// NFAs in Scala based on sets of partial functions

// type abbreviation for partial functions

type :=>[A, B] = PartialFunction[A, B]

case class NFA[A, C](starts: Set[A],            // starting states

                     delta: Set[(A, C) :=> A],  // transitions

                     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] = 

  def nexts(qs: Set[A], c: C) : Set[A] =

    qs.flatMap(next(_, c))

  def deltas(qs: Set[A], s: List[C]) : Set[A] = s match {

    case Nil => qs

    case c::cs => deltas(nexts(qs, c), cs)

  }

  def accepts(s: List[C]) : Boolean = 

    deltas(starts, s).exists(fins)

}