```{- |
This module provides the 'Str' data type, which is used by the
underlying 'uniplate' and 'biplate' methods. It should not
be used directly under normal circumstances.
-}

module Data.Generics.Str where

import Data.Generics.PlateInternal

import Data.Traversable
import Data.Foldable
import Control.Applicative
import Data.Monoid

-- * The Data Type

data Str a = Zero | One a | Two (Str a) (Str a)
deriving Show

instance Eq a => Eq (Str a) where
Zero == Zero = True
One x == One y = x == y
Two x1 x2 == Two y1 y2 = x1 == y1 && x2 == y2
_ == _ = False

instance Functor Str where
fmap f Zero = Zero
fmap f (One x) = One (f x)
fmap f (Two x y) = Two (fmap f x) (fmap f y)

instance Foldable Str where
foldMap m Zero = mempty
foldMap m (One x) = m x
foldMap m (Two l r) = foldMap m l `mappend` foldMap m r

instance Traversable Str where
traverse f Zero = pure Zero
traverse f (One x) = One <\$> f x
traverse f (Two x y) = Two <\$> traverse f x <*> traverse f y

-- | Take the type of the method, will crash if called
strType :: Str a -> a
strType = error "Data.Generics.Str.strType: Cannot be called"

-- | Convert a 'Str' to a list, assumes the value was created
--   with 'listStr'
strList :: Str a -> [a]
strList x = builder (f x)
where
f (Two (One x) xs) cons nil = x `cons` f xs cons nil
f Zero cons nil = nil

-- | Convert a list to a 'Str'
listStr :: [a] -> Str a
listStr (x:xs) = Two (One x) (listStr xs)
listStr [] = Zero

-- | Transform a 'Str' to a list, and back again, in a structure
--   preserving way. The output and input lists must be equal in
--   length.
strStructure :: Str a -> ([a], [a] -> Str a)
strStructure x = (g x [], fst . f x)
where
g :: Str a -> [a] -> [a]
g Zero xs = xs
g (One x) xs = x:xs
g (Two a b) xs = g a (g b xs)

f :: Str a -> [a] -> (Str a, [a])
f Zero rs = (Zero, rs)
f (One _) (r:rs) = (One r, rs)
f (Two a b) rs1 = (Two a2 b2, rs3)
where
(a2,rs2) = f a rs1
(b2,rs3) = f b rs2
```