thys2/blexer1.sc
changeset 403 6291181fad07
child 409 f71df68776bb
equal deleted inserted replaced
396:cc8e231529fb 403:6291181fad07
       
     1 // A simple lexer inspired by work of Sulzmann & Lu
       
     2 //==================================================
       
     3 //
       
     4 // Call the test cases with 
       
     5 //
       
     6 //   amm lexer.sc small
       
     7 //   amm lexer.sc fib
       
     8 //   amm lexer.sc loops
       
     9 //   amm lexer.sc email
       
    10 //
       
    11 //   amm lexer.sc all
       
    12 
       
    13 
       
    14 // regular expressions including records
       
    15 abstract class Rexp 
       
    16 case object ZERO extends Rexp
       
    17 case object ONE extends Rexp
       
    18 case object ANYCHAR extends Rexp
       
    19 case class CHAR(c: Char) extends Rexp
       
    20 case class ALTS(r1: Rexp, r2: Rexp) extends Rexp 
       
    21 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 
       
    22 case class STAR(r: Rexp) extends Rexp 
       
    23 case class RECD(x: String, r: Rexp) extends Rexp  
       
    24 case class NTIMES(n: Int, r: Rexp) extends Rexp
       
    25 case class OPTIONAL(r: Rexp) extends Rexp
       
    26 case class NOT(r: Rexp) extends Rexp
       
    27                 // records for extracting strings or tokens
       
    28   
       
    29 // values  
       
    30 abstract class Val
       
    31 case object Empty extends Val
       
    32 case class Chr(c: Char) extends Val
       
    33 case class Sequ(v1: Val, v2: Val) extends Val
       
    34 case class Left(v: Val) extends Val
       
    35 case class Right(v: Val) extends Val
       
    36 case class Stars(vs: List[Val]) extends Val
       
    37 case class Rec(x: String, v: Val) extends Val
       
    38 case class Ntime(vs: List[Val]) extends Val
       
    39 case class Optionall(v: Val) extends Val
       
    40 case class Nots(s: String) extends Val
       
    41 
       
    42 
       
    43 
       
    44 abstract class Bit
       
    45 case object Z extends Bit
       
    46 case object S extends Bit
       
    47 
       
    48 
       
    49 type Bits = List[Bit]
       
    50 
       
    51 abstract class ARexp 
       
    52 case object AZERO extends ARexp
       
    53 case class AONE(bs: Bits) extends ARexp
       
    54 case class ACHAR(bs: Bits, c: Char) extends ARexp
       
    55 case class AALTS(bs: Bits, rs: List[ARexp]) extends ARexp 
       
    56 case class ASEQ(bs: Bits, r1: ARexp, r2: ARexp) extends ARexp 
       
    57 case class ASTAR(bs: Bits, r: ARexp) extends ARexp 
       
    58 case class ANOT(bs: Bits, r: ARexp) extends ARexp
       
    59 case class AANYCHAR(bs: Bits) extends ARexp
       
    60 
       
    61 
       
    62    
       
    63 // some convenience for typing in regular expressions
       
    64 
       
    65 def charlist2rexp(s : List[Char]): Rexp = s match {
       
    66   case Nil => ONE
       
    67   case c::Nil => CHAR(c)
       
    68   case c::s => SEQ(CHAR(c), charlist2rexp(s))
       
    69 }
       
    70 implicit def string2rexp(s : String) : Rexp = 
       
    71   charlist2rexp(s.toList)
       
    72 
       
    73 implicit def RexpOps(r: Rexp) = new {
       
    74   def | (s: Rexp) = ALTS(r, s)
       
    75   def % = STAR(r)
       
    76   def ~ (s: Rexp) = SEQ(r, s)
       
    77 }
       
    78 
       
    79 implicit def stringOps(s: String) = new {
       
    80   def | (r: Rexp) = ALTS(s, r)
       
    81   def | (r: String) = ALTS(s, r)
       
    82   def % = STAR(s)
       
    83   def ~ (r: Rexp) = SEQ(s, r)
       
    84   def ~ (r: String) = SEQ(s, r)
       
    85   def $ (r: Rexp) = RECD(s, r)
       
    86 }
       
    87 
       
    88 def nullable(r: Rexp) : Boolean = r match {
       
    89   case ZERO => false
       
    90   case ONE => true
       
    91   case CHAR(_) => false
       
    92   case ANYCHAR => false
       
    93   case ALTS(r1, r2) => nullable(r1) || nullable(r2)
       
    94   case SEQ(r1, r2) => nullable(r1) && nullable(r2)
       
    95   case STAR(_) => true
       
    96   case RECD(_, r1) => nullable(r1)
       
    97   case NTIMES(n, r) => if (n == 0) true else nullable(r)
       
    98   case OPTIONAL(r) => true
       
    99   case NOT(r) => !nullable(r)
       
   100 }
       
   101 
       
   102 def der(c: Char, r: Rexp) : Rexp = r match {
       
   103   case ZERO => ZERO
       
   104   case ONE => ZERO
       
   105   case CHAR(d) => if (c == d) ONE else ZERO
       
   106   case ANYCHAR => ONE 
       
   107   case ALTS(r1, r2) => ALTS(der(c, r1), der(c, r2))
       
   108   case SEQ(r1, r2) => 
       
   109     if (nullable(r1)) ALTS(SEQ(der(c, r1), r2), der(c, r2))
       
   110     else SEQ(der(c, r1), r2)
       
   111   case STAR(r) => SEQ(der(c, r), STAR(r))
       
   112   case RECD(_, r1) => der(c, r1)
       
   113   case NTIMES(n, r) => if(n > 0) SEQ(der(c, r), NTIMES(n - 1, r)) else ZERO
       
   114   case OPTIONAL(r) => der(c, r)
       
   115   case NOT(r) =>  NOT(der(c, r))
       
   116 }
       
   117 
       
   118 
       
   119 // extracts a string from a value
       
   120 def flatten(v: Val) : String = v match {
       
   121   case Empty => ""
       
   122   case Chr(c) => c.toString
       
   123   case Left(v) => flatten(v)
       
   124   case Right(v) => flatten(v)
       
   125   case Sequ(v1, v2) => flatten(v1) ++ flatten(v2)
       
   126   case Stars(vs) => vs.map(flatten).mkString
       
   127   case Ntime(vs) => vs.map(flatten).mkString
       
   128   case Optionall(v) => flatten(v)
       
   129   case Rec(_, v) => flatten(v)
       
   130 }
       
   131 
       
   132 
       
   133 // extracts an environment from a value;
       
   134 // used for tokenising a string
       
   135 def env(v: Val) : List[(String, String)] = v match {
       
   136   case Empty => Nil
       
   137   case Chr(c) => Nil
       
   138   case Left(v) => env(v)
       
   139   case Right(v) => env(v)
       
   140   case Sequ(v1, v2) => env(v1) ::: env(v2)
       
   141   case Stars(vs) => vs.flatMap(env)
       
   142   case Ntime(vs) => vs.flatMap(env)
       
   143   case Rec(x, v) => (x, flatten(v))::env(v)
       
   144   case Optionall(v) => env(v)
       
   145   case Nots(s) => ("Negative", s) :: Nil
       
   146 }
       
   147 
       
   148 
       
   149 // The injection and mkeps part of the lexer
       
   150 //===========================================
       
   151 
       
   152 def mkeps(r: Rexp) : Val = r match {
       
   153   case ONE => Empty
       
   154   case ALTS(r1, r2) => 
       
   155     if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
       
   156   case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))
       
   157   case STAR(r) => Stars(Nil)
       
   158   case RECD(x, r) => Rec(x, mkeps(r))
       
   159   case NTIMES(n, r) => Ntime(List.fill(n)(mkeps(r)))
       
   160   case OPTIONAL(r) => Optionall(Empty)
       
   161   case NOT(rInner) => if(nullable(rInner)) throw new Exception("error")  
       
   162                          else Nots("")//Nots(s.reverse.toString)
       
   163 //   case NOT(ZERO) => Empty
       
   164 //   case NOT(CHAR(c)) => Empty
       
   165 //   case NOT(SEQ(r1, r2)) => Sequ(mkeps(NOT(r1)), mkeps(NOT(r2)))
       
   166 //   case NOT(ALTS(r1, r2)) => if(!nullable(r1)) Left(mkeps(NOT(r1))) else Right(mkeps(NOT(r2)))
       
   167 //   case NOT(STAR(r)) => Stars(Nil) 
       
   168 
       
   169 }
       
   170 
       
   171 def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {
       
   172   case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
       
   173   case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)
       
   174   case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)
       
   175   case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))
       
   176   case (ALTS(r1, r2), Left(v1)) => Left(inj(r1, c, v1))
       
   177   case (ALTS(r1, r2), Right(v2)) => Right(inj(r2, c, v2))
       
   178   case (CHAR(d), Empty) => Chr(c) 
       
   179   case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
       
   180   case (NTIMES(n, r), Sequ(v1, Ntime(vs))) => Ntime(inj(r, c, v1)::vs)
       
   181   case (OPTIONAL(r), v) => Optionall(inj(r, c, v))
       
   182   case (NOT(r), Nots(s)) => Nots(c.toString ++ s)
       
   183   case (ANYCHAR, Empty) => Chr(c)
       
   184 }
       
   185 
       
   186 // some "rectification" functions for simplification
       
   187 def F_ID(v: Val): Val = v
       
   188 def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v))
       
   189 def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v))
       
   190 def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
       
   191   case Right(v) => Right(f2(v))
       
   192   case Left(v) => Left(f1(v))
       
   193 }
       
   194 def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
       
   195   case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))
       
   196 }
       
   197 def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 
       
   198   (v:Val) => Sequ(f1(Empty), f2(v))
       
   199 def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 
       
   200   (v:Val) => Sequ(f1(v), f2(Empty))
       
   201 
       
   202 def F_ERROR(v: Val): Val = throw new Exception("error")
       
   203 
       
   204 // simplification
       
   205 def simp(r: Rexp): (Rexp, Val => Val) = r match {
       
   206   case ALTS(r1, r2) => {
       
   207     val (r1s, f1s) = simp(r1)
       
   208     val (r2s, f2s) = simp(r2)
       
   209     (r1s, r2s) match {
       
   210       case (ZERO, _) => (r2s, F_RIGHT(f2s))
       
   211       case (_, ZERO) => (r1s, F_LEFT(f1s))
       
   212       case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))
       
   213                 else (ALTS (r1s, r2s), F_ALT(f1s, f2s)) 
       
   214     }
       
   215   }
       
   216   case SEQ(r1, r2) => {
       
   217     val (r1s, f1s) = simp(r1)
       
   218     val (r2s, f2s) = simp(r2)
       
   219     (r1s, r2s) match {
       
   220       case (ZERO, _) => (ZERO, F_ERROR)
       
   221       case (_, ZERO) => (ZERO, F_ERROR)
       
   222       case (ONE, _) => (r2s, F_SEQ_Empty1(f1s, f2s))
       
   223       case (_, ONE) => (r1s, F_SEQ_Empty2(f1s, f2s))
       
   224       case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))
       
   225     }
       
   226   }
       
   227   case r => (r, F_ID)
       
   228 }
       
   229 
       
   230 // lexing functions including simplification
       
   231 def lex_simp(r: Rexp, s: List[Char]) : Val = s match {
       
   232   case Nil => if (nullable(r)) mkeps(r) else 
       
   233     { throw new Exception(s"lexing error $r not nullable") } 
       
   234   case c::cs => {
       
   235     val (r_simp, f_simp) = simp(der(c, r))
       
   236     inj(r, c, f_simp(lex_simp(r_simp, cs)))
       
   237   }
       
   238 }
       
   239 
       
   240 def lexing_simp(r: Rexp, s: String) = 
       
   241   env(lex_simp(r, s.toList))
       
   242 
       
   243 // The Lexing Rules for the WHILE Language
       
   244 
       
   245 def PLUS(r: Rexp) = r ~ r.%
       
   246 
       
   247 def Range(s : List[Char]) : Rexp = s match {
       
   248   case Nil => ZERO
       
   249   case c::Nil => CHAR(c)
       
   250   case c::s => ALTS(CHAR(c), Range(s))
       
   251 }
       
   252 def RANGE(s: String) = Range(s.toList)
       
   253 
       
   254 val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_")
       
   255 val DIGIT = RANGE("0123456789")
       
   256 val ID = SYM ~ (SYM | DIGIT).% 
       
   257 val NUM = PLUS(DIGIT)
       
   258 val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" 
       
   259 val SEMI: Rexp = ";"
       
   260 val OP: Rexp = ":=" | "=" | "-" | "+" | "*" | "!=" | "<" | ">"
       
   261 val WHITESPACE = PLUS(" " | "\n" | "\t" | "\r")
       
   262 val RPAREN: Rexp = "{"
       
   263 val LPAREN: Rexp = "}"
       
   264 val STRING: Rexp = "\"" ~ SYM.% ~ "\""
       
   265 
       
   266 
       
   267 //ab \ a --> 1b
       
   268 //
       
   269 val WHILE_REGS = (("k" $ KEYWORD) | 
       
   270                   ("i" $ ID) | 
       
   271                   ("o" $ OP) | 
       
   272                   ("n" $ NUM) | 
       
   273                   ("s" $ SEMI) | 
       
   274                   ("str" $ STRING) |
       
   275                   ("p" $ (LPAREN | RPAREN)) | 
       
   276                   ("w" $ WHITESPACE)).%
       
   277 
       
   278 val NREGS = NTIMES(5, OPTIONAL(SYM))
       
   279 val NREGS1 = ("test" $ NREGS)
       
   280 // Two Simple While Tests
       
   281 //========================
       
   282 val NOTREG = "hehe" ~ NOT((ANYCHAR.%) ~ "haha" ~ (ANYCHAR.%))
       
   283 
       
   284 
       
   285   // bnullable function: tests whether the aregular 
       
   286   // expression can recognise the empty string
       
   287 def bnullable (r: ARexp) : Boolean = r match {
       
   288     case AZERO => false
       
   289     case AONE(_) => true
       
   290     case ACHAR(_,_) => false
       
   291     case AALTS(_, rs) => rs.exists(bnullable)
       
   292     case ASEQ(_, r1, r2) => bnullable(r1) && bnullable(r2)
       
   293     case ASTAR(_, _) => true
       
   294     case ANOT(_, rn) => !bnullable(rn)
       
   295   }
       
   296 
       
   297 def mkepsBC(r: ARexp) : Bits = r match {
       
   298     case AONE(bs) => bs
       
   299     case AALTS(bs, rs) => {
       
   300       val n = rs.indexWhere(bnullable)
       
   301       bs ++ mkepsBC(rs(n))
       
   302     }
       
   303     case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
       
   304     case ASTAR(bs, r) => bs ++ List(Z)
       
   305     case ANOT(bs, rn) => bs
       
   306   }
       
   307 
       
   308 
       
   309 def bder(c: Char, r: ARexp) : ARexp = r match {
       
   310     case AZERO => AZERO
       
   311     case AONE(_) => AZERO
       
   312     case ACHAR(bs, f) => if (c == f) AONE(bs) else AZERO
       
   313     case AALTS(bs, rs) => AALTS(bs, rs.map(bder(c, _)))
       
   314     case ASEQ(bs, r1, r2) => 
       
   315       if (bnullable(r1)) AALTS(bs, ASEQ(Nil, bder(c, r1), r2) :: fuse(mkepsBC(r1), bder(c, r2)) :: Nil )
       
   316       else ASEQ(bs, bder(c, r1), r2)
       
   317     case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), bder(c, r)), ASTAR(Nil, r))
       
   318     case ANOT(bs, rn) => ANOT(bs, bder(c, rn))
       
   319     case AANYCHAR(bs) => AONE(bs)
       
   320   } 
       
   321 
       
   322 def fuse(bs: Bits, r: ARexp) : ARexp = r match {
       
   323     case AZERO => AZERO
       
   324     case AONE(cs) => AONE(bs ++ cs)
       
   325     case ACHAR(cs, f) => ACHAR(bs ++ cs, f)
       
   326     case AALTS(cs, rs) => AALTS(bs ++ cs, rs)
       
   327     case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)
       
   328     case ASTAR(cs, r) => ASTAR(bs ++ cs, r)
       
   329     case ANOT(cs, r) => ANOT(bs ++ cs, r)
       
   330   }
       
   331 
       
   332 
       
   333 def internalise(r: Rexp) : ARexp = r match {
       
   334     case ZERO => AZERO
       
   335     case ONE => AONE(Nil)
       
   336     case CHAR(c) => ACHAR(Nil, c)
       
   337     //case PRED(f) => APRED(Nil, f)
       
   338     case ALTS(r1, r2) => 
       
   339       AALTS(Nil, List(fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2))))
       
   340     // case ALTS(r1::rs) => {
       
   341     //   val AALTS(Nil, rs2) = internalise(ALTS(rs))
       
   342     //   AALTS(Nil, fuse(List(Z), internalise(r1)) :: rs2.map(fuse(List(S), _)))
       
   343     // }
       
   344     case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
       
   345     case STAR(r) => ASTAR(Nil, internalise(r))
       
   346     case RECD(x, r) => internalise(r)
       
   347     case NOT(r) => ANOT(Nil, internalise(r))
       
   348     case ANYCHAR => AANYCHAR(Nil)
       
   349   }
       
   350 
       
   351 
       
   352 def bsimp(r: ARexp): ARexp = 
       
   353   {
       
   354     r match {
       
   355       case ASEQ(bs1, r1, r2) => (bsimp(r1), bsimp(r2)) match {
       
   356           case (AZERO, _) => AZERO
       
   357           case (_, AZERO) => AZERO
       
   358           case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
       
   359           case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
       
   360       }
       
   361       case AALTS(bs1, rs) => {
       
   362             val rs_simp = rs.map(bsimp(_))
       
   363             val flat_res = flats(rs_simp)
       
   364             val dist_res = strongDistinctBy(flat_res)//distinctBy(flat_res, erase)
       
   365             dist_res match {
       
   366               case Nil => AZERO
       
   367               case s :: Nil => fuse(bs1, s)
       
   368               case rs => AALTS(bs1, rs)  
       
   369             }
       
   370           
       
   371       }
       
   372       case r => r
       
   373     }
       
   374   }
       
   375   def bders (s: List[Char], r: ARexp) : ARexp = s match {
       
   376     case Nil => r
       
   377     case c::s => bders(s, bder(c, r))
       
   378   }
       
   379 
       
   380   def flats(rs: List[ARexp]): List[ARexp] = rs match {
       
   381       case Nil => Nil
       
   382       case AZERO :: rs1 => flats(rs1)
       
   383       case AALTS(bs, rs1) :: rs2 => rs1.map(fuse(bs, _)) ::: flats(rs2)
       
   384       case r1 :: rs2 => r1 :: flats(rs2)
       
   385     }
       
   386 
       
   387   def distinctBy[B, C](xs: List[B], f: B => C, acc: List[C] = Nil): List[B] = xs match {
       
   388     case Nil => Nil
       
   389     case (x::xs) => {
       
   390       val res = f(x)
       
   391       if (acc.contains(res)) distinctBy(xs, f, acc)  
       
   392       else x::distinctBy(xs, f, res::acc)
       
   393     }
       
   394   } 
       
   395 
       
   396   def prettyRexp(r: Rexp) : String = r match {
       
   397       case STAR(r0) => s"${prettyRexp(r0)}*"
       
   398       case SEQ(CHAR(c), r2) => c.toString ++ prettyRexp(r2)
       
   399       case SEQ(r1, r2) => s"${prettyRexp(r1)}~${prettyRexp(r2)}"
       
   400       case CHAR(c) => c.toString
       
   401       case ANYCHAR => "."
       
   402     //   case NOT(r0) => s
       
   403   }
       
   404 
       
   405   def decode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {
       
   406     case (ONE, bs) => (Empty, bs)
       
   407     case (CHAR(f), bs) => (Chr(f), bs)
       
   408     case (ALTS(r1, r2), Z::bs1) => {
       
   409         val (v, bs2) = decode_aux(r1, bs1)
       
   410         (Left(v), bs2)
       
   411     }
       
   412     case (ALTS(r1, r2), S::bs1) => {
       
   413         val (v, bs2) = decode_aux(r2, bs1)
       
   414         (Right(v), bs2)
       
   415     }
       
   416     case (SEQ(r1, r2), bs) => {
       
   417       val (v1, bs1) = decode_aux(r1, bs)
       
   418       val (v2, bs2) = decode_aux(r2, bs1)
       
   419       (Sequ(v1, v2), bs2)
       
   420     }
       
   421     case (STAR(r1), S::bs) => {
       
   422       val (v, bs1) = decode_aux(r1, bs)
       
   423       //println(v)
       
   424       val (Stars(vs), bs2) = decode_aux(STAR(r1), bs1)
       
   425       (Stars(v::vs), bs2)
       
   426     }
       
   427     case (STAR(_), Z::bs) => (Stars(Nil), bs)
       
   428     case (RECD(x, r1), bs) => {
       
   429       val (v, bs1) = decode_aux(r1, bs)
       
   430       (Rec(x, v), bs1)
       
   431     }
       
   432     case (NOT(r), bs) => (Nots(prettyRexp(r)), bs)
       
   433   }
       
   434 
       
   435   def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
       
   436     case (v, Nil) => v
       
   437     case _ => throw new Exception("Not decodable")
       
   438   }
       
   439 
       
   440 
       
   441 
       
   442 def blexSimp(r: Rexp, s: String) : List[Bit] = {
       
   443     blex_simp(internalise(r), s.toList)
       
   444 }
       
   445 
       
   446 def blexing_simp(r: Rexp, s: String) : Val = {
       
   447     val bit_code = blex_simp(internalise(r), s.toList)
       
   448     decode(r, bit_code)
       
   449   }
       
   450 
       
   451 
       
   452 
       
   453   def bders_simp(s: List[Char], r: ARexp) : ARexp = s match {
       
   454     case Nil => r
       
   455     case c::s => bders_simp(s, bsimp(bder(c, r)))
       
   456   }
       
   457   
       
   458   def bdersSimp(s: String, r: Rexp) : ARexp = bders_simp(s.toList, internalise(r))
       
   459 
       
   460 
       
   461   def erase(r:ARexp): Rexp = r match{
       
   462     case AZERO => ZERO
       
   463     case AONE(_) => ONE
       
   464     case ACHAR(bs, c) => CHAR(c)
       
   465     case AALTS(bs, Nil) => ZERO
       
   466     case AALTS(bs, a::Nil) => erase(a)
       
   467     case AALTS(bs, a::as) => ALTS(erase(a), erase(AALTS(bs, as)))
       
   468     case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))
       
   469     case ASTAR(cs, r)=> STAR(erase(r))
       
   470     case ANOT(bs, r) => NOT(erase(r))
       
   471     case AANYCHAR(bs) => ANYCHAR
       
   472   }
       
   473 
       
   474 def breakHead(r: ARexp) : List[ARexp] = r match {
       
   475     case AALTS(bs, rs) => rs
       
   476     case r => r::Nil
       
   477 }
       
   478 
       
   479 def distinctByWithAcc[B, C](xs: List[B], f: B => C, 
       
   480     acc: List[C] = Nil, accB: List[B] = Nil): (List[B], List[C]) = xs match {
       
   481     case Nil => (accB.reverse, acc)
       
   482     case (x::xs) => {
       
   483       val res = f(x)
       
   484       if (acc.contains(res)) distinctByWithAcc(xs, f, acc, accB)  
       
   485       else distinctByWithAcc(xs, f, res::acc, x::accB)
       
   486     }
       
   487   } 
       
   488 
       
   489 
       
   490   def strongDistinctBy(xs: List[ARexp], 
       
   491                        acc1: List[Rexp] = Nil, 
       
   492                        acc2 : List[(List[Rexp], Rexp)] = Nil): List[ARexp] = xs match {
       
   493     case Nil => Nil
       
   494     case (x::xs) => 
       
   495         if(acc1.contains(erase(x)))
       
   496             strongDistinctBy(xs, acc1, acc2)
       
   497         else{
       
   498             x match {
       
   499                 case ASTAR(bs0, r0) => 
       
   500                     val headList : List[ARexp] = List[ARexp](AONE(Nil))
       
   501                     val i = acc2.indexWhere(
       
   502                         r2stl => {val (r2s, tl) = r2stl; tl == erase(r0) } 
       
   503                     )
       
   504                     if(i == -1){ 
       
   505                         x::strongDistinctBy(
       
   506                             xs, erase(x)::acc1, (ONE::Nil, erase(r0))::acc2
       
   507                         )
       
   508                     }
       
   509                     else{
       
   510                         val headListAlready = acc2(i)
       
   511                         val (newHeads, oldHeadsUpdated) = 
       
   512                                 distinctByWithAcc(headList, erase, headListAlready._1)
       
   513                         newHeads match{
       
   514                             case newHead::Nil =>
       
   515                                 ASTAR(bs0, r0) :: 
       
   516                                 strongDistinctBy(xs, erase(x)::acc1, 
       
   517                                 acc2.updated(i, (oldHeadsUpdated, headListAlready._2)) )//TODO: acc2 already contains headListAlready
       
   518                             case Nil =>
       
   519                                 strongDistinctBy(xs, erase(x)::acc1, 
       
   520                                 acc2)
       
   521                         }
       
   522                     }                
       
   523                 case ASEQ(bs, r1, ASTAR(bs0, r0)) => 
       
   524                     val headList = breakHead(r1)
       
   525                     val i = acc2.indexWhere(
       
   526                         r2stl => {val (r2s, tl) = r2stl; tl == erase(r0) } 
       
   527                     )
       
   528                     if(i == -1){ 
       
   529                         x::strongDistinctBy(
       
   530                             xs, erase(x)::acc1, (headList.map(erase(_)), erase(r0))::acc2
       
   531                         )
       
   532                     }
       
   533                     else{
       
   534                         val headListAlready = acc2(i)
       
   535                         val (newHeads, oldHeadsUpdated) = 
       
   536                                 distinctByWithAcc(headList, erase, headListAlready._1)
       
   537                         newHeads match{
       
   538                             case newHead::Nil =>
       
   539                                 ASEQ(bs, newHead, ASTAR(bs0, r0)) :: 
       
   540                                 strongDistinctBy(xs, erase(x)::acc1, 
       
   541                                 acc2.updated(i, (oldHeadsUpdated, headListAlready._2)) )//TODO: acc2 already contains headListAlready
       
   542                             case Nil =>
       
   543                                 strongDistinctBy(xs, erase(x)::acc1, 
       
   544                                 acc2)
       
   545                             case hds => val AALTS(bsp, rsp) = r1
       
   546                                 ASEQ(bs, AALTS(bsp, hds), ASTAR(bs0, r0)) ::
       
   547                                 strongDistinctBy(xs, erase(x)::acc1,
       
   548                                 acc2.updated(i, (oldHeadsUpdated, headListAlready._2)))
       
   549                         }
       
   550                     }
       
   551                 case rPrime => x::strongDistinctBy(xs, erase(x)::acc1, acc2)    
       
   552             }
       
   553                 
       
   554         }
       
   555     
       
   556 }
       
   557 
       
   558 
       
   559 def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
       
   560     case Nil => {
       
   561       if (bnullable(r)) {
       
   562         //println(asize(r))
       
   563         val bits = mkepsBC(r)
       
   564         bits
       
   565       }
       
   566     else throw new Exception("Not matched")
       
   567     }
       
   568     case c::cs => {
       
   569       val der_res = bder(c,r)
       
   570       val simp_res = bsimp(der_res)  
       
   571       blex_simp(simp_res, cs)      
       
   572     }
       
   573   }
       
   574   def size(r: Rexp) : Int = r match {
       
   575     case ZERO => 1
       
   576     case ONE => 1
       
   577     case CHAR(_) => 1
       
   578     case ANYCHAR => 1
       
   579     case NOT(r0) => 1 + size(r0)
       
   580     case SEQ(r1, r2) => 1 + size(r1) + size(r2)
       
   581     case ALTS(r1, r2) => 1 + List(r1, r2).map(size).sum
       
   582     case STAR(r) => 1 + size(r)
       
   583   }
       
   584 
       
   585   def asize(a: ARexp) = size(erase(a))
       
   586 
       
   587 
       
   588 // @arg(doc = "small tests")
       
   589 val STARREG = ("a" | "aa").%
       
   590 
       
   591 @main
       
   592 def small() = {
       
   593 
       
   594   val prog0 = """aaa"""
       
   595   println(s"test: $prog0")
       
   596 //   println(lexing_simp(NOTREG, prog0))
       
   597 //   val v = lex_simp(NOTREG, prog0.toList)
       
   598 //   println(v)
       
   599 
       
   600 //   val d =  (lex_simp(NOTREG, prog0.toList))
       
   601 //   println(d)
       
   602 
       
   603   val bd = bdersSimp(prog0, STARREG)
       
   604     println(erase(bd))
       
   605     println(asize(bd))
       
   606 
       
   607     val vres = blexing_simp( STARREG, prog0)
       
   608     println(vres)
       
   609 //   println(vs.length)
       
   610 //   println(vs)
       
   611    
       
   612 
       
   613   // val prog1 = """read  n; write n"""  
       
   614   // println(s"test: $prog1")
       
   615   // println(lexing_simp(WHILE_REGS, prog1))
       
   616 }
       
   617 
       
   618 // // Bigger Tests
       
   619 // //==============
       
   620 
       
   621 // // escapes strings and prints them out as "", "\n" and so on
       
   622 // def esc(raw: String): String = {
       
   623 //   import scala.reflect.runtime.universe._
       
   624 //   Literal(Constant(raw)).toString
       
   625 // }
       
   626 
       
   627 // def escape(tks: List[(String, String)]) =
       
   628 //   tks.map{ case (s1, s2) => (s1, esc(s2))}
       
   629 
       
   630 
       
   631 // val prog2 = """
       
   632 // write "Fib";
       
   633 // read n;
       
   634 // minus1 := 0;
       
   635 // minus2 := 1;
       
   636 // while n > 0 do {
       
   637 //   temp := minus2;
       
   638 //   minus2 := minus1 + minus2;
       
   639 //   minus1 := temp;
       
   640 //   n := n - 1
       
   641 // };
       
   642 // write "Result";
       
   643 // write minus2
       
   644 // """
       
   645 
       
   646 // @arg(doc = "Fibonacci test")
       
   647 // @main
       
   648 // def fib() = {
       
   649 //   println("lexing fib program")
       
   650 //   println(escape(lexing_simp(WHILE_REGS, prog2)).mkString("\n"))
       
   651 // }
       
   652 
       
   653 
       
   654 // val prog3 = """
       
   655 // start := 1000;
       
   656 // x := start;
       
   657 // y := start;
       
   658 // z := start;
       
   659 // while 0 < x do {
       
   660 //  while 0 < y do {
       
   661 //   while 0 < z do {
       
   662 //     z := z - 1
       
   663 //   };
       
   664 //   z := start;
       
   665 //   y := y - 1
       
   666 //  };     
       
   667 //  y := start;
       
   668 //  x := x - 1
       
   669 // }
       
   670 // """
       
   671 
       
   672 // @arg(doc = "Loops test")
       
   673 // @main
       
   674 // def loops() = {
       
   675 //   println("lexing Loops")
       
   676 //   println(escape(lexing_simp(WHILE_REGS, prog3)).mkString("\n"))
       
   677 // }
       
   678 
       
   679 // @arg(doc = "Email Test")
       
   680 // @main
       
   681 // def email() = {
       
   682 //   val lower = "abcdefghijklmnopqrstuvwxyz"
       
   683 
       
   684 //   val NAME = RECD("name", PLUS(RANGE(lower ++ "_.-")))
       
   685 //   val DOMAIN = RECD("domain", PLUS(RANGE(lower ++ "-")))
       
   686 //   val RE = RANGE(lower ++ ".")
       
   687 //   val TOPLEVEL = RECD("top", (RE ~ RE) |
       
   688 //                              (RE ~ RE ~ RE) | 
       
   689 //                              (RE ~ RE ~ RE ~ RE) | 
       
   690 //                              (RE ~ RE ~ RE ~ RE ~ RE) |
       
   691 //                              (RE ~ RE ~ RE ~ RE ~ RE ~ RE))
       
   692 
       
   693 //   val EMAIL = NAME ~ "@" ~ DOMAIN ~ "." ~ TOPLEVEL
       
   694 
       
   695 //   println(lexing_simp(EMAIL, "christian.urban@kcl.ac.uk"))
       
   696 // }
       
   697 
       
   698 
       
   699 // @arg(doc = "All tests.")
       
   700 // @main
       
   701 // def all() = { small(); fib() ; loops() ; email() } 
       
   702 
       
   703 
       
   704 
       
   705 
       
   706 // runs with amm2 and amm3
       
   707 
       
   708 
       
   709