// NFAs in Scala using partial functions (returning
// sets of states)
import scala.util.Try

// type abbreviation for partial functions
type :=>[A, B] = PartialFunction[A, B]

// return an empty set when not defined
def applyOrElse[A, B](f: A :=> Set[B], x: A) : Set[B] =
  Try(f(x)) getOrElse Set[B]()


// NFAs
case class NFA[A, C](starts: Set[A],           // starting states
                     delta: (A, C) :=> Set[A], // transition function
                     fins:  A => Boolean) {    // final states 

  // given a state and a character, what is the set of 
  // next states? if there is none => empty set
  def next(q: A, c: C) : Set[A] = 
    applyOrElse(delta, (q, c))

  def nexts(qs: Set[A], c: C) : Set[A] =
    qs.flatMap(next(_, c))

  // given some states and a string, what is the set 
  // of next states?
  def deltas(qs: Set[A], s: List[C]) : Set[A] = s match {
    case Nil => qs
    case c::cs => deltas(nexts(qs, c), cs)
  }

  // is a string accepted by an NFA?
  def accepts(s: List[C]) : Boolean = 
    deltas(starts, s).exists(fins)
}