// 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)