1 // Main Part 3 about Regular Expression Matching

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

     3 

     4 object M3 {

     5 

     6 // Regular Expressions

     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 ALTs(rs: List[Rexp]) extends Rexp      // alternatives 

    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 regular expressions

    17 

    18 //the usual binary choice can be defined in terms of ALTs

    19 def ALT(r1: Rexp, r2: Rexp) = ALTs(List(r1, r2))

    20 

    21 

    22 import scala.language.implicitConversions    

    23 import scala.language.reflectiveCalls 

    24 

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

    26   case Nil => ONE

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

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

    29 }

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

    31 

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

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

    34   def % = STAR(r)

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

    36 }

    37 

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

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

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

    41   def % = STAR(s)

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

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

    44 }

    45 

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

    47 // the definition given in the coursework; this 

    48 // function checks whether a regular expression

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

    50 // accordingly.

    51 

    52 def nullable (r: Rexp) : Boolean = ???

    53 

    54 

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

    56 // the definition given in the coursework; this

    57 // function calculates the derivative of a 

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

    59 

    60 def der (c: Char, r: Rexp) : Rexp = ???

    61 

    62 

    63 // (3) Implement the flatten function flts. It

    64 // deletes 0s from a list of regular expressions

    65 // and also 'spills out', or flattens, nested 

    66 // ALTernativeS.

    67 

    68 def flts(rs: List[Rexp]) : List[Rexp] = ???

    69 

    70 

    71 

    72 // (4) Complete the simp function according to

    73 // the specification given in the coursework description; 

    74 // this function simplifies a regular expression from

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

    76 // expressions; however it does not simplify inside 

    77 // STAR-regular expressions. Use the _.distinct and 

    78 // flts functions.

    79 

    80 def simp(r: Rexp) : Rexp = ???

    81 

    82 

    83 // (5) Complete the two functions below; the first 

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

    85 // is the regular expression matcher taking a regular

    86 // expression and a string and checks whether the

    87 // string matches the regular expression

    88 

    89 def ders (s: List[Char], r: Rexp) : Rexp = ???

    90 

    91 def matcher(r: Rexp, s: String): Boolean = ???

    92 

    93 

    94 // (6) Complete the size function for regular

    95 // expressions according to the specification 

    96 // given in the coursework.

    97 

    98 def size(r: Rexp): Int = ???

    99 

   100 

   101 // some testing data

   102 

   103 /*

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

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

   106 

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

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

   109 

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

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

   112 

   113 // size without simplifications

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

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

   116 

   117 // size with simplification

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

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

   120 

   121 // Python needs around 30 seconds for matching 28 a's with EVIL. 

   122 // Java 9 and later increase this to an "astonishing" 40000 a's in

   123 // 30 seconds.

   124 //

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

   126 // 5 Million a's...it should be in the range of a couple

   127 // of seconds.

   128 

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

   130   val start = System.nanoTime()

   131   for (j <- 1 to i) code

   132   val end = System.nanoTime()

   133   "%.5f".format((end - start)/(i * 1.0e9))

   134 }

   135 

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

   137   println(s"$i ${time_needed(2, matcher(EVIL, "a" * i))} secs.") 

   138 }

   139 

   140 // another "power" test case 

   141 simp(Iterator.iterate(ONE:Rexp)(r => SEQ(r, ONE | ONE)).drop(50).next()) == ONE

   142 

   143 // the Iterator produces the rexp

   144 //

   145 //      SEQ(SEQ(SEQ(..., ONE | ONE) , ONE | ONE), ONE | ONE)

   146 //

   147 //    where SEQ is nested 50 times.

   148 

   149 */

   150 

   151 }