--- a/progs/enfa.scala Sat Jul 04 16:58:12 2020 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,66 +0,0 @@
-// epsilon NFAs...immediately translated into NFAs
-// (needs :load dfa.scala
-// :load nfa.scala in REPL)
-
-// 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))