# HG changeset patch
# User Christian Urban <christian.urban@kcl.ac.uk>
# Date 1611881779 0
# Node ID 175a950470a96cd19f958cdd73e2e91ae85404b8
# Parent  4113d4d8cf629409469a214000c0827e1402ceda
updated

diff -r 4113d4d8cf62 -r 175a950470a9 cws/main_cw03.tex
--- a/cws/main_cw03.tex	Mon Jan 25 00:21:00 2021 +0000
+++ b/cws/main_cw03.tex	Fri Jan 29 00:56:19 2021 +0000
@@ -406,7 +406,7 @@
 
   \noindent correctly to just \texttt{ONE}, where \texttt{SEQ} is nested
   50 or more times?\\
-  \mbox{}\hfill[2 Mark]
+  \mbox{}\hfill[2 Marks]
 \end{itemize}
 
 \subsection*{Background}
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking2/danube_test.sh
--- a/main_marking2/danube_test.sh	Mon Jan 25 00:21:00 2021 +0000
+++ b/main_marking2/danube_test.sh	Fri Jan 29 00:56:19 2021 +0000
@@ -19,12 +19,6 @@
 # marks for core CW7
 marks=$(( 0.0 ))
 
-echo -e "" >> $out
-echo -e  "Below is the feedback for your submission danube.scala" >> $out
-echo -e  "" >> $out
-
-
-
 
 # compilation tests
 
@@ -49,6 +43,13 @@
 }
 
 
+echo -e "" >> $out
+echo -e  "Below is the feedback for your submission danube.scala" >> $out
+echo -e  "" >> $out
+
+
+
+
 ### compilation test
 
 echo -e  "danube.scala runs?" | tee -a $out
@@ -66,8 +67,8 @@
 # var, .par return, ListBuffer test
 #
 
-if  [ $tsts -eq 0 ]
-  then 
+if [ $tsts -eq 0 ]
+then 
       echo -e  "danube.scala does not contain VARS, RETURNS etc?" | tee -a $out
 
       if (scala_vars danube.scala)
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/mk
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/mk	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,33 @@
+#!/bin/sh
+###set -e
+
+trap "exit" INT
+
+files=${1:-*/main3}
+
+for sd in $files; do
+  cd $sd
+  echo $sd
+  touch .
+  cp ../../../../../main_marking3/re_test.sh .
+  cp ../../../../../main_marking3/re_test1.scala .
+  cp ../../../../../main_marking3/re_test2.scala .
+  cp ../../../../../main_marking3/re_test3.scala .
+  cp ../../../../../main_marking3/re_test4.scala .
+  cp ../../../../../main_marking3/re_test5.scala .
+  cp ../../../../../main_marking3/re_test6.scala .
+  cp ../../../../../main_marking3/re_test7.scala .
+  ./re_test.sh output
+  rm re_test.sh
+  rm re_test1.scala
+  rm re_test2.scala
+  rm re_test3.scala
+  rm re_test4.scala
+  rm re_test5.scala
+  rm re_test6.scala
+  rm re_test7.scala
+  cd ..
+  cd ..
+done
+
+
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/re.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/re.scala	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,176 @@
+// Core Part about Regular Expression Matching
+//=============================================
+
+object CW8c {
+
+// Regular Expressions
+abstract class Rexp
+case object ZERO extends Rexp
+case object ONE extends Rexp
+case class CHAR(c: Char) extends Rexp
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp 
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 
+case class STAR(r: Rexp) extends Rexp 
+
+// some convenience for typing in regular expressions
+
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls 
+
+
+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)
+}
+
+// (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 and Returns a boolean
+// accordingly.
+
+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
+}
+
+// (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.
+
+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))
+}
+
+// (3) Complete the simp function according to
+// the specification given in the coursework; this
+// 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 {
+    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
+}
+
+
+// (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.
+
+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))
+
+// (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
+  case CHAR(_) => 1
+  case ALT(r1, r2) => 1 + size(r1) + size (r2)
+  case SEQ(r1, r2) => 1 + size(r1) + size (r2)
+  case STAR(r1) => 1 + size(r1)
+}
+
+
+
+// some testing data
+
+//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
+
+// size without simplifications
+//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
+
+// 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 
+// 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()
+  for (j <- 1 to i) code
+  val end = System.nanoTime()
+  (end - start)/(i * 1.0e9)
+}
+
+//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.
+ 
+
+
+}
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/re_test.sh
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/re_test.sh	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,284 @@
+#!/bin/bash
+
+# to make the script fail safely
+set -euo pipefail
+
+out=${1:-output}
+
+echo -e "" > $out
+
+echo -e `date` >> $out
+echo -e  "" >> $out
+echo -e "Below is the feedback and provisional marks for your submission" >> $out
+echo -e "for the Main Part 3 (Scala). Please note all marks are provisional until" >> $out
+echo -e "ratified by the assessment board -- this is not an official" >> $out
+echo -e "results transcript." >> $out
+echo -e "" >> $out
+
+# marks for CW8
+marks=$(( 0 ))
+
+# compilation tests
+
+function scala_compile {
+  (ulimit -t 30; JAVA_OPTS="-Xmx1g" scala -Xprint:parser "$1" 2> c$out 1> c$out)
+}
+
+# functional tests
+
+function scala_assert {
+  (ulimit -t 30; JAVA_OPTS="-Xmx1g" scala -i "$1" -- "$2" -e "" 2> /dev/null 1> /dev/null)
+}
+
+function scala_assert_thirty {
+  (ulimit -t 40; JAVA_OPTS="-Xmx1g" scala -i "$1" -- "$2" -e "" 2> /dev/null 1> /dev/null)  
+}
+
+# purity test
+
+function scala_vars {
+   (egrep '\bvar\b|\breturn\b|\.par\.|\.par |ListBuffer|AtomicInteger|mutable|util.control|new Array' c$out 2> /dev/null 1> /dev/null)
+}
+
+echo -e "" >> $out
+echo -e  "Below is the feedback for your submission re.scala" >> $out
+echo -e  "" >> $out
+
+
+
+### compilation test
+
+echo -e "re.scala runs?" | tee -a $out
+
+if (scala_compile re.scala)
+then
+    echo -e "  --> success" | tee -a $out
+    tsts=$(( 0 ))
+else
+    echo -e "  --> SCALA DID NOT RUN re.scala" | tee -a $out
+    tsts=$(( 1 )) 
+fi
+
+
+# var, return, ListBuffer test
+#
+
+if [ $tsts -eq 0 ]
+then 
+    echo -e "re.scala does not contain VARS, RETURNS etc?" | tee -a $out
+
+    if (scala_vars re.scala)
+    then
+	echo -e  "  --> TEST FAILED\n" | tee -a $out
+	tsts=$(( 1 ))  
+    else
+	echo -e "  --> success" | tee -a $out
+	tsts=$(( 0 )) 
+    fi
+else
+    tsts=$(( 1 ))  
+fi
+
+
+
+### re1 test
+
+if [ $tsts -eq 0 ]
+then
+  echo -e " nullable(ZERO) == false" | tee -a $out
+  echo -e " nullable(ONE) == true" | tee -a $out
+  echo -e " nullable(CHAR('a')) == false" | tee -a $out
+  echo -e " nullable(ZERO | ONE) == true" | tee -a $out
+  echo -e " nullable(ZERO | CHAR('a')) == false" | tee -a $out
+  echo -e " nullable(ONE ~  ONE) == true" | tee -a $out
+  echo -e " nullable(ONE ~ CHAR('a')) == false" | tee -a $out
+  echo -e " nullable(STAR(ZERO)) == true" | tee -a $out
+  
+  if (scala_assert "re.scala" "re_test1.scala")
+  then
+      echo -e "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+      echo -e "  --> ONE OF THE TESTS FAILED\n" | tee -a $out
+  fi
+fi
+
+### re2 test
+
+if [ $tsts -eq 0 ]
+then
+  echo -e " der('a', ZERO | ONE) == (ZERO | ZERO)" | tee -a $out
+  echo -e " der('a', (CHAR('a') | ONE) ~ CHAR('a')) == ALT((ONE | ZERO) ~ CHAR('a'), ONE)" | tee -a $out
+  echo -e " der('a', (CHAR('a') | CHAR('a')) ~ CHAR('a')) == (ONE | ONE) ~ CHAR('a')" | tee -a $out
+  echo -e " der('a', STAR(CHAR('a'))) == (ONE ~ STAR(CHAR('a')))" | tee -a $out
+  echo -e " der('b', STAR(CHAR('a'))) == (ZERO ~ STAR(CHAR('a')))" | tee -a $out
+  echo -e "" | tee -a $out
+  echo -e " val r0 = \"a\" ~ \"b\" ~ \"c\"" | tee -a $out
+  echo -e " der('a', r0) == (ONE ~ \"b\") ~ \"c\"" | tee -a $out
+  echo -e " der('b', r0) == (ZERO ~ \"b\") ~ \"c\"" | tee -a $out
+  echo -e " der('c', r0) == (ZERO ~ \"b\") ~ \"c\"" | tee -a $out
+  echo -e "" | tee -a $out
+  echo -e " val r1 = (ONE ~ \"b\") ~ \"c\"" | tee -a $out
+  echo -e " der('a', r1) == ((ZERO ~ \"b\") | ZERO) ~ \"c\"" | tee -a $out
+  echo -e " der('b', r1) == ((ZERO ~ \"b\") | ONE) ~ \"c\"" | tee -a $out
+  echo -e " der('c', r1) == ((ZERO ~ \"b\") | ZERO) ~ \"c\"" | tee -a $out
+  echo -e "" | tee -a $out
+  echo -e " val r2 = ((ZERO ~ \"b\") | ONE) ~ \"c\"" | tee -a $out
+  echo -e " der('a', r2) == ((((ZERO ~ \"b\") | ZERO) ~ \"c\") | ZERO)" | tee -a $out
+  echo -e " der('b', r2) == ((((ZERO ~ \"b\") | ZERO) ~ \"c\") | ZERO)" | tee -a $out
+  echo -e " der('c', r2) == ((((ZERO ~ \"b\") | ZERO) ~ \"c\") | ONE)" | tee -a $out
+
+  if (scala_assert "re.scala" "re_test2.scala")
+  then
+      echo -e "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+      echo -e "  --> ONE OF THE TESTS FAILED\n" | tee -a $out
+  fi
+fi
+
+### re3 test
+
+if [ $tsts -eq 0 ]
+then
+  echo -e " simp(ZERO | ONE) == ONE" | tee -a $out
+  echo -e " simp(STAR(ZERO | ONE)) == STAR(ZERO | ONE)" | tee -a $out
+  echo -e " simp(ONE ~ (ONE ~ (ONE ~ CHAR('a')))) == CHAR('a')" | tee -a $out
+  echo -e " simp(((ONE ~ ONE) ~ ONE) ~ CHAR('a')) == CHAR('a')" | tee -a $out
+  echo -e " simp(((ONE | ONE) ~ ONE) ~ CHAR('a')) == CHAR('a')" | tee -a $out
+  echo -e " simp(ONE ~ (ONE ~ (ONE ~ ZERO))) == ZERO" | tee -a $out
+  echo -e " simp(ALT(ONE ~ (ONE ~ (ONE ~ ZERO)), CHAR('a'))) == CHAR('a')" | tee -a $out
+  echo -e " simp(CHAR('a') | CHAR('a')) == CHAR('a')" | tee -a $out
+  echo -e " simp(CHAR('a') ~ CHAR('a')) == CHAR('a') ~ CHAR('a')" | tee -a $out
+  echo -e " simp(ONE | CHAR('a')) == (ONE | CHAR('a'))" | tee -a $out
+  echo -e " simp(ALT((CHAR('a') | ZERO) ~ ONE," | tee -a $out
+  echo -e "          ((ONE | CHAR('b')) | CHAR('c')) ~ (CHAR('d') ~ ZERO))) == CHAR('a')" | tee -a $out
+  echo -e " simp((ZERO | ((ZERO | ZERO) | (ZERO | ZERO))) ~ ((ONE | ZERO) | ONE ) ~ (CHAR('a'))) == ZERO" | tee -a $out
+  echo -e " simp(ALT(ONE | ONE, ONE | ONE)) == ONE" | tee -a $out
+  echo -e " simp(ALT(ZERO | CHAR('a'), CHAR('a') | ZERO)) == CHAR('a')" | tee -a $out
+  echo -e " 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 -e "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+      echo -e "  --> ONE OF THE TESTS FAILED\n" | tee -a $out
+  fi
+fi
+
+### re4 test
+
+if [ $tsts -eq 0 ]
+then
+  echo -e " val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))" | tee -a $out
+  echo -e " ders((\"a\" * 5).toList,EVIL) == SEQ(SEQ(STAR(CHAR('a')),STAR(STAR(CHAR('a')))),CHAR('b'))" | tee -a $out
+  echo -e " ders(List('b'),EVIL) == ONE" | tee -a $out
+  echo -e " ders(List('b','b'),EVIL) == ZERO" | tee -a $out
+  echo -e " matcher(EVIL, \"a\" * 5 ++ \"b\") == true" | tee -a $out
+  echo -e " matcher(EVIL, \"a\" * 50 ++ \"b\") == true" | tee -a $out
+  echo -e " matcher(EVIL, \"a\" * 50) == false" | tee -a $out
+  echo -e " matcher(EVIL, \"b\") == true" | tee -a $out
+  echo -e " matcher(EVIL, \"bb\") == false" | tee -a $out
+  echo -e " matcher(\"abc\", \"abc\") == true" | tee -a $out
+  echo -e " matcher(\"abc\", \"ab\") == false" | tee -a $out
+  echo -e " matcher((\"ab\" | \"a\") ~ (ONE | \"bc\"), \"abc\") == true" | tee -a $out
+  echo -e " matcher(ONE, \"\") == true" | tee -a $out
+  echo -e " matcher(ZERO, \"\") == false" | tee -a $out
+  echo -e " matcher(ONE | CHAR('a'), \"\") == true" | tee -a $out
+  echo -e " matcher(ONE | CHAR('a'), \"a\") == true" | tee -a $out
+  
+  if (scala_assert "re.scala" "re_test4.scala")
+  then
+      echo -e "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+      echo -e "  --> ONE OF THE TESTS FAILED\n" | tee -a $out
+  fi
+fi
+
+### re5 test
+
+
+if [ $tsts -eq 0 ]
+then
+  echo -e " val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))" | tee -a $out  
+  echo -e " size(der('a', der('a', EVIL))) == 28" | tee -a $out
+  echo -e " size(der('a', der('a', der('a', EVIL)))) == 58" | tee -a $out
+  echo -e " size(ders(\"aaaaaa\".toList, EVIL)) == 8" | tee -a $out
+  echo -e " size(ders((\"a\" * 50).toList, EVIL)) == 8" | tee -a $out
+  
+  if (scala_assert "re.scala" "re_test5.scala")
+  then
+      echo -e "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+      echo -e "  --> ONE OF THE TESTS FAILED\n" | tee -a $out
+  fi
+fi
+
+### re6 'power' test 1
+
+sleep 5
+
+if [ $tsts -eq 0 ]
+then
+  echo -e " simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE" | tee -a $out
+  echo -e "    ...the Iterator produces the rexp" | tee -a $out
+  echo -e "" | tee -a $out
+  echo -e "      SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)" | tee -a $out
+  echo -e "" | tee -a $out
+  echo -e "    where SEQ is nested 50 times." | tee -a $out  
+  echo -e "" | tee -a $out
+  echo -e " simp(Iterator.iterate(ONE:Rexp)(r => ALT(r, r)).drop(20).next) == ONE" | tee -a $out
+  echo -e "    ... the Iterator produces a rexp of size 2097151" | tee -a $out
+  START=$(date +%s)
+  
+  if (scala_assert_thirty "re.scala" "re_test6.scala")
+  then
+      END=$(date +%s)
+      DIFF=$(( $END - $START ))
+      echo "   This test ran for $DIFF seconds" | tee -a $out
+      echo -e "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+      END=$(date +%s)
+      DIFF=$(( $END - $START ))
+      echo "  This test ran for $DIFF seconds" | tee -a $out
+      echo -e "  --> ONE OF THE TESTS FAILED\n" | tee -a $out
+  fi
+fi
+
+sleep 10
+
+### re7 'power' test 2
+
+if [ $tsts -eq 0 ]
+then
+  echo -e " val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))" | tee -a $out
+  echo -e " matcher(EVIL, \"a\" * 1000000 ++ \"b\") == true" | tee -a $out
+  echo -e " matcher(EVIL, \"a\" * 1000000) == false" | tee -a $out
+  START=$(date +%s)
+  
+  if (scala_assert_thirty "re.scala" "re_test7.scala")
+  then
+      END=$(date +%s)
+      DIFF=$(( $END - $START ))
+      echo "   This test ran for $DIFF seconds" | tee -a $out
+      echo -e "  --> success" | tee -a $out
+      marks=$(( marks + 1 ))
+  else
+      END=$(date +%s)
+      DIFF=$(( $END - $START ))
+      echo "  This test ran for $DIFF seconds" | tee -a $out
+      echo -e "  --> ONE OF THE TESTS FAILED\n" | tee -a $out
+  fi
+fi
+
+sleep 10
+
+## final marks
+echo -e "Overall mark for Main Part 3 (Scala)" | tee -a $out
+echo -e "$marks" | tee -a $out
+
+
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/re_test1.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/re_test1.scala	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,11 @@
+import CW8c._
+
+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)
+
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/re_test2.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/re_test2.scala	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,25 @@
+import CW8c._
+
+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))
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/re_test3.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/re_test3.scala	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,21 @@
+import CW8c._
+
+
+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))
+
+
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/re_test4.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/re_test4.scala	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,19 @@
+import CW8c._
+
+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)
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/re_test5.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/re_test5.scala	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,9 @@
+import CW8c._
+ 
+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)
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/re_test6.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/re_test6.scala	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,4 @@
+import CW8c._
+
+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)
diff -r 4113d4d8cf62 -r 175a950470a9 main_marking3/re_test7.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main_marking3/re_test7.scala	Fri Jan 29 00:56:19 2021 +0000
@@ -0,0 +1,6 @@
+import CW8c._
+
+val EVIL_urban = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+
+assert(matcher(EVIL_urban, "a" * 1000000) == false)
+assert(matcher(EVIL_urban, "a" * 1000000 ++ "b") == true)