1     

     2 abstract class Rexp

     3 

     4 case object NULL extends Rexp

     5 case object EMPTY extends Rexp

     6 case class CHAR(c: Char) extends Rexp

     7 case class ALT(r1: Rexp, r2: Rexp) extends Rexp 

     8 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 

     9 case class STAR(r: Rexp) extends Rexp 

    10 

    11 // some convenience for typing in regular expressions

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

    13   case Nil => EMPTY

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

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

    16 }

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

    18 

    19 

    20 // nullable function: tests whether the regular 

    21 // expression can recognise the empty string

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

    23   case NULL => false

    24   case EMPTY => true

    25   case CHAR(_) => false

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

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

    28   case STAR(_) => true

    29 }

    30 

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

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

    33   case NULL => NULL

    34   case EMPTY => NULL

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

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

    37   case SEQ(r1, r2) => 

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

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

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

    41 }

    42 

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

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

    45   case Nil => r

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

    47 }

    48 

    49 // main matcher function

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

    51 

    52 //example

    53 //val r = STAR(ALT(SEQ(CHAR('a'), CHAR('b')), CHAR('b')))

    54 //der('b', r)

    55 //der('b', r)

    56 

    57 //one or zero

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

    59 

    60 //n-times

    61 def NTIMES(r: Rexp, n: Int) : Rexp = n match {

    62   case 0 => EMPTY

    63   case 1 => r

    64   case n => SEQ(r, NTIMES(r, n - 1))

    65 }

    66 

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

    68 

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

    70   val start = System.nanoTime()

    71   for (j <- 1 to i) code

    72   val end = System.nanoTime()

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

    74 }

    75 

    76 for (i <- 1 to 29) {

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

    78 }

    79 

    80