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package Handouts
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import io.Source
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import scala.util.matching.Regex
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import scala.util._
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object Handout2 {
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abstract class Rexp
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case object NULL extends Rexp
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case object EMPTY extends Rexp
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case class CHAR(c: Char) extends Rexp
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case class ALT(r1: Rexp, r2: Rexp) extends Rexp
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case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
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case class STAR(r: Rexp) extends Rexp
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case class NTIMES(r: Rexp, n: Int) extends Rexp
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def OPT(r: Rexp) = ALT(r, EMPTY) //> OPT: (r: Handouts.Handout2.Rexp)Handouts.Handout2.ALT
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def nullable(r: Rexp): Boolean = r match {
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case NULL => false
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case EMPTY => true
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case CHAR(_) => false
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case ALT(r1, r2) => nullable(r1) || nullable(r2)
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case SEQ(r1, r2) => nullable(r1) && nullable(r2)
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case STAR(_) => true
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case NTIMES(r, i) => if (i == 0) true else nullable(r)
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} //> nullable: (r: Handouts.Handout2.Rexp)Boolean
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def der(c: Char, r: Rexp): Rexp = r match {
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case NULL => NULL
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case EMPTY => NULL
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case CHAR(d) => if (c == d) EMPTY else NULL
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case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
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case SEQ(r1, r2) =>
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if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
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else SEQ(der(c, r1), r2)
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case STAR(r) => SEQ(der(c, r), STAR(r))
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case NTIMES(r, i) =>
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if (i == 0) NULL else SEQ(der(c, r), NTIMES(r, i - 1))
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} //> der: (c: Char, r: Handouts.Handout2.Rexp)Handouts.Handout2.Rexp
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def _ders(s: List[Char], r: Rexp): Rexp = s match {
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case Nil => r
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case c :: s => ders(s, der(c, r))
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} //> _ders: (s: List[Char], r: Handouts.Handout2.Rexp)Handouts.Handout2.Rexp
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def ders(s: List[Char], r: Rexp): Rexp = s match {
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case Nil => r
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case c :: s => ders(s, simp(der(c, r)))
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} //> ders: (s: List[Char], r: Handouts.Handout2.Rexp)Handouts.Handout2.Rexp
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def matches(r: Rexp, s: String): Boolean =
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nullable(ders(s.toList, r)) //> matches: (r: Handouts.Handout2.Rexp, s: String)Boolean
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def simp(r: Rexp): Rexp = r match {
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case ALT(r1, r2) => {
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val r1s = simp(r1)
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val r2s = simp(r2)
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(r1s, r2s) match {
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case (NULL, _) => r2s
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case (_, NULL) => r1s
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case _ => if (r1s == r2s) r1s else ALT(r1s, r2s)
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}
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}
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case SEQ(r1, r2) => {
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val r1s = simp(r1)
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val r2s = simp(r2)
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(r1s, r2s) match {
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case (NULL, _) => NULL
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case (_, NULL) => NULL
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case (EMPTY, _) => r2s
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case (_, EMPTY) => r1s
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case _ => SEQ(r1s, r2s)
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}
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}
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case NTIMES(r, n) => NTIMES(simp(r), n)
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case r => r
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} //> simp: (r: Handouts.Handout2.Rexp)Handouts.Handout2.Rexp
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/************************************************************************************************************************************/
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// der test
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// r = {(a.b) + b}*
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val r = STAR(ALT(SEQ(CHAR('a'), CHAR('b')), CHAR('b')))
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//> r : Handouts.Handout2.STAR = STAR(ALT(SEQ(CHAR(a),CHAR(b)),CHAR(b)))
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// => [{(_.b) + null} . {(a.b)+b}*]
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der('a', r) //> res0: Handouts.Handout2.Rexp = SEQ(ALT(SEQ(EMPTY,CHAR(b)),NULL),STAR(ALT(SE
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//| Q(CHAR(a),CHAR(b)),CHAR(b))))
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// => [{(null.b) + _} . {(a.b)+b}*]
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der('b', r) //> res1: Handouts.Handout2.Rexp = SEQ(ALT(SEQ(NULL,CHAR(b)),EMPTY),STAR(ALT(SE
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//| Q(CHAR(a),CHAR(b)),CHAR(b))))
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// => [{(null.b) + _} . {(a.b)+b}*]
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der('c', r) //> res2: Handouts.Handout2.Rexp = SEQ(ALT(SEQ(NULL,CHAR(b)),NULL),STAR(ALT(SEQ
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//| (CHAR(a),CHAR(b)),CHAR(b))))
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val r2 = ALT(SEQ(CHAR('a'), CHAR('b')), CHAR('b'))
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//> r2 : Handouts.Handout2.ALT = ALT(SEQ(CHAR(a),CHAR(b)),CHAR(b))
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der('a', r2) //> res3: Handouts.Handout2.Rexp = ALT(SEQ(EMPTY,CHAR(b)),NULL)
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val r3 = SEQ(CHAR('a'), CHAR('b')) //> r3 : Handouts.Handout2.SEQ = SEQ(CHAR(a),CHAR(b))
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der('a', r3) //> res4: Handouts.Handout2.Rexp = SEQ(EMPTY,CHAR(b))
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val r4 = CHAR('a') //> r4 : Handouts.Handout2.CHAR = CHAR(a)
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der('a', r4) //> res5: Handouts.Handout2.Rexp = EMPTY
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nullable(r) //> res6: Boolean = true
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nullable(r2) //> res7: Boolean = false
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nullable(r3) //> res8: Boolean = false
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nullable(r4) //> res9: Boolean = false
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} |