1 // A Simple Tokenizer according to Sulzmann & Lu

     2 

     3 import scala.language.implicitConversions    

     4 import scala.language.reflectiveCalls

     5 

     6 abstract class Rexp 

     7 case object ZERO extends Rexp

     8 case object ONE extends Rexp

     9 case class CHAR(c: Char) extends Rexp

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

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

    12 case class STAR(r: Rexp) extends Rexp 

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

    14    

    15 abstract class Val

    16 case object Empty extends Val

    17 case class Chr(c: Char) extends Val

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

    19 case class Left(v: Val) extends Val

    20 case class Right(v: Val) extends Val

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

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

    23    

    24 // some convenience for typing in regular expressions

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

    26   case Nil => ONE

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

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

    29 }

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

    31   charlist2rexp(s.toList)

    32 

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

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

    35   def % = STAR(r)

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

    37 }

    38 

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

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

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

    42   def % = STAR(s)

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

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

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

    46 }

    47 

    48 // A test for more conveninet syntax

    49 val re : Rexp = ("ab" | "a") ~ ("b" | ONE)

    50 

    51 // the nullable function: tests whether the regular 

    52 // expression can recognise the empty string

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

    54   case ZERO => false

    55   case ONE => true

    56   case CHAR(_) => false

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

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

    59   case STAR(_) => true

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

    61 }

    62 

    63 // the derivative of a regular expression w.r.t. a character

    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 // the derivative w.r.t. a string (iterates der)

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

    78   case Nil => r

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

    80 }

    81 

    82 // extracts a string from value

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

    84   case Empty => ""

    85   case Chr(c) => c.toString

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

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

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

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

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

    91 }

    92 

    93 // extracts an environment from a value;

    94 // used for tokenise a string

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

    96   case Empty => Nil

    97   case Chr(c) => Nil

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

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

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

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

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

   103 }

   104 

   105 // The Injection Part of the Tokeniser

   106 

   107 // calculates a value for how a nullable regex 

   108 // matches the empty string 

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

   110   case ONE => Empty

   111   case ALT(r1, r2) => 

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

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

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

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

   116 }

   117 

   118 // injects back a character into a value

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

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

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

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

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

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

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

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

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

   128 }

   129 

   130 // the main lexing function (produces a value)

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

   132   case Nil => if (nullable(r)) mkeps(r) 

   133               else throw new Exception("Not matched")

   134   case c::cs => inj(r, c, lex(der(c, r), cs))

   135 }

   136 

   137 def lexing(r: Rexp, s: String) : Val = lex(r, s.toList)

   138 

   139 // a simple test for extracting an environment

   140 val re1 : Rexp = ("first" $ ("a" | "ab")) ~ ("second" $ ("b" | ONE))

   141 env(lexing(re1, "ab"))

   142 

   143 // some "rectification" functions for simplification

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

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

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

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

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

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

   150 }

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

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

   153 }

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

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

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

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

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

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

   160 }

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

   162 

   163 // simplification of regular expressions returns now also 

   164 // an rectification function; no simplification under STAR 

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

   166   case ALT(r1, r2) => {

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

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

   169     (r1s, r2s) match {

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

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

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

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

   174     }

   175   }

   176   case SEQ(r1, r2) => {

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

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

   179     (r1s, r2s) match {

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

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

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

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

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

   185     }

   186   }

   187   case RECD(x, r1) => {

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

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

   190   }

   191   case r => (r, F_ID)

   192 }

   193 

   194 // lexing functions including simplification

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

   196   case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")

   197   case c::cs => {

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

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

   200   }

   201 }

   202 

   203 def lexing_simp(r: Rexp, s: String) : Val = lex_simp(r, s.toList)

   204 

   205 lexing_simp(("a" | "ab") ~ ("b" | ""), "ab")

   206 

   207 // The Lexing Rules for a Small While Language

   208 

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

   210 

   211 val SYM = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z"

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

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

   214 val NUM = PLUS(DIGIT)

   215 val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"

   216 val SEMI: Rexp = ";"

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

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

   219 val RPAREN: Rexp = ")"

   220 val LPAREN: Rexp = "("

   221 val BEGIN: Rexp = "{"

   222 val END: Rexp = "}"

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

   224 

   225 

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

   227                   ("i" $ ID) | 

   228                   ("o" $ OP) | 

   229                   ("n" $ NUM) | 

   230                   ("s" $ SEMI) | 

   231                   ("str" $ STRING) |

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

   233                   ("b" $ (BEGIN | END)) | 

   234                   ("w" $ WHITESPACE)).%

   235 

   236 //   Testing

   237 //============

   238 

   239 def time[T](code: => T) = {

   240   val start = System.nanoTime()

   241   val result = code

   242   val end = System.nanoTime()

   243   println((end - start)/1.0e9)

   244   result

   245 }

   246 

   247 val r1 = ("a" | "ab") ~ ("bcd" | "c")

   248 println(lexing(r1, "abcd"))

   249 

   250 val r2 = ("" | "a") ~ ("ab" | "b")

   251 println(lexing(r2, "ab"))

   252 

   253 

   254 // Two Simple While Tests

   255 //========================

   256 println("prog0 test")

   257 

   258 val prog0 = """read if"""

   259 println(env(lexing_simp(WHILE_REGS, prog0)))

   260 

   261 println("prog1 test")

   262 

   263 val prog1 = """read  n; write (n)"""

   264 println(env(lexing_simp(WHILE_REGS, prog1)))

   265 

   266 

   267 // Bigger Test

   268 //=============

   269 

   270 val prog2 = """

   271 write "fib";

   272 read n;

   273 minus1 := 0;

   274 minus2 := 1;

   275 while n > 0 do {

   276   temp := minus2;

   277   minus2 := minus1 + minus2;

   278   minus1 := temp;

   279   n := n - 1

   280 };

   281 write "result";

   282 write minus2

   283 """

   284 

   285 println("Tokens")

   286 println(env(lexing_simp(WHILE_REGS, prog2)))

   287 println(env(lexing_simp(WHILE_REGS, prog2)).filterNot{_._1 == "w"}.mkString("\n"))

   288 

   289 // some more timing tests with

   290 // i copies of the program

   291 

   292 for (i <- 0 to 20 by 10) {

   293   print(i.toString + ":  ")

   294   time(lexing_simp(WHILE_REGS, prog2 * i))

   295 }

   296 

   297 

   298 val fib = """

   299 write "Fib";

   300 read n;

   301 minus1 := 0;

   302 minus2 := 1;

   303 while n > 0 do {

   304 temp := minus2;

   305 minus2 := minus1 + minus2;

   306 minus1 := temp;

   307 n := n - 1

   308 };

   309 write "Result";

   310 write minus2

   311 """

   312 

   313 println(env(lexing_simp(WHILE_REGS, prog2)).filterNot{_._1 == "w"})