
+  -> NonEmptyDMap k f
+fromAscListWithKey f xs
+  = fromDistinctAscList $ combineEq xs
+  where
+  -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
+  combineEq :: NonEmpty (DSum k f) -> NonEmpty (DSum k f)
+  combineEq (z :| []) = z :| []
+  combineEq (z@(kz :=> zz) :| (x@(kx :=> xx):xs')) =
+    case geq kx kz of
+        Just Refl   -> let yy = f kx xx zz in combineEq $ (kx :=> yy) :| xs'
+        Nothing     -> NEL.cons z $ combineEq $ x :| xs'
+
+
+-- | /O(n)/. Build a map from an ascending list of distinct elements in linear time.
+-- /The precondition is not checked./
+fromDistinctAscList :: NonEmpty (DSum k f) -> NonEmptyDMap k f
+fromDistinctAscList = snd makeFromDistinctAscList
+
+{--------------------------------------------------------------------
+  Split
+--------------------------------------------------------------------}
+
+-- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@ where
+-- the keys in @map1@ are smaller than @k@ and the keys in @map2@ larger than @k@.
+-- Any key equal to @k@ is found in neither @map1@ nor @map2@.
+split :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> (Maybe (NonEmptyDMap k f), Maybe (NonEmptyDMap k f))
+split = fmap (bimap nonEmpty nonEmpty) . snd . makeSplit
+{-# INLINABLE split #-}
+
+-- | /O(log n)/. The expression (@'splitLookup' k map@) splits a map just
+-- like 'split' but also returns @'lookup' k map@.
+splitLookup :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> (Maybe (NonEmptyDMap k f), Maybe (f v), Maybe (NonEmptyDMap k f))
+splitLookup = fmap f . snd . makeSplitLookup
+  where f (a, b, c) = (nonEmpty a, b, nonEmpty c)
+
+-- | /O(log n)/. The expression (@'splitMember' k map@) splits a map just
+-- like 'split' but also returns @'member' k map@.
+splitMember :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> (Maybe (NonEmptyDMap k f), Bool, Maybe (NonEmptyDMap k f))
+splitMember = fmap f . snd . makeSplitMember
+  where f (a, b, c) = (nonEmpty a, b, nonEmpty c)
+
+-- | /O(log n)/.
+splitLookupWithKey :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> (Maybe (NonEmptyDMap k f), Maybe (k v, f v), Maybe (NonEmptyDMap k f))
+splitLookupWithKey = fmap f . snd . makeSplitLookupWithKey
+  where f (a, b, c) = (nonEmpty a, b, nonEmpty c)
+
+{--------------------------------------------------------------------
+  Eq converts the tree to a list. In a lazy setting, this
+  actually seems one of the faster methods to compare two trees
+  and it is certainly the simplest :-)
+--------------------------------------------------------------------}
+instance (GEq k, Has' Eq k f) => Eq (NonEmptyDMap k f) where
+  t1 == t2  = (sizeNE t1 == sizeNE t2) && (toAscList t1 == toAscList t2)
+
+{--------------------------------------------------------------------
+  Ord
+--------------------------------------------------------------------}
+
+instance (GCompare k, Has' Eq k f, Has' Ord k f) => Ord (NonEmptyDMap k f) where
+  compare m1 m2 = compare (toAscList m1) (toAscList m2)
+
+{--------------------------------------------------------------------
+  Read
+--------------------------------------------------------------------}
+
+instance (GCompare k, GRead k, Has' Read k f) => Read (NonEmptyDMap k f) where
+  readPrec = parens $ prec 10 $ do
+    Ident "fromList" <- lexP
+    xs <- readPrec
+    return (fromList xs)
+
+  readListPrec = readListPrecDefault
+
+{--------------------------------------------------------------------
+  Show
+--------------------------------------------------------------------}
+instance (GShow k, Has' Show k f) => Show (NonEmptyDMap k f) where
+    showsPrec p m = showParen (p>10)
+        ( showString "fromList "
+        . showsPrec 11 (toList m)
+        )
+
+-- | /O(n)/. Show the tree that implements the map. The tree is shown
+-- in a compressed, hanging format. See 'showTreeWith'.
+showTree :: (GShow k, Has' Show k f) => NonEmptyDMap k f -> String
+showTree m
+  = showTreeWith showElem True False m
+  where
+    showElem :: (GShow k, Has' Show k f) => k v -> f v -> String
+    showElem k x  = show (k :=> x)
+
+
+{- | /O(n)/. The expression (@'showTreeWith' showelem hang wide map@) shows
+ the tree that implements the map. Elements are shown using the @showElem@ function. If @hang@ is
+ 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
+ @wide@ is 'True', an extra wide version is shown.
+-}
+showTreeWith :: (forall v. k v -> f v -> String) -> Bool -> Bool -> NonEmptyDMap k f -> String
+showTreeWith showelem hang wide t
+  | hang      = (showsTreeHang showelem wide [] t) ""
+  | otherwise = (showsTree showelem wide [] [] t) ""
+
+showsTree :: (forall v. k v -> f v -> String) -> Bool -> [String] -> [String] -> NonEmptyDMap k f -> ShowS
+showsTree showelem wide = snd $ makeShowsTree showelem wide
+
+showsTreeHang :: (forall v. k v -> f v -> String) -> Bool -> [String] -> NonEmptyDMap k f -> ShowS
+showsTreeHang showelem wide = snd $ makeShowsTreeHang showelem wide
+
+{--------------------------------------------------------------------
+  Assertions
+--------------------------------------------------------------------}
+
+-- | /O(n)/. Test if the internal map structure is valid.
+valid :: GCompare k => NonEmptyDMap k f -> Bool
+valid t
+  = balanced t && ordered t && validsize t
+
+ordered :: GCompare k => NonEmptyDMap k f -> Bool
+ordered = snd makeOrdered
+
+-- | Exported only for "Debug.QuickCheck"
+balanced :: NonEmptyDMap k f -> Bool
+balanced = snd makeBalanced
+
+validsize :: NonEmptyDMap k f -> Bool
+validsize = snd makeValidsize

From 9bb4fd03911e0b76377a50f8d5d23a272d5efa20 Mon Sep 17 00:00:00 2001
From: John Ericson <git@JohnEricson.me>
Date: Sun, 17 Feb 2019 21:00:11 -0500
Subject: [PATCH 06/10] Create module `Dependent.Map.NonEmpty.Lens`

These required creating an `adjustF` function, which was added to both
the empty and non empty map modules for consistency.
---
 dependent-map.cabal                     |  1 +
 src/Data/Dependent/Map.hs               | 10 +++
 src/Data/Dependent/Map/Internal2.hs     | 21 ++++++
 src/Data/Dependent/Map/Lens.hs          |  4 +-
 src/Data/Dependent/Map/NonEmpty.hs      | 10 +++
 src/Data/Dependent/Map/NonEmpty/Lens.hs | 87 +++++++++++++++++++++++++
 6 files changed, 131 insertions(+), 2 deletions(-)
 create mode 100644 src/Data/Dependent/Map/NonEmpty/Lens.hs

diff --git a/dependent-map.cabal b/dependent-map.cabal
index 9d1254c..9372b84 100644
--- a/dependent-map.cabal
+++ b/dependent-map.cabal
@@ -35,6 +35,7 @@ Library
   exposed-modules:      Data.Dependent.Map,
                         Data.Dependent.Map.Lens,
                         Data.Dependent.Map.NonEmpty,
+                        Data.Dependent.Map.NonEmpty.Lens,
                         Data.Dependent.Map.Internal,
                         Data.Dependent.Map.Internal2
   other-modules:        Data.Dependent.Map.PtrEquality
diff --git a/src/Data/Dependent/Map.hs b/src/Data/Dependent/Map.hs
index ea72c9f..d9631a6 100644
--- a/src/Data/Dependent/Map.hs
+++ b/src/Data/Dependent/Map.hs
@@ -43,6 +43,7 @@ module Data.Dependent.Map
     -- ** Delete\/Update
     , delete
     , adjust
+    , adjustF
     , adjustWithKey
     , adjustWithKey'
     , update
@@ -309,6 +310,15 @@ delete k = fst $ makeDelete k
 adjust :: GCompare k => (f v -> f v) -> k v -> DMap k f -> DMap k f
 adjust f = adjustWithKey (\_ x -> f x)
 
+-- | Works the same as 'adjust' except the new value is return in some 'Applicative' @f@.
+adjustF
+  :: forall k f v g
+  .  (GCompare  k, Applicative f)
+  => k v
+  -> (g v -> f (g v))
+  -> DMap k g -> f (DMap k g)
+adjustF k f = fst $ makeAdjustF f k
+
 -- | /O(log n)/. Adjust a value at a specific key. When the key is not
 -- a member of the map, the original map is returned.
 adjustWithKey :: GCompare k => (k v -> f v -> f v) -> k v -> DMap k f -> DMap k f
diff --git a/src/Data/Dependent/Map/Internal2.hs b/src/Data/Dependent/Map/Internal2.hs
index 7282e98..1b8debd 100644
--- a/src/Data/Dependent/Map/Internal2.hs
+++ b/src/Data/Dependent/Map/Internal2.hs
@@ -179,6 +179,27 @@ makeDelete k = (k `seq` go, k `seq` nonEmpty . go')
             GGT -> Bin' $! balance kx x l (go r)
             GEQ -> glue l r
 
+makeAdjustF
+  :: forall f k v g
+  .  (GCompare k, Applicative f)
+  => (g v -> f (g v))
+  -> k v
+  -> ( DMap k g -> f (DMap k g)
+     , NonEmptyDMap k g -> f (NonEmptyDMap k g)
+     )
+makeAdjustF f k = (k `seq` go, k `seq` go')
+  where
+    go :: DMap k g -> f (DMap k g)
+    go Tip = pure Tip
+    go (Bin' ne) = Bin' <$> go' ne
+
+    go' :: NonEmptyDMap k g -> f (NonEmptyDMap k g)
+    go' (NonEmptyDMap sx kx x l r) =
+      case gcompare k kx of
+        GLT -> NonEmptyDMap sx kx x <$> go l <*> pure r
+        GGT -> NonEmptyDMap sx kx x l <$> go r
+        GEQ -> NonEmptyDMap sx kx <$> f x <*> pure l <*> pure r
+
 makeAdjustWithKey
   :: forall k f v
   .  GCompare k
diff --git a/src/Data/Dependent/Map/Lens.hs b/src/Data/Dependent/Map/Lens.hs
index 0847528..51f9699 100644
--- a/src/Data/Dependent/Map/Lens.hs
+++ b/src/Data/Dependent/Map/Lens.hs
@@ -15,7 +15,7 @@ import           Prelude             hiding (lookup)
 import           Control.Applicative (Applicative (pure))
 #endif
 
-import           Data.Dependent.Map  (DMap, alterF, insert, lookup)
+import           Data.Dependent.Map  (DMap, alterF, adjustF)
 
 import           Data.GADT.Compare   (GCompare)
 
@@ -83,5 +83,5 @@ dmat k f = alterF k f
 -- >>> DMap.fromList [AString :=> Identity "Shoe", AFloat :=> Identity 3.5] ^? dmix AInt
 -- Nothing
 dmix :: (GCompare k, Applicative f) => k v -> (g v -> f (g v)) -> DMap k g -> f (DMap k g)
-dmix k f dmap = maybe (pure dmap) (fmap (flip (insert k) dmap) . f) $ lookup k dmap
+dmix = adjustF
 {-# INLINE dmix #-}
diff --git a/src/Data/Dependent/Map/NonEmpty.hs b/src/Data/Dependent/Map/NonEmpty.hs
index 575346b..c5bb545 100644
--- a/src/Data/Dependent/Map/NonEmpty.hs
+++ b/src/Data/Dependent/Map/NonEmpty.hs
@@ -43,6 +43,7 @@ module Data.Dependent.Map.NonEmpty
     -- ** Delete\/Update
     , delete
     , adjust
+    , adjustF
     , adjustWithKey
     , adjustWithKey'
     , update
@@ -306,6 +307,15 @@ delete k = snd $ makeDelete k
 adjust :: GCompare k => (f v -> f v) -> k v -> NonEmptyDMap k f -> NonEmptyDMap k f
 adjust f = adjustWithKey (\_ x -> f x)
 
+-- | Works the same as 'adjust' except the new value is return in some 'Applicative' @f@.
+adjustF
+  :: forall k f v g
+  .  (GCompare  k, Applicative f)
+  => k v
+  -> (g v -> f (g v))
+  -> NonEmptyDMap k g -> f (NonEmptyDMap k g)
+adjustF k f = snd $ makeAdjustF f k
+
 -- | /O(log n)/. Adjust a value at a specific key. When the key is not
 -- a member of the map, the original map is returned.
 adjustWithKey :: GCompare k => (k v -> f v -> f v) -> k v -> NonEmptyDMap k f -> NonEmptyDMap k f
diff --git a/src/Data/Dependent/Map/NonEmpty/Lens.hs b/src/Data/Dependent/Map/NonEmpty/Lens.hs
new file mode 100644
index 0000000..1503140
--- /dev/null
+++ b/src/Data/Dependent/Map/NonEmpty/Lens.hs
@@ -0,0 +1,87 @@
+{-# LANGUAGE CPP #-}
+-- |
+-- Some functions for using lenses with 'NonEmptyDMap'.
+module Data.Dependent.Map.NonEmpty.Lens
+  ( -- * At
+    dmat
+    -- * Ix
+  , dmix
+  )
+  where
+
+import           Prelude             hiding (lookup)
+
+#if !MIN_VERSION_base(4,8,0)
+import           Control.Applicative (Applicative (pure))
+#endif
+
+import           Data.Dependent.Map.NonEmpty (NonEmptyDMap, adjustF, alterF)
+
+import           Data.GADT.Compare   (GCompare)
+
+-- |
+-- These functions have been specialised for use with 'NonEmptyDMap' but without any of the
+-- specific 'lens' types used so that we have compatilibity without needing the
+-- dependency just for these functions.
+--
+
+-- |
+-- This is equivalent to the <https://hackage.haskell.org/package/lens-4.16.1/docs/Control-Lens-At.html#v:at at> <https://hackage.haskell.org/package/lens-4.16.1/docs/Control-Lens-Type.html#t:Lens-39- Lens'> from <https://hackage.haskell.org/package/lens-4.16.1/docs/Control-Lens-At.html Control.Lens.At>:
+--
+-- @
+-- type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t
+--
+-- at :: Index m -> Lens' m (Maybe (IxValue m))
+-- @
+--
+-- So the type of 'dmat' is equivalent to:
+--
+-- @
+-- dmat :: GCompare k => Lens' (NonEmptyDMap k f) (Maybe (f v))
+-- @
+--
+-- >>> NonEmptyDMap.fromList [AInt :=> Identity 33, AFloat :=> Identity 3.5] & dmat AString ?~ "Hat"
+-- NonEmptyDMap.fromList [AString :=> Identity "Hat", AInt :=> Identity 33, AFloat :=> Identity 3.5]
+--
+-- >>> NonEmptyDMap.fromList [AString :=> Identity "Shoe", AInt :=> Identity 33, AFloat :=> Identity 3.5] ^? dmat AFloat
+-- Just (AFloat :=> 3.5)
+--
+dmat :: (GCompare k, Functor f) => k v -> (Maybe (g v) -> f (Maybe (g v))) -> NonEmptyDMap k g -> f (Maybe (NonEmptyDMap k g))
+dmat k f = alterF k f
+{-# INLINE dmat #-}
+
+-- |
+-- This is equivalent to the <https://hackage.haskell.org/package/lens-4.16.1/docs/Control-Lens-At.html#v:ix ix> <https://hackage.haskell.org/package/lens-4.16.1/docs/Control-Lens-Type.html#t:Traversal-39- Traversal'> from <https://hackage.haskell.org/package/lens-4.16.1/docs/Control-Lens-At.html Control.Lens.At>:
+--
+-- @
+-- type Traversal s t a b = forall f. Applicative f => (a -> f b) -> s -> f t
+--
+-- ix :: Index m -> Traversal' m (IxValue m)
+-- @
+--
+-- So the type of 'dmix' is equivalent to:
+--
+-- @
+-- dmix :: GCompare k => k v -> Traversal' (NonEmptyDMap k f) (f v)
+-- @
+--
+-- /NB:/ Setting the value of this
+-- <https://hackage.haskell.org/package/lens-4.16.1/docs/Control-Lens-Type.html#t:Traversal Traversal>
+-- will only set the value in 'dmix' if it is already present.
+--
+-- If you want to be able to insert /missing/ values, you want 'dmat'.
+--
+-- >>> NonEmptyDMap.fromList [AString :=> Identity "Shoe", AInt :=> Identity 33, AFloat :=> Identity 3.5] & dmix AInt %~ f
+-- NonEmptyDMap.fromList [AString :=> Identity "Shoe", AInt :=> Identity (f 33), AFloat :=> Identity 3.5]
+--
+-- >>> NonEmptyDMap.fromList [AString :=> Identity "Shoe", AInt :=> Identity 33, AFloat :=> Identity 3.5] & dmix AString .~ "Hat"
+-- NonEmptyDMap.fromList [AString :=> Identity "Hat", AInt :=> Identity 33, AFloat :=> Identity 3.5]
+--
+-- >>> NonEmptyDMap.fromList [AString :=> Identity "Shoe", AInt :=> Identity 33, AFloat :=> Identity 3.5] ^? dmix AFloat
+-- Just (AFloat :=> 3.5)
+--
+-- >>> NonEmptyDMap.fromList [AString :=> Identity "Shoe", AFloat :=> Identity 3.5] ^? dmix AInt
+-- Nothing
+dmix :: (GCompare k, Applicative f) => k v -> (g v -> f (g v)) -> NonEmptyDMap k g -> f (NonEmptyDMap k g)
+dmix = adjustF
+{-# INLINE dmix #-}

From fabb687c79dbad9eb9c2f6c64d53217961637df2 Mon Sep 17 00:00:00 2001
From: John Ericson <git@JohnEricson.me>
Date: Tue, 19 Feb 2019 12:00:53 -0500
Subject: [PATCH 07/10] Expose some non-empty-specific functions

---
 src/Data/Dependent/Map/NonEmpty.hs | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/src/Data/Dependent/Map/NonEmpty.hs b/src/Data/Dependent/Map/NonEmpty.hs
index c5bb545..05ae216 100644
--- a/src/Data/Dependent/Map/NonEmpty.hs
+++ b/src/Data/Dependent/Map/NonEmpty.hs
@@ -16,6 +16,10 @@ module Data.Dependent.Map.NonEmpty
     , DSum(..), Some(..)
     , GCompare(..), GOrdering(..)
 
+    -- * non-empty specific
+    , nonEmpty
+    , toDMap
+
     -- * Operators
     , (!), (\\)
 
@@ -171,6 +175,13 @@ import Text.Read
 instance (GCompare k) => Semigroup (NonEmptyDMap k f) where
   (<>) = union
 
+{--------------------------------------------------------------------
+  NonEmpty* Specific
+--------------------------------------------------------------------}
+
+toDMap :: NonEmptyDMap k f -> DMap k f
+toDMap = Bin'
+
 {--------------------------------------------------------------------
   Operators
 --------------------------------------------------------------------}

From bcbeca34f0db5b561b0db1468cb04bb82a7edfb8 Mon Sep 17 00:00:00 2001
From: John Ericson <git@JohnEricson.me>
Date: Wed, 27 Feb 2019 01:41:31 -0500
Subject: [PATCH 08/10] Fix singleton, size, and lookup exports

---
 src/Data/Dependent/Map.hs           |  22 ++++
 src/Data/Dependent/Map/Internal.hs  | 172 ++++++++++++++--------------
 src/Data/Dependent/Map/Internal2.hs | 118 +++++++++----------
 src/Data/Dependent/Map/NonEmpty.hs  |  23 +++-
 4 files changed, 189 insertions(+), 146 deletions(-)

diff --git a/src/Data/Dependent/Map.hs b/src/Data/Dependent/Map.hs
index d9631a6..2414de2 100644
--- a/src/Data/Dependent/Map.hs
+++ b/src/Data/Dependent/Map.hs
@@ -210,10 +210,25 @@ m1 \\ m2 = difference m1 m2
 --
 -- #endif
 
+{--------------------------------------------------------------------
+  Construction
+--------------------------------------------------------------------}
+
+-- | /O(1)/. A map with a single element.
+--
+-- > singleton 1 'a'        == fromList [(1, 'a')]
+-- > size (singleton 1 'a') == 1
+singleton :: k v -> f v -> DMap k f
+singleton = singletonE
+
 {--------------------------------------------------------------------
   Query
 --------------------------------------------------------------------}
 
+-- | /O(1)/. The number of elements in the map.
+size :: DMap k f -> Int
+size = sizeE
+
 -- | /O(log n)/. Is the key a member of the map? See also 'notMember'.
 member :: GCompare k => k a -> DMap k f -> Bool
 member k = isJust . lookup k
@@ -222,6 +237,13 @@ member k = isJust . lookup k
 notMember :: GCompare k => k v -> DMap k f -> Bool
 notMember k m = not (member k m)
 
+-- | /O(log n)/. Lookup the value at a key in the map.
+--
+-- The function will return the corresponding value as @('Just' value)@,
+-- or 'Nothing' if the key isn't in the map.
+lookup :: forall k f v. GCompare k => k v -> DMap k f -> Maybe (f v)
+lookup = lookupE
+
 -- | /O(log n)/. Find the value at a key.
 -- Calls 'error' when the element can not be found.
 -- Consider using 'lookup' when elements may not be present.
diff --git a/src/Data/Dependent/Map/Internal.hs b/src/Data/Dependent/Map/Internal.hs
index 803d5fa..dc2b3a4 100644
--- a/src/Data/Dependent/Map/Internal.hs
+++ b/src/Data/Dependent/Map/Internal.hs
@@ -87,9 +87,9 @@ singletonNE k x = NonEmptyDMap 1 k x Tip Tip
 -- | /O(1)/. A map with a single element.
 --
 -- > singleton 1 'a'        == fromList [(1, 'a')]
--- > size (singleton 1 'a') == 1
-singleton :: k v -> f v -> DMap k f
-singleton k x = Bin' $! singletonNE k x
+-- > size (singletonE 1 'a') == 1
+singletonE :: k v -> f v -> DMap k f
+singletonE k x = Bin' $! singletonNE k x
 
 {--------------------------------------------------------------------
   Query
@@ -105,9 +105,9 @@ sizeNE :: NonEmptyDMap k f -> Int
 sizeNE (NonEmptyDMap n _ _ _ _) = n
 
 -- | /O(1)/. The number of elements in the map.
-size :: DMap k f -> Int
-size Tip      = 0
-size (Bin' ne) = sizeNE ne
+sizeE :: DMap k f -> Int
+sizeE Tip      = 0
+sizeE (Bin' ne) = sizeNE ne
 
 -- | /O(log n)/. Lookup the value at a key in the map.
 --
@@ -120,29 +120,29 @@ lookupNE k ne = k `seq` lookupNE' k ne
 {-# INLINE lookupNE' #-}
 lookupNE' :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> Maybe (f v)
 lookupNE' k (NonEmptyDMap _ kx x l r) = case gcompare k kx of
-    GLT -> lookup' k l
-    GGT -> lookup' k r
+    GLT -> lookupE' k l
+    GGT -> lookupE' k r
     GEQ -> Just x
 
 -- | /O(log n)/. Lookup the value at a key in the map.
 --
 -- The function will return the corresponding value as @('Just' value)@,
 -- or 'Nothing' if the key isn't in the map.
-lookup :: forall k f v. GCompare k => k v -> DMap k f -> Maybe (f v)
-lookup k m = k `seq` lookup' k m
+lookupE :: forall k f v. GCompare k => k v -> DMap k f -> Maybe (f v)
+lookupE k m = k `seq` lookupE' k m
 
 -- | Skips the seq
-{-# INLINE lookup' #-}
-lookup' :: forall k f v. GCompare k => k v -> DMap k f -> Maybe (f v)
-lookup' k = \case
+{-# INLINE lookupE' #-}
+lookupE' :: forall k f v. GCompare k => k v -> DMap k f -> Maybe (f v)
+lookupE' k = \case
     Tip -> Nothing
     (Bin' ne) -> lookupNE' k ne
 
 lookupAssocNE :: forall k f v. GCompare k => Some k -> NonEmptyDMap k f -> Maybe (DSum k f)
 lookupAssocNE (This k) m = (k :=>) <$> lookupNE k m
 
-lookupAssoc :: forall k f v. GCompare k => Some k -> DMap k f -> Maybe (DSum k f)
-lookupAssoc (This k) m = (k :=>) <$> lookup k m
+lookupAssocE :: forall k f v. GCompare k => Some k -> DMap k f -> Maybe (DSum k f)
+lookupAssocE (This k) m = (k :=>) <$> lookupE k m
 
 {--------------------------------------------------------------------
   Utility functions that maintain the balance properties of the tree.
@@ -151,12 +151,12 @@ lookupAssoc (This k) m = (k :=>) <$> lookup k m
 
   In order of sophistication:
     [Bin' sz k x l r]  The type constructor.
-    [bin k x l r]     Maintains the correct size, assumes that both [l]
+    [bin k x l r]     Maintains the correct sizeE, assumes that both [l]
                       and [r] are balanced with respect to each other.
-    [balance k x l r] Restores the balance and size.
+    [balance k x l r] Restores the balance and sizeE.
                       Assumes that the original tree was balanced and
                       that [l] or [r] has changed by at most one element.
-    [combine k x l r] Restores balance and size.
+    [combine k x l r] Restores balance and sizeE.
 
   Furthermore, we can construct a new tree from two trees. Both operations
   assume that all values in [l] < all values in [r] and that [l] and [r]
@@ -177,9 +177,9 @@ lookupAssoc (This k) m = (k :=>) <$> lookup k m
   Combine
 --------------------------------------------------------------------}
 combineNE :: GCompare k => k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
-combineNE kx x l@(NonEmptyDMap sizeL ky y ly ry) r@(NonEmptyDMap sizeR kz z lz rz)
-    | delta*sizeL <= sizeR  = balanceNEL kz z (combineNEL kx x l lz) rz
-    | delta*sizeR <= sizeL  = balanceNER ky y ly (combineNER kx x ry r)
+combineNE kx x l@(NonEmptyDMap sizeEL ky y ly ry) r@(NonEmptyDMap sizeER kz z lz rz)
+    | delta*sizeEL <= sizeER  = balanceNEL kz z (combineNEL kx x l lz) rz
+    | delta*sizeER <= sizeEL  = balanceNER ky y ly (combineNER kx x ry r)
     | otherwise             = binNE kx x (Bin' l) (Bin' r)
 
 combineNEL :: GCompare k => k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
@@ -190,10 +190,10 @@ combineNER :: GCompare k => k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmp
 combineNER kx x Tip r = insertMinNE kx x r
 combineNER kx x (Bin' l) r = combineNE kx x l r
 
-combine :: GCompare k => k v -> f v -> DMap k f -> DMap k f -> NonEmptyDMap k f
-combine kx x Tip r  = insertMin kx x r
-combine kx x l Tip  = insertMax kx x l
-combine kx x (Bin' l) (Bin' r) = combineNE kx x l r
+combineE :: GCompare k => k v -> f v -> DMap k f -> DMap k f -> NonEmptyDMap k f
+combineE kx x Tip r  = insertMin kx x r
+combineE kx x l Tip  = insertMax kx x l
+combineE kx x (Bin' l) (Bin' r) = combineNE kx x l r
 
 -- insertMin and insertMax don't perform potentially expensive comparisons.
 
@@ -214,9 +214,9 @@ insertMin kx x t = case t of
   [merge l r]: merges two trees.
 --------------------------------------------------------------------}
 mergeNE :: NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
-mergeNE l@(NonEmptyDMap sizeL kx x lx rx) r@(NonEmptyDMap sizeR ky y ly ry)
-    | delta*sizeL <= sizeR = balanceNEL ky y (mergeNEL l ly) ry
-    | delta*sizeR <= sizeL = balanceNER kx x lx (mergeNER rx r)
+mergeNE l@(NonEmptyDMap sizeEL kx x lx rx) r@(NonEmptyDMap sizeER ky y ly ry)
+    | delta*sizeEL <= sizeER = balanceNEL ky y (mergeNEL l ly) ry
+    | delta*sizeER <= sizeEL = balanceNER kx x lx (mergeNER rx r)
     | otherwise            = glueNE l r
 
 mergeNEL :: NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
@@ -281,7 +281,7 @@ minViewWithKeyNE (NonEmptyDMap _ k0 x0 l0 r0) = toPair $ go k0 x0 l0 r0
     go k x Tip r = (k :=> x) :*: r
     go k x (Bin _ kl xl ll lr) r =
       let !(km :*: l') = go kl xl ll lr
-      in (km :*: (Bin' $! balance k x l' r))
+      in (km :*: (Bin' $! balanceE k x l' r))
 
 -- | /O(log n)/. Retrieves the minimal (key :=> value) entry of the map, and
 -- the map stripped of that element, or 'Nothing' if passed an empty map.
@@ -298,7 +298,7 @@ maxViewWithKeyNE (NonEmptyDMap _ k0 x0 l0 r0) = toPair $ go k0 x0 l0 r0
     go k x l Tip = (k :=> x) :*: l
     go k x l (Bin _ kr xr rl rr) =
       let !(km :*: r') = go kr xr rl rr
-      in (km :*: (Bin' $! balance k x l r'))
+      in (km :*: (Bin' $! balanceE k x l r'))
 
 -- | /O(log n)/. Retrieves the maximal (key :=> value) entry of the map, and
 -- the map stripped of that element, or 'Nothing' if passed an empty map.
@@ -317,10 +317,10 @@ deleteFindMax = maxViewWithKeyNE
 
 {--------------------------------------------------------------------
   [balance l x r] balances two trees with value x.
-  The sizes of the trees should balance after decreasing the
-  size of one of them. (a rotation).
+  The sizeEs of the trees should balance after decreasing the
+  sizeE of one of them. (a rotation).
 
-  [delta] is the maximal relative difference between the sizes of
+  [delta] is the maximal relative difference between the sizeEs of
           two trees, it corresponds with the [w] in Adams' paper.
   [ratio] is the ratio between an outer and inner sibling of the
           heavier subtree in an unbalanced setting. It determines
@@ -353,99 +353,99 @@ ratio = 2
 
 balanceNE :: k v -> f v -> NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
 balanceNE k x l r
-  | sizeL + sizeR <= 1    = NonEmptyDMap sizeX k x (Bin' l) (Bin' r)
-  | sizeR >= delta*sizeL  = rotateL k x (Bin' l) r
-  | sizeL >= delta*sizeR  = rotateR k x l (Bin' r)
-  | otherwise             = NonEmptyDMap sizeX k x (Bin' l) (Bin' r)
+  | sizeEL + sizeER <= 1    = NonEmptyDMap sizeEX k x (Bin' l) (Bin' r)
+  | sizeER >= delta*sizeEL  = rotateL k x (Bin' l) r
+  | sizeEL >= delta*sizeER  = rotateR k x l (Bin' r)
+  | otherwise             = NonEmptyDMap sizeEX k x (Bin' l) (Bin' r)
   where
-    sizeL = sizeNE l
-    sizeR = sizeNE r
-    sizeX = sizeL + sizeR + 1
+    sizeEL = sizeNE l
+    sizeER = sizeNE r
+    sizeEX = sizeEL + sizeER + 1
 
 balanceNEL :: k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
 balanceNEL k x l r
-  | sizeL + sizeR <= 1    = NonEmptyDMap sizeX k x (Bin' l) r
-  | sizeR >= delta*sizeL  = let
+  | sizeEL + sizeER <= 1    = NonEmptyDMap sizeEX k x (Bin' l) r
+  | sizeER >= delta*sizeEL  = let
       r' = case r of
-          Tip -> error "balanceNEL: Declared size of 'r' is greater than 1, shouldn't be empty"
+          Tip -> error "balanceNEL: Declared sizeE of 'r' is greater than 1, shouldn't be empty"
           Bin' ne -> ne
     in rotateL k x (Bin' l) r'
-  | sizeL >= delta*sizeR  = rotateR k x l r
-  | otherwise             = NonEmptyDMap sizeX k x (Bin' l) r
+  | sizeEL >= delta*sizeER  = rotateR k x l r
+  | otherwise             = NonEmptyDMap sizeEX k x (Bin' l) r
   where
-    sizeL = sizeNE l
-    sizeR = size r
-    sizeX = sizeL + sizeR + 1
+    sizeEL = sizeNE l
+    sizeER = sizeE r
+    sizeEX = sizeEL + sizeER + 1
 
 balanceNER :: k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
 balanceNER k x l r
-  | sizeL + sizeR <= 1    = NonEmptyDMap sizeX k x l (Bin' r)
-  | sizeR >= delta*sizeL  = rotateL k x l r
-  | sizeL >= delta*sizeR  = let
+  | sizeEL + sizeER <= 1    = NonEmptyDMap sizeEX k x l (Bin' r)
+  | sizeER >= delta*sizeEL  = rotateL k x l r
+  | sizeEL >= delta*sizeER  = let
       l' = case l of
-          Tip -> error "balanceNER: Declared size of 'l' is greater than 1, shouldn't be empty"
+          Tip -> error "balanceNER: Declared sizeE of 'l' is greater than 1, shouldn't be empty"
           Bin' ne -> ne
     in rotateR k x l' (Bin' r)
-  | otherwise             = NonEmptyDMap sizeX k x l (Bin' r)
+  | otherwise             = NonEmptyDMap sizeEX k x l (Bin' r)
   where
-    sizeL = size l
-    sizeR = sizeNE r
-    sizeX = sizeL + sizeR + 1
+    sizeEL = sizeE l
+    sizeER = sizeNE r
+    sizeEX = sizeEL + sizeER + 1
 
 
-balance :: k v -> f v -> DMap k f -> DMap k f -> NonEmptyDMap k f
-balance k x l r
-  | sizeL + sizeR <= 1    = NonEmptyDMap sizeX k x l r
-  | sizeR >= delta*sizeL  = let
+balanceE :: k v -> f v -> DMap k f -> DMap k f -> NonEmptyDMap k f
+balanceE k x l r
+  | sizeEL + sizeER <= 1    = NonEmptyDMap sizeEX k x l r
+  | sizeER >= delta*sizeEL  = let
       r' = case r of
-          Tip -> error "balance: Declared size of 'r' is greater than 1, shouldn't be empty"
+          Tip -> error "balance: Declared sizeE of 'r' is greater than 1, shouldn't be empty"
           Bin' ne -> ne
     in rotateL k x l r'
-  | sizeL >= delta*sizeR  = let
+  | sizeEL >= delta*sizeER  = let
       l' = case l of
-          Tip -> error "balance: Declared size of 'l' is greater than 1, shouldn't be empty"
+          Tip -> error "balance: Declared sizeE of 'l' is greater than 1, shouldn't be empty"
           Bin' ne -> ne
     in rotateR k x l' r
-  | otherwise             = NonEmptyDMap sizeX k x l r
+  | otherwise             = NonEmptyDMap sizeEX k x l r
   where
-    sizeL = size l
-    sizeR = size r
-    sizeX = sizeL + sizeR + 1
+    sizeEL = sizeE l
+    sizeER = sizeE r
+    sizeEX = sizeEL + sizeER + 1
 
 -- rotate
 rotateL :: k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
 rotateL k x l r@(NonEmptyDMap _ _ _ ly ry)
-  | size ly < ratio*size ry = singleL k x l r
+  | sizeE ly < ratio*sizeE ry = singleL k x l r
   | otherwise               = doubleL k x l r
 
 rotateR :: k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
 rotateR k x l@(NonEmptyDMap _ _ _ ly ry) r
-  | size ry < ratio*size ly = singleR k x l r
+  | sizeE ry < ratio*sizeE ly = singleR k x l r
   | otherwise               = doubleR k x l r
 
 -- basic rotations
 singleL :: k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
-singleL k1 x1 t1 (NonEmptyDMap _ k2 x2 t2 t3)  = binNE k2 x2 (bin k1 x1 t1 t2) t3
+singleL k1 x1 t1 (NonEmptyDMap _ k2 x2 t2 t3)  = binNE k2 x2 (binE k1 x1 t1 t2) t3
 
 singleR :: k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
-singleR k1 x1 (NonEmptyDMap _ k2 x2 t1 t2) t3  = binNE k2 x2 t1 (bin k1 x1 t2 t3)
+singleR k1 x1 (NonEmptyDMap _ k2 x2 t1 t2) t3  = binNE k2 x2 t1 (binE k1 x1 t2 t3)
 
 doubleL :: k v -> f v -> DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
-doubleL k1 x1 t1 (NonEmptyDMap _ k2 x2 (Bin _ k3 x3 t2 t3) t4) = binNE k3 x3 (bin k1 x1 t1 t2) (bin k2 x2 t3 t4)
+doubleL k1 x1 t1 (NonEmptyDMap _ k2 x2 (Bin _ k3 x3 t2 t3) t4) = binNE k3 x3 (binE k1 x1 t1 t2) (binE k2 x2 t3 t4)
 doubleL _ _ _ _ = error "doubleL"
 
 doubleR :: k v -> f v -> NonEmptyDMap k f -> DMap k f -> NonEmptyDMap k f
-doubleR k1 x1 (NonEmptyDMap _ k2 x2 t1 (Bin _ k3 x3 t2 t3)) t4 = binNE k3 x3 (bin k2 x2 t1 t2) (bin k1 x1 t3 t4)
+doubleR k1 x1 (NonEmptyDMap _ k2 x2 t1 (Bin _ k3 x3 t2 t3)) t4 = binNE k3 x3 (binE k2 x2 t1 t2) (binE k1 x1 t3 t4)
 doubleR _ _ _ _ = error "doubleR"
 
 {--------------------------------------------------------------------
-  The bin constructor maintains the size of the tree
+  The bin constructor maintains the sizeE of the tree
 --------------------------------------------------------------------}
 binNE :: k v -> f v -> DMap k f -> DMap k f -> NonEmptyDMap k f
-binNE k x l r = NonEmptyDMap (size l + size r + 1) k x l r
+binNE k x l r = NonEmptyDMap (sizeE l + sizeE r + 1) k x l r
 
-bin :: k v -> f v -> DMap k f -> DMap k f -> DMap k f
-bin k x l r = Bin' $! binNE k x l r
+binE :: k v -> f v -> DMap k f -> DMap k f -> DMap k f
+binE k x l r = Bin' $! binNE k x l r
 
 {--------------------------------------------------------------------
   Utility functions that return sub-ranges of the original
@@ -460,7 +460,7 @@ bin k x l r = Bin' $! binNE k x l r
 
   [split k t]           Returns two trees [l] and [r] where all keys
                         in [l] are <[k] and all keys in [r] are >[k].
-  [splitLookup k t]     Just like [split] but also returns whether [k]
+  [splitLookupE k t]     Just like [split] but also returns whether [k]
                         was found in the tree.
 --------------------------------------------------------------------}
 
@@ -478,14 +478,14 @@ trim cmplo cmphi t@(Bin _ kx _ l r)
               _  -> trim cmplo cmphi l
       _  -> trim cmplo cmphi r
 
-trimLookupLo :: GCompare k => Some k -> (Some k -> Ordering) -> DMap k f -> (Maybe (DSum k f), DMap k f)
-trimLookupLo _  _     Tip = (Nothing,Tip)
-trimLookupLo lo cmphi t@(Bin _ kx x l r)
+trimLookupELo :: GCompare k => Some k -> (Some k -> Ordering) -> DMap k f -> (Maybe (DSum k f), DMap k f)
+trimLookupELo _  _     Tip = (Nothing,Tip)
+trimLookupELo lo cmphi t@(Bin _ kx x l r)
   = case compare lo (This kx) of
       LT -> case cmphi (This kx) of
-              GT -> (lookupAssoc lo t, t)
-              _  -> trimLookupLo lo cmphi l
-      GT -> trimLookupLo lo cmphi r
+              GT -> (lookupAssocE lo t, t)
+              _  -> trimLookupELo lo cmphi l
+      GT -> trimLookupELo lo cmphi r
       EQ -> (Just (kx :=> x),trim (compare lo) cmphi r)
 
 
@@ -498,7 +498,7 @@ filterGt cmp = go
   where
     go Tip              = Tip
     go (Bin _ kx x l r) = case cmp (This kx) of
-              LT -> Bin' $! combine kx x (go l) r
+              LT -> Bin' $! combineE kx x (go l) r
               GT -> go r
               EQ -> r
 
@@ -508,5 +508,5 @@ filterLt cmp = go
     go Tip              = Tip
     go (Bin _ kx x l r) = case cmp (This kx) of
           LT -> go l
-          GT -> Bin' $! combine kx x l (go r)
+          GT -> Bin' $! combineE kx x l (go r)
           EQ -> l
diff --git a/src/Data/Dependent/Map/Internal2.hs b/src/Data/Dependent/Map/Internal2.hs
index 1b8debd..4bd2f07 100644
--- a/src/Data/Dependent/Map/Internal2.hs
+++ b/src/Data/Dependent/Map/Internal2.hs
@@ -175,8 +175,8 @@ makeDelete k = (k `seq` go, k `seq` nonEmpty . go')
     go' :: NonEmptyDMap k f -> DMap k f
     go' (NonEmptyDMap _ kx x l r) =
         case gcompare k kx of
-            GLT -> Bin' $! balance kx x (go l) r
-            GGT -> Bin' $! balance kx x l (go r)
+            GLT -> Bin' $! balanceE kx x (go l) r
+            GGT -> Bin' $! balanceE kx x l (go r)
             GEQ -> glue l r
 
 makeAdjustF
@@ -259,8 +259,8 @@ makeUpdateWithKey f k = (k `seq` go, k `seq` nonEmpty . go')
     go' :: NonEmptyDMap k f -> DMap k f
     go' (NonEmptyDMap sx kx x l r) =
         case gcompare k kx of
-           GLT -> Bin' $! balance kx x (go l) r
-           GGT -> Bin' $! balance kx x l (go r)
+           GLT -> Bin' $! balanceE kx x (go l) r
+           GGT -> Bin' $! balanceE kx x l (go r)
            GEQ -> case f kx x of
                    Just x' -> Bin sx kx x' l r
                    Nothing -> glue l r
@@ -282,11 +282,11 @@ makeUpdateLookupWithKey f k = (k `seq` go, k `seq` fmap nonEmpty . go')
     go' :: NonEmptyDMap k f -> (Maybe (f v), DMap k f)
     go' (NonEmptyDMap sx kx x l r) =
            case gcompare k kx of
-                GLT -> let (found,l') = go l in (found,Bin' $! balance kx x l' r)
-                GGT -> let (found,r') = go r in (found,Bin' $! balance kx x l r')
+                GLT -> let (found,l') = go l in (found,Bin' $! balanceE kx x l' r)
+                GGT -> let (found,r') = go r in (found,Bin' $! balanceE kx x l r')
                 GEQ -> case f kx x of
-                        Just x' -> (Just x',Bin sx kx x' l r)
-                        Nothing -> (Just x,glue l r)
+                        Just x' -> (Just x', Bin sx kx x' l r)
+                        Nothing -> (Just x, glue l r)
 
 makeAlter
   :: forall k f v
@@ -301,13 +301,13 @@ makeAlter f k = (k `seq` go, k `seq` nonEmpty . go')
     go :: DMap k f -> DMap k f
     go Tip = case f Nothing of
                Nothing -> Tip
-               Just x  -> singleton k x
+               Just x  -> singletonE k x
     go (Bin' ne) = go' ne
 
     go' :: NonEmptyDMap k f -> DMap k f
     go' (NonEmptyDMap sx kx x l r) = case gcompare k kx of
-               GLT -> Bin' $! balance kx x (go l) r
-               GGT -> Bin' $! balance kx x l (go r)
+               GLT -> Bin' $! balanceE kx x (go l) r
+               GGT -> Bin' $! balanceE kx x l (go r)
                GEQ -> case f (Just x) of
                        Just x' -> Bin sx kx x' l r
                        Nothing -> glue l r
@@ -327,13 +327,13 @@ makeAlterF
 makeAlterF k f = (go, fmap nonEmpty . go')
   where
     go :: DMap k g -> f (DMap k g)
-    go Tip = maybe Tip (singleton k) <$> f Nothing
+    go Tip = maybe Tip (singletonE k) <$> f Nothing
     go (Bin' ne) = go' ne
 
     go' :: NonEmptyDMap k g -> f (DMap k g)
     go' (NonEmptyDMap sx kx x l r) = case gcompare k kx of
-      GLT -> (\l' -> Bin' $! balance kx x l' r) <$> go l
-      GGT -> (\r' -> Bin' $! balance kx x l r') <$> go r
+      GLT -> (\l' -> Bin' $! balanceE kx x l' r) <$> go l
+      GGT -> (\r' -> Bin' $! balanceE kx x l r') <$> go r
       GEQ -> maybe (glue l r) (\x' -> Bin sx kx x' l r) <$> f (Just x)
 
 makeLookupIndex
@@ -353,8 +353,8 @@ makeLookupIndex k = (k `seq` go 0, k `seq` go' 0)
     go' !idx (NonEmptyDMap _ kx _ l r)
       = case gcompare k kx of
           GLT -> go idx l
-          GGT -> go (idx + size l + 1) r
-          GEQ -> Just (idx + size l)
+          GGT -> go (idx + sizeE l + 1) r
+          GEQ -> Just (idx + sizeE l)
 
 makElemAt
   :: ( Int -> DMap k f -> DSum k f
@@ -372,7 +372,7 @@ makElemAt = (go, go')
           GT -> go (i-sizeL-1) r
           EQ -> kx :=> x
       where
-        sizeL = size l
+        sizeL = sizeE l
 
 makeUpdateAt
   :: forall k f v
@@ -389,13 +389,13 @@ makeUpdateAt f i0 = (i0 `seq` go i0, i0 `seq` nonEmpty . go' i0)
 
     go' :: Int -> NonEmptyDMap k f -> DMap k f
     go' i (NonEmptyDMap sx kx x l r) = case compare i sizeL of
-      LT -> Bin' $! balance kx x (go i l) r
-      GT -> Bin' $! balance kx x l (go (i-sizeL-1) r)
+      LT -> Bin' $! balanceE kx x (go i l) r
+      GT -> Bin' $! balanceE kx x l (go (i-sizeL-1) r)
       EQ -> case f kx x of
               Just x' -> Bin sx kx x' l r
               Nothing -> glue l r
       where
-        sizeL = size l
+        sizeL = sizeE l
 
 {--------------------------------------------------------------------
   Minimal, Maximal Worker Builders
@@ -452,7 +452,7 @@ makeDeleteMin = (go, nonEmpty . go')
 
     go' :: NonEmptyDMap k f -> DMap k f
     go' (NonEmptyDMap _ _  _ Tip r) = r
-    go' (NonEmptyDMap _ kx x l r)   = Bin' $! balance kx x (go l) r
+    go' (NonEmptyDMap _ kx x l r)   = Bin' $! balanceE kx x (go l) r
 
 makeDeleteMax
   :: forall k f
@@ -467,7 +467,7 @@ makeDeleteMax = (go, nonEmpty . go')
 
     go' :: NonEmptyDMap k f -> DMap k f
     go' (NonEmptyDMap _ _  _ l Tip) = l
-    go' (NonEmptyDMap _ kx x l r)   = Bin' $! balance kx x l (go r)
+    go' (NonEmptyDMap _ kx x l r)   = Bin' $! balanceE kx x l (go r)
 
 
 -- | /O(log n)/. Update the value at the minimal key.
@@ -483,7 +483,7 @@ makeUpdateMinWithKey f = (go, nonEmpty . go')
     go' (NonEmptyDMap sx kx x Tip r) = case f kx x of
                                   Nothing -> r
                                   Just x' -> Bin sx kx x' Tip r
-    go' (NonEmptyDMap _ kx x l r)    = Bin' $! balance kx x (go l) r
+    go' (NonEmptyDMap _ kx x l r)    = Bin' $! balanceE kx x (go l) r
 
 makeUpdateMaxWithKey
   :: (forall v. k v -> f v -> Maybe (f v))
@@ -497,7 +497,7 @@ makeUpdateMaxWithKey f = (go, nonEmpty . go')
     go' (NonEmptyDMap sx kx x l Tip) = case f kx x of
                               Nothing -> l
                               Just x' -> Bin sx kx x' l Tip
-    go' (NonEmptyDMap _ kx x l r)    = Bin' $! balance kx x l (go r)
+    go' (NonEmptyDMap _ kx x l r)    = Bin' $! balanceE kx x l (go r)
 
 {--------------------------------------------------------------------
   Union Worker Builders
@@ -516,7 +516,7 @@ makeUnion = (go, go')
     go t1@(Bin _ k1 x1 l1 r1) t2 = case fst (makeSplit k1) t2 of
       (l2, r2)
         | l1 `ptrEq` l1l2 && r1 `ptrEq` r1r2 -> t1
-        | otherwise -> Bin' $! combine k1 x1 l1l2 r1r2
+        | otherwise -> Bin' $! combineE k1 x1 l1l2 r1r2
         where !l1l2 = l1 `go` l2
               !r1r2 = r1 `go` r2
 
@@ -525,7 +525,7 @@ makeUnion = (go, go')
     go' t1@(NonEmptyDMap _ k1 x1 l1 r1) t2 = case snd (makeSplit k1) t2 of
       (l2, r2)
         | l1 `ptrEq` l1l2 && r1 `ptrEq` r1r2 -> t1
-        | otherwise -> combine k1 x1 l1l2 r1r2
+        | otherwise -> combineE k1 x1 l1l2 r1r2
         where !l1l2 = l1 `go` l2
               !r1r2 = r1 `go` r2
 
@@ -540,15 +540,15 @@ makeUnionWithKey f = (go, go')
     go Tip t2  = t2
     go (Bin _ k1 x1 l1 r1) t2 = case fst (makeSplitLookup k1) t2 of
       (l2, mx2, r2) -> case mx2 of
-          Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
-          Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
+          Nothing -> Bin' $! combineE k1 x1 l1l2 r1r2
+          Just x2 -> Bin' $! combineE k1 (f k1 x1 x2) l1l2 r1r2
         where !l1l2 = go l1 l2
               !r1r2 = go r1 r2
 
     go' (NonEmptyDMap _ k1 x1 l1 r1) t2 = case snd (makeSplitLookup k1) t2 of
       (l2, mx2, r2) -> case mx2 of
-          Nothing -> combine k1 x1 l1l2 r1r2
-          Just x2 -> combine k1 (f k1 x1 x2) l1l2 r1r2
+          Nothing -> combineE k1 x1 l1l2 r1r2
+          Just x2 -> combineE k1 (f k1 x1 x2) l1l2 r1r2
         where !l1l2 = go l1 l2
               !r1r2 = go r1 r2
 
@@ -567,7 +567,7 @@ makeDifference = (go, go')
     go t1 Tip  = t1
     go t1 (Bin _ k2 _x2 l2 r2) = case fst (makeSplit k2) t1 of
       (l1, r1)
-        | size t1 == size l1l2 + size r1r2 -> t1
+        | sizeE t1 == sizeE l1l2 + sizeE r1r2 -> t1
         | otherwise -> merge l1l2 r1r2
         where
           !l1l2 = l1 `go` l2
@@ -575,7 +575,7 @@ makeDifference = (go, go')
 
     go' t1 (NonEmptyDMap _ k2 _x2 l2 r2) = case snd (makeSplit k2) t1 of
       (l1, r1)
-        | sizeNE t1 == size l1l2 + size r1r2 -> Bin' t1
+        | sizeNE t1 == sizeE l1l2 + sizeE r1r2 -> Bin' t1
         | otherwise -> merge l1l2 r1r2
         where
           !l1l2 = l1 `go` l2
@@ -593,19 +593,19 @@ makeDifferenceWithKey f = (go, go')
     go t1 Tip  = t1
     go (Bin _ k1 x1 l1 r1) t2 = case fst (makeSplitLookup k1) t2 of
       (l2, mx2, r2) -> case mx2 of
-          Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
+          Nothing -> Bin' $! combineE k1 x1 l1l2 r1r2
           Just x2 -> case f k1 x1 x2 of
             Nothing -> merge l1l2 r1r2
-            Just x1x2 -> Bin' $! combine k1 x1x2 l1l2 r1r2
+            Just x1x2 -> Bin' $! combineE k1 x1x2 l1l2 r1r2
         where !l1l2 = go l1 l2
               !r1r2 = go r1 r2
 
     go' (NonEmptyDMap _ k1 x1 l1 r1) t2 = case snd (makeSplitLookup k1) t2 of
       (l2, mx2, r2) -> case mx2 of
-          Nothing -> Bin' $! combine k1 x1 l1l2 r1r2
+          Nothing -> Bin' $! combineE k1 x1 l1l2 r1r2
           Just x2 -> case f k1 x1 x2 of
             Nothing -> merge l1l2 r1r2
-            Just x1x2 -> Bin' $! combine k1 x1x2 l1l2 r1r2
+            Just x1x2 -> Bin' $! combineE k1 x1x2 l1l2 r1r2
         where !l1l2 = go l1 l2
               !r1r2 = go r1 r2
 
@@ -629,7 +629,7 @@ makeIntersection = (go, go')
       in if found
          then if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1
               then t1
-              else Bin' $! combine k1 x1 l1l2 r1r2
+              else Bin' $! combineE k1 x1 l1l2 r1r2
          else merge l1l2 r1r2
 
     go' t1@(NonEmptyDMap s1 k1 x1 l1 r1) t2 =
@@ -639,7 +639,7 @@ makeIntersection = (go, go')
       in if found
          then if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1
               then Bin' t1
-              else Bin' $! combine k1 x1 l1l2 r1r2
+              else Bin' $! combineE k1 x1 l1l2 r1r2
          else merge l1l2 r1r2
 
 makeIntersectionWithKey
@@ -660,7 +660,7 @@ makeIntersectionWithKey f = (go, go')
           !r1r2 = go r1 r2
       in case found of
            Nothing -> merge l1l2 r1r2
-           Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
+           Just x2 -> Bin' $! combineE k1 (f k1 x1 x2) l1l2 r1r2
 
     go' :: NonEmptyDMap k f -> NonEmptyDMap k g -> DMap k h
     go' (NonEmptyDMap s1 k1 x1 l1 r1) t2 =
@@ -669,7 +669,7 @@ makeIntersectionWithKey f = (go, go')
           !r1r2 = go r1 r2
       in case found of
            Nothing -> merge l1l2 r1r2
-           Just x2 -> Bin' $! combine k1 (f k1 x1 x2) l1l2 r1r2
+           Just x2 -> Bin' $! combineE k1 (f k1 x1 x2) l1l2 r1r2
 
 {--------------------------------------------------------------------
   Submap Worker Builders
@@ -713,7 +713,7 @@ makeFilterWithKey p = go
     go t@(Bin _ kx x l r)
       | p kx x    = if l' `ptrEq` l && r' `ptrEq` r
                     then t
-                    else Bin' $! combine kx x l' r'
+                    else Bin' $! combineE kx x l' r'
       | otherwise = merge l' r'
       where !l' = go l
             !r' = go r
@@ -729,8 +729,8 @@ makePartitionWithKey p m0 = toPair (go m0)
     go :: DMap k f -> (DMap k f :*: DMap k f)
     go Tip = (Tip :*: Tip)
     go (Bin _ kx x l r)
-      | p kx x    = ((Bin' $! combine kx x l1 r1) :*: merge l2 r2)
-      | otherwise = (merge l1 r1 :*: (Bin' $! combine kx x l2 r2))
+      | p kx x    = ((Bin' $! combineE kx x l1 r1) :*: merge l2 r2)
+      | otherwise = (merge l1 r1 :*: (Bin' $! combineE kx x l2 r2))
       where
         (l1 :*: l2) = go l
         (r1 :*: r2) = go r
@@ -744,7 +744,7 @@ makeMapMaybeWithKey f = go
   where
     go Tip = Tip
     go (Bin _ kx x l r) = case f kx x of
-        Just y  -> Bin' $! combine kx y (go l) (go r)
+        Just y  -> Bin' $! combineE kx y (go l) (go r)
         Nothing -> merge (go l) (go r)
 
 makeMapEitherWithKey
@@ -759,8 +759,8 @@ makeMapEitherWithKey f = toPair . go
        => DMap k f -> (DMap k g :*: DMap k h)
     go Tip = (Tip :*: Tip)
     go (Bin _ kx x l r) = case f kx x of
-      Left y  -> ((Bin' $! combine kx y l1 r1) :*: merge l2 r2)
-      Right z -> (merge l1 r1 :*: (Bin' $! combine kx z l2 r2))
+      Left y  -> ((Bin' $! combineE kx y l1 r1) :*: merge l2 r2)
+      Right z -> (merge l1 r1 :*: (Bin' $! combineE kx z l2 r2))
       where
         (l1 :*: l2) = go l
         (r1 :*: r2) = go r
@@ -917,7 +917,7 @@ makeFromDistinctAscList
     build c 0 xs'  = c Tip xs'
     build c 5 xs'  = case xs' of
                        ((k1:=>x1):(k2:=>x2):(k3:=>x3):(k4:=>x4):(k5:=>x5):xx)
-                            -> c (bin k4 x4 (bin k2 x2 (singleton k1 x1) (singleton k3 x3)) (singleton k5 x5)) xx
+                            -> c (binE k4 x4 (binE k2 x2 (singletonE k1 x1) (singletonE k3 x3)) (singletonE k5 x5)) xx
                        _ -> error "fromDistinctAscList build"
     build c n xs'  = seq nr $ build (buildR nr c) nl xs'
                    where
@@ -931,7 +931,7 @@ makeFromDistinctAscList
       -> b
     build' c 5 xs'  = case xs' of
                        (k1:=>x1) :| ((k2:=>x2):(k3:=>x3):(k4:=>x4):(k5:=>x5):xx)
-                            -> c (binNE k4 x4 (bin k2 x2 (singleton k1 x1) (singleton k3 x3)) (singleton k5 x5)) xx
+                            -> c (binNE k4 x4 (binE k2 x2 (singletonE k1 x1) (singletonE k3 x3)) (singletonE k5 x5)) xx
                        _ -> error "fromDistinctAscList build'"
     build' c n xs'  = seq nr $ build' (build'R nr c) nl xs'
                    where
@@ -957,7 +957,7 @@ makeFromDistinctAscList
       :: DMap k f -> k v -> f v
       -> (DMap k f -> a -> b)
       -> DMap k f -> a -> b
-    buildB l k x c r zs = c (bin k x l r) zs
+    buildB l k x c r zs = c (binE k x l r) zs
 
     build'B
       :: NonEmptyDMap k f -> k v -> f v
@@ -983,8 +983,8 @@ makeSplit k = (toPair . go, toPair . go')
 
     go' :: NonEmptyDMap k f -> (DMap k f :*: DMap k f)
     go' (NonEmptyDMap _ kx x l r) = case gcompare k kx of
-          GLT -> let !(lt :*: gt) = go l in (lt :*: (Bin' $! combine kx x gt r))
-          GGT -> let !(lt :*: gt) = go r in ((Bin' $! combine kx x l lt) :*: gt)
+          GLT -> let !(lt :*: gt) = go l in (lt :*: (Bin' $! combineE kx x gt r))
+          GGT -> let !(lt :*: gt) = go r in ((Bin' $! combineE kx x l lt) :*: gt)
           GEQ -> (l :*: r)
 {-# INLINABLE makeSplit #-}
 
@@ -1003,8 +1003,8 @@ makeSplitLookup k = (toTriple . go, toTriple . go')
 
     go' :: NonEmptyDMap k f -> Triple' (DMap k f) (Maybe (f v)) (DMap k f)
     go' (NonEmptyDMap _ kx x l r) = case gcompare k kx of
-      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
-      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
+      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combineE kx x gt r)
+      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combineE kx x l lt) z gt
       GEQ -> Triple' l (Just x) r
 
 makeSplitMember
@@ -1022,8 +1022,8 @@ makeSplitMember k = (toTriple . go, toTriple . go')
 
     go' :: NonEmptyDMap k f -> Triple' (DMap k f) Bool (DMap k f)
     go' (NonEmptyDMap _ kx x l r) = case gcompare k kx of
-      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
-      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
+      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combineE kx x gt r)
+      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combineE kx x l lt) z gt
       GEQ -> Triple' l True r
 
 makeSplitLookupWithKey
@@ -1041,8 +1041,8 @@ makeSplitLookupWithKey k = (toTriple . go, toTriple . go')
 
     go' :: NonEmptyDMap k f -> Triple' (DMap k f) (Maybe (k v, f v)) (DMap k f)
     go' (NonEmptyDMap _ kx x l r) = case gcompare k kx of
-      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combine kx x gt r)
-      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combine kx x l lt) z gt
+      GLT -> let !(Triple' lt z gt) = go l in Triple' lt z (Bin' $! combineE kx x gt r)
+      GGT -> let !(Triple' lt z gt) = go r in Triple' (Bin' $! combineE kx x l lt) z gt
       GEQ -> Triple' l (Just (kx, x)) r
 
 {--------------------------------------------------------------------
@@ -1154,7 +1154,7 @@ makeBalanced = (go, go')
         Bin' ne -> go' ne
 
     go' t = case t of
-        NonEmptyDMap _ _ _ l r  -> (size l + size r <= 1 || (size l <= delta*size r && size r <= delta*size l)) &&
+        NonEmptyDMap _ _ _ l r  -> (sizeE l + sizeE r <= 1 || (sizeE l <= delta*sizeE r && sizeE r <= delta*sizeE l)) &&
                         go l && go r
 
 makeValidsize
@@ -1162,7 +1162,7 @@ makeValidsize
      , NonEmptyDMap k f -> Bool
      )
 makeValidsize =
-  ( \t -> realsize t == Just (size t)
+  ( \t -> realsize t == Just (sizeE t)
   , \t -> realsize' t == Just (sizeNE t)
   )
   where
diff --git a/src/Data/Dependent/Map/NonEmpty.hs b/src/Data/Dependent/Map/NonEmpty.hs
index 05ae216..7503835 100644
--- a/src/Data/Dependent/Map/NonEmpty.hs
+++ b/src/Data/Dependent/Map/NonEmpty.hs
@@ -24,7 +24,6 @@ module Data.Dependent.Map.NonEmpty
     , (!), (\\)
 
     -- * Query
-    , null
     , size
     , member
     , notMember
@@ -218,10 +217,25 @@ m1 \\ m2 = difference m1 m2
 --
 -- #endif
 
+{--------------------------------------------------------------------
+  Construction
+--------------------------------------------------------------------}
+
+-- | /O(1)/. A map with a single element.
+--
+-- > singleton 1 'a'        == fromList [(1, 'a')]
+-- > size (singleton 1 'a') == 1
+singleton :: k v -> f v -> NonEmptyDMap k f
+singleton = singletonNE
+
 {--------------------------------------------------------------------
   Query
 --------------------------------------------------------------------}
 
+-- | /O(1)/. The number of elements in the map.
+size :: NonEmptyDMap k f -> Int
+size = sizeNE
+
 -- | /O(log n)/. Is the key a member of the map? See also 'notMember'.
 member :: GCompare k => k a -> NonEmptyDMap k f -> Bool
 member k = isJust . lookupNE k
@@ -230,6 +244,13 @@ member k = isJust . lookupNE k
 notMember :: GCompare k => k v -> NonEmptyDMap k f -> Bool
 notMember k m = not (member k m)
 
+-- | /O(log n)/. Lookup the value at a key in the map.
+--
+-- The function will return the corresponding value as @('Just' value)@,
+-- or 'Nothing' if the key isn't in the map.
+lookup :: forall k f v. GCompare k => k v -> NonEmptyDMap k f -> Maybe (f v)
+lookup = lookupNE
+
 -- | /O(log n)/. Find the value at a key.
 -- Calls 'error' when the element can not be found.
 -- Consider using 'lookup' when elements may not be present.

From bd76d8dd2ef665c68fe1cc1fd664278ccc448405 Mon Sep 17 00:00:00 2001
From: John Ericson <git@JohnEricson.me>
Date: Wed, 27 Feb 2019 10:13:29 -0500
Subject: [PATCH 09/10] Fix deleteFind{Min,Max} {min,max}ViewWithKey exports

---
 dependent-map.cabal                 |  2 +-
 src/Data/Dependent/Map.hs           | 28 +++++++++++++++++
 src/Data/Dependent/Map/Internal.hs  | 47 ++++++++++-------------------
 src/Data/Dependent/Map/Internal2.hs | 40 ++++++++++++------------
 src/Data/Dependent/Map/NonEmpty.hs  | 24 +++++++++++++++
 5 files changed, 89 insertions(+), 52 deletions(-)

diff --git a/dependent-map.cabal b/dependent-map.cabal
index 9372b84..455c0dd 100644
--- a/dependent-map.cabal
+++ b/dependent-map.cabal
@@ -1,5 +1,5 @@
 name:                   dependent-map
-version:                0.2.5.1
+version:                0.2.6.0
 stability:              provisional
 
 cabal-version:          >= 1.6
diff --git a/src/Data/Dependent/Map.hs b/src/Data/Dependent/Map.hs
index 2414de2..d16949e 100644
--- a/src/Data/Dependent/Map.hs
+++ b/src/Data/Dependent/Map.hs
@@ -445,6 +445,24 @@ deleteMin = fst makeDeleteMin
 deleteMax :: DMap k f -> DMap k f
 deleteMax = fst makeDeleteMax
 
+-- | /O(log n)/. Delete and find the minimal element.
+--
+-- > deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")])
+-- > deleteFindMin                                            Error: can not return the minimal element of an empty map
+deleteFindMin :: DMap k f -> (DSum k f, DMap k f)
+deleteFindMin t = case minViewWithKey t of
+  Nothing -> error "Error: can not return the minimal element of an empty map"
+  Just x -> x
+
+-- | /O(log n)/. Delete and find the maximal element.
+--
+-- > deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")])
+-- > deleteFindMax empty                                      Error: can not return the maximal element of an empty map
+deleteFindMax :: DMap k f -> (DSum k f, DMap k f)
+deleteFindMax t = case maxViewWithKey t of
+  Nothing -> error "Error: can not return the maximal element of an empty map"
+  Just x -> x
+
 -- | /O(log n)/. Update the value at the minimal key.
 updateMinWithKey :: (forall v. k v -> f v -> Maybe (f v)) -> DMap k f -> DMap k f
 updateMinWithKey f = fst $ makeUpdateMinWithKey f
@@ -453,6 +471,16 @@ updateMinWithKey f = fst $ makeUpdateMinWithKey f
 updateMaxWithKey :: (forall v. k v -> f v -> Maybe (f v)) -> DMap k f -> DMap k f
 updateMaxWithKey f = fst $ makeUpdateMaxWithKey f
 
+-- | /O(log n)/. Retrieves the minimal (key :=> value) entry of the map, and
+-- the map stripped of that element, or 'Nothing' if passed an empty map.
+minViewWithKey :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
+minViewWithKey = minViewWithKeyE
+
+-- | /O(log n)/. Retrieves the maximal (key :=> value) entry of the map, and
+-- the map stripped of that element, or 'Nothing' if passed an empty map.
+maxViewWithKey :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
+maxViewWithKey = maxViewWithKeyE
+
 {--------------------------------------------------------------------
   Union.
 --------------------------------------------------------------------}
diff --git a/src/Data/Dependent/Map/Internal.hs b/src/Data/Dependent/Map/Internal.hs
index dc2b3a4..d14dd48 100644
--- a/src/Data/Dependent/Map/Internal.hs
+++ b/src/Data/Dependent/Map/Internal.hs
@@ -227,10 +227,10 @@ mergeNER :: DMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
 mergeNER Tip r = r
 mergeNER (Bin' l) r = mergeNE l r
 
-merge :: DMap k f -> DMap k f -> DMap k f
-merge Tip r   = r
-merge l Tip   = l
-merge (Bin' l) (Bin' r) = Bin' $! mergeNE l r
+mergeE :: DMap k f -> DMap k f -> DMap k f
+mergeE Tip r   = r
+mergeE l Tip   = l
+mergeE (Bin' l) (Bin' r) = Bin' $! mergeNE l r
 
 {--------------------------------------------------------------------
   [glue l r]: glues two trees together.
@@ -238,23 +238,15 @@ merge (Bin' l) (Bin' r) = Bin' $! mergeNE l r
 --------------------------------------------------------------------}
 glueNE :: NonEmptyDMap k f -> NonEmptyDMap k f -> NonEmptyDMap k f
 glueNE l r
-    | sizeNE l > sizeNE r = case deleteFindMax l of
+    | sizeNE l > sizeNE r = case maxViewWithKeyNE l of
         (km :=> m, l') -> balanceNER km m l' r
-    | otherwise = case deleteFindMin r of
+    | otherwise = case minViewWithKeyNE r of
         (km :=> m, r') -> balanceNEL km m l r'
 
-glue :: DMap k f -> DMap k f -> DMap k f
-glue Tip r = r
-glue l Tip = l
-glue (Bin' l) (Bin' r) = Bin' $! glueNE l r
-
--- | /O(log n)/. Delete and find the minimal element.
---
--- > deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")])
--- > deleteFindMin                                            Error: can not return the minimal element of an empty map
-
-deleteFindMin :: NonEmptyDMap k f -> (DSum k f, DMap k f)
-deleteFindMin = minViewWithKeyNE
+glueE :: DMap k f -> DMap k f -> DMap k f
+glueE Tip r = r
+glueE l Tip = l
+glueE (Bin' l) (Bin' r) = Bin' $! glueNE l r
 
 -- | A strict pair.
 data (:*:) a b = !a :*: !b
@@ -285,9 +277,9 @@ minViewWithKeyNE (NonEmptyDMap _ k0 x0 l0 r0) = toPair $ go k0 x0 l0 r0
 
 -- | /O(log n)/. Retrieves the minimal (key :=> value) entry of the map, and
 -- the map stripped of that element, or 'Nothing' if passed an empty map.
-minViewWithKey :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
-minViewWithKey Tip = Nothing
-minViewWithKey (Bin' ne) = Just $! minViewWithKeyNE ne
+minViewWithKeyE :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
+minViewWithKeyE Tip = Nothing
+minViewWithKeyE (Bin' ne) = Just $! minViewWithKeyNE ne
 
 -- | /O(log n)/. Retrieves the maximal (key :=> value) entry of the map, and
 -- the map stripped of that element, or 'Nothing' if passed an empty map.
@@ -302,17 +294,10 @@ maxViewWithKeyNE (NonEmptyDMap _ k0 x0 l0 r0) = toPair $ go k0 x0 l0 r0
 
 -- | /O(log n)/. Retrieves the maximal (key :=> value) entry of the map, and
 -- the map stripped of that element, or 'Nothing' if passed an empty map.
-maxViewWithKey :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
-maxViewWithKey Tip = Nothing
-maxViewWithKey (Bin' ne) = Just $! maxViewWithKeyNE ne
-
--- | /O(log n)/. Delete and find the maximal element.
---
--- > deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")])
--- > deleteFindMax empty                                      Error: can not return the maximal element of an empty map
+maxViewWithKeyE :: forall k f . DMap k f -> Maybe (DSum k f, DMap k f)
+maxViewWithKeyE Tip = Nothing
+maxViewWithKeyE (Bin' ne) = Just $! maxViewWithKeyNE ne
 
-deleteFindMax :: NonEmptyDMap k f -> (DSum k f, DMap k f)
-deleteFindMax = maxViewWithKeyNE
 
 
 {--------------------------------------------------------------------
diff --git a/src/Data/Dependent/Map/Internal2.hs b/src/Data/Dependent/Map/Internal2.hs
index 4bd2f07..8f8fd7e 100644
--- a/src/Data/Dependent/Map/Internal2.hs
+++ b/src/Data/Dependent/Map/Internal2.hs
@@ -177,7 +177,7 @@ makeDelete k = (k `seq` go, k `seq` nonEmpty . go')
         case gcompare k kx of
             GLT -> Bin' $! balanceE kx x (go l) r
             GGT -> Bin' $! balanceE kx x l (go r)
-            GEQ -> glue l r
+            GEQ -> glueE l r
 
 makeAdjustF
   :: forall f k v g
@@ -263,7 +263,7 @@ makeUpdateWithKey f k = (k `seq` go, k `seq` nonEmpty . go')
            GGT -> Bin' $! balanceE kx x l (go r)
            GEQ -> case f kx x of
                    Just x' -> Bin sx kx x' l r
-                   Nothing -> glue l r
+                   Nothing -> glueE l r
 
 makeUpdateLookupWithKey
   :: forall k f v
@@ -286,7 +286,7 @@ makeUpdateLookupWithKey f k = (k `seq` go, k `seq` fmap nonEmpty . go')
                 GGT -> let (found,r') = go r in (found,Bin' $! balanceE kx x l r')
                 GEQ -> case f kx x of
                         Just x' -> (Just x', Bin sx kx x' l r)
-                        Nothing -> (Just x, glue l r)
+                        Nothing -> (Just x, glueE l r)
 
 makeAlter
   :: forall k f v
@@ -310,7 +310,7 @@ makeAlter f k = (k `seq` go, k `seq` nonEmpty . go')
                GGT -> Bin' $! balanceE kx x l (go r)
                GEQ -> case f (Just x) of
                        Just x' -> Bin sx kx x' l r
-                       Nothing -> glue l r
+                       Nothing -> glueE l r
 
 {--------------------------------------------------------------------
   Indexing Worker Builders
@@ -334,7 +334,7 @@ makeAlterF k f = (go, fmap nonEmpty . go')
     go' (NonEmptyDMap sx kx x l r) = case gcompare k kx of
       GLT -> (\l' -> Bin' $! balanceE kx x l' r) <$> go l
       GGT -> (\r' -> Bin' $! balanceE kx x l r') <$> go r
-      GEQ -> maybe (glue l r) (\x' -> Bin sx kx x' l r) <$> f (Just x)
+      GEQ -> maybe (glueE l r) (\x' -> Bin sx kx x' l r) <$> f (Just x)
 
 makeLookupIndex
   :: forall k f v
@@ -393,7 +393,7 @@ makeUpdateAt f i0 = (i0 `seq` go i0, i0 `seq` nonEmpty . go' i0)
       GT -> Bin' $! balanceE kx x l (go (i-sizeL-1) r)
       EQ -> case f kx x of
               Just x' -> Bin sx kx x' l r
-              Nothing -> glue l r
+              Nothing -> glueE l r
       where
         sizeL = sizeE l
 
@@ -568,7 +568,7 @@ makeDifference = (go, go')
     go t1 (Bin _ k2 _x2 l2 r2) = case fst (makeSplit k2) t1 of
       (l1, r1)
         | sizeE t1 == sizeE l1l2 + sizeE r1r2 -> t1
-        | otherwise -> merge l1l2 r1r2
+        | otherwise -> mergeE l1l2 r1r2
         where
           !l1l2 = l1 `go` l2
           !r1r2 = r1 `go` r2
@@ -576,7 +576,7 @@ makeDifference = (go, go')
     go' t1 (NonEmptyDMap _ k2 _x2 l2 r2) = case snd (makeSplit k2) t1 of
       (l1, r1)
         | sizeNE t1 == sizeE l1l2 + sizeE r1r2 -> Bin' t1
-        | otherwise -> merge l1l2 r1r2
+        | otherwise -> mergeE l1l2 r1r2
         where
           !l1l2 = l1 `go` l2
           !r1r2 = r1 `go` r2
@@ -595,7 +595,7 @@ makeDifferenceWithKey f = (go, go')
       (l2, mx2, r2) -> case mx2 of
           Nothing -> Bin' $! combineE k1 x1 l1l2 r1r2
           Just x2 -> case f k1 x1 x2 of
-            Nothing -> merge l1l2 r1r2
+            Nothing -> mergeE l1l2 r1r2
             Just x1x2 -> Bin' $! combineE k1 x1x2 l1l2 r1r2
         where !l1l2 = go l1 l2
               !r1r2 = go r1 r2
@@ -604,7 +604,7 @@ makeDifferenceWithKey f = (go, go')
       (l2, mx2, r2) -> case mx2 of
           Nothing -> Bin' $! combineE k1 x1 l1l2 r1r2
           Just x2 -> case f k1 x1 x2 of
-            Nothing -> merge l1l2 r1r2
+            Nothing -> mergeE l1l2 r1r2
             Just x1x2 -> Bin' $! combineE k1 x1x2 l1l2 r1r2
         where !l1l2 = go l1 l2
               !r1r2 = go r1 r2
@@ -630,7 +630,7 @@ makeIntersection = (go, go')
          then if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1
               then t1
               else Bin' $! combineE k1 x1 l1l2 r1r2
-         else merge l1l2 r1r2
+         else mergeE l1l2 r1r2
 
     go' t1@(NonEmptyDMap s1 k1 x1 l1 r1) t2 =
       let !(l2, found, r2) = snd (makeSplitMember k1) t2
@@ -640,7 +640,7 @@ makeIntersection = (go, go')
          then if l1l2 `ptrEq` l1 && r1r2 `ptrEq` r1
               then Bin' t1
               else Bin' $! combineE k1 x1 l1l2 r1r2
-         else merge l1l2 r1r2
+         else mergeE l1l2 r1r2
 
 makeIntersectionWithKey
   :: forall k f g h
@@ -659,7 +659,7 @@ makeIntersectionWithKey f = (go, go')
           !l1l2 = go l1 l2
           !r1r2 = go r1 r2
       in case found of
-           Nothing -> merge l1l2 r1r2
+           Nothing -> mergeE l1l2 r1r2
            Just x2 -> Bin' $! combineE k1 (f k1 x1 x2) l1l2 r1r2
 
     go' :: NonEmptyDMap k f -> NonEmptyDMap k g -> DMap k h
@@ -668,7 +668,7 @@ makeIntersectionWithKey f = (go, go')
           !l1l2 = go l1 l2
           !r1r2 = go r1 r2
       in case found of
-           Nothing -> merge l1l2 r1r2
+           Nothing -> mergeE l1l2 r1r2
            Just x2 -> Bin' $! combineE k1 (f k1 x1 x2) l1l2 r1r2
 
 {--------------------------------------------------------------------
@@ -714,7 +714,7 @@ makeFilterWithKey p = go
       | p kx x    = if l' `ptrEq` l && r' `ptrEq` r
                     then t
                     else Bin' $! combineE kx x l' r'
-      | otherwise = merge l' r'
+      | otherwise = mergeE l' r'
       where !l' = go l
             !r' = go r
 
@@ -729,8 +729,8 @@ makePartitionWithKey p m0 = toPair (go m0)
     go :: DMap k f -> (DMap k f :*: DMap k f)
     go Tip = (Tip :*: Tip)
     go (Bin _ kx x l r)
-      | p kx x    = ((Bin' $! combineE kx x l1 r1) :*: merge l2 r2)
-      | otherwise = (merge l1 r1 :*: (Bin' $! combineE kx x l2 r2))
+      | p kx x    = ((Bin' $! combineE kx x l1 r1) :*: mergeE l2 r2)
+      | otherwise = (mergeE l1 r1 :*: (Bin' $! combineE kx x l2 r2))
       where
         (l1 :*: l2) = go l
         (r1 :*: r2) = go r
@@ -745,7 +745,7 @@ makeMapMaybeWithKey f = go
     go Tip = Tip
     go (Bin _ kx x l r) = case f kx x of
         Just y  -> Bin' $! combineE kx y (go l) (go r)
-        Nothing -> merge (go l) (go r)
+        Nothing -> mergeE (go l) (go r)
 
 makeMapEitherWithKey
   :: forall k f g h
@@ -759,8 +759,8 @@ makeMapEitherWithKey f = toPair . go
        => DMap k f -> (DMap k g :*: DMap k h)
     go Tip = (Tip :*: Tip)
     go (Bin _ kx x l r) = case f kx x of
-      Left y  -> ((Bin' $! combineE kx y l1 r1) :*: merge l2 r2)
-      Right z -> (merge l1 r1 :*: (Bin' $! combineE kx z l2 r2))
+      Left y  -> ((Bin' $! combineE kx y l1 r1) :*: mergeE l2 r2)
+      Right z -> (mergeE l1 r1 :*: (Bin' $! combineE kx z l2 r2))
       where
         (l1 :*: l2) = go l
         (r1 :*: r2) = go r
diff --git a/src/Data/Dependent/Map/NonEmpty.hs b/src/Data/Dependent/Map/NonEmpty.hs
index 7503835..772b829 100644
--- a/src/Data/Dependent/Map/NonEmpty.hs
+++ b/src/Data/Dependent/Map/NonEmpty.hs
@@ -448,6 +448,20 @@ deleteMin = snd makeDeleteMin
 deleteMax :: NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
 deleteMax = snd makeDeleteMax
 
+-- | /O(log n)/. Delete and find the minimal element.
+--
+-- > deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")])
+-- > deleteFindMin                                            Error: can not return the minimal element of an empty map
+deleteFindMin :: NonEmptyDMap k f -> (DSum k f, Maybe (NonEmptyDMap k f))
+deleteFindMin = minViewWithKey
+
+-- | /O(log n)/. Delete and find the maximal element.
+--
+-- > deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")])
+-- > deleteFindMax empty                                      Error: can not return the maximal element of an empty map
+deleteFindMax :: NonEmptyDMap k f -> (DSum k f, Maybe (NonEmptyDMap k f))
+deleteFindMax = maxViewWithKey
+
 -- | /O(log n)/. Update the value at the minimal key.
 updateMinWithKey :: (forall v. k v -> f v -> Maybe (f v)) -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
 updateMinWithKey f = snd $ makeUpdateMinWithKey f
@@ -456,6 +470,16 @@ updateMinWithKey f = snd $ makeUpdateMinWithKey f
 updateMaxWithKey :: (forall v. k v -> f v -> Maybe (f v)) -> NonEmptyDMap k f -> Maybe (NonEmptyDMap k f)
 updateMaxWithKey f = snd $ makeUpdateMaxWithKey f
 
+-- | /O(log n)/. Retrieves the minimal (key :=> value) entry of the map, and
+-- the map stripped of that element, or 'Nothing' if passed an empty map.
+minViewWithKey :: forall k f . NonEmptyDMap k f -> (DSum k f, Maybe (NonEmptyDMap k f))
+minViewWithKey = fmap nonEmpty . minViewWithKeyNE
+
+-- | /O(log n)/. Retrieves the maximal (key :=> value) entry of the map, and
+-- the map stripped of that element, or 'Nothing' if passed an empty map.
+maxViewWithKey :: forall k f . NonEmptyDMap k f -> (DSum k f, Maybe (NonEmptyDMap k f))
+maxViewWithKey = fmap nonEmpty . maxViewWithKeyNE
+
 {--------------------------------------------------------------------
   Union.
 --------------------------------------------------------------------}

From 59f5bffaa4fd10579d22c62850929177e1903ce3 Mon Sep 17 00:00:00 2001
From: John Ericson <git@JohnEricson.me>
Date: Wed, 27 Feb 2019 10:14:43 -0500
Subject: [PATCH 10/10] Remove `empty` export from NonEmpty module

---
 src/Data/Dependent/Map/NonEmpty.hs | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/Data/Dependent/Map/NonEmpty.hs b/src/Data/Dependent/Map/NonEmpty.hs
index 772b829..c2e793d 100644
--- a/src/Data/Dependent/Map/NonEmpty.hs
+++ b/src/Data/Dependent/Map/NonEmpty.hs
@@ -31,7 +31,6 @@ module Data.Dependent.Map.NonEmpty
     , findWithDefault
 
     -- * Construction
-    , empty
     , singleton
 
     -- ** Insertion