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// DFAs in Scala using partial functions
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import scala.util.Try
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// type abbreviation for partial functions
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type :=>[A, B] = PartialFunction[A, B]
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case class DFA[A, C](start: A, // starting state
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delta: (A, C) :=> A, // transition (partial fun)
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fins: A => Boolean) { // final states
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def deltas(q: A, s: List[C]) : A = s match {
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case Nil => q
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case c::cs => deltas(delta(q, c), cs)
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145
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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}
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def accepts(s: List[C]) : Boolean =
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Try(fins(deltas(start, s))) getOrElse false
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}
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// the example shown in the handout
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145
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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abstract class State
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case object Q0 extends State
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case object Q1 extends State
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case object Q2 extends State
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case object Q3 extends State
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case object Q4 extends State
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145
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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val delta : (State, Char) :=> State =
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{ case (Q0, 'a') => Q1
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case (Q0, 'b') => Q2
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case (Q1, 'a') => Q4
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case (Q1, 'b') => Q2
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case (Q2, 'a') => Q3
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case (Q2, 'b') => Q2
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case (Q3, 'a') => Q4
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case (Q3, 'b') => Q0
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case (Q4, 'a') => Q4
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case (Q4, 'b') => Q4 }
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145
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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val dfa = DFA(Q0, delta, Set[State](Q4))
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145
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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dfa.accepts("bbabaab".toList) // true
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dfa.accepts("baba".toList) // false
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// another DFA test with a Sink state
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abstract class S
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case object S0 extends S
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case object S1 extends S
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case object S2 extends S
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case object Sink extends S
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// transition function with a sink state
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val sigma : (S, Char) :=> S =
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{ case (S0, 'a') => S1
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case (S1, 'a') => S2
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case _ => Sink
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}
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val dfa1a = DFA(S0, sigma, Set[S](S2))
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dfa1a.accepts("aa".toList) // true
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dfa1a.accepts("".toList) // false
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dfa1a.accepts("ab".toList) // false
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