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

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

     3 

     4 

     5 object Lexer {

     6 

     7 import scala.language.implicitConversions    

     8 import scala.language.reflectiveCalls

     9 

    10 // regular expressions including records

    11 abstract class Rexp 

    12 case object ZERO extends Rexp

    13 case object ONE extends Rexp

    14 case class CHAR(c: Char) extends Rexp

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

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

    17 case class STAR(r: Rexp) extends Rexp 

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

    19   

    20 // values  

    21 abstract class Val

    22 case object Empty extends Val

    23 case class Chr(c: Char) extends Val

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

    25 case class Left(v: Val) extends Val

    26 case class Right(v: Val) extends Val

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

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

    29    

    30 // some convenience for typing in regular expressions

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

    32   case Nil => ONE

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

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

    35 }

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

    37   charlist2rexp(s.toList)

    38 

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

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

    41   def % = STAR(r)

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

    43 }

    44 

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

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

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

    48   def % = STAR(s)

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

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

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

    52 }

    53 

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

    55   case ZERO => false

    56   case ONE => true

    57   case CHAR(_) => false

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

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

    60   case STAR(_) => true

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

    62 }

    63 

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

    65   case ZERO => ZERO

    66   case ONE => ZERO

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

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

    69   case SEQ(r1, r2) => 

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

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

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

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

    74 }

    75 

    76 

    77 // extracts a string from value

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

    79   case Empty => ""

    80   case Chr(c) => c.toString

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

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

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

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

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

    86 }

    87 

    88 

    89 // extracts an environment from a value;

    90 // used for tokenise a string

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

    92   case Empty => Nil

    93   case Chr(c) => Nil

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

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

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

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

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

    99 }

   100 

   101 // The Injection Part of the lexer

   102 

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

   104   case ONE => Empty

   105   case ALT(r1, r2) => 

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

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

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

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

   110 }

   111 

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

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

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

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

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

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

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

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

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

   121 }

   122 

   123 // some "rectification" functions for simplification

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

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

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

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

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

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

   130 }

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

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

   133 }

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

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

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

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

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

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

   140 }

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

   142 

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

   144   case ALT(r1, r2) => {

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

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

   147     (r1s, r2s) match {

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

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

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

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

   152     }

   153   }

   154   case SEQ(r1, r2) => {

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

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

   157     (r1s, r2s) match {

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

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

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

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

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

   163     }

   164   }

   165   case RECD(x, r1) => {

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

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

   168   }

   169   case r => (r, F_ID)

   170 }

   171 

   172 // lexing functions including simplification

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

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

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

   176   case c::cs => {

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

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

   179   }

   180 }

   181 

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

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

   184 

   185 

   186 // The Lexing Rules for the Fun Language

   187 

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

   189 

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

   191   case Nil => ZERO

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

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

   194 }

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

   196 

   197 val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_")

   198 val DIGIT = RANGE("0123456789")

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

   200 val NUM = PLUS(DIGIT)

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

   202 val SEMI: Rexp = ";"

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

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

   205 val RPAREN: Rexp = "{"

   206 val LPAREN: Rexp = "}"

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

   208 

   209 

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

   211                   ("i" $ ID) | 

   212                   ("o" $ OP) | 

   213                   ("n" $ NUM) | 

   214                   ("s" $ SEMI) | 

   215                   ("str" $ STRING) |

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

   217                   ("w" $ WHITESPACE)).%

   218 

   219 

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

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

   222   import scala.reflect.runtime.universe._

   223   Literal(Constant(raw)).toString

   224 }

   225 

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

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

   228 

   229 val prog2 = """

   230 write "Fib";

   231 read n;

   232 minus1 := 0;

   233 minus2 := 1;

   234 while n > 0 do {

   235   temp := minus2;

   236   minus2 := minus1 + minus2;

   237   minus1 := temp;

   238   n := n - 1

   239 };

   240 write "Result";

   241 write minus2

   242 """

   243 

   244 val prog3 = """

   245 start := 1000;

   246 x := start;

   247 y := start;

   248 z := start;

   249 while 0 < x do {

   250  while 0 < y do {

   251   while 0 < z do {

   252     z := z - 1

   253   };

   254   z := start;

   255   y := y - 1

   256  };     

   257  y := start;

   258  x := x - 1

   259 }

   260 """

   261 

   262 // Generating tokens for the WHILE language

   263 

   264 import java.io._

   265 

   266 abstract class Token extends Serializable 

   267 case object T_SEMI extends Token

   268 case object T_LPAREN extends Token

   269 case object T_RPAREN extends Token

   270 case class T_ID(s: String) extends Token

   271 case class T_OP(s: String) extends Token

   272 case class T_NUM(n: Int) extends Token

   273 case class T_KWD(s: String) extends Token

   274 case class T_STR(s: String) extends Token

   275 

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

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

   278   case ("p", "{") => T_LPAREN

   279   case ("p", "}") => T_RPAREN

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

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

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

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

   284   case ("str", s) => T_STR(s)

   285 }

   286 

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

   288   lexing_simp(WHILE_REGS, s).collect(token)

   289 

   290 

   291 def serialise[T](fname: String, data: T) = {

   292   val out = new ObjectOutputStream(new FileOutputStream(fname))

   293   out.writeObject(data)

   294   out.close

   295 }

   296 

   297 def main(args: Array[String]) = {

   298   serialise("/tmp/nflx", tokenise(prog3))

   299 }

   300 

   301 

   302 }