// CW1

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 

// extended Rexps

case class RANGE(s: Set[Char]) extends Rexp

case class PLUS(r: Rexp) extends Rexp

case class OPTIONAL(r: Rexp) extends Rexp

case class NTIMES(r: Rexp, n: Int) extends Rexp 

case class UPTO(r: Rexp, n: Int) extends Rexp

case class FROM(r: Rexp, n: Int) extends Rexp

case class BETWEEN(r: Rexp, n: Int, m: Int) extends Rexp

case class NOT(r: Rexp) extends Rexp

// functions

case class CFUN(f: Char => Boolean) extends Rexp

// abbreviations

def FCHAR(c: Char) = CFUN((a: Char) => a == c)

def FSET(s: Set[Char]) = CFUN((a: Char) => s.contains(a))

val FALL = CFUN(_ => true)

def nullable (r: Rexp) : Boolean = r match {

  case ZERO => false

  case ONE => true

  case CHAR(_) => false

  case ALT(r1, r2) => nullable(r1) || nullable(r2)

  case SEQ(r1, r2) => nullable(r1) && nullable(r2)

  case STAR(_) => true

  case RANGE(_) => false 

  case PLUS(r1) => nullable(r1)

  case OPTIONAL(_) => true

  case NTIMES(r1, i) => if (i == 0) true else nullable(r1)

  case UPTO(_, _) => true

  case FROM(r1, i) => if (i == 0) true else nullable(r1)

  case BETWEEN(r1, i, _) => if (i == 0) true else nullable(r1)

  case NOT(r1) => !nullable(r1)

  case CFUN(f) => false

}

def der (c: Char, r: Rexp) : Rexp = r match {

  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 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))

  case RANGE(s) =>

    if (s.contains(c)) ONE else ZERO 

  case PLUS(r1) => SEQ(der(c, r1), STAR(r1))

  case OPTIONAL(r1) => der(c, r1)

  case NTIMES(r, i) => 

    if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))

  case UPTO(r1, i) => 

    if (i == 0) ZERO else SEQ(der(c, r1), UPTO(r1, i - 1)) 

  case FROM(r1, i) =>

    if (i == 0) SEQ(der(c, r1), FROM(r1, 0)) else

    SEQ(der(c, r1), FROM(r1, i - 1))

  case BETWEEN(r1, i, j) => 

    if (i == 0) {

      if (j == 0) ZERO else SEQ(der(c, r1), BETWEEN(r1, 0, j - 1))

    } else SEQ(der(c, r1), BETWEEN(r1, i - 1, j - 1))

  case NOT(r1) => NOT(der(c, r1))

  case CFUN(f) => if (f(c)) ONE else ZERO

}

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 SEQ(r1, r2) =>  (simp(r1), simp(r2)) match {

    case (ZERO, _) => ZERO

    case (_, ZERO) => ZERO

    case (ONE, r2s) => r2s

    case (r1s, ONE) => r1s

    case (r1s, r2s) => SEQ(r1s, r2s)

  }

  case r => r

}

def ders(s: List[Char], r: Rexp) : Rexp = s match {

  case Nil => r

  case c::s => ders(s, simp(der(c, r)))

}

def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))

val Regex31 = NTIMES(CHAR('a'),3)

val Regex32 = NTIMES(OPTIONAL(CHAR('a')),3)

val Regex33 = UPTO(CHAR('a'),3)

val Regex34 = UPTO(OPTIONAL(CHAR('a')),3)

val Regex35 = BETWEEN(CHAR('a'),3,5)

val Regex36 = BETWEEN(OPTIONAL(CHAR('a')),3,5)

val string31 = ""

val string32 = "a"

val string33 = "aa"

val string34 = "aaa"

val string35 = "aaaa"

val string36 = "aaaaa"

val string37 = "aaaaaa"

println("Question3")

println(matcher(Regex31, string31))

println(matcher(Regex31, string32))

println(matcher(Regex31, string33))

println(matcher(Regex31, string34))

println(matcher(Regex31, string35))

println(matcher(Regex31, string36))

println(matcher(Regex31, string37)); println("")

println(matcher(Regex32, string31))

println(matcher(Regex32, string32))

println(matcher(Regex32, string33))

println(matcher(Regex32, string34))

println(matcher(Regex32, string35))

println(matcher(Regex32, string36))

println(matcher(Regex32, string37)); println("")

println(matcher(Regex33, string31))

println(matcher(Regex33, string32))

println(matcher(Regex33, string33))

println(matcher(Regex33, string34))

println(matcher(Regex33, string35))

println(matcher(Regex33, string36))

println(matcher(Regex33, string37)); println("")

println(matcher(Regex34, string31))

println(matcher(Regex34, string32))

println(matcher(Regex34, string33))

println(matcher(Regex34, string34))

println(matcher(Regex34, string35))

println(matcher(Regex34, string36))

println(matcher(Regex34, string37)); println("")

println(matcher(Regex35, string31))

println(matcher(Regex35, string32))

println(matcher(Regex35, string33))

println(matcher(Regex35, string34))

println(matcher(Regex35, string35))

println(matcher(Regex35, string36))

println(matcher(Regex35, string37)); println("")

println(matcher(Regex36, string31))

println(matcher(Regex36, string32))

println(matcher(Regex36, string33))

println(matcher(Regex36, string34))

println(matcher(Regex36, string35))

println(matcher(Regex36, string36))

println(matcher(Regex36, string37)); println("")

val RegexX = BETWEEN(CHAR('a'), 0, 5)

val stringX = ""

println(matcher(RegexX, stringX))

val str0 = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

val str1 = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

val str2 = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

val matchA = (c:Char) => c == 'a'

val reg_1 = SEQ(SEQ(CFUN(matchA), CFUN(matchA)), CFUN(matchA))

val reg_2 = SEQ(NTIMES(CFUN(matchA), 19), OPTIONAL(CFUN(matchA)))

val reg_1_mod = PLUS(PLUS(reg_1))

val reg_2_mod = PLUS(PLUS(reg_2))

matcher(reg_1_mod, str0)

matcher(reg_1_mod, str1)

matcher(reg_1_mod, str2)

matcher(reg_2_mod, str0)

matcher(reg_2_mod, str1)

matcher(reg_2_mod, str2)

//Q3: matcher test (table)

// a^{3}

val re1 = NTIMES(CHAR('a'), 3)

matcher(re1, "")        //false

matcher(re1, "a")       //false

matcher(re1, "aa")      //false

matcher(re1, "aaa")     //true

matcher(re1, "aaaaa")   //false

matcher(re1, "aaaaaa")  //false

// (a?)^{3}

val re2 = NTIMES(OPTIONAL(CHAR('a')), 3)

matcher(re2, "")        //true

matcher(re2, "a")       //true

matcher(re2, "aa")      //true

matcher(re2, "aaa")     //true

matcher(re2, "aaaaa")   //false

matcher(re2, "aaaaaa")  //false

// (a)^{..3}

val re3 = UPTO((CHAR('a')), 3)

matcher(re3, "")        //true

matcher(re3, "a")       //true

matcher(re3, "aa")      //true

matcher(re3, "aaa")     //true

matcher(re3, "aaaaa")   //false

matcher(re3, "aaaaaa")  //false

// (a?)^{..3}

val re4 = UPTO(OPTIONAL(CHAR('a')), 3)

matcher(re4, "")        //true

matcher(re4, "a")       //true

matcher(re4, "aa")      //true

matcher(re4, "aaa")     //true

matcher(re4, "aaaaa")   //false

matcher(re4, "aaaaaa")  //false

// (a)^{3..5}

val re5 = BETWEEN(CHAR('a'), 3, 5)

matcher(re5, "")        //false

matcher(re5, "a")       //false

matcher(re5, "aa")      //false

matcher(re5, "aaa")     //true

matcher(re5, "aaaaa")   //true

matcher(re5, "aaaaaa")  //false

// (a?)^{3..5}

val re6 = BETWEEN(OPTIONAL(CHAR('a')), 3, 5)

matcher(re6, "")        //true

matcher(re6, "a")       //true

matcher(re6, "aa")      //true

matcher(re6, "aaa")     //true

matcher(re6, "aaaaa")   //true

matcher(re6, "aaaaaa")  //false

//Q5: regular expression for email addresses

val alphaNum = ('a' to 'z').toSet ++ ('0' to '9')

val Q5email = SEQ(

                PLUS(RANGE(alphaNum + '_' + '-' + '.')), 

                SEQ(

                    CHAR('@'), 

                    SEQ(

                        PLUS(RANGE(alphaNum + '-' + '.')), 

                        SEQ(

                            CHAR('.'), 

                            BETWEEN(RANGE(('a' to 'z').toSet + '.'), 2, 6)

                            )

                      )

                )

              )

ders("nicolas.volken@kcl.ac.uk".toList, Q5email)

// Q6

val Q6 = SEQ(CHAR('/'),

            SEQ(CHAR('*'),

                SEQ(

                    NOT(

                      SEQ(

                        STAR(FALL),

                        SEQ(

                          CHAR('*'),

                          SEQ(

                            CHAR('/'),

                            STAR(FALL)

                          )

                        )

                      )

                    )

                    ,

                    SEQ(CHAR('*'),

                    CHAR('/')

                    )

                )

            )

        )

matcher(Q6, "/**/")

matcher(Q6, "/*foobar*/")

matcher(Q6, "/*test*/test*/")

matcher(Q6, "/*test/*test*/")

// Q7

val Q7r1 = SEQ(CHAR('a'), SEQ(CHAR('a'), CHAR('a')))

val Q7r2 = SEQ(BETWEEN(CHAR('a'), 19, 19), OPTIONAL(CHAR('a')))

val Q7str5 = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

val Q7str6 = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

val Q7str7 = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

matcher(PLUS(PLUS(Q7r1)), Q7str5)

matcher(PLUS(PLUS(Q7r2)), Q7str5)

matcher(PLUS(PLUS(Q7r1)), Q7str6)

matcher(PLUS(PLUS(Q7r2)), Q7str6)

matcher(PLUS(PLUS(Q7r1)), Q7str7)

matcher(PLUS(PLUS(Q7r2)), Q7str7)