diff -r b528d1d3d3c3 -r 59e005dcf163 main_testing3/re.scala
--- a/main_testing3/re.scala	Thu Nov 02 13:53:37 2023 +0000
+++ b/main_testing3/re.scala	Thu Nov 02 23:34:53 2023 +0000
@@ -19,240 +19,159 @@
 
 
 // some convenience for typing regular expressions
-import scala.language.implicitConversions    
-import scala.language.reflectiveCalls 
 
 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)
+
+import scala.language.implicitConversions
 
-implicit def RexpOps (r: Rexp) = new {
+given Conversion[String, Rexp] = (s => charlist2rexp(s.toList))
+
+extension (r: Rexp) {
   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)
-}
+// some examples for the conversion and extension:
 
-// examples for the implicits:
-// ALT(CHAR('a'), CHAR('b'))
 // val areg : Rexp = "a" | "b"
-
-// SEQ(CHAR('a'), CHAR('b')) 
+//  => ALTs(List(CHAR('a'), CHAR('b')))
+//
 // val sreg : Rexp = "a" ~ "b"
-
+//  => SEQs(List(CHAR('a'), CHAR('b'))) 
+//
+// val star_reg : Rexp = ("a" ~ "b").%
+//  => STAR(SEQs(List(CHAR('a'), CHAR('b')))) 
 
 // ADD YOUR CODE BELOW
 //======================
 
-// (1)
+// (1) 
 def nullable (r: Rexp) : Boolean = r match {
-  case ZERO     => false
-  case ONE      => true
-  case CHAR(_)  => false
-  case ALTs(rs) => (for(reg <- rs) yield nullable(reg)).exists(_ == true)
-  case SEQs(rs) => (for(reg <- rs) yield nullable(reg)).forall(_ == true)
-  case STAR(_)  => true
+  case ZERO => false
+  case ONE => true
+  case CHAR(_) => false
+  case ALTs(rs) => rs.exists(nullable)
+  case SEQs(rs) => rs.forall(nullable)
+  case STAR(_) => true
 }
 
-/*
-nullable(ZERO) == false
-nullable(ONE) == true
-nullable(CHAR('a')) == false
-nullable(ZERO | ONE) == true
-nullable(ZERO | CHAR('a')) == false
-nullable(ONE ~ ONE) == true
-nullable(ONE ~ CHAR('a')) == false
-nullable(STAR(ZERO)) == true
-nullable(ALTs(List(ONE, CHAR('a'), ZERO))) == true
-nullable(SEQs(List(ONE, ALTs(List(ONE, CHAR('a'), ZERO)), STAR(ZERO)))) == true
-*/
-
 // (2) 
-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 ALTs(rs)       => ALTs(for(reg <- rs) yield der(c, reg))
-  case SEQs(Nil)      => ZERO
-  case SEQs(r :: rs)  => if(nullable(r)) ALT(SEQs(der(c, r) :: rs), der(c, SEQs(rs))) else SEQs(der(c, r) :: rs)
-  case STAR(r)        => SEQ(der(c,r), STAR(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 ALTs(rs) => ALTs(rs.map(der(c, _)))
+  case SEQs(Nil) => ZERO
+  case SEQs(r1::rs) => 
+    if (nullable(r1)) ALT(SEQs(der(c, r1)::rs), der(c, SEQs(rs)))
+    else SEQs(der(c, r1) :: rs)
+  case STAR(r1) => SEQ(der(c, r1), STAR(r1))
 }
 
-/*
-der('a', ZERO | ONE) == (ZERO | ZERO)
-der('a', (CHAR('a') | ONE) ~ CHAR('a')) == ALT((ONE | ZERO) ~ CHAR('a'), SEQs(List(ONE)))
-der('a', (CHAR('a') | CHAR('a')) ~ CHAR('a')) == (ONE | ONE) ~ CHAR('a')
-der('a', STAR(CHAR('a'))) == (ONE ~ STAR(CHAR('a')))
-der('b', STAR(CHAR('a'))) == (ZERO ~ STAR(CHAR('a')))
-*/
 
 // (3) 
 def denest(rs: List[Rexp]) : List[Rexp] = rs match {
-  case Nil                => Nil
-  case ZERO :: rest       => denest(rest)
-  case ALTs(rgs) :: rest  => rgs ::: denest(rest)
-  case r :: rest          => r :: denest(rest)
+  case Nil => Nil
+  case ZERO::tl => denest(tl)
+  case ALTs(rs1)::rs2 => rs1 ::: denest(rs2)  
+  case r::rs => r :: denest(rs) 
 }
 
-/*
-denest(List(ONE, ZERO, ALTs(List(ONE, CHAR('a'))))) == List(ONE, ONE, CHAR('a'))
-denest(List(ONE ~ ONE, ZERO, ZERO | ONE)) == List(ONE ~ ONE, ZERO, ONE)
-*/
-
 // (4)
 def flts(rs: List[Rexp], acc: List[Rexp] = Nil) : List[Rexp] = rs match {
-  case Nil                => acc
-  case ZERO :: rest       => List(ZERO)
-  case ONE :: rest        => flts(rest, acc)
-  case SEQs(rgs) :: rest  => flts(rest, acc ::: rgs)
-  case r :: rest          => flts(rest, acc ::: List(r)) 
+  case Nil => acc
+  case ZERO::rs => ZERO::Nil
+  case ONE::rs => flts(rs, acc)
+  case SEQs(rs1)::rs => flts(rs, acc ::: rs1)
+  case r::rs => flts(rs, acc :+ r) 
 }
 
-/*
-flts(List(CHAR('a'), ZERO, ONE), Nil) == List(ZERO)
-flts(List(CHAR('a'), ONE, ONE, CHAR('b')), Nil) == List(CHAR('a'), CHAR('b'))
-flts(List(ONE ~ CHAR('a'), CHAR('b') ~ ONE), Nil) == List(ONE, CHAR('a'), CHAR('b'), ONE)
-*/
-
 // (5)
 def ALTs_smart(rs: List[Rexp]) : Rexp = rs match {
-  case Nil      => ZERO
-  case List(r)  => r
-  case _        => ALTs(rs)
+  case Nil => ZERO
+  case r::Nil => r  
+  case rs => ALTs(rs)
 }
 
 def SEQs_smart(rs: List[Rexp]) : Rexp = rs match {
-  case Nil      => ONE
-  case List(r)  => r
-  case _        => SEQs(rs)
+  case Nil => ONE
+  case ZERO::Nil => ZERO
+  case r::Nil => r
+  case rs => SEQs(rs) 
 }
 
-/*
-SEQs_smart(Nil) == ONE
-SEQs_smart(List(ZERO)) == ZERO
-SEQs_smart(List(CHAR('a'))) == CHAR('a')
-SEQs_smart(List(ONE ~ ONE)) == ONE ~ ONE
-SEQs_smart(List(ONE, ONE)) == SEQs(List(ONE, ONE))
-ALTs_smart(Nil) == ZERO
-ALTs_smart(List(ONE ~ ONE)) == ONE ~ ONE
-ALTs_smart(List(ZERO, ZERO)) == ALTs(List(ZERO, ZERO))
-*/
+// (6) 
 
-// (6)
 def simp(r: Rexp) : Rexp = r match {
-  case ALTs(rs) => ALTs_smart(denest(for(reg <- rs) yield simp(reg)).distinct)
-  case SEQs(rs) => SEQs_smart(flts(for(reg <- rs) yield simp(reg)))
-  case _        => r
+  case ALTs(rs) => 
+    ALTs_smart(denest(rs.map(simp)).distinct)
+  case SEQs(rs) => 
+    SEQs_smart(flts(rs.map(simp)))
+  case r => r
 }
 
-/*
-simp(ZERO | ONE) == ONE
-simp(STAR(ZERO | ONE)) == STAR(ZERO | ONE)
-simp(ONE ~ (ONE ~ (ONE ~ CHAR('a')))) == CHAR('a')
-simp(((ONE ~ ONE) ~ ONE) ~ CHAR('a')) == CHAR('a')
-simp(((ONE | ONE) ~ ONE) ~ CHAR('a')) == CHAR('a')
-simp(ONE ~ (ONE ~ (ONE ~ ZERO))) == ZERO
-simp(ALT(ONE ~ (ONE ~ (ONE ~ ZERO)), CHAR('a'))) == CHAR('a')
-simp(CHAR('a') | CHAR('a')) == CHAR('a')
-simp(CHAR('a') ~ CHAR('a')) == CHAR('a') ~ CHAR('a')
-simp(ONE | CHAR('a')) == (ONE | CHAR('a'))
-simp(ALT((CHAR('a') | ZERO) ~ ONE,((ONE | CHAR('b')) | CHAR('c')) ~ (CHAR('d') ~ ZERO))) == CHAR('a')
-simp((ZERO | ((ZERO | ZERO) | (ZERO | ZERO))) ~ ((ONE | ZERO) | ONE ) ~ (CHAR('a'))) == ZERO
-simp(ALT(ONE | ONE, ONE | ONE)) == ONE
-simp(ALT(ZERO | CHAR('a'), CHAR('a') | ZERO)) == CHAR('a')
-simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE)) == ALT(ONE, CHAR('a'))
-simp(ALTs(Nil)) == ZERO
-simp(SEQs(List(CHAR('a')))) == CHAR('a')
-*/
+//println("Simp tests")
+//println(simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE)))
+//println(simp(((CHAR('a') | ZERO) ~ ONE) | 
+//              (((ONE | CHAR('b')) | CHAR('c')) ~ (CHAR('d') ~ ZERO))))
 
-// (7)
+// (7) 
+
 def ders (s: List[Char], r: Rexp) : Rexp = s match {
-  case Nil      => r
-  case c :: cs  => ders(cs, simp(der(c, r)))
-}
-def matcher(r: Rexp, s: String): Boolean = {
-  val derivatives = ders(s.toList, r)
-  nullable(derivatives)
+  case Nil => r
+  case c::s => ders(s, simp(der(c, r)))
 }
 
-/*
-val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
-ders("aaaaa".toList, EVIL) == SEQs(List(STAR(CHAR('a')), STAR(STAR(CHAR('a'))), CHAR('b')))
-ders(List('b'), EVIL) == ONE
-ders("bb".toList, EVIL) == ZERO
-matcher(EVIL, "a" * 5 ++ "b") == true
-matcher(EVIL, "b") == true
-matcher(EVIL, "bb") == false
-matcher("abc", "abc") == true
-matcher(("ab" | "a") ~ (ONE | "bc"), "abc") == true
-matcher(ONE, "") == true
-matcher(ZERO, "") == false
-matcher(ONE | CHAR('a'), "") == true
-matcher(ONE | CHAR('a'), "a") == true
-*/
+// main matcher function
+def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
 
 // (8) 
+
 def size(r: Rexp): Int = r match {
-  case ZERO     => 1
-  case ONE      => 1
-  case CHAR(_)  => 1
-  case ALTs(rs) => 1 + (for(reg <- rs) yield size(reg)).sum
-  case SEQs(rs) => 1 + (for(reg <- rs) yield size(reg)).sum
-  case STAR(r)  => 1 + size(r)
+  case ZERO => 1
+  case ONE => 1
+  case CHAR(_) => 1
+  case ALTs(rs) => 1 + rs.map(size).sum
+  case SEQs(rs) => 1 + rs.map(size).sum
+  case STAR(r1) => 1 + size(r1)
 }
 
-/*
-val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
-size(der('a', der('a', EVIL))) == 36
-size(der('a', der('a', der('a', EVIL)))) == 83
-size(ders("aaaaaa".toList, EVIL)) == 7
-size(ders(("a" * 50).toList, EVIL)) == 7
-*/
 
 
-// Some testing data
-//===================
+// some testing data
 /*
-
-simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE))   // => ALTs(List(ONE, CHAR(a)))
-simp(((CHAR('a') | ZERO) ~ ONE) | (((ONE | CHAR('b')) | CHAR('c')) ~ (CHAR('d') ~ ZERO)))   // => CHAR(a)
-
-matcher(("a" ~ "b") ~ "c", "ab")   // => false
-matcher(("a" ~ "b") ~ "c", "abc")  // => true
-
+println(matcher(("a" ~ "b") ~ "c", "abc"))  // => true
+println(matcher(("a" ~ "b") ~ "c", "ab"))   // => false
 
 // the supposedly 'evil' regular expression (a*)* b
 val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
 
-matcher(EVIL, "a" * 1000)          // => false
-matcher(EVIL, "a" * 1000 ++ "b")   // => true
-
+println(matcher(EVIL, "a" * 1000 ++ "b"))   // => true
+println(matcher(EVIL, "a" * 1000))          // => false
 
 // size without simplifications
-size(der('a', der('a', EVIL)))             // => 36
-size(der('a', der('a', der('a', EVIL))))   // => 83
+println(size(der('a', der('a', EVIL))))             // => 36
+println(size(der('a', der('a', der('a', EVIL)))))   // => 83
 
 // size with simplification
-size(simp(der('a', der('a', EVIL))))           // => 7
-size(simp(der('a', der('a', der('a', EVIL))))) // => 7
+println(simp(der('a', der('a', EVIL))))          
+println(simp(der('a', der('a', der('a', EVIL)))))
+
+println(size(simp(der('a', der('a', EVIL)))))           // => 7
+println(size(simp(der('a', der('a', der('a', EVIL)))))) // => 7
 
 // Python needs around 30 seconds for matching 28 a's with EVIL. 
 // Java 9 and later increase this to an "astonishing" 40000 a's in
-// 30 seconds.
+// around 30 seconds.
 //
-// Lets see how long it really takes to match strings with 
-// 5 Million a's...it should be in the range of a few
-// of seconds.
+// Lets see how long it takes to match strings with 
+// 5 Million a's...it should be in the range of a 
+// few seconds.
 
 def time_needed[T](i: Int, code: => T) = {
   val start = System.nanoTime()
@@ -266,15 +185,15 @@
 }
 
 // another "power" test case 
-simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next()) == ONE
+println(simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next()) == ONE)
 
 // the Iterator produces the rexp
 //
 //      SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)
 //
-//    where SEQ is nested 50 times.
+//    where SEQ is nested 100 times.
+*/ 
 
-*/
 
 }