diff -r e9d14d58be3c -r daf561a83ba6 main_testing3/re.scala
--- a/main_testing3/re.scala	Thu Jan 13 12:55:03 2022 +0000
+++ b/main_testing3/re.scala	Mon Apr 11 23:55:27 2022 +0100
@@ -13,12 +13,10 @@
 case class STAR(r: Rexp) extends Rexp             // star
 
 
-// some convenience for typing regular expressions
-
 //the usual binary choice can be defined in terms of ALTs
 def ALT(r1: Rexp, r2: Rexp) = ALTs(List(r1, r2))
 
-
+// some convenience for typing in regular expressions
 import scala.language.implicitConversions    
 import scala.language.reflectiveCalls 
 
@@ -52,18 +50,12 @@
 def nullable (r: Rexp) : Boolean = r match {
   case ZERO => false
   case ONE => true
-  case CHAR(c) => false
-  case ALTs(rs) => {
-    if (rs.size == 0) false
-    else if (nullable(rs.head)) true
-    else nullable(ALTs(rs.tail))
-  }
-  case SEQ(c, s) => nullable(c) && nullable(s)
-  case STAR(r) => true
-  case _ => false
+  case CHAR(_) => false
+  case ALTs(rs) => rs.exists(nullable)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+  case STAR(_) => true
 }
 
-
 // (2) Complete the function der according to
 // the definition given in the coursework; this
 // function calculates the derivative of a 
@@ -72,16 +64,12 @@
 def der (c: Char, r: Rexp) : Rexp = r match {
   case ZERO => ZERO
   case ONE => ZERO
-  case CHAR(x) => {
-    if (x==c) ONE
-    else ZERO
-  }
-  case ALTs(rs) => ALTs(for (i <- rs) yield der(c, i))
-  case SEQ(x, y) => {
-    if (nullable(x)) ALTs(List(SEQ(der(c, x), y), der(c, y)))
-    else SEQ(der(c, x), y)
-  }
-  case STAR(x) => SEQ(der(c, x), STAR(x))
+  case CHAR(d) => if (c == d) ONE else ZERO
+  case ALTs(rs) => ALTs(rs.map(der(c, _)))
+  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))
 }
 
 
@@ -92,118 +80,119 @@
 
 def flts(rs: List[Rexp]) : List[Rexp] = rs match {
   case Nil => Nil
-  case ZERO::rest => flts(rest)
-  case ALTs(rs_other)::rest => rs_other ::: flts(rest)
-  case r::rest => r::flts(rest)
+  case ZERO::tl => flts(tl)
+  case ALTs(rs1)::rs2 => rs1 ::: flts(rs2)  
+  case r::rs => r :: flts(rs) 
 }
 
 
 
 // (4) Complete the simp function according to
-// the specification given in the coursework description; 
-// this function simplifies a regular expression from
+// 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. Use the _.distinct and 
-// flts functions.
+// STAR-regular expressions.
+
 
 def simp(r: Rexp) : Rexp = r match {
-  case SEQ(x, ZERO) => ZERO
-  case SEQ(ZERO, x) => ZERO
-  case SEQ(x, ONE) => x
-  case SEQ(ONE, x) => x
-  case SEQ(x, y) => SEQ(simp(x), simp(y))
-  case ALTs(rs) => {
-    val list = flts(for (x <- rs) yield simp(x)).distinct
-    if (list.size == 0) ZERO
-    else if (list.size == 1) list.head
-    else ALTs(list)
+  case ALTs(rs) => (flts(rs.map(simp)).distinct) match {
+    case Nil => ZERO
+    case r::Nil => r  
+    case rs => ALTs(rs)
   }
-  case x => x
+  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
 }
 
+simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE))
 
 // (5) 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::rest => {
-    val deriv = simp(der(c,r))
-    ders(rest, deriv)
-  }
+  case c::s => ders(s, simp(der(c, r)))
 }
 
-def matcher(r: Rexp, s: String): Boolean = nullable(ders(s.toList, r))
-
+// main matcher function
+def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
 
 // (6) Complete the size function for regular
 // expressions according to the specification 
 // given in the coursework.
 
+
 def size(r: Rexp): Int = r match {
-  case Nil => 0
   case ZERO => 1
   case ONE => 1
-  case CHAR(x) => 1
-  case ALTs(rs) => 1 + (for (x <- rs) yield size(x)).sum
-  case SEQ(x, y) => 1 + size(x) + size(y)
-  case STAR(x) => 1 + size(x)
+  case CHAR(_) => 1
+  case ALTs(rs) => 1 + rs.map(size).sum
+  case SEQ(r1, r2) => 1 + size(r1) + size (r2)
+  case STAR(r1) => 1 + size(r1)
 }
 
 
+
 // 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'))
 
-// matcher(EVIL, "a" * 1000 ++ "b")   // => true
-// matcher(EVIL, "a" * 1000)          // => false
+//println(matcher(EVIL, "a" * 1000 ++ "b"))   // => true
+//println(matcher(EVIL, "a" * 1000))          // => false
 
 // size without simplifications
-// size(der('a', der('a', EVIL)))             // => 28
-// size(der('a', der('a', der('a', EVIL))))   // => 58
+//println(size(der('a', der('a', EVIL))))             // => 28
+//println(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
+//println(simp(der('a', der('a', EVIL))))          
+//println(simp(der('a', der('a', der('a', EVIL)))))
+
+//println(size(simp(der('a', der('a', EVIL)))))           // => 8
+//println(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
-// 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 couple
-// of 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.
 
-// def time_needed[T](i: Int, code: => T) = {
-//   val start = System.nanoTime()
-//   for (j <- 1 to i) code
-//   val end = System.nanoTime()
-//   "%.5f".format((end - start)/(i * 1.0e9))
-// }
+def time_needed[T](i: Int, code: => T) = {
+  val start = System.nanoTime()
+  for (j <- 1 to i) code
+  val end = System.nanoTime()
+  "%.5f".format((end - start)/(i * 1.0e9))
+}
 
-// for (i <- 0 to 5000000 by 500000) {
-//   println(s"$i ${time_needed(2, matcher(EVIL, "a" * i))} secs.") 
-// }
+//for (i <- 0 to 5000000 by 500000) {
+//  println(s"$i ${time_needed(2, matcher(EVIL, "a" * i))} secs.") 
+//}
 
 // another "power" test case 
-// simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next()) == ONE
+//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.
+ 
 
-// This a dummy comment. Hopefully it works!
 
 }
-