--- a/testing4/re.scala Thu Dec 06 18:56:26 2018 +0000
+++ b/testing4/re.scala Thu Dec 06 21:49:43 2018 +0000
@@ -1,23 +1,21 @@
// 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
-
def charlist2rexp(s: List[Char]): Rexp = s match {
case Nil => ONE
case c::Nil => CHAR(c)
@@ -46,30 +44,38 @@
// 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
+ 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.
+//TODO: debug
+//TODO: understand this more.
+// first test runs
+// test 2 fails
+// test 3 runs
+// test 4 runs
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))
+ //TODO: debug
+ case ZERO => ZERO
+ case ONE => ZERO
+ case CHAR(r1) => if (c == r1) 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
@@ -78,19 +84,21 @@
// 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
+ case STAR(_) => r
+ case SEQ(r1, r2) => (simp(r1), simp(r2)) match { // potential failure
+ case (_, ZERO) => ZERO
+ case (ZERO, _) => ZERO
+ case (r1, ONE) => simp(r1)
+ case (ONE, r2) => simp(r2)
+ case (r1, r2) => SEQ(r1, r2)
+ }
+ case ALT(r1, r2) => (simp(r1), simp(r2)) match {
+ case (r1, ZERO) => simp(r1)
+ case (ZERO, r1) => simp(r1)
+ case (r1, r2) if r1 == r2 => simp(r1)
+ case (r1, r2) => ALT(r1, r2)
+ }
+ case r => r
}
@@ -98,58 +106,60 @@
// 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
- case c::s => ders(s, simp(der(c, r)))
+ case Nil => r
+ case c::cs => ders(cs, simp(der(c, r)))
}
-// main matcher function
-def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
+def matcher(r: Rexp, s: String): Boolean = {
+ 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)
+ case ZERO => 1
+ case ONE => 1
+ case CHAR(_) => 1
+ case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+ case ALT(r1, r2) => 1 + size(r1) + size(r2)
+ case STAR(r1) => 1 + size(r1)
}
+// some testing data
-// 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
// 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()
@@ -158,19 +168,17 @@
(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))))
+//}
// another "power" test case
-simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(100).next) == ONE
+println(simp(Iterator.iterate(ONE:Rexp)(r => ALT(r, r)).drop(40).next))
// 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.
-//}
+