--- a/progs/cw1.scala Wed May 10 17:03:21 2017 +0100
+++ b/progs/cw1.scala Sun May 21 00:43:02 2017 +0100
@@ -1,137 +1,90 @@
+// CW 1
import scala.language.implicitConversions
import scala.language.reflectiveCalls
-abstract class Rexp {
- def simp : Rexp = this
-}
+abstract class Rexp
+case object ZERO extends Rexp // matches nothing
+case object ONE extends Rexp // matches the empty string
+case class CHAR(c: Char) extends Rexp // matches a character c
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp // alternative
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp // sequence
+case class STAR(r: Rexp) extends Rexp // star
+case class RANGE(cs: Set[Char]) extends Rexp // set of characters
+case class PLUS(r: Rexp) extends Rexp // plus
+case class OPT(r: Rexp) extends Rexp // optional
+case class NTIMES(r: Rexp, n: Int) extends Rexp // n-times
+case class UPNTIMES(r: Rexp, n: Int) extends Rexp // up n-times
+case class FROMNTIMES(r: Rexp, n: Int) extends Rexp // from n-times
+case class NMTIMES(r: Rexp, n: Int, m: Int) extends Rexp // between nm-times
+case class NOT(r: Rexp) extends Rexp // not
+case class CFUN(f: Char => Boolean) extends Rexp // subsuming CHAR and RANGE
-case object NULL extends Rexp
-case object EMPTY extends Rexp
-case class CHAR(c: Char) extends Rexp
-case class ALT(r1: Rexp, r2: Rexp) extends Rexp {
- override def toString = r1.toString + " | " + r2.toString
- override def simp = (r1.simp, r2.simp) match {
- case (NULL, r) => r
- case (r, NULL) => r
- case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY)
- case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY)
- case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2)
- }
-}
-case class RANGE(cs: List[Char]) extends Rexp {
- //override def toString = cs.mkString("[",",","]")
- override def toString = "[" + cs.head + " .. " + cs.last + "]"
-}
-object RANGE {
- def apply(s: String) : RANGE = RANGE(s.toList)
-}
-case class SEQ(r1: Rexp, r2: Rexp) extends Rexp {
- override def toString = r1.toString + " ~ " + r2.toString
- override def simp = (r1.simp, r2.simp) match {
- case (NULL, _) => NULL
- case (_, NULL) => NULL
- case (EMPTY, r) => r
- case (r, EMPTY) => r
- case (r1, r2) => SEQ(r1, r2)
- }
-}
-case class PLUS(r: Rexp) extends Rexp {
- override def simp = r.simp match {
- case NULL => EMPTY
- case EMPTY => EMPTY
- case r => PLUS(r)
- }
-}
-case class STAR(r: Rexp) extends Rexp {
- override def simp = r.simp match {
- case NULL => EMPTY
- case EMPTY => EMPTY
- case r => STAR(r)
- }
-}
-case class NTIMES(r: Rexp, n: Int) extends Rexp {
- override def simp = if (n == 0) EMPTY else
- r.simp match {
- case NULL => NULL
- case EMPTY => EMPTY
- case r => NTIMES(r, n)
- }
-}
-case class NUPTOM(r: Rexp, n: Int, m: Int) extends Rexp {
- override def simp = if (m == 0) EMPTY else
- r.simp match {
- case NULL => NULL
- case EMPTY => EMPTY
- case r => NUPTOM(r, n, m)
- }
-}
-def NMTIMES(r: Rexp, n: Int, m: Int) = {
- if(m < n) throw new IllegalArgumentException("the number m cannot be smaller than n.")
- else NUPTOM(r, n, m - n)
-}
-
-
-case class NOT(r: Rexp) extends Rexp {
- override def simp = NOT(r.simp)
-}
-case class OPT(r: Rexp) extends Rexp {
- override def simp = OPT(r.simp)
-}
// nullable function: tests whether the regular
// expression can recognise the empty string
def nullable (r: Rexp) : Boolean = r match {
- case NULL => false
- case EMPTY => true
+ 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(r) => nullable(r)
- case NTIMES(r, i) => if (i == 0) true else nullable(r)
- case NUPTOM(r, i, j) => if (i == 0) true else nullable(r)
- case RANGE(_) => false
- case NOT(r) => !(nullable(r))
case OPT(_) => true
-}
-
-def zeroable (r: Rexp) : Boolean = r match {
- case NULL => true
- case EMPTY => false
- case CHAR(_) => false
- case ALT(r1, r2) => zeroable(r1) && zeroable(r2)
- case SEQ(r1, r2) => zeroable(r1) || zeroable(r2)
- case STAR(_) => false
- case PLUS(r) => zeroable(r)
- case NTIMES(r, i) => if (i == 0) false else zeroable(r)
- case NUPTOM(r, i, j) => if (i == 0) false else zeroable(r)
- case RANGE(_) => false
- case NOT(r) => !(zeroable(r))
- case OPT(_) => false
+ case NTIMES(r, n) => if (n == 0) true else nullable(r)
+ case UPNTIMES(_, _) => true
+ case FROMNTIMES(r, n) => if (n == 0) true else nullable(r)
+ case NMTIMES(r, n, m) => if (n == 0) true else nullable(r)
+ case NOT(r) => !(nullable(r))
+ case CFUN(_) => false
}
// derivative of a regular expression w.r.t. a character
def der (c: Char, r: Rexp) : Rexp = r match {
- case NULL => NULL
- case EMPTY => NULL
- case CHAR(d) => if (c == d) EMPTY else NULL
+ 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 RANGE(cs) => if (cs contains c) ONE else ZERO
case PLUS(r) => SEQ(der(c, r), STAR(r))
- case NTIMES(r, i) =>
- if (i == 0) NULL else der(c, SEQ(r, NTIMES(r, i - 1)))
- case NUPTOM(r, i, j) =>
- if (i == 0 && j == 0) NULL else
- if (i == 0) ALT(der(c, NTIMES(r, j)), der(c, NUPTOM(r, 0, j - 1)))
- else der(c, SEQ(r, NUPTOM(r, i - 1, j)))
- case RANGE(cs) => if (cs contains c) EMPTY else NULL
+ case OPT(r) => der(c, r)
+ case NTIMES(r, n) =>
+ if (n == 0) ZERO else SEQ(der(c, r), NTIMES(r, n - 1))
+ case UPNTIMES(r, n) =>
+ if (n == 0) ZERO else SEQ(der(c, r), UPNTIMES(r, n - 1))
+ case FROMNTIMES(r, n) =>
+ if (n == 0) ZERO else SEQ(der(c, r), FROMNTIMES(r, n - 1))
+ case NMTIMES(r, n, m) =>
+ if (m < n) ZERO else
+ if (n == 0 && m == 0) ZERO else
+ if (n == 0) SEQ(der(c, r), UPNTIMES(r, m - 1))
+ else SEQ(der(c, r), NMTIMES(r, n - 1, m - 1))
case NOT(r) => NOT(der (c, r))
- case OPT(r) => der(c, r)
+ 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
+}
+
+
// derivative w.r.t. a string (iterates der)
def ders (s: List[Char], r: Rexp) : Rexp = s match {
case Nil => r
@@ -140,15 +93,18 @@
def ders_simp (s: List[Char], r: Rexp) : Rexp = s match {
case Nil => r
- case c::s => ders_simp(s, der(c, r).simp)
+ case c::s => ders_simp(s, simp(der(c, r)))
}
-// main matcher function
-def matcher(r: Rexp, s: String) : Boolean = nullable(ders_simp(s.toList, r))
+// main matcher function including simplification
+def matcher(r: Rexp, s: String) : Boolean =
+ nullable(ders_simp(s.toList, r))
+
+
// some convenience for typing in regular expressions
def charlist2rexp(s : List[Char]) : Rexp = s match {
- case Nil => EMPTY
+ case Nil => ONE
case c::Nil => CHAR(c)
case c::s => SEQ(CHAR(c), charlist2rexp(s))
}
@@ -168,12 +124,29 @@
def ~ (r: String) = SEQ(s, r)
}
+val r1 = NTIMES("a", 3)
+val r2 = NTIMES(OPT("a"), 3)
+val r3 = UPNTIMES("a", 3)
+val r4 = UPNTIMES(OPT("a"), 3)
+val r5 = NMTIMES("a", 3, 5)
+val r6 = NMTIMES(OPT("a"), 3, 5)
+
+val rs = List(r1, r2, r3, r4, r5, r6)
+
+rs.map(matcher(_, ""))
+rs.map(matcher(_, "a"))
+rs.map(matcher(_, "aa"))
+rs.map(matcher(_, "aaa"))
+rs.map(matcher(_, "aaaa"))
+rs.map(matcher(_, "aaaaa"))
+rs.map(matcher(_, "aaaaaa"))
+
println("EMAIL:")
-val LOWERCASE = "abcdefghijklmnopqrstuvwxyz"
-val DIGITS = "0123456789"
-val EMAIL = PLUS(RANGE(LOWERCASE + DIGITS + "_" + "." + "-")) ~ "@" ~
- PLUS(RANGE(LOWERCASE + DIGITS + "." + "-")) ~ "." ~
- NMTIMES(RANGE(LOWERCASE + "."), 2, 6)
+val LOWERCASE = ('a' to 'z').toSet
+val DIGITS = ('0' to '9').toSet
+val EMAIL = { PLUS(CFUN(LOWERCASE | DIGITS | ("_.-").toSet)) ~ "@" ~
+ PLUS(CFUN(LOWERCASE | DIGITS | (".-").toSet)) ~ "." ~
+ NMTIMES(CFUN(LOWERCASE | Set('.')), 2, 6) }
val my_email = "christian.urban@kcl.ac.uk"
@@ -182,7 +155,7 @@
println(ders_simp(my_email.toList, EMAIL))
println("COMMENTS:")
-val ALL = RANGE(LOWERCASE + " ")
+val ALL = CFUN((c:Char) => true)
val COMMENT = "/*" ~ (NOT(ALL.% ~ "*/" ~ ALL.%)) ~ "*/"
println(matcher(COMMENT, "/**/"))