====== Lab 4. Algebraic Datatype definition ======
Consider the following type defined to represent lists of integers:
trait IList
case object Void extends IList
case class Cons(x: Int, xs: IList) extends IList
**4.1.** Implement ''isEmpty'' which checks if a list is empty:
def isEmpty(l: IList): Boolean = ???
**4.2.** Implement ''size'' which returns the size of the list:
def size(l: IList): Int = ???
**4.3.** Implement ''append'' which concatenates two lists:
def append(l1: IList, l2: IList): IList = ???
**4.4.** (!) Implement ''last'' which returns the last element from a list:
def last(l: IList): Int = ???
**4.5.** (!) Implement ''reverse''. There are two different ways to implement reverse (with direct and with tail-end recursion). Try both implementations.
def reverse(l: IList): IList = ???
**4.6.** Implement ''contains'' which checks if an element is a member of a list.
def contains(e: Int, l: IList): Boolean = ???
**4.7.** Implement ''max'' which returns the largest integer from a list:
def max(l: IList): Int = ???
**4.8.** Implement ''take'' which returns a new list containing the first ''n'' elements of the original list:
def take(n: Int)(l: IList): IList = ???
**4.9.** Implement ''drop'' which returns a new list containing the original list without the first ''n'' elements:
def drop(n: Int)(l: IList): IList = ???
**4.10.** Implement ''isSorted'' which checks if a list is sorted:
def isSorted(l: IList): Boolean = ???
**4.11.** Implement ''merge'' which merges two sorted lists:
def merge(l1: IList, l2: IList): IList = ???
**4.12.** Implement ''mergeSort'' which sorts a list:
def mergesort(l: IList) IList = ???