{-# LANGUAGE GADTs #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE FlexibleContexts, FlexibleInstances #-}

module Events.Types.NDT
  ( NDT
  , foldNDT
  , cons
  , fromFoldable
  ) where

import Data.Monoid
import Data.Foldable (foldr)
import Data.Maybe
import Data.Either

import Control.Monad
import Control.Monad.Identity

import Control.Monad.Trans

import Debug.Trace

data NDT m a where
  NDTBind :: NDT m a -> (a -> NDT m b) -> NDT m b
  NDTCons :: m (Maybe (a, NDT m a)) -> NDT m a

instance Show (NDT Identity a) where
  show (NDTBind x _) = "Bind (" ++ show x ++ ") _"
  show x = show . (\(NDTCons x) -> x) $ fmap (const ()) x

instance Functor m => Functor (NDT m) where
  fmap f (NDTBind a g) = NDTBind a (fmap f . g)
  fmap f (NDTCons x) = NDTCons $ fmap f' x
    where
      f' Nothing = Nothing
      f' (Just (x, xs)) = Just (f x, fmap f xs)

instance Applicative m => Applicative (NDT m) where
  pure x = NDTCons . pure $ Just (x, empty)
  fs <*> xs = fs >>= (\f -> xs >>= pure . (f $))

instance Applicative m => Monad (NDT m) where
  return = pure
  fail = const empty
  (>>=) = NDTBind

instance Monad m => Monoid (NDT m a) where
  mempty = empty
  mappend (NDTCons x) y'@(NDTCons y) = trace "(cons <> cons)" . NDTCons . trace "[cons <> cons]" $ maybe y (\(x, xs) -> return $ Just (x, xs <> y')) =<< x
  mappend (NDTBind x f) (NDTBind y g) = trace "(bind <> bind)" $ NDTBind (fmap Left x <> fmap Right y) (either f g)
  mappend x@(NDTBind _ _) y = trace "(bind <>)" $ x <> NDTBind y return
  mappend x y@(NDTBind _ _) = trace "(<> bind)" $ NDTBind x return <> y

instance MonadTrans NDT where
  lift = NDTCons . fmap Just . fmap (,empty)

empty :: Applicative m => NDT m a
empty = NDTCons $ pure Nothing

cons :: Applicative m => a -> NDT m a -> NDT m a
cons x xs = NDTCons . pure $ Just (x, xs)
  
foldNDT :: (Monoid a, Monad m) => (a -> m Bool) -> NDT m a -> m a
foldNDT sel = fmap snd . foldNDT' sel

foldNDT' :: (Monoid a, Monad m) => (a -> m Bool) -> NDT m a -> m (Any, a)
-- ^ Evaluate depth-first, pruning leaves under the assumption that the selection predicate is monotonic on siblings
foldNDT' sel (NDTCons mx) = do
  mx' <- mx
  case mx' of
    Nothing -> return mempty
    Just (x, mxs) -> do
      continue <- sel x
      case trace ("(cons "++ show continue ++ ")") continue of
        False -> return (Any True, mempty)
        True  -> ((Any True, x) <>) <$> foldNDT' sel mxs
foldNDT' sel (NDTBind (NDTCons x) f) = trace "(bind cons)" $ do
  x' <- x
  case x' of
    Nothing -> return mempty
    Just (x'', xs) -> do -- foldNDT' sel . NDTCons $ Just . (, NDTBind xs f) . snd <$> foldNDT' sel (f x'')
      (productive, x3) <- foldNDT' sel $ f x''
      continue <- sel x3
      case trace ("(bind cons " ++ show (productive, continue) ++ ")") $ continue || not (getAny productive) of
        False -> return mempty
        True -> ((mempty, x3) <>) <$> foldNDT' sel (NDTBind xs f)
foldNDT' sel (NDTBind (NDTBind x g) f) = trace "(bind bind)" . foldNDT' sel $ NDTBind x (f <=< g)

fromFoldable :: (Foldable f, Monad m) => f a -> NDT m a
fromFoldable = foldr cons empty