1 | using System;
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2 | using System.Collections.Generic;
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3 | using System.Diagnostics;
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4 | using System.Linq;
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5 | using HeuristicLab.Algorithms.DataAnalysis.SymRegGrammarEnumeration.GrammarEnumeration;
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6 | using HeuristicLab.Common;
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7 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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8 | using HeuristicLab.Problems.DataAnalysis.Symbolic;
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9 |
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10 | namespace HeuristicLab.Algorithms.DataAnalysis.SymRegGrammarEnumeration {
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11 | public class Grammar {
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12 |
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13 | public Symbol StartSymbol { get; }
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14 |
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15 | #region Symbols
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16 | public VariableSymbol Var;
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17 |
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18 | public NonterminalSymbol Expr;
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19 | public NonterminalSymbol Term;
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20 | public NonterminalSymbol Factor;
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21 | public NonterminalSymbol LogFactor;
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22 | public NonterminalSymbol ExpFactor;
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23 | public NonterminalSymbol SinFactor;
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24 | public NonterminalSymbol CosFactor;
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25 |
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26 | public NonterminalSymbol SimpleExpr;
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27 | public NonterminalSymbol SimpleTerm;
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28 |
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29 | public NonterminalSymbol InvExpr;
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30 | public NonterminalSymbol InvTerm;
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31 |
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32 | public TerminalSymbol Addition;
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33 | public TerminalSymbol Multiplication;
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34 | public TerminalSymbol Log;
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35 | public TerminalSymbol Exp;
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36 | public TerminalSymbol Sin;
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37 | public TerminalSymbol Cos;
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38 | public TerminalSymbol Inv;
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39 |
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40 | // For infix notation
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41 | public TerminalSymbol OpeningBracket;
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42 | public TerminalSymbol ClosingBracket;
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43 |
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44 | #endregion
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45 |
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46 | #region HL Symbols for Parsing ExpressionTrees
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47 |
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48 | private ISymbol constSy;
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49 | private ISymbol varSy;
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50 |
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51 | private ISymbol addSy;
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52 | private ISymbol mulSy;
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53 | private ISymbol logSy;
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54 | private ISymbol expSy;
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55 | private ISymbol divSy;
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56 | private ISymbol sinSy;
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57 | private ISymbol cosSy;
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58 |
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59 | private ISymbol rootSy;
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60 | private ISymbol startSy;
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61 |
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62 | private InfixExpressionFormatter infixExpressionFormatter;
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63 | #endregion
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64 |
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65 | public Grammar(string[] variables) {
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66 | #region Define Symbols
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67 | Var = new VariableSymbol("var", variables);
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68 |
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69 | Expr = new NonterminalSymbol("Expr");
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70 | Term = new NonterminalSymbol("Term");
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71 | Factor = new NonterminalSymbol("Factor");
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72 | LogFactor = new NonterminalSymbol("LogFactor");
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73 | ExpFactor = new NonterminalSymbol("ExpFactor");
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74 | SinFactor = new NonterminalSymbol("SinFactor");
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75 | CosFactor = new NonterminalSymbol("CosFactor");
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76 |
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77 | SimpleExpr = new NonterminalSymbol("SimpleExpr");
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78 | SimpleTerm = new NonterminalSymbol("SimpleTerm");
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79 |
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80 | InvExpr = new NonterminalSymbol("InvExpr");
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81 | InvTerm = new NonterminalSymbol("InvTerm");
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82 |
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83 | Addition = new TerminalSymbol("+");
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84 | Multiplication = new TerminalSymbol("*");
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85 | Log = new TerminalSymbol("log");
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86 | Exp = new TerminalSymbol("exp");
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87 | Sin = new TerminalSymbol("sin");
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88 | Cos = new TerminalSymbol("cos");
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89 | Inv = new TerminalSymbol("inv");
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90 |
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91 | OpeningBracket = new TerminalSymbol("(");
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92 | ClosingBracket = new TerminalSymbol(")");
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93 | #endregion
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94 |
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95 | #region Production rules
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96 | StartSymbol = Expr;
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97 |
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98 | Expr.AddProduction(Term, Expr, Addition);
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99 | Expr.AddProduction(Term);
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100 |
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101 | Term.AddProduction(Factor, Term, Multiplication);
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102 | Term.AddProduction(Factor);
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103 | Term.AddProduction(InvExpr, Inv);
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104 |
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105 | Factor.AddProduction(Var);
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106 | Factor.AddProduction(LogFactor);
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107 | Factor.AddProduction(ExpFactor);
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108 | Factor.AddProduction(SinFactor);
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109 | Factor.AddProduction(CosFactor);
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110 |
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111 | LogFactor.AddProduction(SimpleExpr, Log);
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112 | ExpFactor.AddProduction(SimpleTerm, Exp);
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113 | SinFactor.AddProduction(SimpleExpr, Sin);
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114 | CosFactor.AddProduction(SimpleExpr, Cos);
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115 |
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116 | SimpleExpr.AddProduction(SimpleTerm, SimpleExpr, Addition);
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117 | SimpleExpr.AddProduction(SimpleTerm);
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118 |
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119 | SimpleTerm.AddProduction(Var, SimpleTerm, Multiplication);
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120 | SimpleTerm.AddProduction(Var);
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121 |
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122 | InvExpr.AddProduction(InvTerm, InvExpr, Addition);
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123 | InvExpr.AddProduction(InvTerm);
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124 |
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125 | InvTerm.AddProduction(Factor, InvTerm, Multiplication);
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126 | InvTerm.AddProduction(Factor);
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127 | #endregion
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128 |
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129 | #region Parsing to SymbolicExpressionTree
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130 | var symbolicExpressionGrammar = new TypeCoherentExpressionGrammar();
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131 | symbolicExpressionGrammar.ConfigureAsDefaultRegressionGrammar();
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132 |
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133 | constSy = symbolicExpressionGrammar.Symbols.OfType<Constant>().First();
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134 | varSy = symbolicExpressionGrammar.Symbols.OfType<Variable>().First();
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135 | addSy = symbolicExpressionGrammar.Symbols.OfType<Addition>().First();
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136 | mulSy = symbolicExpressionGrammar.Symbols.OfType<Multiplication>().First();
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137 | logSy = symbolicExpressionGrammar.Symbols.OfType<Logarithm>().First();
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138 | expSy = symbolicExpressionGrammar.Symbols.OfType<Exponential>().First();
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139 | divSy = symbolicExpressionGrammar.Symbols.OfType<Division>().First();
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140 | sinSy = symbolicExpressionGrammar.Symbols.OfType<Sine>().First();
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141 | cosSy = symbolicExpressionGrammar.Symbols.OfType<Cosine>().First();
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142 |
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143 | rootSy = symbolicExpressionGrammar.Symbols.OfType<ProgramRootSymbol>().First();
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144 | startSy = symbolicExpressionGrammar.Symbols.OfType<StartSymbol>().First();
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145 |
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146 | infixExpressionFormatter = new InfixExpressionFormatter();
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147 | #endregion
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148 | }
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149 |
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150 | #region Hashing
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151 | public int CalcHashCode(SymbolString sentence) {
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152 | return CalcHashCode<int>(sentence, AggregateIntHashes);
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153 | }
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154 |
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155 | private int CalcHashCode<THashType>(SymbolString sentence, Func<Symbol, THashType[], THashType> aggregateFunction) {
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156 | Debug.Assert(sentence.Any(), "Trying to evaluate empty sentence!");
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157 |
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158 | Stack<Symbol> parseStack = new Stack<Symbol>(sentence);
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159 |
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160 | Symbol peek = parseStack.Peek();
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161 | return aggregateFunction(peek, GetSubtreeHashes(parseStack, aggregateFunction)).GetHashCode();
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162 | }
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163 |
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164 | private THashType[] GetSubtreeHashes<THashType>(Stack<Symbol> parseStack, Func<Symbol, THashType[], THashType> aggregateHashes) {
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165 | Symbol currentSymbol = parseStack.Pop();
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166 |
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167 | // ADDITION
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168 | if (ReferenceEquals(currentSymbol, Addition)) {
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169 | var uniqueChildHashes = new HashSet<THashType>();
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170 |
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171 | // First subtree
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172 | if (ReferenceEquals(parseStack.Peek(), Addition)) {
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173 | uniqueChildHashes.UnionWith(GetSubtreeHashes(parseStack, aggregateHashes));
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174 | } else {
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175 | var peek = parseStack.Peek();
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176 | uniqueChildHashes.Add(aggregateHashes(peek, GetSubtreeHashes(parseStack, aggregateHashes)));
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177 | }
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178 | // Second subtree
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179 | if (ReferenceEquals(parseStack.Peek(), Addition)) {
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180 | uniqueChildHashes.UnionWith(GetSubtreeHashes(parseStack, aggregateHashes));
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181 | } else {
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182 | var peek = parseStack.Peek();
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183 | uniqueChildHashes.Add(aggregateHashes(peek, GetSubtreeHashes(parseStack, aggregateHashes)));
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184 | }
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185 |
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186 | var result = uniqueChildHashes.ToArray();
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187 | Array.Sort(result);
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188 | return result;
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189 | }
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190 |
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191 | // MULTIPLICATION
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192 | if (ReferenceEquals(currentSymbol, Multiplication)) {
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193 | var childHashes = new List<THashType>();
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194 |
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195 | // First subtree
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196 | if (ReferenceEquals(parseStack.Peek(), Multiplication)) {
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197 | childHashes.AddRange(GetSubtreeHashes(parseStack, aggregateHashes));
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198 | } else {
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199 | childHashes.Add(aggregateHashes(parseStack.Peek(), GetSubtreeHashes(parseStack, aggregateHashes)));
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200 | }
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201 | // Second subtree
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202 | if (ReferenceEquals(parseStack.Peek(), Multiplication)) {
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203 | childHashes.AddRange(GetSubtreeHashes(parseStack, aggregateHashes));
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204 | } else {
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205 | childHashes.Add(aggregateHashes(parseStack.Peek(), GetSubtreeHashes(parseStack, aggregateHashes)));
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206 | }
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207 |
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208 | // Sort due to commutativity
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209 | childHashes.Sort();
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210 |
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211 | // Cancel out inverse factors.
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212 | bool[] isFactorRemaining = Enumerable.Repeat(true, childHashes.Count).ToArray();
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213 |
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214 | for (int i = 0; i < isFactorRemaining.Length; i++) {
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215 | if (!isFactorRemaining[i]) continue;
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216 | if (isFactorRemaining.Count() <= 2) break; // Until we have constants, we can't cancel out all terms.
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217 |
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218 | var currFactor = childHashes[i];
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219 | var invFactor = aggregateHashes(Inv, new[] { currFactor });
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220 |
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221 | int indexOfInv = childHashes.IndexOf(invFactor);
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222 | if (indexOfInv >= 0 && isFactorRemaining[indexOfInv]) {
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223 | isFactorRemaining[i] = isFactorRemaining[indexOfInv] = false;
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224 | }
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225 | }
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226 | return Enumerable
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227 | .Range(0, isFactorRemaining.Length)
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228 | .Where(i => isFactorRemaining[i])
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229 | .Select(i => childHashes[i])
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230 | .ToArray();
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231 | }
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232 |
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233 | // LOG, EXP, SIN, INV
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234 | if (ReferenceEquals(currentSymbol, Log) || ReferenceEquals(currentSymbol, Exp) ||
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235 | ReferenceEquals(currentSymbol, Sin) || ReferenceEquals(currentSymbol, Cos) ||
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236 | ReferenceEquals(currentSymbol, Inv)) {
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237 | return new[] { aggregateHashes(parseStack.Peek(), GetSubtreeHashes(parseStack, aggregateHashes)) };
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238 | }
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239 |
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240 | // var or nonterminal symbol
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241 | return new[] { aggregateHashes(currentSymbol, new THashType[0]) };
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242 | }
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243 |
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244 | private string AggregateStringHashes(Symbol operatorSym, string[] hashes) {
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245 | var hashesArray = hashes.ToArray();
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246 |
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247 | if ((ReferenceEquals(operatorSym, Addition) || ReferenceEquals(operatorSym, Multiplication)) && hashesArray.Count() <= 1) {
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248 | return hashesArray[0];
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249 | }
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250 | if (operatorSym is NonterminalSymbol || ((TerminalSymbol)operatorSym).IsVariable) {
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251 | return operatorSym.StringRepresentation;
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252 | }
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253 |
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254 | return $"[{hashesArray.Aggregate(operatorSym.StringRepresentation, (result, ti) => string.Concat(result, " ° ", ti))}]"; // TODO: use string join instead of string.Concat
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255 | }
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256 |
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257 | private int AggregateIntHashes(Symbol operatorSym, int[] hashes) {
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258 | int start;
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259 | if ((ReferenceEquals(operatorSym, Addition) || ReferenceEquals(operatorSym, Multiplication)) &&
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260 | hashes.Length <= 1) {
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261 | start = 0;
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262 |
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263 | } else if (operatorSym is NonterminalSymbol || ((TerminalSymbol)operatorSym).IsVariable) {
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264 | return operatorSym.StringRepresentation.GetHashCode();
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265 |
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266 | } else {
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267 | start = operatorSym.StringRepresentation.GetHashCode();
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268 | }
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269 |
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270 | for (int i = 0; i < hashes.Length; i++) {
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271 | start = ((start << 5) + start) ^ hashes[i];
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272 | }
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273 | return start;
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274 | }
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275 | #endregion
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276 |
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277 | #region Parse to SymbolicExpressionTree
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278 |
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279 | public string ToInfixString(SymbolString sentence) {
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280 | Debug.Assert(sentence.Any(), "Trying to evaluate empty sentence!");
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281 | Debug.Assert(sentence.All(s => s is TerminalSymbol), "Trying to evaluate symbol sequence with nonterminalsymbols!");
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282 |
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283 | return infixExpressionFormatter.Format(ParseSymbolicExpressionTree(sentence));
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284 | }
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285 |
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286 | public SymbolicExpressionTree ParseSymbolicExpressionTree(SymbolString sentence) {
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287 | Debug.Assert(sentence.Any(), "Trying to evaluate empty sentence!");
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288 | Debug.Assert(sentence.All(s => s is TerminalSymbol), "Trying to evaluate symbol sequence with nonterminalsymbols!");
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289 |
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290 | var rootNode = rootSy.CreateTreeNode();
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291 | var startNode = startSy.CreateTreeNode();
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292 | rootNode.AddSubtree(startNode);
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293 |
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294 | Stack<TerminalSymbol> parseStack = new Stack<TerminalSymbol>(sentence.OfType<TerminalSymbol>());
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295 | startNode.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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296 |
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297 | return new SymbolicExpressionTree(rootNode);
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298 | }
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299 |
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300 | public ISymbolicExpressionTreeNode ParseSymbolicExpressionTree(Stack<TerminalSymbol> parseStack) {
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301 | TerminalSymbol currentSymbol = parseStack.Pop();
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302 |
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303 | ISymbolicExpressionTreeNode parsedSubTree = null;
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304 |
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305 | if (ReferenceEquals(currentSymbol, Addition)) {
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306 | parsedSubTree = addSy.CreateTreeNode();
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307 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack)); // left part
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308 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack)); // right part
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309 |
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310 | } else if (ReferenceEquals(currentSymbol, Multiplication)) {
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311 | parsedSubTree = mulSy.CreateTreeNode();
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312 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack)); // left part
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313 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack)); // right part
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314 |
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315 | } else if (ReferenceEquals(currentSymbol, Log)) {
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316 | parsedSubTree = logSy.CreateTreeNode();
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317 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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318 |
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319 | } else if (ReferenceEquals(currentSymbol, Exp)) {
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320 | parsedSubTree = expSy.CreateTreeNode();
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321 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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322 |
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323 | } else if (ReferenceEquals(currentSymbol, Sin)) {
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324 | parsedSubTree = sinSy.CreateTreeNode();
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325 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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326 |
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327 | } else if (ReferenceEquals(currentSymbol, Cos)) {
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328 | parsedSubTree = cosSy.CreateTreeNode();
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329 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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330 |
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331 | } else if (ReferenceEquals(currentSymbol, Inv)) {
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332 | parsedSubTree = divSy.CreateTreeNode();
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333 | ConstantTreeNode dividend = (ConstantTreeNode)constSy.CreateTreeNode();
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334 | dividend.Value = 1.0;
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335 | parsedSubTree.AddSubtree(dividend);
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336 | parsedSubTree.AddSubtree(ParseSymbolicExpressionTree(parseStack));
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337 |
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338 | } else if (currentSymbol.IsVariable) {
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339 | VariableTreeNode varNode = (VariableTreeNode)varSy.CreateTreeNode();
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340 | varNode.Weight = 1.0;
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341 | varNode.VariableName = currentSymbol.StringRepresentation;
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342 | parsedSubTree = varNode;
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343 | }
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344 |
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345 | Debug.Assert(parsedSubTree != null);
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346 | return parsedSubTree;
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347 | }
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348 | #endregion
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349 | }
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350 | }
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