--- a/testing4/re.scala Fri Nov 30 14:13:11 2018 +0000
+++ b/testing4/re.scala Sat Dec 01 15:09:37 2018 +0000
@@ -1,22 +1,20 @@
// Part 1 about Regular Expression Matching
//==========================================
-//object CW9a {
-
// 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
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp // alternative
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence
+case class STAR(r: Rexp) extends Rexp // star
+
-// some convenience for typing in regular expressions
+// some convenience for typing regular expressions
-import scala.language.implicitConversions
-import scala.language.reflectiveCalls
-
+import scala.language.implicitConversions
+import scala.language.reflectiveCalls
def charlist2rexp(s: List[Char]): Rexp = s match {
case Nil => ONE
@@ -40,116 +38,190 @@
}
// (1) Complete the function nullable according to
-// the definition given in the coursework; this
+// 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 {
+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 ALT(a,b)=>nullable(a)||nullable(b)
+ case SEQ(a,b) => nullable(a) && nullable(b)
case STAR(_) => true
}
+
+/*val rex = "1~0.%|11"
+
+assert(der('1',rex) == SEQ(ONE,SEQ(CHAR(~),SEQ(CHAR(0),SEQ(CHAR(.),SEQ(CHAR(%),SEQ(CHAR(|),SEQ(CHAR(1),CHAR(1)))))))))
+
+assert(der('1',der('1',rex)) ==
+ ALT(SEQ(ZERO,SEQ(CHAR(~),SEQ(CHAR(0),SEQ(CHAR(.),SEQ(CHAR(%),SEQ(CHAR(|),
+ SEQ(CHAR(1),CHAR(1)))))))),SEQ(ZERO,SEQ(CHAR(0),SEQ(CHAR(.),SEQ(CHAR(%),
+ SEQ(CHAR(|),SEQ(CHAR(1),CHAR(1))))))))*/
+
// (2) Complete the function der according to
// the definition given in the coursework; this
-// function calculates the derivative of a
+// function calculates the derivative of a
// regular expression w.r.t. a character.
-def der (c: Char, r: Rexp) : Rexp = r match {
+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))
+ case CHAR(d) => if (c==d) ONE else ZERO
+ case ALT(a,b) => der(c,a)|der(c,b)
+ case SEQ(a,b) => if(nullable(a)) {(der(c,a)~b)|der(c,b)}
+ else der(c,a)~b
+ case STAR(a) => der(c,a)~STAR(a)
}
+println(der('a', ZERO | ONE))// == (ZERO | ZERO)
+println(der('a', (CHAR('a') | ONE) ~ CHAR('a')))// ==ALT((ONE | ZERO) ~ CHAR('a'), ONE)
+println(der('a', STAR(CHAR('a'))))// == (ONE ~ STAR(CHAR('a')))
+println(der('b', STAR(CHAR('a'))))// == (ZERO ~ STAR(CHAR('a'))))
+
+
+//ALT(SEQ(ZERO,ZERO),ZERO)
+//ALT(ALT(ZERO,ZERO),ALT(ZERO,ZERO))
+
+// * == |
+// + == ~
// (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
+// 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
+/*
+def simp(r: Rexp) : Rexp = r match{
+ case SEQ(ZERO,_) => ZERO
+ case SEQ(_,ZERO) => ZERO
+ case SEQ(ONE,a) => simp(a)
+ case SEQ(a,ONE) => simp(a)
+ case ALT(ZERO,a) => simp(a)
+ case ALT(a,ZERO) => simp(a)
+ case ALT(a,b) => if(a == b) simp(a) else r
+ case _ => r
+}*/
+
+def simp(r: Rexp) : Rexp = r match{
+ case SEQ(a,b) =>{ val sa = simp(a)
+ val sb = simp(b)
+ if(sa == ZERO || sb == ZERO) ZERO
+ else if(sa == ONE) sb
+ else if(sb == ONE) sa
+ else SEQ(sa,sb)
+ }
+ case ALT(a,b) =>{ val sa = simp(a)
+ val sb = simp(b)
+ if(sa == ONE || sb == ONE) ONE
+ else if(sa == ZERO) sb
+ else if(sb == ZERO) sa
+ else if(sa == sb) sa
+ else ALT(sa,sb)
+ }
+ //case STAR(STAR(a)) => simp(STAR(a))
+ //case STAR(a) => STAR(simp(a))
+ case _ => r
+ /*
+ case SEQ(ZERO,_) => ZERO
+ case SEQ(_,ZERO) => ZERO
+ case SEQ(ONE,a) => simp(a)
+ case SEQ(a,ONE) => simp(a)
+ case SEQ(a,b) => SEQ(simp(a),simp(b))
+ //case ALT(ZERO,a) => simp(a)
+ case ALT(a,ZERO) => simp(a)
+ case ALT(ONE,_) => ONE
+ case ALT(_,ONE) => ONE
+ case ALT(a,b) => {val sa = simp(a)
+ if(sa == simp(b)) sa else r
+ }
+ case STAR(STAR(a)) => simp(STAR(a))
+ case STAR(a) => STAR(simp(a))
+ case _ => r*/
}
-// (4) Complete the two functions below; the first
+/*val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+println("TEST: " + simp(der('a', der('a', EVIL))))
+println(simp(ONE))
+val r1 = ALT(ZERO,ONE)
+val r2 = SEQ(ONE,ZERO)
+val r3 = SEQ(r1,SEQ(r2,r1))
+println("R1 = " + simp(r1))
+println(simp(r2))
+println(simp(r3))
+*/
+
+// (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 {
+def ders (s: List[Char], r: Rexp ="") : Rexp = s match{
case Nil => r
- case c::s => ders(s, simp(der(c, r)))
+ case a::z => ders(z,simp(der(a,r)))
}
-// main matcher function
-def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
+def matcher(r: Rexp, s: String): Boolean = {
+ val derivatives = simp(ders(s.toList,r))
+ nullable(derivatives)
+}
// (5) Complete the size function for regular
-// expressions according to the specification
+// expressions according to the specification
// given in the coursework.
-
-def size(r: Rexp): Int = r match {
+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)
+ case SEQ(a,b) => 1 + size(a) + size(b)
+ case ALT(a,b) => 1 + size(a) + size(b)
+ case STAR(a) => 1 + size(a)
}
-
-
+println(der('a', ZERO | ONE))// == (ZERO | ZERO)
+println(der('a', (CHAR('a') | ONE) ~ CHAR('a')))// ==ALT((ONE | ZERO) ~ CHAR('a'), ONE)
+println(der('a', STAR(CHAR('a'))))// == (ONE ~ STAR(CHAR('a')))
+println(der('b', STAR(CHAR('a'))))// == (ZERO ~ STAR(CHAR('a'))))
// some testing data
/*
-matcher(("a" ~ "b") ~ "c", "abc") // => true
-matcher(("a" ~ "b") ~ "c", "ab") // => false
+
+assert(matcher(("a" ~ "b") ~ "c", "abc") == true) // => true
+assert(matcher(("a" ~ "b") ~ "c", "ab") == false) // => false
+
// the supposedly 'evil' regular expression (a*)* b
-val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+//val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))
+
-matcher(EVIL, "a" * 1000 ++ "b") // => true
-matcher(EVIL, "a" * 1000) // => false
+assert(matcher(EVIL, "a" * 1000 ++ "b") == true) // => true
+assert(matcher(EVIL, "a" * 1000) == false) // => false
// size without simplifications
-size(der('a', der('a', EVIL))) // => 28
-size(der('a', der('a', der('a', EVIL)))) // => 58
+assert("28 " + size(der('a', der('a', EVIL))) ==28)// => 28
+assert("58 " + size(der('a', der('a', der('a', EVIL)))) ==58)// => 58
// size with simplification
-size(simp(der('a', der('a', EVIL)))) // => 8
-size(simp(der('a', der('a', der('a', EVIL))))) // => 8
+assert("8 " + size(simp(der('a', der('a', EVIL)))) ==8)// => 8
+assert("8 " + size(simp(der('a', der('a', der('a', EVIL))))) ==8) // => 8
-// Python 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.
+// 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.
+// Lets see how long it really 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()
@@ -162,15 +234,13 @@
println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))))
}
-// another "power" test case
-simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE
+// another "power" test case
+simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next) == ONE
// the Iterator produces the rexp
//
// SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)
//
-// where SEQ is nested 100 times.
-
+// where SEQ is nested 50 times.
+
*/
-
-//}