`Semigroup`(s), `Monoid`(s) and `Alt`(s) instances

Maybe.hs

{-# LANGUAGE NoImplicitPrelude, GeneralizedNewtypeDeriving #-}

class Semigroup a where
  (<>) :: a -> a -> a
class (Semigroup a) => Monoid a where
  mempty :: a

class Functor f where
  fmap :: (a -> b) -> f a -> f b
class (Functor f) => Alt f where
  (<|>) :: f a -> f a -> f a
class (Alt f) => Plus f where
  zero :: f a

data Maybe a = Nothing | Just a
instance (Semigroup a) => Semigroup (Maybe a) where
  Nothing <> r = r
  l <> Nothing = l
  (Just l) <> (Just r) = Just (l <> r)
instance (Semigroup a) => Monoid (Maybe a) where
  mempty = Nothing
-- instance (Semigroup a) => Semigroup (Maybe a) where
--   Nothing <> _ = Nothing
--   _ <> Nothing = Nothing
--   (Just l) <> (Just r) = Just (l <> r)
-- instance (Monoid a) => Monoid (Maybe a) where
--   mempty = Just mempty

instance Functor Maybe where
  fmap _ Nothing = Nothing
  fmap f (Just x) = Just (f x)

newtype First a = First (Maybe a)
  deriving Functor
instance Alt First where
  (First Nothing) <|> r = r
  l <|> _ = l
instance Plus First where
  zero = First Nothing
-- instance Alt First where
--   _ <|> r@(First Nothing) = r
--   l <|> _ = l

newtype Last a = Last (Maybe a)
  deriving Functor
instance Alt Last where
  l <|> (Last Nothing) = l
  _ <|> r = r
instance Plus Last where
  zero = Last Nothing
-- instance Alt Last where
--   l@(Last Nothing) <|> _ = l
--   _ <|> r = r