Scala FunSets

gistfile1.scala

object FunSets {
  /**
   * We represent a set by its characteristic function, i.e.
   * its `contains` predicate.
   */
  type Set = Int => Boolean

  /**
   * Indicates whether a set contains a given element.
   */
  def contains(s: Set, elem: Int): Boolean = s(elem)

  /**
   * Returns the set of the one given element.
   */
  def singletonSet(elem: Int): Set = ((x:Int) => elem == x)
    

  /**
   * Returns the union of the two given sets,
   * the sets of all elements that are in either `s` or `t`.
   */
  def union(s: Set, t: Set): Set = ((x:Int) => contains(s, x) || contains(t, x))
}