1 // version with explicit n-times regular expression |
1 // version with explicit n-times regular expression |
2 |
2 |
3 abstract class Rexp |
3 abstract class Rexp |
4 case object NULL extends Rexp |
4 case object ZERO extends Rexp |
5 case object EMPTY extends Rexp |
5 case object ONE extends Rexp |
6 case class CHAR(c: Char) extends Rexp |
6 case class CHAR(c: Char) extends Rexp |
7 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
7 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
8 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
8 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
9 case class STAR(r: Rexp) extends Rexp |
9 case class STAR(r: Rexp) extends Rexp |
10 case class NTIMES(r: Rexp, n: Int) extends Rexp //explicit constructor |
10 case class NTIMES(r: Rexp, n: Int) extends Rexp //explicit constructor |
11 |
11 |
12 def nullable (r: Rexp) : Boolean = r match { |
12 def nullable (r: Rexp) : Boolean = r match { |
13 case NULL => false |
13 case ZERO => false |
14 case EMPTY => true |
14 case ONE => true |
15 case CHAR(_) => false |
15 case CHAR(_) => false |
16 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
16 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
17 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
17 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
18 case STAR(_) => true |
18 case STAR(_) => true |
19 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
19 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
20 } |
20 } |
21 |
21 |
22 def der (c: Char, r: Rexp) : Rexp = r match { |
22 def der (c: Char, r: Rexp) : Rexp = r match { |
23 case NULL => NULL |
23 case ZERO => ZERO |
24 case EMPTY => NULL |
24 case ONE => ZERO |
25 case CHAR(d) => if (c == d) EMPTY else NULL |
25 case CHAR(d) => if (c == d) ONE else ZERO |
26 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
26 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
27 case SEQ(r1, r2) => |
27 case SEQ(r1, r2) => |
28 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
28 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
29 else SEQ(der(c, r1), r2) |
29 else SEQ(der(c, r1), r2) |
30 case STAR(r) => SEQ(der(c, r), STAR(r)) |
30 case STAR(r) => SEQ(der(c, r), STAR(r)) |
31 case NTIMES(r, i) => |
31 case NTIMES(r, i) => |
32 if (i == 0) NULL else SEQ(der(c, r), NTIMES(r, i - 1)) |
32 if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1)) |
33 } |
33 } |
34 |
34 |
35 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
35 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
36 case Nil => r |
36 case Nil => r |
37 case c::s => ders(s, der(c, r)) |
37 case c::s => ders(s, der(c, r)) |
39 |
39 |
40 def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
40 def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
41 |
41 |
42 |
42 |
43 //optional: one or zero times |
43 //optional: one or zero times |
44 def OPT(r: Rexp) = ALT(r, EMPTY) |
44 def OPT(r: Rexp) = ALT(r, ONE) |
45 |
45 |
46 //evil regular expressions |
46 //evil regular expressions |
47 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
47 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
48 val EVIL2 = SEQ(STAR(CHAR('a')), CHAR('b')) |
48 val EVIL2 = SEQ(STAR(CHAR('a')), CHAR('b')) |
49 |
49 |