1 // NFAs in Scala using partial functions (returning

     2 // sets of states)

     3 import scala.util.Try

     4 

     5 // type abbreviation for partial functions

     6 type :=>[A, B] = PartialFunction[A, B]

     7 

     8 // return an empty set when not defined

     9 def applyOrElse[A, B](f: A :=> Set[B], x: A) : Set[B] =

    10   Try(f(x)) getOrElse Set[B]()

    11 

    12 

    13 // NFAs

    14 case class NFA[A, C](starts: Set[A],           // starting states

    15                      delta: (A, C) :=> Set[A], // transition function

    16                      fins:  A => Boolean) {    // final states 

    17 

    18   // given a state and a character, what is the set of 

    19   // next states? if there is none => empty set

    20   def next(q: A, c: C) : Set[A] = 

    21     applyOrElse(delta, (q, c))

    22 

    23   def nexts(qs: Set[A], c: C) : Set[A] =

    24     qs.flatMap(next(_, c))

    25 

    26   // given some states and a string, what is the set 

    27   // of next states?

    28   def deltas(qs: Set[A], s: List[C]) : Set[A] = s match {

    29     case Nil => qs

    30     case c::cs => deltas(nexts(qs, c), cs)

    31   }

    32 

    33   // is a string accepted by an NFA?

    34   def accepts(s: List[C]) : Boolean = 

    35     deltas(starts, s).exists(fins)

    36 }