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--- fp2023:lab04 [2023/03/21 07:23]
pdmatei
+++ fp2023:lab04 [2023/03/24 14:53] (current)
pdmatei
@@ Line 1: / Line 1: @@
 ====== Lab 4. Algebraic Datatype definition ======
-==== 4.1. The type Nat =====
-Consider the following type defined to represent natural numbers:
-<code scala>
-trait Nat
-case object Zero extends Nat
-case class Succ(n: Nat) extends Nat
-</code>
-**4.1.1.** Implement the following function:
-<code scala>
-def isZero(n: Nat): Nat =
-   n match {
-       case Zero => ???
-       case Succ(np) => ???
-   }
-</code>
-**4.1.2.** Implement the addition function over natural numbers:
-<code scala>
-def add(n: Nat, m: Nat): Nat =
-   n match {
-       case Zero => ???
-       case Succ(np) => ???
-   }
-</code>
-**4.1.3.** Implement the subtraction function over natural numbers. If $math[n > m] then $math[m - n = 0].
-<code scala>
-def subtract(n: Nat, m: Nat): Nat = ???
-</code>
-**4.1.4.** Implement ''greater'' which checks if a natural number is strictly larger than the other:
-<code scala>
-def greater(n: Nat, m: Nat): Nat =
-   (n,m) match {
-      ???
-   }
-</code>
-**4.1.5.** Equality is already defined for all case classes, as structural equality (objects built in the same way are equal). However, re-implement equality over naturals:
-<code scala>
-def equal(n: Nat, m: Nat): Nat = ???
-</code>
-**4.1.6.** Implement a function which converts a Nat to a Scala Int:
-<code scala>
-def toInt(n: Nat): Int = ???
-</code>
-**4.1.7.** Implement a function which converts an Int to a Nat:
-<code scala>
-def fromInt(i: Int): Nat = ???
-</code>
-===== 4.2. The type IList (list over integers) =====
 Consider the following type defined to represent lists of integers:
@@ Line 63: / Line 8: @@
 </code>
-**4.2.1.** Implement ''isEmpty'' which checks if a list is empty:
+**4.1.** Implement ''isEmpty'' which checks if a list is empty:
 <code scala>
 def isEmpty(l: IList): Boolean = ???
 </code>
-**4.2.2.** Implement ''size'' which returns the size of the list:
+**4.2.** Implement ''size'' which returns the size of the list:
 <code scala>
 def size(l: IList): Int = ???
 </code>
-**4.2.3.** Implement ''append'' which concatenates two lists:
+**4.3.** Implement ''append'' which concatenates two lists:
 <code scala>
 def append(l1: IList, l2: IList): IList = ???
 </code>
-**4.2.4.** (!) Implement ''last'' which returns the last element from a list:
+**4.4.** (!) Implement ''last'' which returns the last element from a list:
 <code scala>
 def last(l: IList): Int = ???
 </code>
-**4.2.5.** (!) Implement ''reverse''. There are two different ways to implement reverse (with direct and with tail-end recursion). Try both implementations.
+**4.5.** (!) Implement ''reverse''. There are two different ways to implement reverse (with direct and with tail-end recursion). Try both implementations.
 <code scala>
 def reverse(l: IList): IList = ???
 </code>
-**4.2.6.** Implement ''contains'' which checks if an element is a member of a list.
+**4.6.** Implement ''contains'' which checks if an element is a member of a list.
+<code scala>
+def contains(e: Int, l: IList): Boolean = ???
+</code>
+**4.7.** Implement ''max'' which returns the largest integer from a list:
+<code scala>
+def max(l: IList): Int = ???
+</code>
+**4.8.** Implement ''take'' which returns a new list containing the first ''n'' elements of the original list:
 <code scala>
-def contains(e: Int, l: IList): IList = ???
+def take(n: Int)(l: IList): IList = ???
 </code>
-**4.2.7.** Implement ''max'' which returns the largest integer from a list:
+**4.9.** Implement ''drop'' which returns a new list containing the original list without the first ''n'' elements:
 <code scala>
-def max(l: Ilist): IList = ???
+def drop(n: Int)(l: IList): IList = ???
 </code>
-**4.2.8.** Implement ''isSorted'' which checks if a list is sorted:
+**4.10.** Implement ''isSorted'' which checks if a list is sorted:
 <code scala>
-def isSorted(l: IList): IList = ???
+def isSorted(l: IList): Boolean = ???
 </code>
-**4.2.9.** Implement ''merge'' which merges two sorted lists:
+**4.11.** Implement ''merge'' which merges two sorted lists:
 <code scala>
 def merge(l1: IList, l2: IList): IList = ???
 </code>
-**4.2.10.** Implement ''mergeSort'' which sorts a list:
+**4.12.** Implement ''mergeSort'' which sorts a list:
 <code scala>
 def mergesort(l: IList) IList = ???
 </code>