Answers

1. A functor is a type constructor, f, with an instance of the Functor type class:

   class Functor f where
     fmap :: (a -> b) -> (f a -> f b)
     (<$) :: b -> (f a -> f b)
     x <$ t = fmap (\_ -> x) t

   This is subject to the identity and fusion laws:

   fmap id = id
   fmap f . fmap g = fmap (f . g)

2. An applicative functor, f, is a functor with an instance of the Applicative type class:

   class Functor f => Applicative f where
     pure :: a -> f a
     (<*>) :: f (a -> b) -> f a -> f b
     fs <*> xs = liftA2 ($) fs xs
     liftA2 :: (a -> b -> c) -> f a -> f b -> f c
     liftA2 f xs ys = fmap f xs <*> ys
     (*>) :: f a -> f b -> f b
     xs *> ys = liftA2 (\_ y -> y) xs ys
     (<*) :: f a -> f b -> f a
     xs <* ys = liftA2 (\x _ -> x) xs ys

   This is subject to four laws:

   pure id <*> v...