abstract class Rexp

case object NULL extends Rexp

case object EMPTY 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 NOT(r: Rexp) extends Rexp

case class REP(r: Rexp, n: Int) extends Rexp 

// some convenience for typing in regular expressions

def charlist2rexp(s : List[Char]) : Rexp = s match {

  case Nil => EMPTY

  case c::Nil => CHAR(c)

  case c::s => SEQ(CHAR(c), charlist2rexp(s))

}

implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)

implicit def RexpOps(r: Rexp) = new {

  def | (s: Rexp) = ALT(r, s)

  def % = STAR(r)

  def %(n: Int) = REP(r, n) 

  def %%(n: Int) = SEQ(REP(r, n), STAR(r)) 

  def ? = ALT(EMPTY, r)

  def unary_! = NOT(r)

  def ~ (s: Rexp) = SEQ(r, s)

}

implicit def stringOps(s: String) = new {

  def | (r: Rexp) = ALT(s, r)

  def | (r: String) = ALT(s, r)

  def % = STAR(s)

  def %(n: Int) = REP(s, n)

  def %%(n: Int) = SEQ(REP(s, n), STAR(s)) 

  def ? = ALT(EMPTY, s)

  def unary_! = NOT(s)

  def ~ (r: Rexp) = SEQ(s, r)

  def ~ (r: String) = SEQ(s, r)

}

// nullable function: tests whether the regular 

// expression can recognise the empty string

def nullable (r: Rexp) : Boolean = r match {

  case NULL => false

  case EMPTY => true

  case CHAR(_) => false

  case ALT(r1, r2) => nullable(r1) || nullable(r2)

  case SEQ(r1, r2) => nullable(r1) && nullable(r2)

  case STAR(_) => true

  case NOT(r) => !(nullable(r))

  case REP(r, i) => if (i == 0) true else nullable(r)

}

// derivative of a regular expression w.r.t. a character

def der (c: Char, r: Rexp) : Rexp = r match {

  case NULL => NULL

  case EMPTY => NULL

  case CHAR(d) => if (c == d) EMPTY else NULL

  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(r) => SEQ(der(c, r), STAR(r))

  case NOT(r) => NOT(der (c, r))

  case REP(r, i) => 

    if (i == 0) NULL else SEQ(der(c, r), REP(r, i - 1))

}

// 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, der(c, r))

}

// main matcher function

def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))

//examples

val digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

val int = ("+" | "-").? ~ digit.%%(1)

val real = ("+" | "-").? ~ digit.%%(1) ~ ("." ~ digit.%%(1)).? ~ (("e" | "E") ~ ("+" | "-").? ~ digit.%%(1)).?

val ints = List("0", "-4534", "+049", "99")

val reals = List("0.9", "-12.8", "+91.0", "9e12", "+9.21E-12", "-512E+01")

val errs = List("", "-", "+", "+-1", "-+2", "2-")

ints.map(s => matcher(int, s))

reals.map(s => matcher(int, s))

errs.map(s => matcher(int, s))

ints.map(s => matcher(real, s))

reals.map(s => matcher(real, s))

errs.map(s => matcher(real, s))

def RTEST(n: Int) = ("a".? %(n)) ~ ("a" %(n))

def time_needed[T](i: Int, code: => T) = {

  val start = System.nanoTime()

  for (j <- 1 to i) code

  val end = System.nanoTime()

  (end - start)/(i * 1.0e9)

}

for (i <- 1 to 29) {

  println(i + ": " + "%.5f".format(time_needed(1, matcher(RTEST(i), "a" * i))))

}