- type HAppend HNil l = l
- hAppend _ l = l
-
-instance (HAppendable l l',
- HList (HAppend l l')) => HAppendable (HCons e l) l' where
- type HAppend (HCons e l) l' = HCons e (HAppend l l')
- hAppend (HCons e l) l' = hCons e (hAppend l l')
-
--- :*:
-infixr 2 :*:
-infixr 2 .*.
-
-type e :*: l = HCons e l
-
-(.*.) :: HExtendable e l => e -> l -> HExtend e l
-e .*. l = hExtend e l
+ type HNil :++: l = l
+ _ .++. l = l
+
+instance ( HAppendable l l'
+ , HList (l :++: l')
+ ) => HAppendable (e :*: l) l' where
+ type (e :*: l) :++: l' = e :*: (l :++: l')
+ (e :*: l) .++. l' = e .*. (l .++. l')
+
+-- Applyable
+class Applyable f a where
+ type Apply f a
+ apply :: f -> a -> Apply f a
+
+-- Applyable2
+class Applyable2 f a b where
+ type Apply2 f a b
+ apply2 :: f -> a -> b -> Apply2 f a b
+
+-- Id
+data Id = Id
+
+instance Applyable Id a where
+ type Apply Id a = a
+ apply _ a = a
+
+-- ApplyHAppend
+data ApplyHAppend = ApplyHAppend
+
+instance HAppendable a b => Applyable2 ApplyHAppend a b where
+ type Apply2 ApplyHAppend a b = a :++: b
+ apply2 _ a b = a .++. b
+
+-- HFoldrable
+class HFoldrable f v l where
+ type HFoldr f v l
+ hFoldr :: f -> v -> l -> HFoldr f v l
+
+instance HFoldrable f v HNil where
+ type HFoldr f v HNil = v
+ hFoldr _ v _ = v
+
+instance ( HFoldrable f v l
+ , Applyable2 f e (HFoldr f v l)
+ ) => HFoldrable f v (e :*: l) where
+ type HFoldr f v (e :*: l) = Apply2 f e (HFoldr f v l)
+ hFoldr f v (e :*: l) = apply2 f e (hFoldr f v l)
+
+-- HConcatable
+class HConcatable ls where
+ type HConcat ls
+ hConcat :: ls -> HConcat ls
+
+instance HFoldrable ApplyHAppend HNil ls => HConcatable ls where
+ type HConcat ls = HFoldr ApplyHAppend HNil ls
+ hConcat ls = hFoldr ApplyHAppend hNil ls
+
+-- HMappable
+class HMappable f l where
+ type HMap f l
+ hMap :: f -> l -> HMap f l
+
+instance HMappable f HNil where
+ type HMap f HNil = HNil
+ hMap _ _ = HNil
+
+instance ( HList (HMap f xs)
+ , Applyable f x
+ , HMappable f xs
+ ) => HMappable f (x :*: xs) where
+ type HMap f (x :*: xs) = Apply f x :*: HMap f xs
+ hMap f (x :*: xs) = apply f x .*. hMap f xs