1 // Part 1 about Regular Expression Matching

     2 //==========================================

     3 

     4 

     5 object CW8a {

     6 

     7 abstract class Rexp

     8 case object ZERO extends Rexp

     9 case object ONE extends Rexp

    10 case class CHAR(c: Char) extends Rexp

    11 case class ALT(r1: Rexp, r2: Rexp) extends Rexp   // alternative 

    12 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp   // sequence

    13 case class STAR(r: Rexp) extends Rexp             // star

    14 

    15 

    16 // some convenience for typing in regular expressions

    17 

    18 import scala.language.implicitConversions    

    19 import scala.language.reflectiveCalls 

    20 

    21 def charlist2rexp(s: List[Char]): Rexp = s match {

    22   case Nil => ONE

    23   case c::Nil => CHAR(c)

    24   case c::s => SEQ(CHAR(c), charlist2rexp(s))

    25 }

    26 implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList)

    27 

    28 implicit def RexpOps (r: Rexp) = new {

    29   def | (s: Rexp) = ALT(r, s)

    30   def % = STAR(r)

    31   def ~ (s: Rexp) = SEQ(r, s)

    32 }

    33 

    34 implicit def stringOps (s: String) = new {

    35   def | (r: Rexp) = ALT(s, r)

    36   def | (r: String) = ALT(s, r)

    37   def % = STAR(s)

    38   def ~ (r: Rexp) = SEQ(s, r)

    39   def ~ (r: String) = SEQ(s, r)

    40 }

    41 

    42 // (1a) Complete the function nullable according to

    43 // the definition given in the coursework; this 

    44 // function checks whether a regular expression

    45 // can match the empty string and Returns a boolean

    46 // accordingly.

    47 

    48 //def nullable (r: Rexp) : Boolean = ...

    49 

    50 

    51 // (1b) Complete the function der according to

    52 // the definition given in the coursework; this

    53 // function calculates the derivative of a 

    54 // regular expression w.r.t. a character.

    55 

    56 //def der (c: Char, r: Rexp) : Rexp = ...

    57 

    58 

    59 // (1c) Complete the simp function according to

    60 // the specification given in the coursework; this

    61 // function simplifies a regular expression from

    62 // the inside out, like you would simplify arithmetic 

    63 // expressions; however it does not simplify inside 

    64 // STAR-regular expressions.

    65 

    66 //def simp(r: Rexp) : Rexp = ... 

    67 

    68 

    69 // (1d) Complete the two functions below; the first 

    70 // calculates the derivative w.r.t. a string; the second

    71 // is the regular expression matcher taking a regular

    72 // expression and a string and checks whether the

    73 // string matches the regular expression

    74 

    75 //def ders (s: List[Char], r: Rexp) : Rexp = ... 

    76 

    77 //def matcher(r: Rexp, s: String): Boolean = ...

    78 

    79 

    80 // (1e) Complete the size function for regular

    81 // expressions according to the specification 

    82 // given in the coursework.

    83 

    84 //def size(r: Rexp): Int = ...

    85 

    86 

    87 // some testing data

    88 

    89 /*

    90 matcher(("a" ~ "b") ~ "c", "abc")  // => true

    91 matcher(("a" ~ "b") ~ "c", "ab")   // => false

    92 

    93 // the supposedly 'evil' regular expression (a*)* b

    94 val EVIL = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))

    95 

    96 matcher(EVIL, "a" * 1000 ++ "b")   // => true

    97 matcher(EVIL, "a" * 1000)          // => false

    98 

    99 // size without simplifications

   100 size(der('a', der('a', EVIL)))             // => 28

   101 size(der('a', der('a', der('a', EVIL))))   // => 58

   102 

   103 // size with simplification

   104 size(simp(der('a', der('a', EVIL))))           // => 8

   105 size(simp(der('a', der('a', der('a', EVIL))))) // => 8

   106 

   107 // Java needs around 30 seconds for matching 28 a's with EVIL. 

   108 //

   109 // Lets see how long it takes to match strings with 

   110 // 0.5 Million a's...it should be in the range of some

   111 // seconds.

   112 

   113 def time_needed[T](i: Int, code: => T) = {

   114   val start = System.nanoTime()

   115   for (j <- 1 to i) code

   116   val end = System.nanoTime()

   117   (end - start)/(i * 1.0e9)

   118 }

   119 

   120 for (i <- 0 to 5000000 by 500000) {

   121   println(i + " " + "%.5f".format(time_needed(2, matcher(EVIL, "a" * i))))

   122 }

   123 

   124 */

   125 

   126 

   127 }