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1 package greeter |
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2 |
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3 object POSIX { |
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4 println("Posix Algorithm") //> Posix Algorithm |
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5 |
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6 abstract class Rexp |
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7 case object NULL extends Rexp |
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8 case object EMPTY extends Rexp |
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9 case class CHAR(c: Char) extends Rexp |
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10 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
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11 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
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12 case class STAR(r: Rexp) extends Rexp |
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13 case class RECD(x: String, r: Rexp) extends Rexp |
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14 |
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15 abstract class Val |
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16 case object Void extends Val |
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17 case class Chr(c: Char) extends Val |
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18 case class Sequ(v1: Val, v2: Val) extends Val |
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19 case class Left(v: Val) extends Val |
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20 case class Right(v: Val) extends Val |
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21 case class Stars(vs: List[Val]) extends Val |
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22 case class Rec(x: String, v: Val) extends Val |
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23 |
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24 def charlist2rexp(s: List[Char]): Rexp = s match { |
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25 case Nil => EMPTY |
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26 case c :: Nil => CHAR(c) |
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27 case c :: s => SEQ(CHAR(c), charlist2rexp(s)) |
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28 } //> charlist2rexp: (s: List[Char])greeter.POSIX.Rexp |
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29 implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList) |
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30 //> string2rexp: (s: String)greeter.POSIX.Rexp |
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31 |
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32 implicit def RexpOps(r: Rexp) = new { |
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33 def |(s: Rexp) = ALT(r, s) |
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34 def % = STAR(r) |
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35 def ~(s: Rexp) = SEQ(r, s) |
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36 } //> RexpOps: (r: greeter.POSIX.Rexp)AnyRef{def |(s: greeter.POSIX.Rexp): greete |
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37 //| r.POSIX.ALT; def %: greeter.POSIX.STAR; def ~(s: greeter.POSIX.Rexp): greet |
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38 //| er.POSIX.SEQ} |
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39 |
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40 implicit def stringOps(s: String) = new { |
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41 def |(r: Rexp) = ALT(s, r) |
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42 def |(r: String) = ALT(s, r) |
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43 def % = STAR(s) |
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44 def ~(r: Rexp) = SEQ(s, r) |
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45 def ~(r: String) = SEQ(s, r) |
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46 def $(r: Rexp) = RECD(s, r) |
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47 } //> stringOps: (s: String)AnyRef{def |(r: greeter.POSIX.Rexp): greeter.POSIX.AL |
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48 //| T; def |(r: String): greeter.POSIX.ALT; def %: greeter.POSIX.STAR; def ~(r: |
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49 //| greeter.POSIX.Rexp): greeter.POSIX.SEQ; def ~(r: String): greeter.POSIX.SE |
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50 //| Q; def $(r: greeter.POSIX.Rexp): greeter.POSIX.RECD} |
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51 |
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52 // size of a regular expressions - for testing purposes |
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53 def size(r: Rexp): Int = r match { |
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54 case NULL => 1 |
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55 case EMPTY => 1 |
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56 case CHAR(_) => 1 |
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57 case ALT(r1, r2) => 1 + size(r1) + size(r2) |
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58 case SEQ(r1, r2) => 1 + size(r1) + size(r2) |
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59 case STAR(r) => 1 + size(r) |
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60 case RECD(_, r) => 1 + size(r) |
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61 } //> size: (r: greeter.POSIX.Rexp)Int |
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62 |
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63 // nullable function: tests whether the regular |
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64 // expression can recognise the empty string |
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65 def nullable(r: Rexp): Boolean = r match { |
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66 case NULL => false |
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67 case EMPTY => true |
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68 case CHAR(_) => false |
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69 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
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70 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
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71 case STAR(_) => true |
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72 case RECD(_, r1) => nullable(r1) |
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73 } //> nullable: (r: greeter.POSIX.Rexp)Boolean |
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74 |
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75 // derivative of a regular expression w.r.t. a character |
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76 def der(c: Char, r: Rexp): Rexp = r match { |
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77 case NULL => NULL |
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78 case EMPTY => NULL |
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79 case CHAR(d) => if (c == d) EMPTY else NULL |
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80 case ALT(r1, r2) => ALT(der(c, r1), der(c, r2)) |
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81 case SEQ(r1, r2) => |
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82 if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2)) |
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83 else SEQ(der(c, r1), r2) |
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84 case STAR(r) => SEQ(der(c, r), STAR(r)) |
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85 case RECD(_, r1) => der(c, r1) |
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86 } //> der: (c: Char, r: greeter.POSIX.Rexp)greeter.POSIX.Rexp |
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87 |
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88 // derivative w.r.t. a string (iterates der) |
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89 def ders(s: List[Char], r: Rexp): Rexp = s match { |
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90 case Nil => r |
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91 case c :: s => ders(s, der(c, r)) |
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92 } //> ders: (s: List[Char], r: greeter.POSIX.Rexp)greeter.POSIX.Rexp |
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93 |
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94 // extracts a string from value |
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95 def flatten(v: Val): String = v match { |
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96 case Void => "" |
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97 case Chr(c) => c.toString |
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98 case Left(v) => flatten(v) |
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99 case Right(v) => flatten(v) |
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100 case Sequ(v1, v2) => flatten(v1) + flatten(v2) |
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101 case Stars(vs) => vs.map(flatten).mkString |
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102 case Rec(_, v) => flatten(v) |
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103 } //> flatten: (v: greeter.POSIX.Val)String |
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104 |
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105 // extracts an environment from a value |
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106 def env(v: Val): List[(String, String)] = v match { |
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107 case Void => Nil |
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108 case Chr(c) => Nil |
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109 case Left(v) => env(v) |
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110 case Right(v) => env(v) |
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111 case Sequ(v1, v2) => env(v1) ::: env(v2) |
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112 case Stars(vs) => vs.flatMap(env) |
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113 case Rec(x, v) => (x, flatten(v)) :: env(v) |
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114 } //> env: (v: greeter.POSIX.Val)List[(String, String)] |
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115 |
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116 def mkeps(r: Rexp): Val = r match { |
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117 case EMPTY => Void |
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118 case ALT(r1, r2) => |
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119 if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2)) |
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120 case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2)) |
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121 case STAR(r) => Stars(Nil) |
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122 case RECD(x, r) => Rec(x, mkeps(r)) |
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123 } //> mkeps: (r: greeter.POSIX.Rexp)greeter.POSIX.Val |
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124 |
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125 def inj(r: Rexp, c: Char, v: Val): Val = (r, v) match { |
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126 case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1) :: vs) |
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127 case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2) |
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128 case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2) |
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129 case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2)) |
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130 case (ALT(r1, r2), Left(v1)) => Left(inj(r1, c, v1)) |
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131 case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2)) |
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132 case (CHAR(d), Void) => Chr(d) |
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133 case (RECD(x, r1), _) => Rec(x, inj(r1, c, v)) |
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134 } //> inj: (r: greeter.POSIX.Rexp, c: Char, v: greeter.POSIX.Val)greeter.POSIX.Va |
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135 //| l |
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136 |
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137 // main lexing function (produces a value) |
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138 def lex(r: Rexp, s: List[Char]): Val = s match { |
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139 case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched") |
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140 case c :: cs => inj(r, c, lex(der(c, r), cs)) |
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141 } //> lex: (r: greeter.POSIX.Rexp, s: List[Char])greeter.POSIX.Val |
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142 |
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143 def lexing(r: Rexp, s: String): Val = lex(r, s.toList) |
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144 //> lexing: (r: greeter.POSIX.Rexp, s: String)greeter.POSIX.Val |
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145 |
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146 val r = (("1" $ "a") | (("2" $ "b") | ("3" $ "ab"))).% |
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147 //> r : greeter.POSIX.STAR = STAR(ALT(RECD(1,CHAR(a)),ALT(RECD(2,CHAR(b)),RECD |
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148 //| (3,SEQ(CHAR(a),CHAR(b)))))) |
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149 env(lexing(r, "ba")) //> res0: List[(String, String)] = List((2,b), (1,a)) |
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150 |
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151 val r1 = "a" | "b" //> r1 : greeter.POSIX.ALT = ALT(CHAR(a),CHAR(b)) |
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152 lexing(r1, "a") //> res1: greeter.POSIX.Val = Left(Chr(a)) |
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153 |
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154 // Lexing Rules for a Small While Language |
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155 |
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156 def PLUS(r: Rexp) = r ~ r.% //> PLUS: (r: greeter.POSIX.Rexp)greeter.POSIX.SEQ |
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157 val SYM = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z" |
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158 //> SYM : greeter.POSIX.ALT = ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT( |
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159 //| ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(a),CHAR(b)),CHAR(c |
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160 //| )),CHAR(d)),CHAR(e)),CHAR(f)),CHAR(g)),CHAR(h)),CHAR(i)),CHAR(j)),CHAR(k)), |
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161 //| CHAR(l)),CHAR(m)),CHAR(n)),CHAR(o)),CHAR(p)),CHAR(q)),CHAR(r)),CHAR(s)),CHA |
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162 //| R(t)),CHAR(u)),CHAR(v)),CHAR(w)),CHAR(x)),CHAR(y)),CHAR(z)) |
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163 val DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" |
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164 //> DIGIT : greeter.POSIX.ALT = ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(0),CH |
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165 //| AR(1)),CHAR(2)),CHAR(3)),CHAR(4)),CHAR(5)),CHAR(6)),CHAR(7)),CHAR(8)),CHAR( |
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166 //| 9)) |
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167 val ID = SYM ~ (SYM | DIGIT).% //> ID : greeter.POSIX.SEQ = SEQ(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(A |
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168 //| LT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(a),CHAR(b)),CHA |
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169 //| R(c)),CHAR(d)),CHAR(e)),CHAR(f)),CHAR(g)),CHAR(h)),CHAR(i)),CHAR(j)),CHAR(k |
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170 //| )),CHAR(l)),CHAR(m)),CHAR(n)),CHAR(o)),CHAR(p)),CHAR(q)),CHAR(r)),CHAR(s)), |
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171 //| CHAR(t)),CHAR(u)),CHAR(v)),CHAR(w)),CHAR(x)),CHAR(y)),CHAR(z)),STAR(ALT(ALT |
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172 //| (ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(AL |
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173 //| T(ALT(ALT(ALT(ALT(ALT(CHAR(a),CHAR(b)),CHAR(c)),CHAR(d)),CHAR(e)),CHAR(f)), |
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174 //| CHAR(g)),CHAR(h)),CHAR(i)),CHAR(j)),CHAR(k)),CHAR(l)),CHAR(m)),CHAR(n)),CHA |
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175 //| R(o)),CHAR(p)),CHAR(q)),CHAR(r)),CHAR(s)),CHAR(t)),CHAR(u)),CHAR(v)),CHAR(w |
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176 //| )),CHAR(x)),CHAR(y)),CHAR(z)),ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(0),C |
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177 //| HAR(1)),CHAR(2)),CHAR(3)),CHAR(4)),CHAR(5)),CHAR(6)),CHAR(7)),CHAR(8)),CHAR |
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178 //| (9))))) |
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179 val NUM = PLUS(DIGIT) //> NUM : greeter.POSIX.SEQ = SEQ(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(0), |
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180 //| CHAR(1)),CHAR(2)),CHAR(3)),CHAR(4)),CHAR(5)),CHAR(6)),CHAR(7)),CHAR(8)),CHA |
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181 //| R(9)),STAR(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(0),CHAR(1)),CHAR(2)),CH |
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182 //| AR(3)),CHAR(4)),CHAR(5)),CHAR(6)),CHAR(7)),CHAR(8)),CHAR(9)))) |
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183 val KEYWORD: Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false" |
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184 //> KEYWORD : greeter.POSIX.Rexp = ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(SEQ(CHA |
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185 //| R(s),SEQ(CHAR(k),SEQ(CHAR(i),CHAR(p)))),SEQ(CHAR(w),SEQ(CHAR(h),SEQ(CHAR(i) |
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186 //| ,SEQ(CHAR(l),CHAR(e)))))),SEQ(CHAR(d),CHAR(o))),SEQ(CHAR(i),CHAR(f))),SEQ(C |
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187 //| HAR(t),SEQ(CHAR(h),SEQ(CHAR(e),CHAR(n))))),SEQ(CHAR(e),SEQ(CHAR(l),SEQ(CHAR |
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188 //| (s),CHAR(e))))),SEQ(CHAR(r),SEQ(CHAR(e),SEQ(CHAR(a),CHAR(d))))),SEQ(CHAR(w) |
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189 //| ,SEQ(CHAR(r),SEQ(CHAR(i),SEQ(CHAR(t),CHAR(e)))))),SEQ(CHAR(t),SEQ(CHAR(r),S |
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190 //| EQ(CHAR(u),CHAR(e))))),SEQ(CHAR(f),SEQ(CHAR(a),SEQ(CHAR(l),SEQ(CHAR(s),CHAR |
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191 //| (e)))))) |
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192 val SEMI: Rexp = ";" //> SEMI : greeter.POSIX.Rexp = CHAR(;) |
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193 val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/" |
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194 //> OP : greeter.POSIX.Rexp = ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(SEQ( |
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195 //| CHAR(:),CHAR(=)),SEQ(CHAR(=),CHAR(=))),CHAR(-)),CHAR(+)),CHAR(*)),SEQ(CHAR( |
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196 //| !),CHAR(=))),CHAR(<)),CHAR(>)),SEQ(CHAR(<),CHAR(=))),SEQ(CHAR(>),CHAR(=))), |
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197 //| CHAR(%)),CHAR(/)) |
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198 val WHITESPACE = PLUS(" " | "\n" | "\t") //> WHITESPACE : greeter.POSIX.SEQ = SEQ(ALT(ALT(CHAR( ),CHAR( |
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199 //| )),CHAR( )),STAR(ALT(ALT(CHAR( ),CHAR( |
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200 //| )),CHAR( )))) |
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201 val RPAREN: Rexp = ")" //> RPAREN : greeter.POSIX.Rexp = CHAR()) |
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202 val LPAREN: Rexp = "(" //> LPAREN : greeter.POSIX.Rexp = CHAR(() |
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203 val BEGIN: Rexp = "{" //> BEGIN : greeter.POSIX.Rexp = CHAR({) |
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204 val END: Rexp = "}" //> END : greeter.POSIX.Rexp = CHAR(}) |
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205 |
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206 /* |
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207 * val WHILE_REGS = (("k" $ KEYWORD) | |
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208 ("i" $ ID) | |
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209 ("o" $ OP) | |
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210 ("n" $ NUM) | |
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211 ("s" $ SEMI) | |
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212 ("p" $ (LPAREN | RPAREN)) | |
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213 ("b" $ (BEGIN | END)) | |
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214 ("w" $ WHITESPACE)).% |
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215 */ |
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216 |
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217 val WHILE_REGS = (KEYWORD | |
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218 ID | |
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219 OP | |
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220 NUM | |
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221 SEMI | |
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222 LPAREN | RPAREN | |
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223 BEGIN | END | |
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224 WHITESPACE).% //> WHILE_REGS : greeter.POSIX.STAR = STAR(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT |
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225 //| (ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(SEQ(CHAR(s),SEQ(CHAR(k),SEQ(CHAR(i),CH |
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226 //| AR(p)))),SEQ(CHAR(w),SEQ(CHAR(h),SEQ(CHAR(i),SEQ(CHAR(l),CHAR(e)))))),SEQ(C |
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227 //| HAR(d),CHAR(o))),SEQ(CHAR(i),CHAR(f))),SEQ(CHAR(t),SEQ(CHAR(h),SEQ(CHAR(e), |
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228 //| CHAR(n))))),SEQ(CHAR(e),SEQ(CHAR(l),SEQ(CHAR(s),CHAR(e))))),SEQ(CHAR(r),SEQ |
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229 //| (CHAR(e),SEQ(CHAR(a),CHAR(d))))),SEQ(CHAR(w),SEQ(CHAR(r),SEQ(CHAR(i),SEQ(CH |
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230 //| AR(t),CHAR(e)))))),SEQ(CHAR(t),SEQ(CHAR(r),SEQ(CHAR(u),CHAR(e))))),SEQ(CHAR |
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231 //| (f),SEQ(CHAR(a),SEQ(CHAR(l),SEQ(CHAR(s),CHAR(e)))))),SEQ(ALT(ALT(ALT(ALT(AL |
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232 //| T(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(A |
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233 //| LT(ALT(CHAR(a),CHAR(b)),CHAR(c)),CHAR(d)),CHAR(e)),CHAR(f)),CHAR(g)),CHAR(h |
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234 //| )),CHAR(i)),CHAR(j)),CHAR(k)),CHAR(l)),CHAR(m)),CHAR(n)),CHAR(o)),CHAR(p)), |
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235 //| CHAR(q)),CHAR(r)),CHAR(s)),CHAR(t)),CHAR(u)),CHAR(v)),CHAR(w)),CHAR(x)),CHA |
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236 //| R(y)),CHAR(z)),STAR(ALT |
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237 //| Output exceeds cutoff limit. |
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238 |
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239 // Some Tests |
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240 //============ |
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241 |
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242 def time[T](code: => T) = { |
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243 val start = System.nanoTime() |
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244 val result = code |
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245 val end = System.nanoTime() |
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246 println((end - start) / 1.0e9) |
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247 result |
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248 } //> time: [T](code: => T)T |
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249 |
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250 val prog0 = """read n""" //> prog0 : String = read n |
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251 //env(lexing_simp(WHILE_REGS, prog0)) |
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252 |
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253 println("Next test") //> Next test |
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254 } |