1 // A simple lexer inspired by work of Sulzmann & Lu

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

     3 

     4 

     5 import scala.language.implicitConversions    

     6 import scala.language.reflectiveCalls

     7 

     8 // regular expressions including records

     9 abstract class Rexp 

    10 case object ZERO extends Rexp

    11 case object ONE extends Rexp

    12 case class CHAR(c: Char) extends Rexp

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

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

    15 case class STAR(r: Rexp) extends Rexp 

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

    17   

    18 // values  

    19 abstract class Val

    20 case object Empty extends Val

    21 case class Chr(c: Char) extends Val

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

    23 case class Left(v: Val) extends Val

    24 case class Right(v: Val) extends Val

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

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

    27    

    28 // some convenience for typing in regular expressions

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

    30   case Nil => ONE

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

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

    33 }

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

    35   charlist2rexp(s.toList)

    36 

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

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

    39   def % = STAR(r)

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

    41 }

    42 

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

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

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

    46   def % = STAR(s)

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

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

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

    50 }

    51 

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

    53   case ZERO => false

    54   case ONE => true

    55   case CHAR(_) => false

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

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

    58   case STAR(_) => true

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

    60 }

    61 

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

    63   case ZERO => ZERO

    64   case ONE => ZERO

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

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

    67   case SEQ(r1, r2) => 

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

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

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

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

    72 }

    73 

    74 

    75 // extracts a string from value

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

    77   case Empty => ""

    78   case Chr(c) => c.toString

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

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

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

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

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

    84 }

    85 

    86 

    87 // extracts an environment from a value;

    88 // used for tokenise a string

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

    90   case Empty => Nil

    91   case Chr(c) => Nil

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

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

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

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

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

    97 }

    98 

    99 // The Injection Part of the lexer

   100 

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

   102   case ONE => Empty

   103   case ALT(r1, r2) => 

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

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

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

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

   108 }

   109 

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

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

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

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

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

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

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

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

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

   119 }

   120 

   121 // some "rectification" functions for simplification

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

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

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

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

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

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

   128 }

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

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

   131 }

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

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

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

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

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

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

   138 }

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

   140 

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

   142   case ALT(r1, r2) => {

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

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

   145     (r1s, r2s) match {

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

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

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

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

   150     }

   151   }

   152   case SEQ(r1, r2) => {

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

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

   155     (r1s, r2s) match {

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

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

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

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

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

   161     }

   162   }

   163   case r => (r, F_ID)

   164 }

   165 

   166 // lexing functions including simplification

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

   168   case Nil => if (nullable(r)) mkeps(r) else 

   169     { throw new Exception("lexing error") } 

   170   case c::cs => {

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

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

   173   }

   174 }

   175 

   176 def lexing_simp(r: Rexp, s: String) = 

   177   env(lex_simp(r, s.toList))

   178 

   179 

   180 // The Lexing Rules for the Fun Language

   181 

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

   183 

   184 def Range(s : List[Char]) : Rexp = s match {

   185   case Nil => ZERO

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

   187   case c::s => ALT(CHAR(c), Range(s))

   188 }

   189 def RANGE(s: String) = Range(s.toList)

   190 

   191 val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_")

   192 val DIGIT = RANGE("0123456789")

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

   194 val NUM = PLUS(DIGIT)

   195 val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" 

   196 val SEMI: Rexp = ";"

   197 val OP: Rexp = ":=" | "=" | "-" | "+" | "*" | "!=" | "<" | ">"

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

   199 val RPAREN: Rexp = "{"

   200 val LPAREN: Rexp = "}"

   201 val STRING: Rexp = "\"" ~ SYM.% ~ "\""

   202 

   203 

   204 val WHILE_REGS = (("k" $ KEYWORD) | 

   205                   ("i" $ ID) | 

   206                   ("o" $ OP) | 

   207                   ("n" $ NUM) | 

   208                   ("s" $ SEMI) | 

   209                   ("str" $ STRING) |

   210                   ("p" $ (LPAREN | RPAREN)) | 

   211                   ("w" $ WHITESPACE)).%

   212 

   213 

   214 // Two Simple While Tests

   215 //========================

   216 

   217 println("test: read n")

   218 

   219 val prog0 = """read n"""

   220 println(lexing_simp(WHILE_REGS, prog0))

   221 

   222 println("test: read  n; write n ")

   223 

   224 val prog1 = """read  n; write n"""

   225 println(lexing_simp(WHILE_REGS, prog1))

   226 

   227 

   228 // Bigger Tests

   229 //==============

   230 

   231 // escapes strings and prints them out as "", "\n" and so on

   232 def esc(raw: String): String = {

   233   import scala.reflect.runtime.universe._

   234   Literal(Constant(raw)).toString

   235 }

   236 

   237 def escape(tks: List[(String, String)]) =

   238   tks.map{ case (s1, s2) => (s1, esc(s2))}

   239 

   240 val prog2 = """

   241 write "Fib";

   242 read n;

   243 minus1 := 0;

   244 minus2 := 1;

   245 while n > 0 do {

   246   temp := minus2;

   247   minus2 := minus1 + minus2;

   248   minus1 := temp;

   249   n := n - 1

   250 };

   251 write "Result";

   252 write minus2

   253 """

   254 

   255 println("lexing Fib")

   256 println(escape(lexing_simp(WHILE_REGS, prog2)).mkString("\n"))

   257 

   258 

   259 

   260 val prog3 = """

   261 start := 1000;

   262 x := start;

   263 y := start;

   264 z := start;

   265 while 0 < x do {

   266  while 0 < y do {

   267   while 0 < z do {

   268     z := z - 1

   269   };

   270   z := start;

   271   y := y - 1

   272  };     

   273  y := start;

   274  x := x - 1

   275 }

   276 """

   277 

   278 println("lexing Loops")

   279 println(escape(lexing_simp(WHILE_REGS, prog3)).mkString("\n"))

   280