\begin{code}
module Data.String.DFST.Lens
  (
  ) where

import Data.String.DFST
import Control.Lens.Edit
import Control.Edit

import Numeric.Natural
import Data.Sequence (Seq((:<|), (:|>)))
import qualified Data.Sequence as Seq

data StringEdit = Insert Natural Char
                | Delete Natural
  deriving (Eq, Ord, Show, Read)

data StringEdits = StringEdits (Seq StringEdit)
                 | SEFail
  deriving (Eq, Ord, Show, Read)

insert :: Natural -> Char -> StringEdits
insert n c = StringEdits .  Seq.singleton $ Insert n c
  
delete :: Natural -> StringEdits
delete n = StringEdits .  Seq.singleton $ Delete n

instance Monoid StringEdits where
  mempty = StringEdits Seq.empty
  SEFail `mappend` _ = SEFail
  _ `mappend` SEFail = SEFail
  (StringEdits Seq.Empty) `mappend` x = x
  x `mappend` (StringEdits Seq.Empty) = x
  (StringEdits x@(bs :|> b)) `mappend` (StringEdits y@(a :<| as))
    | (Insert n _) <- a
    , (Delete n') <- b
    , n == n'
    = StringEdits bs `mappend` StringEdits as
    | otherwise = StringEdits $ x `mappend` y

instance Module StringEdits where
  type Domain StringEdits = String
  apply str SEFail = Nothing
  apply str (StringEdits Seq.Empty) = Just str
  apply str (StringEdits (es :|> Insert n c)) = (flip apply) (StringEdits es) =<< go str n c
    where
      go [] n c
        | n == 0 = Just [c]
        | otherwise = Nothing
      go str@(x:xs) n c
        | n == 0 = Just $ c : str
        | otherwise = (x:) <$> go xs (pred n) c
  apply str (StringEdits (es :|> Delete n)) = (flip apply) (StringEdits es) =<< go str n
    where
      go [] _ = Nothing
      go (x:xs) n
        | n == 0 = Just xs
        | otherwise = (x:) <$> go xs (pred n)

  init = ""
  divInit = StringEdits . Seq.unfoldl go . (0,)
    where
      go (_, []) = Nothing
      go (n, (c:cs)) = Just ((succ n, cs), Insert n c)

data DFSTAction state = DFSTBranch (Map state (state, String)) (DFSTAction state) (DFSTAction state)
                      | DFSTLeaf

dfstLens :: forall state. Ord state => DFST state -> EditLens (DFSTAction state) StringEdits StringEdits
dfstLens DFST{..} = EditLens ground propR propL
  where
    ground :: DFSTAction state
    ground = DFSTLeaf

    propR :: (DFSTAction state, StringEdits) -> (DFSTAction state, StringEdits)
    propR = undefined
    propL :: (DFSTAction state, StringEdits) -> (DFSTAction state, StringEdits)
    propL = undefined
\end{code}