-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Type-level sets
--   
--   Please see the README on GitHub at
--   <a>https://github.com/isovector/type-sets#readme</a>
@package type-sets
@version 0.1.1.0


-- | See <a>here</a> for the original term-level code by Stefan Kahrs.
module Type.RBSet

-- | A Red-Black tree.
data TypeSet a
E :: TypeSet a
N :: Color -> TypeSet a -> a -> TypeSet a -> TypeSet a

-- | A map without entries.
type Empty = E

-- | <i>O(log n)</i>. Determine membership in the 'TypeSet.'
type family Member (t :: k) (bst :: TypeSet k) :: Bool

-- | The associated type family <a>Insert</a> produces the resulting map.
class Insertable (k :: ki) (t :: TypeSet ki) where {
    type family Insert k t :: TypeSet ki;
}

-- | Insert a list of type level key / value pairs into a type-level map.
type family InsertAll (es :: [k]) (t :: TypeSet k) :: TypeSet k

-- | Build a type-level map out of a list of type level key / value pairs.
type FromList (es :: [k]) = InsertAll es Empty

-- | The associated type family <a>Remove</a> produces the resulting map.
class Removable (k :: ki) (t :: TypeSet ki) where {
    type family Remove k t :: TypeSet ki;
}

-- | <i>O(m log n)</i> for <tt>Merge m n</tt>; put your smaller set on the
--   left side. Merge two <a>TypeSet</a>s together.
type family Merge (small :: TypeSet k) (big :: TypeSet k) :: TypeSet k
instance GHC.Show.Show Type.RBSet.BalanceAction
instance GHC.Classes.Eq a => GHC.Classes.Eq (Type.RBSet.TypeSet a)
instance GHC.Show.Show a => GHC.Show.Show (Type.RBSet.TypeSet a)
instance GHC.Classes.Eq Type.RBSet.Color
instance GHC.Show.Show Type.RBSet.Color
instance forall ki (k :: ki) (t :: Type.RBSet.TypeSet ki) (deleted :: Type.RBSet.TypeSet ki). (Type.RBSet.Delable k t, Type.RBSet.Del k t Data.Type.Equality.~ deleted, Type.RBSet.CanMakeBlack deleted) => Type.RBSet.Removable k t
instance forall a (kx :: a) (k :: a) (ordering :: GHC.Types.Ordering) (left :: Type.RBSet.TypeSet a) (right :: Type.RBSet.TypeSet a) (color :: Type.RBSet.Color). (Type.Compare.CmpType kx k Data.Type.Equality.~ ordering, Type.RBSet.DelableHelper ordering k left kx right) => Type.RBSet.Delable k ('Type.RBSet.N color left kx right)
instance forall ki (k :: ki) (left :: Type.RBSet.TypeSet ki) (kx :: ki) (right :: Type.RBSet.TypeSet ki). Type.RBSet.DelableL k left kx right => Type.RBSet.DelableHelper 'GHC.Types.GT k left kx right
instance forall ki (left :: Type.RBSet.TypeSet ki) (right :: Type.RBSet.TypeSet ki) (k :: ki). Type.RBSet.Fuseable left right => Type.RBSet.DelableHelper 'GHC.Types.EQ k left k right
instance forall ki (k :: ki) (left :: Type.RBSet.TypeSet ki) (kx :: ki) (right :: Type.RBSet.TypeSet ki). Type.RBSet.DelableR k left kx right => Type.RBSet.DelableHelper 'GHC.Types.LT k left kx right
instance forall a (leftz :: Type.RBSet.TypeSet a) (kz :: a) (rightz :: Type.RBSet.TypeSet a) (g :: Type.RBSet.TypeSet a) (k :: a) (deleted :: Type.RBSet.TypeSet a) (left :: Type.RBSet.TypeSet a) (kx :: a). ('Type.RBSet.N 'Type.RBSet.B leftz kz rightz Data.Type.Equality.~ g, Type.RBSet.Delable k g, Type.RBSet.Del k g Data.Type.Equality.~ deleted, Type.RBSet.BalanceableR left kx deleted) => Type.RBSet.DelableR k left kx ('Type.RBSet.N 'Type.RBSet.B leftz kz rightz)
instance forall a (k :: a) (leftz :: Type.RBSet.TypeSet a) (kz :: a) (rightz :: Type.RBSet.TypeSet a) (left :: Type.RBSet.TypeSet a) (kx :: a). Type.RBSet.Delable k ('Type.RBSet.N 'Type.RBSet.R leftz kz rightz) => Type.RBSet.DelableR k left kx ('Type.RBSet.N 'Type.RBSet.R leftz kz rightz)
instance forall ki (k :: ki) (left :: Type.RBSet.TypeSet ki) (kx :: ki). Type.RBSet.DelableR k left kx 'Type.RBSet.E
instance forall a (leftz :: Type.RBSet.TypeSet a) (kz :: a) (rightz :: Type.RBSet.TypeSet a) (g :: Type.RBSet.TypeSet a) (k :: a) (deleted :: Type.RBSet.TypeSet a) (kx :: a) (right :: Type.RBSet.TypeSet a). ('Type.RBSet.N 'Type.RBSet.B leftz kz rightz Data.Type.Equality.~ g, Type.RBSet.Delable k g, Type.RBSet.Del k g Data.Type.Equality.~ deleted, Type.RBSet.BalanceableL deleted kx right) => Type.RBSet.DelableL k ('Type.RBSet.N 'Type.RBSet.B leftz kz rightz) kx right
instance forall a (k :: a) (leftz :: Type.RBSet.TypeSet a) (kz :: a) (rightz :: Type.RBSet.TypeSet a) (kx :: a) (right :: Type.RBSet.TypeSet a). Type.RBSet.Delable k ('Type.RBSet.N 'Type.RBSet.R leftz kz rightz) => Type.RBSet.DelableL k ('Type.RBSet.N 'Type.RBSet.R leftz kz rightz) kx right
instance forall ki (k :: ki) (kx :: ki) (right :: Type.RBSet.TypeSet ki). Type.RBSet.DelableL k 'Type.RBSet.E kx right
instance forall ki (k :: ki). Type.RBSet.Delable k 'Type.RBSet.E
instance forall a (right1 :: Type.RBSet.TypeSet a) (left2 :: Type.RBSet.TypeSet a) (fused :: Type.RBSet.TypeSet a) (left1 :: Type.RBSet.TypeSet a) (k1 :: a) (k2 :: a) (right2 :: Type.RBSet.TypeSet a). (Type.RBSet.Fuseable right1 left2, Type.RBSet.Fuse right1 left2 Data.Type.Equality.~ fused, Type.RBSet.FuseableHelper2 fused ('Type.RBSet.N 'Type.RBSet.B left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.B left2 k2 right2)) => Type.RBSet.Fuseable ('Type.RBSet.N 'Type.RBSet.B left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.B left2 k2 right2)
instance forall a (right1 :: Type.RBSet.TypeSet a) (left2 :: Type.RBSet.TypeSet a) (s1 :: Type.RBSet.TypeSet a) (z :: a) (s2 :: Type.RBSet.TypeSet a) (left1 :: Type.RBSet.TypeSet a) (k1 :: a) (k2 :: a) (right2 :: Type.RBSet.TypeSet a). (Type.RBSet.Fuseable right1 left2, Type.RBSet.Fuse right1 left2 Data.Type.Equality.~ 'Type.RBSet.N 'Type.RBSet.R s1 z s2) => Type.RBSet.FuseableHelper2 ('Type.RBSet.N 'Type.RBSet.R s1 z s2) ('Type.RBSet.N 'Type.RBSet.B left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.B left2 k2 right2)
instance forall a (right1 :: Type.RBSet.TypeSet a) (left2 :: Type.RBSet.TypeSet a) (s1 :: Type.RBSet.TypeSet a) (z :: a) (s2 :: Type.RBSet.TypeSet a) (left1 :: Type.RBSet.TypeSet a) (k1 :: a) (k2 :: a) (right2 :: Type.RBSet.TypeSet a). (Type.RBSet.Fuseable right1 left2, Type.RBSet.Fuse right1 left2 Data.Type.Equality.~ 'Type.RBSet.N 'Type.RBSet.B s1 z s2, Type.RBSet.BalanceableL left1 k1 ('Type.RBSet.N 'Type.RBSet.B ('Type.RBSet.N 'Type.RBSet.B s1 z s2) k2 right2)) => Type.RBSet.FuseableHelper2 ('Type.RBSet.N 'Type.RBSet.B s1 z s2) ('Type.RBSet.N 'Type.RBSet.B left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.B left2 k2 right2)
instance forall a (left1 :: Type.RBSet.TypeSet a) (k1 :: a) (k2 :: a) (right2 :: Type.RBSet.TypeSet a). Type.RBSet.BalanceableL left1 k1 ('Type.RBSet.N 'Type.RBSet.B 'Type.RBSet.E k2 right2) => Type.RBSet.FuseableHelper2 'Type.RBSet.E ('Type.RBSet.N 'Type.RBSet.B left1 k1 'Type.RBSet.E) ('Type.RBSet.N 'Type.RBSet.B 'Type.RBSet.E k2 right2)
instance forall a (right1 :: Type.RBSet.TypeSet a) (left2 :: Type.RBSet.TypeSet a) (fused :: Type.RBSet.TypeSet a) (left1 :: Type.RBSet.TypeSet a) (k1 :: a) (k2 :: a) (right2 :: Type.RBSet.TypeSet a). (Type.RBSet.Fuseable right1 left2, Type.RBSet.Fuse right1 left2 Data.Type.Equality.~ fused, Type.RBSet.FuseableHelper1 fused ('Type.RBSet.N 'Type.RBSet.R left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.R left2 k2 right2)) => Type.RBSet.Fuseable ('Type.RBSet.N 'Type.RBSet.R left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.R left2 k2 right2)
instance forall a (right1 :: Type.RBSet.TypeSet a) (left2 :: Type.RBSet.TypeSet a) (s1 :: Type.RBSet.TypeSet a) (z :: a) (s2 :: Type.RBSet.TypeSet a) (left1 :: Type.RBSet.TypeSet a) (k1 :: a) (k2 :: a) (right2 :: Type.RBSet.TypeSet a). (Type.RBSet.Fuseable right1 left2, Type.RBSet.Fuse right1 left2 Data.Type.Equality.~ 'Type.RBSet.N 'Type.RBSet.R s1 z s2) => Type.RBSet.FuseableHelper1 ('Type.RBSet.N 'Type.RBSet.R s1 z s2) ('Type.RBSet.N 'Type.RBSet.R left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.R left2 k2 right2)
instance forall a (right1 :: Type.RBSet.TypeSet a) (left2 :: Type.RBSet.TypeSet a) (s1 :: Type.RBSet.TypeSet a) (z :: a) (s2 :: Type.RBSet.TypeSet a) (left1 :: Type.RBSet.TypeSet a) (k1 :: a) (k2 :: a) (right2 :: Type.RBSet.TypeSet a). (Type.RBSet.Fuseable right1 left2, Type.RBSet.Fuse right1 left2 Data.Type.Equality.~ 'Type.RBSet.N 'Type.RBSet.B s1 z s2) => Type.RBSet.FuseableHelper1 ('Type.RBSet.N 'Type.RBSet.B s1 z s2) ('Type.RBSet.N 'Type.RBSet.R left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.R left2 k2 right2)
instance forall ki (left1 :: Type.RBSet.TypeSet ki) (k1 :: ki) (k2 :: ki) (right2 :: Type.RBSet.TypeSet ki). Type.RBSet.FuseableHelper1 'Type.RBSet.E ('Type.RBSet.N 'Type.RBSet.R left1 k1 'Type.RBSet.E) ('Type.RBSet.N 'Type.RBSet.R 'Type.RBSet.E k2 right2)
instance Type.RBSet.Fuseable 'Type.RBSet.E 'Type.RBSet.E
instance forall ki (color :: Type.RBSet.Color) (left :: Type.RBSet.TypeSet ki) (k :: ki) (right :: Type.RBSet.TypeSet ki). Type.RBSet.Fuseable 'Type.RBSet.E ('Type.RBSet.N color left k right)
instance forall ki (color :: Type.RBSet.Color) (left :: Type.RBSet.TypeSet ki) (k :: ki) (right :: Type.RBSet.TypeSet ki). Type.RBSet.Fuseable ('Type.RBSet.N color left k right) 'Type.RBSet.E
instance forall a (left1 :: Type.RBSet.TypeSet a) (k1 :: a) (right1 :: Type.RBSet.TypeSet a) (left2 :: Type.RBSet.TypeSet a) (k2 :: a) (right2 :: Type.RBSet.TypeSet a). Type.RBSet.Fuseable ('Type.RBSet.N 'Type.RBSet.B left1 k1 right1) left2 => Type.RBSet.Fuseable ('Type.RBSet.N 'Type.RBSet.B left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.R left2 k2 right2)
instance forall a (right1 :: Type.RBSet.TypeSet a) (left2 :: Type.RBSet.TypeSet a) (k2 :: a) (right2 :: Type.RBSet.TypeSet a) (left1 :: Type.RBSet.TypeSet a) (k1 :: a). Type.RBSet.Fuseable right1 ('Type.RBSet.N 'Type.RBSet.B left2 k2 right2) => Type.RBSet.Fuseable ('Type.RBSet.N 'Type.RBSet.R left1 k1 right1) ('Type.RBSet.N 'Type.RBSet.B left2 k2 right2)
instance forall ki (l :: Type.RBSet.TypeSet ki) (r :: Type.RBSet.TypeSet ki) (b :: GHC.Types.Bool) (k :: ki). (Type.RBSet.DiscriminateBalR l r Data.Type.Equality.~ b, Type.RBSet.BalanceableHelperR b l k r) => Type.RBSet.BalanceableR l k r
instance forall ki (right2 :: Type.RBSet.TypeSet ki) (k2 :: ki) (left1 :: Type.RBSet.TypeSet ki) (k1 :: ki) (right1 :: Type.RBSet.TypeSet ki). Type.RBSet.BalanceableHelperR 'GHC.Types.False right2 k2 ('Type.RBSet.N 'Type.RBSet.R left1 k1 right1)
instance forall ki (t2 :: Type.RBSet.TypeSet ki) (z :: ki) (t3 :: Type.RBSet.TypeSet ki) (g :: Type.RBSet.TypeSet ki) (t1 :: Type.RBSet.TypeSet ki) (shouldbalance :: Type.RBSet.BalanceAction) (y :: ki). ('Type.RBSet.N 'Type.RBSet.R t2 z t3 Data.Type.Equality.~ g, Type.RBSet.ShouldBalance g t1 Data.Type.Equality.~ shouldbalance, Type.RBSet.BalanceableHelper shouldbalance g y t1) => Type.RBSet.BalanceableHelperR 'GHC.Types.True ('Type.RBSet.N 'Type.RBSet.B t2 z t3) y t1
instance forall ki (t2 :: Type.RBSet.TypeSet ki) (u :: ki) (t3 :: Type.RBSet.TypeSet ki) (g :: Type.RBSet.TypeSet ki) (l :: Type.RBSet.TypeSet ki) (shouldbalance :: Type.RBSet.BalanceAction) (z :: ki) (k :: ki) (r :: Type.RBSet.TypeSet ki) (y :: ki) (t1 :: Type.RBSet.TypeSet ki). ('Type.RBSet.N 'Type.RBSet.R t2 u t3 Data.Type.Equality.~ g, Type.RBSet.ShouldBalance g l Data.Type.Equality.~ shouldbalance, Type.RBSet.BalanceableHelper shouldbalance g z l) => Type.RBSet.BalanceableHelperR 'GHC.Types.True ('Type.RBSet.N 'Type.RBSet.R ('Type.RBSet.N 'Type.RBSet.B t2 u t3) z ('Type.RBSet.N 'Type.RBSet.B l k r)) y t1
instance forall ki (l :: Type.RBSet.TypeSet ki) (r :: Type.RBSet.TypeSet ki) (b :: GHC.Types.Bool) (k :: ki). (Type.RBSet.DiscriminateBalL l r Data.Type.Equality.~ b, Type.RBSet.BalanceableHelperL b l k r) => Type.RBSet.BalanceableL l k r
instance forall ki (left1 :: Type.RBSet.TypeSet ki) (k1 :: ki) (right1 :: Type.RBSet.TypeSet ki) (k2 :: ki) (right2 :: Type.RBSet.TypeSet ki). Type.RBSet.BalanceableHelperL 'GHC.Types.False ('Type.RBSet.N 'Type.RBSet.R left1 k1 right1) k2 right2
instance forall a (t2 :: Type.RBSet.TypeSet a) (z :: a) (t3 :: Type.RBSet.TypeSet a) (g :: Type.RBSet.TypeSet a) (t1 :: Type.RBSet.TypeSet a) (y :: a). ('Type.RBSet.N 'Type.RBSet.R t2 z t3 Data.Type.Equality.~ g, Type.RBSet.BalanceableHelper (Type.RBSet.ShouldBalance t1 g) t1 y g) => Type.RBSet.BalanceableHelperL 'GHC.Types.True t1 y ('Type.RBSet.N 'Type.RBSet.B t2 z t3)
instance forall ki (l :: Type.RBSet.TypeSet ki) (k :: ki) (r :: Type.RBSet.TypeSet ki) (g :: Type.RBSet.TypeSet ki) (t3 :: Type.RBSet.TypeSet ki) (z :: ki) (t1 :: Type.RBSet.TypeSet ki) (y :: ki) (t2 :: Type.RBSet.TypeSet ki) (u :: ki). ('Type.RBSet.N 'Type.RBSet.R l k r Data.Type.Equality.~ g, Type.RBSet.BalanceableHelper (Type.RBSet.ShouldBalance t3 g) t3 z g) => Type.RBSet.BalanceableHelperL 'GHC.Types.True t1 y ('Type.RBSet.N 'Type.RBSet.R ('Type.RBSet.N 'Type.RBSet.B t2 u t3) z ('Type.RBSet.N 'Type.RBSet.B l k r))
instance forall ki (left :: Type.RBSet.TypeSet ki) (right :: Type.RBSet.TypeSet ki) (action :: Type.RBSet.BalanceAction) (k :: ki). (Type.RBSet.ShouldBalance left right Data.Type.Equality.~ action, Type.RBSet.BalanceableHelper action left k right) => Type.RBSet.Balanceable left k right
instance forall ki (left1 :: Type.RBSet.TypeSet ki) (k1 :: ki) (right1 :: Type.RBSet.TypeSet ki) (kx :: ki) (left2 :: Type.RBSet.TypeSet ki) (k2 :: ki) (right2 :: Type.RBSet.TypeSet ki). Type.RBSet.BalanceableHelper 'Type.RBSet.BalanceSpecial ('Type.RBSet.N 'Type.RBSet.R left1 k1 right1) kx ('Type.RBSet.N 'Type.RBSet.R left2 k2 right2)
instance forall ki (a :: Type.RBSet.TypeSet ki) (k1 :: ki) (b :: Type.RBSet.TypeSet ki) (k2 :: ki) (c :: Type.RBSet.TypeSet ki) (k3 :: ki) (d :: Type.RBSet.TypeSet ki). Type.RBSet.BalanceableHelper 'Type.RBSet.BalanceLL ('Type.RBSet.N 'Type.RBSet.R ('Type.RBSet.N 'Type.RBSet.R a k1 b) k2 c) k3 d
instance forall ki (a :: Type.RBSet.TypeSet ki) (k1 :: ki) (b :: Type.RBSet.TypeSet ki) (k2 :: ki) (c :: Type.RBSet.TypeSet ki) (k3 :: ki) (d :: Type.RBSet.TypeSet ki). Type.RBSet.BalanceableHelper 'Type.RBSet.BalanceLR ('Type.RBSet.N 'Type.RBSet.R a k1 ('Type.RBSet.N 'Type.RBSet.R b k2 c)) k3 d
instance forall ki (a :: Type.RBSet.TypeSet ki) (k1 :: ki) (b :: Type.RBSet.TypeSet ki) (k2 :: ki) (c :: Type.RBSet.TypeSet ki) (k3 :: ki) (d :: Type.RBSet.TypeSet ki). Type.RBSet.BalanceableHelper 'Type.RBSet.BalanceRL a k1 ('Type.RBSet.N 'Type.RBSet.R ('Type.RBSet.N 'Type.RBSet.R b k2 c) k3 d)
instance forall ki (a :: Type.RBSet.TypeSet ki) (k1 :: ki) (b :: Type.RBSet.TypeSet ki) (k2 :: ki) (c :: Type.RBSet.TypeSet ki) (k3 :: ki) (d :: Type.RBSet.TypeSet ki). Type.RBSet.BalanceableHelper 'Type.RBSet.BalanceRR a k1 ('Type.RBSet.N 'Type.RBSet.R b k2 ('Type.RBSet.N 'Type.RBSet.R c k3 d))
instance forall ki (a :: Type.RBSet.TypeSet ki) (k :: ki) (b :: Type.RBSet.TypeSet ki). Type.RBSet.BalanceableHelper 'Type.RBSet.DoNotBalance a k b
instance forall ki (k :: ki) (left :: Type.RBSet.TypeSet ki) (inserted :: Type.RBSet.TypeSet ki) (k' :: ki) (right :: Type.RBSet.TypeSet ki). (Type.RBSet.InsertableHelper1 k left, Type.RBSet.Insert1 k left Data.Type.Equality.~ inserted, Type.RBSet.Balanceable inserted k' right) => Type.RBSet.InsertableHelper2 'GHC.Types.LT k 'Type.RBSet.B left k' right
instance forall ki (k :: ki) (left :: Type.RBSet.TypeSet ki) (inserted :: Type.RBSet.TypeSet ki) (k' :: ki) (right :: Type.RBSet.TypeSet ki). (Type.RBSet.InsertableHelper1 k left, Type.RBSet.Insert1 k left Data.Type.Equality.~ inserted, Type.RBSet.Balanceable inserted k' right) => Type.RBSet.InsertableHelper2 'GHC.Types.LT k 'Type.RBSet.R left k' right
instance forall ki (k :: ki) (right :: Type.RBSet.TypeSet ki) (inserted :: Type.RBSet.TypeSet ki) (left :: Type.RBSet.TypeSet ki) (k' :: ki). (Type.RBSet.InsertableHelper1 k right, Type.RBSet.Insert1 k right Data.Type.Equality.~ inserted, Type.RBSet.Balanceable left k' inserted) => Type.RBSet.InsertableHelper2 'GHC.Types.GT k 'Type.RBSet.B left k' right
instance forall ki (k :: ki) (right :: Type.RBSet.TypeSet ki) (inserted :: Type.RBSet.TypeSet ki) (left :: Type.RBSet.TypeSet ki) (k' :: ki). (Type.RBSet.InsertableHelper1 k right, Type.RBSet.Insert1 k right Data.Type.Equality.~ inserted, Type.RBSet.Balanceable left k' inserted) => Type.RBSet.InsertableHelper2 'GHC.Types.GT k 'Type.RBSet.R left k' right
instance forall a (k :: a) (k' :: a) (ordering :: GHC.Types.Ordering) (color :: Type.RBSet.Color) (left :: Type.RBSet.TypeSet a) (right :: Type.RBSet.TypeSet a). (Type.Compare.CmpType k k' Data.Type.Equality.~ ordering, Type.RBSet.InsertableHelper2 ordering k color left k' right) => Type.RBSet.InsertableHelper1 k ('Type.RBSet.N color left k' right)
instance forall ki (k :: ki) (color :: Type.RBSet.Color) (left :: Type.RBSet.TypeSet ki) (right :: Type.RBSet.TypeSet ki). Type.RBSet.InsertableHelper2 'GHC.Types.EQ k color left k right
instance forall ki (k :: ki) (t :: Type.RBSet.TypeSet ki) (inserted :: Type.RBSet.TypeSet ki). (Type.RBSet.InsertableHelper1 k t, Type.RBSet.Insert1 k t Data.Type.Equality.~ inserted, Type.RBSet.CanMakeBlack inserted) => Type.RBSet.Insertable k t
instance forall ki (k :: ki). Type.RBSet.InsertableHelper1 k 'Type.RBSet.E
instance forall ki (color :: Type.RBSet.Color) (left :: Type.RBSet.TypeSet ki) (k :: ki) (right :: Type.RBSet.TypeSet ki). Type.RBSet.CanMakeBlack ('Type.RBSet.N color left k right)
instance Type.RBSet.CanMakeBlack 'Type.RBSet.E

module Type.Set

-- | A binary search tree. When <tt>-XDataKinds</tt> is turned on, this
--   becomes the backbone of the type-level set.
--   
--   <pre>
--   &gt;&gt;&gt; type MySet = Insert Bool (Insert String (Insert (Maybe Int) 'Empty))
--   </pre>
data TypeSet a
Empty :: TypeSet a
Branch :: a -> TypeSet a -> TypeSet a -> TypeSet a

-- | <i>O(log n)</i>. Determine membership in the 'TypeSet.'
type family Member (t :: k) (bst :: TypeSet k) :: Bool

-- | <i>O(log n)</i>. Insert an element into the <a>TypeSet</a>.
type family Insert (t :: k) (bst :: TypeSet k) :: TypeSet k

-- | <i>O(log n)</i>. Remove an element from the <a>TypeSet</a>.
type family Remove (t :: k) (bst :: TypeSet k) :: TypeSet k

-- | <i>O(m log n)</i> for <tt>Merge m n</tt>; put your smaller set on the
--   left side. Merge two <a>TypeSet</a>s together.
type family Merge (small :: TypeSet k) (big :: TypeSet k) :: TypeSet k

-- | <i>O(log n)</i>. Compute a <tt>[<a>Side</a>]</tt> which finds the
--   desired element in the tree. The result of this can be passed to
--   <a>Follow</a> in order to look up the same element again later.
type family Locate (t :: k) (bst :: TypeSet k) :: [Side]

-- | <i>O(log n)</i>. Follow the result of a <a>Locate</a> to get a
--   particular element in the tree.
type family Follow (ss :: [Side]) (bst :: TypeSet k) :: k

-- | Either left or right down a path.
data Side
L :: Side
R :: Side
instance GHC.Show.Show Type.Set.Side
instance GHC.Classes.Ord Type.Set.Side
instance GHC.Classes.Eq Type.Set.Side

module Type.Set.Variant

-- | A <a>Variant</a> is like an <a>Either</a>, except that it can store
--   any of the types contained in the <a>TypeSet</a>. You can use
--   <a>toVariant</a> to construct one, and <a>fromVariant</a> to pattern
--   match it out.
data Variant (v :: TypeSet *)
[Variant] :: SSide ss -> Follow ss v -> Variant v

-- | A proof that the set <tt>bst</tt> contains type <tt>t</tt>.
class Has t bst

-- | Inject a <tt>t</tt> into a <a>Variant</a>.
toVariant :: Has t bst => t -> Variant bst

-- | Attempt to project a <a>Variant</a> into <tt>t</tt>. This might fail,
--   because there is no guarantee that the <a>Variant</a> <i>actually
--   contains</i> <tt>t</tt>.
--   
--   You can use <a>decompRoot</a> instead of this function if you'd like a
--   proof that the <a>Variant</a> doesn't contain <tt>t</tt> in the case
--   of failure.
fromVariant :: Has t bst => Variant bst -> Maybe t

-- | Like <a>fromVariant</a>, but decomposes the <a>Variant</a> into its
--   left and right branches, depending on where <tt>t</tt> is.
decompRoot :: Variant ( 'Branch t lbst rbst) -> Split t lbst rbst
data Split t lbst rbst
Root :: t -> Split t lbst rbst
LSplit :: Variant lbst -> Split t lbst rbst
RSplit :: Variant rbst -> Split t lbst rbst

-- | Weaken a <a>Variant</a> so that it can contain something else.
weaken :: forall t bst. Variant bst -> Variant (Insert t bst)

-- | A proof that inserting into a <tt>bst</tt> doesn't affect the position
--   of anything already in the tree.
proveFollowInsert :: Follow ss (Insert t bst) :~: Follow ss bst

-- | Singletons for <a>Side</a>s.
data SSide (ss :: [Side])
[SNil] :: SSide '[]
[SL] :: SSide ss -> SSide ( 'L : ss)
[SR] :: SSide ss -> SSide ( 'R : ss)

-- | Get a singleton for a list of <a>Side</a>s.
class FromSides (ss :: [Side])
fromSides :: FromSides ss => SSide ss
instance (Type.Set.Follow (Type.Set.Locate t bst) bst Data.Type.Equality.~ t, Type.Set.Variant.FromSides (Type.Set.Locate t bst)) => Type.Set.Variant.Has t bst
instance Type.Set.Variant.FromSides '[]
instance Type.Set.Variant.FromSides ss => Type.Set.Variant.FromSides ('Type.Set.L : ss)
instance Type.Set.Variant.FromSides ss => Type.Set.Variant.FromSides ('Type.Set.R : ss)
instance Data.Type.Equality.TestEquality Type.Set.Variant.SSide