--- a/main_marking3/re.scala Thu Jan 13 12:55:03 2022 +0000
+++ b/main_marking3/re.scala Mon Apr 11 23:55:27 2022 +0100
@@ -1,23 +1,25 @@
-// Core Part about Regular Expression Matching
+// Main Part 3 about Regular Expression Matching
//=============================================
-object CW8c {
+object M3 {
// 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 ALTs(rs: List[Rexp]) extends Rexp // alternatives
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence
+case class STAR(r: Rexp) extends Rexp // star
+
+
+//the usual binary choice can be defined in terms of ALTs
+def ALT(r1: Rexp, r2: Rexp) = ALTs(List(r1, r2))
// 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)
@@ -49,7 +51,7 @@
case ZERO => false
case ONE => true
case CHAR(_) => false
- case ALT(r1, r2) => nullable(r1) || nullable(r2)
+ case ALTs(rs) => rs.exists(nullable)
case SEQ(r1, r2) => nullable(r1) && nullable(r2)
case STAR(_) => true
}
@@ -63,25 +65,39 @@
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 ALTs(rs) => ALTs(rs.map(der(c, _)))
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
+
+// (3) Implement the flatten function flts. It
+// deletes 0s from a list of regular expressions
+// and also 'spills out', or flattens, nested
+// ALTernativeS.
+
+def flts(rs: List[Rexp]) : List[Rexp] = rs match {
+ case Nil => Nil
+ case ZERO::tl => flts(tl)
+ case ALTs(rs1)::rs2 => rs1 ::: flts(rs2)
+ case r::rs => r :: flts(rs)
+}
+
+// (4) 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 ALTs(rs) => (flts(rs.map(simp)).distinct) match {
+ case Nil => ZERO
+ case r::Nil => r
+ case rs => ALTs(rs)
}
case SEQ(r1, r2) => (simp(r1), simp(r2)) match {
case (ZERO, _) => ZERO
@@ -93,8 +109,9 @@
case r => r
}
+simp(ALT(ONE | CHAR('a'), CHAR('a') | ONE))
-// (4) Complete the two functions below; the first
+// (5) 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
@@ -108,7 +125,7 @@
// main matcher function
def matcher(r: Rexp, s: String) = nullable(ders(s.toList, r))
-// (5) Complete the size function for regular
+// (6) Complete the size function for regular
// expressions according to the specification
// given in the coursework.
@@ -117,7 +134,7 @@
case ZERO => 1
case ONE => 1
case CHAR(_) => 1
- case ALT(r1, r2) => 1 + size(r1) + size (r2)
+ case ALTs(rs) => 1 + rs.map(size).sum
case SEQ(r1, r2) => 1 + size(r1) + size (r2)
case STAR(r1) => 1 + size(r1)
}
@@ -130,18 +147,21 @@
//matcher(("a" ~ "b") ~ "c", "ab") // => 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
+//println(matcher(EVIL, "a" * 1000 ++ "b")) // => true
+//println(matcher(EVIL, "a" * 1000)) // => false
// size without simplifications
-//size(der('a', der('a', EVIL))) // => 28
-//size(der('a', der('a', der('a', EVIL)))) // => 58
+//println(size(der('a', der('a', EVIL)))) // => 28
+//println(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
+//println(simp(der('a', der('a', EVIL))))
+//println(simp(der('a', der('a', der('a', EVIL)))))
+
+//println(size(simp(der('a', der('a', EVIL))))) // => 8
+//println(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
@@ -155,11 +175,11 @@
val start = System.nanoTime()
for (j <- 1 to i) code
val end = System.nanoTime()
- (end - start)/(i * 1.0e9)
+ "%.5f".format((end - start)/(i * 1.0e9))
}
//for (i <- 0 to 5000000 by 500000) {
-// println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))) + " secs.")
+// println(s"$i ${time_needed(2, matcher(EVIL, "a" * i))} secs.")
//}
// another "power" test case
@@ -169,7 +189,7 @@
//
// SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)
//
-// where SEQ is nested 100 times.
+// where SEQ is nested 50 times.