--- a/progs/re4.scala	Thu Jul 25 14:39:37 2019 +0100
+++ b/progs/re4.scala	Sun Jul 28 01:00:41 2019 +0100
@@ -1,4 +1,4 @@
-// Version which attempts to move whole strings, not
+// A version which attempts to move whole strings, not
 // just characters, under derivatives whenever possible
    
 abstract class Rexp
@@ -10,7 +10,7 @@
 case class STAR(r: Rexp) extends Rexp 
 case class NTIMES(r: Rexp, n: Int) extends Rexp 
 
-// nullable function: tests whether the regular 
+// the nullable function: tests whether the regular 
 // expression can recognise the empty string
 def nullable (r: Rexp) : Boolean = r match {
   case ZERO => false
@@ -22,7 +22,7 @@
   case NTIMES(r, i) => if (i == 0) true else nullable(r)
 }
 
-// derivative of a regular expression w.r.t. a character
+// 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
@@ -52,7 +52,7 @@
   case r => r
 }
 
-//example
+// an example
 val r = SEQ(SEQ(CHAR('x'), CHAR('y')), CHAR('z'))
 der('x', r)
 der('y', der('x', r))
@@ -60,7 +60,7 @@
 simp(der('z', der('y', der('x', r))))
 
 // *new*
-// derivative w.r.t. a string (iterates der)
+// the derivative w.r.t. a string (iterates der)
 def ders2(s: List[Char], r: Rexp) : Rexp = (s, r) match {
   case (Nil, r) => r
   case (s, ZERO) => ZERO
@@ -71,11 +71,11 @@
   case (c::s, r) => ders2(s, simp(der(c, r)))
 }
 
-// main matcher function
-def matcher(r: Rexp, s: String) : Boolean = nullable(ders2(s.toList, r))
+// the main matcher function
+def matches(r: Rexp, s: String) : Boolean = nullable(ders2(s.toList, r))
 
 
-//one or zero
+// one or zero
 def OPT(r: Rexp) = ALT(r, ONE)
 
 
@@ -84,35 +84,29 @@
 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
 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})
-for (i <- 1 to 7000001 by 500000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
+  "%.5f".format((end - start) / (i * 1.0e9))
 }
 
-for (i <- 1 to 7000001 by 500000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL1(i), "a" * i))))
+
+// test: (a?{n}) (a{n})
+for (i <- 0 to 7000000 by 500000) {
+  println(s"$i: ${time_needed(2, matches(EVIL1(i), "a" * i))}")
 }
 
-//test: (a*)* b
+
+// test: (a*)* b
 for (i <- 1 to 7000001 by 500000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
-}
-
-for (i <- 1 to 7000001 by 500000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL2, "a" * i))))
+  println(s"$i: ${time_needed(2, matches(EVIL2, "a" * i))}")
 }
 
 
 
-// size of a regular expressions - for testing purposes 
+// the size of a regular expressions - for testing purposes 
 def size(r: Rexp) : Int = r match {
   case ZERO => 1
   case ONE => 1
@@ -140,7 +134,7 @@
 // test: ("a" | "aa")*
 val EVIL3 = STAR(ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a'))))
 
-//test: ("" | "a" | "aa")*
+// test: ("" | "a" | "aa")*
 val EVIL3 = STAR(ALT(ONE, ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a')))))
 
 val t1  = ders2("a".toList, EVIL3)