diff -r 9aebc106549b -r ac7a7a9048c6 token1.scala
--- a/token1.scala	Wed Jan 30 12:13:41 2019 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,598 +0,0 @@
-
-import scala.language.implicitConversions    
-import scala.language.reflectiveCalls
-import scala.annotation.tailrec   
-
-def distinctBy[B, C](xs: List[B], f: B => C, acc: List[C] = Nil): List[B] = xs match {
-  case Nil => Nil
-  case (x::xs) => {
-    val res = f(x)
-    if (acc.contains(res)) distinctBy(xs, f, acc)  
-    else x::distinctBy(xs, f, res::acc)
-  }
-} 
-
-abstract class Bit
-case object Z extends Bit
-case object S extends Bit
-case class C(c: Char) extends Bit
-
-
-type Bits = List[Bit]
-
-abstract class Action
-case object ST extends Action
-case object NST extends Action
-case object AL extends Action
-
-abstract class PartialValue
-case object Plhdr extends PartialValue
-case object STS extends PartialValue
-case object ENDSTS extends PartialValue
-case class Ch(c: Char) extends PartialValue
-case object Empt extends PartialValue
-case object Seque extends PartialValue
-case class Posi(i: Int) extends PartialValue
-case class RECRD(x: String) extends PartialValue
-case object ALTSTART extends  PartialValue
-case object ALTEND extends PartialValue
-case object RIG extends PartialValue
-case object LEF extends PartialValue
-
-abstract class Rexp 
-case object ZERO extends Rexp
-case object ONE extends Rexp
-case class PRED(f: Char => Boolean) extends Rexp
-case class ALTS(rs: List[Rexp]) extends Rexp 
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 
-case class STAR(r: Rexp) extends Rexp 
-case class RECD(x: String, r: Rexp) extends Rexp
-
-// abbreviations
-def CHAR(c: Char) = PRED(_ == c)
-def ALT(r1: Rexp, r2: Rexp) = ALTS(List(r1, r2))
-def PLUS(r: Rexp) = SEQ(r, STAR(r))
-
-abstract class ARexp 
-case object AZERO extends ARexp
-case class AONE(bs: Bits) extends ARexp
-case class APRED(bs: Bits, f: Char => Boolean) extends ARexp
-case class AALTS(bs: Bits, rs: List[ARexp]) extends ARexp 
-case class ASEQ(bs: Bits, r1: ARexp, r2: ARexp) extends ARexp 
-case class ASTAR(bs: Bits, r: ARexp) extends ARexp 
-
-
-def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, List(r1, r2))
-
-abstract class Val
-case object Empty extends Val
-case class Chr(c: Char) extends Val
-case class Sequ(v1: Val, v2: Val) extends Val
-case class Left(v: Val) extends Val
-case class Right(v: Val) extends Val
-case class Stars(vs: List[Val]) extends Val
-case class Rec(x: String, v: Val) extends Val
-case class Pos(i: Int, v: Val) extends Val
-case object Prd extends Val
-   
-// some convenience for typing in regular expressions
-def charlist2rexp(s : List[Char]): Rexp = s match {
-  case Nil => ONE
-  case c::Nil => CHAR(c)
-  case c::s => SEQ(CHAR(c), charlist2rexp(s))
-}
-implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
-
-implicit def RexpOps(r: Rexp) = new {
-  def | (s: Rexp) = ALT(r, s)
-  def % = STAR(r)
-  def ~ (s: Rexp) = SEQ(r, s)
-}
-
-implicit def stringOps(s: String) = new {
-  def | (r: Rexp) = ALT(s, r)
-  def | (r: String) = ALT(s, r)
-  def % = STAR(s)
-  def ~ (r: Rexp) = SEQ(s, r)
-  def ~ (r: String) = SEQ(s, r)
-  def $ (r: Rexp) = RECD(s, r)
-}
-
-// translation into ARexps
-def fuse(bs: Bits, r: ARexp) : ARexp = r match {
-  case AZERO => AZERO
-  case AONE(cs) => AONE(bs ++ cs)
-  case APRED(cs, f) => APRED(bs ++ cs, f)
-  case AALTS(cs, rs) => AALTS(bs ++ cs, rs)
-  case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)
-  case ASTAR(cs, r) => ASTAR(bs ++ cs, r)
-}
-
-def internalise(r: Rexp) : ARexp = r match {
-  case ZERO => AZERO
-  case ONE => AONE(Nil)
-  case PRED(f) => APRED(Nil, f)
-  case ALTS(List(r1, r2)) => 
-    AALTS(Nil, List(fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2))))
-  case ALTS(r1::rs) => {
-     val AALTS(Nil, rs2) = internalise(ALTS(rs))
-     AALTS(Nil, fuse(List(Z), internalise(r1)) :: rs2.map(fuse(List(S), _)))
-  }
-  case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
-  case STAR(r) => ASTAR(Nil, internalise(r))
-  case RECD(x, r) => internalise(r)
-}
-
-internalise(("a" | "ab") ~ ("b" | ""))
-val action_stack = scala.collection.mutable.ArrayBuffer.empty[Action]
-val next_stack = scala.collection.mutable.ArrayBuffer.empty[Int]
-val regx_stack = scala.collection.mutable.ArrayBuffer.empty[Rexp]
-val pv_stack = scala.collection.mutable.ArrayBuffer.empty[PartialValue]
-var top = 0
-//st is the global var stack, made with a linked list?
-@tailrec
-def decode_stack(sp: Int, bs: Bits): Unit = {
-if(action_stack.isEmpty){
-  return 
-}
-val action = action_stack.last
-action_stack.trimEnd(1)
-val r = regx_stack.last
-regx_stack.trimEnd(1)
-if(action == ST)//we have the rest of the star to finish(ST -> STAR)
-{
-  bs match {
-    case Z::bs => {//pv -> partial value  Each grid in a stack does not hold a whole value but a partial one.
-      pv_stack(sp) = ENDSTS
-      if(next_stack.isEmpty)
-        return 
-      val n = next_stack.last
-      next_stack.trimEnd(1)
-      decode_stack(n, bs)
-    }
-    case S::bs => {
-      for(i <- 0 to next_stack.length - 1){
-        next_stack(i) = next_stack(i) + 1
-      }
-      next_stack += (sp + 1)
-      regx_stack += r  
-      action_stack += ST
-      pv_stack.insert(sp + 1, Plhdr)
-      action_stack += NST
-      regx_stack += r 
-      decode_stack(sp, bs)
-    }
-    case _ => println("Sequence not decodable")
-  }
-
-}
-else if(action == NST){
-  (r, bs) match{
-    case (ONE, bs) => {
-      pv_stack(sp) = Empt
-      if(next_stack.isEmpty)
-        return 
-      val n = next_stack.last
-      next_stack.trimEnd(1)
-      decode_stack(n, bs)
-    }
-    case (PRED(f), C(c)::bs) => {
-      pv_stack(sp) = Ch(c)
-      if(next_stack.isEmpty)
-        return 
-      val n = next_stack.last
-      next_stack.trimEnd(1)
-      decode_stack(n, bs)
-    }
-    case (ALTS(rs), Z::bs1) => {
-      pv_stack(sp) = ALTSTART
-      pv_stack.insert(sp + 1, LEF)
-      pv_stack.insert(sp + 2, Plhdr)
-      pv_stack.insert(sp + 3, ALTEND)
-      for(i <- 0 to next_stack.length - 1){
-        next_stack(i) = next_stack(i) + 3
-      }
-      regx_stack += rs.head
-      action_stack += NST
-      decode_stack(sp + 2, bs1)
-    }
-    case (ALTS(rs), S::bs1) => {
-      pv_stack(sp) = ALTSTART
-      pv_stack.insert(sp + 1, RIG)
-      pv_stack.insert(sp + 2, Plhdr)
-      for(i <- 0 to next_stack.length - 1){
-        next_stack(i) = next_stack(i) + 2
-      }
-      regx_stack += ALTS(rs.tail)
-      action_stack += AL
-      decode_stack(sp + 2, bs1)		
-    }
-      /*
-      val le = rs.length
-      val det = bs.take(le - 1)
-      val chosen =  det.indexWhere(_ == Z)
-      action_stack += NST
-      pv_stack.insert(sp + 1, Plhdr)
-      for(i <- 0 to next_stack.length - 1){
-        next_stack(i) = next_stack(i) + 1
-      }
-      if(chosen ==  -1){
-        pv_stack(sp) = Posi(le)
-        regx_stack += rs(le - 1)
-        decode_stack(sp + 1, bs.drop(le - 1))
-      }
-      else{
-        pv_stack(sp) = Posi(chosen + 1)
-        regx_stack += rs(chosen)
-        decode_stack(sp + 1, bs.drop(chosen + 1))
-      }*/
-    case (SEQ(r1, r2), bs) => {
-      action_stack += NST
-      action_stack += NST
-      for(i <- 0 to next_stack.length - 1){
-        next_stack(i) = next_stack(i) + 2
-      }
-      next_stack += (sp + 2)
-      regx_stack += r2
-      regx_stack += r1
-      pv_stack.insert(sp + 1, Plhdr)
-      pv_stack.insert(sp + 2, Plhdr)
-      pv_stack(sp) = Seque
-      decode_stack(sp + 1, bs)
-    }
-    case (STAR(r1), S::bs) => {
-      action_stack += ST
-      regx_stack += r1
-      action_stack += NST
-      regx_stack += r1
-      for(i <- 0 to next_stack.length - 1){
-        next_stack(i) = next_stack(i) + 2
-      }
-      next_stack += sp + 2
-      pv_stack(sp) = STS
-      pv_stack.insert(sp + 1, Plhdr)
-      pv_stack.insert(sp + 1, Plhdr)
-      decode_stack(sp + 1, bs)
-    }
-    case (STAR(_), Z::bs) => {
-      pv_stack(sp) = STS 
-      pv_stack.insert(sp + 1, ENDSTS)
-      if(next_stack.isEmpty)
-        return 
-      for(i <- 0 to next_stack.length - 1){
-        next_stack(i) = next_stack(i) + 1
-      }
-      val n = next_stack.last
-      next_stack.trimEnd(1)
-      decode_stack(n, bs)
-    }
-    case (RECD(x, r1), bs) => {
-      pv_stack(sp) = RECRD(x)
-      pv_stack.insert(sp + 1, Plhdr)
-      for(i <- 0 to next_stack.length - 1){
-        next_stack(i) = next_stack(i) + 1
-      }
-      action_stack += NST
-      regx_stack += r1
-      decode_stack(sp + 1, bs)
-    }//shouldn't go beyond this point
-    case (_, _) => println("Error with NST")
-  }
-}
-else{//action is AL
-  r match {
-    case (ALTS(r1::Nil)) => {
-      pv_stack.insert(sp + 1, ALTEND)
-      for(i <- 0 to next_stack.length - 1){
-        next_stack(i) = next_stack(i) + 1
-      }
-      action_stack += NST
-      regx_stack += r1
-      decode_stack(sp, bs)
-    }
-    case (ALTS(rs)) => {
-      bs match {
-        case (Z::bs1) => {
-          pv_stack(sp) = LEF
-          pv_stack.insert(sp + 1, ALTEND)
-          pv_stack.insert(sp + 1, Plhdr)
-          for(i <- 0 to next_stack.length - 1){
-            next_stack(i) = next_stack(i) + 2
-          }
-          regx_stack += rs.head
-          action_stack += NST
-          decode_stack(sp + 1, bs1)
-        }
-        case (S::bs2) => {
-          pv_stack(sp) = RIG
-          pv_stack.insert(sp + 1, Plhdr)
-          for(i <- 0 to next_stack.length - 1){
-            next_stack(i) = next_stack(i) + 1
-          }
-          regx_stack += ALTS(rs.tail)
-          action_stack += AL
-          decode_stack(sp + 1, bs2)
-        }
-        case _ => println("Not decodable")
-      }
-    }
-    case (rs) => println(r,bs)
-  }
-}
-}
-//advantage: may decode chunks of bits
-def decode(r: Rexp, bs: Bits) = {
-  action_stack.clear()
-  next_stack.clear()
-  regx_stack.clear()
-  pv_stack.clear()
-
-  action_stack += NST
-  regx_stack += r
-  pv_stack += Plhdr
-
-  decode_stack(0, bs)
-}
-/*
-def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
-  case (v, Nil) => v
-  case _ => throw new Exception("Not decodable")
-}
-*/
-
-//erase function: extracts the regx from Aregex
-def erase(r:ARexp): Rexp = r match{
-  case AZERO => ZERO
-  case AONE(_) => ONE
-  case APRED(bs, f) => PRED(f)
-  case AALTS(bs, rs) => ALTS(rs.map(erase(_)))
-  case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))
-  case ASTAR(cs, r)=> STAR(erase(r))
-}
-
-// nullable function: tests whether the aregular 
-// expression can recognise the empty string
-def nullable (r: ARexp) : Boolean = r match {
-  case AZERO => false
-  case AONE(_) => true
-  case APRED(_,_) => false
-  case AALTS(_, rs) => rs.exists(nullable)
-  case ASEQ(_, r1, r2) => nullable(r1) && nullable(r2)
-  case ASTAR(_, _) => true
-}
-
-def mkepsBC(r: ARexp) : Bits = r match {
-  case AONE(bs) => bs
-  case AALTS(bs, rs) => {
-    val n = rs.indexWhere(nullable)
-    bs ++ mkepsBC(rs(n))
-  }
-  case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
-  case ASTAR(bs, r) => bs ++ List(Z)
-}
-
-// derivative of a regular expression w.r.t. a character
-def der(c: Char, r: ARexp) : ARexp = r match {
-  case AZERO => AZERO
-  case AONE(_) => AZERO
-  case APRED(bs, f) => if (f(c)) AONE(bs:::List(C(c))) else AZERO
-  case AALTS(bs, rs) => AALTS(bs, rs.map(der(c, _)))
-  case ASEQ(bs, r1, r2) => 
-    if (nullable(r1)) AALT(bs, ASEQ(Nil, der(c, r1), r2), fuse(mkepsBC(r1), der(c, r2)))
-    else ASEQ(bs, der(c, r1), r2)
-  case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), der(c, r)), ASTAR(Nil, r))
-}
-
-// derivative w.r.t. a string (iterates der)
-@tailrec
-def ders (s: List[Char], r: ARexp) : ARexp = s match {
-  case Nil => r
-  case c::s => ders(s, der(c, r))
-}
-
-// main unsimplified lexing function (produces a value)
-def lex(r: ARexp, s: List[Char]) : Bits = s match {
-  case Nil => if (nullable(r)) mkepsBC(r) else throw new Exception("Not matched")
-  case c::cs => lex(der(c, r), cs)
-}
-
-def pre_lexing(r: Rexp, s: String) = lex(internalise(r), s.toList)
-//def lexing(r: Rexp, s: String) : Val = decode(r, lex(internalise(r), s.toList))
-
-
-def flats(rs: List[ARexp]): List[ARexp] = rs match {
-    case Nil => Nil
-    case AZERO :: rs1 => flats(rs1)
-    case AALTS(bs, rs1) :: rs2 => rs1.map(fuse(bs, _)) ::: flats(rs2)
-    case r1 :: rs2 => r1 :: flats(rs2)
-  }
-
-def simp(r: ARexp): ARexp = r match {
-  case ASEQ(bs1, r1, r2) => (simp(r1), simp(r2)) match {
-      case (AZERO, _) => AZERO
-      case (_, AZERO) => AZERO
-      case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
-      case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
-  }
-  case AALTS(bs1, rs) => distinctBy(flats(rs.map(simp)), erase) match {
-    case Nil => AZERO
-    case s :: Nil => fuse(bs1, s)
-    case rs => AALTS(bs1, rs)  
-  }
-  case r => r
-}
-
-def ders_simp (s: List[Char], r: ARexp) : ARexp = s match {
-  case Nil => r
-  case c::s => ders_simp(s, simp(der(c, r)))
-}
-
-def lex_simp(r: ARexp, s: List[Char]) : Bits = s match {
-  case Nil => {
-    if (nullable(r)) {
-      //println(asize(r))
-      mkepsBC(r)
-    }
-   else throw new Exception("Not matched")
-  }
-  case c::cs => lex_simp(simp(der(c, r)), cs)
-}
-
-//size: of a Aregx for testing purposes 
-def size(r: Rexp) : Int = r match {
-  case ZERO => 1
-  case ONE => 1
-  case PRED(_) => 1
-  case SEQ(r1, r2) => 1 + size(r1) + size(r2)
-  case ALTS(rs) => 1 + rs.map(size).sum
-  case STAR(r) => 1 + size(r)
-}
-
-def asize(a: ARexp) = size(erase(a))
-
-
-// decoding does not work yet
-def lexing_simp(r: Rexp, s: String) = {
-  val final_derivative = lex_simp(internalise(r), s.toList)
-  println("The length of bit sequence:")
-  println((final_derivative.length))
-  //println(final_derivative)
-  decode(r, final_derivative) 
-  //println(vsize(value))
-}
-
-
-def vsize(v: Val): Int = v match {
-  case Empty => 1
-  case Chr(c) => 1
-  case Sequ(v1, v2) => vsize(v1) + vsize(v2) + 1
-  case Left(v1) => vsize(v1) + 1
-  case Right(v1) => vsize(v1) + 1
-  case Stars(vs) => vs.map(vsize(_)).sum + 1
-  case Rec(x, v1) => vsize(v1) + 1
-  case Pos(i, v1) => vsize(v1) + 1
-  case Prd => 1
-}
-
-
-// Lexing Rules for a Small While Language
-
-//symbols
-val SYM = PRED("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ".contains(_))
-//digits
-val DIGIT = PRED("0123456789".contains(_))
-//identifiers
-val ID = SYM ~ (SYM | DIGIT).% 
-//numbers
-val NUM = PLUS(DIGIT)
-//keywords
-val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
-//semicolons
-val SEMI: Rexp = ";"
-//operators
-val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
-//whitespaces
-val WHITESPACE = PLUS(" " | "\n" | "\t")
-//parentheses
-val RPAREN: Rexp = ")"
-val LPAREN: Rexp = "("
-val BEGIN: Rexp = "{"
-val END: Rexp = "}"
-//strings...but probably needs not
-val STRING: Rexp = "\"" ~ SYM.% ~ "\""
-
-
-
-val WHILE_REGS = (("k" $ KEYWORD) | 
-                  ("i" $ ID) | 
-                  ("o" $ OP) | 
-                  ("n" $ NUM) | 
-                  ("s" $ SEMI) | 
-                  ("str" $ STRING) |
-                  ("p" $ (LPAREN | RPAREN)) | 
-                  ("b" $ (BEGIN | END)) | 
-                  ("w" $ WHITESPACE)).%
-
-// filters out all white spaces
-//def tokenise(r: Rexp, s: String) = 
-//  env(lexing_simp(r, s)).filterNot { _._1 == "w"}
-
-
-//reads the string from a file 
-//def fromFile(name: String) : String = 
-//  io.Source.fromFile(name).mkString
-
-//def tokenise_file(r: Rexp, name: String) = 
-//  tokenise(r, fromFile(name))
- 
-
-// Some Tests
-//============
-def compute_and_print(r: Rexp, s: String){
-  //println(r)
-  //println(s)
-  lexing_simp(r, s)
-  println(pv_stack)
-}
-println("simple tests:")
-/*
-println(lexing_simp((SYM.%), "abcd"))
-println(lexing_simp(((SYM.%) | NUM), "12345"))
-println(lexing_simp((WHILE_REGS), "abcd"))
-println(lexing_simp((WHILE_REGS), "12345"))
-println(lexing_simp((WHILE_REGS), "\nwrite \"Fib\";"))
-*/
-compute_and_print((SYM.%), "abcd")
-compute_and_print(((SYM.%) | NUM), "12345")
-compute_and_print((WHILE_REGS), "abcd")
-compute_and_print((WHILE_REGS), "12345")
-compute_and_print((WHILE_REGS), "\nwrite \"Fib\";")
-
-def time[T](code: => T) = {
-  val start = System.nanoTime()
-  val result = code
-  val end = System.nanoTime()
-  println((end - start)/1.0e9)
-  result
-}
-
-val prog2 = """
-write "Fib";
-read n;
-minus1 := 0;
-minus2 := 1;
-while n > 0 do {
-  temp := minus2;
-  minus2 := minus1 + minus2;
-  minus1 := temp;
-  n := n -x 1
-};
-write "Result";
-write minus2
-"""
-/*
-
-val prog2 = """
-write "Fib";
-"""
-
-*/
-
-println("Iteration test with fib")
-for (i <- 900 to 1000 by 50) {
-  print(i.toString + ":  ")
-  time(lexing_simp((WHILE_REGS), (prog2 * i)))
-  //time(lex_simp(internalise(WHILE_REGS), (prog2 * i).toList))
-}
-
-
-/*
-def recurseTest(i:Int):Unit={
-   try{
-      recurseTest(i+1)
-   } catch { case e:java.lang.StackOverflowError => 
-      println("Recursion depth on this system is " + i + ".")
-   }
-}
-recurseTest(0)
-*/
\ No newline at end of file