Consider the function

second xs $=$ head $($tail xs$)$

$($a$)(10$ points$).$ What is the type of second? Note: that type has a formal meaning in Haskell,

that is$,$ there is only one correct $($and very precise$)$ answer.

$($b$)(10$ points$).$ Explain why second has the type that it has. That is$,$ why does chaining tail

and head together $($or composing them$)$ in the function definition above give rise to the type

that second has?

$2.$ Consider the functions swap and pair, defined respectively as

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

pair x y $=($x$,$y$)$

$($a$)(10$ points$).$ What is the type of swap?

$($b$)(10$ points$).$ What is the type of pair?

$($c$)(10$ points$).$ Notice that, in the types of swap and pair, that x and y $($from the respective

function definitions above$)$ correspond to two different polymorphic type variables. Why is

this, i$.$e$.,$ why wouldn$$t they be the same?

$3.$ Consider the functions double and palindrome, defined