1 | include "LTL/LTL.ma". |
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2 | include "ERTL/Interference.ma". |
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3 | include "ASM/Arithmetic.ma". |
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4 | |
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5 | definition fresh_label ≝ |
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6 | λglobals: list ident. |
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7 | λluniv. |
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8 | fresh LabelTag luniv. |
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9 | |
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10 | definition ltl_statement_graph ≝ |
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11 | λglobals. |
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12 | graph … (ltl_statement globals). |
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13 | |
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14 | definition add_graph ≝ |
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15 | λglobals. |
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16 | λlabel. |
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17 | λstmt: ltl_statement globals. |
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18 | λgraph: ltl_statement_graph globals. |
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19 | add LabelTag ? graph label stmt. |
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20 | |
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21 | definition generate ≝ |
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22 | λglobals: list ident. |
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23 | λluniv. |
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24 | λgraph: ltl_statement_graph globals. |
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25 | λstmt: ltl_statement globals. |
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26 | let 〈l, luniv〉 ≝ fresh_label globals luniv in |
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27 | let graph ≝ add_graph globals l stmt graph in |
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28 | 〈l, graph, luniv〉. |
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29 | |
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30 | definition num_locals ≝ |
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31 | λspilled_no. |
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32 | λglobals. |
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33 | λint_fun. |
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34 | spilled_no + (joint_if_stacksize globals (ertl_params globals) int_fun). |
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35 | |
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36 | definition stacksize ≝ |
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37 | λspilled_no. |
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38 | λglobals. |
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39 | λint_fun. |
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40 | spilled_no + (joint_if_stacksize globals (ertl_params globals) int_fun). |
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41 | |
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42 | definition adjust_off ≝ |
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43 | λspilled_no. |
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44 | λglobals. |
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45 | λint_fun. |
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46 | λoff. |
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47 | let 〈ignore, int_off〉 ≝ half_add ? int_size off in |
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48 | let 〈sub, ignore〉 ≝ sub_8_with_carry (bitvector_of_nat ? (num_locals spilled_no globals int_fun)) int_off false in |
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49 | sub. |
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50 | |
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51 | definition get_stack: |
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52 | nat → ∀globals. ertl_internal_function globals → graph (ltl_statement globals) → Register → Byte → label → ? ≝ |
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53 | λspilled_no. |
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54 | λglobals: list ident. |
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55 | λint_fun. |
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56 | λgraph: graph (ltl_statement (globals)). |
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57 | λr. |
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58 | λoff. |
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59 | λl. |
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60 | λoriginal_label. |
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61 | let off ≝ adjust_off spilled_no globals int_fun off in |
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62 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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63 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc r)) l) in |
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64 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (LOAD … globals it it it) l) in |
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65 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc RegisterDPH)) l) in |
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66 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (OP2 … globals Addc it it RegisterSPH) l) in |
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67 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (INT … globals RegisterA (zero ?)) l) in |
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68 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc RegisterDPL)) l) in |
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69 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (OP2 … globals Add it it RegisterSPL) l) in |
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70 | 〈add_graph globals original_label (sequential (ltl_params globals) globals (INT … (ltl_params globals) globals RegisterA off) l) graph, luniv〉. |
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71 | |
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72 | definition set_stack: |
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73 | nat → ∀globals. ertl_internal_function globals → ltl_statement_graph globals → Byte |
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74 | → Register → label → ? ≝ |
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75 | λspilled_no. |
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76 | λglobals: list ident. |
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77 | λint_fun. |
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78 | λgraph: graph (ltl_statement (globals)). |
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79 | λoff. |
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80 | λr. |
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81 | λl. |
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82 | λoriginal_label. |
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83 | let off ≝ adjust_off spilled_no globals int_fun off in |
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84 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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85 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (STORE … globals it it it) l) in |
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86 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (to_acc r)) l) in |
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87 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc RegisterDPH)) l) in |
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88 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (OP2 … globals Addc it it RegisterSPH) l) in |
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89 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (INT … globals RegisterA (zero ?)) l) in |
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90 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc RegisterDPL)) l) in |
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91 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (OP2 … globals Add it it RegisterSPL) l) in |
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92 | 〈add_graph globals original_label (sequential (ltl_params globals) globals (INT … (ltl_params globals) globals RegisterA off) l) graph, luniv〉. |
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93 | |
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94 | |
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95 | definition write ≝ |
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96 | λglobals: list ident. |
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97 | λint_fun: ertl_internal_function globals. |
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98 | λvaluation. |
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99 | λcoloured_graph. |
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100 | λgraph. |
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101 | λr. |
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102 | λl. |
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103 | λoriginal_label: label. |
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104 | match colouring valuation coloured_graph (inl … r) with |
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105 | [ decision_spill off ⇒ |
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106 | let luniv ≝ joint_if_luniverse … int_fun in |
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107 | let 〈graph, luniv〉 ≝ set_stack (spilled_no … coloured_graph) globals int_fun graph (bitvector_of_nat … off) RegisterSST l original_label in |
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108 | 〈RegisterSST, l, graph, luniv〉 |
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109 | | decision_colour hwr ⇒ |
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110 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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111 | 〈hwr, l, graph, luniv〉 |
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112 | ]. |
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113 | |
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114 | definition read ≝ |
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115 | λglobals: list ident. |
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116 | λint_fun: ertl_internal_function globals. |
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117 | λvaluation. |
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118 | λcoloured_graph. |
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119 | λgraph. |
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120 | λr. |
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121 | λstmt. |
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122 | λoriginal_label: label. |
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123 | match colouring valuation coloured_graph (inl … r) with |
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124 | [ decision_colour hwr ⇒ |
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125 | let luniv ≝ joint_if_luniverse … int_fun in |
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126 | 〈add_graph globals original_label (stmt hwr) graph, luniv〉 |
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127 | | decision_spill off ⇒ |
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128 | let temphwr ≝ RegisterSST in |
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129 | let luniv ≝ joint_if_luniverse … int_fun in |
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130 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (stmt temphwr) in |
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131 | get_stack (spilled_no … coloured_graph) globals int_fun graph temphwr (bitvector_of_nat … off) l original_label |
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132 | ]. |
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133 | |
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134 | definition move ≝ |
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135 | λspilled_no. |
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136 | λglobals: list ident. |
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137 | λint_fun. |
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138 | λgraph: graph (ltl_statement globals). |
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139 | λdest: decision. |
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140 | λsrc: decision. |
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141 | λl: label. |
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142 | λoriginal_label: label. |
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143 | match dest with |
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144 | [ decision_colour dest_hwr ⇒ |
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145 | match src with |
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146 | [ decision_colour src_hwr ⇒ |
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147 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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148 | if eq_Register dest_hwr src_hwr then |
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149 | 〈add_graph globals original_label (GOTO … globals l) graph, luniv〉 |
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150 | else |
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151 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc dest_hwr)) l) in |
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152 | 〈add_graph globals original_label (sequential (ltl_params globals) globals (MOVE … globals (to_acc src_hwr)) l) graph, luniv〉 |
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153 | | decision_spill src_off ⇒ get_stack spilled_no globals int_fun graph dest_hwr (bitvector_of_nat … src_off) l original_label |
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154 | ] |
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155 | | decision_spill dest_off ⇒ |
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156 | match src with |
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157 | [ decision_colour src_hwr ⇒ set_stack spilled_no globals int_fun graph (bitvector_of_nat … dest_off) src_hwr l original_label |
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158 | | decision_spill src_off ⇒ |
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159 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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160 | if eq_nat dest_off src_off then |
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161 | 〈add_graph globals original_label (GOTO … globals l) graph, luniv〉 |
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162 | else |
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163 | let temp_hwr ≝ RegisterSST in |
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164 | let 〈graph, luniv〉 ≝ set_stack spilled_no globals int_fun graph (bitvector_of_nat … dest_off) temp_hwr l original_label in |
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165 | get_stack spilled_no globals int_fun graph temp_hwr (bitvector_of_nat … src_off) l original_label |
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166 | ] |
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167 | ]. |
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168 | |
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169 | definition newframe ≝ |
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170 | λspilled_no. |
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171 | λglobals: list ident. |
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172 | λint_fun: ertl_internal_function globals. |
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173 | λgraph: ltl_statement_graph globals. |
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174 | λl: label. |
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175 | λoriginal_label: label. |
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176 | if eq_nat (stacksize spilled_no globals int_fun) 0 then |
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177 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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178 | 〈add_graph globals original_label (GOTO … globals l) graph, luniv〉 |
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179 | else |
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180 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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181 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc RegisterSPH)) l) in |
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182 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (OP2 … globals Sub it it RegisterDPH) l) in |
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183 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (INT … globals RegisterDPH (zero ?)) l) in |
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184 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (to_acc RegisterSPH)) l) in |
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185 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc RegisterSPL)) l) in |
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186 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (OP2 … globals Sub it it RegisterDPL) l) in |
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187 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (CLEAR_CARRY … globals) l) in |
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188 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (INT … globals RegisterDPL (bitvector_of_nat ? (stacksize spilled_no globals int_fun))) l) in |
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189 | 〈add_graph globals original_label (sequential (ltl_params globals) globals (MOVE … globals (to_acc RegisterSPL)) l) graph, luniv〉. |
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190 | |
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191 | definition delframe ≝ |
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192 | λspilled_no. |
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193 | λglobals. |
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194 | λint_fun. |
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195 | λgraph: graph (ltl_statement globals). |
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196 | λl. |
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197 | λoriginal_label: label. |
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198 | if eq_nat (stacksize spilled_no globals int_fun) 0 then |
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199 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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200 | 〈add_graph globals original_label (GOTO (ltl_params globals) globals l) graph, luniv〉 |
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201 | else |
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202 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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203 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc RegisterSPH)) l) in |
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204 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (OP2 … globals Addc it it RegisterSPH) l) in |
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205 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (INT … globals RegisterA (zero ?)) l) in |
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206 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc RegisterSPL)) l) in |
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207 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (OP2 … globals Add it it RegisterSPL) l) in |
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208 | 〈add_graph globals original_label (sequential (ltl_params globals) globals (INT ? globals RegisterA (bitvector_of_nat ? (stacksize spilled_no globals int_fun))) l) graph, luniv〉. |
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209 | |
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210 | definition translate_statement: |
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211 | ∀globals: list ident. ertl_internal_function globals → ∀v: valuation. |
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212 | coloured_graph v → ltl_statement_graph globals → ertl_statement globals → |
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213 | label → ((ltl_statement_graph globals) × (universe LabelTag)) ≝ |
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214 | λglobals: list ident. |
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215 | λint_fun. |
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216 | λvaluation. |
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217 | λcoloured_graph: coloured_graph valuation. |
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218 | λgraph: ltl_statement_graph globals. |
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219 | λstmt: ertl_statement globals. |
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220 | λoriginal_label: label. |
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221 | match stmt with |
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222 | [ sequential seq l ⇒ |
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223 | let luniv ≝ joint_if_luniverse globals (ertl_params globals) int_fun in |
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224 | match seq with |
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225 | [ COMMENT c ⇒ |
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226 | 〈add_graph globals original_label (sequential … (COMMENT … c) l) graph, luniv〉 |
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227 | | COST_LABEL cost_lbl ⇒ |
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228 | 〈add_graph globals original_label (sequential … (COST_LABEL … cost_lbl) l) graph, luniv〉 |
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229 | | POP r ⇒ |
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230 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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231 | let int_fun ≝ set_luniverse globals ? int_fun luniv in |
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232 | let 〈hdw, l, graph, luniv〉 ≝ write globals int_fun valuation coloured_graph graph r l fresh_lbl in |
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233 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc hdw)) l) in |
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234 | 〈add_graph globals original_label (sequential ltl_params_ globals (POP … it) l) graph, luniv〉 |
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235 | | PUSH r ⇒ |
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236 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (PUSH … globals it) l) in |
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237 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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238 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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239 | let int_fun ≝ set_luniverse globals ? int_fun luniv in |
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240 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph r (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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241 | 〈add_graph globals original_label (GOTO … fresh_lbl) graph, luniv〉 |
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242 | | COND srcr lbl_true ⇒ |
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243 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (COND … it lbl_true) l) in |
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244 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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245 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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246 | let int_fun' ≝ set_luniverse globals ? int_fun luniv in |
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247 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph srcr (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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248 | 〈add_graph globals original_label (GOTO … fresh_lbl) graph, luniv〉 |
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249 | | CALL_ID f ignore ignore' ⇒ 〈add_graph globals original_label (sequential … (CALL_ID … f ignore ignore') l) graph, luniv〉 |
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250 | | STORE addr1 addr2 srcr ⇒ |
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251 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (STORE … it it it) l) in |
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252 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (to_acc RegisterST1)) l) in |
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253 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc RegisterDPH)) l) in |
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254 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (to_acc RegisterST0)) l) in |
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255 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc RegisterDPL)) l) in |
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256 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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257 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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258 | let int_fun ≝ set_luniverse globals ? int_fun luniv in |
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259 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph addr1 (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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260 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc RegisterST0)) fresh_lbl) in |
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261 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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262 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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263 | let int_fun ≝ set_luniverse globals ? int_fun luniv in |
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264 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph addr2 (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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265 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc RegisterST1)) fresh_lbl) in |
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266 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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267 | let int_fun ≝ set_luniverse globals ? int_fun luniv in |
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268 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph srcr (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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269 | 〈add_graph globals original_label (GOTO … l) graph, luniv〉 |
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270 | | LOAD destr addr1 addr2 ⇒ |
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271 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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272 | let int_fun ≝ set_luniverse globals ? int_fun luniv in |
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273 | let 〈hdw, l, graph, luniv〉 ≝ write globals int_fun valuation coloured_graph graph destr l fresh_lbl in |
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274 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc hdw)) l) in |
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275 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (LOAD … it it it) l) in |
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276 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc RegisterDPH)) l) in |
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277 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (to_acc RegisterST0)) l) in |
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278 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc RegisterDPL)) l) in |
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279 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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280 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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281 | let int_fun ≝ set_luniverse globals ? int_fun luniv in |
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282 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph addr1 (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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283 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc RegisterST0)) fresh_lbl) in |
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284 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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285 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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286 | let int_fun ≝ set_luniverse globals ? int_fun luniv in |
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287 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph addr2 (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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288 | 〈add_graph globals original_label (GOTO … fresh_lbl) graph, luniv〉 |
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289 | | CLEAR_CARRY ⇒ 〈add_graph globals original_label (sequential … (CLEAR_CARRY …) l) graph, luniv〉 |
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290 | | SET_CARRY ⇒ 〈add_graph globals original_label (sequential … (SET_CARRY …) l) graph, luniv〉 |
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291 | | OP2 op2 destr srcr1 srcr2 ⇒ |
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292 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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293 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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294 | let 〈hdw, l, graph, luniv〉 ≝ write globals int_fun valuation coloured_graph graph destr l fresh_lbl in |
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295 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc hdw)) l) in |
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296 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (OP2 … op2 it it RegisterB) l) in |
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297 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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298 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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299 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph srcr1 (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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300 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc RegisterB)) fresh_lbl) in |
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301 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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302 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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303 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph srcr2 (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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304 | 〈add_graph globals original_label (GOTO … l) graph, luniv〉 |
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305 | | OP1 op1 destr srcr ⇒ |
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306 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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307 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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308 | let 〈hdw, l, graph, luniv〉 ≝ write globals int_fun valuation coloured_graph graph destr l fresh_lbl in |
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309 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc hdw)) l) in |
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310 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (OP1 … op1 it it) l) in |
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311 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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312 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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313 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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314 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph srcr (λhdw. sequential … (MOVE … (to_acc hdw)) l) fresh_lbl in |
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315 | 〈add_graph globals original_label (GOTO … l) graph, luniv〉 |
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316 | | INT r i ⇒ |
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317 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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318 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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319 | let 〈hdw, l, graph, luniv〉 ≝ write globals int_fun valuation coloured_graph graph r l fresh_lbl in |
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320 | 〈add_graph globals original_label (sequential ltl_params_ globals (INT … hdw i) l) graph, luniv〉 |
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321 | | MOVE pair_regs ⇒ |
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322 | let regl ≝ \fst pair_regs in |
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323 | let regr ≝ \snd pair_regs in |
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324 | match regl with |
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325 | [ pseudo p1 ⇒ |
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326 | match regr with |
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327 | [ pseudo p2 ⇒ move (spilled_no … coloured_graph) globals int_fun graph (colouring valuation coloured_graph (inl … p1)) (colouring valuation coloured_graph (inl … p2)) l original_label |
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328 | | hardware h ⇒ move (spilled_no … coloured_graph) globals int_fun graph (colouring valuation coloured_graph (inl … p1)) (decision_colour h) l original_label |
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329 | ] |
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330 | | hardware h1 ⇒ |
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331 | match regr with |
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332 | [ pseudo p ⇒ move (spilled_no … coloured_graph) globals int_fun graph (decision_colour h1) (colouring valuation coloured_graph (inl … p)) l original_label |
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333 | | hardware h2 ⇒ |
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334 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc h1)) l) in |
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335 | 〈add_graph globals original_label (sequential ltl_params_ … (MOVE … (to_acc h2)) l) graph, luniv〉 |
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336 | ] |
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337 | ] |
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338 | | ADDRESS lbl prf dpl dph ⇒ |
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339 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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340 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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341 | let 〈hdw1, l, graph, luniv〉 ≝ write globals int_fun valuation coloured_graph graph dph l fresh_lbl in |
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342 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc hdw1)) l) in |
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343 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (to_acc RegisterDPH)) l) in |
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344 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (ADDRESS … globals lbl prf it it) l) in |
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345 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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346 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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347 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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348 | let 〈hdw2, l, graph, luniv〉 ≝ write globals int_fun valuation coloured_graph graph dpl l fresh_lbl in |
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349 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc hdw2)) l) in |
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350 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (to_acc RegisterDPL)) l) in |
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351 | 〈add_graph globals original_label (sequential ltl_params_ globals (ADDRESS … lbl prf it it) l) graph, luniv〉 |
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352 | | extension ext ⇒ |
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353 | match ext with |
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354 | [ ertl_st_ext_new_frame ⇒ newframe (spilled_no … coloured_graph)globals int_fun graph l original_label |
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355 | | ertl_st_ext_del_frame ⇒ delframe (spilled_no … coloured_graph) globals int_fun graph l original_label |
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356 | | ertl_st_ext_frame_size r ⇒ |
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357 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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358 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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359 | let 〈hdw, l, graph, luniv〉 ≝ write globals int_fun valuation coloured_graph graph r l fresh_lbl in |
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360 | 〈add_graph globals original_label (sequential ltl_params_ globals (INT … hdw (bitvector_of_nat … (stacksize (spilled_no … coloured_graph) … int_fun))) l) graph, luniv〉 |
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361 | ] |
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362 | | OPACCS opaccs dacc_a_reg dacc_b_reg sacc_a_reg sacc_b_reg ⇒ |
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363 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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364 | let 〈hdw, l, graph, luniv〉 ≝ write globals int_fun valuation coloured_graph graph dacc_a_reg l fresh_lbl in |
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365 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (MOVE … (from_acc hdw)) l) in |
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366 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … (OPACCS … opaccs it it it it) l) in |
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367 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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368 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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369 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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370 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph sacc_a_reg (λhdw. sequential … globals (MOVE … globals (to_acc hdw)) l) fresh_lbl in |
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371 | let 〈l, graph, luniv〉 ≝ generate globals luniv graph (sequential … globals (MOVE … globals (from_acc RegisterB)) fresh_lbl) in |
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372 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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373 | let 〈fresh_lbl, luniv〉 ≝ fresh_label globals luniv in |
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374 | let int_fun ≝ set_luniverse globals (ertl_params globals) int_fun luniv in |
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375 | let 〈graph, luniv〉 ≝ read globals int_fun valuation coloured_graph graph sacc_b_reg (λhdw. sequential … globals (MOVE … globals (to_acc hdw)) l) fresh_lbl in |
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376 | 〈add_graph globals original_label (GOTO … globals fresh_lbl) graph, luniv〉 |
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377 | ] |
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378 | | RETURN ⇒ 〈add_graph globals original_label (RETURN ltl_params_ globals) graph, joint_if_luniverse globals (ertl_params globals) int_fun〉 |
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379 | | GOTO l ⇒ 〈add_graph globals original_label (GOTO ltl_params_ globals l) graph, joint_if_luniverse globals (ertl_params globals) int_fun〉 |
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380 | ]. |
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381 | |
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382 | definition graph_fold ≝ |
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383 | λglobals. |
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384 | λb : Type[0]. |
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385 | λf : label → ertl_statement globals → b → b. |
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386 | λgraph: graph (ertl_statement globals). |
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387 | λseed : b. |
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388 | foldi (ertl_statement globals) b ? f graph seed. |
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389 | |
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390 | definition translate_internal: ∀globals: list ident. |
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391 | ertl_internal_function globals → ltl_internal_function globals ≝ |
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392 | λglobals: list ident. |
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393 | λint_fun: ertl_internal_function globals. |
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394 | let graph ≝ (empty_map … : ltl_statement_graph globals) in |
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395 | let valuation ≝ analyse globals int_fun in |
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396 | let coloured_graph ≝ build valuation in |
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397 | let 〈graph, luniv〉 ≝ graph_fold globals ((ltl_statement_graph globals) × (universe LabelTag)) (λlabel: label. λstmt: ertl_statement globals. λgraph_luniv: (? × (universe LabelTag)). |
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398 | let 〈graph, luniv〉 ≝ graph_luniv in |
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399 | match eliminable globals (valuation label) stmt with |
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400 | [ Some successor ⇒ 〈add_graph globals label (GOTO … successor) graph, luniv〉 |
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401 | | None ⇒ |
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402 | translate_statement globals int_fun valuation coloured_graph graph stmt label |
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403 | ]) (joint_if_code globals (ertl_params globals) int_fun) 〈graph, joint_if_luniverse … int_fun〉 |
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404 | in |
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405 | match joint_if_entry … int_fun with |
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406 | [ dp entry_label entry_label_prf ⇒ |
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407 | match joint_if_exit … int_fun with |
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408 | [ dp exit_label exit_label_prf ⇒ |
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409 | mk_joint_internal_function globals (ltl_params globals) |
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410 | luniv (joint_if_runiverse … int_fun) |
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411 | it it it (joint_if_stacksize … int_fun) |
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412 | graph ? ? |
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413 | ] |
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414 | ]. |
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415 | [1: % |
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416 | [1: @entry_label |
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417 | |2: cases daemon (* XXX *) |
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418 | ] |
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419 | |2: % |
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420 | [1: @exit_label |
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421 | |2: cases daemon (* XXX *) |
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422 | ] |
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423 | ] |
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424 | qed. |
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425 | |
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426 | definition ertl_to_ltl: ertl_program → ltl_program ≝ |
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427 | λp.transform_program … p (transf_fundef … (translate_internal …)). |
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