1 

     2 // regular expressions including NOT

     3 abstract class Rexp

     4 

     5 case object NULL extends Rexp

     6 case object EMPTY extends Rexp

     7 case class CHAR(c: Char) extends Rexp

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

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

    10 case class STAR(r: Rexp) extends Rexp

    11 case class NOT(r: Rexp) extends Rexp

    12 

    13 

    14 // some convenience for typing in regular expressions

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

    16   case Nil => EMPTY

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

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

    19 }

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

    21 

    22 

    23 // nullable function: tests whether the regular 

    24 // expression can recognise the empty string

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

    26   case NULL => false

    27   case EMPTY => true

    28   case CHAR(_) => false

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

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

    31   case STAR(_) => true

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

    33 }

    34 

    35 // tests whether a regular expression 

    36 // cannot recognise more

    37 def no_more (r: Rexp) : Boolean = r match {

    38   case NULL => true

    39   case EMPTY => false

    40   case CHAR(_) => false

    41   case ALT(r1, r2) => no_more(r1) && no_more(r2)

    42   case SEQ(r1, r2) => if (nullable(r1)) (no_more(r1) && no_more(r2)) else no_more(r1)

    43   case STAR(_) => false

    44   case NOT(r) => !(no_more(r))

    45 }

    46 

    47 

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

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

    50   case NULL => NULL

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

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

    53   case SEQ(r1, r2) => 

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

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

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

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

    58 }

    59 

    60 // regular expression for specifying 

    61 // ranges of characters

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

    63   case Nil => NULL

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

    65   case c::s => ALT(CHAR(c), RANGE(s))

    66 }

    67 

    68 // one or more

    69 def PLUS(r: Rexp) = SEQ(r, STAR(r))

    70 

    71 

    72 type Rule[T] = (Rexp, List[Char] => T)

    73 

    74 def error (s: String) = throw new IllegalArgumentException ("Cannot tokenize: " + s)

    75 

    76 def munch[T](r: Rexp, action: List[Char] => T, s: List[Char], t: List[Char]) : Option[(List[Char], T)] = 

    77   s match {

    78     case Nil if (nullable(r)) => Some(Nil, action(t))

    79     case Nil => None

    80     case c::s if (no_more(der (c, r)) && nullable(r)) => Some(c::s, action(t))

    81     case c::s if (no_more(der (c, r))) => None

    82     case c::s => munch(der (c, r), action, s, t ::: List(c))

    83   }

    84 

    85 def one_token[T](rs: List[Rule[T]], s: List[Char]) : (List[Char], T) = {

    86  val somes = rs.map { (r) => munch(r._1, r._2, s, Nil) } .flatten

    87  if (somes == Nil) error(s.mkString) else (somes sortBy (_._1.length) head)

    88 }

    89 

    90 def tokenize[T](rs: List[Rule[T]], s: List[Char]) : List[T] = s match {

    91   case Nil => Nil

    92   case _ => one_token(rs, s) match {

    93     case (rest, token) => token :: tokenize(rs, rest) 

    94   }

    95 }

    96 

    97 

    98 

    99 

   100