+ −
abstract class Rexp+ −
case object ZERO extends Rexp+ −
case object ONE extends Rexp+ −
case class CHAR(c: Char) extends Rexp+ −
case 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 string+ −
def 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 character+ −
def 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 function+ −
def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))+ −
+ −
// one or zero+ −
def OPT(r: Rexp) = ALT(r, ONE)+ −
+ −
// evil regular expressions+ −
def 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: ${time_needed(2, matches(EVIL1(i), "a" * i))}")+ −
}+ −
+ −
// test: (a*)* b+ −
for (i <- 0 to 6000000 by 500000) {+ −
println(s"$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"))}")+ −
}+ −
*/+ −
+ −