623
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// A version which attempts to move whole strings, not
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477
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// just characters, under derivatives whenever possible
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422
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abstract class Rexp
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case object ZERO extends Rexp
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case object ONE extends Rexp
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
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case class CHAR(c: Char) extends Rexp
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422
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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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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
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623
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// the nullable function: tests whether the regular
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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// expression can recognise the empty string
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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def nullable (r: Rexp) : Boolean = r match {
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case ZERO => false
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case ONE => true
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case CHAR(_) => false
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case ALT(r1, r2) => nullable(r1) || nullable(r2)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case SEQ(r1, r2) => nullable(r1) && nullable(r2)
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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case STAR(_) => true
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121
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case NTIMES(r, i) => if (i == 0) true else nullable(r)
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
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623
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// the derivative of a regular expression w.r.t. a character
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
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def der (c: Char, r: Rexp) : Rexp = r match {
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case ZERO => ZERO
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case ONE => ZERO
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case CHAR(d) => if (c == d) ONE else ZERO
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
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case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
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case SEQ(r1, r2) =>
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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else SEQ(der(c, r1), r2)
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441
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case STAR(r1) => SEQ(der(c, r1), STAR(r1))
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455
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case NTIMES(r1, i) =>
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631
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if (i == 0) ZERO else SEQ(der(c, r1), NTIMES(r1, i - 1))
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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422
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def simp(r: Rexp) : Rexp = r match {
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case ALT(r1, r2) => (simp(r1), simp(r2)) match {
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case (ZERO, r2s) => r2s
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case (r1s, ZERO) => r1s
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case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)
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}
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case SEQ(r1, r2) => (simp(r1), simp(r2)) match {
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case (ZERO, _) => ZERO
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case (_, ZERO) => ZERO
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case (ONE, r2s) => r2s
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case (r1s, ONE) => r1s
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case (r1s, r2s) => SEQ(r1s, r2s)
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}
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case r => r
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}
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// an example
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546
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val r = SEQ(SEQ(CHAR('x'), CHAR('y')), CHAR('z'))
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der('x', r)
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der('y', der('x', r))
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der('z', der('y', der('x', r)))
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simp(der('z', der('y', der('x', r))))
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477
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// *new*
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623
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// the derivative w.r.t. a string (iterates der)
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414
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def ders2(s: List[Char], r: Rexp) : Rexp = (s, r) match {
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case (Nil, r) => r
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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case (s, ZERO) => ZERO
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case (s, ONE) => if (s == Nil) ONE else ZERO
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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case (s, CHAR(c)) => if (s == List(c)) ONE else
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Christian Urban <christian dot urban at kcl dot ac dot uk>
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if (s == Nil) CHAR(c) else ZERO
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467
Christian Urban <christian dot urban at kcl dot ac dot uk>
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case (s, ALT(r1, r2)) => ALT(ders2(s, r1), ders2(s, r2))
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422
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case (c::s, r) => ders2(s, simp(der(c, r)))
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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623
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// the main matcher function
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631
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def matcher(r: Rexp, s: String) : Boolean =
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nullable(ders2(s.toList, r))
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
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623
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// one or zero
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407
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
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def OPT(r: Rexp) = ALT(r, ONE)
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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477
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// Test Cases
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422
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def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
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441
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val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
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422
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623
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// for measuring time
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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89 |
def time_needed[T](i: Int, code: => T) = {
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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val start = System.nanoTime()
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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for (j <- 1 to i) code
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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val end = System.nanoTime()
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631
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(end - start) / (i * 1.0e9)
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441
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}
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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623
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// test: (a?{n}) (a{n})
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638
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for (i <- 0 to 11000 by 1000) {
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631
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println(f"$i: ${time_needed(2, matcher(EVIL1(i), "a" * i))}%.5f")
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92
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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}
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
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623
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// test: (a*)* b
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631
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for (i <- 0 to 7000000 by 500000) {
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println(f"$i: ${time_needed(2, matcher(EVIL2, "a" * i))}%.5f")
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441
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}
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623
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// the size of a regular expressions - for testing purposes
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550
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def size(r: Rexp) : Int = r match {
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case ZERO => 1
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case ONE => 1
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case CHAR(_) => 1
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case ALT(r1, r2) => 1 + size(r1) + size(r2)
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case SEQ(r1, r2) => 1 + size(r1) + size(r2)
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case STAR(r) => 1 + size(r)
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case NTIMES(r, _) => 1 + size(r)
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}
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// string of a regular expressions - for testing purposes
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def string(r: Rexp) : String = r match {
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case ZERO => "0"
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case ONE => "1"
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case CHAR(c) => c.toString
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case ALT(r1, r2) => s"(${string(r1)} + ${string(r2)})"
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case SEQ(CHAR(c), CHAR(d)) => s"${c}${d}"
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case SEQ(r1, r2) => s"(${string(r1)} ~ ${string(r2)})"
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case STAR(r) => s"(${string(r)})*"
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case NTIMES(r, n) => s"(${string(r)}){${n}}"
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}
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// test: ("a" | "aa")*
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val EVIL3 = STAR(ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a'))))
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// test: ("" | "a" | "aa")*
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631
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val EVIL4 = STAR(ALT(ONE, ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a')))))
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550
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val t1 = ders2("a".toList, EVIL3)
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val t1s = simp(t1)
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val t2 = ders2("aa".toList, t1s)
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val t2s = simp(t2)
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val t3 = ders2("aaa".toList, t2s)
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val t3s = simp(t3)
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val t4 = ders2("aaaa".toList, t3s)
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val t4s = simp(t4)
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println(string(t1) + " " + size(t1))
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println("s " + string(t1s) + " " + size(t1s))
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println(string(t2) + " " + size(t2))
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println("s " + string(t2s) + " " + size(t2s))
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println(string(t3) + " " + size(t3))
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println("s " + string(t3s) + " " + size(t3s))
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println(string(t4) + " " + size(t4))
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println("s " + string(t4s) + " " + size(t4s))
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