1 import scala.language.implicitConversions    

     2 import scala.language.reflectiveCalls

     3 import scala.annotation.tailrec   

     4 

     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 

    14 

    15 

    16 abstract class Bit

    17 case object Z extends Bit

    18 case object S extends Bit

    19 

    20 type Bits = List[Bit]

    21 

    22 abstract class ARexp 

    23 case object AZERO extends ARexp

    24 case class AONE(bs: Bits) extends ARexp

    25 case class ACHAR(bs: Bits, c: Char) extends ARexp

    26 case class AALTS(bs: Bits, rs: List[ARexp]) extends ARexp 

    27 case class ASEQ(bs: Bits, r1: ARexp, r2: ARexp) extends ARexp 

    28 case class ASTAR(bs: Bits, r: ARexp) extends ARexp 

    29 

    30 def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, List(r1, r2))

    31 

    32 abstract class Val

    33 case object Empty extends Val

    34 case class Chr(c: Char) extends Val

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

    36 case class Left(v: Val) extends Val

    37 case class Right(v: Val) extends Val

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

    39 case class Position(i: Int, v: Val) extends Val  // for testing purposes

    40 case object Undefined extends Val                // for testing purposes

    41    

    42 // some convenience for typing in regular expressions

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

    44   case Nil => ONE

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

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

    47 }

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

    49 

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

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

    52   def % = STAR(r)

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

    54 }

    55 

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

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

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

    59   def % = STAR(s)

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

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

    62 }

    63 

    64 

    65 // nullable function: tests whether the regular 

    66 // expression can recognise the empty string

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

    68   case ZERO => false

    69   case ONE => true

    70   case CHAR(_) => false

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

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

    73   case STAR(_) => true

    74 }

    75 

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

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

    78   case ZERO => ZERO

    79   case ONE => ZERO

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

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

    82   case SEQ(r1, r2) => 

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

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

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

    86 }

    87 

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

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

    90   case Nil => r

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

    92 }

    93 

    94 // mkeps and injection part

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

    96   case ONE => Empty

    97   case ALT(r1, r2) => 

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

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

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

   101 }

   102 

   103 

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

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

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

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

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

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

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

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

   112 }

   113 

   114 // main lexing function (produces a value)

   115 // - no simplification

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

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

   118               else throw new Exception("Not matched")

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

   120 }

   121 

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

   123 

   124 

   125 

   126 // Bitcoded + Annotation

   127 //=======================

   128 

   129 //erase function: extracts the regx from Aregex

   130 def erase(r:ARexp): Rexp = r match{

   131   case AZERO => ZERO

   132   case AONE(_) => ONE

   133   case ACHAR(bs, c) => CHAR(c)

   134   case AALTS(bs, Nil) => ZERO

   135   case AALTS(bs, r::Nil) => erase(r)

   136   case AALTS(bs, r::rs) => ALT(erase(r), erase(AALTS(bs, rs)))

   137   case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))

   138   case ASTAR(cs, r)=> STAR(erase(r))

   139 }

   140 

   141 // translation into ARexps

   142 def fuse(bs: Bits, r: ARexp) : ARexp = r match {

   143   case AZERO => AZERO

   144   case AONE(cs) => AONE(bs ++ cs)

   145   case ACHAR(cs, c) => ACHAR(bs ++ cs, c)

   146   case AALTS(cs, rs) => AALTS(bs ++ cs, rs)

   147   case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)

   148   case ASTAR(cs, r) => ASTAR(bs ++ cs, r)

   149 }

   150 

   151 def internalise(r: Rexp) : ARexp = r match {

   152   case ZERO => AZERO

   153   case ONE => AONE(Nil)

   154   case CHAR(c) => ACHAR(Nil, c)

   155   case ALT(r1, r2) => AALT(Nil, fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2)))

   156   case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))

   157   case STAR(r) => ASTAR(Nil, internalise(r))

   158 }

   159 

   160 

   161 internalise(("a" | "ab") ~ ("b" | ""))

   162 

   163 

   164 

   165 def decode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {

   166   case (ONE, bs) => (Empty, bs)

   167   case (CHAR(c), bs) => (Chr(c), bs)

   168   case (ALT(r1, r2), Z::bs) => {

   169     val (v, bs1) = decode_aux(r1, bs)

   170     (Left(v), bs1)

   171   }

   172   case (ALT(r1, r2), S::bs) => {

   173     val (v, bs1) = decode_aux(r2, bs)

   174     (Right(v), bs1)

   175   }

   176   case (SEQ(r1, r2), bs) => {

   177     val (v1, bs1) = decode_aux(r1, bs)

   178     val (v2, bs2) = decode_aux(r2, bs1)

   179     (Sequ(v1, v2), bs2)

   180   }

   181   case (STAR(r1), Z::bs) => {

   182     val (v, bs1) = decode_aux(r1, bs)

   183     val (Stars(vs), bs2) = decode_aux(STAR(r1), bs1)

   184     (Stars(v::vs), bs2)

   185   }

   186   case (STAR(_), S::bs) => (Stars(Nil), bs)

   187 }

   188 

   189 def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {

   190   case (v, Nil) => v

   191   case _ => throw new Exception("Not decodable")

   192 }

   193 

   194 def encode(v: Val) : Bits = v match {

   195   case Empty => Nil

   196   case Chr(c) => Nil

   197   case Left(v) => Z :: encode(v)

   198   case Right(v) => S :: encode(v)

   199   case Sequ(v1, v2) => encode(v1) ::: encode(v2)

   200   case Stars(Nil) => List(S)

   201   case Stars(v::vs) =>  Z :: encode(v) ::: encode(Stars(vs))

   202 }

   203 

   204 

   205 // nullable function: tests whether the aregular 

   206 // expression can recognise the empty string

   207 def bnullable (r: ARexp) : Boolean = r match {

   208   case AZERO => false

   209   case AONE(_) => true

   210   case ACHAR(_,_) => false

   211   case AALTS(_, rs) => rs.exists(bnullable)

   212   case ASEQ(_, r1, r2) => bnullable(r1) && bnullable(r2)

   213   case ASTAR(_, _) => true

   214 }

   215 

   216 def bmkeps(r: ARexp) : Bits = r match {

   217   case AONE(bs) => bs

   218   case AALTS(bs, r::Nil) => bs ++ bmkeps(r) 

   219   case AALTS(bs, r::rs) => 

   220     if (bnullable(r)) bs ++ bmkeps(r) else bmkeps(AALTS(bs, rs))  

   221   case ASEQ(bs, r1, r2) => bs ++ bmkeps(r1) ++ bmkeps(r2)

   222   case ASTAR(bs, r) => bs ++ List(S)

   223 }

   224 

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

   226 def bder(c: Char, r: ARexp) : ARexp = r match {

   227   case AZERO => AZERO

   228   case AONE(_) => AZERO

   229   case ACHAR(bs, d) => if (c == d) AONE(bs) else AZERO

   230   case AALTS(bs, rs) => AALTS(bs, rs.map(bder(c, _)))

   231   case ASEQ(bs, r1, r2) => 

   232     if (bnullable(r1)) AALT(bs, ASEQ(Nil, bder(c, r1), r2), fuse(bmkeps(r1), bder(c, r2)))

   233     else ASEQ(bs, bder(c, r1), r2)

   234   case ASTAR(bs, r) => ASEQ(bs, fuse(List(Z), bder(c, r)), ASTAR(Nil, r))

   235 }

   236 

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

   238 @tailrec

   239 def bders (s: List[Char], r: ARexp) : ARexp = s match {

   240   case Nil => r

   241   case c::s => bders(s, bder(c, r))

   242 }

   243 

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

   245 def blex(r: ARexp, s: List[Char]) : Bits = s match {

   246   case Nil => if (bnullable(r)) bmkeps(r) else throw new Exception("Not matched")

   247   case c::cs => blex(bder(c, r), cs)

   248 }

   249 

   250 def pre_blexing(r: ARexp, s: String)  : Bits = blex(r, s.toList)

   251 def blexing(r: Rexp, s: String) : Val = decode(r, pre_blexing(internalise(r), s))

   252 

   253 

   254 // example by Tudor

   255 val reg = ((("a".%)) ~ ("b" | "c")).%

   256 

   257 println(blexing(reg, "aab"))

   258 

   259 

   260 //=======================

   261 // simplification 

   262 //

   263 

   264 

   265 def flts(rs: List[ARexp]) : List[ARexp] = rs match {

   266   case Nil => Nil

   267   case AZERO :: rs => flts(rs)

   268   case AALTS(bs, rs1) :: rs => rs1.map(fuse(bs, _)) ++ flts(rs)

   269   case r1 :: rs => r1 :: flts(rs)

   270 }

   271 

   272 def distinctBy[B, C](xs: List[B], 

   273                      f: B => C, 

   274                      acc: List[C] = Nil): List[B] = xs match {

   275   case Nil => Nil

   276   case x::xs => {

   277     val res = f(x)

   278     if (acc.contains(res)) distinctBy(xs, f, acc)

   279     else x::distinctBy(xs, f, res::acc)

   280   }

   281 } 

   282 

   283 

   284 def bsimp(r: ARexp): ARexp = r match {

   285   case ASEQ(bs1, r1, r2) => (bsimp(r1), bsimp(r2)) match {

   286       case (AZERO, _) => AZERO

   287       case (_, AZERO) => AZERO

   288       case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)

   289       //case (AALTS(bs, rs), r2) => AALTS(bs, rs.map(ASEQ(Nil, _, r2)))

   290       case (r1s, r2s) => ASEQ(bs1, r1s, r2s)

   291   }

   292   case AALTS(bs1, rs) => distinctBy(flts(rs.map(bsimp)), erase) match {

   293       case Nil => AZERO

   294       case r::Nil => fuse(bs1, r)

   295       case rs => AALTS(bs1, rs)

   296   }

   297   case r => r

   298 }

   299 

   300 def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {

   301   case Nil => if (bnullable(r)) bmkeps(r) 

   302               else throw new Exception("Not matched")

   303   case c::cs => blex(bsimp(bder(c, r)), cs)

   304 }

   305 

   306 def blexing_simp(r: Rexp, s: String) : Val = 

   307   decode(r, blex_simp(internalise(r), s.toList))

   308 

   309 println(blexing_simp(reg, "aab"))

   310 

   311 // bsimp2 by Chengsong

   312 

   313 def pos_i(rs: List[ARexp], v: Val): Int = (rs, v) match {

   314     case (r::Nil,        v1) => 0

   315     case ( r::rs1, Right(v)) => pos_i(rs1, v) + 1

   316     case ( r::rs1, Left(v) ) => 0

   317 }

   318 

   319 def pos_v(rs: List[ARexp], v: Val): Val = (rs, v) match {

   320     case (r::Nil,       v1) => v1

   321     case (r::rs1, Right(v)) => pos_v(rs1, v)

   322     case (r::rs1, Left(v) ) => v

   323 }

   324 

   325 def unify(rs: List[ARexp], v: Val): Val = {

   326   Position(pos_i(rs, v), pos_v(rs, v))

   327 }

   328 

   329 // coat does the job of "coating" a value

   330 // given the number of right outside it

   331 def coat(v: Val, i: Int) : Val = i match {

   332   case 0 => v

   333   case i => if (i > 0) coat(Right(v), i - 1) else { println(v, i); throw new Exception("coat minus")}

   334 }

   335 

   336 def distinctBy2[B, C](v: Val, xs: List[B], f: B => C, acc: List[C] = Nil, res: List[B] = Nil): (List[B], Val) = xs match {

   337     case Nil => (res, v)

   338     case (x::xs) => {

   339       val re = f(x)

   340       if (acc.contains(re)) v match { 

   341         case Position(i, v0) => distinctBy2(Position(i - 1, v0), xs, f, acc, res)  

   342         case _ => throw new Exception("dB2")

   343       }

   344       else distinctBy2(v, xs, f, re::acc, x::res)

   345     }

   346   }

   347 

   348 

   349 def flats(rs: List[ARexp]): List[ARexp] = rs match {

   350       case Nil => Nil

   351       case AZERO :: rs1 => flats(rs1)

   352       case AALTS(bs, rs1) :: rs2 => rs1.map(fuse(bs, _)) ::: flats(rs2)

   353       case r1 :: rs2 => r1 :: flats(rs2)

   354   }

   355 

   356 

   357 

   358 def flats2(front: List[ARexp], i: Int, rs: List[ARexp], v: Val): (List[ARexp], Val) = v match {

   359     case Position(j, v0) => {

   360       if (i < 0) (front ::: flats(rs), Position(j, v0) ) 

   361       else if(i == 0){

   362         rs match {

   363           case AALTS(bs, rs1) :: rs2 => ( (front ::: rs1.map(fuse(bs, _))):::flats(rs2), Position(j + rs1.length - 1, pos_v(rs1, v0)))

   364           case r::rs2 => (front ::: List(r) ::: flats(rs2), Position(j, v0))

   365           case _ => throw new Exception("flats2 i = 0")

   366         }

   367       }

   368       else{

   369         rs match {

   370           case AZERO::rs1 => flats2(front, i - 1, rs1, Position(j - 1, v0))

   371           case AALTS(bs, rs1) ::rs2 => flats2(front:::rs1.map(fuse(bs, _)), i - 1, rs2, Position(j + rs1.length - 1, v0))

   372           case r::rs1 => flats2(front:::List(r), i - 1, rs1, Position(j, v0)) 

   373           case _ => throw new Exception("flats2 i>0")

   374         }

   375       }

   376     }

   377     case _ => throw new Exception("flats2 error")

   378   }

   379 

   380 def deunify(rs_length: Int, v: Val): Val = v match{

   381   case Position(i, v0) => {

   382       if (i <0 ) { println(rs_length, v); throw new Exception("deunify minus") } 

   383       else if (rs_length == 1) {println(v); v}

   384       else if (rs_length - 1 == i) coat(v0, i) 

   385       else coat(Left(v0), i)

   386   }

   387   case _ => throw new Exception("deunify error")

   388 }

   389 

   390 

   391 def bsimp2(r: ARexp, v: Val): (ARexp, Val) = (r, v) match {

   392     case (ASEQ(bs1, r1, r2), Sequ(v1, v2)) => (bsimp2(r1, v1), bsimp2(r2, v2)) match {

   393         case ((AZERO, _), (_, _)) => (AZERO, Undefined)

   394         case ((_, _), (AZERO, _)) => (AZERO, Undefined)

   395         case ((AONE(bs2), v1s) , (r2s, v2s)) => (fuse(bs1 ++ bs2, r2s), v2s)

   396                  // v2 tells how to retrieve bits in r2s, which is enough as the bits 

   397                  // of the first part of the sequence has already been integrated to 

   398                  // the top level of the second regx.

   399         case ((r1s, v1s), (r2s, v2s)) => (ASEQ(bs1, r1s, r2s),  Sequ(v1s, v2s))

   400     }

   401     case (AALTS(bs1, rs), v) => {

   402       val vlist = unify(rs, v)

   403       vlist match {

   404         case Position(i, v0) => {

   405           val v_simp = bsimp2(rs(i), v0)._2

   406           val rs_simp = rs.map(bsimp)

   407           val flat_res = flats2( Nil, i, rs_simp, Position(i, v_simp) )

   408           val dist_res = distinctBy2(flat_res._2, flat_res._1, erase)

   409           val rs_new = dist_res._1

   410           val v_new = deunify(rs_new.length, dist_res._2)

   411           rs_new match {

   412             case Nil => (AZERO, Undefined)

   413             case s :: Nil => (fuse(bs1, s), v_new)

   414             case rs => (AALTS(bs1, rs), v_new)

   415           }

   416         }

   417         case _ => throw new Exception("Funny vlist bsimp2")

   418       }

   419     }

   420     // STAR case

   421     // case ASTAR(bs, r) => ASTAR(bs, bsimp(r))

   422     case (r, v) => (r, v)  

   423   }

   424 

   425 

   426 

   427 val dr = ASEQ(List(),AALTS(List(S),List(AONE(List(Z)), AONE(List(S)))),ASTAR(List(),AALTS(List(),List(ACHAR(List(Z),'a'), ACHAR(List(S),'a')))))

   428 val dv = Sequ(Left(Empty),Stars(List()))

   429 println(bsimp2(dr, dv))

   430   

   431 

   432 /*

   433 def blex_simp2(r: ARexp, s: List[Char]) : Bits = s match {

   434   case Nil => if (bnullable(r)) bmkeps(r) 

   435               else throw new Exception("Not matched")

   436   case c::cs => blex(bsimp2(bder(c, r)), cs)

   437 }

   438 

   439 def blexing_simp2(r: Rexp, s: String) : Val = 

   440   decode(r, blex_simp2(internalise(r), s.toList))

   441 

   442 println(blexing_simp2(reg, "aab"))

   443 */

   444 

   445 // extracts a string from value

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

   447   case Empty => ""

   448   case Chr(c) => c.toString

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

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

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

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

   453 }

   454 

   455 // extracts an environment from a value

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

   457   case Empty => Nil

   458   case Chr(c) => Nil

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

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

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

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

   463 }

   464 

   465 // Some Tests

   466 //============

   467 

   468 /*

   469 def time_needed[T](i: Int, code: => T) = {

   470   val start = System.nanoTime()

   471   for (j <- 1 to i) code

   472   val end = System.nanoTime()

   473   (end - start)/(i * 1.0e9)

   474 }

   475 

   476 

   477 val evil1 = (("a").%) ~ "b"

   478 val evil2 = (((("a").%).%).%) ~ "b"

   479 val evil3 = (("a"~"a") | ("a")).%

   480 

   481 for(i <- 1 to 10000 by 1000) {

   482     println(time_needed(1, blex_simp(internalise(evil1), ("a"*i + "b").toList)))

   483 }

   484 

   485 for(i <- 1 to 10000 by 1000) {

   486     println(time_needed(1, blexing_simp(evil1, "a"*i + "b")))

   487 }

   488 

   489 for(i <- 1 to 10000 by 1000) {

   490     println(time_needed(1, blexing_simp(evil2, "a"*i + "b")))

   491 }

   492 

   493 for(i <- 1 to 10000 by 1000) {

   494     println(time_needed(1, blexing_simp(evil3, "a"*i)))

   495 }

   496 */

   497 

   498 

   499 

   500 

   501 

   502 /////////////////////////

   503 /////////////////////////

   504 ///// Below not relevant

   505 

   506 /*

   507 val rf = ("a" | "ab") ~ ("ab" | "")

   508 println(pre_blexing(internalise(rf), "ab"))

   509 println(blexing(rf, "ab"))

   510 println(blexing_simp(rf, "ab"))

   511 

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

   513 println(pre_blexing(internalise(r0), "ab"))

   514 println(blexing(r0, "ab"))

   515 println(blexing_simp(r0, "ab"))

   516 

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

   518 println(blexing(r1, "abcd"))

   519 println(blexing_simp(r1, "abcd"))

   520 

   521 println(blexing((("" | "a") ~ ("ab" | "b")), "ab"))

   522 println(blexing_simp((("" | "a") ~ ("ab" | "b")), "ab"))

   523 

   524 println(blexing((("" | "a") ~ ("b" | "ab")), "ab"))

   525 println(blexing_simp((("" | "a") ~ ("b" | "ab")), "ab"))

   526 

   527 println(blexing((("" | "a") ~ ("c" | "ab")), "ab"))

   528 println(blexing_simp((("" | "a") ~ ("c" | "ab")), "ab"))

   529 

   530 

   531 // Sulzmann's tests

   532 //==================

   533 

   534 val sulzmann = ("a" | "b" | "ab").%

   535 

   536 println(blexing(sulzmann, "a" * 10))

   537 println(blexing_simp(sulzmann, "a" * 10))

   538 

   539 for (i <- 0 to 4000 by 500) {

   540   println(i + ": " + "%.5f".format(time_needed(1, blexing_simp(sulzmann, "a" * i))))

   541 }

   542 

   543 for (i <- 0 to 15 by 5) {

   544   println(i + ": " + "%.5f".format(time_needed(1, blexing_simp(sulzmann, "ab" * i))))

   545 }

   546 

   547 */

   548 

   549 

   550 // some automatic testing

   551 

   552 /*

   553 def clear() = {

   554   print("")

   555   //print("\33[H\33[2J")

   556 }

   557 

   558 def merge[A](l1: LazyList[A], l2: LazyList[A], l3: LazyList[A]) : LazyList[A] =

   559   l1.head #:: l2.head #:: l3.head #:: merge(l1.tail, l2.tail, l3.tail)

   560 

   561 

   562 // enumerates regular expressions until a certain depth

   563 def enum(rs: LazyList[Rexp]) : LazyList[Rexp] = {

   564   rs #::: enum( (for (r1 <- rs; r2 <- rs) yield ALT(r1, r2)) ++ 

   565                 (for (r1 <- rs; r2 <- rs) yield SEQ(r1, r2)) ++

   566                 (for (r1 <- rs) yield STAR(r1)))

   567 }

   568 

   569 

   570 enum(LazyList(ZERO, ONE, CHAR('a'), CHAR('b'))).take(200).force.mkString("\n")

   571 enum(LazyList(ZERO, ONE, CHAR('a'), CHAR('b'))).take(200_000).force

   572 

   573 

   574 

   575 import scala.util.Try

   576 

   577 def test_mkeps(r: Rexp) = {

   578   val res1 = Try(Some(mkeps(r))).getOrElse(None)

   579   val res2 = Try(Some(decode(r, bmkeps(internalise(r))))).getOrElse(None) 

   580   if (res1 != res2) println(s"Mkeps disagrees on ${r}")

   581   if (res1 != res2) Some(r) else (None)

   582 }

   583 

   584 println("Testing mkeps")

   585 enum(LazyList(ZERO, ONE, CHAR('a'), CHAR('b'))).take(100).exists(test_mkeps(_).isDefined)

   586 //enum(3, "ab").map(test_mkeps).toSet

   587 //enum(3, "abc").map(test_mkeps).toSet

   588 

   589 

   590 //enumerates strings of length n over alphabet cs

   591 def strs(n: Int, cs: String) : Set[String] = {

   592   if (n == 0) Set("")

   593   else {

   594     val ss = strs(n - 1, cs)

   595     ss ++

   596     (for (s <- ss; c <- cs.toList) yield c + s)

   597   }

   598 }

   599 

   600 //tests lexing and lexingB

   601 def tests_inj(ss: Set[String])(r: Rexp) = {

   602   clear()

   603   println(s"Testing ${r}")

   604   for (s <- ss.par) yield {

   605     val res1 = Try(Some(alexing(r, s))).getOrElse(None)

   606     val res2 = Try(Some(alexing_simp(r, s))).getOrElse(None)

   607     if (res1 != res2) println(s"Disagree on ${r} and ${s}")

   608     if (res1 != res2) println(s"   ${res1} !=  ${res2}")

   609     if (res1 != res2) Some((r, s)) else None

   610   }

   611 }

   612 

   613 //println("Testing lexing 1")

   614 //enum(2, "ab").map(tests_inj(strs(2, "ab"))).toSet

   615 //println("Testing lexing 2")

   616 //enum(2, "ab").map(tests_inj(strs(3, "abc"))).toSet

   617 //println("Testing lexing 3")

   618 //enum(3, "ab").map(tests_inj(strs(3, "abc"))).toSet

   619 

   620 

   621 def tests_alexer(ss: Set[String])(r: Rexp) = {

   622   clear()

   623   println(s"Testing ${r}")

   624   for (s <- ss.par) yield {

   625     val d = der('b', r)

   626     val ad = bder('b', internalise(r))

   627     val res1 = Try(Some(encode(inj(r, 'a', alexing(d, s))))).getOrElse(None)

   628     val res2 = Try(Some(pre_alexing(ad, s))).getOrElse(None)

   629     if (res1 != res2) println(s"Disagree on ${r} and 'a'::${s}")

   630     if (res1 != res2) println(s"   ${res1} !=  ${res2}")

   631     if (res1 != res2) Some((r, s)) else None

   632   }

   633 }

   634 

   635 println("Testing alexing 1")

   636 println(enum(2, "ab").map(tests_alexer(strs(2, "ab"))).toSet)

   637 

   638 

   639 def values(r: Rexp) : Set[Val] = r match {

   640   case ZERO => Set()

   641   case ONE => Set(Empty)

   642   case CHAR(c) => Set(Chr(c))

   643   case ALT(r1, r2) => (for (v1 <- values(r1)) yield Left(v1)) ++ 

   644                       (for (v2 <- values(r2)) yield Right(v2))

   645   case SEQ(r1, r2) => for (v1 <- values(r1); v2 <- values(r2)) yield Sequ(v1, v2)

   646   case STAR(r) => (Set(Stars(Nil)) ++ 

   647                   (for (v <- values(r)) yield Stars(List(v)))) 

   648     // to do more would cause the set to be infinite

   649 }

   650 

   651 def tests_bder(c: Char)(r: Rexp) = {

   652   val d = der(c, r)

   653   val vals = values(d)

   654   for (v <- vals) {

   655     println(s"Testing ${r} and ${v}")

   656     val res1 = retrieve(bder(c, internalise(r)), v)

   657     val res2 = encode(inj(r, c, decode(d, retrieve(internalise(der(c, r)), v))))

   658     if (res1 != res2) println(s"Disagree on ${r}, ${v} and der = ${d}")

   659     if (res1 != res2) println(s"   ${res1} !=  ${res2}")

   660     if (res1 != res2) Some((r, v)) else None

   661   }

   662 }

   663 

   664 println("Testing bder/der")

   665 println(enum(2, "ab").map(tests_bder('a')).toSet)

   666 

   667 val er = SEQ(ONE,CHAR('a')) 

   668 val ev = Right(Empty) 

   669 val ed = ALT(SEQ(ZERO,CHAR('a')),ONE)

   670 

   671 retrieve(internalise(ed), ev) // => [true]

   672 internalise(er)

   673 bder('a', internalise(er))

   674 retrieve(bder('a', internalise(er)), ev) // => []

   675 decode(ed, List(true)) // gives the value for derivative

   676 decode(er, List())     // gives the value for original value

   677 

   678 

   679 val dr = STAR(CHAR('a'))

   680 val dr_der = SEQ(ONE,STAR(CHAR('a'))) // derivative of dr

   681 val dr_val = Sequ(Empty,Stars(List())) // value of dr_def

   682 

   683 

   684 val res1 = retrieve(internalise(der('a', dr)), dr_val) // => [true]

   685 val res2 = retrieve(bder('a', internalise(dr)), dr_val) // => [false, true]

   686 decode(dr_der, res1) // gives the value for derivative

   687 decode(dr, res2)     // gives the value for original value

   688 

   689 encode(inj(dr, 'a', decode(dr_der, res1)))

   690 

   691 */