1 | include "LIN/LIN.ma". |
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2 | include "joint/SemanticUtils.ma". |
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3 | |
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4 | let rec pre_erase_lin_internal_function' |
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5 | (globals: list ident) (the_program: list (lin_statement globals)) |
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6 | (labels: list label) |
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7 | on the_program: ((identifier_map ? label) × (list (lin_statement globals))) ≝ |
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8 | match the_program with |
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9 | [ nil ⇒ |
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10 | match labels with |
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11 | [ nil ⇒ 〈empty_map …, [ ]〉 (* XXX: labels should be empty *) |
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12 | | _ ⇒ ⊥ |
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13 | ] |
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14 | | cons hd tl ⇒ |
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15 | let 〈lbl, instr〉 ≝ hd in |
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16 | match lbl with |
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17 | [ None ⇒ |
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18 | let 〈maps, instructions〉 ≝ pre_erase_lin_internal_function' globals tl labels in |
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19 | match instr with |
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20 | [ sequential seq l ⇒ |
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21 | match seq with |
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22 | [ COST_LABEL cost ⇒ 〈maps, instructions〉 |
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23 | | _ ⇒ 〈maps, 〈None …, instr〉 :: instructions〉 |
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24 | ] |
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25 | | _ ⇒ 〈maps, 〈None …, instr〉 :: instructions〉 |
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26 | ] |
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27 | | Some lbl ⇒ |
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28 | match instr with |
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29 | [ sequential seq l ⇒ |
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30 | match seq with |
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31 | [ COST_LABEL cost ⇒ pre_erase_lin_internal_function' globals tl (lbl :: labels) |
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32 | | _ ⇒ |
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33 | let 〈maps, instructions〉 ≝ pre_erase_lin_internal_function' globals tl labels in |
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34 | let maps ≝ foldr ? ? (λl. λmap. add … map l lbl) maps (lbl :: labels) |
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35 | in |
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36 | 〈maps, instructions〉 |
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37 | ] |
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38 | | _ ⇒ |
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39 | let 〈maps, instructions〉 ≝ pre_erase_lin_internal_function' globals tl labels in |
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40 | let maps ≝ foldr ? ? (λl. λmap. add … map l lbl) maps (lbl :: labels) |
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41 | in |
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42 | 〈maps, instructions〉 |
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43 | ] |
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44 | ] |
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45 | ]. |
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46 | @daemon |
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47 | qed. |
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48 | |
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49 | definition pre_erase_lin_internal_function ≝ |
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50 | λglobals: list ident. |
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51 | λint_fun: joint_internal_function … (lin_params globals). |
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52 | pre_erase_lin_internal_function' … (joint_if_code … (lin_params …) int_fun) [ ]. |
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53 | |
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54 | definition relabel_joint_instruction: |
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55 | ∀globals: list ident. |
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56 | ∀params: params_. |
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57 | identifier_map LabelTag label → joint_instruction params globals → joint_instruction params globals ≝ |
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58 | λglobals: list ident. |
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59 | λparams. |
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60 | λmap. |
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61 | λinstr. |
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62 | match instr with |
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63 | [ COND acc_a lbl ⇒ |
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64 | let located ≝ lookup_def ?? map lbl lbl in |
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65 | COND params globals acc_a located |
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66 | | _ ⇒ instr |
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67 | ]. |
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68 | |
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69 | definition relabel_joint_statement: |
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70 | ∀globals: list ident. |
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71 | ∀params: params_. |
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72 | identifier_map LabelTag label → joint_statement params globals → joint_statement params globals ≝ |
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73 | λglobals: list ident. |
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74 | λparams: params_. |
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75 | λmap: identifier_map LabelTag label. |
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76 | λstmt: joint_statement params globals. |
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77 | match stmt with |
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78 | [ sequential seq l ⇒ |
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79 | let relabelled ≝ relabel_joint_instruction globals params map seq in |
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80 | sequential params globals relabelled l |
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81 | | RETURN ⇒ RETURN params globals |
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82 | | GOTO l ⇒ |
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83 | let located ≝ lookup_def ?? map l l in |
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84 | GOTO params globals located |
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85 | ]. |
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86 | |
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87 | let rec relabel_lin_internal_function' |
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88 | (globals: list ident) (map: identifier_map LabelTag label) |
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89 | (program: list (lin_statement globals)) |
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90 | on program: list (lin_statement globals) ≝ |
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91 | match program with |
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92 | [ nil ⇒ [ ] |
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93 | | cons hd tl ⇒ |
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94 | let 〈label, stmt〉 ≝ hd in |
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95 | let relabelled ≝ relabel_joint_statement globals lin_params_ map stmt in |
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96 | let label ≝ |
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97 | match label with |
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98 | [ None ⇒ None … |
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99 | | Some label ⇒ |
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100 | Some … (lookup_def ?? map label label) |
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101 | ] |
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102 | in |
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103 | 〈label, relabelled〉 :: relabel_lin_internal_function' globals map tl |
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104 | ]. |
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105 | |
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106 | definition relabel_lin_internal_function ≝ |
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107 | λglobals. |
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108 | λmap. |
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109 | λint_fun: joint_internal_function globals (lin_params globals). |
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110 | relabel_lin_internal_function' globals map (joint_if_code … int_fun). |
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111 | |
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112 | definition empty_graph ≝ |
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113 | λa: Type[0]. |
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114 | empty_map LabelTag a. |
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115 | |
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116 | let rec pre_erase_graph_internal_function' |
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117 | (params1: params1) (globals: list ident) |
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118 | (the_graph: codeT globals (graph_params params1 globals)) (labels: list label) |
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119 | (entry_point: label) (size_counter: nat) (map: identifier_map LabelTag label) |
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120 | (visited: identifier_map LabelTag bool) |
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121 | on size_counter: ((identifier_map LabelTag label) × (identifier_map LabelTag bool) × (codeT globals (graph_params params1 globals))) ≝ |
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122 | match size_counter return λ_. ((identifier_map LabelTag label) × (identifier_map LabelTag bool) × (codeT globals (graph_params params1 globals))) with |
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123 | [ O ⇒ |
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124 | match labels with |
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125 | [ nil ⇒ 〈map, visited, the_graph〉 |
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126 | | _ ⇒ ⊥ |
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127 | ] |
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128 | | S size_counter ⇒ |
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129 | let statement ≝ lookup LabelTag ? the_graph entry_point in |
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130 | match statement return λs: option (joint_statement (graph_params params1 globals) globals). ((identifier_map LabelTag label) × (identifier_map LabelTag bool) × (codeT globals (graph_params params1 globals))) with |
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131 | [ None ⇒ ⊥ (* XXX: should not happen *) |
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132 | | Some statement ⇒ |
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133 | let entered_previously ≝ lookup_def … visited entry_point false in |
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134 | match entered_previously return λe: bool. ((identifier_map LabelTag label) × (identifier_map LabelTag bool) × (codeT globals (graph_params params1 globals))) with |
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135 | [ true ⇒ 〈map, visited, the_graph〉 |
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136 | | false ⇒ (* XXX: never visited here before *) |
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137 | let visited ≝ add … visited entry_point true in |
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138 | match statement return λs: joint_statement (graph_params params1 globals) globals. ((identifier_map LabelTag label) × (identifier_map LabelTag bool) × (codeT globals (graph_params params1 globals))) with |
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139 | [ sequential seq l ⇒ |
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140 | match seq with |
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141 | [ COST_LABEL cost_label ⇒ |
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142 | pre_erase_graph_internal_function' params1 globals the_graph (entry_point :: labels) l size_counter map visited |
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143 | | COND acc_a cond_label ⇒ |
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144 | let 〈map, visited, the_graph〉 ≝ pre_erase_graph_internal_function' params1 globals the_graph [ ] l size_counter map visited in |
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145 | let 〈map, visited, the_graph〉 ≝ pre_erase_graph_internal_function' params1 globals the_graph [ ] cond_label size_counter map visited in |
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146 | let map ≝ foldr … (λl. λmap. add … map l entry_point) map (entry_point :: labels) in |
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147 | 〈map, visited, the_graph〉 |
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148 | | _ ⇒ |
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149 | let 〈map, visited, the_graph〉 ≝ pre_erase_graph_internal_function' params1 globals the_graph [ ] l size_counter map visited in |
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150 | let map ≝ foldr … (λl. λmap. add … map l entry_point) map (entry_point :: labels) in |
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151 | 〈map, visited, the_graph〉 |
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152 | ] |
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153 | | RETURN ⇒ |
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154 | let map ≝ foldr … (λl. λmap. add … map l entry_point) map (entry_point :: labels) in |
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155 | 〈map, visited, the_graph〉 |
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156 | | GOTO l ⇒ |
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157 | let 〈map, visited, the_graph〉 ≝ pre_erase_graph_internal_function' params1 globals the_graph [ ] l size_counter map visited in |
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158 | let map ≝ foldr … (λl. λmap. add … map l entry_point) map (entry_point :: labels) in |
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159 | 〈map, visited, the_graph〉 |
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160 | ] |
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161 | ] |
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162 | ] |
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163 | ]. |
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164 | cases daemon |
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165 | qed. |
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166 | |
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167 | definition pre_erase_graph_internal_function ≝ |
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168 | λparams1: params1. |
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169 | λglobals: list ident. |
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170 | λint_fun: joint_internal_function globals (graph_params params1 globals). |
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171 | match joint_if_entry … int_fun with |
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172 | [ dp entry entry_proof ⇒ |
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173 | let code ≝ joint_if_code … int_fun in |
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174 | let 〈map, visited, the_graph〉 ≝ pre_erase_graph_internal_function' params1 globals code [ ] entry (graph_num_nodes … code) (empty_map …) (empty_map …) in |
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175 | 〈map, the_graph〉 |
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176 | ]. |
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177 | |
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178 | let rec relabel_graph' |
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179 | (params1: params1) (globals: list ident) |
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180 | (the_graph: codeT globals (graph_params params1 globals)) (map: identifier_map LabelTag label) |
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181 | (visited: identifier_map LabelTag bool) (entry_point: label) (size_counter: nat) |
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182 | on size_counter: codeT globals (graph_params params1 globals) ≝ |
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183 | match size_counter return λs: nat. codeT globals (graph_params params1 globals) with |
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184 | [ O ⇒ empty_graph … |
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185 | | S size_counter ⇒ |
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186 | let relabelled_entry_point ≝ lookup_def … map entry_point entry_point in |
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187 | let statement ≝ lookup LabelTag ? the_graph entry_point in |
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188 | match statement return λs: option (joint_statement (graph_params params1 globals) globals). codeT globals (graph_params params1 globals) with |
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189 | [ None ⇒ ⊥ (* XXX: should not happen *) |
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190 | | Some statement ⇒ |
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191 | let entered_previously ≝ lookup_def … visited entry_point false in |
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192 | match entered_previously return λe: bool. codeT globals (graph_params params1 globals) with |
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193 | [ true ⇒ the_graph |
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194 | | false ⇒ (* XXX: never visited here before *) |
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195 | let visited ≝ add … visited entry_point true in |
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196 | match statement return λs: joint_statement (graph_params params1 globals) globals. codeT globals (graph_params params1 globals) with |
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197 | [ sequential seq l ⇒ |
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198 | let 〈the_graph, new_seq〉 ≝ |
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199 | match seq return λs. (codeT globals (graph_params params1 globals)) × ? with |
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200 | [ COND acc_a cond_label ⇒ |
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201 | let relabelled ≝ lookup_def … map cond_label cond_label in |
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202 | let tail_graph ≝ relabel_graph' params1 globals the_graph map visited cond_label size_counter in |
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203 | 〈tail_graph, COND … acc_a relabelled〉 |
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204 | | _ ⇒ 〈the_graph, seq〉 |
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205 | ] |
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206 | in |
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207 | let tail_graph ≝ relabel_graph' params1 globals the_graph map visited l size_counter in |
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208 | let relabelled ≝ lookup_def … map l l in |
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209 | add LabelTag … tail_graph relabelled_entry_point (sequential … new_seq relabelled) |
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210 | | RETURN ⇒ the_graph |
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211 | | GOTO l ⇒ |
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212 | let relabelled ≝ lookup_def … map l l in |
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213 | add LabelTag … the_graph relabelled_entry_point (GOTO … relabelled) |
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214 | ] |
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215 | ] |
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216 | ] |
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217 | ]. |
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218 | cases daemon |
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219 | qed. |
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220 | |
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221 | definition relabel_graph ≝ |
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222 | λglobals: list ident. |
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223 | λparams1: params1. |
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224 | λmap: identifier_map LabelTag label. |
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225 | λint_fun: joint_internal_function globals (graph_params params1 globals). |
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226 | match joint_if_entry … int_fun with |
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227 | [ dp entry entry_prf ⇒ |
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228 | let code ≝ joint_if_code … int_fun in |
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229 | relabel_graph' … code map (empty_map …) entry (graph_num_nodes … code) |
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230 | ]. |
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231 | |
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232 | definition pre_erase_joint_internal_function ≝ |
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233 | λglobals: list ident. |
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234 | λpars: params globals. |
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235 | λerasure_function: joint_internal_function globals pars → (identifier_map LabelTag label) × (codeT … pars). |
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236 | λrelabelling_function: identifier_map LabelTag label → joint_internal_function globals pars → codeT … pars. |
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237 | λint_fun: joint_internal_function globals pars. |
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238 | match joint_if_entry … int_fun with |
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239 | [ dp entry entry_prf ⇒ |
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240 | match joint_if_exit … int_fun with |
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241 | [ dp exit exit_prf ⇒ |
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242 | let 〈maps, code〉 ≝ erasure_function int_fun in |
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243 | let int_fun ≝ set_joint_code globals pars int_fun code entry exit in |
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244 | let code ≝ relabelling_function maps int_fun in |
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245 | set_joint_code globals pars int_fun code (lookup_def … maps entry entry) |
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246 | (lookup_def … maps exit exit) |
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247 | ] |
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248 | ]. |
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249 | cases daemon (* XXX *) |
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250 | qed. |
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251 | |
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252 | definition erase_graph_program: |
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253 | ∀params1: params1. joint_program (graph_params params1) → joint_program (graph_params params1) ≝ |
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254 | λparams1. |
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255 | λprogram. |
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256 | transform_program … program (transf_fundef … (pre_erase_joint_internal_function … (pre_erase_graph_internal_function …) (relabel_graph …))). |
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257 | |
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258 | definition erase_lin_program: lin_program → lin_program ≝ |
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259 | λprogram. |
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260 | transform_program … program (transf_fundef … (pre_erase_joint_internal_function … (pre_erase_lin_internal_function …) (relabel_lin_internal_function …))). |
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