diff -r 33c2655be47d -r 5549016ab10f testing4/re.scala
--- a/testing4/re.scala	Sat Dec 01 15:09:37 2018 +0000
+++ b/testing4/re.scala	Thu Dec 06 13:15:28 2018 +0000
@@ -1,20 +1,22 @@
 // Part 1 about Regular Expression Matching
 //==========================================
 
+//object CW9a {
+
 // Regular Expressions
 abstract class Rexp
 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   // alternative
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp   // sequence
-case class STAR(r: Rexp) extends Rexp             // star
-
+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 
 
-// some convenience for typing regular expressions
+// some convenience for typing in regular expressions
 
-import scala.language.implicitConversions
-import scala.language.reflectiveCalls
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls 
+
 
 def charlist2rexp(s: List[Char]): Rexp = s match {
   case Nil => ONE
@@ -38,190 +40,116 @@
 }
 
 // (1) Complete the function nullable according to
-// the definition given in the coursework; this
+// 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{
+def nullable (r: Rexp) : Boolean = r match {
   case ZERO => false
   case ONE => true
   case CHAR(_) => false
-  case ALT(a,b)=>nullable(a)||nullable(b)
-  case SEQ(a,b) => nullable(a) && nullable(b)
+  case ALT(r1, r2) => nullable(r1) || nullable(r2)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
   case STAR(_) => true
 }
 
-
-/*val rex = "1~0.%|11"
-
-assert(der('1',rex) == SEQ(ONE,SEQ(CHAR(~),SEQ(CHAR(0),SEQ(CHAR(.),SEQ(CHAR(%),SEQ(CHAR(|),SEQ(CHAR(1),CHAR(1)))))))))
-
-assert(der('1',der('1',rex)) ==
-        ALT(SEQ(ZERO,SEQ(CHAR(~),SEQ(CHAR(0),SEQ(CHAR(.),SEQ(CHAR(%),SEQ(CHAR(|),
-        SEQ(CHAR(1),CHAR(1)))))))),SEQ(ZERO,SEQ(CHAR(0),SEQ(CHAR(.),SEQ(CHAR(%),
-        SEQ(CHAR(|),SEQ(CHAR(1),CHAR(1))))))))*/
-
 // (2) Complete the function der according to
 // the definition given in the coursework; this
-// function calculates the derivative of a
+// function calculates the derivative of a 
 // regular expression w.r.t. a character.
 
-def der (c: Char, r: Rexp) : Rexp = r match{
+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(a,b) => der(c,a)|der(c,b)
-  case SEQ(a,b) => if(nullable(a)) {(der(c,a)~b)|der(c,b)}
-                   else der(c,a)~b
-  case STAR(a) => der(c,a)~STAR(a)
+  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))
 }
 
-println(der('a', ZERO | ONE))// == (ZERO | ZERO)
-println(der('a', (CHAR('a') | ONE) ~ CHAR('a')))// ==ALT((ONE | ZERO) ~ CHAR('a'), ONE)
-println(der('a', STAR(CHAR('a'))))// == (ONE ~ STAR(CHAR('a')))
-println(der('b', STAR(CHAR('a'))))// == (ZERO ~ STAR(CHAR('a'))))
-
-
-//ALT(SEQ(ZERO,ZERO),ZERO)
-//ALT(ALT(ZERO,ZERO),ALT(ZERO,ZERO))
-
-// * == |
-// + == ~
 // (3) 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
+// 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 SEQ(ZERO,_) => ZERO
-  case SEQ(_,ZERO) => ZERO
-  case SEQ(ONE,a) => simp(a)
-  case SEQ(a,ONE) => simp(a)
-  case ALT(ZERO,a) => simp(a)
-  case ALT(a,ZERO) => simp(a)
-  case ALT(a,b) => if(a == b) simp(a) else r
-  case _ => r
-}*/
-
-def simp(r: Rexp) : Rexp = r match{
-  case SEQ(a,b) =>{ val sa = simp(a)
-                    val sb = simp(b)
-                    if(sa == ZERO || sb == ZERO) ZERO
-                    else if(sa == ONE) sb
-                    else if(sb == ONE) sa
-                    else SEQ(sa,sb)
-                    }
-  case ALT(a,b) =>{ val sa = simp(a)
-                    val sb = simp(b)
-                    if(sa == ONE || sb == ONE) ONE
-                    else if(sa == ZERO) sb
-                    else if(sb == ZERO) sa
-                    else if(sa == sb) sa
-                    else ALT(sa,sb)
-                    }
-  //case STAR(STAR(a)) => simp(STAR(a))
-  //case STAR(a) => STAR(simp(a))
-  case _ => r
-  /*
-  case SEQ(ZERO,_) => ZERO
-  case SEQ(_,ZERO) => ZERO
-  case SEQ(ONE,a) => simp(a)
-  case SEQ(a,ONE) => simp(a)
-  case SEQ(a,b) => SEQ(simp(a),simp(b))
-  //case ALT(ZERO,a) => simp(a)
-  case ALT(a,ZERO) => simp(a)
-  case ALT(ONE,_) => ONE
-  case ALT(_,ONE) => ONE
-  case ALT(a,b) => {val sa = simp(a)
-                    if(sa == simp(b)) sa else r
-                    }
-  case STAR(STAR(a)) => simp(STAR(a))
-  case STAR(a) => STAR(simp(a))
-  case _ => r*/
+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
 }
 
 
-/*val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
-println("TEST: " + simp(der('a', der('a', EVIL))))
-println(simp(ONE))
-val r1 = ALT(ZERO,ONE)
-val r2 = SEQ(ONE,ZERO)
-val r3 = SEQ(r1,SEQ(r2,r1))
-println("R1 = " + simp(r1))
-println(simp(r2))
-println(simp(r3))
-*/
-
-// (4) Complete the two functions below; the first
+// (4) 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{
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
   case Nil => r
-  case a::z => ders(z,simp(der(a,r)))
+  case c::s => ders(s, simp(der(c, r)))
 }
 
-def matcher(r: Rexp, s: String): Boolean = {
-  val derivatives = simp(ders(s.toList,r))
-  nullable(derivatives)
-}
+// main matcher function
+def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
 
 // (5) Complete the size function for regular
-// expressions according to the specification
+// expressions according to the specification 
 // given in the coursework.
 
-def size(r: Rexp): Int = r match{
+
+def size(r: Rexp): Int = r match {
   case ZERO => 1
   case ONE => 1
   case CHAR(_) => 1
-  case SEQ(a,b) => 1 + size(a) + size(b)
-  case ALT(a,b) => 1 + size(a) + size(b)
-  case STAR(a) => 1 + size(a)
+  case ALT(r1, r2) => 1 + size(r1) + size (r2)
+  case SEQ(r1, r2) => 1 + size(r1) + size (r2)
+  case STAR(r1) => 1 + size(r1)
 }
 
-println(der('a', ZERO | ONE))// == (ZERO | ZERO)
-println(der('a', (CHAR('a') | ONE) ~ CHAR('a')))// ==ALT((ONE | ZERO) ~ CHAR('a'), ONE)
-println(der('a', STAR(CHAR('a'))))// == (ONE ~ STAR(CHAR('a')))
-println(der('b', STAR(CHAR('a'))))// == (ZERO ~ STAR(CHAR('a'))))
-// some testing data
-/*
-
-assert(matcher(("a" ~ "b") ~ "c", "abc") == true)  // => true
-assert(matcher(("a" ~ "b") ~ "c", "ab") == false)   // => false
-
-
-// the supposedly 'evil' regular expression (a*)* b
-//val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
 
 
-assert(matcher(EVIL, "a" * 1000 ++ "b") == true) // => true
-assert(matcher(EVIL, "a" * 1000) == false)          // => false
+// some testing data
+/*
+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
 
 // size without simplifications
-assert("28 " + size(der('a', der('a', EVIL)))             ==28)// => 28
-assert("58 " + size(der('a', der('a', der('a', EVIL))))   ==58)// => 58
+size(der('a', der('a', EVIL)))             // => 28
+size(der('a', der('a', der('a', EVIL))))   // => 58
 
 // size with simplification
-assert("8 " + size(simp(der('a', der('a', EVIL))))           ==8)// => 8
-assert("8 " + size(simp(der('a', der('a', der('a', EVIL))))) ==8) // => 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.
+// 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()
@@ -234,13 +162,15 @@
   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(50).next) == ONE
+// another "power" test case 
+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.
+ 
+*/
 
-*/
+//}