diff -r d94fdbef1a4f -r 1c9a23304b85 solution/cw1/cw1.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/solution/cw1/cw1.scala	Mon Sep 07 12:18:07 2020 +0100
@@ -0,0 +1,264 @@
+// CW 1
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls 
+
+abstract class Rexp
+case object ZERO extends Rexp                            // matches nothing
+case object ONE extends Rexp                             // matches the empty string
+case class CHAR(c: Char) extends Rexp                    // matches a character c
+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 RANGE(cs: Set[Char]) extends Rexp             // set of characters
+case class PLUS(r: Rexp) extends Rexp                    // plus
+case class OPT(r: Rexp) extends Rexp                     // optional
+case class NTIMES(r: Rexp, n: Int) extends Rexp          // n-times
+case class UPNTIMES(r: Rexp, n: Int) extends Rexp        // up n-times
+case class FROMNTIMES(r: Rexp, n: Int) extends Rexp      // from n-times
+case class NMTIMES(r: Rexp, n: Int, m: Int) extends Rexp // between nm-times
+case class NOT(r: Rexp) extends Rexp                     // not
+case class CFUN(f: Char => Boolean) extends Rexp         // subsuming CHAR and RANGE
+
+def CHAR(c: Char) = CFUN(d => c == d)
+val ALL = CFUN(_ => true)
+def RANGE(cs: Set[Char]) = CFUN(d => cs.contains(d))
+
+def CHAR(c: Char) = CFUN(c == _)
+val ALL = CFUN(_ => true)
+def RANGE(cs: Set[Char]) = CFUN(cs.contains(_))
+
+
+// nullable function: tests whether the regular 
+// expression can recognise the empty string
+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
+  case RANGE(_) => false
+  case PLUS(r) => nullable(r)
+  case OPT(_) => true
+  case NTIMES(r, n) => if (n == 0) true else nullable(r)
+  case UPNTIMES(_, _) => true
+  case FROMNTIMES(r, n) => if (n == 0) true else nullable(r)
+  case NMTIMES(r, n, m) => if (n == 0) true else nullable(r)
+  case NOT(r) => !nullable(r)
+  case CFUN(_) => false
+}
+
+// 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(r) => SEQ(der(c, r), STAR(r))
+  case RANGE(cs) => if (cs contains c) ONE else ZERO
+  case PLUS(r) => SEQ(der(c, r), STAR(r))
+  case OPT(r) => der(c, r)
+  case NTIMES(r, n) => 
+    if (n == 0) ZERO else SEQ(der(c, r), NTIMES(r, n - 1))
+  case UPNTIMES(r, n) =>
+    if (n == 0) ZERO else SEQ(der(c, r), UPNTIMES(r, n - 1))
+  case FROMNTIMES(r, n) =>
+    if (n == 0) SEQ(der(c, r), STAR(r)) else SEQ(der(c, r), FROMNTIMES(r, n - 1))
+  case NMTIMES(r, n, m) =>
+    if (m < n) ZERO else
+    if (n == 0 && m == 0) ZERO else 
+    if (n == 0) SEQ(der(c, r), UPNTIMES(r, m - 1)) 
+    else SEQ(der(c, r), NMTIMES(r, n - 1, m - 1)) 
+  case NOT(r) => NOT(der (c, r))
+  case CFUN(f) => if (f(c)) ONE else ZERO
+}
+
+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
+}
+
+
+// derivative w.r.t. a string (iterates der)
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders(s, der(c, r))
+}
+
+def ders_simp (s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders_simp(s, simp(der(c, r)))
+}
+
+// main matcher function including simplification
+def matcher(r: Rexp, s: String) : Boolean = 
+  nullable(ders_simp(s.toList, r))
+
+
+
+// some convenience for typing in regular expressions
+def charlist2rexp(s : List[Char]) : Rexp = s match {
+  case Nil => ONE
+  case c::Nil => CHAR(c)
+  case c::s => SEQ(CHAR(c), charlist2rexp(s))
+}
+implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
+
+implicit def RexpOps (r: Rexp) = new {
+  def | (s: Rexp) = ALT(r, s)
+  def % = STAR(r)
+  def ~ (s: Rexp) = SEQ(r, s)
+}
+
+implicit def stringOps (s: String) = new {
+  def | (r: Rexp) = ALT(s, r)
+  def | (r: String) = ALT(s, r)
+  def % = STAR(s)
+  def ~ (r: Rexp) = SEQ(s, r)
+  def ~ (r: String) = SEQ(s, r)
+}
+
+val r1 = NTIMES("a", 3)
+val r2 = NTIMES(OPT("a"), 3)
+val r3 = UPNTIMES("a", 3)
+val r4 = UPNTIMES(OPT("a"), 3)
+val r5 = NMTIMES("a", 3, 5)
+val r6 = NMTIMES(OPT("a"), 3, 5)
+
+val rs = List(r1, r2, r3, r4, r5, r6)
+
+rs.map(matcher(_, ""))
+rs.map(matcher(_, "a"))
+rs.map(matcher(_, "aa"))
+rs.map(matcher(_, "aaa"))
+rs.map(matcher(_, "aaaa"))
+rs.map(matcher(_, "aaaaa"))
+rs.map(matcher(_, "aaaaaa"))
+
+println("EMAIL:")
+val LOWERCASE = ('a' to 'z').toSet
+val DIGITS = ('0' to '9').toSet
+val EMAIL = { PLUS(CFUN(LOWERCASE | DIGITS | ("_.-").toSet)) ~ "@" ~ 
+              PLUS(CFUN(LOWERCASE | DIGITS | (".-").toSet)) ~ "." ~
+              NMTIMES(CFUN(LOWERCASE | Set('.')), 2, 6) }
+
+val my_email = "christian.urban@kcl.ac.uk"
+
+println(EMAIL);
+println(matcher(EMAIL, my_email))
+println(ders_simp(my_email.toList, EMAIL))
+
+println("COMMENTS:")
+val ALL = CFUN((c:Char) => true)
+val COMMENT = "/*" ~ (NOT(ALL.% ~ "*/" ~ ALL.%)) ~ "*/"
+
+println(matcher(COMMENT, "/**/"))
+println(matcher(COMMENT, "/*foobar*/"))
+println(matcher(COMMENT, "/*test*/test*/"))
+println(matcher(COMMENT, "/*test/*test*/"))
+
+println("EVILS:")
+val EVIL1 = PLUS(PLUS("a" ~ "a" ~ "a"))
+val EVIL2 = PLUS(PLUS("aaaaaaaaaaaaaaaaaaa" ~ OPT("a")))  // 19 as ~ a?
+
+
+//40 * aaa matches
+//43 * aaa + aa does not
+//45 * aaa + a
+
+println("EVIL1:")
+println(matcher(EVIL1, "aaa" * 40))
+println(matcher(EVIL1, "aaa" * 43 + "aa"))
+println(matcher(EVIL1, "aaa" * 45 + "a"))
+println("EVIL2:")
+println(matcher(EVIL2, "aaa" * 40))
+println(matcher(EVIL2, "aaa" * 43 + "aa"))
+println(matcher(EVIL2, "aaa" * 45 + "a"))
+
+println("TEST for bug pointed out by Filips Ivanovs")
+val test = NMTIMES(CFUN(LOWERCASE | Set('.')), 2, 6)
+  
+println(matcher(test,"a"))
+println(matcher(test,"ab"))
+println(matcher(test,"abcdef"))
+println(matcher(test,"abc"))
+println(matcher(test,"...."))
+println(matcher(test,"asdfg"))
+println(matcher(test,"abcdefg"))
+
+println(test)
+println(ders_simp("a".toList, test))
+println(ders_simp("aa".toList, test))
+println(ders_simp("aaa".toList, test))
+println(ders_simp("aaaa".toList, test))
+println(ders_simp("aaaaa".toList, test))
+println(ders_simp("aaaaaa".toList, test))
+println(ders_simp("aaaaaaa".toList, test))
+
+def TEST(s: String, r: Rexp) = {
+  println("Rexp |" + s + "|")
+  println("Derivative:\n" + ders_simp(s.toList, r))
+  println("Is Nullable: " + nullable(ders_simp(s.toList, r)))
+  Console.readLine
+}
+
+
+val ALL2 = "a" | "f"
+val COMMENT2 = ("/*" ~ NOT(ALL2.% ~ "*/" ~ ALL2.%) ~ "*/")
+
+println("1) TEST TEST")
+TEST("", COMMENT2)
+TEST("/", COMMENT2)
+TEST("/*", COMMENT2)
+TEST("/*f", COMMENT2)
+TEST("/*f*", COMMENT2)
+TEST("/*f*/", COMMENT2)
+TEST("/*f*/ ", COMMENT2)
+
+val ALL3 = "a" | "f"
+val COMMENT3 = ("/" ~ NOT(ALL3.% ~ "&" ~ ALL3.%) ~ "&")
+
+println("2) TEST TEST")
+TEST("", COMMENT3)
+TEST("/", COMMENT3)
+TEST("/", COMMENT3)
+TEST("/f", COMMENT3)
+TEST("/f&", COMMENT3)
+TEST("/f& ", COMMENT3)
+
+//test: ("a" | "aa") ~ ("a" | "aa")*
+val auxEVIL3 = ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a')))
+val EVIL3 = SEQ(auxEVIL3, STAR(auxEVIL3))
+val EVIL3p = FROMNTIMES(auxEVIL3, 1)
+
+
+for (i <- 1 to 100 by 1) {
+  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL3, "a" * i))) + " size: " + 
+	  size(ders(("a" * i).toList, EVIL3)))
+}
+
+
+
+val t1 = EVIL3
+val t2 = simp(der('a', t1))
+val t3 = simp(der('a', t2))
+val t4 = simp(der('a', t3))
+
+val t1 = EVIL3p
+val t2 = simp(der('a', t1))
+val t3 = simp(der('a', t2))
+val t4 = simp(der('a', t3))