Below you will find the algebraic definition of the datatype IList:
Void : IList Cons : Int x IList -> IList
This definition has already been implemented in Scala, below. Please copy-paste this definition in your worksheet.
trait IList case object Void extends IList case class Cons(x: Int, xs: IList) extends IList
4.1. Consider the following axioms for the operator isEmpty.
isEmpty : IList -> Boolean isEmpty(Void) = true isEmpty(Cons(h,t)) = false.
Implement isEmpty in Scala:
def isEmpty(l: IList): Boolean = ???
4.2. Write down axioms for size : IList → Int and implement the operator in Scala:
def size(l: IList): Int = ???
4.3. Implement contains which checks if an element is a member of a list.
def contains(e: Int, l: IList): Boolean = ???
4.4. Implement max which returns the largest integer from a list:
def max(l: IList): Int = ???
4.5. Implement take which returns a new list containing the first n elements of the original list:
def take(n: Int)(l: IList): IList = ???
4.6. Implement drop which returns a new list containing the original list without the first n elements:
def drop(n: Int)(l: IList): IList = ???
4.7. Implement append which concatenates two lists:
def append(l1: IList, l2: IList): IList = ???
4.8. (!) Implement last which returns the last element from a list:
def last(l: IList): Int = ???
4.9. (!) 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 = ???
4.10. 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 = ???