1 import scala.language.implicitConversions    

     2 import scala.language.reflectiveCalls

     3 

     4 // Rexp

     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 case class RANGE(s: Set[Char]) extends Rexp

    15 case class PLUS(r: Rexp) extends Rexp

    16 case class OPTIONAL(r: Rexp) extends Rexp

    17 case class NTIMES(r: Rexp, n: Int) extends Rexp 

    18 

    19 // Values

    20 abstract class Val

    21 case object Empty extends Val

    22 case class Chr(c: Char) extends Val

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

    24 case class Left(v: Val) extends Val

    25 case class Right(v: Val) extends Val

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

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

    28 

    29 

    30 // Convenience typing

    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 

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

    38   charlist2rexp(s.toList)

    39 

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

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

    42   def % = STAR(r)

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

    44 }

    45 

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

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

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

    49   def % = STAR(s)

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

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

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

    53 }

    54 

    55 // nullable

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

    57   case ZERO => false

    58   case ONE => true

    59   case CHAR(_) => false

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

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

    62   case STAR(_) => true

    63 

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

    65   case RANGE(_) => false

    66   case PLUS(r1) => nullable(r1)

    67   case OPTIONAL(_) => true

    68   case NTIMES(r1, i) => if (i == 0) true else nullable(r1)

    69 }

    70 

    71 // der

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

    73   case ZERO => ZERO

    74   case ONE => ZERO

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

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

    77   case SEQ(r1, r2) => 

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

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

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

    81 

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

    83   case RANGE(s) => if (s.contains(c)) ONE else ZERO 

    84   case PLUS(r1) => SEQ(der(c, r1), STAR(r1))

    85   case OPTIONAL(r1) => ALT(der(c, r1), ZERO)

    86   case NTIMES(r, i) => 

    87     if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))

    88 }

    89 

    90 // Flatten

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

    92   case Empty => ""

    93   case Chr(c) => c.toString

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

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

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

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

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

    99 }

   100 

   101 // Env

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

   103   case Empty => Nil

   104   case Chr(c) => Nil

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

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

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

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

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

   110 }

   111 

   112 // Mkeps

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

   114   case ONE => Empty

   115   case ALT(r1, r2) => 

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

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

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

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

   120 

   121   case PLUS(r) => Stars(List(mkeps(r)))   // the first copy must match the empty string

   122   case OPTIONAL(r) => Right(Empty)

   123   case NTIMES(r, i) => Stars(List.fill(i)(mkeps(r)))

   124 }

   125 

   126 // Inj

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

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

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

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

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

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

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

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

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

   136 

   137   case (RANGE(_), Empty) => Chr(c)

   138   case (PLUS(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)

   139   case (OPTIONAL(r), Left(v1)) => Left(inj(r, c, v1))

   140   case (NTIMES(r, n), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)

   141 }

   142 

   143 // Rectification functions

   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 // Simp

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

   165   case ALT(r1, r2) => {

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

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

   168     (r1s, r2s) match {

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

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

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

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

   173     }

   174   }

   175   case SEQ(r1, r2) => {

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

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

   178     (r1s, r2s) match {

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

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

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

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

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

   184     }

   185   }

   186   case r => (r, F_ID)

   187 }

   188 

   189 // Lex

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

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

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

   193   case c::cs => {

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

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

   196   }

   197 }

   198 

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

   200 

   201 // Language specific code

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

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

   204 val LET: Rexp = RANGE(('A' to 'Z').toSet ++ ('a' to 'z'))

   205 val SYM : Rexp = LET | RANGE(Set('.', '_', '>', '<', '=', ';', ',', ':'))

   206 val PARENS : Rexp = "(" | "{" | ")" | "}"

   207 val SEMI : Rexp = ";"

   208 val WHITESPACE : Rexp = PLUS(" ") | "\n" | "\t"

   209 val DIGIT : Rexp = RANGE(('0' to '9').toSet)

   210 val DIGIT1 : Rexp = RANGE(('1' to '9').toSet)

   211 val STRING : Rexp = "\"" ~ (SYM | " " | "\\n" | DIGIT).% ~ "\""

   212 val ID : Rexp = LET ~ (LET | "_" | DIGIT).%

   213 val NUM : Rexp = "0" | (DIGIT1 ~ DIGIT.%)

   214 val COMMENT : Rexp = "//" ~ (SYM | " " | DIGIT).% ~ "\n" 

   215 

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

   217                   ("o" $ OP) | 

   218                   ("str" $ STRING) |

   219                   ("p" $ PARENS) |

   220                   ("s" $ SEMI) | 

   221                   ("w" $ WHITESPACE) | 

   222                   ("i" $ ID) | 

   223                   ("n" $ NUM) |

   224 		  ("c" $ COMMENT)).%

   225 

   226 // Token

   227 abstract class Token extends Serializable 

   228 case class T_KEYWORD(s: String) extends Token

   229 case class T_OP(s: String) extends Token

   230 case class T_STRING(s: String) extends Token

   231 case class T_PAREN(s: String) extends Token

   232 case object T_SEMI extends Token

   233 case class T_ID(s: String) extends Token

   234 case class T_NUM(n: Int) extends Token

   235 

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

   237   case ("k", s) => T_KEYWORD(s)

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

   239   case ("str", s) => T_STRING(s)

   240   case ("p", s) => T_PAREN(s)

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

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

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

   244 }

   245 

   246 // Tokenise

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

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

   249 

   250