1 // Part 1 about Regular Expression Matching

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

     3 

     4 

     5 abstract class Rexp

     6 case object ZERO extends Rexp

     7 case object ONE extends Rexp

     8 case class CHAR(c: Char) extends Rexp

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

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

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

    12 

    13 

    14 // some convenience for typing in regular expressions

    15 

    16 import scala.language.implicitConversions    

    17 import scala.language.reflectiveCalls 

    18 

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

    20   case Nil => ONE

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

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

    23 }

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

    25 

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

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

    28   def % = STAR(r)

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

    30 }

    31 

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

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

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

    35   def % = STAR(s)

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

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

    38 }

    39 

    40 // (1) Complete the function nullable according to

    41 // the definition given in the coursework; this 

    42 // function checks whether a regular expression

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

    44 // accordingly.

    45 

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

    47 

    48 

    49 // (2) Complete the function der according to

    50 // the definition given in the coursework; this

    51 // function calculates the derivative of a 

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

    53 

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

    55 

    56 

    57 // (3) Complete the simp function according to

    58 // the specification given in the coursework; this

    59 // function simplifies a regular expression from

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

    61 // expressions; however it does not simplify inside 

    62 // STAR-regular expressions.

    63 

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

    65 

    66 

    67 // (4) Complete the two functions below; the first 

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

    69 // is the regular expression matcher taking a regular

    70 // expression and a string and checks whether the

    71 // string matches the regular expression

    72 

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

    74 

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

    76 

    77 

    78 // (5) Complete the size function for regular

    79 // expressions according to the specification 

    80 // given in the coursework.

    81 

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

    83 

    84 

    85 // some testing data

    86 

    87 /*

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

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

    90 

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

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

    93 

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

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

    96 

    97 // size without simplifications

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

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

   100 

   101 // size with simplification

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

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

   104 

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

   106 //

   107 // Lets see how long it really takes to match strings with 

   108 // 0.5 Million a's...it should be in the range of some

   109 // seconds.

   110 

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

   112   val start = System.nanoTime()

   113   for (j <- 1 to i) code

   114   val end = System.nanoTime()

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

   116 }

   117 

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

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

   120 }

   121 

   122 */

   123