1 // A tokeniser for the Fun language

     2 //==================================

     3 //

     4 // call with 

     5 //

     6 //     amm fun_tokens.sc fact.fun

     7 //

     8 //     amm fun_tokens.sc defs.fun

     9 //

    10 

    11 

    12 

    13 import scala.language.implicitConversions    

    14 import scala.language.reflectiveCalls 

    15 

    16 abstract class Rexp 

    17 case object ZERO extends Rexp

    18 case object ONE extends Rexp

    19 case class CHAR(c: Char) extends Rexp

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

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

    22 case class STAR(r: Rexp) extends Rexp 

    23 case class RECD(x: String, r: Rexp) extends Rexp

    24   

    25 abstract class Val

    26 case object Empty extends Val

    27 case class Chr(c: Char) extends Val

    28 case class Sequ(v1: Val, v2: Val) extends Val

    29 case class Left(v: Val) extends Val

    30 case class Right(v: Val) extends Val

    31 case class Stars(vs: List[Val]) extends Val

    32 case class Rec(x: String, v: Val) extends Val

    33    

    34 // some convenience for typing in regular expressions

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

    36   case Nil => ONE

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

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

    39 }

    40 implicit def string2rexp(s : String) : Rexp = 

    41   charlist2rexp(s.toList)

    42 

    43 implicit def RexpOps(r: Rexp) = new {

    44   def | (s: Rexp) = ALT(r, s)

    45   def % = STAR(r)

    46   def ~ (s: Rexp) = SEQ(r, s)

    47 }

    48 

    49 implicit def stringOps(s: String) = new {

    50   def | (r: Rexp) = ALT(s, r)

    51   def | (r: String) = ALT(s, r)

    52   def % = STAR(s)

    53   def ~ (r: Rexp) = SEQ(s, r)

    54   def ~ (r: String) = SEQ(s, r)

    55   def $ (r: Rexp) = RECD(s, r)

    56 }

    57 

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

    59   case ZERO => false

    60   case ONE => true

    61   case CHAR(_) => false

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

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

    64   case STAR(_) => true

    65   case RECD(_, r1) => nullable(r1)

    66 }

    67 

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

    69   case ZERO => ZERO

    70   case ONE => ZERO

    71   case CHAR(d) => if (c == d) ONE else ZERO

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

    73   case SEQ(r1, r2) => 

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

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

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

    77   case RECD(_, r1) => der(c, r1)

    78 }

    79 

    80 

    81 // extracts a string from value

    82 def flatten(v: Val) : String = v match {

    83   case Empty => ""

    84   case Chr(c) => c.toString

    85   case Left(v) => flatten(v)

    86   case Right(v) => flatten(v)

    87   case Sequ(v1, v2) => flatten(v1) + flatten(v2)

    88   case Stars(vs) => vs.map(flatten).mkString

    89   case Rec(_, v) => flatten(v)

    90 }

    91 

    92 // extracts an environment from a value;

    93 // used for tokenise a string

    94 def env(v: Val) : List[(String, String)] = v match {

    95   case Empty => Nil

    96   case Chr(c) => Nil

    97   case Left(v) => env(v)

    98   case Right(v) => env(v)

    99   case Sequ(v1, v2) => env(v1) ::: env(v2)

   100   case Stars(vs) => vs.flatMap(env)

   101   case Rec(x, v) => (x, flatten(v))::env(v)

   102 }

   103 

   104 // The Injection Part of the lexer

   105 

   106 def mkeps(r: Rexp) : Val = r match {

   107   case ONE => Empty

   108   case ALT(r1, r2) => 

   109     if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))

   110   case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))

   111   case STAR(r) => Stars(Nil)

   112   case RECD(x, r) => Rec(x, mkeps(r))

   113 }

   114 

   115 def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {

   116   case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)

   117   case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)

   118   case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)

   119   case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))

   120   case (ALT(r1, r2), Left(v1)) => Left(inj(r1, c, v1))

   121   case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))

   122   case (CHAR(d), Empty) => Chr(c) 

   123   case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))

   124   case _ => { println ("Injection error") ; sys.exit(-1) } 

   125 }

   126 

   127 // some "rectification" functions for simplification

   128 def F_ID(v: Val): Val = v

   129 def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v))

   130 def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v))

   131 def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {

   132   case Right(v) => Right(f2(v))

   133   case Left(v) => Left(f1(v))

   134 }

   135 def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {

   136   case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))

   137 }

   138 def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 

   139   (v:Val) => Sequ(f1(Empty), f2(v))

   140 def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 

   141   (v:Val) => Sequ(f1(v), f2(Empty))

   142 def F_RECD(f: Val => Val) = (v:Val) => v match {

   143   case Rec(x, v) => Rec(x, f(v))

   144 }

   145 def F_ERROR(v: Val): Val = throw new Exception("error")

   146 

   147 def simp(r: Rexp): (Rexp, Val => Val) = r match {

   148   case ALT(r1, r2) => {

   149     val (r1s, f1s) = simp(r1)

   150     val (r2s, f2s) = simp(r2)

   151     (r1s, r2s) match {

   152       case (ZERO, _) => (r2s, F_RIGHT(f2s))

   153       case (_, ZERO) => (r1s, F_LEFT(f1s))

   154       case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))

   155                 else (ALT (r1s, r2s), F_ALT(f1s, f2s)) 

   156     }

   157   }

   158   case SEQ(r1, r2) => {

   159     val (r1s, f1s) = simp(r1)

   160     val (r2s, f2s) = simp(r2)

   161     (r1s, r2s) match {

   162       case (ZERO, _) => (ZERO, F_ERROR)

   163       case (_, ZERO) => (ZERO, F_ERROR)

   164       case (ONE, _) => (r2s, F_SEQ_Empty1(f1s, f2s))

   165       case (_, ONE) => (r1s, F_SEQ_Empty2(f1s, f2s))

   166       case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))

   167     }

   168   }

   169   case RECD(x, r1) => {

   170     val (r1s, f1s) = simp(r1)

   171     (RECD(x, r1s), F_RECD(f1s))

   172   }

   173   case r => (r, F_ID)

   174 }

   175 

   176 // lexing functions including simplification

   177 def lex_simp(r: Rexp, s: List[Char]) : Val = s match {

   178   case Nil => if (nullable(r)) mkeps(r) else { println ("Lexing Error") ; sys.exit(-1) } 

   179   case c::cs => {

   180     val (r_simp, f_simp) = simp(der(c, r))

   181     inj(r, c, f_simp(lex_simp(r_simp, cs)))

   182   }

   183 }

   184 

   185 def lexing_simp(r: Rexp, s: String) = env(lex_simp(r, s.toList))

   186 

   187 

   188 // The Lexing Rules for the Fun Language

   189 

   190 def PLUS(r: Rexp) = r ~ r.%

   191 

   192 val SYM = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | 

   193           "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | 

   194           "w" | "x" | "y" | "z" | "T" | "_"

   195 val DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

   196 val ID = SYM ~ (SYM | DIGIT).% 

   197 val NUM = PLUS(DIGIT)

   198 val KEYWORD : Rexp = "if" | "then" | "else" | "write" | "def"

   199 val SEMI: Rexp = ";"

   200 val OP: Rexp = "=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"

   201 val WHITESPACE = PLUS(" " | "\n" | "\t")

   202 val RPAREN: Rexp = ")"

   203 val LPAREN: Rexp = "("

   204 val COMMA: Rexp = ","

   205 val ALL = SYM | DIGIT | OP | " " | ":" | ";" | "\"" | "=" | "," | "(" | ")"

   206 val ALL2 = ALL | "\n"

   207 val COMMENT = ("/*" ~ ALL2.% ~ "*/") | ("//" ~ ALL.% ~ "\n")

   208 

   209 

   210 val FUN_REGS = (("k" $ KEYWORD) | 

   211                   ("i" $ ID) | 

   212                   ("o" $ OP) | 

   213                   ("n" $ NUM) | 

   214                   ("s" $ SEMI) | 

   215                   ("c" $ COMMA) |

   216                   ("pl" $ LPAREN) |

   217                   ("pr" $ RPAREN) |

   218                   ("w" $ (WHITESPACE | COMMENT))).%

   219 

   220 

   221 

   222 // The tokens for the Fun language

   223 

   224 abstract class Token extends Serializable 

   225 case object T_SEMI extends Token

   226 case object T_COMMA extends Token

   227 case object T_LPAREN extends Token

   228 case object T_RPAREN extends Token

   229 case class T_ID(s: String) extends Token

   230 case class T_OP(s: String) extends Token

   231 case class T_NUM(n: Int) extends Token

   232 case class T_KWD(s: String) extends Token

   233 

   234 val token : PartialFunction[(String, String), Token] = {

   235   case ("k", s) => T_KWD(s)

   236   case ("i", s) => T_ID(s)

   237   case ("o", s) => T_OP(s)

   238   case ("n", s) => T_NUM(s.toInt)

   239   case ("s", _) => T_SEMI

   240   case ("c", _) => T_COMMA

   241   case ("pl", _) => T_LPAREN

   242   case ("pr", _) => T_RPAREN

   243 }

   244 

   245 

   246 def tokenise(s: String) : List[Token] = {

   247   val tks = lexing_simp(FUN_REGS, s).collect(token)

   248   if (tks.length != 0) tks

   249   else { println (s"Tokenise Error") ; sys.exit(-1) }     

   250 }

   251 

   252 import ammonite.ops._

   253 

   254 @doc("Tokenising a file.")

   255 @main

   256 def main(fname: String) = {

   257   println(tokenise(os.read(os.pwd / fname)))

   258 }