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 System.Security.Cryptography;
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6 | using HeuristicLab.Algorithms.DataAnalysis.SymRegGrammarEnumeration;
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7 | using Microsoft.VisualStudio.TestTools.UnitTesting;
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8 | using HierarchicalFormatter = HeuristicLab.Encodings.SymbolicExpressionTreeEncoding.SymbolicExpressionTreeHierarchicalFormatter;
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9 |
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10 | namespace Test {
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11 | [TestClass]
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12 | public class TreeHashingTest {
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13 |
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14 | private Grammar grammar;
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15 | private TerminalSymbol varA;
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16 | private TerminalSymbol varB;
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17 | private TerminalSymbol varC;
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18 | private TerminalSymbol c;
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19 |
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20 | Func<Grammar, SymbolList, int> ComputeHash = (grammar, sentence) => grammar.ComputeHash(null, sentence);
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21 |
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22 | [TestInitialize]
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23 | public void InitTest() {
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24 | grammar = new Grammar(new[] { "a", "b", "c" });
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25 |
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26 | varA = grammar.VarTerminals.First(s => s.StringRepresentation == "a");
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27 | varB = grammar.VarTerminals.First(s => s.StringRepresentation == "b");
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28 | varC = grammar.VarTerminals.First(s => s.StringRepresentation == "c");
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29 | c = grammar.Const;
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30 | }
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31 |
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32 | [TestMethod]
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33 | [TestCategory("TreeHashing")]
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34 | public void SimpleEqualityAddition() {
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35 | SymbolList s1 = new SymbolList(new[] { varA, varB, grammar.Addition, varC, grammar.Addition });
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36 | SymbolList s2 = new SymbolList(new[] { varA, varB, grammar.Addition, varC, grammar.Addition });
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37 |
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38 | int hash1 = ComputeHash(grammar, s1);
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39 | int hash2 = ComputeHash(grammar, s2);
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40 |
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41 | Assert.AreEqual(hash1, hash2);
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42 | }
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43 |
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44 | [TestMethod]
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45 | [TestCategory("TreeHashing")]
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46 | public void SimpleInequalityAddition() {
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47 | SymbolList s1 = new SymbolList(new[] { varA, varB, grammar.Addition, varC, grammar.Addition });
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48 | SymbolList s2 = new SymbolList(new[] { varB, varB, grammar.Addition, varB, grammar.Addition });
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49 |
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50 | int hash1 = ComputeHash(grammar, s1);
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51 | int hash2 = ComputeHash(grammar, s2);
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52 |
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53 | Assert.AreNotEqual(hash1, hash2);
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54 | }
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55 |
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56 | [TestMethod]
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57 | [TestCategory("TreeHashing")]
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58 | public void CommutativityAddition() {
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59 | SymbolList s1 = new SymbolList(new[] { varA, varB, grammar.Addition });
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60 | SymbolList s2 = new SymbolList(new[] { varB, varA, grammar.Addition });
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61 |
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62 | int hash1 = ComputeHash(grammar, s1);
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63 | int hash2 = ComputeHash(grammar, s2);
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64 |
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65 | Assert.AreEqual(hash1, hash2);
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66 | }
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67 |
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68 | [TestMethod]
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69 | [TestCategory("TreeHashing")]
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70 | public void AssociativityAddition() {
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71 | SymbolList s1 = new SymbolList(new[] { varA, varB, grammar.Addition, varA, grammar.Addition });
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72 | SymbolList s2 = new SymbolList(new[] { varA, varB, varA, grammar.Addition, grammar.Addition });
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73 |
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74 | int hash1 = ComputeHash(grammar, s1);
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75 | int hash2 = ComputeHash(grammar, s2);
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76 |
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77 | Assert.AreEqual(hash1, hash2);
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78 | }
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79 |
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80 | [TestMethod]
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81 | [TestCategory("TreeHashing")]
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82 | public void RepeatedAddition() {
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83 | SymbolList s1 = new SymbolList(new[] { varA, varA, grammar.Addition, varA, grammar.Addition });
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84 | SymbolList s2 = new SymbolList(new[] { varA });
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85 |
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86 | int hash1 = ComputeHash(grammar, s1);
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87 | int hash2 = ComputeHash(grammar, s2);
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88 |
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89 | Assert.AreEqual(hash1, hash2);
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90 | }
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91 |
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92 | [TestMethod]
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93 | [TestCategory("TreeHashing")]
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94 | public void ComplexInequality() {
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95 | SymbolList s1 = new SymbolList(new[] { varA, varA, varA, grammar.Multiplication, grammar.Multiplication });
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96 | SymbolList s2 = new SymbolList(new[] { varA, varA, varA, grammar.Multiplication, grammar.Addition });
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97 |
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98 | int hash1 = ComputeHash(grammar, s1);
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99 | int hash2 = ComputeHash(grammar, s2);
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100 |
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101 | Assert.AreNotEqual(hash1, hash2);
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102 | }
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103 |
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104 | [TestMethod]
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105 | [TestCategory("TreeHashing")]
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106 | public void NonterminalHashing() {
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107 | SymbolList s1 = new SymbolList(new Symbol[] { varA, varA, grammar.Expr, grammar.Addition, grammar.Addition });
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108 | SymbolList s2 = new SymbolList(new Symbol[] { varA, grammar.Expr, grammar.Addition });
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109 |
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110 | int hash1 = ComputeHash(grammar, s1);
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111 | int hash2 = ComputeHash(grammar, s2);
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112 |
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113 | Assert.AreEqual(hash1, hash2);
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114 | }
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115 |
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116 | [TestMethod]
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117 | [TestCategory("TreeHashing")]
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118 | public void InverseFactorCancelationSimple() {
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119 | // 1/a * b * a * a
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120 | SymbolList s1 = new SymbolList(new Symbol[] { varA, grammar.Inv, varB, grammar.Multiplication, varA, grammar.Multiplication, varA, grammar.Multiplication });
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121 | // a * b
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122 | SymbolList s2 = new SymbolList(new Symbol[] { varA, varB, grammar.Multiplication });
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123 |
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124 | int hash1 = ComputeHash(grammar, s1);
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125 | int hash2 = ComputeHash(grammar, s2);
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126 |
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127 | Assert.AreEqual(hash1, hash2);
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128 | }
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129 |
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130 | [TestMethod]
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131 | [TestCategory("TreeHashing")]
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132 | public void InverseFactorCancelationComplex() {
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133 | SymbolList s1 = new SymbolList(new Symbol[] { varA, grammar.Sin, varA, varA, grammar.Multiplication, varA, grammar.Addition, grammar.Sin, grammar.Addition });
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134 | SymbolList s2 = new SymbolList(new Symbol[] { varA, varA, varA, grammar.Multiplication, grammar.Addition, grammar.Sin, varA, grammar.Inv, varA, grammar.Sin, varA, grammar.Multiplication, grammar.Multiplication, grammar.Addition });
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135 |
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136 | int hash1 = ComputeHash(grammar, s1);
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137 | int hash2 = ComputeHash(grammar, s2);
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138 |
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139 | Console.WriteLine(s1);
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140 | Console.WriteLine(PrintTree(s1));
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141 | Console.WriteLine(grammar.Simplify(null, s1));
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142 | Console.WriteLine(hash1);
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143 | Console.WriteLine();
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144 | Console.WriteLine(s2);
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145 | Console.WriteLine(PrintTree(s2));
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146 | Console.WriteLine(grammar.Simplify(null, s2));
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147 | Console.WriteLine(hash2);
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148 |
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149 |
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150 | Assert.AreEqual(hash1, hash2);
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151 | }
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152 |
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153 | // Constants
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154 | [TestMethod]
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155 | [TestCategory("TreeHashing")]
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156 | public void SimpleConst() {
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157 | SymbolList s1 = new SymbolList(new Symbol[] { c, varA, grammar.Multiplication, c, grammar.Addition });
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158 | SymbolList s2 = new SymbolList(new Symbol[] { c, varA, grammar.Multiplication, c, varA, grammar.Multiplication, grammar.Addition, c, grammar.Addition });
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159 |
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160 | int hash1 = ComputeHash(grammar, s1);
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161 | int hash2 = ComputeHash(grammar, s2);
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162 |
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163 | Assert.AreEqual(hash1, hash2);
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164 | }
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165 |
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166 | [TestMethod]
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167 | [TestCategory("TreeHashing")]
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168 | public void EnumerateGrammarTest() {
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169 | //const int nvars = 1;
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170 | //var variables = Enumerable.Range(1, nvars).Select(x => $"x{x}").ToArray();
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171 | var variables = new[] { "a", "b" };
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172 | var grammar = new Grammar(variables, Enum.GetValues(typeof(GrammarRule)).Cast<GrammarRule>());
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173 |
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174 | Func<SymbolList, int> hash = s => grammar.Hasher.CalcHashCode(s);
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175 | int length = 100;
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176 | int depth = 20;
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177 |
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178 | //List<SymbolList> sentences = EnumerateGrammarBreadth(grammar, length: length, hashPhrases: false).ToList();
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179 | //Console.WriteLine("Breadth: {0} generated, {1} distinct sentences", sentences.Count, sentences.GroupBy(hash).Count());
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180 |
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181 | //var sentences = EnumerateGrammarBreadth(grammar, length: length, hashPhrases: true).ToList();
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182 | //Console.WriteLine("Breadth (hashed): {0} generated, {1} distinct sentences", sentences.Count, sentences.GroupBy(hash).Count());
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183 |
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184 | var sentences = EnumerateGrammarDepth(grammar, length: length, depth: depth, hashPhrases: false).ToList();
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185 | Console.WriteLine("Depth: {0} generated, {1} distinct sentences", sentences.Count, sentences.GroupBy(hash).Count());
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186 |
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187 | sentences = EnumerateGrammarDepth(grammar, length: length, depth: depth, hashPhrases: true).ToList();
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188 | Console.WriteLine("Depth (hashed): {0} generated, {1} distinct sentences", sentences.Count, sentences.GroupBy(hash).Count());
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189 | }
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190 |
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191 | [TestMethod]
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192 | [TestCategory("TreeHashing")]
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193 | public void HashExtensionsTest() {
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194 | var variables = new[] { "x", "y", "z" };
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195 | var rules = Enum.GetValues(typeof(GrammarRule)).Cast<GrammarRule>();
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196 | var grammar = new Grammar(variables, rules);
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197 | var add = grammar.Addition;
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198 | var mul = grammar.Multiplication;
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199 | var exp = grammar.Exp;
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200 | var log = grammar.Log;
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201 | var inv = grammar.Inv;
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202 | var sin = grammar.Sin;
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203 |
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204 | var c = grammar.Const;
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205 | var x = grammar.VarTerminals.Single(v => v.StringRepresentation == "x");
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206 | var y = grammar.VarTerminals.Single(v => v.StringRepresentation == "y");
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207 | var z = grammar.VarTerminals.Single(v => v.StringRepresentation == "z");
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208 |
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209 |
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210 | var ha = SHA512.Create();
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211 |
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212 | var sentences = new[] {
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213 | new SymbolList(c, c, x, mul, c, add, inv, mul, c, add),
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214 | new SymbolList(c, c, x, mul, c, add, log, mul, c, add),
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215 | new SymbolList(x, x, add),
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216 | new SymbolList(x, x, add, x, add),
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217 | new SymbolList(x, x, add, y, add),
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218 | new SymbolList(x, x, add, x, add, x, add),
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219 | new SymbolList(x, x, add, y, add, x, add),
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220 | new SymbolList(x, y, mul, x, y, mul, add),
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221 | new SymbolList(x, y, mul, y, x, mul, add),
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222 | new SymbolList(x, y, mul, z, y, mul, add),
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223 | new SymbolList(x, x, add, y, mul),
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224 | new SymbolList(x, x, add, y, mul, y, mul),
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225 | new SymbolList(x, x, inv, mul),
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226 | new SymbolList(x, inv, x, inv, mul, x, mul, x, mul),
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227 | new SymbolList(c, x, x, x, x, x, x, mul, mul, mul, mul, mul, mul, c, x, mul, c, add, add),
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228 | new SymbolList(c, x, x, x, x, x, x, mul, mul, mul, mul, mul, mul, c, x, mul, c, add, add),
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229 | new SymbolList(c, x, mul, c, x, x, x, x, x, x, mul, mul, mul, mul, mul, mul, c, add, add),
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230 | new SymbolList(c, x, x, x, x, mul, mul, mul, mul, c, x, mul, c, x, mul, c, add, add, add),
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231 | new SymbolList(c, x, mul, c, x, x, x, x, mul, mul, mul, mul, c, x, mul, c, add, add, add)
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232 | };
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233 |
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234 | foreach (var sentence in sentences) {
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235 | var simplified = grammar.Simplify(ha, sentence);
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236 | Console.WriteLine($"{sentence} -> {simplified} {grammar.Hasher.CalcHashCode(sentence)} {grammar.ComputeHash(ha, sentence)}");
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237 | Console.WriteLine();
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238 | }
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239 | }
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240 |
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241 | string PrintTree(SymbolList s) {
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242 | var t = grammar.ParseSymbolicExpressionTree(s);
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243 | return HierarchicalFormatter.Format(t.Root.GetSubtree(0).GetSubtree(0));
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244 | }
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245 |
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246 | [TestMethod]
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247 | [TestCategory("TreeHashing")]
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248 | public void HashCollisionsTest() {
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249 | var variables = new[] { "x", "y", "z", "w" };
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250 | //var rules = Enum.GetValues(typeof(GrammarRule)).Cast<GrammarRule>().Except(new[] { GrammarRule.InverseTerm, GrammarRule.Exponentiation, GrammarRule.Logarithm, GrammarRule.Sine });
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251 | var rules = Enum.GetValues(typeof(GrammarRule)).Cast<GrammarRule>();
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252 | var grammar = new Grammar(variables, rules);
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253 |
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254 | int maxLength = 20, maxDepth = int.MaxValue;
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255 | var sentences = EnumerateGrammarDepth(grammar, length: maxLength, depth: maxDepth, hashPhrases: false).ToList();
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256 | var count = sentences.Count;
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257 |
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258 | var sw = new Stopwatch();
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259 | sw.Start();
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260 | var hashes = sentences.Select(grammar.Hasher.CalcHashCode).ToList();
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261 | sw.Stop();
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262 | Console.WriteLine($"Old hash: {sentences.Count} ({hashes.Distinct().Count()}) hashed in {sw.ElapsedMilliseconds / 1000.0} seconds ({1000d * sentences.Count / sw.ElapsedMilliseconds} hashes/s)");
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263 |
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264 | var ha = SHA512.Create();
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265 | sw.Restart();
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266 | var hashes_new = sentences.Select(x => grammar.ComputeHash(ha, x)).ToList();
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267 | sw.Stop();
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268 | Console.WriteLine($"New hash: {sentences.Count} ({hashes_new.Distinct().Count()}) hashed in {sw.ElapsedMilliseconds / 1000.0} seconds ({1000.0 * sentences.Count / sw.ElapsedMilliseconds} hashes/s)");
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269 |
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270 | var distinct = Enumerable.Range(0, count).GroupBy(x => hashes_new[x]).Select(g => g.OrderBy(x => x).First()).ToList();
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271 | var collisions = distinct.ToLookup(x => hashes[x], x => Tuple.Create(hashes_new[x], sentences[x]));
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272 |
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273 | foreach (var pair in collisions) {
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274 | if (pair.Count() > 1) {
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275 | Console.WriteLine(pair.Key);
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276 | foreach (var t in pair) {
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277 | Console.WriteLine($"\t{t}");
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278 | Console.WriteLine($"\t{grammar.ToInfixString(t.Item2)}");
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279 | var simplified = grammar.Simplify(ha, t.Item2);
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280 | Console.WriteLine($"\t{simplified}");
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281 | Console.Write($"\t");
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282 | PrintTree(t.Item2);
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283 | Console.WriteLine();
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284 | }
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285 | }
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286 | }
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287 | }
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288 |
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289 | [TestMethod]
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290 | [TestCategory("TreeHashing")]
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291 | public void HashPerformance() {
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292 | var nvars = 4;
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293 | var variables = Enumerable.Range(0, nvars).Select(x => $"X{x}").ToArray();
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294 | //var rules = Enum.GetValues(typeof(GrammarRule)).Cast<GrammarRule>().Except(new[] { GrammarRule.InverseTerm, GrammarRule.Exponentiation, GrammarRule.Logarithm, GrammarRule.Sine });
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295 | var rules = Enum.GetValues(typeof(GrammarRule)).Cast<GrammarRule>();
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296 | var grammar = new Grammar(variables, rules);
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297 |
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298 | int maxLength = 20, maxDepth = int.MaxValue;
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299 | var sentences = EnumerateGrammarDepth(grammar, length: maxLength, depth: maxDepth, hashPhrases: false).ToList();
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300 | var count = sentences.Count;
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301 |
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302 | var ha = SHA512.Create();
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303 |
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304 | var sw = new Stopwatch();
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305 | sw.Start();
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306 | var hashes = sentences.Select(x => grammar.ComputeHash(ha, x)).ToList();
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307 | sw.Stop();
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308 |
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309 | Console.WriteLine($"New: {sentences.Count} ({hashes.Distinct().Count()}) hashed in {sw.ElapsedMilliseconds / 1000.0} seconds ({1000d * sentences.Count / sw.ElapsedMilliseconds} hashes/s)");
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310 |
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311 | sw.Restart();
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312 | var hashes_old = sentences.Select(x => grammar.Hasher.CalcHashCode(x)).ToList();
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313 | sw.Stop();
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314 |
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315 | Console.WriteLine($"Old: {sentences.Count} ({hashes_old.Distinct().Count()}) hashed in {sw.ElapsedMilliseconds / 1000.0} seconds ({1000d * sentences.Count / sw.ElapsedMilliseconds} hashes/s)");
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316 | }
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317 |
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318 | #region enumerate the grammar
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319 | private static IEnumerable<SymbolList> EnumerateGrammarBreadth(Grammar grammar, int length, bool hashPhrases = true) {
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320 | var phrases = new Queue<SymbolList>();
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321 | phrases.Enqueue(new SymbolList(grammar.StartSymbol));
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322 | var sentences = new List<SymbolList>();
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323 | var archive = new HashSet<int>();
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324 |
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325 | while (phrases.Any()) {
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326 | var phrase = phrases.Dequeue();
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327 |
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328 | if (phrase.Count > length)
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329 | continue;
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330 |
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331 | if (phrase.IsSentence()) {
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332 | sentences.Add(phrase);
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333 | continue;
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334 | }
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335 |
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336 | if (hashPhrases && !archive.Add(grammar.Hasher.CalcHashCode(phrase))) {
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337 | continue;
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338 | }
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339 |
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340 | var idx = phrase.NextNonterminalIndex();
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341 | var productions = grammar.Productions[phrase[idx]];
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342 | var derived = productions.Select(p => phrase.DerivePhrase(idx, p)).Where(p => p.Count <= length);
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343 | foreach (var d in derived)
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344 | phrases.Enqueue(d);
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345 | }
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346 | return sentences;
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347 | }
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348 |
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349 | private static IEnumerable<SymbolList> EnumerateGrammarDepth(Grammar grammar, int length, int depth, bool hashPhrases = true) {
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350 | return Expand(new SymbolList(grammar.StartSymbol), grammar, length, 0, depth, hashPhrases ? new HashSet<int>() : null);
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351 | }
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352 |
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353 | private static IEnumerable<SymbolList> Expand(SymbolList phrase, Grammar grammar, int maxLength, int depth, int maxDepth, HashSet<int> visited) {
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354 | if (maxDepth < depth || maxLength < phrase.Count) {
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355 | yield break;
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356 | }
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357 |
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358 | if (phrase.IsSentence()) {
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359 | yield return phrase;
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360 | yield break;
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361 | }
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362 |
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363 | if (visited != null && !visited.Add(HashExtensions.ComputeHash(grammar, null, phrase))) {
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364 | yield break;
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365 | }
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366 |
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367 | var i = phrase.NextNonterminalIndex();
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368 | var productions = grammar.Productions[phrase[i]];
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369 |
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370 | foreach (var s in productions.SelectMany(p => Expand(phrase.DerivePhrase(i, p), grammar, maxLength, depth + 1, maxDepth, visited)))
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371 | yield return s;
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372 | }
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373 | #endregion
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374 | }
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375 | }
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