testing4/re.scala
changeset 347 4de31fdc0d67
parent 346 663c2a9108d1
child 348 b5b6ed38c2f2
--- a/testing4/re.scala	Sun Nov 01 01:21:31 2020 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,196 +0,0 @@
-// Core Part about Regular Expression Matching
-//=============================================
-
-object CW9c {
-
-// 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   // alternative 
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp   // sequence
-case class STAR(r: Rexp) extends Rexp             // star
-
-
-// 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)
-  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)
-}
-
-// (5) 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(c) => false
-		case ALT(r1, r2) => (nullable(r1) || nullable(r2))
-		case SEQ(r1, r2) => (nullable(r1) && nullable(r2))
-		case STAR(r) => true
-	}
-}
-
-// (6) 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(d == c) 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(r) => SEQ(der(c, r), STAR(r))
-	}
-}
-
-
-// (7) 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 STAR(r) => STAR(r) // does not process r star
-		case SEQ(r1, r2) => {
-			val x = (simp(r1), simp(r2))
-			if(x._1 == ZERO) ZERO else
-			if(x._2 == ZERO) ZERO else
-			if(x._1 == ONE) simp(x._2) else 
-			if(x._2 == ONE) simp(x._1) else
-			if(x._1 == x._2) simp(x._2) else
-			SEQ(simp(x._1), simp(x._2))
-		}
-		case ALT(r1, r2) => {
-			val x = (simp(r1), simp(r2))
-			if(x._1 == ZERO) simp(x._2) else
-			if(x._2 == ZERO) simp(x._1) else
-			if(x._1 == x._2) simp(x._2) else
-			ALT(simp(x._1), simp(x._2))
-		}
-		case r => r // if single regex, return it
-	}
-}
-
-
-// (8) 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 :: cs => ders(cs, simp(der(c,r)))
-	}
-}
-
-def matcher(r: Rexp, s: String): Boolean = {
-	val listOfCharacters = s.toList
-	val result = ders(listOfCharacters, r)
-	nullable(result)
-}
-
-
-// (9) 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(c) => 1
-		case ALT(r1, r2) => 1 + size(r1) + size(r2)
-		case SEQ(r1, r2) => 1 + size(r1) + size(r2)
-		case STAR(r) => 1 + size(r)
-	}
-}
-
-// 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
-// 30 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()
-  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))))
-}
-
-// 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 50 times.
-
-*/
-
-}