abstract class Rexpcase object ZERO extends Rexpcase object ONE extends Rexpcase class CHAR(c: Char) extends Rexpcase class ALT(r1: Rexp, r2: Rexp) extends Rexp case class SEQ(r1: Rexp, r2: Rexp) extends Rexp case class STAR(r: Rexp) extends Rexp case class NTIMES(r: Rexp, n: Int) extends Rexp case class UPNTIMES(r: Rexp, n: Int) extends Rexp // the nullable function: tests whether the regular // expression can recognise the empty stringdef nullable (r: Rexp) : Boolean = r match { case ZERO => false case ONE => true case CHAR(_) => false case ALT(r1, r2) => nullable(r1) || nullable(r2) case SEQ(r1, r2) => nullable(r1) && nullable(r2) case STAR(_) => true case NTIMES(r, i) => if (i == 0) true else nullable(r) case UPNTIMES(r: Rexp, n: Int) => true}// the derivative of a regular expression w.r.t. a characterdef der (c: Char, r: Rexp) : Rexp = r match { case ZERO => ZERO case ONE => ZERO case CHAR(d) => if (c == d) ONE else ZERO case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) case SEQ(r1, r2) => if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) else SEQ(der(c, r1), r2) case STAR(r1) => SEQ(der(c, r1), STAR(r1)) case NTIMES(r1, i) => if (i == 0) ZERO else if (nullable(r1)) SEQ(der(c, r1), UPNTIMES(r1, i - 1)) else SEQ(der(c, r1), NTIMES(r1, i - 1)) case UPNTIMES(r1, i) => if (i == 0) ZERO else SEQ(der(c, r1), UPNTIMES(r1, i - 1)) }def simp(r: Rexp) : Rexp = r match { case ALT(r1, r2) => (simp(r1), simp(r2)) match { case (ZERO, r2s) => r2s case (r1s, ZERO) => r1s case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s) } case SEQ(r1, r2) => (simp(r1), simp(r2)) match { case (ZERO, _) => ZERO case (_, ZERO) => ZERO case (ONE, r2s) => r2s case (r1s, ONE) => r1s case (r1s, r2s) => SEQ(r1s, r2s) } case r => r}// the derivative w.r.t. a string (iterates der)def ders (s: List[Char], r: Rexp) : Rexp = s match { case Nil => r case c::s => ders(s, simp(der(c, r)))}// the main matcher functiondef matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))// one or zerodef OPT(r: Rexp) = ALT(r, ONE)// evil regular expressionsdef EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))val EVIL3 = SEQ(STAR(ALT(CHAR('a'), SEQ(CHAR('a'),CHAR('a')))), CHAR('b'))def time_needed[T](i: Int, code: => T) = { val start = System.nanoTime() for (j <- 1 to i) code val end = System.nanoTime() "%.5f".format((end - start) / (i * 1.0e9))}// test: (a?{n}) (a{n})for (i <- 0 to 8000 by 1000) { println(s"$i: ${time_needed(2, matches(EVIL1(i), "a" * i))}")}// test: (a*)* bfor (i <- 0 to 6000000 by 500000) { println(s"$i: ${time_needed(2, matches(EVIL2, "a" * i))}")}val r0 = simp(der('a', EVIL3))val r1 = simp(der('a', r0))val r2 = simp(der('a', r1))val r3 = simp(der('a', r2))val r4 = simp(der('a', r3))val r5 = simp(der('a', r4))val r6 = simp(der('a', r5))//test: (a|aa)* b/*for (i <- 0 to 100 by 10) { println(s"$i: ${time_needed(2, matches(EVIL3, "a" * i ++ "c"))}")} */