1 | (* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *) |
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2 | (* Interpret.ma: Operational semantics for the 8051/8052 processor. *) |
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3 | (* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *) |
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4 | |
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5 | include "ASM/ASM.ma". |
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6 | include "ASM/Arithmetic.ma". |
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7 | include "ASM/BitVectorTrie.ma". |
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8 | include "basics/russell.ma". |
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9 | |
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10 | definition Time ≝ nat. |
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11 | |
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12 | inductive SerialBufferType: Type[0] ≝ |
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13 | Eight: Byte → SerialBufferType |
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14 | | Nine: Bit → Byte → SerialBufferType. |
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15 | |
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16 | inductive LineType: Type[0] ≝ |
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17 | P1: Byte → LineType |
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18 | | P3: Byte → LineType |
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19 | | SerialBuffer: SerialBufferType → LineType. |
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20 | |
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21 | (* What is a continuation, now? *) |
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22 | |
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23 | inductive SFR8051: Type[0] ≝ |
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24 | SFR_SP: SFR8051 |
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25 | | SFR_DPL: SFR8051 |
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26 | | SFR_DPH: SFR8051 |
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27 | | SFR_PCON: SFR8051 |
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28 | | SFR_TCON: SFR8051 |
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29 | | SFR_TMOD: SFR8051 |
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30 | | SFR_TL0: SFR8051 |
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31 | | SFR_TL1: SFR8051 |
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32 | | SFR_TH0: SFR8051 |
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33 | | SFR_TH1: SFR8051 |
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34 | | SFR_P1: SFR8051 |
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35 | | SFR_SCON: SFR8051 |
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36 | | SFR_SBUF: SFR8051 |
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37 | | SFR_IE: SFR8051 |
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38 | | SFR_P3: SFR8051 |
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39 | | SFR_IP: SFR8051 |
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40 | | SFR_PSW: SFR8051 |
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41 | | SFR_ACC_A: SFR8051 |
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42 | | SFR_ACC_B: SFR8051. |
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43 | |
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44 | definition sfr_8051_index ≝ |
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45 | λs: SFR8051. |
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46 | match s with |
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47 | [ SFR_SP ⇒ O |
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48 | | SFR_DPL ⇒ 1 |
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49 | | SFR_DPH ⇒ 2 |
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50 | | SFR_PCON ⇒ 3 |
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51 | | SFR_TCON ⇒ 4 |
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52 | | SFR_TMOD ⇒ 5 |
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53 | | SFR_TL0 ⇒ 6 |
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54 | | SFR_TL1 ⇒ 7 |
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55 | | SFR_TH0 ⇒ 8 |
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56 | | SFR_TH1 ⇒ 9 |
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57 | | SFR_P1 ⇒ 10 |
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58 | | SFR_SCON ⇒ 11 |
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59 | | SFR_SBUF ⇒ 12 |
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60 | | SFR_IE ⇒ 13 |
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61 | | SFR_P3 ⇒ 14 |
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62 | | SFR_IP ⇒ 15 |
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63 | | SFR_PSW ⇒ 16 |
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64 | | SFR_ACC_A ⇒ 17 |
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65 | | SFR_ACC_B ⇒ 18 |
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66 | ]. |
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67 | |
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68 | inductive SFR8052: Type[0] ≝ |
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69 | SFR_T2CON: SFR8052 |
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70 | | SFR_RCAP2L: SFR8052 |
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71 | | SFR_RCAP2H: SFR8052 |
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72 | | SFR_TL2: SFR8052 |
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73 | | SFR_TH2: SFR8052. |
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74 | |
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75 | definition sfr_8052_index ≝ |
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76 | λs: SFR8052. |
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77 | match s with |
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78 | [ SFR_T2CON ⇒ O |
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79 | | SFR_RCAP2L ⇒ 1 |
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80 | | SFR_RCAP2H ⇒ 2 |
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81 | | SFR_TL2 ⇒ 3 |
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82 | | SFR_TH2 ⇒ 4 |
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83 | ]. |
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84 | |
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85 | (* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *) |
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86 | (* Processor status. *) |
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87 | (* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *) |
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88 | record PreStatus (M: Type[0]) (code_memory: M) : Type[0] ≝ |
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89 | { |
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90 | low_internal_ram: BitVectorTrie Byte 7; |
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91 | high_internal_ram: BitVectorTrie Byte 7; |
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92 | external_ram: BitVectorTrie Byte 16; |
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93 | |
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94 | program_counter: Word; |
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95 | |
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96 | special_function_registers_8051: Vector Byte 19; |
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97 | special_function_registers_8052: Vector Byte 5; |
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98 | |
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99 | p1_latch: Byte; |
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100 | p3_latch: Byte; |
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101 | |
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102 | clock: Time |
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103 | }. |
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104 | |
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105 | definition Status ≝ PreStatus (BitVectorTrie Byte 16). |
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106 | definition PseudoStatus ≝ PreStatus (pseudo_assembly_program). |
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107 | |
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108 | lemma sfr8051_index_19: |
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109 | ∀i: SFR8051. |
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110 | sfr_8051_index i < 19. |
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111 | # i |
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112 | cases i |
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113 | normalize |
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114 | repeat (@ le_S_S) |
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115 | @ le_O_n |
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116 | qed. |
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117 | |
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118 | lemma sfr8052_index_5: |
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119 | ∀i: SFR8052. |
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120 | sfr_8052_index i < 5. |
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121 | # i |
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122 | cases i |
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123 | normalize |
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124 | repeat (@ le_S_S) |
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125 | @ le_O_n |
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126 | qed. |
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127 | |
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128 | definition set_clock ≝ |
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129 | λM: Type[0]. |
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130 | λcode_memory:M. |
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131 | λs: PreStatus M code_memory. |
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132 | λt: Time. |
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133 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
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134 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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135 | let old_external_ram ≝ external_ram ?? s in |
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136 | let old_program_counter ≝ program_counter ?? s in |
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137 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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138 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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139 | let old_p1_latch ≝ p1_latch ?? s in |
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140 | let old_p3_latch ≝ p3_latch ?? s in |
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141 | mk_PreStatus M code_memory |
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142 | old_low_internal_ram |
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143 | old_high_internal_ram |
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144 | old_external_ram |
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145 | old_program_counter |
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146 | old_special_function_registers_8051 |
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147 | old_special_function_registers_8052 |
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148 | old_p1_latch |
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149 | old_p3_latch |
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150 | t. |
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151 | |
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152 | definition set_p1_latch ≝ |
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153 | λM: Type[0]. |
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154 | λcode_memory:M. |
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155 | λs: PreStatus M code_memory. |
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156 | λb: Byte. |
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157 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
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158 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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159 | let old_external_ram ≝ external_ram ?? s in |
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160 | let old_program_counter ≝ program_counter ?? s in |
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161 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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162 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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163 | let old_p3_latch ≝ p3_latch ?? s in |
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164 | let old_clock ≝ clock ?? s in |
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165 | mk_PreStatus M code_memory |
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166 | old_low_internal_ram |
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167 | old_high_internal_ram |
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168 | old_external_ram |
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169 | old_program_counter |
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170 | old_special_function_registers_8051 |
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171 | old_special_function_registers_8052 |
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172 | b |
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173 | old_p3_latch |
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174 | old_clock. |
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175 | |
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176 | definition set_p3_latch ≝ |
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177 | λM: Type[0]. |
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178 | λcode_memory:M. |
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179 | λs: PreStatus M code_memory. |
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180 | λb: Byte. |
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181 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
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182 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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183 | let old_external_ram ≝ external_ram ?? s in |
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184 | let old_program_counter ≝ program_counter ?? s in |
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185 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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186 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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187 | let old_p1_latch ≝ p1_latch ?? s in |
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188 | let old_clock ≝ clock ?? s in |
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189 | mk_PreStatus M code_memory |
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190 | old_low_internal_ram |
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191 | old_high_internal_ram |
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192 | old_external_ram |
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193 | old_program_counter |
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194 | old_special_function_registers_8051 |
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195 | old_special_function_registers_8052 |
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196 | old_p1_latch |
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197 | b |
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198 | old_clock. |
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199 | |
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200 | definition get_8051_sfr ≝ |
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201 | λM: Type[0]. |
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202 | λcode_memory:M. |
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203 | λs: PreStatus M code_memory. |
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204 | λi: SFR8051. |
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205 | let sfr ≝ special_function_registers_8051 ?? s in |
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206 | let index ≝ sfr_8051_index i in |
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207 | get_index_v … sfr index ?. |
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208 | @ sfr8051_index_19 |
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209 | qed. |
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210 | |
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211 | definition get_8052_sfr ≝ |
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212 | λM: Type[0]. |
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213 | λcode_memory:M. |
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214 | λs: PreStatus M code_memory. |
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215 | λi: SFR8052. |
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216 | let sfr ≝ special_function_registers_8052 ?? s in |
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217 | let index ≝ sfr_8052_index i in |
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218 | get_index_v … sfr index ?. |
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219 | @ sfr8052_index_5 |
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220 | qed. |
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221 | |
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222 | definition set_8051_sfr ≝ |
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223 | λM: Type[0]. |
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224 | λcode_memory:M. |
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225 | λs: PreStatus M code_memory. |
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226 | λi: SFR8051. |
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227 | λb: Byte. |
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228 | let index ≝ sfr_8051_index i in |
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229 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
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230 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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231 | let old_external_ram ≝ external_ram ?? s in |
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232 | let old_program_counter ≝ program_counter ?? s in |
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233 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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234 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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235 | let new_special_function_registers_8051 ≝ |
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236 | set_index Byte 19 old_special_function_registers_8051 index b ? in |
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237 | let old_p1_latch ≝ p1_latch ?? s in |
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238 | let old_p3_latch ≝ p3_latch ?? s in |
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239 | let old_clock ≝ clock ?? s in |
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240 | mk_PreStatus M code_memory |
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241 | old_low_internal_ram |
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242 | old_high_internal_ram |
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243 | old_external_ram |
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244 | old_program_counter |
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245 | new_special_function_registers_8051 |
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246 | old_special_function_registers_8052 |
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247 | old_p1_latch |
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248 | old_p3_latch |
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249 | old_clock. |
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250 | @ (sfr8051_index_19 i) |
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251 | qed. |
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252 | |
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253 | definition set_8052_sfr ≝ |
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254 | λM: Type[0]. |
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255 | λcode_memory:M. |
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256 | λs: PreStatus M code_memory. |
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257 | λi: SFR8052. |
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258 | λb: Byte. |
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259 | let index ≝ sfr_8052_index i in |
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260 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
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261 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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262 | let old_external_ram ≝ external_ram ?? s in |
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263 | let old_program_counter ≝ program_counter ?? s in |
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264 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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265 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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266 | let new_special_function_registers_8052 ≝ |
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267 | set_index Byte 5 old_special_function_registers_8052 index b ? in |
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268 | let old_p1_latch ≝ p1_latch ?? s in |
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269 | let old_p3_latch ≝ p3_latch ?? s in |
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270 | let old_clock ≝ clock ?? s in |
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271 | mk_PreStatus M code_memory |
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272 | old_low_internal_ram |
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273 | old_high_internal_ram |
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274 | old_external_ram |
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275 | old_program_counter |
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276 | old_special_function_registers_8051 |
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277 | new_special_function_registers_8052 |
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278 | old_p1_latch |
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279 | old_p3_latch |
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280 | old_clock. |
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281 | @ (sfr8052_index_5 i) |
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282 | qed. |
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283 | |
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284 | definition set_program_counter ≝ |
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285 | λM: Type[0]. |
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286 | λcode_memory:M. |
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287 | λs: PreStatus M code_memory. |
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288 | λw: Word. |
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289 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
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290 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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291 | let old_external_ram ≝ external_ram ?? s in |
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292 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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293 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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294 | let old_p1_latch ≝ p1_latch ?? s in |
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295 | let old_p3_latch ≝ p3_latch ?? s in |
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296 | let old_clock ≝ clock ?? s in |
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297 | mk_PreStatus M code_memory |
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298 | old_low_internal_ram |
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299 | old_high_internal_ram |
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300 | old_external_ram |
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301 | w |
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302 | old_special_function_registers_8051 |
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303 | old_special_function_registers_8052 |
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304 | old_p1_latch |
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305 | old_p3_latch |
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306 | old_clock. |
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307 | |
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308 | definition set_code_memory ≝ |
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309 | λM,M': Type[0]. |
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310 | λcode_memory:M. |
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311 | λs: PreStatus M code_memory. |
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312 | λr: M'. |
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313 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
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314 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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315 | let old_external_ram ≝ external_ram ?? s in |
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316 | let old_program_counter ≝ program_counter ?? s in |
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317 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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318 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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319 | let old_p1_latch ≝ p1_latch ?? s in |
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320 | let old_p3_latch ≝ p3_latch ?? s in |
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321 | let old_clock ≝ clock ?? s in |
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322 | mk_PreStatus M' r |
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323 | old_low_internal_ram |
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324 | old_high_internal_ram |
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325 | old_external_ram |
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326 | old_program_counter |
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327 | old_special_function_registers_8051 |
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328 | old_special_function_registers_8052 |
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329 | old_p1_latch |
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330 | old_p3_latch |
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331 | old_clock. |
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332 | |
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333 | definition set_low_internal_ram ≝ |
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334 | λM: Type[0]. |
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335 | λcode_memory:M. |
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336 | λs: PreStatus M code_memory. |
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337 | λr: BitVectorTrie Byte 7. |
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338 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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339 | let old_external_ram ≝ external_ram ?? s in |
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340 | let old_program_counter ≝ program_counter ?? s in |
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341 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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342 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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343 | let old_p1_latch ≝ p1_latch ?? s in |
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344 | let old_p3_latch ≝ p3_latch ?? s in |
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345 | let old_clock ≝ clock ?? s in |
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346 | mk_PreStatus M code_memory |
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347 | r |
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348 | old_high_internal_ram |
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349 | old_external_ram |
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350 | old_program_counter |
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351 | old_special_function_registers_8051 |
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352 | old_special_function_registers_8052 |
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353 | old_p1_latch |
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354 | old_p3_latch |
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355 | old_clock. |
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356 | |
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357 | definition set_high_internal_ram ≝ |
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358 | λM: Type[0]. |
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359 | λcode_memory:M. |
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360 | λs: PreStatus M code_memory. |
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361 | λr: BitVectorTrie Byte 7. |
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362 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
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363 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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364 | let old_external_ram ≝ external_ram ?? s in |
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365 | let old_program_counter ≝ program_counter ?? s in |
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366 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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367 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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368 | let old_p1_latch ≝ p1_latch ?? s in |
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369 | let old_p3_latch ≝ p3_latch ?? s in |
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370 | let old_clock ≝ clock ?? s in |
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371 | mk_PreStatus M code_memory |
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372 | old_low_internal_ram |
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373 | r |
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374 | old_external_ram |
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375 | old_program_counter |
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376 | old_special_function_registers_8051 |
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377 | old_special_function_registers_8052 |
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378 | old_p1_latch |
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379 | old_p3_latch |
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380 | old_clock. |
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381 | |
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382 | definition set_external_ram ≝ |
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383 | λM: Type[0]. |
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384 | λcode_memory:M. |
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385 | λs: PreStatus M code_memory. |
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386 | λr: BitVectorTrie Byte 16. |
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387 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
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388 | let old_high_internal_ram ≝ high_internal_ram ?? s in |
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389 | let old_program_counter ≝ program_counter ?? s in |
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390 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ?? s in |
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391 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ?? s in |
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392 | let old_p1_latch ≝ p1_latch ?? s in |
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393 | let old_p3_latch ≝ p3_latch ?? s in |
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394 | let old_clock ≝ clock ?? s in |
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395 | mk_PreStatus M code_memory |
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396 | old_low_internal_ram |
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397 | old_high_internal_ram |
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398 | r |
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399 | old_program_counter |
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400 | old_special_function_registers_8051 |
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401 | old_special_function_registers_8052 |
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402 | old_p1_latch |
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403 | old_p3_latch |
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404 | old_clock. |
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405 | |
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406 | definition get_cy_flag ≝ |
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407 | λM: Type[0]. |
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408 | λcode_memory:M. |
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409 | λs: PreStatus M code_memory. |
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410 | let sfr ≝ special_function_registers_8051 ?? s in |
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411 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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412 | get_index_v bool 8 psw O ?. |
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413 | normalize |
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414 | @ (le_S_S ? ?) |
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415 | [ @ le_O_n |
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416 | | repeat (@ (le_S_S)); |
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417 | // |
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418 | ] |
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419 | qed. |
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420 | |
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421 | definition get_ac_flag ≝ |
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422 | λM: Type[0]. |
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423 | λcode_memory:M. |
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424 | λs: PreStatus M code_memory. |
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425 | let sfr ≝ special_function_registers_8051 ?? s in |
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426 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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427 | get_index_v bool 8 psw 1 ?. |
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428 | normalize |
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429 | repeat (@ (le_S_S ? ?)) |
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430 | @ le_O_n |
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431 | qed. |
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432 | |
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433 | definition get_fo_flag ≝ |
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434 | λM: Type[0]. |
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435 | λcode_memory:M. |
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436 | λs: PreStatus M code_memory. |
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437 | let sfr ≝ special_function_registers_8051 ?? s in |
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438 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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439 | get_index_v bool 8 psw 2 ?. |
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440 | normalize |
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441 | repeat (@ (le_S_S ? ?)) |
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442 | @ le_O_n |
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443 | qed. |
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444 | |
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445 | definition get_rs1_flag ≝ |
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446 | λM: Type[0]. |
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447 | λcode_memory:M. |
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448 | λs: PreStatus M code_memory. |
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449 | let sfr ≝ special_function_registers_8051 ?? s in |
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450 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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451 | get_index_v bool 8 psw 3 ?. |
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452 | normalize |
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453 | repeat (@ (le_S_S ? ?)) |
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454 | @ le_O_n |
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455 | qed. |
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456 | |
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457 | definition get_rs0_flag ≝ |
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458 | λM: Type[0]. |
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459 | λcode_memory:M. |
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460 | λs: PreStatus M code_memory. |
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461 | let sfr ≝ special_function_registers_8051 ?? s in |
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462 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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463 | get_index_v bool 8 psw 4 ?. |
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464 | normalize |
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465 | repeat (@ (le_S_S ? ?)) |
---|
466 | @ le_O_n |
---|
467 | qed. |
---|
468 | |
---|
469 | definition get_ov_flag ≝ |
---|
470 | λM: Type[0]. |
---|
471 | λcode_memory:M. |
---|
472 | λs: PreStatus M code_memory. |
---|
473 | let sfr ≝ special_function_registers_8051 ?? s in |
---|
474 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
---|
475 | get_index_v bool 8 psw 5 ?. |
---|
476 | normalize |
---|
477 | repeat (@ (le_S_S ? ?)) |
---|
478 | @ le_O_n |
---|
479 | qed. |
---|
480 | |
---|
481 | definition get_ud_flag ≝ |
---|
482 | λM: Type[0]. |
---|
483 | λcode_memory:M. |
---|
484 | λs: PreStatus M code_memory. |
---|
485 | let sfr ≝ special_function_registers_8051 ?? s in |
---|
486 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
---|
487 | get_index_v bool 8 psw 6 ?. |
---|
488 | normalize |
---|
489 | repeat (@ (le_S_S ? ?)) |
---|
490 | @ le_O_n |
---|
491 | qed. |
---|
492 | |
---|
493 | definition get_p_flag ≝ |
---|
494 | λM: Type[0]. |
---|
495 | λcode_memory:M. |
---|
496 | λs: PreStatus M code_memory. |
---|
497 | let sfr ≝ special_function_registers_8051 ?? s in |
---|
498 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
---|
499 | get_index_v bool 8 psw 7 ?. |
---|
500 | normalize |
---|
501 | repeat (@ (le_S_S ? ?)) |
---|
502 | @ le_O_n |
---|
503 | qed. |
---|
504 | |
---|
505 | definition set_flags ≝ |
---|
506 | λM: Type[0]. |
---|
507 | λcode_memory:M. |
---|
508 | λs: PreStatus M code_memory. |
---|
509 | λcy: Bit. |
---|
510 | λac: option Bit. |
---|
511 | λov: Bit. |
---|
512 | let old_cy ≝ get_index_v ?? (get_8051_sfr ?? s SFR_PSW) O ? in |
---|
513 | let old_ac ≝ get_index_v ?? (get_8051_sfr ?? s SFR_PSW) 1 ? in |
---|
514 | let old_fo ≝ get_index_v ?? (get_8051_sfr ?? s SFR_PSW) 2 ? in |
---|
515 | let old_rs1 ≝ get_index_v ?? (get_8051_sfr ?? s SFR_PSW) 3 ? in |
---|
516 | let old_rs0 ≝ get_index_v ?? (get_8051_sfr ?? s SFR_PSW) 4 ? in |
---|
517 | let old_ov ≝ get_index_v ?? (get_8051_sfr ?? s SFR_PSW) 5 ? in |
---|
518 | let old_ud ≝ get_index_v ?? (get_8051_sfr ?? s SFR_PSW) 6 ? in |
---|
519 | let old_p ≝ get_index_v ?? (get_8051_sfr ?? s SFR_PSW) 7 ? in |
---|
520 | let new_ac ≝ match ac with [ None ⇒ old_ac | Some j ⇒ j ] in |
---|
521 | set_8051_sfr ?? s SFR_PSW |
---|
522 | [[ old_cy ; new_ac ; old_fo ; old_rs1 ; |
---|
523 | old_rs0 ; old_ov ; old_ud ; old_p ]]. |
---|
524 | [1,2,3,4,5,6,7,8: |
---|
525 | normalize |
---|
526 | repeat (@ le_S_S) |
---|
527 | @ le_O_n |
---|
528 | ] |
---|
529 | qed. |
---|
530 | |
---|
531 | definition initialise_status ≝ |
---|
532 | λM: Type[0]. |
---|
533 | λcode_mem: M. |
---|
534 | let status ≝ mk_PreStatus M code_mem (* Code mem. *) |
---|
535 | (Stub Byte 7) (* Low mem. *) |
---|
536 | (Stub Byte 7) (* High mem. *) |
---|
537 | (Stub Byte 16) (* Ext mem. *) |
---|
538 | (zero 16) (* PC. *) |
---|
539 | (replicate Byte 19 (zero 8)) (* 8051 SFR. *) |
---|
540 | (replicate Byte 5 (zero 8)) (* 8052 SFR. *) |
---|
541 | (zero 8) (* P1 latch. *) |
---|
542 | (zero 8) (* P3 latch. *) |
---|
543 | O (* Clock. *) |
---|
544 | in |
---|
545 | set_8051_sfr ?? status SFR_SP (bitvector_of_nat 8 7). |
---|
546 | |
---|
547 | definition get_bit_addressable_sfr ≝ |
---|
548 | λM: Type[0]. |
---|
549 | λcode_memory:M. |
---|
550 | λs: PreStatus M code_memory. |
---|
551 | λn: nat. |
---|
552 | λb: BitVector n. |
---|
553 | λl: bool. |
---|
554 | let address ≝ nat_of_bitvector … b in |
---|
555 | if (eqb address 128) then |
---|
556 | ? |
---|
557 | else if (eqb address 144) then |
---|
558 | if l then |
---|
559 | (p1_latch ?? s) |
---|
560 | else |
---|
561 | (get_8051_sfr ?? s SFR_P1) |
---|
562 | else if (eqb address 160) then |
---|
563 | ? |
---|
564 | else if (eqb address 176) then |
---|
565 | if l then |
---|
566 | (p3_latch ?? s) |
---|
567 | else |
---|
568 | (get_8051_sfr ?? s SFR_P3) |
---|
569 | else if (eqb address 153) then |
---|
570 | get_8051_sfr ?? s SFR_SBUF |
---|
571 | else if (eqb address 138) then |
---|
572 | get_8051_sfr ?? s SFR_TL0 |
---|
573 | else if (eqb address 139) then |
---|
574 | get_8051_sfr ?? s SFR_TL1 |
---|
575 | else if (eqb address 140) then |
---|
576 | get_8051_sfr ?? s SFR_TH0 |
---|
577 | else if (eqb address 141) then |
---|
578 | get_8051_sfr ?? s SFR_TH1 |
---|
579 | else if (eqb address 200) then |
---|
580 | get_8052_sfr ?? s SFR_T2CON |
---|
581 | else if (eqb address 202) then |
---|
582 | get_8052_sfr ?? s SFR_RCAP2L |
---|
583 | else if (eqb address 203) then |
---|
584 | get_8052_sfr ?? s SFR_RCAP2H |
---|
585 | else if (eqb address 204) then |
---|
586 | get_8052_sfr ?? s SFR_TL2 |
---|
587 | else if (eqb address 205) then |
---|
588 | get_8052_sfr ?? s SFR_TH2 |
---|
589 | else if (eqb address 135) then |
---|
590 | get_8051_sfr ?? s SFR_PCON |
---|
591 | else if (eqb address 136) then |
---|
592 | get_8051_sfr ?? s SFR_TCON |
---|
593 | else if (eqb address 137) then |
---|
594 | get_8051_sfr ?? s SFR_TMOD |
---|
595 | else if (eqb address 152) then |
---|
596 | get_8051_sfr ?? s SFR_SCON |
---|
597 | else if (eqb address 168) then |
---|
598 | get_8051_sfr ?? s SFR_IE |
---|
599 | else if (eqb address 184) then |
---|
600 | get_8051_sfr ?? s SFR_IP |
---|
601 | else if (eqb address 129) then |
---|
602 | get_8051_sfr ?? s SFR_SP |
---|
603 | else if (eqb address 130) then |
---|
604 | get_8051_sfr ?? s SFR_DPL |
---|
605 | else if (eqb address 131) then |
---|
606 | get_8051_sfr ?? s SFR_DPH |
---|
607 | else if (eqb address 208) then |
---|
608 | get_8051_sfr ?? s SFR_PSW |
---|
609 | else if (eqb address 224) then |
---|
610 | get_8051_sfr ?? s SFR_ACC_A |
---|
611 | else if (eqb address 240) then |
---|
612 | get_8051_sfr ?? s SFR_ACC_B |
---|
613 | else |
---|
614 | ?. |
---|
615 | cases not_implemented |
---|
616 | qed. |
---|
617 | |
---|
618 | definition set_bit_addressable_sfr ≝ |
---|
619 | λM: Type[0]. |
---|
620 | λcode_memory:M. |
---|
621 | λs: PreStatus M code_memory. |
---|
622 | λb: Byte. |
---|
623 | λv: Byte. |
---|
624 | let address ≝ nat_of_bitvector … b in |
---|
625 | if (eqb address 128) then |
---|
626 | ? |
---|
627 | else if (eqb address 144) then |
---|
628 | let status_1 ≝ set_8051_sfr ?? s SFR_P1 v in |
---|
629 | let status_2 ≝ set_p1_latch ?? s v in |
---|
630 | status_2 |
---|
631 | else if (eqb address 160) then |
---|
632 | ? |
---|
633 | else if (eqb address 176) then |
---|
634 | let status_1 ≝ set_8051_sfr ?? s SFR_P3 v in |
---|
635 | let status_2 ≝ set_p3_latch ?? s v in |
---|
636 | status_2 |
---|
637 | else if (eqb address 153) then |
---|
638 | set_8051_sfr ?? s SFR_SBUF v |
---|
639 | else if (eqb address 138) then |
---|
640 | set_8051_sfr ?? s SFR_TL0 v |
---|
641 | else if (eqb address 139) then |
---|
642 | set_8051_sfr ?? s SFR_TL1 v |
---|
643 | else if (eqb address 140) then |
---|
644 | set_8051_sfr ?? s SFR_TH0 v |
---|
645 | else if (eqb address 141) then |
---|
646 | set_8051_sfr ?? s SFR_TH1 v |
---|
647 | else if (eqb address 200) then |
---|
648 | set_8052_sfr ?? s SFR_T2CON v |
---|
649 | else if (eqb address 202) then |
---|
650 | set_8052_sfr ?? s SFR_RCAP2L v |
---|
651 | else if (eqb address 203) then |
---|
652 | set_8052_sfr ?? s SFR_RCAP2H v |
---|
653 | else if (eqb address 204) then |
---|
654 | set_8052_sfr ?? s SFR_TL2 v |
---|
655 | else if (eqb address 205) then |
---|
656 | set_8052_sfr ?? s SFR_TH2 v |
---|
657 | else if (eqb address 135) then |
---|
658 | set_8051_sfr ?? s SFR_PCON v |
---|
659 | else if (eqb address 136) then |
---|
660 | set_8051_sfr ?? s SFR_TCON v |
---|
661 | else if (eqb address 137) then |
---|
662 | set_8051_sfr ?? s SFR_TMOD v |
---|
663 | else if (eqb address 152) then |
---|
664 | set_8051_sfr ?? s SFR_SCON v |
---|
665 | else if (eqb address 168) then |
---|
666 | set_8051_sfr ?? s SFR_IE v |
---|
667 | else if (eqb address 184) then |
---|
668 | set_8051_sfr ?? s SFR_IP v |
---|
669 | else if (eqb address 129) then |
---|
670 | set_8051_sfr ?? s SFR_SP v |
---|
671 | else if (eqb address 130) then |
---|
672 | set_8051_sfr ?? s SFR_DPL v |
---|
673 | else if (eqb address 131) then |
---|
674 | set_8051_sfr ?? s SFR_DPH v |
---|
675 | else if (eqb address 208) then |
---|
676 | set_8051_sfr ?? s SFR_PSW v |
---|
677 | else if (eqb address 224) then |
---|
678 | set_8051_sfr ?? s SFR_ACC_A v |
---|
679 | else if (eqb address 240) then |
---|
680 | set_8051_sfr ?? s SFR_ACC_B v |
---|
681 | else |
---|
682 | ?. |
---|
683 | cases not_implemented |
---|
684 | qed. |
---|
685 | |
---|
686 | definition bit_address_of_register ≝ |
---|
687 | λM: Type[0]. |
---|
688 | λcode_memory:M. |
---|
689 | λs: PreStatus M code_memory. |
---|
690 | λr: BitVector 3. |
---|
691 | let b ≝ get_index_v … r O ? in |
---|
692 | let c ≝ get_index_v … r 1 ? in |
---|
693 | let d ≝ get_index_v … r 2 ? in |
---|
694 | let 〈 un, ln 〉 ≝ split ? 4 4 (get_8051_sfr ?? s SFR_PSW) in |
---|
695 | let 〈 r1, r0 〉 ≝ 〈 get_index_v … 4 un 2 ?, get_index_v … 4 un 3 ? 〉 in |
---|
696 | let offset ≝ |
---|
697 | if ¬r1 ∧ ¬r0 then |
---|
698 | O |
---|
699 | else if ¬r1 ∧ r0 then |
---|
700 | 8 |
---|
701 | else if r1 ∧ r0 then |
---|
702 | 24 |
---|
703 | else |
---|
704 | 16 |
---|
705 | in |
---|
706 | bitvector_of_nat 7 (offset + (nat_of_bitvector ? [[ false ; b ; c ; d ]])). |
---|
707 | [1,2,3,4,5: |
---|
708 | normalize |
---|
709 | repeat (@ le_S_S) |
---|
710 | @ le_O_n; |
---|
711 | ] |
---|
712 | qed. |
---|
713 | |
---|
714 | definition get_register ≝ |
---|
715 | λM: Type[0]. |
---|
716 | λcode_memory:M. |
---|
717 | λs: PreStatus M code_memory. |
---|
718 | λr: BitVector 3. |
---|
719 | let address ≝ bit_address_of_register … s r in |
---|
720 | lookup ?? address (low_internal_ram … s) (zero 8). |
---|
721 | |
---|
722 | definition set_register ≝ |
---|
723 | λM: Type[0]. |
---|
724 | λcode_memory:M. |
---|
725 | λs: PreStatus M code_memory. |
---|
726 | λr: BitVector 3. |
---|
727 | λv: Byte. |
---|
728 | let address ≝ bit_address_of_register … s r in |
---|
729 | let old_low_internal_ram ≝ low_internal_ram ?? s in |
---|
730 | let new_low_internal_ram ≝ insert … address v old_low_internal_ram in |
---|
731 | set_low_internal_ram … s new_low_internal_ram. |
---|
732 | |
---|
733 | definition read_at_stack_pointer ≝ |
---|
734 | λM: Type[0]. |
---|
735 | λcode_memory:M. |
---|
736 | λs: PreStatus M code_memory. |
---|
737 | let 〈 nu, nl 〉 ≝ split ? 4 4 (get_8051_sfr ?? s SFR_SP) in |
---|
738 | let m ≝ get_index_v ?? nu O ? in |
---|
739 | let r1 ≝ get_index_v ?? nu 1 ? in |
---|
740 | let r2 ≝ get_index_v ?? nu 2 ? in |
---|
741 | let r3 ≝ get_index_v ?? nu 3 ? in |
---|
742 | let address ≝ [[ r1 ; r2 ; r3 ]] @@ nl in |
---|
743 | let memory ≝ |
---|
744 | if m then |
---|
745 | (low_internal_ram ?? s) |
---|
746 | else |
---|
747 | (high_internal_ram ?? s) |
---|
748 | in |
---|
749 | lookup … address memory (zero 8). |
---|
750 | [1,2,3,4: |
---|
751 | normalize |
---|
752 | repeat (@ le_S_S) |
---|
753 | @ le_O_n |
---|
754 | ] |
---|
755 | qed. |
---|
756 | |
---|
757 | definition write_at_stack_pointer ≝ |
---|
758 | λM: Type[0]. |
---|
759 | λcode_memory:M. |
---|
760 | λs: PreStatus M code_memory. |
---|
761 | λv: Byte. |
---|
762 | let 〈 nu, nl 〉 ≝ split … 4 4 (get_8051_sfr ?? s SFR_SP) in |
---|
763 | let bit_zero ≝ get_index_v ?? nu O ? in |
---|
764 | let bit_1 ≝ get_index_v ?? nu 1 ? in |
---|
765 | let bit_2 ≝ get_index_v ?? nu 2 ? in |
---|
766 | let bit_3 ≝ get_index_v ?? nu 3 ? in |
---|
767 | if bit_zero then |
---|
768 | let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl) |
---|
769 | v (low_internal_ram ?? s) in |
---|
770 | set_low_internal_ram ?? s memory |
---|
771 | else |
---|
772 | let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl) |
---|
773 | v (high_internal_ram ?? s) in |
---|
774 | set_high_internal_ram ?? s memory. |
---|
775 | [1,2,3,4: |
---|
776 | normalize |
---|
777 | repeat (@ le_S_S) |
---|
778 | @ le_O_n |
---|
779 | ] |
---|
780 | qed. |
---|
781 | |
---|
782 | definition set_arg_16': ∀M: Type[0]. ∀code_memory:M. ∀s:PreStatus M code_memory. Word → [[ dptr ]] → Σs':PreStatus M code_memory. clock ?? s = clock ?? s' ≝ |
---|
783 | λM,code_memory,s,v,a. |
---|
784 | match a return λx. bool_to_Prop (is_in ? [[ dptr ]] x) → Σs'. clock M ? s = clock M ? s' with |
---|
785 | [ DPTR ⇒ λ_:True. |
---|
786 | let 〈 bu, bl 〉 ≝ split … 8 8 v in |
---|
787 | let status ≝ set_8051_sfr … s SFR_DPH bu in |
---|
788 | let status ≝ set_8051_sfr … status SFR_DPL bl in |
---|
789 | status |
---|
790 | | _ ⇒ λK. |
---|
791 | match K in False with |
---|
792 | [ |
---|
793 | ] |
---|
794 | ] (subaddressing_modein … a). |
---|
795 | // |
---|
796 | qed. |
---|
797 | |
---|
798 | definition set_arg_16: ∀M: Type[0]. ∀code_memory:M. ∀s:PreStatus M code_memory. Word → [[ dptr ]] → PreStatus M code_memory ≝ |
---|
799 | set_arg_16'. |
---|
800 | |
---|
801 | lemma set_arg_16_ok: ∀M,cm,s,v,x. clock M cm s = clock M cm (set_arg_16 M cm s v x). |
---|
802 | #M #cm #s #x #v whd in match set_arg_16; normalize nodelta @pi2 |
---|
803 | qed. |
---|
804 | |
---|
805 | |
---|
806 | definition get_arg_16: ∀M: Type[0]. ∀code_memory:M. PreStatus M code_memory → [[ data16 ]] → Word ≝ |
---|
807 | λm, cm, s, a. |
---|
808 | match a return λx. bool_to_Prop (is_in ? [[ data16 ]] x) → ? with |
---|
809 | [ DATA16 d ⇒ λ_:True. d |
---|
810 | | _ ⇒ λK. |
---|
811 | match K in False with |
---|
812 | [ |
---|
813 | ] |
---|
814 | ] (subaddressing_modein … a). |
---|
815 | |
---|
816 | definition get_arg_8: ∀M: Type[0]. ∀code_memory:M. PreStatus M code_memory → bool → [[ direct ; indirect ; registr ; |
---|
817 | acc_a ; acc_b ; data ; acc_dptr ; |
---|
818 | acc_pc ; ext_indirect ; |
---|
819 | ext_indirect_dptr ]] → Byte ≝ |
---|
820 | λm, cm, s, l, a. |
---|
821 | match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; registr ; |
---|
822 | acc_a ; acc_b ; data ; acc_dptr ; |
---|
823 | acc_pc ; ext_indirect ; |
---|
824 | ext_indirect_dptr ]] x) → ? with |
---|
825 | [ ACC_A ⇒ λacc_a: True. get_8051_sfr ?? s SFR_ACC_A |
---|
826 | | ACC_B ⇒ λacc_b: True. get_8051_sfr ?? s SFR_ACC_B |
---|
827 | | DATA d ⇒ λdata: True. d |
---|
828 | | REGISTER r ⇒ λregister: True. get_register ?? s r |
---|
829 | | EXT_INDIRECT_DPTR ⇒ |
---|
830 | λext_indirect_dptr: True. |
---|
831 | let address ≝ (get_8051_sfr ?? s SFR_DPH) @@ (get_8051_sfr ?? s SFR_DPL) in |
---|
832 | lookup ? 16 address (external_ram ?? s) (zero 8) |
---|
833 | | EXT_INDIRECT e ⇒ |
---|
834 | λext_indirect: True. |
---|
835 | let address ≝ get_register ?? s [[ false; false; e ]] in |
---|
836 | let padded_address ≝ pad 8 8 address in |
---|
837 | lookup ? 16 padded_address (external_ram ?? s) (zero 8) |
---|
838 | | ACC_DPTR ⇒ |
---|
839 | λacc_dptr: True. |
---|
840 | let dptr ≝ (get_8051_sfr ?? s SFR_DPH) @@ (get_8051_sfr ?? s SFR_DPL) in |
---|
841 | let padded_acc ≝ pad 8 8 (get_8051_sfr ?? s SFR_ACC_A) in |
---|
842 | let 〈 carry, address 〉 ≝ half_add 16 dptr padded_acc in |
---|
843 | lookup ? 16 address (external_ram ?? s) (zero 8) |
---|
844 | | ACC_PC ⇒ |
---|
845 | λacc_pc: True. |
---|
846 | let padded_acc ≝ pad 8 8 (get_8051_sfr ?? s SFR_ACC_A) in |
---|
847 | let 〈 carry, address 〉 ≝ half_add 16 (program_counter ?? s) padded_acc in |
---|
848 | lookup ? 16 address (external_ram ?? s) (zero 8) |
---|
849 | | DIRECT d ⇒ |
---|
850 | λdirect: True. |
---|
851 | let 〈 nu, nl 〉 ≝ split ? 4 4 d in |
---|
852 | let bit_one ≝ get_index_v ? ? nu 0 ? in |
---|
853 | let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in |
---|
854 | match bit_one with |
---|
855 | [ false ⇒ |
---|
856 | let address ≝ three_bits @@ nl in |
---|
857 | lookup ? 7 address (low_internal_ram ?? s) (zero 8) |
---|
858 | | true ⇒ get_bit_addressable_sfr ?? s 8 d l |
---|
859 | ] |
---|
860 | | INDIRECT i ⇒ |
---|
861 | λindirect: True. |
---|
862 | let 〈 nu, nl 〉 ≝ split ? 4 4 (get_register ?? s [[ false; false; i]]) in |
---|
863 | let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in |
---|
864 | let bit_1 ≝ get_index_v ?? bit_one_v O ? in |
---|
865 | match bit_1 with |
---|
866 | [ false ⇒ |
---|
867 | lookup ? 7 (three_bits @@ nl) (low_internal_ram ?? s) (zero 8) |
---|
868 | | true ⇒ |
---|
869 | lookup ? 7 (three_bits @@ nl) (high_internal_ram ?? s) (zero 8) |
---|
870 | ] |
---|
871 | | _ ⇒ λother. |
---|
872 | match other in False with [ ] |
---|
873 | ] (subaddressing_modein … a). |
---|
874 | [1,2: |
---|
875 | normalize |
---|
876 | repeat (@ le_S_S) |
---|
877 | @ le_O_n |
---|
878 | ] |
---|
879 | qed. |
---|
880 | |
---|
881 | axiom clock_set_bit_addressable_sfr: ∀m,cm,s,d,v. clock m cm s = clock … (set_bit_addressable_sfr … s d v). |
---|
882 | |
---|
883 | definition set_arg_8': ∀M: Type[0]. ∀code_memory:M. ∀s:PreStatus M code_memory. [[ direct ; indirect ; registr ; |
---|
884 | acc_a ; acc_b ; ext_indirect ; |
---|
885 | ext_indirect_dptr ]] → Byte → Σs':PreStatus M code_memory. |
---|
886 | clock … code_memory s = clock … code_memory s' ≝ |
---|
887 | λm, cm, s, a, v. |
---|
888 | match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; registr ; |
---|
889 | acc_a ; acc_b ; ext_indirect ; |
---|
890 | ext_indirect_dptr ]] x) → |
---|
891 | Σs':PreStatus m cm. clock m cm s = clock m cm s' |
---|
892 | (*CSC: bug here if one specified the two clock above*) |
---|
893 | with |
---|
894 | [ DIRECT d ⇒ |
---|
895 | λdirect: True. |
---|
896 | let 〈 nu, nl 〉 ≝ split … 4 4 d in |
---|
897 | let bit_one ≝ get_index_v ? ? nu 0 ? in |
---|
898 | let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in |
---|
899 | match bit_one with |
---|
900 | [ true ⇒ set_bit_addressable_sfr ?? s d v |
---|
901 | | false ⇒ |
---|
902 | let memory ≝ insert ? 7 (three_bits @@ nl) v (low_internal_ram ?? s) in |
---|
903 | set_low_internal_ram ?? s memory |
---|
904 | ] |
---|
905 | | INDIRECT i ⇒ |
---|
906 | λindirect: True. |
---|
907 | let register ≝ get_register ?? s [[ false; false; i ]] in |
---|
908 | let 〈nu, nl〉 ≝ split ? 4 4 register in |
---|
909 | let bit_1 ≝ get_index_v … nu 0 ? in |
---|
910 | let 〈ignore, three_bits〉 ≝ split ? 1 3 nu in |
---|
911 | match bit_1 with |
---|
912 | [ false ⇒ |
---|
913 | let memory ≝ insert … (three_bits @@ nl) v (low_internal_ram ?? s) in |
---|
914 | set_low_internal_ram ?? s memory |
---|
915 | | true ⇒ |
---|
916 | let memory ≝ insert … (three_bits @@ nl) v (high_internal_ram ?? s) in |
---|
917 | set_high_internal_ram ?? s memory |
---|
918 | ] |
---|
919 | | REGISTER r ⇒ λregister: True. set_register ?? s r v |
---|
920 | | ACC_A ⇒ λacc_a: True. set_8051_sfr ?? s SFR_ACC_A v |
---|
921 | | ACC_B ⇒ λacc_b: True. set_8051_sfr ?? s SFR_ACC_B v |
---|
922 | | EXT_INDIRECT e ⇒ |
---|
923 | λext_indirect: True. |
---|
924 | let address ≝ get_register ?? s [[ false; false; e ]] in |
---|
925 | let padded_address ≝ pad 8 8 address in |
---|
926 | let memory ≝ insert ? 16 padded_address v (external_ram ?? s) in |
---|
927 | set_external_ram ?? s memory |
---|
928 | | EXT_INDIRECT_DPTR ⇒ |
---|
929 | λext_indirect_dptr: True. |
---|
930 | let address ≝ (get_8051_sfr ?? s SFR_DPH) @@ (get_8051_sfr ?? s SFR_DPL) in |
---|
931 | let memory ≝ insert ? 16 address v (external_ram ?? s) in |
---|
932 | set_external_ram ?? s memory |
---|
933 | | _ ⇒ |
---|
934 | λother: False. |
---|
935 | match other in False with [ ] |
---|
936 | ] (subaddressing_modein … a). |
---|
937 | // qed. |
---|
938 | |
---|
939 | definition set_arg_8: ∀M: Type[0]. ∀code_memory:M. ∀s:PreStatus M code_memory. [[ direct ; indirect ; registr ; acc_a ; acc_b ; ext_indirect ; ext_indirect_dptr ]] → Byte → PreStatus M code_memory ≝ |
---|
940 | set_arg_8'. |
---|
941 | |
---|
942 | lemma set_arg_8_ok: ∀M,cm,s,x,v. clock M cm s = clock … (set_arg_8 M cm s x v). |
---|
943 | #M #cm #s #x #v whd in match set_arg_8; normalize nodelta @pi2 |
---|
944 | qed. |
---|
945 | |
---|
946 | theorem modulus_less_than: |
---|
947 | ∀m,n: nat. (m mod (S n)) < S n. |
---|
948 | #n #m |
---|
949 | normalize |
---|
950 | @ le_S_S |
---|
951 | lapply (le_n n) |
---|
952 | generalize in ⊢ (?%? → ?(??%?)?); |
---|
953 | elim n in ⊢ (∀_:?. ??% → ?(?%??)?); |
---|
954 | [ normalize |
---|
955 | #n |
---|
956 | @ (less_than_or_equal_b_elim n m) |
---|
957 | normalize |
---|
958 | [ // |
---|
959 | | #H #K |
---|
960 | @(le_inv_ind ?? K …) |
---|
961 | [ # H1 |
---|
962 | < H1 |
---|
963 | // |
---|
964 | | #x #H1 #H2 #H3 |
---|
965 | destruct |
---|
966 | ] |
---|
967 | ] |
---|
968 | | normalize |
---|
969 | # y # H1 # n # H2 |
---|
970 | @ (less_than_or_equal_b_elim n m) |
---|
971 | normalize |
---|
972 | [ // |
---|
973 | | # K |
---|
974 | @ H1 |
---|
975 | cut (n ≤ S y → n - S m ≤ y) |
---|
976 | /2 by/ |
---|
977 | cases n |
---|
978 | normalize |
---|
979 | // |
---|
980 | # x # K1 |
---|
981 | lapply (le_S_S_to_le … K1) |
---|
982 | generalize in match m; |
---|
983 | elim x |
---|
984 | normalize |
---|
985 | // |
---|
986 | # w1 # H # m |
---|
987 | cases m |
---|
988 | normalize |
---|
989 | // |
---|
990 | # q # K2 |
---|
991 | @H |
---|
992 | /3/ |
---|
993 | ] |
---|
994 | ] |
---|
995 | qed. |
---|
996 | |
---|
997 | definition get_arg_1: ∀M: Type[0]. ∀code_memory:M. PreStatus M code_memory → [[ bit_addr ; n_bit_addr ; carry ]] → |
---|
998 | bool → bool ≝ |
---|
999 | λm, cm, s, a, l. |
---|
1000 | match a return λx. bool_to_Prop (is_in ? [[ bit_addr ; |
---|
1001 | n_bit_addr ; |
---|
1002 | carry ]] x) → ? with |
---|
1003 | [ BIT_ADDR b ⇒ |
---|
1004 | λbit_addr: True. |
---|
1005 | let 〈 nu, nl 〉 ≝ split … 4 4 b in |
---|
1006 | let bit_1 ≝ get_index_v ? ? nu 0 ? in |
---|
1007 | let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in |
---|
1008 | match bit_1 with |
---|
1009 | [ true ⇒ |
---|
1010 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
1011 | let d ≝ address ÷ 8 in |
---|
1012 | let m ≝ address mod 8 in |
---|
1013 | let trans ≝ bitvector_of_nat 8 ((d * 8) + 128) in |
---|
1014 | let sfr ≝ get_bit_addressable_sfr ?? s ? trans l in |
---|
1015 | get_index_v … sfr m ? |
---|
1016 | | false ⇒ |
---|
1017 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
1018 | let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in |
---|
1019 | let t ≝ lookup … 7 address' (low_internal_ram ?? s) (zero 8) in |
---|
1020 | get_index_v … t (modulus address 8) ? |
---|
1021 | ] |
---|
1022 | | N_BIT_ADDR n ⇒ |
---|
1023 | λn_bit_addr: True. |
---|
1024 | let 〈 nu, nl 〉 ≝ split … 4 4 n in |
---|
1025 | let bit_1 ≝ get_index_v ? ? nu 0 ? in |
---|
1026 | let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in |
---|
1027 | match bit_1 with |
---|
1028 | [ true ⇒ |
---|
1029 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
1030 | let d ≝ address ÷ 8 in |
---|
1031 | let m ≝ address mod 8 in |
---|
1032 | let trans ≝ bitvector_of_nat 8 ((d * 8) + 128) in |
---|
1033 | let sfr ≝ get_bit_addressable_sfr ?? s ? trans l in |
---|
1034 | ¬(get_index_v … sfr m ?) |
---|
1035 | | false ⇒ |
---|
1036 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
1037 | let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in |
---|
1038 | let trans ≝ lookup ? 7 address' (low_internal_ram ?? s) (zero 8) in |
---|
1039 | ¬(get_index_v … trans (modulus address 8) ?) |
---|
1040 | ] |
---|
1041 | | CARRY ⇒ λcarry: True. get_cy_flag ?? s |
---|
1042 | | _ ⇒ λother. |
---|
1043 | match other in False with [ ] |
---|
1044 | ] (subaddressing_modein … a). |
---|
1045 | [3,6: |
---|
1046 | normalize |
---|
1047 | repeat (@ le_S_S) |
---|
1048 | @ le_O_n |
---|
1049 | |1,2,4,5: |
---|
1050 | @modulus_less_than |
---|
1051 | ] |
---|
1052 | qed. |
---|
1053 | |
---|
1054 | definition set_arg_1': ∀M: Type[0]. ∀code_memory:M. ∀s:PreStatus M code_memory. [[bit_addr; carry]] → Bit → Σs':PreStatus M code_memory. clock ? code_memory s = clock ? code_memory s' ≝ |
---|
1055 | λm: Type[0]. |
---|
1056 | λcm. |
---|
1057 | λs: PreStatus m cm. |
---|
1058 | λa: [[bit_addr; carry]]. |
---|
1059 | λv: Bit. |
---|
1060 | match a return λx. bool_to_Prop (is_in ? [[bit_addr ; carry]] x) → Σs'. clock m cm s = clock m cm s' with |
---|
1061 | [ BIT_ADDR b ⇒ λbit_addr: True. |
---|
1062 | let 〈nu, nl〉 ≝ split ? 4 4 (get_8051_sfr ?? s SFR_PSW) in |
---|
1063 | let bit_1 ≝ get_index_v ?? nu 0 ? in |
---|
1064 | let 〈ignore, three_bits〉 ≝ split ? 1 3 nu in |
---|
1065 | match bit_1 return λ_. ? with |
---|
1066 | [ true ⇒ |
---|
1067 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
1068 | let d ≝ address ÷ 8 in |
---|
1069 | let m ≝ address mod 8 in |
---|
1070 | let t ≝ bitvector_of_nat 8 ((d * 8) + 128) in |
---|
1071 | let sfr ≝ get_bit_addressable_sfr ?? s ? t true in |
---|
1072 | let new_sfr ≝ set_index … sfr m v ? in |
---|
1073 | set_bit_addressable_sfr ?? s new_sfr t |
---|
1074 | | false ⇒ |
---|
1075 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
1076 | let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in |
---|
1077 | let t ≝ lookup ? 7 address' (low_internal_ram ?? s) (zero 8) in |
---|
1078 | let n_bit ≝ set_index … t (modulus address 8) v ? in |
---|
1079 | let memory ≝ insert ? 7 address' n_bit (low_internal_ram ?? s) in |
---|
1080 | set_low_internal_ram ?? s memory |
---|
1081 | ] |
---|
1082 | | CARRY ⇒ |
---|
1083 | λcarry: True. |
---|
1084 | let 〈nu, nl〉 ≝ split ? 4 4 (get_8051_sfr ?? s SFR_PSW) in |
---|
1085 | let bit_1 ≝ get_index_v… nu 1 ? in |
---|
1086 | let bit_2 ≝ get_index_v… nu 2 ? in |
---|
1087 | let bit_3 ≝ get_index_v… nu 3 ? in |
---|
1088 | let new_psw ≝ [[ v; bit_1 ; bit_2; bit_3 ]] @@ nl in |
---|
1089 | set_8051_sfr ?? s SFR_PSW new_psw |
---|
1090 | | _ ⇒ |
---|
1091 | λother: False. |
---|
1092 | match other in False with |
---|
1093 | [ ] |
---|
1094 | ] (subaddressing_modein … a). |
---|
1095 | try (repeat @le_S_S @le_O_n) |
---|
1096 | /by/ |
---|
1097 | qed. |
---|
1098 | |
---|
1099 | definition set_arg_1: ∀M: Type[0]. ∀code_memory:M. PreStatus M code_memory → [[bit_addr; carry]] → Bit → PreStatus M code_memory ≝ set_arg_1'. |
---|
1100 | |
---|
1101 | lemma set_arg_1_ok: ∀M,cm,s,x,v. clock M cm s = clock … (set_arg_1 M cm s x v). |
---|
1102 | #M #cm #s #x #v whd in match set_arg_1; normalize nodelta @pi2 |
---|
1103 | qed. |
---|
1104 | |
---|
1105 | definition load_code_memory ≝ |
---|
1106 | fold_left_i … ( |
---|
1107 | λi, mem, v. |
---|
1108 | insert … (bitvector_of_nat … i) v mem) (Stub Byte 16). |
---|
1109 | |
---|
1110 | definition load ≝ |
---|
1111 | λl,cm. |
---|
1112 | λstatus. |
---|
1113 | set_code_memory (BitVectorTrie Word 16) ? cm status (load_code_memory l). |
---|
1114 | |
---|
1115 | definition fetch_pseudo_instruction: list labelled_instruction → Word → (pseudo_instruction × Word) ≝ |
---|
1116 | λcode_mem. |
---|
1117 | λpc: Word. |
---|
1118 | let 〈lbl, instr〉 ≝ nth (nat_of_bitvector ? pc) … code_mem ? in |
---|
1119 | let 〈flags, new_pc〉 ≝ half_add ? pc (bitvector_of_nat ? 1) in |
---|
1120 | 〈instr, new_pc〉. |
---|
1121 | cases not_implemented. |
---|
1122 | qed. |
---|
1123 | |
---|
1124 | lemma snd_fetch_pseudo_instruction: |
---|
1125 | ∀l,ppc. \snd (fetch_pseudo_instruction l ppc) = \snd (half_add ? ppc (bitvector_of_nat ? 1)). |
---|
1126 | #l #ppc whd in ⊢ (??(???%)?); @pair_elim |
---|
1127 | #lft #rgt @pair_elim #x #y #_ #_ % |
---|
1128 | qed. |
---|
1129 | |
---|
1130 | definition instruction_matches_identifier ≝ |
---|
1131 | λy: Identifier. |
---|
1132 | λx: labelled_instruction. |
---|
1133 | match \fst x with |
---|
1134 | [ None ⇒ false |
---|
1135 | | Some x ⇒ eq_identifier ? x y |
---|
1136 | ]. |
---|
1137 | |
---|
1138 | let rec does_not_occur (id:Identifier) (l:list labelled_instruction) on l: bool ≝ |
---|
1139 | match l with |
---|
1140 | [ nil ⇒ true |
---|
1141 | | cons hd tl ⇒ notb (instruction_matches_identifier id hd) ∧ does_not_occur id tl]. |
---|
1142 | |
---|
1143 | lemma does_not_occur_None: |
---|
1144 | ∀id,i,list_instr. |
---|
1145 | does_not_occur id (list_instr@[〈None …,i〉]) = |
---|
1146 | does_not_occur id list_instr. |
---|
1147 | #id #i #list_instr elim list_instr |
---|
1148 | [ % | #hd #tl #IH whd in ⊢ (??%%); >IH %] |
---|
1149 | qed. |
---|
1150 | |
---|
1151 | lemma does_not_occur_Some: |
---|
1152 | ∀id,id',i,list_instr. |
---|
1153 | eq_identifier ? id' id = false → |
---|
1154 | does_not_occur id (list_instr@[〈Some ? id',i〉]) = |
---|
1155 | does_not_occur id list_instr. |
---|
1156 | #id #id' #i #list_instr elim list_instr |
---|
1157 | [ #H normalize in H ⊢ %; >H % |
---|
1158 | | * #x #i' #tl #IH #H whd in ⊢ (??%%); >(IH H) %] |
---|
1159 | qed. |
---|
1160 | |
---|
1161 | lemma does_not_occur_absurd: |
---|
1162 | ∀id,i,list_instr. |
---|
1163 | does_not_occur id (list_instr@[〈Some ? id,i〉]) = false. |
---|
1164 | #id #i #list_instr elim list_instr |
---|
1165 | [ normalize change with (if (if eq_identifier ??? then ? else ?) then ? else ? = ?) |
---|
1166 | >eq_identifier_refl % |
---|
1167 | | * #x #i' #tl #IH whd in ⊢ (??%%); >IH cases (notb ?) %] |
---|
1168 | qed. |
---|
1169 | |
---|
1170 | |
---|
1171 | let rec occurs_exactly_once (id:Identifier) (l:list labelled_instruction) on l : bool ≝ |
---|
1172 | match l with |
---|
1173 | [ nil ⇒ false |
---|
1174 | | cons hd tl ⇒ |
---|
1175 | if instruction_matches_identifier id hd then |
---|
1176 | does_not_occur id tl |
---|
1177 | else |
---|
1178 | occurs_exactly_once id tl ]. |
---|
1179 | |
---|
1180 | lemma occurs_exactly_once_None: |
---|
1181 | ∀id,i,list_instr. |
---|
1182 | occurs_exactly_once id (list_instr@[〈None …,i〉]) = |
---|
1183 | occurs_exactly_once id list_instr. |
---|
1184 | #id #i #list_instr elim list_instr |
---|
1185 | [ % | #hd #tl #IH whd in ⊢ (??%%); >IH >does_not_occur_None %] |
---|
1186 | qed. |
---|
1187 | |
---|
1188 | lemma occurs_exactly_once_Some: |
---|
1189 | ∀id,id',i,prefix. |
---|
1190 | occurs_exactly_once id (prefix@[〈Some ? id',i〉]) → eq_identifier ? id' id ∨ occurs_exactly_once id prefix. |
---|
1191 | #id #id' #i #prefix elim prefix |
---|
1192 | [ whd in ⊢ (?% → ?); |
---|
1193 | change with (eq_identifier ? id' id) in ⊢ (?(match % with [_ ⇒ ? | _ ⇒ ?]) → ?); |
---|
1194 | @eq_identifier_elim normalize nodelta; /2/ |
---|
1195 | | *; #he #i' #tl #IH whd in ⊢ (?% → ?); whd in ⊢ (?(match % with [_ ⇒ ? | _ ⇒ ?]) → ?); |
---|
1196 | cases he; normalize nodelta |
---|
1197 | [ #H @ (IH H) |
---|
1198 | | #x whd in ⊢ (? → ?(??%)); change with (eq_identifier ? x id) in match (instruction_matches_identifier ??); |
---|
1199 | @eq_identifier_elim #E normalize nodelta |
---|
1200 | [ destruct @eq_identifier_elim normalize nodelta; |
---|
1201 | /2/ #H >does_not_occur_Some /2/ |
---|
1202 | | #H @IH @H]]] |
---|
1203 | qed. |
---|
1204 | |
---|
1205 | lemma occurs_exactly_once_Some_stronger: |
---|
1206 | ∀id,id',i,prefix. |
---|
1207 | occurs_exactly_once id (prefix@[〈Some ? id',i〉]) → |
---|
1208 | (eq_identifier ? id' id ∧ does_not_occur id prefix) ∨ |
---|
1209 | (¬eq_identifier ? id' id ∧ occurs_exactly_once id prefix). |
---|
1210 | #id #id' #i #prefix elim prefix |
---|
1211 | [ whd in ⊢ (?% → ?); change with (eq_identifier ???) in ⊢ (?(match % with [_ ⇒ ?| _ ⇒ ?]) → ?); |
---|
1212 | @eq_identifier_elim #E |
---|
1213 | [ normalize // |
---|
1214 | | normalize #H @⊥ @H |
---|
1215 | ] |
---|
1216 | | *; #he #i' #tl #IH whd in ⊢ (?% → ?); whd in ⊢ (?(match % with [_ ⇒ ? | _ ⇒ ?]) → ?); |
---|
1217 | cases he; normalize nodelta |
---|
1218 | [ #H @ (IH H) |
---|
1219 | | #x @eq_identifier_elim #Heq |
---|
1220 | [ @eq_identifier_elim normalize nodelta |
---|
1221 | [ #H >H >does_not_occur_absurd #Hf @⊥ @Hf |
---|
1222 | | #H >(does_not_occur_Some) |
---|
1223 | [ #H2 whd in match (does_not_occur ??); |
---|
1224 | change with (eq_identifier ???) in match (instruction_matches_identifier ??); |
---|
1225 | >Heq >eq_identifier_refl normalize nodelta |
---|
1226 | @orb_elim normalize nodelta whd in match (occurs_exactly_once ??); |
---|
1227 | change with (eq_identifier ???) in match (instruction_matches_identifier ??); |
---|
1228 | >eq_identifier_refl |
---|
1229 | normalize nodelta @H2 |
---|
1230 | | /2/ |
---|
1231 | ] |
---|
1232 | ] |
---|
1233 | | normalize nodelta #H lapply (IH H) -IH -H; |
---|
1234 | @eq_identifier_elim #Heq2 |
---|
1235 | #Hor @orb_elim |
---|
1236 | [ <Heq2 in Hor; #Hor normalize in Hor; |
---|
1237 | whd in match (does_not_occur ??); change with (eq_identifier ???) in match (instruction_matches_identifier ??); |
---|
1238 | >eq_identifier_false // normalize nodelta |
---|
1239 | cases (does_not_occur id' tl) in Hor; normalize nodelta // |
---|
1240 | | normalize nodelta whd in match (occurs_exactly_once ??); |
---|
1241 | change with (eq_identifier ???) in match (instruction_matches_identifier ??); |
---|
1242 | >eq_identifier_false // |
---|
1243 | ] |
---|
1244 | ] |
---|
1245 | ] |
---|
1246 | ] |
---|
1247 | qed. |
---|
1248 | |
---|
1249 | let rec index_of_internal (A: Type[0]) (pred: A → bool) (l: list A) (acc: nat) on l: nat ≝ |
---|
1250 | match l with |
---|
1251 | [ nil ⇒ ? |
---|
1252 | | cons hd tl ⇒ |
---|
1253 | if pred hd then |
---|
1254 | acc |
---|
1255 | else |
---|
1256 | index_of_internal A pred tl (S acc) |
---|
1257 | ]. |
---|
1258 | cases not_implemented. |
---|
1259 | qed. |
---|
1260 | |
---|
1261 | |
---|
1262 | definition index_of ≝ |
---|
1263 | λA. |
---|
1264 | λeq. |
---|
1265 | λl. |
---|
1266 | index_of_internal A eq l 0. |
---|
1267 | |
---|
1268 | lemma index_of_internal_None: ∀i,id,instr_list,n. |
---|
1269 | occurs_exactly_once id (instr_list@[〈None …,i〉]) → |
---|
1270 | index_of_internal ? (instruction_matches_identifier id) instr_list n = |
---|
1271 | index_of_internal ? (instruction_matches_identifier id) (instr_list@[〈None …,i〉]) n. |
---|
1272 | #i #id #instr_list elim instr_list |
---|
1273 | [ #n #abs whd in abs; cases abs |
---|
1274 | | #hd #tl #IH #n whd in ⊢ (% → ??%%); whd in ⊢ (match % with [_ ⇒ ? | _ ⇒ ?] → ?); |
---|
1275 | cases (instruction_matches_identifier id hd) whd in ⊢ (match % with [_ ⇒ ? | _ ⇒ ?] → ??%%); |
---|
1276 | [ #H % |
---|
1277 | | #H @IH whd in H; cases (occurs_exactly_once ??) in H ⊢ %; |
---|
1278 | [ #_ % | #abs cases abs ]]] |
---|
1279 | qed. |
---|
1280 | |
---|
1281 | lemma index_of_internal_Some_miss: ∀i,id,id'. |
---|
1282 | eq_identifier ? id' id = false → |
---|
1283 | ∀instr_list,n. |
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1284 | occurs_exactly_once id (instr_list@[〈Some ? id',i〉]) → |
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1285 | index_of_internal ? (instruction_matches_identifier id) instr_list n = |
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1286 | index_of_internal ? (instruction_matches_identifier id) (instr_list@[〈Some ? id',i〉]) n. |
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1287 | #i #id #id' #EQ #instr_list #n #H generalize in match (occurs_exactly_once_Some … H) in ⊢ ?; >EQ |
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1288 | change with (occurs_exactly_once ?? → ?) generalize in match n; -n -H; elim instr_list |
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1289 | [ #n #abs cases abs |
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1290 | | #hd #tl #IH #n whd in ⊢ (?% → ??%%); cases (instruction_matches_identifier id hd) normalize nodelta; |
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1291 | [ // | #K @IH //]] |
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1292 | qed. |
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1293 | |
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1294 | lemma index_of_internal_Some_hit: ∀i,id. |
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1295 | ∀instr_list,n. |
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1296 | occurs_exactly_once id (instr_list@[〈Some ? id,i〉]) → |
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1297 | index_of_internal ? (instruction_matches_identifier id) (instr_list@[〈Some ? id,i〉]) n |
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1298 | = |instr_list| + n. |
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1299 | #i #id #instr_list elim instr_list |
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1300 | [ #n #_ whd in ⊢ (??%%); change with (if eq_identifier … id id then ? else ? = ?) >eq_identifier_refl % |
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1301 | | #hd #tl #IH #n whd in ⊢ (?% → ??%%); cases (instruction_matches_identifier id hd) normalize nodelta; |
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1302 | [ >does_not_occur_absurd #abs cases abs | #H >plus_n_Sm applyS (IH (S n)) //]] |
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1303 | qed. |
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1304 | |
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1305 | definition address_of_word_labels_code_mem ≝ |
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1306 | λcode_mem. |
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1307 | λid: Identifier. |
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1308 | bitvector_of_nat 16 (index_of ? (instruction_matches_identifier id) code_mem). |
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1309 | |
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1310 | lemma address_of_word_labels_code_mem_None: ∀i,id,instr_list. |
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1311 | occurs_exactly_once id (instr_list@[〈None …,i〉]) → |
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1312 | address_of_word_labels_code_mem instr_list id = |
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1313 | address_of_word_labels_code_mem (instr_list@[〈None …,i〉]) id. |
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1314 | #i #id #instr_list #H whd in ⊢ (??%%); whd in ⊢ (??(??%?)(??%?)); |
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1315 | >(index_of_internal_None … H) % |
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1316 | qed. |
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1317 | |
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1318 | lemma address_of_word_labels_code_mem_Some_miss: ∀i,id,id',instr_list. |
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1319 | eq_identifier ? id' id = false → |
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1320 | occurs_exactly_once id (instr_list@[〈Some ? id',i〉]) → |
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1321 | address_of_word_labels_code_mem instr_list id = |
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1322 | address_of_word_labels_code_mem (instr_list@[〈Some … id',i〉]) id. |
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1323 | #i #id #id' #instr_list #EQ #H whd in ⊢ (??%%); whd in ⊢ (??(??%?)(??%?)); |
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1324 | >(index_of_internal_Some_miss … H) [ @refl | // ] |
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1325 | qed. |
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1326 | |
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1327 | lemma address_of_word_labels_code_mem_Some_hit: ∀i,id,instr_list. |
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1328 | occurs_exactly_once id (instr_list@[〈Some ? id,i〉]) → |
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1329 | address_of_word_labels_code_mem (instr_list@[〈Some … id,i〉]) id |
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1330 | = bitvector_of_nat … (|instr_list|). |
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1331 | #i #id #instr_list #H whd in ⊢ (??%%); whd in ⊢ (??(??%?)?); |
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1332 | >(index_of_internal_Some_hit … H) <plus_n_O @refl |
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1333 | qed. |
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1334 | |
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1335 | definition address_of_word_labels ≝ |
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1336 | λpr: pseudo_assembly_program. |
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1337 | λid: Identifier. |
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1338 | address_of_word_labels_code_mem (\snd pr) id. |
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1339 | |
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1340 | definition construct_datalabels: preamble → ? ≝ |
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1341 | λthe_preamble: preamble. |
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1342 | \fst (foldl ((identifier_map ASMTag Word) × Word) ? ( |
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1343 | λt. λpreamble. |
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1344 | let 〈datalabels, addr〉 ≝ t in |
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1345 | let 〈name, size〉 ≝ preamble in |
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1346 | let 〈carry, sum〉 ≝ half_add … addr size in |
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1347 | 〈add ? ? datalabels name addr, sum〉) |
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1348 | 〈empty_map …, zero 16〉 (\snd the_preamble)). |
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