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1 // (ASIDE!) A version which attempts to move whole strings, |
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2 // not just characters, under derivatives whenever possible |
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3 // |
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4 // call the test cases with X = {1,2} |
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5 // |
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6 // amm re3.sc testX |
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7 // |
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8 // or |
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9 // |
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10 // amm re3.sc all |
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11 |
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12 |
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13 abstract class Rexp |
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14 case object ZERO extends Rexp |
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15 case object ONE extends Rexp |
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16 case class CHAR(c: Char) extends Rexp |
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17 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
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18 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
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19 case class STAR(r: Rexp) extends Rexp |
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20 case class NTIMES(r: Rexp, n: Int) extends Rexp |
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21 |
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22 // the nullable function: tests whether the regular |
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23 // expression can recognise the empty string |
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24 def nullable (r: Rexp) : Boolean = r match { |
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25 case ZERO => false |
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26 case ONE => true |
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27 case CHAR(_) => false |
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28 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
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29 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
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30 case STAR(_) => true |
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31 case NTIMES(r, i) => if (i == 0) true else nullable(r) |
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32 } |
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33 |
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34 // the derivative of a regular expression w.r.t. a character |
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35 def der (c: Char, r: Rexp) : Rexp = r match { |
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36 case ZERO => ZERO |
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37 case ONE => ZERO |
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38 case CHAR(d) => if (c == d) ONE else ZERO |
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39 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
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40 case SEQ(r1, r2) => |
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41 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
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42 else SEQ(der(c, r1), r2) |
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43 case STAR(r1) => SEQ(der(c, r1), STAR(r1)) |
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44 case NTIMES(r1, i) => |
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45 if (i == 0) ZERO else SEQ(der(c, r1), NTIMES(r1, i - 1)) |
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46 } |
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47 |
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48 def simp(r: Rexp) : Rexp = r match { |
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49 case ALT(r1, r2) => (simp(r1), simp(r2)) match { |
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50 case (ZERO, r2s) => r2s |
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51 case (r1s, ZERO) => r1s |
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52 case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s) |
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53 } |
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54 case SEQ(r1, r2) => (simp(r1), simp(r2)) match { |
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55 case (ZERO, _) => ZERO |
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56 case (_, ZERO) => ZERO |
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57 case (ONE, r2s) => r2s |
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58 case (r1s, ONE) => r1s |
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59 case (r1s, r2s) => SEQ(r1s, r2s) |
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60 } |
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61 case r => r |
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62 } |
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63 |
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64 // an example |
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65 val r = SEQ(SEQ(CHAR('x'), CHAR('y')), CHAR('z')) |
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66 der('x', r) |
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67 der('y', der('x', r)) |
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68 der('z', der('y', der('x', r))) |
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69 simp(der('z', der('y', der('x', r)))) |
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70 |
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71 // *new* |
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72 // the derivative w.r.t. a string (iterates der) |
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73 def ders2(s: List[Char], r: Rexp) : Rexp = (s, r) match { |
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74 case (Nil, r) => r |
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75 case (s, ZERO) => ZERO |
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76 case (s, ONE) => if (s == Nil) ONE else ZERO |
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77 case (s, CHAR(c)) => if (s == List(c)) ONE else |
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78 if (s == Nil) CHAR(c) else ZERO |
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79 case (s, ALT(r1, r2)) => ALT(ders2(s, r1), ders2(s, r2)) |
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80 case (c::s, r) => ders2(s, simp(der(c, r))) |
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81 } |
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82 |
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83 // the main matcher function |
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84 def matcher(r: Rexp, s: String) : Boolean = |
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85 nullable(ders2(s.toList, r)) |
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86 |
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87 |
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88 // one or zero |
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89 def OPT(r: Rexp) = ALT(r, ONE) |
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90 |
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91 |
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92 // Test Cases |
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93 |
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94 def EVIL1(n: Int) = SEQ(NTIMES(OPT(CHAR('a')), n), NTIMES(CHAR('a'), n)) |
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95 val EVIL2 = SEQ(STAR(STAR(CHAR('a'))), CHAR('b')) |
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96 |
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97 // for measuring time |
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98 def time_needed[T](i: Int, code: => T) = { |
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99 val start = System.nanoTime() |
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100 for (j <- 1 to i) code |
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101 val end = System.nanoTime() |
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102 (end - start) / (i * 1.0e9) |
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103 } |
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104 |
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105 |
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106 // test: (a?{n}) (a{n}) |
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107 @doc("Test (a?{n}) (a{n})") |
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108 @main |
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109 def test1() = { |
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110 for (i <- 0 to 11000 by 1000) { |
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111 println(f"$i: ${time_needed(2, matcher(EVIL1(i), "a" * i))}%.5f") |
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112 } |
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113 } |
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114 |
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115 // test: (a*)* b |
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116 @doc("Test (a*)* b") |
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117 @main |
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118 def test2() = { |
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119 for (i <- 0 to 7000000 by 500000) { |
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120 println(f"$i: ${time_needed(2, matcher(EVIL2, "a" * i))}%.5f") |
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121 } |
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122 } |
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123 |
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124 @doc("All tests.") |
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125 @main |
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126 def all() = { test1(); test2() } |
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127 |
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128 |
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129 |
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130 // the size of a regular expressions - for testing purposes |
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131 def size(r: Rexp) : Int = r match { |
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132 case ZERO => 1 |
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133 case ONE => 1 |
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134 case CHAR(_) => 1 |
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135 case ALT(r1, r2) => 1 + size(r1) + size(r2) |
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136 case SEQ(r1, r2) => 1 + size(r1) + size(r2) |
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137 case STAR(r) => 1 + size(r) |
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138 case NTIMES(r, _) => 1 + size(r) |
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139 } |
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140 |
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141 |
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142 // string of a regular expressions - for testing purposes |
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143 def string(r: Rexp) : String = r match { |
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144 case ZERO => "0" |
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145 case ONE => "1" |
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146 case CHAR(c) => c.toString |
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147 case ALT(r1, r2) => s"(${string(r1)} + ${string(r2)})" |
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148 case SEQ(CHAR(c), CHAR(d)) => s"${c}${d}" |
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149 case SEQ(r1, r2) => s"(${string(r1)} ~ ${string(r2)})" |
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150 case STAR(r) => s"(${string(r)})*" |
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151 case NTIMES(r, n) => s"(${string(r)}){${n}}" |
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152 } |
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153 |
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154 |
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155 // further testcases: |
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156 |
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157 // test: ("a" | "aa")* |
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158 val EVIL3 = STAR(ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a')))) |
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159 |
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160 // test: ("" | "a" | "aa")* |
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161 val EVIL4 = STAR(ALT(ONE, ALT(CHAR('a'), SEQ(CHAR('a'), CHAR('a'))))) |
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162 |