1 // A naive bottom-up parser with backtracking |
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2 // |
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3 // Needs: |
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4 // :load matcher.scala |
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5 |
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6 // some regular expressions |
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7 val DIGIT = RANGE("0123456789") |
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8 val NONZERODIGIT = RANGE("123456789") |
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9 |
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10 val NUMBER = ALT(SEQ(NONZERODIGIT, STAR(DIGIT)), "0") |
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11 val LPAREN = CHAR('(') |
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12 val RPAREN = CHAR(')') |
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13 val WHITESPACE = PLUS(RANGE(" \n")) |
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14 val OPS = RANGE("+-*") |
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15 |
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16 // for classifying the strings that have been recognised |
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17 |
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18 abstract class Token |
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19 case object T_WHITESPACE extends Token |
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20 case object T_NUM extends Token |
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21 case class T_OP(s: String) extends Token |
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22 case object T_LPAREN extends Token |
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23 case object T_RPAREN extends Token |
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24 case class NT(s: String) extends Token |
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25 |
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26 // lexing rules for arithmetic expressions |
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27 val lexing_rules: List[Rule[Token]]= |
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28 List((NUMBER, (s) => T_NUM), |
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29 (WHITESPACE, (s) => T_WHITESPACE), |
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30 (LPAREN, (s) => T_LPAREN), |
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31 (RPAREN, (s) => T_RPAREN), |
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32 (OPS, (s) => T_OP(s.mkString))) |
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33 |
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34 // the tokenizer |
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35 val Tok = Tokenizer(lexing_rules, List(T_WHITESPACE)) |
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36 |
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37 type Grammar = List[(String, List[Token])] |
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38 |
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39 // grammar for arithmetic expressions |
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40 val grammar = |
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41 List ("F" -> List(T_NUM), |
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42 "E" -> List(T_NUM), |
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43 "E" -> List(NT("E"), T_OP("+"), NT("E")), |
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44 "E" -> List(NT("E"), T_OP("-"), NT("E")), |
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45 "E" -> List(NT("E"), T_OP("*"), NT("E")), |
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46 "E" -> List(T_LPAREN, NT("E"), T_RPAREN)) |
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47 |
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48 |
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49 def chop[A](ts1: List[A], prefix: List[A], ts2: List[A]) : Option[(List[A], List[A])] = |
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50 ts1 match { |
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51 case Nil => None |
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52 case t::ts => |
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53 if (ts1.startsWith(prefix)) Some(ts2.reverse, ts1.drop(prefix.length)) |
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54 else chop(ts, prefix, t::ts2) |
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55 } |
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56 |
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57 // examples for chop |
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58 chop(List(1,2,3,4,5,6,7,8,9), List(4,5), Nil) |
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59 chop(List(1,2,3,4,5,6,7,8,9), List(3,5), Nil) |
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60 |
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61 def replace[A](ts: List[A], out: List[A], in: List [A]) = |
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62 chop(ts, out, Nil) match { |
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63 case None => None |
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64 case Some((before, after)) => Some(before ::: in ::: after) |
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65 } |
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66 |
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67 def parse(g: Grammar, ts: List[Token]) : Boolean = { |
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68 println(ts) |
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69 if (ts == List(NT("E"))) true |
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70 else { |
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71 val tss = for ((lhs, rhs) <- g) yield replace(ts, rhs, List(NT(lhs))) |
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72 tss.flatten.exists(parse(g, _)) |
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73 } |
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74 } |
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75 |
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76 def parser(g: Grammar, s: String) = { |
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77 println("\n") |
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78 parse(g, Tok.fromString(s)) |
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79 } |
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80 |
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81 |
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82 |
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83 parser(grammar, "2 + 3 * 4 + 1") |
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84 parser(grammar, "(2 + 3) * (4 + 1)") |
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85 parser(grammar, "(2 + 3) * 4 (4 + 1)") |
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86 |
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87 |
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88 |
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