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1 |
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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// whether it can match the empty string
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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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}
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// derivative of a regular expression
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def deriv (r: Rexp, c: Char) : 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(deriv(r1, c), deriv(r2, c))
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case SEQ(r1, r2) =>
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if (nullable(r1)) ALT(SEQ(deriv(r1, c), r2), deriv(r2, c))
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else SEQ(deriv(r1, c), r2)
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case STAR(r) => SEQ(deriv(r, c), STAR(r))
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}
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def derivs (r: Rexp, s: List[Char]) : Rexp = s match {
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case Nil => r
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case c::cs => derivs(deriv(r, c), cs)
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}
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// regular expression matching
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def matches(r: Rexp, s: String) : Boolean = nullable(derivs(r, s.toList))
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/* Examples */
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println(matches(SEQ(SEQ(CHAR('c'), CHAR('a')), CHAR('b')),"cab"))
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println(matches(STAR(CHAR('a')),"aaa"))
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/* Convenience using implicits */
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implicit def string2rexp(s : String) : Rexp = {
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s.foldRight (EMPTY: Rexp) ( (c, r) => SEQ(CHAR(c), r) )
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}
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println(matches("cab" ,"cab"))
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println(matches(STAR("a"),"aaa"))
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println(matches(STAR("a"),"aaab"))
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