// NFAs in Scala using partial functions (returning// sets of states)import scala.util.Try// states classabstract class Statecase object Q0 extends Statecase object Q1 extends Statecase object Q2 extends Statecase object Q3 extends Statecase object Q4 extends State// type abbreviation for partial functionstype :=>[A, B] = PartialFunction[A, B]// return an empty set when not defineddef applyOrElse[A, B](f: A :=> Set[B], x: A) : Set[B] = Try(f(x)) getOrElse Set[B]()// NFAscase 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) // depth-first version of accepts def search(q: A, s: List[C]) : Boolean = s match { case Nil => fins(q) case c::cs => next(q, c).exists(search(_, cs)) } def accepts2(s: List[C]) : Boolean = starts.exists(search(_, s))}// NFA examplesval nfa_trans1 : (State, Char) :=> Set[State] = { case (Q0, 'a') => Set(Q0, Q1) case (Q0, 'b') => Set(Q2) case (Q1, 'a') => Set(Q1) case (Q2, 'b') => Set(Q2) }val nfa1 = NFA(Set[State](Q0), nfa_trans1, Set[State](Q2))nfa1.accepts("aa".toList) // falsenfa1.accepts("aaaaa".toList) // falsenfa1.accepts("aaaaab".toList) // truenfa1.accepts("aaaaabbb".toList) // truenfa1.accepts("aaaaabbbaaa".toList) // falsenfa1.accepts("ac".toList) // falsenfa1.accepts2("aa".toList) // falsenfa1.accepts2("aaaaa".toList) // falsenfa1.accepts2("aaaaab".toList) // truenfa1.accepts2("aaaaabbb".toList) // truenfa1.accepts2("aaaaabbbaaa".toList) // falsenfa1.accepts2("ac".toList) // false