diff -r 6512884e03b4 -r 155426396b5f progs/re1.scala
--- a/progs/re1.scala	Mon Jul 27 11:02:48 2020 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,154 +0,0 @@
-// A simple matcher for basic regular expressions
-
-abstract class Rexp
-case object ZERO extends Rexp                    // matches nothing
-case object ONE extends Rexp                     // matches an 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
-
-// nullable function: tests whether a 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
-}
-
-// the 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(r1) => SEQ(der(c, r1), STAR(r1))
-}
-
-// the 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))
-}
-
-// the main matcher function
-def matcher(r: Rexp, s: String) : Boolean = 
-  nullable(ders(s.toList, r))
-
-
-// examples from the homework
-
-val r = STAR(ALT(SEQ(CHAR('a'), CHAR('b')), CHAR('b')))
-der('a', r)
-der('b', r)
-der('c', r)
-
-val r2 = SEQ(SEQ(CHAR('x'), CHAR('y')), CHAR('z'))
-der('x', r2)
-der('y', der('x', r2))
-der('z', der('y', der('x', r2)))
-
-
-// the optional regular expression (one or zero times)
-def OPT(r: Rexp) = ALT(r, ONE)
-
-// the n-times regular expression (explicitly expanded)
-def NTIMES(r: Rexp, n: Int) : Rexp = n match {
-  case 0 => ONE
-  case 1 => r
-  case n => SEQ(r, NTIMES(r, n - 1))
-}
-
-
-// Test Cases
-
-// the evil regular expression  a?{n} a{n}
-def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
-
-// the evil regular expression (a*)*b
-val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
-
-// for measuring time
-def time_needed[T](i: Int, code: => T) = {
-  val start = System.nanoTime()
-  for (j <- 1 to i) code
-  val end = System.nanoTime()
-  (end - start) / (i * 1.0e9)
-}
-
-
-// test: (a?{n}) (a{n})
-println("Test (a?{n}) (a{n})")
-
-for (i <- 0 to 20 by 2) {
-  println(f"$i: ${time_needed(2, matcher(EVIL1(i), "a" * i))}%.5f")
-}
-
-// test: (a*)* b
-println("Test (a*)* b")
-
-for (i <- 0 to 20 by 2) {
-  println(f"$i: ${time_needed(2, matcher(EVIL2, "a" * i))}%.5f")
-}
-
-
-// the size of a regular expressions - for testing purposes 
-def size(r: Rexp) : Int = r match {
-  case ZERO => 1
-  case ONE => 1
-  case CHAR(_) => 1
-  case ALT(r1, r2) => 1 + size(r1) + size(r2)
-  case SEQ(r1, r2) => 1 + size(r1) + size(r2)
-  case STAR(r) => 1 + size(r)
-}
-
-// the expicit expansion in EVIL1(n) increases
-// drastically its size
-
-size(EVIL1(1))  // 5
-size(EVIL1(3))  // 17
-size(EVIL1(5))  // 29
-size(EVIL1(7))  // 41
-size(EVIL1(20)) // 119
-
-// given a regular expression and building successive
-// derivatives might result into bigger and bigger
-// regular expressions...here is an example for this:
-
-// (a+b)* o a o b o (a+b)*
-val BIG_aux = STAR(ALT(CHAR('a'), CHAR('b')))
-val BIG = SEQ(BIG_aux, SEQ(CHAR('a'),SEQ(CHAR('b'), BIG_aux)))
-
-size(ders("".toList, BIG))              // 13
-size(ders("ab".toList, BIG))            // 51
-size(ders("abab".toList, BIG))          // 112
-size(ders("ababab".toList, BIG))        // 191
-size(ders("abababab".toList, BIG))      // 288
-size(ders("ababababab".toList, BIG))    // 403
-size(ders("abababababab".toList, BIG))  // 536
-
-
-size(ders(("ab" * 200).toList, BIG))    // 366808
-
-for (i <- 0 to 200 by 10) {
-  println(f"$i: ${time_needed(2, matcher(BIG, "ab" * i))}%.5f")
-}
-
-
-
-
-//////////////////////////////////////
-def concat(A: Set[String], B: Set[String]) : Set[String] =
-  for (s1 <- A; s2 <- B) yield s1 ++ s2
-  
-
-val A = Set("foo", "bar")
-val B = Set("a", "b")
-
-