diff -r 0e591f806290 -r 8a34b2ebc8cc testing4/re.scala
--- a/testing4/re.scala	Tue Dec 03 11:07:09 2019 +0000
+++ b/testing4/re.scala	Mon Jan 27 10:18:13 2020 +0000
@@ -8,16 +8,16 @@
 case object ZERO extends Rexp
 case object ONE extends Rexp
 case class CHAR(c: Char) extends Rexp
-case class ALT(r1: Rexp, r2: Rexp) extends Rexp 
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 
-case class STAR(r: Rexp) extends Rexp 
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp   // alternative 
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp   // sequence
+case class STAR(r: Rexp) extends Rexp             // star
 
-// some convenience for typing in regular expressions
+
+// 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)
@@ -39,117 +39,137 @@
   def ~ (r: String) = SEQ(s, r)
 }
 
-// (1) Complete the function nullable according to
+// (5) Complete the function nullable according to
 // the definition given in the coursework; this 
 // function checks whether a regular expression
 // can match the empty string and Returns a boolean
 // accordingly.
 
-def nullable (r: Rexp) : Boolean = r match {
-  case ZERO => false
-  case ONE => true
-  case CHAR(_) => false
-  case ALT(r1, r2) => nullable(r1) || nullable(r2)
-  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
-  case STAR(_) => true
+def nullable (r: Rexp) : Boolean = {
+	r match {
+		case ZERO => false
+		case ONE => true
+		case CHAR(c) => false
+		case ALT(r1, r2) => (nullable(r1) || nullable(r2))
+		case SEQ(r1, r2) => (nullable(r1) && nullable(r2))
+		case STAR(r) => true
+	}
 }
 
-// (2) Complete the function der according to
+// (6) Complete the function der according to
 // the definition given in the coursework; this
 // function calculates the 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 CHAR(d) => if (c == d) ONE else ZERO
-  case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
-  case SEQ(r1, r2) => 
-    if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
-    else SEQ(der(c, r1), r2)
-  case STAR(r1) => SEQ(der(c, r1), STAR(r1))
+def der (c: Char, r: Rexp) : Rexp = {
+	r match {
+		case ZERO => ZERO
+		case ONE => ZERO
+		case CHAR(d) => if(d == c) ONE else ZERO
+		case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
+		case SEQ(r1, r2) => if(nullable(r1)) {
+								(ALT(SEQ(der(c, r1), r2), der(c, r2)))
+							} else {
+								SEQ(der(c, r1), r2)
+							}
+		case STAR(r) => SEQ(der(c, r), STAR(r))
+	}
 }
 
-// (3) Complete the simp function according to
+
+// (7) Complete the simp function according to
 // the specification given in the coursework; this
 // function simplifies a regular expression from
 // the inside out, like you would simplify arithmetic 
 // expressions; however it does not simplify inside 
 // STAR-regular expressions.
 
-def simp(r: Rexp) : Rexp = r match {
-  case ALT(r1, r2) => (simp(r1), simp(r2)) match {
-    case (ZERO, r2s) => r2s
-    case (r1s, ZERO) => r1s
-    case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)
-  }
-  case SEQ(r1, r2) =>  (simp(r1), simp(r2)) match {
-    case (ZERO, _) => ZERO
-    case (_, ZERO) => ZERO
-    case (ONE, r2s) => r2s
-    case (r1s, ONE) => r1s
-    case (r1s, r2s) => SEQ(r1s, r2s)
-  }
-  case r => r
+def simp(r: Rexp) : Rexp = {
+	r match {
+		case STAR(r) => STAR(r) // does not process r star
+		case SEQ(r1, r2) => {
+			val x = (simp(r1), simp(r2))
+			if(x._1 == ZERO) ZERO else
+			if(x._2 == ZERO) ZERO else
+			if(x._1 == ONE) simp(x._2) else 
+			if(x._2 == ONE) simp(x._1) else
+			if(x._1 == x._2) simp(x._2) else
+			SEQ(simp(x._1), simp(x._2))
+		}
+		case ALT(r1, r2) => {
+			val x = (simp(r1), simp(r2))
+			if(x._1 == ZERO) simp(x._2) else
+			if(x._2 == ZERO) simp(x._1) else
+			if(x._1 == x._2) simp(x._2) else
+			ALT(simp(x._1), simp(x._2))
+		}
+		case r => r // if single regex, return it
+	}
 }
 
 
-// (4) Complete the two functions below; the first 
+// (8) Complete the two functions below; the first 
 // calculates the derivative w.r.t. a string; the second
 // is the regular expression matcher taking a regular
 // expression and a string and checks whether the
-// string matches the regular expression.
+// string matches the regular expression
 
-def ders (s: List[Char], r: Rexp) : Rexp = s match {
-  case Nil => r
-  case c::s => ders(s, simp(der(c, r)))
+def ders (s: List[Char], r: Rexp) : Rexp = {
+	s match {
+		case Nil => r
+		case c :: cs => ders(cs, simp(der(c,r)))
+	}
 }
 
-// main matcher function
-def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
+def matcher(r: Rexp, s: String): Boolean = {
+	val listOfCharacters = s.toList
+	val result = ders(listOfCharacters, r)
+	nullable(result)
+}
 
-// (5) Complete the size function for regular
+
+// (9) Complete the size function for regular
 // expressions according to the specification 
 // given in the coursework.
 
-
-def size(r: Rexp): Int = r match {
-  case ZERO => 1
-  case ONE => 1
-  case CHAR(_) => 1
-  case ALT(r1, r2) => 1 + size(r1) + size (r2)
-  case SEQ(r1, r2) => 1 + size(r1) + size (r2)
-  case STAR(r1) => 1 + size(r1)
+def size(r: Rexp): Int = {
+	r match {
+		case ZERO => 1
+		case ONE => 1
+		case CHAR(c) => 1
+		case ALT(r1, r2) => 1 + size(r1) + size(r2)
+		case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+		case STAR(r) => 1 + size(r)
+	}
 }
 
-
-
 // some testing data
 
-//matcher(("a" ~ "b") ~ "c", "abc")  // => true
-//matcher(("a" ~ "b") ~ "c", "ab")   // => false
+/*
+matcher(("a" ~ "b") ~ "c", "abc")  // => true
+matcher(("a" ~ "b") ~ "c", "ab")   // => false
 
 // the supposedly 'evil' regular expression (a*)* b
-val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+// val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
 
-//matcher(EVIL, "a" * 1000 ++ "b")   // => true
-//matcher(EVIL, "a" * 1000)          // => false
+matcher(EVIL, "a" * 1000 ++ "b")   // => true
+matcher(EVIL, "a" * 1000)          // => false
 
 // size without simplifications
-//size(der('a', der('a', EVIL)))             // => 28
-//size(der('a', der('a', der('a', EVIL))))   // => 58
+size(der('a', der('a', EVIL)))             // => 28
+size(der('a', der('a', der('a', EVIL))))   // => 58
 
 // size with simplification
-//size(simp(der('a', der('a', EVIL))))           // => 8
-//size(simp(der('a', der('a', der('a', EVIL))))) // => 8
+size(simp(der('a', der('a', EVIL))))           // => 8
+size(simp(der('a', der('a', der('a', EVIL))))) // => 8
 
 // 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
-// around 30 seconds.
+// 30 seconds.
 //
-// Lets see how long it takes to match strings with 
-// 5 Million a's...it should be in the range of a 
-// couple of seconds.
+// Lets see how long it really takes to match strings with 
+// 5 Million a's...it should be in the range of a couple
+// of seconds.
 
 def time_needed[T](i: Int, code: => T) = {
   val start = System.nanoTime()
@@ -158,19 +178,19 @@
   (end - start)/(i * 1.0e9)
 }
 
-//for (i <- 0 to 5000000 by 500000) {
-//  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))) + " secs.") 
-//}
+for (i <- 0 to 5000000 by 500000) {
+  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))))
+}
 
 // another "power" test case 
-//simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE
+simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE
 
 // the Iterator produces the rexp
 //
 //      SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)
 //
-//    where SEQ is nested 100 times.
- 
+//    where SEQ is nested 50 times.
 
+*/
 
 }