data Parser c a = Parser ([c] -> Error (a,[c]))
data Error a =  Valid a | Error String
  deriving Show



instance Monad Error where
  Valid a   >>= f = f a
  Error s   >>= f = Error s

  --Valid f <*> Valid a = Valid (f a)
  --Error s <*> _       = Error s
  --_       <*> Error s = Error s

  --return = Valid

instance Functor Error where
  fmap f (Error s) = Error s
  fmap f (Valid a) = Valid (f a)

instance Applicative Error where
  pure = Valid
  

instance Functor (Parser c) where
  fmap :: (a->b) -> Parser c a -> Parser c b
  fmap f (Parser g) = Parser h
    where 
      h s = g s >>= (\(parsed,rest) -> pure (f parsed, rest))


linkNeighbours :: [a] -> [(a,a)]
linkNeighbours (head:y:xs) = (head,y):(linkNeighbours' head (y:xs)) 
linkNeighbours' :: a -> [a] -> [(a,a)]
linkNeighbours' head (x:y:xs) = (x,y):(linkNeighbours' head (y:xs))
linkNeighbours' head [x]  = [(x,head)]

polyArea :: [(Double,Double)] -> Double
polyArea = (0.5*) . sum . map (\((x1,y1),(x2,y2)) -> (y1+y2)*(x1-x2)) . linkNeighbours

svgPathToPolygon :: Parser Char [(Double,Double)]
svgPathToPolygon = symbol 'm' 'm' 

symbol :: (Show s,Eq s) =>s -> a -> Parser s a
symbol c a = Parser f
  where
    f [] = Error "No symbol"
    f (s:ss) = if s==c then Valid (a,ss) else Error ("Expected "++show c)

--The are if correct should be 4233.8898623135065 <= (maxX-minX)(maxY-minY) = (704.94638+38.986565)(22.381667+55.33534) =