--- a/progs/nfa.scala	Sat Apr 15 22:03:59 2017 +0800
+++ b/progs/nfa.scala	Tue Apr 25 12:28:07 2017 +0100
@@ -1,26 +1,36 @@
-// NFAs in Scala based on sets of partial functions
+// 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: Set[(A, C) :=> A],  // transitions
+                     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
+  // 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] = 
-    delta.flatMap(d => Try(d(q, c)).toOption)
+    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)
 }
-