diff -r 34feeb53c0ba -r 0315d9983cd0 main_testing3/re.scala
--- a/main_testing3/re.scala	Sun Jan 15 10:58:13 2023 +0000
+++ b/main_testing3/re.scala	Sat Mar 11 22:01:53 2023 +0000
@@ -3,7 +3,6 @@
 
 object M3 {
 
-// Regular Expressions
 abstract class Rexp
 case object ZERO extends Rexp
 case object ONE extends Rexp
@@ -18,7 +17,8 @@
 def ALT(r1: Rexp, r2: Rexp) = ALTs(List(r1, r2))
 def SEQ(r1: Rexp, r2: Rexp) = SEQs(List(r1, r2))
 
-// some convenience for typing in regular expressions
+
+// some convenience for typing regular expressions
 import scala.language.implicitConversions    
 import scala.language.reflectiveCalls 
 
@@ -43,129 +43,216 @@
   def ~ (r: String) = SEQ(s, r)
 }
 
-// (1) 
+// examples for the implicits:
+// ALT(CHAR('a'), CHAR('b'))
+// val areg : Rexp = "a" | "b"
+
+// SEQ(CHAR('a'), CHAR('b')) 
+// val sreg : Rexp = "a" ~ "b"
+
+
+// ADD YOUR CODE BELOW
+//======================
+
+// (1)
 def nullable (r: Rexp) : Boolean = r match {
-  case ZERO => false
-  case ONE => true
-  case CHAR(_) => false
-  case ALTs(rs) => rs.exists(nullable)
-  case SEQs(rs) => rs.forall(nullable)
-  case STAR(_) => true
+  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
 }
 
+/*
+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(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))
+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))
 }
 
+/*
+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::tl => denest(tl)
-  case ALTs(rs1)::rs2 => rs1 ::: denest(rs2)  
-  case r::rs => r :: denest(rs) 
+  case Nil                => Nil
+  case ZERO :: rest       => denest(rest)
+  case ALTs(rgs) :: rest  => rgs ::: denest(rest)
+  case r :: rest          => r :: denest(rest)
 }
 
+/*
+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::rs => ZERO::Nil
-  case ONE::rs => flts(rs, acc)
-  case SEQs(rs1)::rs => flts(rs, acc ::: rs1)
-  case r::rs => flts(rs, acc :+ r) 
+  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)) 
 }
 
+/*
+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 r::Nil => r  
-  case rs => ALTs(rs)
+  case Nil      => ZERO
+  case List(r)  => r
+  case _        => ALTs(rs)
 }
 
 def SEQs_smart(rs: List[Rexp]) : Rexp = rs match {
-  case Nil => ONE
-  case ZERO::Nil => ZERO
-  case r::Nil => r
-  case rs => SEQs(rs) 
+  case Nil      => ONE
+  case List(r)  => r
+  case _        => 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)
+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
 }
 
-// (6) 
+/*
+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')
+*/
 
-def simp(r: Rexp) : Rexp = r match {
-  case ALTs(rs) => 
-    ALTs_smart(denest(rs.map(simp)).distinct)
-  case SEQs(rs) => 
-    SEQs_smart(flts(rs.map(simp)))
-  case r => r
+// (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)
 }
 
-//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))))
+/*
+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
+*/
+
+// (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)
+}
+
+/*
+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
+*/
 
 
-// (7) 
-
-def ders (s: List[Char], r: Rexp) : Rexp = s match {
-  case Nil => r
-  case c::s => ders(s, simp(der(c, r)))
-}
-
-// main matcher function
-def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
-
-// (8) 
+// Some testing data
+//===================
+/*
 
-def size(r: Rexp): Int = r match {
-  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)
-}
+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
 
-// some testing data
-/*
-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'))
 
-println(matcher(EVIL, "a" * 1000 ++ "b"))   // => true
-println(matcher(EVIL, "a" * 1000))          // => false
+matcher(EVIL, "a" * 1000)          // => false
+matcher(EVIL, "a" * 1000 ++ "b")   // => true
+
 
 // size without simplifications
-println(size(der('a', der('a', EVIL))))             // => 36
-println(size(der('a', der('a', der('a', EVIL)))))   // => 83
+size(der('a', der('a', EVIL)))             // => 36
+size(der('a', der('a', der('a', EVIL))))   // => 83
 
 // size with simplification
-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
+size(simp(der('a', der('a', EVIL))))           // => 7
+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
-// 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 
-// few 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.
 
 def time_needed[T](i: Int, code: => T) = {
   val start = System.nanoTime()
@@ -179,35 +266,25 @@
 }
 
 // another "power" test case 
-println(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.
 
-assert(simp(ZERO | ONE) == ONE)
-assert(simp(STAR(ZERO | ONE)) == STAR(ZERO | ONE))
-assert(simp(ONE ~ (ONE ~ (ONE ~ CHAR('a')))) == CHAR('a'))
-assert(simp(((ONE ~ ONE) ~ ONE) ~ CHAR('a')) == CHAR('a'))
-assert(simp(((ONE | ONE) ~ ONE) ~ CHAR('a')) == CHAR('a'))
-assert(simp(ONE ~ (ONE ~ (ONE ~ ZERO))) == ZERO)
-assert(simp(ALT(ONE ~ (ONE ~ (ONE ~ ZERO)), CHAR('a'))) == CHAR('a'))
-assert(simp(CHAR('a') | CHAR('a')) == CHAR('a'))
-assert(simp(CHAR('a') ~ CHAR('a')) == CHAR('a') ~ CHAR('a'))
-assert(simp(ONE | CHAR('a')) == (ONE | CHAR('a')))
-assert(simp(ALT((CHAR('a') | ZERO) ~ ONE,
-                  ((ONE | CHAR('b')) | CHAR('c')) ~ (CHAR('d') ~ ZERO))) == CHAR('a'))
-assert(simp((ZERO | ((ZERO | ZERO) | (ZERO | ZERO))) ~ ((ONE | ZERO) | ONE ) ~ (CHAR('a'))) == ZERO)
-assert(simp(ALT(ONE | ONE, ONE | ONE)) == ONE)
-assert(simp(ALT(ZERO | CHAR('a'), CHAR('a') | ZERO)) == CHAR('a'))
-assert(simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE)) == ALT(ONE, CHAR('a')))
-assert(simp(ALTs(Nil)) == ZERO)
-assert(simp(SEQs(List(CHAR('a')))) == CHAR('a'))
-
+*/
 
 }
 
+
+
+
+
+
+// This template code is subject to copyright 
+// by King's College London, 2022. Do not 
+// make the template code public in any shape 
+// or form, and do not exchange it with other 
+// students under any circumstance.