// A Version with an explicit n-times regular expression;+
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// this keeps the size of the regular expression in the+
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// EVIL1 test-case quite small+
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//+
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// call the test cases with X = {1,2}+
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//+
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//   amm re2.sc testX+
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//+
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// or +
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//+
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//   amm re2.sc all+
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+
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+
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abstract class Rexp +
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case object ZERO extends Rexp+
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case object ONE 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   //explicit constructor for n-times+
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+
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+
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def nullable (r: Rexp) : Boolean = r match {+
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  case ZERO => false+
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  case ONE => 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, n) => if (n == 0) true else nullable(r)+
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}+
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+
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+
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def der(c: Char, r: Rexp) : Rexp = r match {+
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  case ZERO => ZERO+
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  case ONE => ZERO+
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  case CHAR(d) => if (c == d) ONE else ZERO+
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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(r1) => SEQ(der(c, r1), STAR(r1))+
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  case NTIMES(r, n) => +
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    if (n == 0) ZERO else SEQ(der(c, r), NTIMES(r, n - 1))+
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}+
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+
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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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}+
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+
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def matcher(r: Rexp, s: String) : Boolean = +
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  nullable(ders(s.toList, r))+
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+
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+
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// the optional regular expression: one or zero times+
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// this regular expression is still defined in terms of ALT+
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def OPT(r: Rexp) = ALT(r, ONE)+
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+
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+
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// Test Cases+
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+
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// evil regular expressions+
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def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))+
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val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))+
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+
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def time_needed[T](i: Int, code: => T) = {+
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  val start = System.nanoTime()+
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  for (j <- 1 to i) code+
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  val end = System.nanoTime()+
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  (end - start) / (i * 1.0e9)+
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}+
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+
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+
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+
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@arg(doc = "Test (a?{n}) (a{n})")+
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@main+
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def test1() = {+
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  println("Test (a?{n}) (a{n})")+
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+
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  for (i <- 0 to 1000 by 100) {+
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    println(f"$i: ${time_needed(1, matcher(EVIL1(i), "a" * i))}%.5f")+
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  }+
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}  +
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+
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+
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@arg(doc = "Test (a*)* b")+
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@main+
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def test2() = {+
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  println("Test (a*)* b")+
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+
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  for (i <- 0 to 30 by 2) {+
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    println(f"$i: ${time_needed(1, matcher(EVIL2, "a" * i))}%.5f")+
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  }+
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}+
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+
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// the size of a regular expressions - for testing purposes +
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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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+
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// EVIL1(n) has now a constant size, no matter+
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// what n is; also the derivative only grows +
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// moderately +
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+
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size(EVIL1(1))  // 7+
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size(EVIL1(3))  // 7+
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size(EVIL1(5))  // 7+
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size(EVIL1(7))  // 7+
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size(EVIL1(20)) // 7+
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+
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size(ders("".toList, EVIL1(5)))       // 7+
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size(ders("a".toList, EVIL1(5)))      // 16+
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size(ders("aa".toList, EVIL1(5)))     // 35+
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size(ders("aaa".toList, EVIL1(5)))    // 59+
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size(ders("aaaa".toList, EVIL1(5)))   // 88+
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size(ders("aaaaa".toList, EVIL1(5)))  // 122+
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size(ders("aaaaaa".toList, EVIL1(5))) // 151+
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+
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size(ders(("a" * 20).toList, EVIL1(5))) +
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+
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// but the size of the derivatives can still grow +
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// quite dramatically in case of EVIL2:  (a*)* b+
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+
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size(ders("".toList, EVIL2))       // 5+
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size(ders("a".toList, EVIL2))      // 12+
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size(ders("aa".toList, EVIL2))     // 28+
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size(ders("aaa".toList, EVIL2))    // 58+
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size(ders("aaaa".toList, EVIL2))   // 116+
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size(ders("aaaaa".toList, EVIL2))  // 230+
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size(ders("aaaaaa".toList, EVIL2)) // 456+
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+
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size(ders(("a" * 20).toList, EVIL2)) // 7340068+
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+
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+
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+
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@arg(doc = "All tests.")+
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@main+
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def all() = { test1(); test2() } +
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+
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+
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+
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+
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// runs with amm2 and amm3+
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