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

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

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

    54   case SEQ(r1, r2) => 

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

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

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

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

    59 }

    60 

    61 

    62 // regular expression for specifying 

    63 // ranges of characters

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

    65   case Nil => NULL

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

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

    68 }

    69 

    70 //one or more

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

    72 

    73 

    74 //some regular expressions

    75 val LOWERCASE = RANGE("abcdefghijklmnopqrstuvwxyz".toList)

    76 val UPPERCASE = RANGE("ABCDEFGHIJKLMNOPQRSTUVWXYZ".toList)

    77 val LETTER = ALT(LOWERCASE, UPPERCASE)

    78 val DIGIT = RANGE("0123456789".toList)

    79 val NONZERODIGIT = RANGE("123456789".toList)

    80 

    81 val IDENT = SEQ(LETTER, STAR(ALT(LETTER,DIGIT)))

    82 val NUMBER = ALT(SEQ(NONZERODIGIT, STAR(DIGIT)), "0")

    83 val WHITESPACE = RANGE(" \n".toList)

    84 val WHITESPACES = PLUS(WHITESPACE)

    85 

    86 val ALL = ALT(ALT(LETTER, DIGIT), WHITESPACE)

    87 val COMMENT = SEQ(SEQ("/*", NOT(SEQ(SEQ(STAR(ALL), "*/"), STAR(ALL)))), "*/")

    88 

    89 

    90 // an example list of regular expressions

    91 val regs: List[Rexp]=  List("if", "then", "else", "+", IDENT, NUMBER, WHITESPACES, COMMENT) 

    92 

    93 

    94 def error (s: String) = throw new IllegalArgumentException ("Could not lex " + s)

    95 

    96 def munch(r: Rexp, s: List[Char], t: List[Char]) : Option[(List[Char], List[Char])] = 

    97   s match {

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

    99     case Nil => None

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

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

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

   103   }

   104 

   105 def one_string (regs: List[Rexp], s: List[Char]) : (List[Char], List[Char]) = {

   106  val somes = regs.map { munch(_, s, Nil) } .flatten

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

   108 }

   109 

   110 def tokenize (regs: List[Rexp], s: List[Char]) : List[String] = s match {

   111   case Nil => Nil

   112   case _ => one_string(regs, s) match {

   113     case (rest, s) => s.mkString :: tokenize(regs, rest) 

   114   }

   115 }

   116 

   117 //examples

   118 println(tokenize(regs, "if true then then 42 else +".toList))

   119 println(tokenize(regs, "if+true+then+then+42+else +".toList))

   120 println(tokenize(regs, "ifff if     34 34".toList))

   121 println(tokenize(regs, "/*ifff if */ hhjj /*34 */".toList))

   122 println(tokenize(regs, "/* if true then */ then 42 else +".toList))

   123 //println(tokenize(regs, "ifff $ if 34".toList)) // causes an error because of the symbol $