--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/automata.scala	Sat Jun 15 09:23:18 2013 -0400
@@ -0,0 +1,106 @@
+
+// a class for deterministic finite automata,
+// the type of states is kept polymorphic
+
+case class Automaton[A](start: A, states: Set[A], delta: Map[(A, Char), A], fins: Set[A]) {
+
+  // the transition function lifted to list of characters
+  def deltas(q: A, cs: List[Char]) : Either[A, String] = 
+    if (states.contains(q)) cs match {
+      case Nil => Left(q)
+      case c::cs => 
+        if (delta.isDefinedAt(q, c)) deltas(delta(q, c), cs)
+        else Right(q + " does not have a transition for " + c)
+    }
+    else Right(q + " is not a state of the automaton")
+
+  // wether a string is accepted by the automaton
+  def accepts(s: String) = deltas(start, s.toList) match {
+    case Left(q) => fins.contains(q)
+    case _ => false
+  } 
+}
+
+
+// translating a regular expression into a finite
+// automaton
+
+abstract class Rexp
+
+case object NULL extends Rexp
+case object EMPTY extends Rexp
+case class CHAR(c: Char) extends Rexp 
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 
+case class STAR(r: Rexp) extends Rexp
+
+implicit def string2rexp(s : String) = { 
+  def chars2rexp (cs: List[Char]) : Rexp = cs match {
+    case Nil => EMPTY
+    case c::Nil => CHAR(c)
+    case c::cs => SEQ(CHAR(c), chars2rexp(cs))
+  }
+  chars2rexp(s.toList)
+}
+
+def nullable (r: Rexp) : Boolean = r match {
+  case NULL => false
+  case EMPTY => true
+  case CHAR(_) => false
+  case ALT(r1, r2) => nullable(r1) || nullable(r2)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+  case STAR(_) => true
+}
+
+def der (r: Rexp, c: Char) : Rexp = r match {
+  case NULL => NULL
+  case EMPTY => NULL
+  case CHAR(d) => if (c == d) EMPTY else NULL
+  case ALT(r1, r2) => ALT(der(r1, c), der(r2, c))
+  case SEQ(r1, r2) => if (nullable(r1)) ALT(SEQ(der(r1, c), r2), der(r2, c))
+                      else SEQ(der(r1, c), r2)
+  case STAR(r) => SEQ(der(r, c), STAR(r))
+}
+
+
+// Here we construct an automaton whose
+// states are regular expressions
+type State = Rexp
+type States = Set[State]
+type Transition =  Map[(State, Char), State]
+
+// we use as an alphabet all lowercase letters
+val alphabet = "abcdefghijklmnopqrstuvwxyz".toSet
+
+def goto(q: State, c: Char, qs: States, delta: Transition) : (States, Transition) = {
+  val q_der : State = der(q, c)
+  if (qs.contains(q_der)) (qs, delta + ((q, c) -> q))
+  else explore(qs + q_der, delta + ((q, c) -> q_der), q_der)
+}
+
+def explore (qs: States, delta: Transition, q: State) : (States, Transition) =
+  alphabet.foldRight[(States, Transition)] (qs, delta) ((c, qsd) => goto(q, c, qsd._1, qsd._2)) 
+
+
+def mk_automaton (r: Rexp) : Automaton[Rexp] = {
+  val (qs, delta) = explore(Set(r), Map(), r);
+  val fins = for (q <- qs if nullable(q)) yield q;
+  Automaton[Rexp](r, qs, delta, fins)
+}
+
+val A = mk_automaton(ALT("ab","ac"))
+
+A.start
+A.states.toList.length
+
+println(A.accepts("bd"))
+println(A.accepts("ab"))
+println(A.accepts("ac"))
+
+val r1 = STAR(ALT("a","b"))
+val r2 = SEQ("b","b")
+val r3 = SEQ(SEQ(SEQ(r1, r2), r1), "a")
+val B = mk_automaton(r3)
+
+B.start
+B.states.toList.length