--- a/TAs	Mon Dec 10 02:23:30 2018 +0000
+++ b/TAs	Fri Dec 14 14:41:54 2018 +0000
@@ -40,6 +40,21 @@
 233 submissions
 
 
+CW8, Part 1 
+               late (232)
+159  => 6       149
+39   => 5        44
+10   => 4        10
+4    => 3         4
+7    => 2         8
+2    => 1         1 
+11   => 0        16
+--------
+232 submissions
+
+
+
+
 =======================
 Ninos Lahdo used var instead of val, but in useless places
 Name: Ninos Lahdo

Binary file cws/cw04.pdf has changed

--- a/cws/cw04.tex	Mon Dec 10 02:23:30 2018 +0000
+++ b/cws/cw04.tex	Fri Dec 14 14:41:54 2018 +0000
@@ -126,11 +126,11 @@
 Since some tasks are time sensitive, you can check the reference
 implementation as follows: if you want to know, for example, how long it takes
 to match strings of $a$'s using the regular expression $(a^*)^*\cdot b$
-you can querry as follows:
+you can query as follows:
 
 
 
-\begin{lstlisting}[language={},xleftmargin=1mm,numbers=none,basicstyle=\ttfamily\small]
+\begin{lstlisting}[xleftmargin=1mm,numbers=none,basicstyle=\ttfamily\small]
 $ scala -cp re.jar
 scala> import CW9a._  
 scala> for (i <- 0 to 5000000 by 500000) {
@@ -231,7 +231,7 @@
 
 \item[(2)] Implement a function, called \textit{der}, by recursion over
   regular expressions. It takes a character and a regular expression
-  as arguments and calculates the derivative regular expression according
+  as arguments and calculates the derivative of a xregular expression according
   to the rules:
 
 \begin{center}
@@ -308,11 +308,11 @@
 
   simplifies to just $r_1$. \textbf{Hint:} Regular expressions can be
   seen as trees and there are several methods for traversing
-  trees. One of them corresponds to the inside-out traversal, which is
-  sometimes also called post-order traversal: you traverse inside the
+  trees. One of them corresponds to the inside-out traversal, which is also
+  sometimes called post-order tra\-versal: you traverse inside the
   tree and on the way up you apply simplification rules.
-  Furthermore,
-  remember numerical expressions from school times: there you had expressions
+  \textbf{Another Hint:}
+  Remember numerical expressions from school times---there you had expressions
   like $u + \ldots + (1 \cdot x) - \ldots (z + (y \cdot 0)) \ldots$
   and simplification rules that looked very similar to rules
   above. You would simplify such numerical expressions by replacing
@@ -378,7 +378,7 @@
   \]  
 
   \noindent correctly to just \texttt{ONE}, where \texttt{SEQ} is nested
-  50 or more times.\\
+  50 or more times?\\
   \mbox{}\hfill[1 Mark]
 \end{itemize}
 

--- a/marking4/mk	Mon Dec 10 02:23:30 2018 +0000
+++ b/marking4/mk	Fri Dec 14 14:41:54 2018 +0000
@@ -3,25 +3,27 @@
 
 trap "exit" INT
 
-files=${1:-assignment20178-*}
+files=${1:-assignment20179-*}
 
 for sd in $files; do
   cd $sd
   echo $sd
   touch .
-  cp ../../../marking3/re_test.sh .
-  cp ../../../marking3/re1a_test.scala .
-  cp ../../../marking3/re1b_test.scala .
-  cp ../../../marking3/re1c_test.scala .
-  cp ../../../marking3/re1d_test.scala .
-  cp ../../../marking3/re1e_test.scala .
+  cp ../../../marking4/re_test.sh .
+  cp ../../../marking4/re_test1.scala .
+  cp ../../../marking4/re_test2.scala .
+  cp ../../../marking4/re_test3.scala .
+  cp ../../../marking4/re_test4.scala .
+  cp ../../../marking4/re_test5.scala .
+  cp ../../../marking4/re_test6.scala .
   ./re_test.sh output
   rm re_test.sh
-  rm re1a_test.scala
-  rm re1b_test.scala
-  rm re1c_test.scala
-  rm re1d_test.scala
-  rm re1e_test.scala
+  rm re_test1.scala
+  rm re_test2.scala
+  rm re_test3.scala
+  rm re_test4.scala
+  rm re_test5.scala
+  rm re_test6.scala
   cd ..
 done
 

--- a/marking4/re.scala	Mon Dec 10 02:23:30 2018 +0000
+++ b/marking4/re.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -1,8 +1,9 @@
 // Part 1 about Regular Expression Matching
 //==========================================
 
-object CW8a {
+//object CW9a {
 
+// Regular Expressions
 abstract class Rexp
 case object ZERO extends Rexp
 case object ONE extends Rexp
@@ -38,10 +39,11 @@
   def ~ (r: String) = SEQ(s, r)
 }
 
-// (1a) Complete the function nullable according to
+// (1) Complete the function nullable according to
 // the definition given in the coursework; this 
 // function checks whether a regular expression
-// can match the empty string
+// can match the empty string and Returns a boolean
+// accordingly.
 
 def nullable (r: Rexp) : Boolean = r match {
   case ZERO => false
@@ -52,10 +54,10 @@
   case STAR(_) => true
 }
 
-// (1b) Complete the function der according to
+// (2) Complete the function der according to
 // the definition given in the coursework; this
 // function calculates the derivative of a 
-// regular expression w.r.t. a character
+// regular expression w.r.t. a character.
 
 def der (c: Char, r: Rexp) : Rexp = r match {
   case ZERO => ZERO
@@ -68,11 +70,12 @@
   case STAR(r1) => SEQ(der(c, r1), STAR(r1))
 }
 
-// (1c) Complete the function der according to
+// (3) Complete the simp function according to
 // the specification given in the coursework; this
-// function simplifies a regular expression;
-// however it does not simplify inside STAR-regular
-// expressions
+// function simplifies a regular expression from
+// the inside out, like you would simplify arithmetic 
+// 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 {
@@ -90,11 +93,12 @@
   case r => r
 }
 
-// (1d) Complete the two functions below; the first 
+
+// (4) Complete the two functions below; the first 
 // calculates the derivative w.r.t. a string; the second
 // is the regular expression matcher taking a regular
 // expression and a string and checks whether the
-// string matches the regular expression
+// string matches the regular expression.
 
 def ders (s: List[Char], r: Rexp) : Rexp = s match {
   case Nil => r
@@ -102,12 +106,13 @@
 }
 
 // main matcher function
-def matcher(r: Rexp, s: String): Boolean = nullable(ders(s.toList, r))
+def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
 
-// (1e) Complete the size function for regular
-// expressions  according to the specification 
+// (5) Complete the size function for regular
+// expressions according to the specification 
 // given in the coursework.
 
+
 def size(r: Rexp): Int = r match {
   case ZERO => 1
   case ONE => 1
@@ -120,29 +125,31 @@
 
 
 // some testing data
-/*
-matcher(("a" ~ "b") ~ "c", "abc")  // => true
-matcher(("a" ~ "b") ~ "c", "ab")   // => false
+
+//matcher(("a" ~ "b") ~ "c", "abc")  // => true
+//matcher(("a" ~ "b") ~ "c", "ab")   // => false
 
 // 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
+//matcher(EVIL, "a" * 1000 ++ "b")   // => true
+//matcher(EVIL, "a" * 1000)          // => false
 
 // size without simplifications
-size(der('a', der('a', EVIL)))             // => 28
-size(der('a', der('a', der('a', EVIL))))   // => 58
+//size(der('a', der('a', EVIL)))             // => 28
+//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
+//size(simp(der('a', der('a', EVIL))))           // => 8
+//size(simp(der('a', der('a', der('a', EVIL))))) // => 8
 
-// Java needs around 30 seconds for matching 28 a's with EVIL. 
+// 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.
 //
 // Lets see how long it takes to match strings with 
-// 0.5 Million a's...it should be in the range of some
-// seconds.
+// 5 Million a's...it should be in the range of a 
+// couple of seconds.
 
 def time_needed[T](i: Int, code: => T) = {
   val start = System.nanoTime()
@@ -151,9 +158,19 @@
   (end - start)/(i * 1.0e9)
 }
 
-for (i <- 0 to 5000000 by 500000) {
-  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))))
-}
-*/
+//for (i <- 0 to 5000000 by 500000) {
+//  println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))) + " secs.") 
+//}
+
+// another "power" test case 
+//simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE
 
-}
+// the Iterator produces the rexp
+//
+//      SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)
+//
+//    where SEQ is nested 100 times.
+ 
+
+
+//}

--- a/marking4/re1a_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,11 +0,0 @@
-import CW8a._
-
-assert(nullable(ZERO) == false)
-assert(nullable(ONE) == true)
-assert(nullable(CHAR('a')) == false)
-assert(nullable(ZERO | ONE) == true)
-assert(nullable(ZERO | CHAR('a')) == false)
-assert(nullable(ONE ~  ONE) == true)
-assert(nullable(ONE ~ CHAR('a')) == false)
-assert(nullable(STAR(ZERO)) == true)
-

--- a/marking4/re1b_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,8 +0,0 @@
-
-import CW8a._
-
-assert(der('a', ZERO | ONE) == (ZERO | ZERO))
-assert(der('a', (CHAR('a') | ONE) ~ CHAR('a')) == ALT((ONE | ZERO) ~ CHAR('a'), ONE))
-assert(der('a', (CHAR('a') | CHAR('a')) ~ CHAR('a')) == (ONE | ONE) ~ CHAR('a'))
-assert(der('a', STAR(CHAR('a'))) == (ONE ~ STAR(CHAR('a'))))
-assert(der('b', STAR(CHAR('a'))) == (ZERO ~ STAR(CHAR('a'))))

--- a/marking4/re1c_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,19 +0,0 @@
-
-import CW8a._
-
-
-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 ~ 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(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE)
-

--- a/marking4/re1d_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,19 +0,0 @@
-
-import CW8a._
-
-val EVIL_urban = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
-
-assert(ders(("a" * 5).toList, EVIL_urban) == SEQ(SEQ(STAR(CHAR('a')),STAR(STAR(CHAR('a')))),CHAR('b')))
-assert(ders(List('b'), EVIL_urban) == ONE)
-assert(ders(List('b','b'), EVIL_urban) == ZERO)
-assert(matcher(EVIL_urban, "a" * 5 ++ "b") == true)
-assert(matcher(EVIL_urban, "a" * 500 ++ "b") == true)
-assert(matcher(EVIL_urban, "a" * 500) == false)
-assert(matcher(EVIL_urban, "b") == true)
-assert(matcher(EVIL_urban, "bb") == false)
-assert(matcher("abc", "abc") == true)
-assert(matcher(("ab" | "a") ~ (ONE | "bc"), "abc") == true)
-assert(matcher(ONE, "") == true)
-assert(matcher(ZERO, "") == false)
-assert(matcher(ONE | CHAR('a'), "") == true)
-assert(matcher(ONE | CHAR('a'), "a") == true)

--- a/marking4/re1e_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,10 +0,0 @@
-
-import CW8a._
-
-val EVIL_urban = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
-
-assert(size(der('a', der('a', EVIL_urban))) == 28)
-assert(size(der('a', der('a', der('a', EVIL_urban)))) == 58)
-
-assert(size(ders("aaaaaa".toList, EVIL_urban)) == 8)
-assert(size(ders(("a" * 50).toList, EVIL_urban)) == 8)

--- a/marking4/re_test.sh	Mon Dec 10 02:23:30 2018 +0000
+++ b/marking4/re_test.sh	Fri Dec 14 14:41:54 2018 +0000
@@ -9,24 +9,28 @@
 
 
 echo "Below is the feedback and provisional marks for your submission" >> $out
-echo "for assignment 8 Part 1.  Please note all marks are provisional until" >> $out
+echo "for assignment 9 Part 1.  Please note all marks are provisional until" >> $out
 echo "ratified by the assessment board -- this is not an official" >> $out
 echo "results transcript." >> $out
 echo "" >> $out
 
-# marks for CW8 part 1
+# marks for CW9 part 1
 marks=$(( 0 ))
 
 # compilation tests
 
 function scala_compile {
-    (ulimit -t 360; JAVA_OPTS="-Xmx1g" scala "$1" 2> /dev/null 1> /dev/null)
+    (ulimit -t 30; JAVA_OPTS="-Xmx1g" scala -nc "$1" 2> /dev/null 1> /dev/null)
 }
 
 # functional tests
 
 function scala_assert {
-    (ulimit -t 360; JAVA_OPTS="-Xmx1g" scala -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null)
+    (ulimit -t 30; JAVA_OPTS="-Xmx1g" scala -nc -i "$1" "$2" -e "") # 2> /dev/null 1> /dev/null)
+}
+
+function scala_assert_long {
+    (ulimit -t 60; JAVA_OPTS="-Xmx1g" scala -nc -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null)
 }
 
 # purity test
@@ -67,7 +71,7 @@
   tsts1=$(( 1 ))     
 fi
 
-
+### re1 test
 
 if [ $tsts1 -eq 0 ]
 then
@@ -80,7 +84,7 @@
   echo " nullable(ONE ~ CHAR('a')) == false" | tee -a $out
   echo " nullable(STAR(ZERO)) == true" | tee -a $out
   
-  if (scala_assert "re.scala" "re1a_test.scala")
+  if (scala_assert "re.scala" "re_test1.scala")
   then
       echo "  --> success" | tee -a $out
       marks=$(( marks + 1 ))
@@ -89,7 +93,7 @@
   fi
 fi
 
-
+### re2 test
 
 if [ $tsts1 -eq 0 ]
 then
@@ -98,8 +102,23 @@
   echo " der('a', (CHAR('a') | CHAR('a')) ~ CHAR('a')) == (ONE | ONE) ~ CHAR('a')" | tee -a $out
   echo " der('a', STAR(CHAR('a'))) == (ONE ~ STAR(CHAR('a')))" | tee -a $out
   echo " der('b', STAR(CHAR('a'))) == (ZERO ~ STAR(CHAR('a')))" | tee -a $out
-  
-  if (scala_assert "re.scala" "re1b_test.scala")
+  echo "" | tee -a $out
+  echo " val r0 = \"a\" ~ \"b\" ~ \"c\"" | tee -a $out
+  echo " assert(der('a', r0) == (ONE ~ \"b\") ~ \"c\")" | tee -a $out
+  echo " assert(der('b', r0) == (ZERO ~ \"b\") ~ \"c\")" | tee -a $out
+  echo " assert(der('c', r0) == (ZERO ~ \"b\") ~ \"c\")" | tee -a $out
+  echo "" | tee -a $out
+  echo " val r1 = (ONE ~ \"b\") ~ \"c\"" | tee -a $out
+  echo " assert(der('a', r1) == ((ZERO ~ \"b\") | ZERO) ~ \"c\")" | tee -a $out
+  echo " assert(der('b', r1) == ((ZERO ~ \"b\") | ONE) ~ \"c\")" | tee -a $out
+  echo " assert(der('c', r1) == ((ZERO ~ \"b\") | ZERO) ~ \"c\")" | tee -a $out
+  echo "" | tee -a $out
+  echo " val r2 = ((ZERO ~ \"b\") | ONE) ~ \"c\"" | tee -a $out
+  echo " assert(der('a', r2) == ((((ZERO ~ \"b\") | ZERO) ~ \"c\") | ZERO))" | tee -a $out
+  echo " assert(der('b', r2) == ((((ZERO ~ \"b\") | ZERO) ~ \"c\") | ZERO))" | tee -a $out
+  echo " assert(der('c', r2) == ((((ZERO ~ \"b\") | ZERO) ~ \"c\") | ONE))" | tee -a $out
+
+  if (scala_assert "re.scala" "re_test2.scala")
   then
       echo "  --> success" | tee -a $out
       marks=$(( marks + 1 ))
@@ -108,13 +127,15 @@
   fi
 fi
 
-
+### re3 test
 
 if [ $tsts1 -eq 0 ]
 then
   echo " simp(ZERO | ONE) == ONE" | tee -a $out
   echo " simp(STAR(ZERO | ONE)) == STAR(ZERO | ONE)" | tee -a $out
   echo " simp(ONE ~ (ONE ~ (ONE ~ CHAR('a')))) == CHAR('a')" | tee -a $out
+  echo " simp(((ONE ~ ONE) ~ ONE) ~ CHAR('a')) == CHAR('a')" | tee -a $out
+  echo " simp(((ONE | ONE) ~ ONE) ~ CHAR('a')) == CHAR('a')" | tee -a $out
   echo " simp(ONE ~ (ONE ~ (ONE ~ ZERO))) == ZERO" | tee -a $out
   echo " simp(ALT(ONE ~ (ONE ~ (ONE ~ ZERO)), CHAR('a'))) == CHAR('a')" | tee -a $out
   echo " simp(CHAR('a') | CHAR('a')) == CHAR('a')" | tee -a $out
@@ -125,21 +146,18 @@
   echo " simp((ZERO | ((ZERO | ZERO) | (ZERO | ZERO))) ~ ((ONE | ZERO) | ONE ) ~ (CHAR('a'))) == ZERO" | tee -a $out
   echo " simp(ALT(ONE | ONE, ONE | ONE)) == ONE" | tee -a $out
   echo " simp(ALT(ZERO | CHAR('a'), CHAR('a') | ZERO)) == CHAR('a')" | tee -a $out
-  echo " simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE" | tee -a $out
-  echo "    the Iterator produces the rexp" | tee -a $out
-  echo "" | tee -a $out
-  echo "      SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)" | tee -a $out
-  echo "" | tee -a $out
-  echo "    where SEQ is nested 50 times." | tee -a $out
-  if (scala_assert "re.scala" "re1c_test.scala")
+  echo " simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE)) == ALT(ONE | CHAR('a'), CHAR('a') | ONE)" tee -a $out
+  
+  if (scala_assert "re.scala" "re_test3.scala")
   then
       echo "  --> success" | tee -a $out
-      marks=$(( marks + 2 ))
+      marks=$(( marks + 1 ))
   else
       echo "  --> test failed" | tee -a $out
   fi
 fi
 
+### re4 test
 
 if [ $tsts1 -eq 0 ]
 then
@@ -153,13 +171,14 @@
   echo " matcher(EVIL, \"b\") == true" | tee -a $out
   echo " matcher(EVIL, \"bb\") == false" | tee -a $out
   echo " matcher(\"abc\", \"abc\") == true" | tee -a $out
+  echo " matcher(\"abc\", \"ab\") == true" | tee -a $out
   echo " matcher((\"ab\" | \"a\") ~ (ONE | \"bc\"), \"abc\") == true" | tee -a $out
   echo " matcher(ONE, \"\") == true" | tee -a $out
   echo " matcher(ZERO, \"\") == false" | tee -a $out
   echo " matcher(ONE | CHAR('a'), \"\") == true" | tee -a $out
   echo " matcher(ONE | CHAR('a'), \"a\") == true" | tee -a $out
   
-  if (scala_assert "re.scala" "re1d_test.scala")
+  if (scala_assert "re.scala" "re_test4.scala")
   then
       echo "  --> success" | tee -a $out
       marks=$(( marks + 1 ))
@@ -168,6 +187,8 @@
   fi
 fi
 
+### re5 test
+
 
 if [ $tsts1 -eq 0 ]
 then
@@ -177,7 +198,37 @@
   echo " size(ders(\"aaaaaa\".toList, EVIL)) == 8" | tee -a $out
   echo " size(ders((\"a\" * 50).toList, EVIL)) == 8" | tee -a $out
   
-  if (scala_assert "re.scala" "re1e_test.scala")
+  if (scala_assert "re.scala" "re_test5.scala")
+  then
+      echo "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+      echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+### re6 'power' test
+
+
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE" | tee -a $out
+  echo "    ...the Iterator produces the rexp" | tee -a $out
+  echo "" | tee -a $out
+  echo "      SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)" | tee -a $out
+  echo "" | tee -a $out
+  echo "    where SEQ is nested 50 times." | tee -a $out  
+  echo "" | tee -a $out
+  echo " simp(Iterator.iterate(ONE:Rexp)(r => ALT(r, r)).drop(20).next) == ONE" | tee -a $out
+  echo "    ... the Iterator produces a rexp of size 2097151" | tee -a $out
+  echo "" | tee -a $out
+  echo " val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))" | tee -a $out
+  echo " matcher(EVIL, \"a\" * 1000000 ++ \"b\") == true" | tee -a $out
+  echo " matcher(EVIL, \"a\" * 1000000) == false" | tee -a $out
+
+  
+  if (time scala_assert_long "re.scala" "re_test6.scala")
   then
       echo "  --> success" | tee -a $out
       marks=$(( marks + 1 ))
@@ -188,7 +239,7 @@
 
 
 ## final marks
-echo "Overall mark for CW 8, Part 1" | tee -a $out
+echo "Overall mark for CW 9, Part 1" | tee -a $out
 echo "$marks" | tee -a $out
 
 

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking4/re_test1.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,10 @@
+
+assert(nullable(ZERO) == false)
+assert(nullable(ONE) == true)
+assert(nullable(CHAR('a')) == false)
+assert(nullable(ZERO | ONE) == true)
+assert(nullable(ZERO | CHAR('a')) == false)
+assert(nullable(ONE ~  ONE) == true)
+assert(nullable(ONE ~ CHAR('a')) == false)
+assert(nullable(STAR(ZERO)) == true)
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking4/re_test2.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,24 @@
+
+assert(der('a', ZERO | ONE) == (ZERO | ZERO))
+assert(der('a', (CHAR('a') | ONE) ~ CHAR('a')) == ALT((ONE | ZERO) ~ CHAR('a'), ONE))
+assert(der('a', (CHAR('a') | CHAR('a')) ~ CHAR('a')) == (ONE | ONE) ~ CHAR('a'))
+assert(der('a', STAR(CHAR('a'))) == (ONE ~ STAR(CHAR('a'))))
+assert(der('b', STAR(CHAR('a'))) == (ZERO ~ STAR(CHAR('a'))))
+
+
+val r0_urban = "a" ~ "b" ~ "c"
+assert(der('a', r0_urban) == (ONE ~ "b") ~ "c")
+assert(der('b', r0_urban) == (ZERO ~ "b") ~ "c")
+assert(der('c', r0_urban) == (ZERO ~ "b") ~ "c")
+
+val r1_urban = (ONE ~ "b") ~ "c"
+
+assert(der('a', r1_urban) == ((ZERO ~ "b") | ZERO) ~ "c")
+assert(der('b', r1_urban) == ((ZERO ~ "b") | ONE) ~ "c")
+assert(der('c', r1_urban) == ((ZERO ~ "b") | ZERO) ~ "c")
+
+val r2_urban = ((ZERO ~ "b") | ONE) ~ "c"
+
+assert(der('a', r2_urban) == ((((ZERO ~ "b") | ZERO) ~ "c") | ZERO))
+assert(der('b', r2_urban) == ((((ZERO ~ "b") | ZERO) ~ "c") | ZERO))
+assert(der('c', r2_urban) == ((((ZERO ~ "b") | ZERO) ~ "c") | ONE))

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking4/re_test3.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,21 @@
+
+
+
+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'), CHAR('a') | ONE))
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking4/re_test4.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,19 @@
+
+
+val EVIL_urban = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+
+assert(ders(("a" * 5).toList, EVIL_urban) == SEQ(SEQ(STAR(CHAR('a')),STAR(STAR(CHAR('a')))),CHAR('b')))
+assert(ders(List('b'), EVIL_urban) == ONE)
+assert(ders(List('b','b'), EVIL_urban) == ZERO)
+assert(matcher(EVIL_urban, "a" * 5 ++ "b") == true)
+assert(matcher(EVIL_urban, "a" * 50 ++ "b") == true)
+assert(matcher(EVIL_urban, "a" * 50) == false)
+assert(matcher(EVIL_urban, "b") == true)
+assert(matcher(EVIL_urban, "bb") == false)
+assert(matcher("abc", "abc") == true)
+assert(matcher("abc", "ab") == false)
+assert(matcher(("ab" | "a") ~ (ONE | "bc"), "abc") == true)
+assert(matcher(ONE, "") == true)
+assert(matcher(ZERO, "") == false)
+assert(matcher(ONE | CHAR('a'), "") == true)
+assert(matcher(ONE | CHAR('a'), "a") == true)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking4/re_test5.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,8 @@
+
+val EVIL_urban = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+
+assert(size(der('a', der('a', EVIL_urban))) == 28)
+assert(size(der('a', der('a', der('a', EVIL_urban)))) == 58)
+
+assert(size(ders("aaaaaa".toList, EVIL_urban)) == 8)
+assert(size(ders(("a" * 50).toList, EVIL_urban)) == 8)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/marking4/re_test6.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,9 @@
+
+
+val EVIL_urban = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+
+
+assert(simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE)
+assert(simp(Iterator.iterate(ONE:Rexp)(r => ALT(r, r)).drop(20).next) == ONE)
+assert(matcher(EVIL_urban, "a" * 1000000) == false)
+assert(matcher(EVIL_urban, "a" * 1000000 ++ "b") == true)

--- a/testing3-bak/knight1.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,133 +0,0 @@
-
-// Part 1 about finding and counting Knight's tours
-//==================================================
-
-object CW7a extends App{
-
-type Pos = (Int, Int)    // a position on a chessboard 
-type Path = List[Pos]    // a path...a list of positions
-
-//(1a) Complete the function that tests whether the position 
-//     is inside the board and not yet element in the path.
-
-//def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = ...
-
-def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = {
-  
-// if ((x._1<dim && x._2<dim) && (x._1>0 || x._2>0)) false else !path.contains(x)
- 
-  if (x._1 < 0 || x._2 < 0) false 
-  else if (x._1 < dim && x._2 < dim && !path.contains(x)) true 
-  else false
- 
-  
-}
-
-
-
-def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = {
-  
-  val allPossibleMoves = List((x._1+1, x._2+2), (x._1+2, x._2+1), (x._1+2, x._2-1), (x._1+1, x._2-2), (x._1-1, x._2-2), (x._1-2, x._2-1), (x._1-2, x._2+1), (x._1-1, x._2+2));
- 
-  //val finalList = allPossibleMoves.filter((a=>a._1<dim && a._2<dim && x._1 >= 0 && a._2 >= 0));
-  
-  val finalList = for(pos<-allPossibleMoves if(is_legal(dim,path)(pos))) yield pos;
-  
-  // println("Space in board: " + dim*dim + " for dim: " + dim)
-   
-  
-  finalList.toList;
-    
-  
-}
-
-println(legal_moves(8, Nil, (2,2)))
-println(legal_moves(8, Nil, (7,7)))
-println(legal_moves(8, List((4,1), (1,0)), (2,2)))
-println(legal_moves(8, List((6,6)), (7,7)))
-println(legal_moves(1, Nil, (0,0)))
-println(legal_moves(2, Nil, (0,0)))
-println(legal_moves(3, Nil, (0,0)))
-
-println("=================================================================================")
-println("================================Comparision output===============================")
-println("=================================================================================")
-
-println(legal_moves(8, Nil, (2,2)) == List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
-println(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
-println(legal_moves(8, List((4,1), (1,0)), (2,2)) == List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
-println(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
-println(legal_moves(1, Nil, (0,0)) == Nil)
-println(legal_moves(2, Nil, (0,0)) == Nil)
-println(legal_moves(3, Nil, (0,0)) == List((1,2), (2,1)))
-
-
-def count_tours(dim: Int, path: Path) : Int = {
-     
-  val allMovesFromCurrentPosition = legal_moves(dim, path, path.head);
-  
-  if (path.length == dim*dim) 1 else  {
-    
-    if (allMovesFromCurrentPosition.size == 0 ) 0  else {
-      
-      allMovesFromCurrentPosition.map( element => count_tours(dim, element::path)).sum
-      
-      
-    }
-    
-  }
-  
-}
-    
-  
-
-println ( count_tours(5, List((0,0))) )
-
-def enum_tours(dim: Int, path: Path) : List[Path] = {
-  
-     val allMovesFromCurrentPosition = legal_moves(dim, path, path.head);
-  
-  if (path.length == dim*dim) List(path) else  {
-    
-  allMovesFromCurrentPosition.map( element => enum_tours(dim, element::path)).flatten ;
-      
-      
-      }
-    }
-  println ( enum_tours(6, List((0,2))).size)
-}
-
-
-
-
-
- 
- 
-//(1b) Complete the function that calculates for a position 
-//     all legal onward moves that are not already in the path. 
-//     The moves should be ordered in a "clockwise" manner.
- 
-//def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = ...
-
-
-
-
-//some test cases
-//
-//assert(legal_moves(8, Nil, (2,2)) == 
-//  List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
-//assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
-//assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == 
-//  List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
-//assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
-
-
-//(1c) Complete the two recursive functions below. 
-//     They exhaustively search for knight's tours starting from the 
-//     given path. The first function counts all possible tours, 
-//     and the second collects all tours in a list of paths.
-
-//def count_tours(dim: Int, path: Path) : Int = ...
-
-
-//def enum_tours(dim: Int, path: Path) : List[Path] = ...

--- a/testing3-bak/knight1_test.sh	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,195 +0,0 @@
-#!/bin/bash
-set -e
-
-out=${1:-output}
-
-echo "" > $out
-
-echo "Below is the feedback for your submission of CW 7, Part 1 and 2." >> $out
-echo "" >> $out
-
-
-# compilation tests
-
-function scala_compile {
-  (ulimit -t 30; JAVA_OPTS="-Xmx1g" scala "$1" 2>> $out 1>> $out) 
-}
-
-# functional tests
-
-function scala_assert_slow {
-  (ulimit -t 120; JAVA_OPTS="-Xmx1g" scala -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null)
-}
-
-function scala_assert_thirty {
-  (ulimit -t 30; JAVA_OPTS="-Xmx1g" scala -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null)
-}
-
-function scala_assert_quick {
-  (ulimit -t 10; JAVA_OPTS="-Xmx1g" scala -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null)
-}
-
-# purity test
-
-function scala_vars {
-   (egrep '\bvar\b|\breturn\b|\.par|ListBuffer|mutable|new Array' "$1" 2> /dev/null 1> /dev/null)
-}
-
-
-# knights1: purity test
-
-echo "knight1.scala does not contain vars, returns etc?" >> $out
-
-if (scala_vars knight1.scala)
-then
-  echo "  --> fail: if you do not fix this, you will receive a mark of zero" >> $out
-  tsts0=$(( 1 ))
-else
-  echo "  --> success" >> $out
-  tsts0=$(( 0 )) 
-fi
-
-
-# compilation test
-
-if [ $tsts0 -eq 0 ]
-then    
-  echo "knight1.scala runs?" >> $out
-
-  if (scala_compile knight1.scala)
-  then
-    echo "  --> success " >> $out
-    tsts1=$(( 0 ))
-  else
-    echo "  --> scala did not run knight1.scala" >> $out
-    tsts1=$(( 1 )) 
-  fi
-else
-  tsts1=$(( 1 ))   
-fi
-
-### knight1a test
-
-if [ $tsts1 -eq 0 ]
-then
-    echo "Takes 10 seconds or less to execute: " >> $out
-    echo " is_legal(8, Nil)(3, 4) == true " >> $out
-    echo " is_legal(8, List((4, 1), (1, 0)))(4, 1) == false " >> $out
-    echo " is_legal(2, Nil)(0, 0) == true" >> $out                          
-
-    if (scala_assert_quick "knight1.scala" "knight1a_test.scala")
-    then
-        echo "  --> success" >> $out
-    else
-        echo "  --> test failed" >> $out
-    fi
-fi
-
-### knight1b test
-
-if [ $tsts1 -eq 0 ]
-then
-  echo "Takes 10 seconds or less to execute: " >> $out
-  echo " legal_moves(8, Nil, (2,2)) == List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4))" >> $out
-  echo " legal_moves(8, Nil, (7,7)) == List((6,5), (5,6))" >> $out
-  echo " legal_moves(8, List((4,1), (1,0)), (2,2)) == List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4))" >> $out
-  echo " legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6))" >> $out
-  echo " legal_moves(1, Nil, (0,0)) == Nil" >> $out
-  echo " legal_moves(2, Nil, (0,0)) == Nil" >> $out
-  echo " legal_moves(3, Nil, (0,0)) == List((1,2), (2,1))" >> $out
-  
-  if (scala_assert_quick "knight1.scala" "knight1b_test.scala")
-  then
-    echo "  --> success" >> $out
-  else
-    echo "  --> test failed" >> $out
-  fi
-fi
-
-
-### knight1c test
-
-if [ $tsts1 -eq 0 ]
-then
-  echo " all_tours from every position on the board, in 2 minutes or less" >> $out
-  echo " dim = 1: 1" >> $out
-  echo "       2: 0,0,0,0" >>  $out
-  echo "       3: 0,0,0,0,0,0,0,0,0" >>  $out
-  echo "       4: 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0" >> $out
-  echo "       5: 304,0,56,0,304,0,56,0,56,0,56,0,64,0,56,0,56,0,56,0,304,0,56,0,304" >> $out
-  echo " enum_tours(5, List((0,2)) ) == 56 and all correct?" >> $out
-  
-  if (scala_assert_slow "knight1.scala" "knight1c_test.scala") 
-  then
-    echo "  --> success" >> $out
-  else
-    echo "  --> test failed" >> $out
-  fi
-fi
-
-
-# knights2: var test
-
-echo "knight2.scala does not contain vars, returns etc?" >> $out
-
-if (scala_vars knight2.scala)
-then
-  echo "  --> fail" >> $out
-  tsts0=$(( 1 ))
-else
-  echo "  --> success" >> $out
-  tsts0=$(( 0 )) 
-fi
-
-
-# compilation test
-if  [ $tsts0 -eq 0 ]
-then    
-  echo "knight2.scala runs?" >> $out
-
-  if (scala_compile knight2.scala)
-  then
-    echo "  --> success" >> $out
-    tsts1=$(( 0 ))
-  else
-    echo "  --> scala did not run knight2.scala" >> $out
-    tsts1=$(( 1 )) 
-  fi
-else
-  tsts1=$(( 1 ))     
-fi
-
-### knight2a test
-
-if [ $tsts1 -eq 0 ]
-then
-  echo "Takes 10 seconds or less to execute: " >> $out
-  echo " Let f = (x:(Int, Int)) => if (x._1 > 3) Some(List(x)) else None " >> $out
-  echo "   first(List((1,0),(2,0),(3,0),(4,0)), f) == Some(List((4,0)))" >> $out
-  echo "   first(List((1,0),(2,0),(3,0)), f) == None" >> $out
-
-  if (scala_assert_quick "knight2.scala" "knight2a_test.scala") 
-  then
-    echo "  --> success" >> $out
-  else
-    echo "  --> test failed" >> $out
-  fi
-fi
-
-
-### knight2b test
-
-if [ $tsts1 -eq 0 ]
-then
-  echo "Takes 30 seconds or less to execute: " >> $out
-  echo " is first_tour(8, List((0, 0))) ok? " >> $out
-  echo " is first_tour(4, List((0, 0))) == None " >> $out
-
-  if (scala_assert_thirty "knight2.scala" "knight2b_test.scala") 
-  then
-    echo "  --> success" >> $out
-  else
-    echo "  --> test failed" >> $out
-  fi
-fi
-

--- a/testing3-bak/knight1a_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,5 +0,0 @@
-
-assert(CW7a.is_legal(8, Nil)(3, 4) == true)
-assert(CW7a.is_legal(8, List((4, 1), (1, 0)))(4, 1) == false)
-assert(CW7a.is_legal(2, Nil)(0, 0) == true)
-

--- a/testing3-bak/knight1b_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,11 +0,0 @@
-
-assert(CW7a.legal_moves(8, Nil, (2,2)) == 
-             List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
-assert(CW7a.legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
-assert(CW7a.legal_moves(8, List((4,1), (1,0)), (2,2)) == 
-       List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
-assert(CW7a.legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
-assert(CW7a.legal_moves(1, Nil, (0,0)) == List())
-assert(CW7a.legal_moves(2, Nil, (0,0)) == List())
-assert(CW7a.legal_moves(3, Nil, (0,0)) == List((1,2), (2,1)))
-

--- a/testing3-bak/knight1c_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,47 +0,0 @@
-
-import scala.concurrent._
-import scala.concurrent.duration._
-import ExecutionContext.Implicits.global
-import scala.language.postfixOps 
-
-type Pos = (Int, Int)    // a position on a chessboard 
-type Path = List[Pos]    // a path...a list of positions
-
-def count_all_tours_urban(dim: Int) = {
-  for (i <- (0 until dim).toList; 
-       j <- (0 until dim).toList) yield CW7a.count_tours(dim, List((i, j)))
-}
-
-def add_pair_urban(x: Pos)(y: Pos): Pos = 
-  (x._1 + y._1, x._2 + y._2)
-
-def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
-  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
-
-def moves_urban(x: Pos): List[Pos] = 
-  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
-       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
-
-def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
-  moves_urban(x).filter(is_legal_urban(dim, path))
-
-def correct_urban(dim: Int)(p: Path): Boolean = p match {
-  case Nil => true
-  case x::Nil => true
-  case x::y::p => if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
-}
-
-
-lazy val f = Future {
-  assert(count_all_tours_urban(1) == List(1))
-  assert(count_all_tours_urban(2) == List(0, 0, 0, 0))
-  assert(count_all_tours_urban(3) == List(0, 0, 0, 0, 0, 0, 0, 0, 0))
-  assert(count_all_tours_urban(4) == List(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
-  assert(count_all_tours_urban(5) == List(304, 0, 56, 0, 304, 0, 56, 0, 56, 0, 56, 0, 64, 0, 56, 0, 56, 0, 56, 0, 304, 0, 56, 0, 304))
-
-  val ts = CW7a.enum_tours(5, List((0, 2)))
-  assert(ts.map(correct_urban(5)).forall(_ == true) == true)
-  assert(ts.length == 56)  
-}
-
-Await.result(f, 360 second)

--- a/testing3-bak/knight2.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,61 +0,0 @@
-// Part 2 about finding a single tour for a board
-//================================================
-
-object CW7b {
-
-type Pos = (Int, Int)    // a position on a chessboard 
-type Path = List[Pos]    // a path...a list of positions
-
-def print_board(dim: Int, path: Path) : Unit = {
-  println
-  for (i <- 0 until dim) {
-    for (j <- 0 until dim) {
-      print(f"${path.reverse.indexOf((i, j))}%3.0f ")
-    }
-    println
-  } 
-}
-
-def add_pair(x: Pos)(y: Pos) : Pos = 
-  (x._1 + y._1, x._2 + y._2)
-
-def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = 
-  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
-
-def moves(x: Pos) : List[Pos] = 
-  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
-       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))
-
-def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = 
-  moves(x).filter(is_legal(dim, path))
-
-
-def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = xs match {
-  case Nil => None
-  case x::xs => {
-    val result = f(x)
-    if (result.isDefined) result else first(xs, f)
-  }
-}
-
-//first(List((1, 0),(2, 0),(3, 0),(4, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
-//first(List((1, 0),(2, 0),(3, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
-
-def first_tour(dim: Int, path: Path) : Option[Path] = {
-  if (path.length == dim * dim) Some(path)
-  else
-    first(legal_moves(dim, path, path.head), (x: Pos) => first_tour(dim, x::path))
-}
-
-/* 
-val ts1 = first_tour(8, List((0, 0))).get
-  assert(correct_urban(8)(ts1) == true)
-
-val ts2 = first_tour(4, List((0, 0)))
-assert(ts2 == None)  
-
-print_board(8, first_tour(8, List((0, 0))).get)
-*/
-
-}
-

--- a/testing3-bak/knight2a_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,5 +0,0 @@
-
-val f = (x:(Int, Int)) => if (x._1 > 3) Some(List(x)) else None
-
-assert(CW7b.first(List((1,0),(2,0),(3,0),(4,0)), f) == Some(List((4,0))))
-assert(CW7b.first(List((1,0),(2,0),(3,0)), f) == None)

--- a/testing3-bak/knight2b_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,40 +0,0 @@
-
-import scala.concurrent._
-import scala.concurrent.duration._
-import ExecutionContext.Implicits.global
-import scala.language.postfixOps 
-
-type Pos = (Int, Int)    // a position on a chessboard 
-type Path = List[Pos]    // a path...a list of positions
-
-def add_pair_urban(x: Pos)(y: Pos): Pos = 
-  (x._1 + y._1, x._2 + y._2)
-
-def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
-  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
-
-def moves_urban(x: Pos): List[Pos] = 
-  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
-       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
-
-def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
-  moves_urban(x).filter(is_legal_urban(dim, path))
-
-def correct_urban(dim: Int)(p: Path): Boolean = p match {
-  case Nil => true
-  case x::Nil => true
-  case x::y::p => 
-    if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
-}
-
-
-lazy val f = Future {
-
-  val ts1 = CW7b.first_tour(8, List((0, 0))).get
-  assert(correct_urban(8)(ts1) == true)
-
-  val ts2 = CW7b.first_tour(4, List((0, 0)))
-  assert(ts2 == None)  
-}
-
-Await.result(f, 300 second)

--- a/testing3-bak/knight3.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,63 +0,0 @@
-// Part 3 about finding a single tour using the Warnsdorf Rule
-//=============================================================
-
-//object CW8c { // for preparing the jar
-
-type Pos = (Int, Int)
-type Path = List[Pos]
-
-
-// for measuring time in the JAR
-def time_needed[T](code: => T) : T = {
-  val start = System.nanoTime()
-  val result = code
-  val end = System.nanoTime()
-  println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.")
-  result
-}
-
-
-def print_board(dim: Int, path: Path): Unit = {
-  println
-  for (i <- 0 until dim) {
-    for (j <- 0 until dim) {
-      print(f"${path.reverse.indexOf((i, j))}%4.0f ")
-    }
-    println
-  } 
-}
-
-def add_pair(x: Pos, y: Pos): Pos = 
-  (x._1 + y._1, x._2 + y._2)
-
-def is_legal(dim: Int, path: Path, x: Pos): Boolean = 
-  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
-
-def moves(x: Pos): List[Pos] = 
-  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
-       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x, _))
-
-def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
-  moves(x).filter(is_legal(dim, path, _))
- 
-def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
-  legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)
-
-import scala.annotation.tailrec
-
-@tailrec
-def tour_on_mega_board_aux(dim: Int, paths: List[Path]): Option[Path] = paths match {
-  case Nil => None
-  case (path::rest) =>
-    if (path.length == dim * dim) Some(path)
-    else tour_on_mega_board_aux(dim, ordered_moves(dim, path, path.head).map(_::path) ::: rest)
-}
-
-def ttour_on_mega_board(dim: Int, path: Path): Option[Path] =
-  tour_on_mega_board_aux(dim, List(path))
-
-
-def tour_on_mega_board(dim: Int, path: Path) =
-  time_needed(ttour_on_mega_board(dim: Int, path: Path))
-
-//}

--- a/testing3-bak/knight3_test.sh	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,118 +0,0 @@
-#!/bin/bash
-set -e
-
-out=${1:-output}
-
-echo "" > $out
-
-echo "Below is the feedback for your submission of CW 7, Part 3." >> $out
-echo "" >> $out
-
-function scala_vars {
-   (egrep '\bvar\b|\breturn\b|ListBuffer|mutable' "$1" 2> /dev/null 1> /dev/null)
-}
-
-# compilation tests
-
-function scala_compile {
-  (ulimit -t 30 ; JAVA_OPTS="-Xmx1g" scala "$1" 2>> $out 1>> $out) 
-}
-
-# functional tests
-
-# not sure yet what the right kind of stack should be
-
-function scala_assert {
-    (ulimit -t 20 ; JAVA_OPTS="-Xmx1g -Xss200m" scala -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null)
-}
-
-# purity test
-
-function scala_vars {
-   (egrep '\bvar\b|\breturn\b|\.par|ListBuffer|mutable|new Array' "$1" 2> /dev/null 1> /dev/null)
-}
-
-
-# knights3: purity test
-#
-echo "knight3.scala does not contain vars, returns etc?" >> $out
-
-if (scala_vars knight3.scala)
-then
-  echo "  --> fail: if you do not fix this, you will receive a mark of zero" >> $out
-  tsts0=$(( 1 ))
-else
-  echo "  --> success" >> $out
-  tsts0=$(( 0 )) 
-fi
-
-
-# compilation test
-if  [ $tsts0 -eq 0 ]
-then    
-  echo "knight3.scala runs?" >> $out
-
-  if (scala_compile knight3.scala)
-  then
-    echo "  --> success" >> $out
-    tsts1=$(( 0 ))
-  else
-    echo "  --> scala knight3.scala did not run successfully" >> $out
-    tsts1=$(( 1 )) 
-  fi
-else
-  tsts1=$(( 1 ))     
-fi
-
-# ordered move test
-
-if [ $tsts1 -eq 0 ]
-then
-  echo "Takes 20 seconds or less to execute: " >> $out
-  echo " ordered_moves(8, List((3,4), (3,2)), (1, 3)) == List((0,1), (0,5), (2,1), (2,5))" >> $out
-  echo " ordered_moves(8, List((4,0)), (0,0)) == List((2,1), (1,2))" >> $out
-  echo " ordered_moves(8, List((0,4)), (0,0)) == List((1,2), (2,1))" >> $out
-  
-  if (scala_assert "knight3.scala" "knight3a_test.scala")
-  then
-    echo "  --> success" >> $out
-  else
-    echo "  --> test failed" >> $out
-  fi
-fi
-
-
-# first-closed-tour test
-
-if [ $tsts1 -eq 0 ]
-then
-  echo " first_closed_tour_heuristic(6, List((3, 3))) found and ok?" >> $out
-  
-  if (scala_assert "knight3.scala" "knight3b_test.scala")
-  then
-    echo "  --> success" >> $out
-  else
-    echo "  --> test failed" >> $out
-  fi
-fi
-
-
-
-if [ $tsts1 -eq 0 ]
-then
-  echo "Takes 20 seconds or less to execute: " >> $out
-  echo " first_tour_heuristic(8, List((0,0))) found and ok?" >> $out
-  echo " first_tour_heuristic(40, List((0,0))) found and ok?" >> $out
-  
-  if (scala_assert "knight3.scala" "knight3c_test.scala")
-  then
-    echo "  --> success" >> $out
-  else
-    echo "  --> test failed" >> $out
-  fi
-fi
-
-
-## final marks
-##echo "Overall mark for CW 7, Part 2" | tee -a $out
-##echo "$marks" | tee -a $out

--- a/testing3-bak/knight3a_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,15 +0,0 @@
-
-import scala.concurrent._
-import scala.concurrent.duration._
-import ExecutionContext.Implicits.global
-import scala.language.postfixOps 
-
-lazy val f = Future {
-
-assert(CW7c.ordered_moves(8, List((3,4), (3,2)), (1, 3)) == List((0,1), (0,5), (2,1), (2,5)))
-assert(CW7c.ordered_moves(8, List((4,0)), (0,0)) == List((2,1), (1,2)))
-assert(CW7c.ordered_moves(8, List((0,4)), (0,0)) == List((1,2), (2,1)))
-
-}
-
-Await.result(f, 120 second)

--- a/testing3-bak/knight3b_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,40 +0,0 @@
-
-//import scala.concurrent._
-//import scala.concurrent.duration._
-//import ExecutionContext.Implicits.global
-//import scala.language.postfixOps 
-
-type Pos = (Int, Int)
-type Path = List[Pos]
-
-def add_pair_urban(x: Pos)(y: Pos): Pos = 
-  (x._1 + y._1, x._2 + y._2)
-
-def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
-  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
-
-def moves_urban(x: Pos): List[Pos] = 
-  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
-       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
-
-def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
-  moves_urban(x).filter(is_legal_urban(dim, path))
-
-def correct_urban(dim: Int)(p: Path): Boolean = p match {
-  case Nil => true
-  case x::Nil => true
-  case x::y::p => 
-    if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
-}
-
-def correct_closed_urban(dim: Int)(p: Path) =
-  correct_urban(6)(p) &&  moves_urban(p.head).contains(p.last)
-
-//lazy val f = Future {
-
-  val tsc = CW7c.first_closed_tour_heuristic(6, List((3, 3))).get
-  assert(correct_closed_urban(6)(tsc) == true)
-
-//}
-
-//Await.result(f, 300 second)

--- a/testing3-bak/knight3c_test.scala	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,49 +0,0 @@
-
-//import scala.concurrent._
-//import scala.concurrent.duration._
-//import ExecutionContext.Implicits.global
-//import scala.language.postfixOps 
-
-type Pos = (Int, Int)
-type Path = List[Pos]
-
-def add_pair_urban(x: Pos)(y: Pos): Pos = 
-  (x._1 + y._1, x._2 + y._2)
-
-def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
-  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
-
-def moves_urban(x: Pos): List[Pos] = 
-  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
-       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
-
-def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
-  moves_urban(x).filter(is_legal_urban(dim, path))
-
-def correct_urban(dim: Int)(p: Path): Boolean = p match {
-  case Nil => true
-  case x::Nil => true
-  case x::y::p => 
-    if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
-}
-
-
-// !!!!!!! the futures need to be removed...otherwise funny results
-//lazy val f1 = Future {
-
-  val ts8 = CW7c.first_tour_heuristic(8, List((0,0))).get
-  assert(correct_urban(8)(ts8) == true)
-
-//}
-
-//Await.result(f1, 360 second)
-
-
-//lazy val f2 = Future {
-
-  val ts40 = CW7c.first_tour_heuristic(40, List((0,0))).get
-  assert(correct_urban(40)(ts40) == true)
-
-//}
-
-//Await.result(f2, 360 second)

--- a/testing3-bak/mark	Mon Dec 10 02:23:30 2018 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,8 +0,0 @@
-#!/bin/bash
-###set -e
-
-trap "exit" INT
-
-./knight1_test.sh output1
-./knight3_test.sh output3
-

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight1.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,133 @@
+
+// Part 1 about finding and counting Knight's tours
+//==================================================
+
+object CW7a extends App{
+
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
+
+//(1a) Complete the function that tests whether the position 
+//     is inside the board and not yet element in the path.
+
+//def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = ...
+
+def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = {
+  
+// if ((x._1<dim && x._2<dim) && (x._1>0 || x._2>0)) false else !path.contains(x)
+ 
+  if (x._1 < 0 || x._2 < 0) false 
+  else if (x._1 < dim && x._2 < dim && !path.contains(x)) true 
+  else false
+ 
+  
+}
+
+
+
+def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = {
+  
+  val allPossibleMoves = List((x._1+1, x._2+2), (x._1+2, x._2+1), (x._1+2, x._2-1), (x._1+1, x._2-2), (x._1-1, x._2-2), (x._1-2, x._2-1), (x._1-2, x._2+1), (x._1-1, x._2+2));
+ 
+  //val finalList = allPossibleMoves.filter((a=>a._1<dim && a._2<dim && x._1 >= 0 && a._2 >= 0));
+  
+  val finalList = for(pos<-allPossibleMoves if(is_legal(dim,path)(pos))) yield pos;
+  
+  // println("Space in board: " + dim*dim + " for dim: " + dim)
+   
+  
+  finalList.toList;
+    
+  
+}
+
+println(legal_moves(8, Nil, (2,2)))
+println(legal_moves(8, Nil, (7,7)))
+println(legal_moves(8, List((4,1), (1,0)), (2,2)))
+println(legal_moves(8, List((6,6)), (7,7)))
+println(legal_moves(1, Nil, (0,0)))
+println(legal_moves(2, Nil, (0,0)))
+println(legal_moves(3, Nil, (0,0)))
+
+println("=================================================================================")
+println("================================Comparision output===============================")
+println("=================================================================================")
+
+println(legal_moves(8, Nil, (2,2)) == List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
+println(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
+println(legal_moves(8, List((4,1), (1,0)), (2,2)) == List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
+println(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
+println(legal_moves(1, Nil, (0,0)) == Nil)
+println(legal_moves(2, Nil, (0,0)) == Nil)
+println(legal_moves(3, Nil, (0,0)) == List((1,2), (2,1)))
+
+
+def count_tours(dim: Int, path: Path) : Int = {
+     
+  val allMovesFromCurrentPosition = legal_moves(dim, path, path.head);
+  
+  if (path.length == dim*dim) 1 else  {
+    
+    if (allMovesFromCurrentPosition.size == 0 ) 0  else {
+      
+      allMovesFromCurrentPosition.map( element => count_tours(dim, element::path)).sum
+      
+      
+    }
+    
+  }
+  
+}
+    
+  
+
+println ( count_tours(5, List((0,0))) )
+
+def enum_tours(dim: Int, path: Path) : List[Path] = {
+  
+     val allMovesFromCurrentPosition = legal_moves(dim, path, path.head);
+  
+  if (path.length == dim*dim) List(path) else  {
+    
+  allMovesFromCurrentPosition.map( element => enum_tours(dim, element::path)).flatten ;
+      
+      
+      }
+    }
+  println ( enum_tours(6, List((0,2))).size)
+}
+
+
+
+
+
+ 
+ 
+//(1b) Complete the function that calculates for a position 
+//     all legal onward moves that are not already in the path. 
+//     The moves should be ordered in a "clockwise" manner.
+ 
+//def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = ...
+
+
+
+
+//some test cases
+//
+//assert(legal_moves(8, Nil, (2,2)) == 
+//  List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
+//assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
+//assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == 
+//  List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
+//assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
+
+
+//(1c) Complete the two recursive functions below. 
+//     They exhaustively search for knight's tours starting from the 
+//     given path. The first function counts all possible tours, 
+//     and the second collects all tours in a list of paths.
+
+//def count_tours(dim: Int, path: Path) : Int = ...
+
+
+//def enum_tours(dim: Int, path: Path) : List[Path] = ...

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight1_test.sh	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,206 @@
+#!/bin/bash
+
+# to make the script fail safely
+set -euo pipefail
+
+out=${1:-output}
+
+echo "" > $out
+
+echo "Below is the feedback and provisional marks for your submission" >> $out
+echo "for assignment 7 Part 1.  Please note all marks are provisional until" >> $out
+echo "ratified by the assessment board -- this is not an official" >> $out
+echo "results transcript." >> $out
+echo "" >> $out
+
+echo "Below is the feedback for your submission of CW 7, Part 1." >> $out
+echo "" >> $out
+
+
+# marks for CW7 part 1
+marks=$(( 0 ))
+
+
+# compilation tests (used to be 30 secs)
+
+function scala_compile {
+  (ulimit -t 360; JAVA_OPTS="-Xmx1g" scala "$1" 2> /dev/null 1> /dev/null) 
+}
+
+# functional tests
+
+function scala_assert {
+  (ulimit -t 360; JAVA_OPTS="-Xmx1g" scala -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null)
+}
+
+# purity test
+
+function scala_vars {
+   (egrep '\bvar\b|\breturn\b|\.par|ListBuffer|mutable|new Array' "$1" 2> /dev/null 1> /dev/null)
+}
+
+
+# knights1: purity test
+
+echo "knight1.scala does not contain vars, returns, Arrays, ListBuffers etc?" | tee -a $out
+
+if (scala_vars knight1.scala)
+then
+  echo "  --> fail" | tee -a $out
+  tsts0=$(( 1 ))
+else
+  echo "  --> success" | tee -a $out
+  tsts0=$(( 0 )) 
+fi
+
+
+# compilation test
+
+if [ $tsts0 -eq 0 ]
+then    
+  echo "knight1.scala runs?" | tee -a $out
+
+  if (scala_compile knight1.scala)
+  then
+    echo "  --> success " | tee -a $out
+    tsts1=$(( 0 ))
+  else
+    echo "  --> scala did not run knight1.scala" | tee -a $out
+    tsts1=$(( 1 )) 
+  fi
+else
+  tsts1=$(( 1 ))   
+fi
+
+### knight1a test
+
+if [ $tsts1 -eq 0 ]
+then
+    echo " is_legal(8, Nil)(3, 4) == true " | tee -a $out
+    echo " is_legal(8, List((4, 1), (1, 0)))(4, 1) == false " | tee -a $out
+    echo " is_legal(2, Nil)(0, 0) == true" | tee -a $out                          
+
+    if (scala_assert "knight1.scala" "knight1a_test.scala")
+    then
+        echo "  --> success" | tee -a $out
+	marks=$(( marks + 1 ))
+    else
+        echo "  --> test failed" | tee -a $out
+    fi
+fi
+
+### knight1b test
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " legal_moves(8, Nil, (2,2)) == List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4))" | tee -a $out
+  echo " legal_moves(8, Nil, (7,7)) == List((6,5), (5,6))" | tee -a $out
+  echo " legal_moves(8, List((4,1), (1,0)), (2,2)) == List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4))" | tee -a $out
+  echo " legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6))" | tee -a $out
+  echo " legal_moves(1, Nil, (0,0)) == Nil" | tee -a $out
+  echo " legal_moves(2, Nil, (0,0)) == Nil" | tee -a $out
+  echo " legal_moves(3, Nil, (0,0)) == List((1,2), (2,1))" | tee -a $out
+  
+  if (scala_assert "knight1.scala" "knight1b_test.scala")
+  then
+     echo "  --> success" | tee -a $out
+     marks=$(( marks + 1 ))
+  else
+    echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+
+### knight1c test
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " all_tours from every position on the board" | tee -a $out
+  echo " dim = 1: 1" | tee -a $out
+  echo "       2: 0,0,0,0" >>  $out
+  echo "       3: 0,0,0,0,0,0,0,0,0" >>  $out
+  echo "       4: 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0" | tee -a $out
+  echo "       5: 304,0,56,0,304,0,56,0,56,0,56,0,64,0,56,0,56,0,56,0,304,0,56,0,304" | tee -a $out
+  echo " enum_tours(5, List((0,2)) ) => 56 tours? and all correct?" | tee -a $out
+  
+  if (scala_assert "knight1.scala" "knight1c_test.scala") 
+  then
+     echo "  --> success" | tee -a $out
+     marks=$(( marks + 2 ))
+  else
+    echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+
+# knights2: var test
+
+echo "knight2.scala does not contain vars, returns, Arrays, ListBuffers etc?" | tee -a $out
+
+if (scala_vars knight2.scala)
+then
+  echo "  --> fail" | tee -a $out
+  tsts0=$(( 1 ))
+else
+  echo "  --> success" | tee -a $out
+  tsts0=$(( 0 )) 
+fi
+
+
+# compilation test
+if  [ $tsts0 -eq 0 ]
+then    
+  echo "knight2.scala runs?" | tee -a $out
+
+  if (scala_compile knight2.scala)
+  then
+    echo "  --> success" | tee -a $out
+    tsts1=$(( 0 ))
+  else
+    echo "  --> scala did not run knight2.scala" | tee -a $out
+    tsts1=$(( 1 )) 
+  fi
+else
+  tsts1=$(( 1 ))     
+fi
+
+### knight2a test
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " val f = (x:(Int, Int)) => if (x._1 > 3) Some(List(x)) else None " | tee -a $out
+  echo "   first(List((1,0),(2,0),(3,0),(4,0)), f) == Some(List((4,0)))" | tee -a $out
+  echo "   first(List((1,0),(2,0),(3,0)), f) == None" | tee -a $out
+
+  if (scala_assert "knight2.scala" "knight2a_test.scala") 
+  then
+    echo "  --> success" | tee -a $out
+    marks=$(( marks + 1 ))
+  else
+    echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+
+### knight2b test
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " is first_tour(8, List((0, 0))) ok? " | tee -a $out
+  echo " is first_tour(4, List((0, 0))) == None " | tee -a $out
+
+  if (scala_assert "knight2.scala" "knight2b_test.scala") 
+  then
+     echo "  --> success" | tee -a $out
+     marks=$(( marks + 2 ))
+  else
+    echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+
+## final marks
+echo "Overall mark for Part 1" | tee -a $out
+echo "$marks" | tee -a $out
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight1a_test.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,5 @@
+
+assert(CW7a.is_legal(8, Nil)(3, 4) == true)
+assert(CW7a.is_legal(8, List((4, 1), (1, 0)))(4, 1) == false)
+assert(CW7a.is_legal(2, Nil)(0, 0) == true)
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight1b_test.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,11 @@
+
+assert(CW7a.legal_moves(8, Nil, (2,2)) == 
+             List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))
+assert(CW7a.legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))
+assert(CW7a.legal_moves(8, List((4,1), (1,0)), (2,2)) == 
+       List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))
+assert(CW7a.legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))
+assert(CW7a.legal_moves(1, Nil, (0,0)) == List())
+assert(CW7a.legal_moves(2, Nil, (0,0)) == List())
+assert(CW7a.legal_moves(3, Nil, (0,0)) == List((1,2), (2,1)))
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight1c_test.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,47 @@
+
+import scala.concurrent._
+import scala.concurrent.duration._
+import ExecutionContext.Implicits.global
+import scala.language.postfixOps 
+
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
+
+def count_all_tours_urban(dim: Int) = {
+  for (i <- (0 until dim).toList; 
+       j <- (0 until dim).toList) yield CW7a.count_tours(dim, List((i, j)))
+}
+
+def add_pair_urban(x: Pos)(y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves_urban(x: Pos): List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
+
+def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves_urban(x).filter(is_legal_urban(dim, path))
+
+def correct_urban(dim: Int)(p: Path): Boolean = p match {
+  case Nil => true
+  case x::Nil => true
+  case x::y::p => if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
+}
+
+
+lazy val f = Future {
+  assert(count_all_tours_urban(1) == List(1))
+  assert(count_all_tours_urban(2) == List(0, 0, 0, 0))
+  assert(count_all_tours_urban(3) == List(0, 0, 0, 0, 0, 0, 0, 0, 0))
+  assert(count_all_tours_urban(4) == List(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
+  assert(count_all_tours_urban(5) == List(304, 0, 56, 0, 304, 0, 56, 0, 56, 0, 56, 0, 64, 0, 56, 0, 56, 0, 56, 0, 304, 0, 56, 0, 304))
+
+  val ts = CW7a.enum_tours(5, List((0, 2)))
+  assert(ts.map(correct_urban(5)).forall(_ == true) == true)
+  assert(ts.length == 56)  
+}
+
+Await.result(f, 360 second)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight2.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,61 @@
+// Part 2 about finding a single tour for a board
+//================================================
+
+object CW7b {
+
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
+
+def print_board(dim: Int, path: Path) : Unit = {
+  println
+  for (i <- 0 until dim) {
+    for (j <- 0 until dim) {
+      print(f"${path.reverse.indexOf((i, j))}%3.0f ")
+    }
+    println
+  } 
+}
+
+def add_pair(x: Pos)(y: Pos) : Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal(dim: Int, path: Path)(x: Pos) : Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves(x: Pos) : List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))
+
+def legal_moves(dim: Int, path: Path, x: Pos) : List[Pos] = 
+  moves(x).filter(is_legal(dim, path))
+
+
+def first(xs: List[Pos], f: Pos => Option[Path]) : Option[Path] = xs match {
+  case Nil => None
+  case x::xs => {
+    val result = f(x)
+    if (result.isDefined) result else first(xs, f)
+  }
+}
+
+//first(List((1, 0),(2, 0),(3, 0),(4, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
+//first(List((1, 0),(2, 0),(3, 0)), (x => if (x._1 > 3) Some(List(x)) else None))
+
+def first_tour(dim: Int, path: Path) : Option[Path] = {
+  if (path.length == dim * dim) Some(path)
+  else
+    first(legal_moves(dim, path, path.head), (x: Pos) => first_tour(dim, x::path))
+}
+
+/* 
+val ts1 = first_tour(8, List((0, 0))).get
+  assert(correct_urban(8)(ts1) == true)
+
+val ts2 = first_tour(4, List((0, 0)))
+assert(ts2 == None)  
+
+print_board(8, first_tour(8, List((0, 0))).get)
+*/
+
+}
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight2a_test.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,5 @@
+
+val f = (x:(Int, Int)) => if (x._1 > 3) Some(List(x)) else None
+
+assert(CW7b.first(List((1,0),(2,0),(3,0),(4,0)), f) == Some(List((4,0))))
+assert(CW7b.first(List((1,0),(2,0),(3,0)), f) == None)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight2b_test.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,40 @@
+
+import scala.concurrent._
+import scala.concurrent.duration._
+import ExecutionContext.Implicits.global
+import scala.language.postfixOps 
+
+type Pos = (Int, Int)    // a position on a chessboard 
+type Path = List[Pos]    // a path...a list of positions
+
+def add_pair_urban(x: Pos)(y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves_urban(x: Pos): List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
+
+def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves_urban(x).filter(is_legal_urban(dim, path))
+
+def correct_urban(dim: Int)(p: Path): Boolean = p match {
+  case Nil => true
+  case x::Nil => true
+  case x::y::p => 
+    if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
+}
+
+
+lazy val f = Future {
+
+  val ts1 = CW7b.first_tour(8, List((0, 0))).get
+  assert(correct_urban(8)(ts1) == true)
+
+  val ts2 = CW7b.first_tour(4, List((0, 0)))
+  assert(ts2 == None)  
+}
+
+Await.result(f, 300 second)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight3.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,63 @@
+// Part 3 about finding a single tour using the Warnsdorf Rule
+//=============================================================
+
+//object CW8c { // for preparing the jar
+
+type Pos = (Int, Int)
+type Path = List[Pos]
+
+
+// for measuring time in the JAR
+def time_needed[T](code: => T) : T = {
+  val start = System.nanoTime()
+  val result = code
+  val end = System.nanoTime()
+  println(f"Time needed: ${(end - start) / 1.0e9}%3.3f secs.")
+  result
+}
+
+
+def print_board(dim: Int, path: Path): Unit = {
+  println
+  for (i <- 0 until dim) {
+    for (j <- 0 until dim) {
+      print(f"${path.reverse.indexOf((i, j))}%4.0f ")
+    }
+    println
+  } 
+}
+
+def add_pair(x: Pos, y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal(dim: Int, path: Path, x: Pos): Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves(x: Pos): List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x, _))
+
+def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves(x).filter(is_legal(dim, path, _))
+ 
+def ordered_moves(dim: Int, path: Path, x: Pos): List[Pos] = 
+  legal_moves(dim, path, x).sortBy((x) => legal_moves(dim, path, x).length)
+
+import scala.annotation.tailrec
+
+@tailrec
+def tour_on_mega_board_aux(dim: Int, paths: List[Path]): Option[Path] = paths match {
+  case Nil => None
+  case (path::rest) =>
+    if (path.length == dim * dim) Some(path)
+    else tour_on_mega_board_aux(dim, ordered_moves(dim, path, path.head).map(_::path) ::: rest)
+}
+
+def ttour_on_mega_board(dim: Int, path: Path): Option[Path] =
+  tour_on_mega_board_aux(dim, List(path))
+
+
+def tour_on_mega_board(dim: Int, path: Path) =
+  time_needed(ttour_on_mega_board(dim: Int, path: Path))
+
+//}

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight3_test.sh	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,124 @@
+#!/bin/bash
+
+# to make the script fail safely
+set -euo pipefail
+
+
+out=${1:-output}
+
+echo "" > $out
+
+echo "Below is the feedback and provisional marks for your submission" >> $out
+echo "for assignment 7 Part 2.  Please note all marks are provisional until" >> $out
+echo "ratified by the assessment board -- this is not an official" >> $out
+echo "results transcript." >> $out
+echo "" >> $out
+
+# marks for CW7 part 2
+marks=$(( 0 ))
+
+# compilation tests
+
+function scala_compile {
+    (ulimit -t 360; JAVA_OPTS="-Xmx1g" scala "$1" 2> /dev/null 1> /dev/null)
+}
+
+# functional tests
+
+function scala_assert {
+    (ulimit -t 360; JAVA_OPTS="-Xmx4g -Xss200m" scala -i "$1" "$2" -e "" 2> /dev/null 1> /dev/null)
+}
+
+
+# purity test
+
+function scala_vars {
+   (egrep '\bvar\b|\breturn\b|\.par|ListBuffer|mutable|new Array' "$1" 2> /dev/null 1> /dev/null)
+}
+
+
+# knights3: purity test
+#
+echo "knight3.scala does not contain vars, returns, Arrays, ListBuffers etc?" | tee -a $out
+
+
+if (scala_vars knight3.scala)
+then
+  echo "  --> test failed" | tee -a $out
+  tsts0=$(( 1 ))
+else
+  echo "  --> success" | tee -a $out
+  tsts0=$(( 0 )) 
+fi
+
+
+# compilation test
+if  [ $tsts0 -eq 0 ]
+then    
+  echo "knight3.scala runs?" | tee -a $out
+
+  if (scala_compile knight3.scala)
+  then
+    echo "  --> success" | tee -a $out
+    tsts1=$(( 0 ))
+  else
+    echo "  --> scala knight3.scala did not run successfully" | tee -a $out
+    tsts1=$(( 1 )) 
+  fi
+else
+  tsts1=$(( 1 ))     
+fi
+
+# ordered move test
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " ordered_moves(8, List((3,4), (3,2)), (1,3)) == List((0,1), (0,5), (2,1), (2,5))" | tee -a $out
+  echo " ordered_moves(8, List((4,0)), (0,0)) == List((2,1), (1,2))" | tee -a $out
+  echo " ordered_moves(8, List((0,4)), (0,0)) == List((1,2), (2,1))" | tee -a $out
+  
+  if (scala_assert "knight3.scala" "knight3a_test.scala")
+  then
+      echo "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+    echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+
+# first-closed-tour test
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " first_closed_tour_heuristic(6, List((3,3))) found and correct?" | tee -a $out
+  
+  if (scala_assert "knight3.scala" "knight3b_test.scala")
+  then
+      echo "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+      echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+
+
+if [ $tsts1 -eq 0 ]
+then
+  echo " first_tour_heuristic(8, List((0,0))) found and correct?" | tee -a $out
+  echo " first_tour_heuristic(40, List((0,0))) found and correct?" | tee -a $out
+  
+  if (scala_assert "knight3.scala" "knight3c_test.scala")
+  then
+      echo "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+    echo "  --> test failed" | tee -a $out
+  fi
+fi
+
+
+## final marks
+echo "Overall mark for CW 7, Part 2" | tee -a $out
+echo "$marks" | tee -a $out

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight3a_test.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,15 @@
+
+import scala.concurrent._
+import scala.concurrent.duration._
+import ExecutionContext.Implicits.global
+import scala.language.postfixOps 
+
+lazy val f = Future {
+
+assert(CW7c.ordered_moves(8, List((3,4), (3,2)), (1, 3)) == List((0,1), (0,5), (2,1), (2,5)))
+assert(CW7c.ordered_moves(8, List((4,0)), (0,0)) == List((2,1), (1,2)))
+assert(CW7c.ordered_moves(8, List((0,4)), (0,0)) == List((1,2), (2,1)))
+
+}
+
+Await.result(f, 120 second)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight3b_test.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,40 @@
+
+//import scala.concurrent._
+//import scala.concurrent.duration._
+//import ExecutionContext.Implicits.global
+//import scala.language.postfixOps 
+
+type Pos = (Int, Int)
+type Path = List[Pos]
+
+def add_pair_urban(x: Pos)(y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves_urban(x: Pos): List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
+
+def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves_urban(x).filter(is_legal_urban(dim, path))
+
+def correct_urban(dim: Int)(p: Path): Boolean = p match {
+  case Nil => true
+  case x::Nil => true
+  case x::y::p => 
+    if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
+}
+
+def correct_closed_urban(dim: Int)(p: Path) =
+  correct_urban(6)(p) &&  moves_urban(p.head).contains(p.last)
+
+//lazy val f = Future {
+
+  val tsc = CW7c.first_closed_tour_heuristic(6, List((3, 3))).get
+  assert(correct_closed_urban(6)(tsc) == true)
+
+//}
+
+//Await.result(f, 300 second)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/knight3c_test.scala	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,49 @@
+
+//import scala.concurrent._
+//import scala.concurrent.duration._
+//import ExecutionContext.Implicits.global
+//import scala.language.postfixOps 
+
+type Pos = (Int, Int)
+type Path = List[Pos]
+
+def add_pair_urban(x: Pos)(y: Pos): Pos = 
+  (x._1 + y._1, x._2 + y._2)
+
+def is_legal_urban(dim: Int, path: Path)(x: Pos): Boolean = 
+  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)
+
+def moves_urban(x: Pos): List[Pos] = 
+  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),
+       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair_urban(x))
+
+def legal_moves_urban(dim: Int, path: Path, x: Pos): List[Pos] = 
+  moves_urban(x).filter(is_legal_urban(dim, path))
+
+def correct_urban(dim: Int)(p: Path): Boolean = p match {
+  case Nil => true
+  case x::Nil => true
+  case x::y::p => 
+    if (legal_moves_urban(dim, p, y).contains(x)) correct_urban(dim)(y::p) else false
+}
+
+
+// !!!!!!! the futures need to be removed...otherwise funny results
+//lazy val f1 = Future {
+
+  val ts8 = CW7c.first_tour_heuristic(8, List((0,0))).get
+  assert(correct_urban(8)(ts8) == true)
+
+//}
+
+//Await.result(f1, 360 second)
+
+
+//lazy val f2 = Future {
+
+  val ts40 = CW7c.first_tour_heuristic(40, List((0,0))).get
+  assert(correct_urban(40)(ts40) == true)
+
+//}
+
+//Await.result(f2, 360 second)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/testing3/testing3-bak/mark	Fri Dec 14 14:41:54 2018 +0000
@@ -0,0 +1,8 @@
+#!/bin/bash
+###set -e
+
+trap "exit" INT
+
+./knight1_test.sh output1
+./knight3_test.sh output3
+