# HG changeset patch
# User Chengsong
# Date 1643585791 0
# Node ID 6291181fad07de91ed58763011e2e0531e4c1bc4
# Parent  cc8e231529fb408fffde99bda9d3803aafc4bb75
blexer1 for size bound with strongDB

diff -r cc8e231529fb -r 6291181fad07 thys2/blexer1.sc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/thys2/blexer1.sc	Sun Jan 30 23:36:31 2022 +0000
@@ -0,0 +1,709 @@
+// A simple lexer inspired by work of Sulzmann & Lu
+//==================================================
+//
+// Call the test cases with 
+//
+//   amm lexer.sc small
+//   amm lexer.sc fib
+//   amm lexer.sc loops
+//   amm lexer.sc email
+//
+//   amm lexer.sc all
+
+
+// regular expressions including records
+abstract class Rexp 
+case object ZERO extends Rexp
+case object ONE extends Rexp
+case object ANYCHAR extends Rexp
+case class CHAR(c: Char) extends Rexp
+case class ALTS(r1: Rexp, r2: 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  
+case class NTIMES(n: Int, r: Rexp) extends Rexp
+case class OPTIONAL(r: Rexp) extends Rexp
+case class NOT(r: Rexp) extends Rexp
+                // records for extracting strings or tokens
+  
+// 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
+case class Ntime(vs: List[Val]) extends Val
+case class Optionall(v: Val) extends Val
+case class Nots(s: String) extends Val
+
+
+
+abstract class Bit
+case object Z extends Bit
+case object S extends Bit
+
+
+type Bits = List[Bit]
+
+abstract class ARexp 
+case object AZERO extends ARexp
+case class AONE(bs: Bits) extends ARexp
+case class ACHAR(bs: Bits, c: Char) 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 
+case class ANOT(bs: Bits, r: ARexp) extends ARexp
+case class AANYCHAR(bs: Bits) extends ARexp
+
+
+   
+// 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) = ALTS(r, s)
+  def % = STAR(r)
+  def ~ (s: Rexp) = SEQ(r, s)
+}
+
+implicit def stringOps(s: String) = new {
+  def | (r: Rexp) = ALTS(s, r)
+  def | (r: String) = ALTS(s, r)
+  def % = STAR(s)
+  def ~ (r: Rexp) = SEQ(s, r)
+  def ~ (r: String) = SEQ(s, r)
+  def $ (r: Rexp) = RECD(s, r)
+}
+
+def nullable(r: Rexp) : Boolean = r match {
+  case ZERO => false
+  case ONE => true
+  case CHAR(_) => false
+  case ANYCHAR => false
+  case ALTS(r1, r2) => nullable(r1) || nullable(r2)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+  case STAR(_) => true
+  case RECD(_, r1) => nullable(r1)
+  case NTIMES(n, r) => if (n == 0) true else nullable(r)
+  case OPTIONAL(r) => true
+  case NOT(r) => !nullable(r)
+}
+
+def der(c: Char, r: Rexp) : Rexp = r match {
+  case ZERO => ZERO
+  case ONE => ZERO
+  case CHAR(d) => if (c == d) ONE else ZERO
+  case ANYCHAR => ONE 
+  case ALTS(r1, r2) => ALTS(der(c, r1), der(c, r2))
+  case SEQ(r1, r2) => 
+    if (nullable(r1)) ALTS(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)
+  case NTIMES(n, r) => if(n > 0) SEQ(der(c, r), NTIMES(n - 1, r)) else ZERO
+  case OPTIONAL(r) => der(c, r)
+  case NOT(r) =>  NOT(der(c, r))
+}
+
+
+// extracts a string from a value
+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 Ntime(vs) => vs.map(flatten).mkString
+  case Optionall(v) => flatten(v)
+  case Rec(_, v) => flatten(v)
+}
+
+
+// extracts an environment from a value;
+// used for tokenising a string
+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 Ntime(vs) => vs.flatMap(env)
+  case Rec(x, v) => (x, flatten(v))::env(v)
+  case Optionall(v) => env(v)
+  case Nots(s) => ("Negative", s) :: Nil
+}
+
+
+// The injection and mkeps part of the lexer
+//===========================================
+
+def mkeps(r: Rexp) : Val = r match {
+  case ONE => Empty
+  case ALTS(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))
+  case NTIMES(n, r) => Ntime(List.fill(n)(mkeps(r)))
+  case OPTIONAL(r) => Optionall(Empty)
+  case NOT(rInner) => if(nullable(rInner)) throw new Exception("error")  
+                         else Nots("")//Nots(s.reverse.toString)
+//   case NOT(ZERO) => Empty
+//   case NOT(CHAR(c)) => Empty
+//   case NOT(SEQ(r1, r2)) => Sequ(mkeps(NOT(r1)), mkeps(NOT(r2)))
+//   case NOT(ALTS(r1, r2)) => if(!nullable(r1)) Left(mkeps(NOT(r1))) else Right(mkeps(NOT(r2)))
+//   case NOT(STAR(r)) => Stars(Nil) 
+
+}
+
+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(r1, r2), Left(v1)) => Left(inj(r1, c, v1))
+  case (ALTS(r1, r2), Right(v2)) => Right(inj(r2, c, v2))
+  case (CHAR(d), Empty) => Chr(c) 
+  case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
+  case (NTIMES(n, r), Sequ(v1, Ntime(vs))) => Ntime(inj(r, c, v1)::vs)
+  case (OPTIONAL(r), v) => Optionall(inj(r, c, v))
+  case (NOT(r), Nots(s)) => Nots(c.toString ++ s)
+  case (ANYCHAR, Empty) => Chr(c)
+}
+
+// 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_ERROR(v: Val): Val = throw new Exception("error")
+
+// simplification
+def simp(r: Rexp): (Rexp, Val => Val) = r match {
+  case ALTS(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 (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 r => (r, F_ID)
+}
+
+// lexing functions including simplification
+def lex_simp(r: Rexp, s: List[Char]) : Val = s match {
+  case Nil => if (nullable(r)) mkeps(r) else 
+    { throw new Exception(s"lexing error $r not nullable") } 
+  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) = 
+  env(lex_simp(r, s.toList))
+
+// The Lexing Rules for the WHILE Language
+
+def PLUS(r: Rexp) = r ~ r.%
+
+def Range(s : List[Char]) : Rexp = s match {
+  case Nil => ZERO
+  case c::Nil => CHAR(c)
+  case c::s => ALTS(CHAR(c), Range(s))
+}
+def RANGE(s: String) = Range(s.toList)
+
+val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_")
+val DIGIT = RANGE("0123456789")
+val ID = SYM ~ (SYM | DIGIT).% 
+val NUM = PLUS(DIGIT)
+val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" 
+val SEMI: Rexp = ";"
+val OP: Rexp = ":=" | "=" | "-" | "+" | "*" | "!=" | "<" | ">"
+val WHITESPACE = PLUS(" " | "\n" | "\t" | "\r")
+val RPAREN: Rexp = "{"
+val LPAREN: Rexp = "}"
+val STRING: Rexp = "\"" ~ SYM.% ~ "\""
+
+
+//ab \ a --> 1b
+//
+val WHILE_REGS = (("k" $ KEYWORD) | 
+                  ("i" $ ID) | 
+                  ("o" $ OP) | 
+                  ("n" $ NUM) | 
+                  ("s" $ SEMI) | 
+                  ("str" $ STRING) |
+                  ("p" $ (LPAREN | RPAREN)) | 
+                  ("w" $ WHITESPACE)).%
+
+val NREGS = NTIMES(5, OPTIONAL(SYM))
+val NREGS1 = ("test" $ NREGS)
+// Two Simple While Tests
+//========================
+val NOTREG = "hehe" ~ NOT((ANYCHAR.%) ~ "haha" ~ (ANYCHAR.%))
+
+
+  // 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 ACHAR(_,_) => false
+    case AALTS(_, rs) => rs.exists(bnullable)
+    case ASEQ(_, r1, r2) => bnullable(r1) && bnullable(r2)
+    case ASTAR(_, _) => true
+    case ANOT(_, rn) => !bnullable(rn)
+  }
+
+def mkepsBC(r: ARexp) : Bits = r match {
+    case AONE(bs) => bs
+    case AALTS(bs, rs) => {
+      val n = rs.indexWhere(bnullable)
+      bs ++ mkepsBC(rs(n))
+    }
+    case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
+    case ASTAR(bs, r) => bs ++ List(Z)
+    case ANOT(bs, rn) => bs
+  }
+
+
+def bder(c: Char, r: ARexp) : ARexp = r match {
+    case AZERO => AZERO
+    case AONE(_) => AZERO
+    case ACHAR(bs, f) => if (c == f) AONE(bs) else AZERO
+    case AALTS(bs, rs) => AALTS(bs, rs.map(bder(c, _)))
+    case ASEQ(bs, r1, r2) => 
+      if (bnullable(r1)) AALTS(bs, ASEQ(Nil, bder(c, r1), r2) :: fuse(mkepsBC(r1), bder(c, r2)) :: Nil )
+      else ASEQ(bs, bder(c, r1), r2)
+    case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), bder(c, r)), ASTAR(Nil, r))
+    case ANOT(bs, rn) => ANOT(bs, bder(c, rn))
+    case AANYCHAR(bs) => AONE(bs)
+  } 
+
+def fuse(bs: Bits, r: ARexp) : ARexp = r match {
+    case AZERO => AZERO
+    case AONE(cs) => AONE(bs ++ cs)
+    case ACHAR(cs, f) => ACHAR(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)
+    case ANOT(cs, r) => ANOT(bs ++ cs, r)
+  }
+
+
+def internalise(r: Rexp) : ARexp = r match {
+    case ZERO => AZERO
+    case ONE => AONE(Nil)
+    case CHAR(c) => ACHAR(Nil, c)
+    //case PRED(f) => APRED(Nil, f)
+    case ALTS(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)
+    case NOT(r) => ANOT(Nil, internalise(r))
+    case ANYCHAR => AANYCHAR(Nil)
+  }
+
+
+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) => {
+            val rs_simp = rs.map(bsimp(_))
+            val flat_res = flats(rs_simp)
+            val dist_res = strongDistinctBy(flat_res)//distinctBy(flat_res, erase)
+            dist_res match {
+              case Nil => AZERO
+              case s :: Nil => fuse(bs1, s)
+              case rs => AALTS(bs1, rs)  
+            }
+          
+      }
+      case r => r
+    }
+  }
+  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 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)
+    }
+  } 
+
+  def prettyRexp(r: Rexp) : String = r match {
+      case STAR(r0) => s"${prettyRexp(r0)}*"
+      case SEQ(CHAR(c), r2) => c.toString ++ prettyRexp(r2)
+      case SEQ(r1, r2) => s"${prettyRexp(r1)}~${prettyRexp(r2)}"
+      case CHAR(c) => c.toString
+      case ANYCHAR => "."
+    //   case NOT(r0) => s
+  }
+
+  def decode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {
+    case (ONE, bs) => (Empty, bs)
+    case (CHAR(f), bs) => (Chr(f), bs)
+    case (ALTS(r1, r2), Z::bs1) => {
+        val (v, bs2) = decode_aux(r1, bs1)
+        (Left(v), bs2)
+    }
+    case (ALTS(r1, r2), S::bs1) => {
+        val (v, bs2) = decode_aux(r2, 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)
+      //println(v)
+      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)
+    }
+    case (NOT(r), bs) => (Nots(prettyRexp(r)), bs)
+  }
+
+  def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
+    case (v, Nil) => v
+    case _ => throw new Exception("Not decodable")
+  }
+
+
+
+def blexSimp(r: Rexp, s: String) : List[Bit] = {
+    blex_simp(internalise(r), s.toList)
+}
+
+def blexing_simp(r: Rexp, s: String) : Val = {
+    val bit_code = blex_simp(internalise(r), s.toList)
+    decode(r, bit_code)
+  }
+
+
+
+  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 bdersSimp(s: String, r: Rexp) : ARexp = bders_simp(s.toList, internalise(r))
+
+
+  def erase(r:ARexp): Rexp = r match{
+    case AZERO => ZERO
+    case AONE(_) => ONE
+    case ACHAR(bs, c) => CHAR(c)
+    case AALTS(bs, Nil) => ZERO
+    case AALTS(bs, a::Nil) => erase(a)
+    case AALTS(bs, a::as) => ALTS(erase(a), erase(AALTS(bs, as)))
+    case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))
+    case ASTAR(cs, r)=> STAR(erase(r))
+    case ANOT(bs, r) => NOT(erase(r))
+    case AANYCHAR(bs) => ANYCHAR
+  }
+
+def breakHead(r: ARexp) : List[ARexp] = r match {
+    case AALTS(bs, rs) => rs
+    case r => r::Nil
+}
+
+def distinctByWithAcc[B, C](xs: List[B], f: B => C, 
+    acc: List[C] = Nil, accB: List[B] = Nil): (List[B], List[C]) = xs match {
+    case Nil => (accB.reverse, acc)
+    case (x::xs) => {
+      val res = f(x)
+      if (acc.contains(res)) distinctByWithAcc(xs, f, acc, accB)  
+      else distinctByWithAcc(xs, f, res::acc, x::accB)
+    }
+  } 
+
+
+  def strongDistinctBy(xs: List[ARexp], 
+                       acc1: List[Rexp] = Nil, 
+                       acc2 : List[(List[Rexp], Rexp)] = Nil): List[ARexp] = xs match {
+    case Nil => Nil
+    case (x::xs) => 
+        if(acc1.contains(erase(x)))
+            strongDistinctBy(xs, acc1, acc2)
+        else{
+            x match {
+                case ASTAR(bs0, r0) => 
+                    val headList : List[ARexp] = List[ARexp](AONE(Nil))
+                    val i = acc2.indexWhere(
+                        r2stl => {val (r2s, tl) = r2stl; tl == erase(r0) } 
+                    )
+                    if(i == -1){ 
+                        x::strongDistinctBy(
+                            xs, erase(x)::acc1, (ONE::Nil, erase(r0))::acc2
+                        )
+                    }
+                    else{
+                        val headListAlready = acc2(i)
+                        val (newHeads, oldHeadsUpdated) = 
+                                distinctByWithAcc(headList, erase, headListAlready._1)
+                        newHeads match{
+                            case newHead::Nil =>
+                                ASTAR(bs0, r0) :: 
+                                strongDistinctBy(xs, erase(x)::acc1, 
+                                acc2.updated(i, (oldHeadsUpdated, headListAlready._2)) )//TODO: acc2 already contains headListAlready
+                            case Nil =>
+                                strongDistinctBy(xs, erase(x)::acc1, 
+                                acc2)
+                        }
+                    }                
+                case ASEQ(bs, r1, ASTAR(bs0, r0)) => 
+                    val headList = breakHead(r1)
+                    val i = acc2.indexWhere(
+                        r2stl => {val (r2s, tl) = r2stl; tl == erase(r0) } 
+                    )
+                    if(i == -1){ 
+                        x::strongDistinctBy(
+                            xs, erase(x)::acc1, (headList.map(erase(_)), erase(r0))::acc2
+                        )
+                    }
+                    else{
+                        val headListAlready = acc2(i)
+                        val (newHeads, oldHeadsUpdated) = 
+                                distinctByWithAcc(headList, erase, headListAlready._1)
+                        newHeads match{
+                            case newHead::Nil =>
+                                ASEQ(bs, newHead, ASTAR(bs0, r0)) :: 
+                                strongDistinctBy(xs, erase(x)::acc1, 
+                                acc2.updated(i, (oldHeadsUpdated, headListAlready._2)) )//TODO: acc2 already contains headListAlready
+                            case Nil =>
+                                strongDistinctBy(xs, erase(x)::acc1, 
+                                acc2)
+                            case hds => val AALTS(bsp, rsp) = r1
+                                ASEQ(bs, AALTS(bsp, hds), ASTAR(bs0, r0)) ::
+                                strongDistinctBy(xs, erase(x)::acc1,
+                                acc2.updated(i, (oldHeadsUpdated, headListAlready._2)))
+                        }
+                    }
+                case rPrime => x::strongDistinctBy(xs, erase(x)::acc1, acc2)    
+            }
+                
+        }
+    
+}
+
+
+def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
+    case Nil => {
+      if (bnullable(r)) {
+        //println(asize(r))
+        val bits = mkepsBC(r)
+        bits
+      }
+    else throw new Exception("Not matched")
+    }
+    case c::cs => {
+      val der_res = bder(c,r)
+      val simp_res = bsimp(der_res)  
+      blex_simp(simp_res, cs)      
+    }
+  }
+  def size(r: Rexp) : Int = r match {
+    case ZERO => 1
+    case ONE => 1
+    case CHAR(_) => 1
+    case ANYCHAR => 1
+    case NOT(r0) => 1 + size(r0)
+    case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+    case ALTS(r1, r2) => 1 + List(r1, r2).map(size).sum
+    case STAR(r) => 1 + size(r)
+  }
+
+  def asize(a: ARexp) = size(erase(a))
+
+
+// @arg(doc = "small tests")
+val STARREG = ("a" | "aa").%
+
+@main
+def small() = {
+
+  val prog0 = """aaa"""
+  println(s"test: $prog0")
+//   println(lexing_simp(NOTREG, prog0))
+//   val v = lex_simp(NOTREG, prog0.toList)
+//   println(v)
+
+//   val d =  (lex_simp(NOTREG, prog0.toList))
+//   println(d)
+
+  val bd = bdersSimp(prog0, STARREG)
+    println(erase(bd))
+    println(asize(bd))
+
+    val vres = blexing_simp( STARREG, prog0)
+    println(vres)
+//   println(vs.length)
+//   println(vs)
+   
+
+  // val prog1 = """read  n; write n"""  
+  // println(s"test: $prog1")
+  // println(lexing_simp(WHILE_REGS, prog1))
+}
+
+// // Bigger Tests
+// //==============
+
+// // escapes strings and prints them out as "", "\n" and so on
+// def esc(raw: String): String = {
+//   import scala.reflect.runtime.universe._
+//   Literal(Constant(raw)).toString
+// }
+
+// def escape(tks: List[(String, String)]) =
+//   tks.map{ case (s1, s2) => (s1, esc(s2))}
+
+
+// val prog2 = """
+// 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
+// """
+
+// @arg(doc = "Fibonacci test")
+// @main
+// def fib() = {
+//   println("lexing fib program")
+//   println(escape(lexing_simp(WHILE_REGS, prog2)).mkString("\n"))
+// }
+
+
+// val prog3 = """
+// start := 1000;
+// x := start;
+// y := start;
+// z := start;
+// while 0 < x do {
+//  while 0 < y do {
+//   while 0 < z do {
+//     z := z - 1
+//   };
+//   z := start;
+//   y := y - 1
+//  };     
+//  y := start;
+//  x := x - 1
+// }
+// """
+
+// @arg(doc = "Loops test")
+// @main
+// def loops() = {
+//   println("lexing Loops")
+//   println(escape(lexing_simp(WHILE_REGS, prog3)).mkString("\n"))
+// }
+
+// @arg(doc = "Email Test")
+// @main
+// def email() = {
+//   val lower = "abcdefghijklmnopqrstuvwxyz"
+
+//   val NAME = RECD("name", PLUS(RANGE(lower ++ "_.-")))
+//   val DOMAIN = RECD("domain", PLUS(RANGE(lower ++ "-")))
+//   val RE = RANGE(lower ++ ".")
+//   val TOPLEVEL = RECD("top", (RE ~ RE) |
+//                              (RE ~ RE ~ RE) | 
+//                              (RE ~ RE ~ RE ~ RE) | 
+//                              (RE ~ RE ~ RE ~ RE ~ RE) |
+//                              (RE ~ RE ~ RE ~ RE ~ RE ~ RE))
+
+//   val EMAIL = NAME ~ "@" ~ DOMAIN ~ "." ~ TOPLEVEL
+
+//   println(lexing_simp(EMAIL, "christian.urban@kcl.ac.uk"))
+// }
+
+
+// @arg(doc = "All tests.")
+// @main
+// def all() = { small(); fib() ; loops() ; email() } 
+
+
+
+
+// runs with amm2 and amm3
+
+
+
diff -r cc8e231529fb -r 6291181fad07 thys2/zre8.sc
--- a/thys2/zre8.sc	Tue Jan 25 13:12:50 2022 +0000
+++ b/thys2/zre8.sc	Sun Jan 30 23:36:31 2022 +0000
@@ -62,6 +62,16 @@
 
 var pos : Int = 0
 
+  //size: of a Aregx for testing purposes 
+  def size(r: Rexp) : Int = r match {
+    case ZERO => 1
+    case ONE => 1
+    case CHAR(_) => 1
+    case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+    case ALT(r1, r2) => 1 + List(r1, r2).map(size).sum
+    case STAR(r) => 1 + size(r)
+  }
+
 
 
 //input ..................
@@ -82,16 +92,16 @@
             // c match {
             //     case StarC(m, vs, inside) => vs.length
             // }
-            val idx = m.parents.lastIndexWhere(c0 => c0.starIters < c.starIters)
-            if(m.parents.size == 2){
-                println("third parent added")
-                println(simpleCtxDisplay(c))
-                println("the other parents")
-                m.parents.foreach(c00 => println(c00.starIters))
-                println(idx + 1)
-                println("c's star iters: "+ c.starIters)
-                println(s"the others' star iters: ${m.parents(0).starIters}")
-            }
+            val idx = m.parents.lastIndexWhere(c0 => c0.starIters <= c.starIters)
+            // if(m.parents.size == 1){
+            //     println("third parent added")
+            //     println(simpleCtxDisplay(c))
+            //     println("the other parents")
+            //     m.parents.foreach(c00 => println(c00.starIters))
+            //     println(idx + 1)
+            //     println("c's star iters: "+ c.starIters)
+            //     println(s"the others' star iters: ${m.parents(0).starIters}")
+            // }
             m.parents.insert(idx + 1, c)
             //m.parents = m.parents:::List(c)
             m.result.find(endPos_value => endPos_value._1 == pos) match {
@@ -461,8 +471,8 @@
 for(i <- 1 to 2) {
     mems.clear()
 println(s"there are $i number of a's")
-val re1 = ("a" | "aa" | "ab").%//(("a" | "b") ~ "c" | ("b" | "e") ~ "c" ) ~ "f"
-val re1Lexed = lex(re1, "a"*i)
+val re1 = ("a" | "ab" ) ~ ("c" | "bc")//(("a" | "b") ~ "c" | ("b" | "e") ~ "c" ) ~ "f"
+val re1Lexed = lex(re1, "abc")
 
 //drawZippers(re1Lexed)
 println("size of actual zipper (including memoized contexts")
@@ -480,13 +490,6 @@
 }
 )
 
-  val mb = 1024*1024
-val runtime = Runtime.getRuntime
-println("ALL RESULTS IN MB")
-println("** Used Memory:  " + (runtime.totalMemory - runtime.freeMemory) / mb)
-println("** Free Memory:  " + runtime.freeMemory / mb)
-println("** Total Memory: " + runtime.totalMemory / mb)
-println("** Max Memory:   " + runtime.maxMemory / mb)
 
 }