Here are some definitions:

> double x = 2*x

> square x = x*x

> twice f x = f (f x)

> quad = twice double

> fourth = twice square

- What is the type quad? Do not use ghci for this. Give your reasons for your type.

- What is the type of fourth? Do not use ghci for this. Give your reasons for your type.

- Check your types in ghci. If they are different, justify the haskell type and where your assumptions differ.

- Generalize the twice function above to repeat with the following specification:

repeat f 0 x yields x

repeat f 1 x yields f x

repeat f 2 x yields f (f x)

repeat f 3 x yields f (f (f x)) and so on.