--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/automata/enfa.sc	Sat Jul 04 21:57:33 2020 +0100
@@ -0,0 +1,69 @@
+// epsilon NFAs...immediately translated into NFAs
+
+import $file.dfa, dfa._ 
+import $file.nfa, nfa._ 
+
+
+
+// a 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],                     // the starting states
+               delta: (A, Option[C]) :=> Set[A],   // the epsilon-transitions
+               fins: A => Boolean) : NFA[A, C] = { // the 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)
+}
+
+
+// eNFA examples
+val enfa_trans1 : (State, Option[Char]) :=> Set[State] =
+  { case (Q0, Some('a')) => Set(Q0)
+    case (Q0, None) => Set(Q1, Q2)
+    case (Q1, Some('a')) => Set(Q1)
+    case (Q2, Some('b')) => Set(Q2) 
+  }
+
+val enfa1 = eNFA(Set[State](Q0), enfa_trans1, Set[State](Q2))
+
+
+//
+case object R1 extends State
+case object R2 extends State
+case object R3 extends State
+
+val enfa_trans2 : (State, Option[Char]) :=> Set[State] =
+  { case (R1, Some('b')) => Set(R3)
+    case (R1, None) => Set(R2)
+    case (R2, Some('a')) => Set(R1, R3) 
+  }
+
+
+val enfa2 = eNFA(Set[State](R1), enfa_trans1, Set[State](R3))