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--- fp:lab06 [2022/03/25 09:30]
pdmatei
+++ fp:lab06 [2022/04/08 12:45] (current)
pdmatei
@@ Line 1: / Line 1: @@
-====== Lab 06. Datatypes in Scala ======
+====== Lab 06. Polymorphism in Scala ======
-Consider the following implementation of a simple datatypes to encode natural number:
+This lab will start with the implementations discussed during lecture. Please find the polymorphic trait ''FList[A]'' below:
 <code scala>
-trait Nat {}
+trait FList[A]{ // list with elements of type A
-case object Zero extends Nat {}
+  def length: Int
-case class Succ(n: Nat) extends Nat {}
+  def head: A
+  def tail: FList[A]
-val three = Succ(Succ(Succ(Zero)))
+  def map[B](f: A => B): FList[B]
+  // a op (b op (c op acc))
+  def foldRight[B](acc: B)(op: (A,B) => B): B
+  // ((acc op a) op b) op c
+  def foldLeft[B](acc: B)(op: (B,A) => B): B
+  def contains(e: A):Boolean =
+    this.foldRight(false)(_ == e || _)
+}
 </code>
-Write a function which converts a ''Nat'' into an ''Int'':
+together with the implementations:
 <code scala>
-def toInt(n: Nat): Int =
+case class FNil[A]() extends FList[A]{
-  n match {
+  override def length: Int = 0
-    case Zero => ???
+  override def head: A = throw new Exception("head on empty list")
-    case Succ(n) => ???
+  override def tail: FList[A] = throw new Exception("head on empty list")
+  override def map[B](f: A => B): FList[B] = FNil[B]
+  override def foldRight[B](acc: B)(op: (A,B) => B): B = acc
+  override def foldLeft[B](acc: B)(op: (B,A) => B): B = acc
+}
+case class Cons[A](x:A, xs:FList[A]) extends FList[A]{
+  override def length = 1 + xs.length
+  override def head:A = x
+  override def tail:FList[A] = xs
+  override def map[B](f: A => B): FList[B] =
+    Cons(f(x),xs.map(f))
+  override def foldRight[B](acc: B)(op: (A,B) => B): B =
+    op(x, xs.foldRight(acc)(op))
+  override def foldLeft[B](acc: B)(op: (B,A) => B): B =
+    xs.foldLeft(op(acc,x))(op)
   }
 </code>
+Add the following methods in the trait ''FList'' and implement them. **Some methods can be directly implemented in the trait, using ''map'', ''foldRight'', ''foldLeft'' or other functions.**
+  * Can you figure which ones are best implemented in the trait and which in the case classes?
+**6.1.** ''indexOf'' determines the position of a value in the list (starting with 0)
+<code scala>
+def indexOf(e: A): Int
+</code>
+**6.2.** ''update'' creates a new list where the given position is modified with a new value:
+<code scala>
+//Cons(1,Cons(2,Cons(3,FNil()))).update(9,1) = Cons(1,Cons(9,Cons(3,FNil())))
+def update(e: A, pos: Int): FList[A]
+</code>
+**6.3.** ''append'' concatenates this list to another:
+<code scala>
+def append(l: FList[A]): FList[A]
+</code>
+**6.4.** ''reverse'' returns the reversed list:
+<code scala>
+def reverse: FList[A]
+</code>
+**6.5.** ''last'' returns the last element of the list:
+<code scala>
+def last: A
+</code>
+**6.6.** ''filter'' filters the elements of the list:
+<code scala>
+def filter(p: A => Boolean): FList[A]
+</code>
+**6.7.** ''zip'' combines two lists into a list of pairs. If **either** list is larger, the remaining elements are discarded.
+<code scala>
+// Cons(1,(Cons(2,Cons(3,FNil()))).zip(Cons(true,Cons(false,Cons(true,FNil())))) =
+// Cons((1,true),Cons((2,false),Cons((3,true),FNil())))
+def zip[B](l: FList[B]): FList[(A,B)]
+</code>
+**6.8.** ''insSorted'' inserts an element into a sorted list so that the result is a sorted list.
+<code scala>
+def insSorted(f: A => Int)(e: A): FList[A]
+</code>
+**6.9.** ''sortBy'' sorts a list using insertion sort.
+<code scala>
+def sortBy(f: A => Int): FList[A]
+</code>
+**6.10 (!)** Implement a method ''pack'' which encodes a sorted list as follows:
+<code scala>
+[1,1,1,2,3,4,4,5,6].pack = [(1,3),(2,1),(3,1),(4,2),(5,1),(6,1)]
+def pack: FList[(A,Int)]
+</code>