258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
1 |
abstract class Rexp
|
422
|
2 |
case object ZERO extends Rexp
|
|
3 |
case object ONE extends Rexp
|
49
|
4 |
case class CHAR(c: Char) extends Rexp
|
258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
5 |
case class ALT(r1: Rexp, r2: Rexp) extends Rexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
6 |
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
7 |
case class STAR(r: Rexp) extends Rexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
8 |
case class NTIMES(r: Rexp, n: Int) extends Rexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
9 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
10 |
def simp(r: Rexp): Rexp = r match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
11 |
case ALT(r1, r2) => {
|
341
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
12 |
(simp(r1), simp(r2)) match {
|
422
|
13 |
case (ZERO, r2s) => r2s
|
|
14 |
case (r1s, ZERO) => r1s
|
341
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
15 |
case (r1s, r2s) => if (r1s == r2s) r1s else ALT(r1s, r2s)
|
258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
16 |
}
|
49
|
17 |
}
|
258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
18 |
case SEQ(r1, r2) => {
|
341
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
19 |
(simp(r1), simp(r2)) match {
|
422
|
20 |
case (ZERO, _) => ZERO
|
|
21 |
case (_, ZERO) => ZERO
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|
22 |
case (ONE, r2s) => r2s
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|
23 |
case (r1s, ONE) => r1s
|
341
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
24 |
case (r1s, r2s) => SEQ(r1s, r2s)
|
258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
25 |
}
|
49
|
26 |
}
|
258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
27 |
case NTIMES(r, n) => NTIMES(simp(r), n)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
28 |
case r => r
|
49
|
29 |
}
|
|
30 |
|
|
31 |
def nullable (r: Rexp) : Boolean = r match {
|
422
|
32 |
case ZERO => false
|
|
33 |
case ONE => true
|
49
|
34 |
case CHAR(_) => false
|
|
35 |
case ALT(r1, r2) => nullable(r1) || nullable(r2)
|
|
36 |
case SEQ(r1, r2) => nullable(r1) && nullable(r2)
|
|
37 |
case STAR(_) => true
|
59
|
38 |
case NTIMES(r, i) => if (i == 0) true else nullable(r)
|
49
|
39 |
}
|
|
40 |
|
|
41 |
def der (c: Char, r: Rexp) : Rexp = r match {
|
422
|
42 |
case ZERO => ZERO
|
|
43 |
case ONE => ZERO
|
|
44 |
case CHAR(d) => if (c == d) ONE else ZERO
|
49
|
45 |
case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
|
|
46 |
case SEQ(r1, r2) =>
|
|
47 |
if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
|
|
48 |
else SEQ(der(c, r1), r2)
|
|
49 |
case STAR(r) => SEQ(der(c, r), STAR(r))
|
|
50 |
case NTIMES(r, i) =>
|
422
|
51 |
if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
|
49
|
52 |
}
|
|
53 |
|
|
54 |
def ders (s: List[Char], r: Rexp) : Rexp = s match {
|
|
55 |
case Nil => r
|
258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
56 |
case c::s => ders(s, simp(der(c, r)))
|
49
|
57 |
}
|
|
58 |
|
261
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
59 |
def matches(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
|
49
|
60 |
|
|
61 |
|
|
62 |
//one or zero
|
422
|
63 |
def OPT(r: Rexp) = ALT(r, ONE)
|
49
|
64 |
|
258
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
65 |
def EVIL(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n))
|
49
|
66 |
|
|
67 |
def time_needed[T](i: Int, code: => T) = {
|
|
68 |
val start = System.nanoTime()
|
|
69 |
for (j <- 1 to i) code
|
|
70 |
val end = System.nanoTime()
|
|
71 |
(end - start)/(i * 1.0e9)
|
|
72 |
}
|
|
73 |
|
422
|
74 |
/*
|
|
75 |
for (i <- 1 to 9001 by 1000) {
|
261
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
76 |
println(i + " " + "%.5f".format(time_needed(1, matches(EVIL(i), "a" * i))))
|
49
|
77 |
}
|
422
|
78 |
*/
|
49
|
79 |
|
363
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
80 |
// some convenience for typing in regular expressions
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
81 |
import scala.language.implicitConversions
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
82 |
import scala.language.reflectiveCalls
|
422
|
83 |
|
363
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
84 |
def charlist2rexp(s : List[Char]) : Rexp = s match {
|
422
|
85 |
case Nil => ONE
|
363
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
86 |
case c::Nil => CHAR(c)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
87 |
case c::s => SEQ(CHAR(c), charlist2rexp(s))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
88 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
89 |
implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
90 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
91 |
implicit def RexpOps (r: Rexp) = new {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
92 |
def | (s: Rexp) = ALT(r, s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
93 |
def % = STAR(r)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
94 |
def ~ (s: Rexp) = SEQ(r, s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
95 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
96 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
97 |
implicit def stringOps (s: String) = new {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
98 |
def | (r: Rexp) = ALT(s, r)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
99 |
def | (r: String) = ALT(s, r)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
100 |
def % = STAR(s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
101 |
def ~ (r: Rexp) = SEQ(s, r)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
102 |
def ~ (r: String) = SEQ(s, r)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
103 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
104 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
105 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
106 |
def PLUS(r: Rexp) = SEQ(r, STAR(r))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
107 |
def RANGE(s: List[Char]) : Rexp = s match {
|
422
|
108 |
case Nil => ZERO
|
363
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
109 |
case c::s => ALT(CHAR(c), RANGE(s))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
110 |
}
|
422
|
111 |
def NMTIMES(r: Rexp, n: Int, m: Int) : Rexp =
|
|
112 |
if (n >= m) NTIMES(r, n) else ALT(NTIMES(r, m), NMTIMES(r, n, m - 1))
|
363
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
113 |
|
422
|
114 |
|
|
115 |
println("Coursework:")
|
|
116 |
val REG1 = PLUS(PLUS("a" ~ "a" ~ "a"))
|
|
117 |
val REG2 = PLUS(PLUS("aaaaaaaaaaaaaaaaaaa" ~ OPT("a"))) // 19 as ~ a?
|
363
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
118 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
119 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
120 |
//40 * aaa matches
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
121 |
//43 * aaa + aa does not
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
122 |
//45 * aaa + a
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
123 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
124 |
println("EVIL1:")
|
422
|
125 |
println(matches(REG1, "aaa" * 40))
|
|
126 |
println(matches(REG1, "aaa" * 43 + "aa"))
|
|
127 |
println(matches(REG1, "aaa" * 45 + "a"))
|
363
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
128 |
println("EVIL2:")
|
422
|
129 |
println(matches(REG2, "aaa" * 40))
|
|
130 |
println(matches(REG2, "aaa" * 43 + "aa"))
|
|
131 |
println(matches(REG2, "aaa" * 45 + "a"))
|
363
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
132 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
133 |
println("EMAIL:")
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
134 |
val LOWERCASE = "abcdefghijklmnopqrstuvwxyz"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
135 |
val DIGITS = "0123456789"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
136 |
val EMAIL = PLUS(RANGE((LOWERCASE + DIGITS + "_" + "." + "-").toList)) ~ "@" ~
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
137 |
PLUS(RANGE((LOWERCASE + DIGITS + "." + "-").toList)) ~ "." ~
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
138 |
NMTIMES(RANGE((LOWERCASE + ".").toList), 2, 6)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
139 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
140 |
val my_email = "christian.urban@kcl.ac.uk"
|
422
|
141 |
|
|
142 |
println(matches(EMAIL, my_email))
|
|
143 |
|
|
144 |
println(matches(NTIMES("a", 2), "a"))
|
|
145 |
println(matches(NTIMES("a", 2), "aa"))
|
|
146 |
println(matches(NTIMES("a", 2), "aaa"))
|
|
147 |
|
|
148 |
println(matches(NMTIMES("a", 2, 3), "a"))
|
|
149 |
println(matches(NMTIMES("a", 2, 3), "aa"))
|
|
150 |
println(matches(NMTIMES("a", 2, 3), "aaa"))
|
|
151 |
println(matches(NMTIMES("a", 2, 3), "aaaa"))
|