--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/display/nfa.scala	Fri Apr 28 11:01:25 2017 +0100
@@ -0,0 +1,36 @@
+// NFAs in Scala using partial functions (returning
+// sets of states)
+import scala.util.Try
+
+// type abbreviation for partial functions
+type :=>[A, B] = PartialFunction[A, B]
+
+// return an empty set when not defined
+def applyOrElse[A, B](f: A :=> Set[B], x: A) : Set[B] =
+  Try(f(x)) getOrElse Set[B]()
+
+
+// NFAs
+case class NFA[A, C](starts: Set[A],           // starting states
+                     delta: (A, C) :=> Set[A], // transition function
+                     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] = 
+    applyOrElse(delta, (q, c))
+
+  def nexts(qs: Set[A], c: C) : Set[A] =
+    qs.flatMap(next(_, c))
+
+  // given some states and a string, what is the set 
+  // of next states?
+  def deltas(qs: Set[A], s: List[C]) : Set[A] = s match {
+    case Nil => qs
+    case c::cs => deltas(nexts(qs, c), cs)
+  }
+
+  // is a string accepted by an NFA?
+  def accepts(s: List[C]) : Boolean = 
+    deltas(starts, s).exists(fins)
+}