1 // Parser Combinators: Simple Version |
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2 //==================================== |
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3 // |
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4 // Call with |
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5 // |
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6 // amm comb1.sc |
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7 |
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8 |
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9 // Note, in the lectures I did not show the implicit type constraint |
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10 // I : IsSeq, which means that the input type 'I' needs to be |
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11 // a sequence. |
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12 |
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13 type IsSeq[A] = A => Seq[_] |
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14 |
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15 abstract class Parser[I : IsSeq, T]{ |
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16 def parse(in: I): Set[(T, I)] |
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17 |
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18 def parse_all(in: I) : Set[T] = |
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19 for ((hd, tl) <- parse(in); |
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20 if tl.isEmpty) yield hd |
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21 } |
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22 |
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23 // parser combinators |
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24 |
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25 // alternative parser |
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26 class AltParser[I : IsSeq, T](p: => Parser[I, T], |
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27 q: => Parser[I, T]) extends Parser[I, T] { |
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28 def parse(in: I) = p.parse(in) ++ q.parse(in) |
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29 } |
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30 |
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31 // sequence parser |
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32 class SeqParser[I : IsSeq, T, S](p: => Parser[I, T], |
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33 q: => Parser[I, S]) extends Parser[I, (T, S)] { |
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34 def parse(in: I) = |
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35 for ((hd1, tl1) <- p.parse(in); |
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36 (hd2, tl2) <- q.parse(tl1)) yield ((hd1, hd2), tl2) |
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37 } |
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38 |
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39 // map parser |
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40 class MapParser[I : IsSeq, T, S](p: => Parser[I, T], |
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41 f: T => S) extends Parser[I, S] { |
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42 def parse(in: I) = for ((hd, tl) <- p.parse(in)) yield (f(hd), tl) |
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43 } |
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44 |
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45 |
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46 |
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47 // an example of an atomic parser for characters |
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48 case class CharParser(c: Char) extends Parser[String, Char] { |
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49 def parse(in: String) = |
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50 if (in != "" && in.head == c) Set((c, in.tail)) else Set() |
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51 } |
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52 |
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53 |
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54 // an atomic parser for parsing strings according to a regex |
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55 import scala.util.matching.Regex |
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56 |
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57 case class RegexParser(reg: Regex) extends Parser[String, String] { |
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58 def parse(in: String) = reg.findPrefixMatchOf(in) match { |
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59 case None => Set() |
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60 case Some(m) => Set((m.matched, m.after.toString)) |
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61 } |
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62 } |
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63 |
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64 // atomic parsers for numbers and "verbatim" strings |
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65 val NumParser = RegexParser("[0-9]+".r) |
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66 def StrParser(s: String) = RegexParser(Regex.quote(s).r) |
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67 |
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68 |
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69 |
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70 // NumParserInt transforms a "string integer" into a propper Int |
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71 // (needs "new" because MapParser is not a case class) |
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72 |
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73 val NumParserInt = new MapParser(NumParser, (s: String) => s.toInt) |
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74 |
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75 |
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76 // the following string interpolation allows us to write |
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77 // StrParser(_some_string_) more conveniently as |
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78 // |
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79 // p"<_some_string_>" |
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80 |
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81 implicit def parser_interpolation(sc: StringContext) = new { |
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82 def p(args: Any*) = StrParser(sc.s(args:_*)) |
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83 } |
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84 |
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85 |
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86 // more convenient syntax for parser combinators |
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87 implicit def ParserOps[I : IsSeq, T](p: Parser[I, T]) = new { |
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88 def ||(q : => Parser[I, T]) = new AltParser[I, T](p, q) |
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89 def ~[S] (q : => Parser[I, S]) = new SeqParser[I, T, S](p, q) |
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90 def map[S](f: => T => S) = new MapParser[I, T, S](p, f) |
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91 } |
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92 |
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93 // these implicits allow us to use an infix notation for |
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94 // sequences and alternatives; we also can write the usual |
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95 // map for a MapParser |
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96 |
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97 |
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98 // with this NumParserInt can now be written more conveniently |
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99 // as: |
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100 |
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101 val NumParserInt2 = NumParser.map(_.toInt) |
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102 |
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103 |
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104 // A parser for palindromes (just returns them as string) |
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105 lazy val Pal : Parser[String, String] = { |
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106 (p"a" ~ Pal ~ p"a").map{ case ((x, y), z) => s"$x$y$z" } || |
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107 (p"b" ~ Pal ~ p"b").map{ case ((x, y), z) => s"$x$y$z" } || |
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108 p"a" || p"b" || p"" |
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109 } |
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110 |
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111 // examples |
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112 Pal.parse_all("abaaaba") |
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113 Pal.parse("abaaaba") |
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114 |
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115 println("Palindrome: " + Pal.parse_all("abaaaba")) |
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116 |
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117 // A parser for wellnested parentheses |
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118 // |
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119 // P ::= ( P ) P | epsilon |
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120 // |
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121 // (transforms '(' -> '{' , ')' -> '}' ) |
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122 lazy val P : Parser[String, String] = { |
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123 (p"(" ~ P ~ p")" ~ P).map{ case (((_, x), _), y) => "{" + x + "}" + y } || |
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124 p"" |
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125 } |
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126 |
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127 println(P.parse_all("(((()()))())")) |
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128 println(P.parse_all("(((()()))()))")) |
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129 println(P.parse_all(")(")) |
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130 println(P.parse_all("()")) |
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131 |
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132 // A parser for arithmetic expressions (Terms and Factors) |
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133 |
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134 lazy val E: Parser[String, Int] = { |
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135 (T ~ p"+" ~ E).map{ case ((x, _), z) => x + z } || |
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136 (T ~ p"-" ~ E).map{ case ((x, _), z) => x - z } || T } |
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137 lazy val T: Parser[String, Int] = { |
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138 (F ~ p"*" ~ T).map{ case ((x, _), z) => x * z } || F } |
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139 lazy val F: Parser[String, Int] = { |
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140 (p"(" ~ E ~ p")").map{ case ((_, y), _) => y } || NumParserInt } |
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141 |
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142 println(E.parse_all("1+3+4")) |
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143 println(E.parse("1+3+4")) |
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144 println(E.parse_all("4*2+3")) |
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145 println(E.parse_all("4*(2+3)")) |
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146 println(E.parse_all("(4)*((2+3))")) |
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147 println(E.parse_all("4/2+3")) |
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148 println(E.parse("1 + 2 * 3")) |
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149 println(E.parse_all("(1+2)+3")) |
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150 println(E.parse_all("1+2+3")) |
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151 |
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152 |
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153 // with parser combinators (and other parsing algorithms) |
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154 // no left-recursion is allowed, otherwise the will loop |
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155 |
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156 lazy val EL: Parser[String, Int] = |
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157 ((EL ~ p"+" ~ EL).map{ case ((x, y), z) => x + z} || |
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158 (EL ~ p"*" ~ EL).map{ case ((x, y), z) => x * z} || |
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159 (p"(" ~ EL ~ p")").map{ case ((x, y), z) => y} || |
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160 NumParserInt) |
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161 |
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162 // this will run forever: |
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163 //println(EL.parse_all("1+2+3")) |
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164 |
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165 |
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166 // non-ambiguous vs ambiguous grammars |
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167 |
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168 // ambiguous |
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169 lazy val S : Parser[String, String] = |
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170 (p"1" ~ S ~ S).map{ case ((x, y), z) => x + y + z } || p"" |
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171 |
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172 //println(time(S.parse("1" * 10))) |
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173 //println(time(S.parse_all("1" * 10))) |
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174 |
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175 // non-ambiguous |
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176 lazy val U : Parser[String, String] = |
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177 (p"1" ~ U).map{ case (x, y) => x + y } || p"" |
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178 |
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179 //println(time(U.parse("1" * 10))) |
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180 //println(time(U.parse_all("1" * 10))) |
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181 println(U.parse("1" * 25)) |
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182 |
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183 U.parse("11") |
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184 U.parse("11111") |
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185 U.parse("11011") |
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186 |
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187 U.parse_all("1" * 100) |
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188 U.parse_all("1" * 100 + "0") |
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189 |
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190 // you can see the difference in second example |
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191 //S.parse_all("1" * 100) // succeeds |
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192 //S.parse_all("1" * 100 + "0") // fails |
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193 |
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194 |
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195 // A variant which counts how many 1s are parsed |
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196 lazy val UCount : Parser[String, Int] = |
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197 (p"1" ~ UCount).map{ case (_, y) => y + 1 } || p"".map{ _ => 0 } |
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198 |
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199 println(UCount.parse("11111")) |
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200 println(UCount.parse_all("11111")) |
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201 |
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202 // Two single character parsers |
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203 lazy val One : Parser[String, String] = p"a" |
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204 lazy val Two : Parser[String, String] = p"b" |
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205 |
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206 One.parse("a") |
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207 One.parse("aaa") |
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208 |
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209 // note how the pairs nest to the left with sequence parsers |
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210 (One ~ One).parse("aaa") |
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211 (One ~ One ~ One).parse("aaa") |
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212 (One ~ One ~ One ~ One).parse("aaaa") |
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213 |
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214 (One || Two).parse("aaa") |
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215 |
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216 |
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217 |
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218 // a problem with the arithmetic expression parser: it |
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219 // gets very slow with deeply nested parentheses |
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220 |
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221 println("Runtime problem") |
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222 println(E.parse("1")) |
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223 println(E.parse("(1)")) |
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224 println(E.parse("((1))")) |
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225 //println(E.parse("(((1)))")) |
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226 //println(E.parse("((((1))))")) |
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227 //println(E.parse("((((((1))))))")) |
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228 //println(E.parse("(((((((1)))))))")) |
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229 //println(E.parse("((((((((1)))))))")) |
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