diff -r e66bd5c563eb -r b5b5583a3a08 progs/re3ext.scala --- a/progs/re3ext.scala Mon Jul 27 11:02:48 2020 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,151 +0,0 @@ -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 -case class NTIMES(r: Rexp, n: Int) extends Rexp - -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 NTIMES(r, n) => NTIMES(simp(r), n) - case r => r -} - -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 NTIMES(r, i) => if (i == 0) true else nullable(r) -} - -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(r) => SEQ(der(c, r), STAR(r)) - case NTIMES(r, i) => - if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1)) -} - -def ders (s: List[Char], r: Rexp) : Rexp = s match { - case Nil => r - case c::s => ders(s, simp(der(c, r))) -} - -def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) - - -//one or zero -def OPT(r: Rexp) = ALT(r, ONE) - -def EVIL(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) - -def time_needed[T](i: Int, code: => T) = { - val start = System.nanoTime() - for (j <- 1 to i) code - val end = System.nanoTime() - (end - start)/(i * 1.0e9) -} - -/* -for (i <- 1 to 9001 by 1000) { - println(i + " " + "%.5f".format(time_needed(1, matches(EVIL(i), "a" * i)))) -} -*/ - -// some convenience for typing in regular expressions -import scala.language.implicitConversions -import scala.language.reflectiveCalls - -def charlist2rexp(s : List[Char]) : Rexp = s match { - case Nil => ONE - case c::Nil => CHAR(c) - case c::s => SEQ(CHAR(c), charlist2rexp(s)) -} -implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList) - -implicit def RexpOps (r: Rexp) = new { - def | (s: Rexp) = ALT(r, s) - def % = STAR(r) - def ~ (s: Rexp) = SEQ(r, s) -} - -implicit def stringOps (s: String) = new { - def | (r: Rexp) = ALT(s, r) - def | (r: String) = ALT(s, r) - def % = STAR(s) - def ~ (r: Rexp) = SEQ(s, r) - def ~ (r: String) = SEQ(s, r) -} - - -def PLUS(r: Rexp) = SEQ(r, STAR(r)) -def RANGE(s: List[Char]) : Rexp = s match { - case Nil => ZERO - case c::s => ALT(CHAR(c), RANGE(s)) -} -def NMTIMES(r: Rexp, n: Int, m: Int) : Rexp = - if (n >= m) NTIMES(r, n) else ALT(NTIMES(r, m), NMTIMES(r, n, m - 1)) - - -println("Coursework:") -val REG1 = PLUS(PLUS("a" ~ "a" ~ "a")) -val REG2 = PLUS(PLUS("aaaaaaaaaaaaaaaaaaa" ~ OPT("a"))) // 19 as ~ a? - - -//40 * aaa matches -//43 * aaa + aa does not -//45 * aaa + a - -println("EVIL1:") -println(matches(REG1, "aaa" * 40)) -println(matches(REG1, "aaa" * 43 + "aa")) -println(matches(REG1, "aaa" * 45 + "a")) -println("EVIL2:") -println(matches(REG2, "aaa" * 40)) -println(matches(REG2, "aaa" * 43 + "aa")) -println(matches(REG2, "aaa" * 45 + "a")) - -println("EMAIL:") -val LOWERCASE = "abcdefghijklmnopqrstuvwxyz" -val DIGITS = "0123456789" -val EMAIL = PLUS(RANGE((LOWERCASE + DIGITS + "_" + "." + "-").toList)) ~ "@" ~ - PLUS(RANGE((LOWERCASE + DIGITS + "." + "-").toList)) ~ "." ~ - NMTIMES(RANGE((LOWERCASE + ".").toList), 2, 6) - -val my_email = "christian.urban@kcl.ac.uk" - -println(matches(EMAIL, my_email)) - -println(matches(NTIMES("a", 2), "a")) -println(matches(NTIMES("a", 2), "aa")) -println(matches(NTIMES("a", 2), "aaa")) - -println(matches(NMTIMES("a", 2, 3), "a")) -println(matches(NMTIMES("a", 2, 3), "aa")) -println(matches(NMTIMES("a", 2, 3), "aaa")) -println(matches(NMTIMES("a", 2, 3), "aaaa"))