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{-# LANGUAGE GADTs #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE FlexibleContexts, FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses, UndecidableInstances #-}
module Events.Types.NDT
( NDT
, foldNDT
, cons
, fromFoldable
) where
import Data.Monoid
import Data.Foldable (foldr)
import Data.Bool (bool)
import Control.Applicative (Alternative)
import qualified Control.Applicative as Alt (Alternative(..))
import Control.Monad
import Control.Monad.Trans
import Control.Monad.Reader (MonadReader(..))
import Control.Monad.Catch (MonadThrow(..))
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 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
(>>=) = NDTBind
instance Monad m => Monoid (NDT m a) where
mempty = empty
mappend (NDTCons x) y'@(NDTCons y) = NDTCons $ maybe y (\(x', xs) -> return $ Just (x', xs <> y')) =<< x
mappend (NDTBind x f) (NDTBind y g) = NDTBind (fmap Left x <> fmap Right y) (either f g)
mappend x@(NDTBind _ _) y = x <> NDTBind y return
mappend x y@(NDTBind _ _) = NDTBind x return <> y
instance MonadTrans NDT where
lift = NDTCons . fmap (Just . (, empty))
instance Monad m => Alternative (NDT m) where
empty = mempty
(<|>) = mappend
instance Monad m => MonadPlus (NDT m) where
mzero = mempty
mplus = mappend
instance MonadReader r m => MonadReader r (NDT m) where
reader = lift . reader
local f (NDTCons x) = NDTCons (local f x)
local f (NDTBind x g) = NDTBind (local f x) g
instance MonadIO m => MonadIO (NDT m) where
liftIO = lift . liftIO
instance MonadThrow m => MonadThrow (NDT m) where
throwM = lift . throwM
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 :: (Foldable f, Applicative f, Monoid (f a), Monad m) => (a -> m Bool) -> NDT m a -> m (f a)
-- ^ Evaluate depth-first, pruning leaves under the assumption that the selection predicate is monotonic on siblings and children
foldNDT sel (NDTCons mx) = do
mx' <- mx
case mx' of
Nothing -> return mempty
Just (x, mxs) -> bool (return mempty) ((pure x <>) <$> foldNDT sel mxs) =<< sel x
foldNDT sel (NDTBind (NDTCons x) f) = do
x' <- x
case x' of
Nothing -> return mempty
Just (x'', xs) -> do
x3 <- foldNDT sel $ f x''
xs' <- if null x3 then return mempty else foldNDT sel (NDTBind xs f)
return $ x3 <> xs'
foldNDT sel (NDTBind (NDTBind x g) f) = foldNDT sel $ NDTBind x (f <=< g)
fromFoldable :: (Foldable f, Monad m) => f a -> NDT m a
fromFoldable = foldr cons empty
|
