9. The countdown problem

Question 1

What is a functor and how do you declare one?

Answer 1

The class of types that support mapping a function over all of it’s elements.

class Functor f where
fmap :: (a -> b) -> f a -> f b

Question 2

What are the two Functor laws

Answer 2

fmap id = id
fmap (g . h) = fmap g . fmap h

Question 3

What are Applicatives and how do you declare one?

Answer 3

A way to use functions with a variable amount of arguments

class Functor f => Applicative f where
pure :: a -> f a
(<*>) :: f (a -> b) -> f a -> f b

Question 4

What are the four applicative laws?

Answer 4

1. pure id <*> x = x
2. pure (g x) = pure g <*> pure x
3. x <> pure y = pure (\g -> g y) <> x
4. x <> (y <> z) = (pure (.) <> x <> y) <*> z

Question 5

What are monads and how do you declare one?

Answer 5

An applicative type m that supports return and&raquo_space;=

class Applicative m => Monad m where
return :: a -> m a
(»=) :: m a -> (a -> m b) -> m b
return = pure