4.

Consider the function

second xs = head (tail xs)

What is its type?

Explain why "second" has the type that it has, i.e., "tail :: [a] -> [a]", hence "xs :: [a]", and "head :: [a] -> a", etc. Why does chaining them together like in the definition of "second" give us the type that it has?

Note: this will use the fact that if "f" is a function that maps arguments of type "a" to results of type "b", and "e" is an expression of type "a", then the application "f e" has type "b", that is:

if "f :: a -> b" and "e :: a" then "f e :: b"

5.

Consider the function

swap (x,y) = (y,x)

What is its type?

Why can "x" and "y" correspond to different types in general?