1 import scala.language.implicitConversions    

     2 import scala.language.reflectiveCalls

     3 import scala.annotation.tailrec   

     4 

     5 abstract class Rexp 

     6 case object ZERO extends Rexp

     7 case object ONE extends Rexp

     8 case class CHAR(c: Char) extends Rexp

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

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

    11 case class STAR(r: Rexp) extends Rexp 

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

    13 

    14 abstract class Val

    15 case object Empty extends Val

    16 case class Chr(c: Char) extends Val

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

    18 case class Left(v: Val) extends Val

    19 case class Right(v: Val) extends Val

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

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

    22    

    23 // some convenience for typing in regular expressions

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

    25   case Nil => ONE

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

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

    28 }

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

    30 

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

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

    33   def % = STAR(r)

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

    35 }

    36 

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

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

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

    40   def % = STAR(s)

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

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

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

    44 }

    45 

    46 // nullable function: tests whether the regular 

    47 // expression can recognise the empty string

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

    49   case ZERO => false

    50   case ONE => true

    51   case CHAR(_) => false

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

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

    54   case STAR(_) => true

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

    56 }

    57 

    58 // derivative of a regular expression w.r.t. a character

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

    60   case ZERO => ZERO

    61   case ONE => ZERO

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

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

    64   case SEQ(r1, r2) => 

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

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

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

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

    69 }

    70 

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

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

    73   case Nil => r

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

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

    91   case Empty => Nil

    92   case Chr(c) => Nil

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

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

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

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

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

    98 }

    99 

   100 // injection part

   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 

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

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

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

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

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

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

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

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

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

   120 }

   121 

   122 // main unsimplified lexing function (produces a value)

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

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

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

   126 }

   127 

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

   129 

   130 

   131 // some "rectification" functions for simplification

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

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

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

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

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

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

   138 }

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

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

   141 }

   142 def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = (v:Val) => Sequ(f1(Empty), f2(v))

   143 def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = (v:Val) => Sequ(f1(v), f2(Empty))

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

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

   146 }

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

   148 

   149 // simplification of regular expressions returning also an

   150 // rectification function; no simplification under STAR 

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

   152   case ALT(r1, r2) => {

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

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

   155     (r1s, r2s) match {

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

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

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

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

   160     }

   161   }

   162   case SEQ(r1, r2) => {

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

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

   165     (r1s, r2s) match {

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

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

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

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

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

   171     }

   172   }

   173   case RECD(x, r1) => {

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

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

   176   }

   177   case r => (r, F_ID)

   178 }

   179 

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

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

   182   case c::cs => {

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

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

   185   }

   186 }

   187 

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

   189 

   190 

   191 // Some Tests

   192 //============

   193 

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

   195   val start = System.nanoTime()

   196   val result = code

   197   val end = System.nanoTime()

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

   199   result

   200 }

   201 

   202 val r0 = ("a" | "ab") ~ ("b" | "")

   203 println(lexing(r0, "ab"))

   204 println(lexing_simp(r0, "ab"))

   205 

   206 val r1 = ("a" | "ab") ~ ("bcd" | "cd")

   207 println(lexing_simp(r1, "abcd"))

   208 

   209 println(lexing_simp((("" | "a") ~ ("ab" | "b")), "ab"))

   210 println(lexing_simp((("" | "a") ~ ("b" | "ab")), "ab"))

   211 println(lexing_simp((("" | "a") ~ ("c" | "ab")), "ab"))

   212 

   213 

   214 

   215 // Two Simple Tests for the While Language

   216 //========================================

   217 

   218 // Lexing Rules 

   219 

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

   221 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"

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

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

   224 val NUM = PLUS(DIGIT)

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

   226 val SEMI: Rexp = ";"

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

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

   229 val RPAREN: Rexp = ")"

   230 val LPAREN: Rexp = "("

   231 val BEGIN: Rexp = "{"

   232 val END: Rexp = "}"

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

   234 

   235 

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

   237                   ("i" $ ID) | 

   238                   ("o" $ OP) | 

   239                   ("n" $ NUM) | 

   240                   ("s" $ SEMI) | 

   241                   ("str" $ STRING) |

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

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

   244                   ("w" $ WHITESPACE)).%

   245 

   246 /*

   247 val WHILE_REGS = (KEYWORD | 

   248                   ID | 

   249                   OP | 

   250                   NUM | 

   251                   SEMI | 

   252                   LPAREN | RPAREN | 

   253                   BEGIN | END | 

   254                   WHITESPACE).%

   255 */

   256 

   257 

   258 println("prog0 test")

   259 

   260 val prog0 = """read n"""

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

   262 

   263 println("prog1 test")

   264 

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

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

   267 

   268 

   269 // Big Test

   270 //==========

   271 val prog2 = """

   272 i := 2;

   273 max := 100;

   274 while i < max do {

   275   isprime := 1;

   276   j := 2;

   277   while (j * j) <= i + 1  do {

   278     if i % j == 0 then isprime := 0  else skip;

   279     j := j + 1

   280   };

   281   if isprime == 1 then write i else skip;

   282   i := i + 1

   283 }"""

   284 

   285 println("prog2 test - tokens")

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

   287 

   288 

   289 val prog3 = """

   290 write "fib";

   291 read n;

   292 minus1 := 0;

   293 minus2 := 1;

   294 while n > 0 do {

   295   temp := minus2;

   296   minus2 := minus1 + minus2;

   297   minus1 := temp;

   298   n := n - 1

   299 };

   300 write "result";

   301 write minus2

   302 """

   303 

   304 println("prog3 test - tokens")

   305 println(env(lexing_simp(WHILE_REGS, prog3)))

   306 

   307 /*

   308 for (i <- 1 to 80) {

   309   print(i.toString + ":  ")

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

   311 }

   312 */

   313