--- a/main_solution3/re.scala	Thu Nov 04 12:20:12 2021 +0000
+++ b/main_solution3/re.scala	Fri Nov 05 16:47:55 2021 +0000
@@ -1,19 +1,24 @@
 // Core Part about Regular Expression Matching
 //=============================================
 
-object CW8c {
+object M3 {
 
 // 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 
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 
-case class STAR(r: Rexp) extends Rexp 
+case class ALTs(rs: List[Rexp]) extends Rexp      // alternatives 
+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
 
+
+//the usual binary choice can be defined in terms of ALTs
+def ALT(r1: Rexp, r2: Rexp) = ALTs(List(r1, r2))
+
+
 import scala.language.implicitConversions    
 import scala.language.reflectiveCalls 
 
@@ -49,7 +54,7 @@
   case ZERO => false
   case ONE => true
   case CHAR(_) => false
-  case ALT(r1, r2) => nullable(r1) || nullable(r2)
+  case ALTs(rs) => rs.exists(nullable)
   case SEQ(r1, r2) => nullable(r1) && nullable(r2)
   case STAR(_) => true
 }
@@ -63,13 +68,22 @@
   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 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))
 }
 
+
+
+def flts(rs: List[Rexp]) : List[Rexp] = rs match {
+  case Nil => Nil
+  case ZERO::tl => flts(tl)
+  case ALTs(rs1)::rs2 => rs1 ::: flts(rs2)  
+  case r::rs => r :: flts(rs) 
+}
+
 // (3) Complete the simp function according to
 // the specification given in the coursework; this
 // function simplifies a regular expression from
@@ -77,11 +91,12 @@
 // 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 ALTs(rs) => (flts(rs.map(simp)).distinct) match {
+    case Nil => ZERO
+    case r::Nil => r  
+    case rs => ALTs(rs)
   }
   case SEQ(r1, r2) =>  (simp(r1), simp(r2)) match {
     case (ZERO, _) => ZERO
@@ -117,7 +132,7 @@
   case ZERO => 1
   case ONE => 1
   case CHAR(_) => 1
-  case ALT(r1, r2) => 1 + size(r1) + size (r2)
+  case ALTs(rs) => 1 + rs.map(size).sum
   case SEQ(r1, r2) => 1 + size(r1) + size (r2)
   case STAR(r1) => 1 + size(r1)
 }
@@ -132,16 +147,19 @@
 // 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))))          // => 8
+//println(simp(der('a', der('a', der('a', EVIL)))))// => 8
+
+//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