1 // regular expressions

     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 case class NOT(r: Rexp) extends Rexp

    11 

    12 

    13 // some convenience for typing in regular expressions

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

    15   case Nil => EMPTY

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

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

    18 }

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

    20 

    21 

    22 // nullable function: tests whether the regular 

    23 // expression can recognise the empty string

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

    25   case NULL => false

    26   case EMPTY => true

    27   case CHAR(_) => false

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

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

    30   case STAR(_) => true

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

    32 }

    33 

    34 // tests whether a regular expression 

    35 // recognises nothing

    36 def zeroable (r: Rexp) : Boolean = r match {

    37   case NULL => true

    38   case EMPTY => false

    39   case CHAR(_) => false

    40   case ALT(r1, r2) => zeroable(r1) && zeroable(r2)

    41   case SEQ(r1, r2) => if (nullable(r1)) (zeroable(r1) && zeroable(r2)) else zeroable(r1)

    42       //zeroable(r1) || zeroable(r2)

    43   case STAR(_) => false

    44   case NOT(r) => !(zeroable(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 // derivative w.r.t. a string (iterates der)

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

    63   case Nil => r

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

    65 }

    66 

    67 // main matcher function

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

    69 

    70 

    71 // regular expression for specifying 

    72 // ranges of characters

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

    74   case Nil => NULL

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

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

    77 }

    78 

    79 //one or more

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

    81 

    82 

    83 //some regular expressions

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

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

    86 val LETTER = ALT(LOWERCASE, UPPERCASE)

    87 val DIGITS = RANGE("0123456789".toList)

    88 val NONZERODIGITS = RANGE("123456789".toList)

    89 

    90 val IDENT = SEQ(LETTER, STAR(ALT(LETTER,DIGITS)))

    91 val NUMBER = ALT(SEQ(NONZERODIGITS, STAR(DIGITS)), "0")

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

    93 

    94 val ALL = ALT(ALT(LETTER, DIGITS), WHITESPACE)

    95 

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

    97 

    98 abstract class Token

    99 

   100 case object T_WHITESPACE extends Token

   101 case class T_IDENT(s: String) extends Token

   102 case class T_OP(s: String) extends Token

   103 case class T_NUM(n: Int) extends Token

   104 case class T_KEYWORD(s: String) extends Token

   105 

   106 

   107 // an example list of rules

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

   109 

   110 val rules: List[Rule]= 

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

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

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

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

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

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

   117        (WHITESPACE, (s) => T_WHITESPACE))

   118 

   119 

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

   121 

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

   123   s match {

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

   125     case Nil => None

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

   127     case c::s if (zeroable(der (c, r))) => None

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

   129   }

   130 

   131 def lex_one (rs: List[Rule], s: List[Char]) : (List[Char], Token) = {

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

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

   134 }

   135 

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

   137   case Nil => Nil

   138   case _ => lex_one(rs, s) match {

   139     case (rest, t) => t :: lex_all(rs, rest) 

   140   }

   141 }

   142 

   143 

   144 

   145 println(lex_all(rules, "if true then 42 else +".toList))

   146 println(lex_all(rules, "ifff if     34 34".toList))

   147 println(lex_all(rules, "ifff $ if 34".toList))

   148 

   149