diff -r 9aebc106549b -r ac7a7a9048c6 exps/token1.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/exps/token1.scala	Wed Jan 30 12:28:44 2019 +0000
@@ -0,0 +1,598 @@
+
+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)
+*/
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