|
1 // A version which attempts to move whole strings, not |
|
2 // just characters, under derivatives whenever possible |
|
3 |
|
4 abstract class Rexp |
|
5 case object ZERO extends Rexp |
|
6 case object ONE extends Rexp |
|
7 case class CHAR(c: Char) extends Rexp |
|
8 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
|
9 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
|
10 case class STAR(r: Rexp) extends Rexp |
|
11 case class NTIMES(r: Rexp, n: Int) extends Rexp |
|
12 |
|
13 // the nullable function: tests whether the regular |
|
14 // expression can recognise the empty string |
|
15 def nullable (r: Rexp) : Boolean = r match { |
|
16 case ZERO => false |
|
17 case ONE => true |
|
18 case CHAR(_) => false |
|
19 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
|
20 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
|
21 case STAR(_) => true |
|
22 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
|
23 } |
|
24 |
|
25 // the derivative of a regular expression w.r.t. a character |
|
26 def der (c: Char, r: Rexp) : Rexp = r match { |
|
27 case ZERO => ZERO |
|
28 case ONE => ZERO |
|
29 case CHAR(d) => if (c == d) ONE else ZERO |
|
30 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
|
31 case SEQ(r1, r2) => |
|
32 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
|
33 else SEQ(der(c, r1), r2) |
|
34 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
|
35 case NTIMES(r1, i) => |
|
36 if (i == 0) ZERO else SEQ(der(c, r1), NTIMES(r1, i - 1)) |
|
37 } |
|
38 |
|
39 def simp(r: Rexp) : Rexp = r match { |
|
40 case ALT(r1, r2) => (simp(r1), simp(r2)) match { |
|
41 case (ZERO, r2s) => r2s |
|
42 case (r1s, ZERO) => r1s |
|
43 case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s) |
|
44 } |
|
45 case SEQ(r1, r2) => (simp(r1), simp(r2)) match { |
|
46 case (ZERO, _) => ZERO |
|
47 case (_, ZERO) => ZERO |
|
48 case (ONE, r2s) => r2s |
|
49 case (r1s, ONE) => r1s |
|
50 case (r1s, r2s) => SEQ(r1s, r2s) |
|
51 } |
|
52 case r => r |
|
53 } |
|
54 |
|
55 // an example |
|
56 val r = SEQ(SEQ(CHAR('x'), CHAR('y')), CHAR('z')) |
|
57 der('x', r) |
|
58 der('y', der('x', r)) |
|
59 der('z', der('y', der('x', r))) |
|
60 simp(der('z', der('y', der('x', r)))) |
|
61 |
|
62 // *new* |
|
63 // the derivative w.r.t. a string (iterates der) |
|
64 def ders2(s: List[Char], r: Rexp) : Rexp = (s, r) match { |
|
65 case (Nil, r) => r |
|
66 case (s, ZERO) => ZERO |
|
67 case (s, ONE) => if (s == Nil) ONE else ZERO |
|
68 case (s, CHAR(c)) => if (s == List(c)) ONE else |
|
69 if (s == Nil) CHAR(c) else ZERO |
|
70 case (s, ALT(r1, r2)) => ALT(ders2(s, r1), ders2(s, r2)) |
|
71 case (c::s, r) => ders2(s, simp(der(c, r))) |
|
72 } |
|
73 |
|
74 // the main matcher function |
|
75 def matcher(r: Rexp, s: String) : Boolean = |
|
76 nullable(ders2(s.toList, r)) |
|
77 |
|
78 |
|
79 // one or zero |
|
80 def OPT(r: Rexp) = ALT(r, ONE) |
|
81 |
|
82 |
|
83 // Test Cases |
|
84 |
|
85 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
|
86 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
|
87 |
|
88 // for measuring time |
|
89 def time_needed[T](i: Int, code: => T) = { |
|
90 val start = System.nanoTime() |
|
91 for (j <- 1 to i) code |
|
92 val end = System.nanoTime() |
|
93 (end - start) / (i * 1.0e9) |
|
94 } |
|
95 |
|
96 |
|
97 // test: (a?{n}) (a{n}) |
|
98 for (i <- 0 to 11000 by 1000) { |
|
99 println(f"$i: ${time_needed(2, matcher(EVIL1(i), "a" * i))}%.5f") |
|
100 } |
|
101 |
|
102 |
|
103 // test: (a*)* b |
|
104 for (i <- 0 to 7000000 by 500000) { |
|
105 println(f"$i: ${time_needed(2, matcher(EVIL2, "a" * i))}%.5f") |
|
106 } |
|
107 |
|
108 |
|
109 |
|
110 // the size of a regular expressions - for testing purposes |
|
111 def size(r: Rexp) : Int = r match { |
|
112 case ZERO => 1 |
|
113 case ONE => 1 |
|
114 case CHAR(_) => 1 |
|
115 case ALT(r1, r2) => 1 + size(r1) + size(r2) |
|
116 case SEQ(r1, r2) => 1 + size(r1) + size(r2) |
|
117 case STAR(r) => 1 + size(r) |
|
118 case NTIMES(r, _) => 1 + size(r) |
|
119 } |
|
120 |
|
121 |
|
122 // string of a regular expressions - for testing purposes |
|
123 def string(r: Rexp) : String = r match { |
|
124 case ZERO => "0" |
|
125 case ONE => "1" |
|
126 case CHAR(c) => c.toString |
|
127 case ALT(r1, r2) => s"(${string(r1)} + ${string(r2)})" |
|
128 case SEQ(CHAR(c), CHAR(d)) => s"${c}${d}" |
|
129 case SEQ(r1, r2) => s"(${string(r1)} ~ ${string(r2)})" |
|
130 case STAR(r) => s"(${string(r)})*" |
|
131 case NTIMES(r, n) => s"(${string(r)}){${n}}" |
|
132 } |
|
133 |
|
134 |
|
135 // test: ("a" | "aa")* |
|
136 val EVIL3 = STAR(ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a')))) |
|
137 |
|
138 // test: ("" | "a" | "aa")* |
|
139 val EVIL4 = STAR(ALT(ONE, ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a'))))) |
|
140 |
|
141 val t1 = ders2("a".toList, EVIL3) |
|
142 val t1s = simp(t1) |
|
143 val t2 = ders2("aa".toList, t1s) |
|
144 val t2s = simp(t2) |
|
145 val t3 = ders2("aaa".toList, t2s) |
|
146 val t3s = simp(t3) |
|
147 val t4 = ders2("aaaa".toList, t3s) |
|
148 val t4s = simp(t4) |
|
149 println(string(t1) + " " + size(t1)) |
|
150 println("s " + string(t1s) + " " + size(t1s)) |
|
151 println(string(t2) + " " + size(t2)) |
|
152 println("s " + string(t2s) + " " + size(t2s)) |
|
153 println(string(t3) + " " + size(t3)) |
|
154 println("s " + string(t3s) + " " + size(t3s)) |
|
155 println(string(t4) + " " + size(t4)) |
|
156 println("s " + string(t4s) + " " + size(t4s)) |