Implemented the functions of the exercise

src/main/scala/funsets/FunSets.scala

@@ -18,32 +18,30 @@ trait FunSets extends FunSetsInterface {
   /**
    * Returns the set of the one given element.
    */
-  def singletonSet(elem: Int): FunSet = ???
-
+  def singletonSet(elem: Int): FunSet = (e: Int) => e == elem
 
   /**
    * Returns the union of the two given sets,
    * the sets of all elements that are in either `s` or `t`.
    */
-  def union(s: FunSet, t: FunSet): FunSet = ???
+  def union(s: FunSet, t: FunSet): FunSet = (e: Int) => s(e) || t(e)
   
   /**
    * Returns the intersection of the two given sets,
    * the set of all elements that are both in `s` and `t`.
    */
-  def intersect(s: FunSet, t: FunSet): FunSet = ???
+  def intersect(s: FunSet, t: FunSet): FunSet = (e: Int) => s(e) && t(e)
 
   /**
    * Returns the difference of the two given sets,
    * the set of all elements of `s` that are not in `t`.
    */
-  def diff(s: FunSet, t: FunSet): FunSet = ???
+  def diff(s: FunSet, t: FunSet): FunSet = (e: Int) => s(e) && !t(e)
 
   /**
    * Returns the subset of `s` for which `p` holds.
    */
-  def filter(s: FunSet, p: Int => Boolean): FunSet = ???
-
+  def filter(s: FunSet, p: Int => Boolean): FunSet = (e: Int) => s(e) && p(e)
 
   /**
    * The bounds for `forall` and `exists` are +/- 1000.
@@ -55,24 +53,24 @@ trait FunSets extends FunSetsInterface {
    */
   def forall(s: FunSet, p: Int => Boolean): Boolean =
     def iter(a: Int): Boolean =
-      if ??? then
-        ???
-      else if ??? then
-        ???
+      if a == bound + 1 then
+        true
+      else if !p(a) && s(a) then
+        false
       else
-        iter(???)
-    iter(???)
+        iter(a+1)
+    iter(-bound)
 
   /**
    * Returns whether there exists a bounded integer within `s`
    * that satisfies `p`.
    */
-  def exists(s: FunSet, p: Int => Boolean): Boolean = ???
+  def exists(s: FunSet, p: Int => Boolean): Boolean = !forall(s, (e: Int) => !p(e))
 
   /**
    * Returns a set transformed by applying `f` to each element of `s`.
    */
-  def map(s: FunSet, f: Int => Int): FunSet = ???
+  def map(s: FunSet, f: Int => Int): FunSet = (e :Int) => exists(s, (x: Int)=> e == f(x))
 
   /**
    * Displays the contents of a set