# HG changeset patch
# User Christian Urban <urbanc@in.tum.de>
# Date 1548925670 0
# Node ID db329a4d2bc0b09fcd77b1fc468ea11d43bb8f22
# Parent  ac7a7a9048c65049ba2e8b36fcb6c6ac058815df
updated

diff -r ac7a7a9048c6 -r db329a4d2bc0 exps/both.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/exps/both.scala	Thu Jan 31 09:07:50 2019 +0000
@@ -0,0 +1,576 @@
+
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls
+import scala.annotation.tailrec   
+import scala.util.Try
+
+def escape(raw: String) : String = {
+  import scala.reflect.runtime.universe._
+  Literal(Constant(raw)).toString
+}
+
+def esc2(r: (String, String)) = (escape(r._1), escape(r._2))
+
+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]
+
+// usual regular expressions
+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))
+
+// annotated regular expressions
+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 
+
+// abbreviations
+def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, List(r1, r2))
+
+// values
+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
+
+
+   
+// 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)
+}
+
+
+//--------------------------------------------------------------------------------------------------------
+// START OF NON-BITCODE PART
+//
+
+// nullable function: tests whether the regular 
+// expression can recognise the empty string
+def nullable (r: Rexp) : Boolean = r match {
+  case ZERO => false
+  case ONE => true
+  case PRED(_) => false
+  case ALTS(rs) => rs.exists(nullable)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+  case STAR(_) => true
+  case RECD(_, r) => nullable(r)
+}
+
+// derivative of a regular expression w.r.t. a character
+def der (c: Char, r: Rexp) : Rexp = r match {
+  case ZERO => ZERO
+  case ONE => ZERO
+  case PRED(f) => if (f(c)) ONE else ZERO
+  case ALTS(List(r1, r2)) => ALTS(List(der(c, r1), der(c, r2)))
+  case SEQ(r1, r2) => 
+    if (nullable(r1)) ALTS(List(SEQ(der(c, r1), r2), der(c, r2)))
+    else SEQ(der(c, r1), r2)
+  case STAR(r) => SEQ(der(c, r), STAR(r))
+  case RECD(_, r1) => der(c, r1)
+}
+
+
+def flatten(v: Val) : String = v match {
+  case Empty => ""
+  case Chr(c) => c.toString
+  case Left(v) => flatten(v)
+  case Right(v) => flatten(v)
+  case Sequ(v1, v2) => flatten(v1) + flatten(v2)
+  case Stars(vs) => vs.map(flatten).mkString
+  case Rec(_, v) => flatten(v)
+}
+
+// extracts an environment from a value
+def env(v: Val) : List[(String, String)] = v match {
+  case Empty => Nil
+  case Chr(c) => Nil
+  case Left(v) => env(v)
+  case Right(v) => env(v)
+  case Sequ(v1, v2) => env(v1) ::: env(v2)
+  case Stars(vs) => vs.flatMap(env)
+  case Rec(x, v) => (x, flatten(v))::env(v)
+}
+
+
+// injection part
+def mkeps(r: Rexp) : Val = r match {
+  case ONE => Empty
+  case ALTS(List(r1, r2)) => 
+    if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
+  case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))
+  case STAR(r) => Stars(Nil)
+  case RECD(x, r) => Rec(x, mkeps(r))
+}
+
+def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {
+  case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+  case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))
+  case (ALTS(List(r1, r2)), Left(v1)) => Left(inj(r1, c, v1))
+  case (ALTS(List(r1, r2)), Right(v2)) => Right(inj(r2, c, v2))
+  case (PRED(_), Empty) => Chr(c) 
+  case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
+}
+
+// lexing without simplification
+def lex(r: Rexp, s: List[Char]) : Val = s match {
+  case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")
+  case c::cs => inj(r, c, lex(der(c, r), cs))
+}
+
+def lexing(r: Rexp, s: String) : Val = lex(r, s.toList)
+
+//println(lexing(("ab" | "ab") ~ ("b" | ONE), "ab"))
+
+// some "rectification" functions for simplification
+def F_ID(v: Val): Val = v
+def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v))
+def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v))
+def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
+  case Right(v) => Right(f2(v))
+  case Left(v) => Left(f1(v))
+}
+def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
+  case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))
+}
+def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 
+  (v:Val) => Sequ(f1(Empty), f2(v))
+def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 
+  (v:Val) => Sequ(f1(v), f2(Empty))
+def F_RECD(f: Val => Val) = (v:Val) => v match {
+  case Rec(x, v) => Rec(x, f(v))
+}
+def F_ERROR(v: Val): Val = throw new Exception("error")
+
+// simplification of regular expressions returning also an
+// rectification function; no simplification under STAR 
+def simp(r: Rexp): (Rexp, Val => Val) = r match {
+  case ALTS(List(r1, r2)) => {
+    val (r1s, f1s) = simp(r1)
+    val (r2s, f2s) = simp(r2)
+    (r1s, r2s) match {
+      case (ZERO, _) => (r2s, F_RIGHT(f2s))
+      case (_, ZERO) => (r1s, F_LEFT(f1s))
+      case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))
+                else (ALTS(List(r1s, r2s)), F_ALT(f1s, f2s)) 
+    }
+  }
+  case SEQ(r1, r2) => {
+    val (r1s, f1s) = simp(r1)
+    val (r2s, f2s) = simp(r2)
+    (r1s, r2s) match {
+      case (ZERO, _) => (ZERO, F_ERROR)
+      case (_, ZERO) => (ZERO, F_ERROR)
+      case (ONE, _) => (r2s, F_SEQ_Empty1(f1s, f2s))
+      case (_, ONE) => (r1s, F_SEQ_Empty2(f1s, f2s))
+      case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))
+    }
+  }
+  case RECD(x, r1) => {
+    val (r1s, f1s) = simp(r1)
+    (RECD(x, r1s), F_RECD(f1s))
+  }
+  case r => (r, F_ID)
+}
+
+def lex_simp(r: Rexp, s: List[Char]) : Val = s match {
+  case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")
+  case c::cs => {
+    val (r_simp, f_simp) = simp(der(c, r))
+    inj(r, c, f_simp(lex_simp(r_simp, cs)))
+  }
+}
+
+def lexing_simp(r: Rexp, s: String) : Val = lex_simp(r, s.toList)
+
+println(lexing_simp(("a" | "ab") ~ ("b" | ""), "ab"))
+
+
+def tokenise_simp(r: Rexp, s: String) = env(lexing_simp(r, s)).map(esc2)
+
+//--------------------------------------------------------------------------------------------------------
+// BITCODED PART
+
+
+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)
+}
+
+// translation into ARexps
+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" | ""))
+
+// decoding of values from bit sequences
+def decode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {
+  case (ONE, bs) => (Empty, bs)
+  case (PRED(f), C(c)::bs) => (Chr(c), bs)
+  case (ALTS(r::Nil), bs) => decode_aux(r, bs)
+  case (ALTS(rs), bs) => bs match {
+    case Z::bs1 => {
+      val (v, bs2) = decode_aux(rs.head, bs1)
+      (Left(v), bs2)
+    }
+    case S::bs1 => {
+      val (v, bs2) = decode_aux(ALTS(rs.tail), bs1)
+      (Right(v), bs2)			
+    }
+  }
+  case (SEQ(r1, r2), bs) => {
+    val (v1, bs1) = decode_aux(r1, bs)
+    val (v2, bs2) = decode_aux(r2, bs1)
+    (Sequ(v1, v2), bs2)
+  }
+  case (STAR(r1), S::bs) => {
+    val (v, bs1) = decode_aux(r1, bs)
+    val (Stars(vs), bs2) = decode_aux(STAR(r1), bs1)
+    (Stars(v::vs), bs2)
+  }
+  case (STAR(_), Z::bs) => (Stars(Nil), bs)
+  case (RECD(x, r1), bs) => {
+    val (v, bs1) = decode_aux(r1, bs)
+    (Rec(x, v), bs1)
+  }
+}
+
+def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
+  case (v, Nil) => v
+  case _ => throw new Exception("Not decodable")
+}
+
+
+//erase function: extracts a Rexp from Arexp
+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))
+}
+
+
+// bnullable function: tests whether the aregular 
+// expression can recognise the empty string
+def bnullable (r: ARexp) : Boolean = r match {
+  case AZERO => false
+  case AONE(_) => true
+  case APRED(_,_) => false
+  case AALTS(_, rs) => rs.exists(bnullable)
+  case ASEQ(_, r1, r2) => bnullable(r1) && bnullable(r2)
+  case ASTAR(_, _) => true
+}
+
+def bmkeps(r: ARexp) : Bits = r match {
+  case AONE(bs) => bs
+  case AALTS(bs, rs) => {
+    val n = rs.indexWhere(bnullable)
+    bs ++ bmkeps(rs(n))
+  }
+  case ASEQ(bs, r1, r2) => bs ++ bmkeps(r1) ++ bmkeps(r2)
+  case ASTAR(bs, r) => bs ++ List(Z)
+}
+
+// derivative of a regular expression w.r.t. a character
+def bder(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(bder(c, _)))
+  case ASEQ(bs, r1, r2) => 
+    if (bnullable(r1)) AALT(bs, ASEQ(Nil, bder(c, r1), r2), fuse(bmkeps(r1), bder(c, r2)))
+    else ASEQ(bs, bder(c, r1), r2)
+  case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), bder(c, r)), ASTAR(Nil, r))
+}
+
+
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders(s, der(c, r))
+}
+
+
+// derivative w.r.t. a string (iterates bder)
+@tailrec
+def bders (s: List[Char], r: ARexp) : ARexp = s match {
+  case Nil => r
+  case c::s => bders(s, bder(c, r))
+}
+
+
+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 bsimp(r: ARexp): ARexp = r match {
+  case ASEQ(bs1, r1, r2) => (bsimp(r1), bsimp(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(bsimp)), erase) match {
+    case Nil => AZERO
+    case s :: Nil => fuse(bs1, s)
+    case rs => AALTS(bs1, rs)  
+  }
+  case r => r
+}
+
+def bders_simp (s: List[Char], r: ARexp) : ARexp = s match {
+  case Nil => r
+  case c::s => bders_simp(s, bsimp(bder(c, r)))
+}
+
+def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
+  case Nil => if (bnullable(r)) bmkeps(r)
+	      else throw new Exception("Not matched")
+  case c::cs => blex_simp(bsimp(bder(c, r)), cs)
+}
+
+
+def blexing_simp(r: Rexp, s: String) : Val = 
+  decode(r, blex_simp(internalise(r), s.toList))
+
+def btokenise_simp(r: Rexp, s: String) = env(blexing_simp(r, s)).map(esc2)
+
+//----------------------------------------------------------------------------
+// This bsimp is the original slow one
+/*
+def bsimp(r: ARexp): ARexp = r match {
+  case ASEQ(bs1, r1, r2) => (bsimp(r1), bsimp(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(bsimp)), erase) match {
+      case Nil => AZERO
+      case s :: Nil => fuse(bs1, s)
+      case rs => AALTS(bs1, rs)  
+    }
+  }
+  case r => r
+}
+*/
+
+
+//----------------------------------------------------------------------------
+//   Testing
+//============
+
+def time[T](code: => T) = {
+  val start = System.nanoTime()
+  val result = code
+  val end = System.nanoTime()
+  ((end - start)/1.0e9).toString
+  //result
+}
+
+//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))
+
+
+// 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 = STAR(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)).%
+
+
+// Some Small Tests
+//==================
+
+/*
+println("simple tests:")
+println(blexing_simp((SYM.%), "abcd"))
+println(blexing_simp(((SYM.%) | ((SYM.% | NUM).%)), "12345"))
+println(blexing_simp((WHILE_REGS), "abcd"))
+println(blexing_simp((WHILE_REGS), "12345"))
+println(blexing_simp((WHILE_REGS), """write "Fib";"""))
+*/
+
+
+// Bigger Tests
+//==============
+
+
+val fib_prog = """
+write "Fib";
+read n;
+minus1 := 0;
+minus2 := 1;
+while n > 0 do {
+  temp := minus2;
+  minus2 := minus1 + minus2;
+  minus1 := temp;
+  n := n - 1
+};
+write "Result";
+write minus2
+"""
+
+
+println("fib prog tests :")
+println(tokenise_simp(WHILE_REGS, fib_prog))
+println(btokenise_simp(WHILE_REGS, fib_prog))
+println(time(tokenise_simp(WHILE_REGS, fib_prog * 7)))
+println(time(btokenise_simp(WHILE_REGS, fib_prog * 7)))
+println("equal? " + (tokenise_simp(WHILE_REGS, fib_prog) == btokenise_simp(WHILE_REGS, fib_prog)))
+
+
+
+
+
+//testing the two lexings produce the same value
+//enumerates strings of length n over alphabet cs
+def strs(n: Int, cs: String) : Set[String] = {
+  if (n == 0) Set("")
+  else {
+    val ss = strs(n - 1, cs)
+    ss ++
+    (for (s <- ss; c <- cs.toList) yield c + s)
+  }
+}
+def enum(n: Int, s: String) : Stream[Rexp] = n match {
+  case 0 => ZERO #:: ONE #:: s.toStream.map(CHAR)
+  case n => {  
+    val rs = enum(n - 1, s)
+    rs #:::
+    (for (r1 <- rs; r2 <- rs) yield ALT(r1, r2)) #:::
+    (for (r1 <- rs; r2 <- rs) yield SEQ(r1, r2)) #:::
+    (for (r1 <- rs) yield STAR(r1))
+  }
+}
+
+//tests blexing and lexing
+def tests(ss: Set[String])(r: Rexp) = {
+  //println(s"Testing ${r}")
+  for (s <- ss.par) yield {
+    val res1 = Try(Some(lexing_simp(r, s))).getOrElse(None)
+    val res2 = Try(Some(blexing_simp(r, s))).getOrElse(None)
+    if (res1 != res2) 
+      { println(s"Disagree on ${r} and ${s}")
+	println(s"   ${res1} !=  ${res2}")
+	Some((r, s)) } else None
+  }
+}
+
+
+println("Partial searching: ")
+enum(2, "abc").map(tests(strs(3, "abc"))).toSet
diff -r ac7a7a9048c6 -r db329a4d2bc0 exps/token1.scala
--- a/exps/token1.scala	Wed Jan 30 12:28:44 2019 +0000
+++ b/exps/token1.scala	Thu Jan 31 09:07:50 2019 +0000
@@ -20,25 +20,6 @@
 
 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
@@ -61,7 +42,7 @@
 case class ASEQ(bs: Bits, r1: ARexp, r2: ARexp) extends ARexp 
 case class ASTAR(bs: Bits, r: ARexp) extends ARexp 
 
-
+// abbreviations
 def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, List(r1, r2))
 
 abstract class Val
@@ -72,8 +53,8 @@
 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 {
@@ -124,221 +105,43 @@
 }
 
 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)
+
+def decode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {
+  case (ONE, bs) => (Empty, bs)
+  case (PRED(f), C(c)::bs) => (Chr(c), bs)
+  case (ALTS(r::Nil), bs) => decode_aux(r, bs)
+  case (ALTS(rs), bs) => bs match {
+    case Z::bs1 => {
+      val (v, bs2) = decode_aux(rs.head, bs1)
+      (Left(v), bs2)
     }
-    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 S::bs1 => {
+      val (v, bs2) = decode_aux(ALTS(rs.tail), bs1)
+      (Right(v), bs2)			
     }
-    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")
+  }
+  case (SEQ(r1, r2), bs) => {
+    val (v1, bs1) = decode_aux(r1, bs)
+    val (v2, bs2) = decode_aux(r2, bs1)
+    (Sequ(v1, v2), bs2)
+  }
+  case (STAR(r1), S::bs) => {
+    val (v, bs1) = decode_aux(r1, bs)
+    val (Stars(vs), bs2) = decode_aux(STAR(r1), bs1)
+    (Stars(v::vs), bs2)
+  }
+  case (STAR(_), Z::bs) => (Stars(Nil), bs)
+  case (RECD(x, r1), bs) => {
+    val (v, bs1) = decode_aux(r1, bs)
+    (Rec(x, v), bs1)
   }
 }
-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{
@@ -405,7 +208,7 @@
     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 {
@@ -462,19 +265,6 @@
 }
 
 
-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
@@ -528,25 +318,16 @@
 
 // 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\";")
+println(lexing_simp((WHILE_REGS), """write "Fib";"""))
+
+
 
 def time[T](code: => T) = {
   val start = System.nanoTime()
@@ -585,14 +366,3 @@
   //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