diff -r 48ce16d61e03 -r 61eff2abb0b6 thys2/blexer2.sc
--- a/thys2/blexer2.sc	Sat Apr 16 09:52:57 2022 +0100
+++ b/thys2/blexer2.sc	Tue Apr 19 09:08:01 2022 +0100
@@ -10,6 +10,7 @@
 //
 //   amm lexer.sc all
 
+import scala.util.Try
 
 // regular expressions including records
 abstract class Rexp 
@@ -28,6 +29,7 @@
   
 // values  
 abstract class Val
+case object Failure extends Val
 case object Empty extends Val
 case class Chr(c: Char) extends Val
 case class Sequ(v1: Val, v2: Val) extends Val
@@ -58,6 +60,166 @@
 case class ANOT(bs: Bits, r: ARexp) extends ARexp
 case class AANYCHAR(bs: Bits) extends ARexp
 
+trait Generator[+T] {
+    self => // an alias for "this"
+    def generate(): T
+  
+    def gen(n: Int) : List[T] = 
+      if (n == 0) Nil else self.generate() :: gen(n - 1)
+    
+    def map[S](f: T => S): Generator[S] = new Generator[S] {
+      def generate = f(self.generate())  
+    }
+    def flatMap[S](f: T => Generator[S]): Generator[S] = new Generator[S] {
+      def generate = f(self.generate()).generate()
+    }
+
+
+}
+
+  // tests a property according to a given random generator
+  def test[T](r: Generator[T], amount: Int = 100)(pred: T => Boolean) {
+    for (_ <- 0 until amount) {
+      val value = r.generate()
+      assert(pred(value), s"Test failed for: $value")
+    }
+    println(s"Test passed $amount times")
+  }
+  def test2[T, S](r: Generator[T], s: Generator[S], amount: Int = 100)(pred: (T, S) => Boolean) {
+    for (_ <- 0 until amount) {
+      val valueR = r.generate()
+      val valueS = s.generate()
+      assert(pred(valueR, valueS), s"Test failed for: $valueR, $valueS")
+    }
+    println(s"Test passed $amount times")
+  }
+
+// random integers
+val integers = new Generator[Int] {
+  val rand = new java.util.Random
+  def generate() = rand.nextInt()
+}
+
+// random booleans
+val booleans = integers.map(_ > 0)
+  
+// random integers in the range lo and high  
+def range(lo: Int, hi: Int): Generator[Int] = 
+  for (x <- integers) yield (lo + x.abs % (hi - lo)).abs
+
+// random characters
+def chars_range(lo: Char, hi: Char) = range(lo, hi).map(_.toChar)  
+val chars = chars_range('a', 'z')
+
+
+def oneOf[T](xs: T*): Generator[T] = 
+  for (idx <- range(0, xs.length)) yield xs(idx)
+  
+def single[T](x: T) = new Generator[T] {
+  def generate() = x
+}   
+
+def pairs[T, U](t: Generator[T], u: Generator[U]): Generator[(T, U)] = 
+  for (x <- t; y <- u) yield (x, y)
+
+// lists
+def emptyLists = single(Nil) 
+
+def nonEmptyLists : Generator[List[Int]] = 
+  for (head <- integers; tail <- lists) yield head :: tail
+
+def lists: Generator[List[Int]] = for {
+  kind <- booleans
+  list <- if (kind) emptyLists else nonEmptyLists
+} yield list
+
+def char_list(len: Int): Generator[List[Char]] = {
+  if(len <= 0) single(Nil)
+  else{
+    for { 
+      c <- chars
+      tail <- char_list(len - 1)
+    } yield c :: tail
+  }
+}
+
+def strings(len: Int): Generator[String] = for(cs <- char_list(len)) yield cs.toString
+
+
+// (simple) binary trees
+trait Tree[T]
+case class Inner[T](left: Tree[T], right: Tree[T]) extends Tree[T]
+case class Leaf[T](x: T) extends Tree[T]
+
+def leafs[T](t: Generator[T]): Generator[Leaf[T]] = 
+  for (x <- t) yield Leaf(x)
+
+def inners[T](t: Generator[T]): Generator[Inner[T]] = 
+  for (l <- trees(t); r <- trees(t)) yield Inner(l, r)
+
+def trees[T](t: Generator[T]): Generator[Tree[T]] = 
+  for (kind <- range(0, 2);  
+       tree <- if (kind == 0) leafs(t) else inners(t)) yield tree
+
+// regular expressions
+
+// generates random leaf-regexes; prefers CHAR-regexes
+def leaf_rexp() : Generator[Rexp] =
+  for (kind <- range(0, 5);
+       c <- chars_range('a', 'd')) yield
+    kind match {
+      case 0 => ZERO
+      case 1 => ONE
+      case _ => CHAR(c) 
+    }
+
+// generates random inner regexes with maximum depth d
+def inner_rexp(d: Int) : Generator[Rexp] =
+  for (kind <- range(0, 3);
+       l <- rexp(d); 
+       r <- rexp(d))
+  yield kind match {
+    case 0 => ALTS(l, r)
+    case 1 => SEQ(l, r)
+    case 2 => STAR(r)
+  }
+
+// generates random regexes with maximum depth d;
+// prefers inner regexes in 2/3 of the cases
+def rexp(d: Int = 100): Generator[Rexp] = 
+  for (kind <- range(0, 3);
+       r <- if (d <= 0 || kind == 0) leaf_rexp() else inner_rexp(d - 1)) yield r
+
+
+// some test functions for rexps
+def height(r: Rexp) : Int = r match {
+  case ZERO => 1
+  case ONE => 1
+  case CHAR(_) => 1
+  case ALTS(r1, r2) => 1 + List(height(r1), height(r2)).max
+  case SEQ(r1, r2) =>  1 + List(height(r1), height(r2)).max
+  case STAR(r) => 1 + height(r)
+}
+
+// def size(r: Rexp) : Int = r match {
+//   case ZERO => 1
+//   case ONE => 1
+//   case CHAR(_) => 1
+//   case ALTS(r1, r2) => 1 + size(r1) + size(r2)
+//   case SEQ(r1, r2) =>  1 + size(r1) + size(r2)
+//   case STAR(r) => 1 + size(r) 
+// }
+
+// randomly subtracts 1 or 2 from the STAR case
+def size_faulty(r: Rexp) : Int = r match {
+  case ZERO => 1
+  case ONE => 1
+  case CHAR(_) => 1
+  case ALTS(r1, r2) => 1 + size_faulty(r1) + size_faulty(r2)
+  case SEQ(r1, r2) =>  1 + size_faulty(r1) + size_faulty(r2)
+  case STAR(r) => 1 + size_faulty(r) - range(0, 2).generate
+}
+
 
    
 // some convenience for typing in regular expressions
@@ -184,104 +346,12 @@
 }
 
 // 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 {
@@ -371,252 +441,186 @@
       }
       case r => r
     }
-  }
-  def strongBsimp(r: ARexp): ARexp =
-  {
-    r match {
-      case ASEQ(bs1, r1, r2) => (strongBsimp(r1), strongBsimp(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(strongBsimp(_))
-            val flat_res = flats(rs_simp)
-            val dist_res = distinctBy4(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 strongBsimp(r: ARexp): ARexp =
+{
+  r match {
+    case ASEQ(bs1, r1, r2) => (strongBsimp(r1), strongBsimp(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(strongBsimp(_))
+          val flat_res = flats(rs_simp)
+          val dist_res = distinctBy4(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 projectFirstChild(rs: List[ARexp]) : List[ARexp] = rs match {
-    case (ASEQ(bs, r1, r2p)::rs1) => r1::projectFirstChild(rs1)
-    case Nil => Nil
-  }
+}
 
-
-  def distinctBy2(xs: List[ARexp], acc: List[Rexp] = Nil): List[ARexp] = xs match {
-    case Nil => Nil
-    case (x::xs) => {
-      val res = erase(x)
-      if(acc.contains(res))
-        distinctBy2(xs, acc)
-      else
-        x match {
-          case ASEQ(bs0, AALTS(bs1, rs), r2) => 
-            val newTerms =  distinctBy2(rs.map(r1 => ASEQ(Nil, r1, r2)), acc)
-            val rsPrime = projectFirstChild(newTerms)
-            newTerms match {
-              case Nil => distinctBy2(xs, acc)
-              case t::Nil => ASEQ(bs0, fuse(bs1, rsPrime.head), r2)::distinctBy2(xs, erase(t)::acc)
-              case ts => ASEQ(bs0, AALTS(bs1, rsPrime), r2)::distinctBy2(xs, newTerms.map(erase(_)):::acc)
-            }
-          case x => x::distinctBy2(xs, res::acc)
-        }
-    }
-  }
-
-  def deepFlts(r: ARexp): List[ARexp] = r match{
+def bders (s: List[Char], r: ARexp) : ARexp = s match {
+  case Nil => r
+  case c::s => bders(s, bder(c, r))
+}
 
-    case ASEQ(bs, r1, r2) => deepFlts(r1).map(r1p => ASEQ(bs, r1p, r2))
-    case ASTAR(bs, r0) => List(r)
-    case ACHAR(_, _) => List(r)
-    case AALTS(bs, rs) => rs.flatMap(deepFlts(_))//throw new Error("doubly nested alts in bsimp r")
-  }
-
-
-  def distinctBy3(xs: List[ARexp], acc: List[Rexp] = Nil): List[ARexp] = xs match {
+def flats(rs: List[ARexp]): List[ARexp] = rs match {
     case Nil => Nil
-    case (x::xs) => {
-      val res = erase(x)
-      if(acc.contains(res))
-        distinctBy3(xs, acc)
-      else
-        x match {
-          case ASEQ(bs0, AALTS(bs1, rs), r2) => 
-            val newTerms =  distinctBy3(rs.flatMap(deepFlts(_)).map(r1 => ASEQ(Nil, r1, r2)), acc)//deepFlts(rs.flatMap(r1 => ASEQ(Nil, r1, r2)), acc)
-            val rsPrime = projectFirstChild(newTerms)
-            newTerms match {
-              case Nil => distinctBy3(xs, acc)
-              case t::Nil => ASEQ(bs0, fuse(bs1, rsPrime.head), r2)::distinctBy3(xs, erase(t)::acc)
-              case ts => ASEQ(bs0, AALTS(bs1, rsPrime), r2)::distinctBy3(xs, newTerms.map(erase(_)):::acc)
-            }
-          case x => x::distinctBy3(xs, res::acc)
-        }
-    }
+    case AZERO :: rs1 => flats(rs1)
+    case AALTS(bs, rs1) :: rs2 => rs1.map(fuse(bs, _)) ::: flats(rs2)
+    case r1 :: rs2 => r1 :: flats(rs2)
   }
 
-  def pruneRexp(r: ARexp, allowableTerms: List[Rexp]) : ARexp = {
-    r match {
-      case ASEQ(bs, r1, r2) => 
-        val termsTruncated = allowableTerms.collect(rt => rt match {
-          case SEQ(r1p, r2p) if(r2p == erase(r2)) => r1p//if(r2p == erase(r2)) 
-        })
-        val pruned : ARexp = pruneRexp(r1, termsTruncated)
-        pruned match {
-          case AZERO => AZERO
-          case AONE(bs1) => fuse(bs ++ bs1, r2)
-          case pruned1 => ASEQ(bs, pruned1, r2)
-        }
-
-      case AALTS(bs, rs) => 
-        //allowableTerms.foreach(a => println(shortRexpOutput(a)))        
-        val rsp = rs.map(r => 
-                      pruneRexp(r, allowableTerms)
-                    )
-                    .filter(r => r != AZERO)
-        rsp match {
-          case Nil => AZERO
-          case r1::Nil => fuse(bs, r1)
-          case rs1 => AALTS(bs, rs1)
-        }
-      case r => 
-        if(allowableTerms.contains(erase(r))) r else AZERO //assert(r != AZERO)
-    }
+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 oneSimp(r: Rexp) : Rexp = r match {
-    case SEQ(ONE, r) => r
-    case SEQ(r1, r2) => SEQ(oneSimp(r1), r2)
-    case r => r//assert r != 0 
-     
-  }
+} 
 
 
-  def distinctBy4(xs: List[ARexp], acc: List[Rexp] = Nil) : List[ARexp] = xs match {
+def pruneRexp(r: ARexp, allowableTerms: List[Rexp]) : ARexp = {
+  r match {
+    case ASEQ(bs, r1, r2) => 
+      val termsTruncated = allowableTerms.collect(rt => rt match {
+        case SEQ(r1p, r2p) if(r2p == erase(r2)) => r1p//if(r2p == erase(r2)) 
+      })
+      val pruned : ARexp = pruneRexp(r1, termsTruncated)
+      pruned match {
+        case AZERO => AZERO
+        case AONE(bs1) => fuse(bs ++ bs1, r2)
+        case pruned1 => ASEQ(bs, pruned1, r2)
+      }
+
+    case AALTS(bs, rs) => 
+      //allowableTerms.foreach(a => println(shortRexpOutput(a)))        
+      val rsp = rs.map(r => 
+                    pruneRexp(r, allowableTerms)
+                  )
+                  .filter(r => r != AZERO)
+      rsp match {
+        case Nil => AZERO
+        case r1::Nil => fuse(bs, r1)
+        case rs1 => AALTS(bs, rs1)
+      }
+    case r => 
+      if(allowableTerms.contains(erase(r))) r else AZERO //assert(r != AZERO)
+  }
+}
+
+def oneSimp(r: Rexp) : Rexp = r match {
+  case SEQ(ONE, r) => r
+  case SEQ(r1, r2) => SEQ(oneSimp(r1), r2)
+  case r => r//assert r != 0 
     
-    case Nil => Nil
-    case x :: xs =>
-      //assert(acc.distinct == acc)
-      val erased = erase(x)
-      if(acc.contains(erased))
-        distinctBy4(xs, acc)
-      else{
-        val addToAcc =  breakIntoTerms(erased).filter(r => !acc.contains(oneSimp(r)))
-        //val xp = pruneRexp(x, addToAcc)
-        pruneRexp(x, addToAcc) match {
-          case AZERO => distinctBy4(xs, addToAcc.map(oneSimp(_)) ::: acc)
-          case xPrime => xPrime :: distinctBy4(xs, addToAcc.map(oneSimp(_)) ::: acc)
-        }
-        
-      }
-  }
+}
 
 
-  def breakIntoTerms(r: Rexp) : List[Rexp] = r match {
-    case SEQ(r1, r2)  => breakIntoTerms(r1).map(r11 => SEQ(r11, r2))
-      // breakIntoTerms(r1).map(r11 => r11 match {
-      //   case ONE => r2
-      //   case r => SEQ(r11, r2)
-      // }
-      //)
-    case ALTS(r1, r2) => breakIntoTerms(r1) ::: breakIntoTerms(r2)
-    case _ => r::Nil
-  } 
-
-  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)
+def distinctBy4(xs: List[ARexp], acc: List[Rexp] = Nil) : List[ARexp] = xs match {
+  case Nil => Nil
+  case x :: xs =>
+    //assert(acc.distinct == acc)
+    val erased = erase(x)
+    if(acc.contains(erased))
+      distinctBy4(xs, acc)
+    else{
+      val addToAcc =  breakIntoTerms(erased).filter(r => !acc.contains(oneSimp(r)))
+      //val xp = pruneRexp(x, addToAcc)
+      pruneRexp(x, addToAcc) match {
+        case AZERO => distinctBy4(xs, addToAcc.map(oneSimp(_)) ::: acc)
+        case xPrime => xPrime :: distinctBy4(xs, addToAcc.map(oneSimp(_)) ::: acc)
+      }
+      
     }
-    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 breakIntoTerms(r: Rexp) : List[Rexp] = r match {
+  case SEQ(r1, r2)  => breakIntoTerms(r1).map(r11 => SEQ(r11, r2))
+  case ALTS(r1, r2) => breakIntoTerms(r1) ::: breakIntoTerms(r2)
+  case _ => r::Nil
+}
 
 
 
-def blexSimp(r: Rexp, s: String) : List[Bit] = {
-    blex_simp(internalise(r), s.toList)
+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(r.toString), bs)
 }
 
+def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
+  case (v, Nil) => v
+  case _ => throw new Exception("Not decodable")
+}
+
+
+
 def blexing_simp(r: Rexp, s: String) : Val = {
     val bit_code = blex_simp(internalise(r), s.toList)
     decode(r, bit_code)
-  }
+}
+def simpBlexer(r: Rexp, s: String) : Val = {
+  Try(blexing_simp(r, s)).getOrElse(Failure)
+}
 
-  def strong_blexing_simp(r: Rexp, s: String) : Val = {
-    decode(r, strong_blex_simp(internalise(r), s.toList))
-  }
+def strong_blexing_simp(r: Rexp, s: String) : Val = {
+  decode(r, strong_blex_simp(internalise(r), s.toList))
+}
+
+def strongBlexer(r: Rexp, s: String) : Val = {
+  Try(strong_blexing_simp(r, s)).getOrElse(Failure)
+}
 
-  def strong_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")
+def strong_blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
+  case Nil => {
+    if (bnullable(r)) {
+      //println(asize(r))
+      val bits = mkepsBC(r)
+      bits
     }
-    case c::cs => {
-      val der_res = bder(c,r)
-      val simp_res = strongBsimp(der_res)  
-      strong_blex_simp(simp_res, cs)      
-    }
+    else 
+      throw new Exception("Not matched")
   }
+  case c::cs => {
+    val der_res = bder(c,r)
+    val simp_res = strongBsimp(der_res)  
+    strong_blex_simp(simp_res, cs)      
+  }
+}
 
 
 
@@ -629,12 +633,12 @@
   
   def bdersSimp(s: String, r: Rexp) : ARexp = bders_simp(s.toList, internalise(r))
 
-  def bders_simpS(s: List[Char], r: ARexp) : ARexp = s match {
+  def bdersStrong(s: List[Char], r: ARexp) : ARexp = s match {
     case Nil => r 
-    case c::s => bders_simpS(s, strongBsimp(bder(c, r)))
+    case c::s => bdersStrong(s, strongBsimp(bder(c, r)))
   }
 
-  def bdersSimpS(s: String, r: Rexp) : ARexp = bders_simpS(s.toList, internalise(r))
+  def bdersStrongRexp(s: String, r: Rexp) : ARexp = bdersStrong(s.toList, internalise(r))
 
   def erase(r:ARexp): Rexp = r match{
     case AZERO => ZERO
@@ -650,59 +654,63 @@
   }
 
 
-def allCharSeq(r: Rexp) : Boolean = r match {
-  case CHAR(c) => true
-  case SEQ(r1, r2) => allCharSeq(r1) && allCharSeq(r2)
-  case _ => false
-}
+  def allCharSeq(r: Rexp) : Boolean = r match {
+    case CHAR(c) => true
+    case SEQ(r1, r2) => allCharSeq(r1) && allCharSeq(r2)
+    case _ => false
+  }
+
+  def flattenSeq(r: Rexp) : String = r match {
+    case CHAR(c) => c.toString
+    case SEQ(r1, r2) => flattenSeq(r1) ++ flattenSeq(r2)
+    case _ => throw new Error("flatten unflattenable rexp")
+  } 
 
-def flattenSeq(r: Rexp) : String = r match {
-  case CHAR(c) => c.toString
-  case SEQ(r1, r2) => flattenSeq(r1) ++ flattenSeq(r2)
-  case _ => throw new Error("flatten unflattenable rexp")
-} 
+  def shortRexpOutput(r: Rexp) : String = r match {
+      case CHAR(c) => c.toString
+      case ONE => "1"
+      case ZERO => "0"
+      case SEQ(r1, r2) if(allCharSeq(r)) => flattenSeq(r)//"[" ++ shortRexpOutput(r1) ++ "~" ++ shortRexpOutput(r2) ++ "]"
+      case SEQ(r1, r2) => "[" ++ shortRexpOutput(r1) ++ "~" ++ shortRexpOutput(r2) ++ "]"
+      case ALTS(r1, r2) => "(" ++ shortRexpOutput(r1) ++ "+" ++ shortRexpOutput(r2) ++ ")"
+      case STAR(STAR(r)) => "(..)*"// ++ shortRexpOutput(r) ++ "]*"
+      case STAR(r) => "STAR(" ++ shortRexpOutput(r) ++ ")"
+      //case RTOP => "RTOP"
+    }
+
 
-def shortRexpOutput(r: Rexp) : String = r match {
-    case CHAR(c) => c.toString
-    case ONE => "1"
-    case ZERO => "0"
-    case SEQ(r1, r2) if(allCharSeq(r)) => flattenSeq(r)//"[" ++ shortRexpOutput(r1) ++ "~" ++ shortRexpOutput(r2) ++ "]"
-    case SEQ(r1, r2) => "[" ++ shortRexpOutput(r1) ++ "~" ++ shortRexpOutput(r2) ++ "]"
-    case ALTS(r1, r2) => "(" ++ shortRexpOutput(r1) ++ "+" ++ shortRexpOutput(r2) ++ ")"
-    case STAR(STAR(r)) => "(..)*"// ++ shortRexpOutput(r) ++ "]*"
-    case STAR(r) => "STAR(" ++ shortRexpOutput(r) ++ ")"
-    //case RTOP => "RTOP"
+  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 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")
+
+
+    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)
     }
-    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))
+    def asize(a: ARexp) = size(erase(a))
 
 //pder related
 type Mon = (Char, Rexp)
@@ -808,6 +816,9 @@
 (((STAR("a") | ( STAR("aaa")) | STAR("aaaaa"| ( STAR("aaaaaaa")) | STAR("aaaaaaaaaaa"))).%).%).%
 
 // @main
+
+
+
 def small() = {
 
 
@@ -834,56 +845,89 @@
   // //println(refSize)
   // println(pderSTAR.size)
 
-  val A : Rexp= ("c" | (ONE | "b") ~ "d") ~((ONE).%)
-  val B : Rexp = ((ONE).%)
-  val C : Rexp = ("d") ~ ((ONE).%)
-  val PRUNE_REG : Rexp = (C | B | A)
-  val APRUNE_REG = internalise(PRUNE_REG)
-  // // val program_solution = pruneRexp(APRUNE_REG, breakIntoTerms(PRUNE_REG))
-  // // println("program executes and gives: as disired!")
-  // // println(shortRexpOutput(erase(program_solution)))
+  // val A : Rexp= ("c" | (ONE | "b") ~ "d") ~((ONE).%)
+  // val B : Rexp = ((ONE).%)
+  // val C : Rexp = ("d") ~ ((ONE).%)
+  // val PRUNE_REG : Rexp = (C | B | A)
+  // val APRUNE_REG = internalise(PRUNE_REG)
+  // val program_solution = pruneRexp(APRUNE_REG, breakIntoTerms(PRUNE_REG))
+  // println("program executes and gives: as disired!")
+  // println(shortRexpOutput(erase(program_solution)))
   // val simpedPruneReg = strongBsimp(APRUNE_REG)
 
   // println(shortRexpOutput(erase(simpedPruneReg)))
-  // for(i <- List(1,2 ) ){// 100, 400, 800, 840, 841, 900
-  //   val prog0 = "a" * i
-  //   //println(s"test: $prog0")
-  //   println(s"testing with $i a's" )
-  //   //val bd = bdersSimp(prog0, STARREG)//DB
-  //   val sbd = bdersSimpS(prog0, STARREG)//strongDB
-  //   starPrint(erase(sbd))
-  //   val subTerms = breakIntoTerms(erase(sbd))
-  //   //val subTermsLarge = breakIntoTerms(erase(bd))
+
+
+  for(i <- List(1,2,3,4,10, 100, 400, 841, 900 ) ){// 100, 400, 800, 840, 841, 900
+    val prog0 = "a" * i
+    //println(s"test: $prog0")
+    println(s"testing with $i a's" )
+    //val bd = bdersSimp(prog0, STARREG)//DB
+    val sbd = bdersStrongRexp(prog0, STARREG)//strongDB
+    starPrint(erase(sbd))
+    val subTerms = breakIntoTerms(erase(sbd))
+    //val subTermsLarge = breakIntoTerms(erase(bd))
     
-  //   println(s"subterms of regex with strongDB: ${subTerms.length}")//, standard DB: ${subTermsLarge.length}")
+    println(s"subterms of regex with strongDB: ${subTerms.length}")//, standard DB: ${subTermsLarge.length}")
 
 
 
-  //   println("the number of distinct subterms for bsimp with strongDB")
-  //   println(subTerms.distinct.size)
-  //   //println(subTermsLarge.distinct.size)
-  //   println("which coincides with the number of PDER terms")
+    println("the number of distinct subterms for bsimp with strongDB")
+    println(subTerms.distinct.size)
+    //println(subTermsLarge.distinct.size)
+    if(pderSTAR.size > subTerms.length)
+      println(s"which is less than or equal to the number of PDER terms: ${pderSTAR.size}")
 
 
-  //   // println(shortRexpOutput(erase(sbd)))
-  //   // println(shortRexpOutput(erase(bd)))
+    // println(shortRexpOutput(erase(sbd)))
+    // println(shortRexpOutput(erase(bd)))
     
-  //   println("pdersize, original, strongSimp")
-  //   println(refSize, size(STARREG),  asize(sbd))
+    println("pdersize, original, strongSimp")
+    println(refSize, size(STARREG),  asize(sbd))
 
-  //   val vres = strong_blexing_simp( STARREG, prog0)
-  //   println(vres)
-  // }
-//   println(vs.length)
-//   println(vs)
+    //val vres = strong_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))
-  val display = ("a"| "ab").%
-  val adisplay = internalise(display)
-  bders_simp( "aaaaa".toList, adisplay)
+  // val display = ("a"| "ab").%
+  // val adisplay = internalise(display)
+  // bders_simp( "aaaaa".toList, adisplay)
 }
 
-small()
+def generator_test() {
+  // println("XXX generates 10 random integers in the range 0..2") 
+  // println(range(0, 3).gen(10).mkString("\n"))
+
+  // println("XXX gnerates random lists and trees")
+  // println(lists.generate())
+  // println(trees(chars).generate())
+
+  // println("XXX generates 10 random characters") 
+  // println(chars.gen(10).mkString("\n"))  
+
+  // println("XXX generates 10 random leaf-regexes") 
+  // println(leaf_rexp().gen(10).mkString("\n"))
+  
+  // println("XXX generates 1000 regexes of maximal 10 height")
+  // println(rexp(10).gen(1000).mkString("\n"))
+  
+  // println("XXX generates 1000 regexes and tests an always true-test")
+  // test(rexp(10), 1000) { _ => true }
+  // println("XXX generates regexes and tests a valid predicate")  
+  // test(rexp(10), 1000) { r => height(r) <= size(r) }
+  // println("XXX faulty test")
+  // test(rexp(10), 100) { r => height(r) <= size_faulty(r) }
+  println("testing strongbsimp against bsimp")
+  test2(rexp(10), strings(2), 100) { (r : Rexp, s: String) => 
+    (simpBlexer(r, s) == strongBlexer(r, s)) 
+  }
+  
+}
+// small()
+generator_test()