+-- left-to-right state transformer
+newtype StateL s a = StateL { runStateL :: s -> (s, a) }
+
+instance Functor (StateL s) where
+ fmap f (StateL k) = StateL $ \ s -> let (s', v) = k s in (s', f v)
+
+instance Applicative (StateL s) where
+ pure x = StateL (\ s -> (s, x))
+ StateL kf <*> StateL kv = StateL $ \ s ->
+ let (s', f) = kf s
+ (s'', v) = kv s'
+ in (s'', f v)
+
+-- |The 'mapAccumL' function behaves like a combination of 'fmap'
+-- and 'foldl'; it applies a function to each element of a structure,
+-- passing an accumulating parameter from left to right, and returning
+-- a final value of this accumulator together with the new structure.
+mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
+mapAccumL f s t = runStateL (traverse (StateL . flip f) t) s
+
+-- right-to-left state transformer
+newtype StateR s a = StateR { runStateR :: s -> (s, a) }
+
+instance Functor (StateR s) where
+ fmap f (StateR k) = StateR $ \ s -> let (s', v) = k s in (s', f v)
+
+instance Applicative (StateR s) where
+ pure x = StateR (\ s -> (s, x))
+ StateR kf <*> StateR kv = StateR $ \ s ->
+ let (s', v) = kv s
+ (s'', f) = kf s'
+ in (s'', f v)
+
+-- |The 'mapAccumR' function behaves like a combination of 'fmap'
+-- and 'foldr'; it applies a function to each element of a structure,
+-- passing an accumulating parameter from right to left, and returning
+-- a final value of this accumulator together with the new structure.
+mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
+mapAccumR f s t = runStateR (traverse (StateR . flip f) t) s
+