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 // some regular expressions

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

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

    74 val LETTER = ALT(LOWERCASE, UPPERCASE)

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

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

    77 

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

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

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

    81 val WHITESPACES = PLUS(WHITESPACE)

    82 

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

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

    85 

    86 

    87 // for classifying the strings that have been recognised

    88 abstract class Token

    89 

    90 case object T_WHITESPACE extends Token

    91 case object T_COMMENT extends Token

    92 case class T_IDENT(s: String) extends Token

    93 case class T_OP(s: String) extends Token

    94 case class T_NUM(n: Int) extends Token

    95 case class T_KEYWORD(s: String) extends Token

    96 

    97 

    98 // an example list of syntactic rules

    99 type Rule = (Rexp, List[Char] => Token)

   100 

   101 val rules: List[Rule]= 

   102   List(("if", (s) => T_KEYWORD(s.mkString)),

   103        ("then", (s) => T_KEYWORD(s.mkString)),

   104        ("else", (s) => T_KEYWORD(s.mkString)),

   105        ("+", (s) => T_OP(s.mkString)),

   106        (IDENT, (s) => T_IDENT(s.mkString)),

   107        (NUMBER, (s) => T_NUM(s.mkString.toInt)),

   108        (WHITESPACES, (s) => T_WHITESPACE),

   109        (COMMENT, (s) => T_COMMENT))

   110 

   111 

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

   113 

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

   115   s match {

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

   117     case Nil => None

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

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

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

   121   }

   122 

   123 def one_token (rs: List[Rule], s: List[Char]) : (List[Char], Token) = {

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

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

   126 }

   127 

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

   129   case Nil => Nil

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

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

   132   }

   133 }

   134 

   135 //examples

   136 println(tokenize(rules, "if true then then 42 else +".toList))

   137 println(tokenize(rules, "if+true+then+then+42+else +".toList))

   138 println(tokenize(rules, "ifff if     34 34".toList))

   139 println(tokenize(rules, "/*ifff if */ hhjj /*34 */".toList))

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

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