// epsilon NFAs...immediately translated into NFAs

// (needs nfa.scala)

// fixpoint construction

import scala.annotation.tailrec

@tailrec

def fixpT[A](f: A => A, x: A): A = {

  val fx = f(x)

  if (fx == x) x else fixpT(f, fx) 

}

// translates eNFAs directly into NFAs 

def eNFA[A, C](starts: Set[A],                     // starting states

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

               fins: A => Boolean) : NFA[A, C] = { // final states 

  // epsilon transitions

  def enext(q: A) : Set[A] = 

    applyOrElse(delta, (q, None))

  def enexts(qs: Set[A]) : Set[A] = 

    qs | qs.flatMap(enext(_))     // | is the set-union in Scala

  // epsilon closure

  def ecl(qs: Set[A]) : Set[A] = 

    fixpT(enexts, qs)

  // "normal" transitions

  def next(q: A, c: C) : Set[A] = 

    applyOrElse(delta, (q, Some(c)))

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

    ecl(ecl(qs).flatMap(next(_, c)))

  // result NFA

  NFA(ecl(starts), 

      { case (q, c) => nexts(Set(q), c) }, 

      q => ecl(Set(q)) exists fins)

}