1     

     2 abstract class Rexp {

     3   def simp : Rexp = this

     4 }

     5 

     6 case object NULL extends Rexp

     7 case object EMPTY extends Rexp

     8 case class CHAR(c: Char) extends Rexp

     9 case class ALT(r1: Rexp, r2: Rexp) extends Rexp {

    10   override def simp = (r1.simp, r2.simp) match {

    11     case (NULL, r) => r

    12     case (r, NULL) => r

    13     case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY)

    14     case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY)

    15     case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2)

    16   }

    17 }

    18 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp {

    19   override def simp = (r1.simp, r2.simp) match {

    20     case (NULL, _) => NULL

    21     case (_, NULL) => NULL

    22     case (EMPTY, r) => r

    23     case (r, EMPTY) => r

    24     case (r1, r2) => SEQ(r1, r2)

    25   }

    26 }

    27 case class STAR(r: Rexp) extends Rexp {

    28   override def simp = r.simp match {

    29     case NULL => EMPTY

    30     case EMPTY => EMPTY

    31     case r => STAR(r)

    32   }

    33 }

    34 case class NTIMES(r: Rexp, n: Int) extends Rexp {

    35   override def simp = if (n == 0) EMPTY else 

    36     r.simp match {

    37       case NULL => NULL

    38       case EMPTY => EMPTY

    39       case r => NTIMES(r, n)

    40     }

    41 }

    42 

    43 // some convenience for typing in regular expressions

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

    45   case Nil => EMPTY

    46   case c::Nil => CHAR(c)

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

    48 }

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

    50 

    51 

    52 // nullable function: tests whether the regular 

    53 // expression can recognise the empty string

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

    55   case NULL => false

    56   case EMPTY => true

    57   case CHAR(_) => false

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

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

    60   case STAR(_) => true

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

    62 }

    63 

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

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

    66   case NULL => NULL

    67   case EMPTY => NULL

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

    69   case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))

    70   case SEQ(r1, r2) => 

    71     if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))

    72     else SEQ(der(c, r1), r2)

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

    74   case NTIMES(r, i) => 

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

    76 }

    77 

    78 // derivative w.r.t. a string (iterates der)

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

    80   case Nil => r

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

    82 }

    83 

    84 // main matcher function

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

    86 

    87 

    88 

    89 //one or zero

    90 def OPT(r: Rexp) = ALT(r, EMPTY)

    91 

    92 def RTEST(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))

    93 

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

    95   val start = System.nanoTime()

    96   for (j <- 1 to i) code

    97   val end = System.nanoTime()

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

    99 }

   100 

   101 

   102 for (i <- 1 to 11001 by 500) {

   103   println(i + " " + + " " + time_needed(1, matcher(RTEST(i), "a" * i)))

   104 }

   105 

   106