object Driver extends App {
  import Sets._

  println(contains(singletonSet(1), 1))
  val s1 = add(add(add(emptySet,1),3),5)
  val s2 = add(add(add(emptySet,1),4),5)
  val s3 = add(add(emptySet,1),5)
  val s4 = add(add(emptySet,1),5)
  print("s1 = ")
  printSet(s1)
  print("s2 = ")
  printSet(s2)
  print("s3 = ")
  printSet(s3)
  print("s4 = ")
  printSet(s4)
  print("s1 union s2 = ")
  printSet(union(s1,s2))
  print("s1 intersect s2 = ")
  printSet(intersect(s1,s2))
  print("s1 difference s2 = ")
  printSet(difference(s1,s2))

  print("s3 subset of s1: ")
  println(subset(s3,s1))

  print("s1 subset of s3: ")
  println(subset(s1,s3))

  print("s3 equal s4: ")
  println(equal(s3,s4))

  print("size of s1: ")
  println(size(s1))

  print("even numbers in s1 are ")
  printSet(filter(s1,x=>x%2==0))
  print("even numbers in s2 are ")
  printSet(filter(s2,x=>x%2==0))
  print("odd numbers in s2 are ")
  printSet(filter(s2,x=>x%2!=0))

  print("forall x, x is even (s1) ")
  println(forall(s1,x=>x%2==0))

  print("forall x, x is odd (s1) ")
  println(forall(s1,x=>x%2!=0))

  print("exists x, x is even (s1) ")
  println(forall(s1,x=>x%2==0))

  print("exists x, x is odd (s1) ")
  println(forall(s1,x=>x%2!=0))
  
  print("squares of s1 ")
  printSet(map(s1,x=>x*x))
  
  val ss = add(add(emptySet,-1000),0)
  println(forall(ss,x=>x<1000))
}