// regular expressions including records

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 SPECIAL(s: String) extends Rexp

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

}

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))

}

def ders(s: List[Char], r: Rexp) : Rexp = s match {

  case Nil => r

  case c::s => ders(s, der(c, r))

}

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

}

def ders_simp(s: List[Char], r: Rexp) : Rexp = s match {

  case Nil => r

  case c::s => ders_simp(s, simp(der(c, r)))

}

def pp(r: Rexp) : TypedTag[String] = r match {

  case CHAR(c) => li(code(c.toString))

  case ALT(r1, r2) => li(code("+"), ul(pp(r1), pp(r2)))

  case SEQ(r1, r2) => li(code(raw("&middot")), ul(pp(r1), pp(r2)))

  case STAR(r1) => li(code("*"), ul(pp(r1)))

  case ZERO => li(code("0"))

  case ONE => li(code("1"))

  case SPECIAL(s) => li(code(raw(s)))

} 

def mktree(r: Rexp) = 

   ul(cls := "tree")(pp(r))

def index(rs: List[Rexp]) = 

  html(

    head(link(rel := "stylesheet", href := "./style.css")),

    body(rs.map(mktree))

  )

/*

println(index(List(simple, test, evil2)))

val simple = CHAR('a')

val test = ALT(CHAR('a'), CHAR('b'))

write.over(pwd/"t1.html", 

    index(List(evil2, 

               ders("a".toList, evil2),

               ders("aa".toList, evil2),

               ders("aaa".toList, evil2))))

*/

val evil2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))

val r1 = STAR(ALT(SPECIAL("<i>r<sub>1</sub></i>"), SPECIAL("<i>r<sub>2</sub></i>")))

val r2 = ALT(SPECIAL("<i>r<sub>1</sub></i>"), STAR(SPECIAL("<i>r<sub>2</sub></i>")))

@main

def main(fname: String) = {

}