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 | |
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9 | definition Time ≝ nat. |
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10 | |
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11 | inductive SerialBufferType: Type[0] ≝ |
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12 | Eight: Byte → SerialBufferType |
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13 | | Nine: Bit → Byte → SerialBufferType. |
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14 | |
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15 | inductive LineType: Type[0] ≝ |
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16 | P1: Byte → LineType |
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17 | | P3: Byte → LineType |
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18 | | SerialBuffer: SerialBufferType → LineType. |
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19 | |
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20 | (* What is a continuation, now? *) |
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21 | |
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22 | inductive SFR8051: Type[0] ≝ |
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23 | SFR_SP: SFR8051 |
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24 | | SFR_DPL: SFR8051 |
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25 | | SFR_DPH: SFR8051 |
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26 | | SFR_PCON: SFR8051 |
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27 | | SFR_TCON: SFR8051 |
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28 | | SFR_TMOD: SFR8051 |
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29 | | SFR_TL0: SFR8051 |
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30 | | SFR_TL1: SFR8051 |
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31 | | SFR_TH0: SFR8051 |
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32 | | SFR_TH1: SFR8051 |
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33 | | SFR_P1: SFR8051 |
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34 | | SFR_SCON: SFR8051 |
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35 | | SFR_SBUF: SFR8051 |
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36 | | SFR_IE: SFR8051 |
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37 | | SFR_P3: SFR8051 |
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38 | | SFR_IP: SFR8051 |
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39 | | SFR_PSW: SFR8051 |
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40 | | SFR_ACC_A: SFR8051 |
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41 | | SFR_ACC_B: SFR8051. |
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42 | |
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43 | definition sfr_8051_index ≝ |
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44 | λs: SFR8051. |
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45 | match s with |
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46 | [ SFR_SP ⇒ O |
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47 | | SFR_DPL ⇒ 1 |
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48 | | SFR_DPH ⇒ 2 |
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49 | | SFR_PCON ⇒ 3 |
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50 | | SFR_TCON ⇒ 4 |
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51 | | SFR_TMOD ⇒ 5 |
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52 | | SFR_TL0 ⇒ 6 |
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53 | | SFR_TL1 ⇒ 7 |
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54 | | SFR_TH0 ⇒ 8 |
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55 | | SFR_TH1 ⇒ 9 |
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56 | | SFR_P1 ⇒ 10 |
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57 | | SFR_SCON ⇒ 11 |
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58 | | SFR_SBUF ⇒ 12 |
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59 | | SFR_IE ⇒ 13 |
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60 | | SFR_P3 ⇒ 14 |
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61 | | SFR_IP ⇒ 15 |
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62 | | SFR_PSW ⇒ 16 |
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63 | | SFR_ACC_A ⇒ 17 |
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64 | | SFR_ACC_B ⇒ 18 |
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65 | ]. |
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66 | |
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67 | inductive SFR8052: Type[0] ≝ |
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68 | SFR_T2CON: SFR8052 |
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69 | | SFR_RCAP2L: SFR8052 |
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70 | | SFR_RCAP2H: SFR8052 |
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71 | | SFR_TL2: SFR8052 |
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72 | | SFR_TH2: SFR8052. |
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73 | |
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74 | definition sfr_8052_index ≝ |
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75 | λs: SFR8052. |
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76 | match s with |
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77 | [ SFR_T2CON ⇒ O |
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78 | | SFR_RCAP2L ⇒ 1 |
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79 | | SFR_RCAP2H ⇒ 2 |
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80 | | SFR_TL2 ⇒ 3 |
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81 | | SFR_TH2 ⇒ 4 |
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82 | ]. |
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83 | |
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84 | (* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *) |
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85 | (* Processor status. *) |
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86 | (* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= *) |
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87 | record PreStatus (M: Type[0]): Type[0] ≝ |
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88 | { |
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89 | code_memory: M; |
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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 | λs: PreStatus M. |
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131 | λt: Time. |
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132 | let old_code_memory ≝ code_memory ? s in |
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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 old_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 | λs: PreStatus M. |
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155 | λb: Byte. |
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156 | let old_code_memory ≝ code_memory ? s in |
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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 old_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 | λs: PreStatus M. |
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179 | λb: Byte. |
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180 | let old_code_memory ≝ code_memory ? s in |
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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 old_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 | λs: PreStatus M. |
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203 | λi: SFR8051. |
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204 | let sfr ≝ special_function_registers_8051 ? s in |
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205 | let index ≝ sfr_8051_index i in |
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206 | get_index_v … sfr index ?. |
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207 | @ sfr8051_index_19 |
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208 | qed. |
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209 | |
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210 | definition get_8052_sfr ≝ |
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211 | λM: Type[0]. |
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212 | λs: PreStatus M. |
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213 | λi: SFR8052. |
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214 | let sfr ≝ special_function_registers_8052 ? s in |
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215 | let index ≝ sfr_8052_index i in |
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216 | get_index_v … sfr index ?. |
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217 | @ sfr8052_index_5 |
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218 | qed. |
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219 | |
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220 | definition set_8051_sfr ≝ |
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221 | λM: Type[0]. |
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222 | λs: PreStatus M. |
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223 | λi: SFR8051. |
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224 | λb: Byte. |
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225 | let index ≝ sfr_8051_index i in |
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226 | let old_code_memory ≝ code_memory ? s in |
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227 | let old_low_internal_ram ≝ low_internal_ram ? s in |
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228 | let old_high_internal_ram ≝ high_internal_ram ? s in |
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229 | let old_external_ram ≝ external_ram ? s in |
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230 | let old_program_counter ≝ program_counter ? s in |
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231 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in |
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232 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in |
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233 | let new_special_function_registers_8051 ≝ |
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234 | set_index Byte 19 old_special_function_registers_8051 index b ? in |
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235 | let old_p1_latch ≝ p1_latch ? s in |
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236 | let old_p3_latch ≝ p3_latch ? s in |
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237 | let old_clock ≝ clock ? s in |
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238 | mk_PreStatus M old_code_memory |
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239 | old_low_internal_ram |
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240 | old_high_internal_ram |
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241 | old_external_ram |
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242 | old_program_counter |
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243 | new_special_function_registers_8051 |
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244 | old_special_function_registers_8052 |
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245 | old_p1_latch |
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246 | old_p3_latch |
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247 | old_clock. |
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248 | @ (sfr8051_index_19 i) |
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249 | qed. |
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250 | |
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251 | definition set_8052_sfr ≝ |
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252 | λM: Type[0]. |
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253 | λs: PreStatus M. |
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254 | λi: SFR8052. |
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255 | λb: Byte. |
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256 | let index ≝ sfr_8052_index i in |
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257 | let old_code_memory ≝ code_memory ? s in |
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258 | let old_low_internal_ram ≝ low_internal_ram ? s in |
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259 | let old_high_internal_ram ≝ high_internal_ram ? s in |
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260 | let old_external_ram ≝ external_ram ? s in |
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261 | let old_program_counter ≝ program_counter ? s in |
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262 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in |
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263 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in |
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264 | let new_special_function_registers_8052 ≝ |
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265 | set_index Byte 5 old_special_function_registers_8052 index b ? in |
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266 | let old_p1_latch ≝ p1_latch ? s in |
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267 | let old_p3_latch ≝ p3_latch ? s in |
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268 | let old_clock ≝ clock ? s in |
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269 | mk_PreStatus M old_code_memory |
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270 | old_low_internal_ram |
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271 | old_high_internal_ram |
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272 | old_external_ram |
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273 | old_program_counter |
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274 | old_special_function_registers_8051 |
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275 | new_special_function_registers_8052 |
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276 | old_p1_latch |
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277 | old_p3_latch |
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278 | old_clock. |
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279 | @ (sfr8052_index_5 i) |
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280 | qed. |
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281 | |
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282 | definition set_program_counter ≝ |
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283 | λM: Type[0]. |
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284 | λs: PreStatus M. |
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285 | λw: Word. |
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286 | let old_code_memory ≝ code_memory ? s in |
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287 | let old_low_internal_ram ≝ low_internal_ram ? s in |
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288 | let old_high_internal_ram ≝ high_internal_ram ? s in |
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289 | let old_external_ram ≝ external_ram ? s in |
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290 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in |
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291 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in |
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292 | let old_p1_latch ≝ p1_latch ? s in |
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293 | let old_p3_latch ≝ p3_latch ? s in |
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294 | let old_clock ≝ clock ? s in |
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295 | mk_PreStatus M old_code_memory |
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296 | old_low_internal_ram |
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297 | old_high_internal_ram |
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298 | old_external_ram |
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299 | w |
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300 | old_special_function_registers_8051 |
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301 | old_special_function_registers_8052 |
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302 | old_p1_latch |
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303 | old_p3_latch |
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304 | old_clock. |
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305 | |
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306 | definition set_code_memory ≝ |
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307 | λM,M': Type[0]. |
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308 | λs: PreStatus M. |
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309 | λr: M'. |
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310 | let old_low_internal_ram ≝ low_internal_ram ? s in |
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311 | let old_high_internal_ram ≝ high_internal_ram ? s in |
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312 | let old_external_ram ≝ external_ram ? s in |
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313 | let old_program_counter ≝ program_counter ? s in |
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314 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in |
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315 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in |
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316 | let old_p1_latch ≝ p1_latch ? s in |
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317 | let old_p3_latch ≝ p3_latch ? s in |
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318 | let old_clock ≝ clock ? s in |
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319 | mk_PreStatus M' r |
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320 | old_low_internal_ram |
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321 | old_high_internal_ram |
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322 | old_external_ram |
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323 | old_program_counter |
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324 | old_special_function_registers_8051 |
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325 | old_special_function_registers_8052 |
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326 | old_p1_latch |
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327 | old_p3_latch |
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328 | old_clock. |
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329 | |
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330 | definition set_low_internal_ram ≝ |
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331 | λM: Type[0]. |
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332 | λs: PreStatus M. |
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333 | λr: BitVectorTrie Byte 7. |
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334 | let old_code_memory ≝ code_memory ? s in |
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335 | let old_high_internal_ram ≝ high_internal_ram ? s in |
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336 | let old_external_ram ≝ external_ram ? s in |
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337 | let old_program_counter ≝ program_counter ? s in |
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338 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in |
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339 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in |
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340 | let old_p1_latch ≝ p1_latch ? s in |
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341 | let old_p3_latch ≝ p3_latch ? s in |
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342 | let old_clock ≝ clock ? s in |
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343 | mk_PreStatus M old_code_memory |
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344 | r |
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345 | old_high_internal_ram |
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346 | old_external_ram |
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347 | old_program_counter |
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348 | old_special_function_registers_8051 |
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349 | old_special_function_registers_8052 |
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350 | old_p1_latch |
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351 | old_p3_latch |
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352 | old_clock. |
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353 | |
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354 | definition set_high_internal_ram ≝ |
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355 | λM: Type[0]. |
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356 | λs: PreStatus M. |
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357 | λr: BitVectorTrie Byte 7. |
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358 | let old_code_memory ≝ code_memory ? s in |
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359 | let old_low_internal_ram ≝ low_internal_ram ? s in |
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360 | let old_high_internal_ram ≝ high_internal_ram ? s in |
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361 | let old_external_ram ≝ external_ram ? s in |
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362 | let old_program_counter ≝ program_counter ? s in |
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363 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in |
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364 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in |
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365 | let old_p1_latch ≝ p1_latch ? s in |
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366 | let old_p3_latch ≝ p3_latch ? s in |
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367 | let old_clock ≝ clock ? s in |
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368 | mk_PreStatus M old_code_memory |
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369 | old_low_internal_ram |
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370 | r |
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371 | old_external_ram |
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372 | old_program_counter |
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373 | old_special_function_registers_8051 |
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374 | old_special_function_registers_8052 |
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375 | old_p1_latch |
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376 | old_p3_latch |
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377 | old_clock. |
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378 | |
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379 | definition set_external_ram ≝ |
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380 | λM: Type[0]. |
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381 | λs: PreStatus M. |
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382 | λr: BitVectorTrie Byte 16. |
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383 | let old_code_memory ≝ code_memory ? s in |
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384 | let old_low_internal_ram ≝ low_internal_ram ? s in |
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385 | let old_high_internal_ram ≝ high_internal_ram ? s in |
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386 | let old_program_counter ≝ program_counter ? s in |
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387 | let old_special_function_registers_8051 ≝ special_function_registers_8051 ? s in |
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388 | let old_special_function_registers_8052 ≝ special_function_registers_8052 ? s in |
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389 | let old_p1_latch ≝ p1_latch ? s in |
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390 | let old_p3_latch ≝ p3_latch ? s in |
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391 | let old_clock ≝ clock ? s in |
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392 | mk_PreStatus M old_code_memory |
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393 | old_low_internal_ram |
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394 | old_high_internal_ram |
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395 | r |
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396 | old_program_counter |
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397 | old_special_function_registers_8051 |
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398 | old_special_function_registers_8052 |
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399 | old_p1_latch |
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400 | old_p3_latch |
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401 | old_clock. |
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402 | |
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403 | definition get_cy_flag ≝ |
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404 | λM: Type[0]. |
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405 | λs: PreStatus M. |
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406 | let sfr ≝ special_function_registers_8051 ? s in |
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407 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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408 | get_index_v bool 8 psw O ?. |
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409 | normalize |
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410 | @ (le_S_S ? ?) |
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411 | [ @ le_O_n |
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412 | | repeat (@ (le_S_S)); |
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413 | // |
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414 | ] |
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415 | qed. |
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416 | |
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417 | definition get_ac_flag ≝ |
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418 | λM: Type[0]. |
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419 | λs: PreStatus M. |
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420 | let sfr ≝ special_function_registers_8051 ? s in |
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421 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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422 | get_index_v bool 8 psw 1 ?. |
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423 | normalize |
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424 | repeat (@ (le_S_S ? ?)) |
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425 | @ le_O_n |
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426 | qed. |
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427 | |
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428 | definition get_fo_flag ≝ |
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429 | λM: Type[0]. |
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430 | λs: PreStatus M. |
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431 | let sfr ≝ special_function_registers_8051 ? s in |
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432 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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433 | get_index_v bool 8 psw 2 ?. |
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434 | normalize |
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435 | repeat (@ (le_S_S ? ?)) |
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436 | @ le_O_n |
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437 | qed. |
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438 | |
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439 | definition get_rs1_flag ≝ |
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440 | λM: Type[0]. |
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441 | λs: PreStatus M. |
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442 | let sfr ≝ special_function_registers_8051 ? s in |
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443 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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444 | get_index_v bool 8 psw 3 ?. |
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445 | normalize |
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446 | repeat (@ (le_S_S ? ?)) |
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447 | @ le_O_n |
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448 | qed. |
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449 | |
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450 | definition get_rs0_flag ≝ |
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451 | λM: Type[0]. |
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452 | λs: PreStatus M. |
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453 | let sfr ≝ special_function_registers_8051 ? s in |
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454 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
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455 | get_index_v bool 8 psw 4 ?. |
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456 | normalize |
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457 | repeat (@ (le_S_S ? ?)) |
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458 | @ le_O_n |
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459 | qed. |
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460 | |
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461 | definition get_ov_flag ≝ |
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462 | λM: Type[0]. |
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463 | λs: PreStatus M. |
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464 | let sfr ≝ special_function_registers_8051 ? s in |
---|
465 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
---|
466 | get_index_v bool 8 psw 5 ?. |
---|
467 | normalize |
---|
468 | repeat (@ (le_S_S ? ?)) |
---|
469 | @ le_O_n |
---|
470 | qed. |
---|
471 | |
---|
472 | definition get_ud_flag ≝ |
---|
473 | λM: Type[0]. |
---|
474 | λs: PreStatus M. |
---|
475 | let sfr ≝ special_function_registers_8051 ? s in |
---|
476 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
---|
477 | get_index_v bool 8 psw 6 ?. |
---|
478 | normalize |
---|
479 | repeat (@ (le_S_S ? ?)) |
---|
480 | @ le_O_n |
---|
481 | qed. |
---|
482 | |
---|
483 | definition get_p_flag ≝ |
---|
484 | λM: Type[0]. |
---|
485 | λs: PreStatus M. |
---|
486 | let sfr ≝ special_function_registers_8051 ? s in |
---|
487 | let psw ≝ get_index_v Byte 19 sfr (sfr_8051_index SFR_PSW) ? in |
---|
488 | get_index_v bool 8 psw 7 ?. |
---|
489 | normalize |
---|
490 | repeat (@ (le_S_S ? ?)) |
---|
491 | @ le_O_n |
---|
492 | qed. |
---|
493 | |
---|
494 | definition set_flags ≝ |
---|
495 | λM: Type[0]. |
---|
496 | λs: PreStatus M. |
---|
497 | λcy: Bit. |
---|
498 | λac: option Bit. |
---|
499 | λov: Bit. |
---|
500 | let old_cy ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) O ? in |
---|
501 | let old_ac ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 1 ? in |
---|
502 | let old_fo ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 2 ? in |
---|
503 | let old_rs1 ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 3 ? in |
---|
504 | let old_rs0 ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 4 ? in |
---|
505 | let old_ov ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 5 ? in |
---|
506 | let old_ud ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 6 ? in |
---|
507 | let old_p ≝ get_index_v… (get_8051_sfr ? s SFR_PSW) 7 ? in |
---|
508 | let new_ac ≝ match ac with [ None ⇒ old_ac | Some j ⇒ j ] in |
---|
509 | let new_psw ≝ [[ old_cy ; new_ac ; old_fo ; old_rs1 ; |
---|
510 | old_rs0 ; old_ov ; old_ud ; old_p ]] in |
---|
511 | set_8051_sfr ? s SFR_PSW new_psw. |
---|
512 | [1,2,3,4,5,6,7,8: |
---|
513 | normalize |
---|
514 | repeat (@ le_S_S) |
---|
515 | @ le_O_n |
---|
516 | ] |
---|
517 | qed. |
---|
518 | |
---|
519 | definition initialise_status ≝ |
---|
520 | λM: Type[0]. |
---|
521 | λcode_mem: M. |
---|
522 | let status ≝ mk_PreStatus M code_mem (* Code mem. *) |
---|
523 | (Stub Byte 7) (* Low mem. *) |
---|
524 | (Stub Byte 7) (* High mem. *) |
---|
525 | (Stub Byte 16) (* Ext mem. *) |
---|
526 | (zero 16) (* PC. *) |
---|
527 | (replicate Byte 19 (zero 8)) (* 8051 SFR. *) |
---|
528 | (replicate Byte 5 (zero 8)) (* 8052 SFR. *) |
---|
529 | (zero 8) (* P1 latch. *) |
---|
530 | (zero 8) (* P3 latch. *) |
---|
531 | O (* Clock. *) |
---|
532 | in |
---|
533 | set_8051_sfr ? status SFR_SP (bitvector_of_nat 8 7). |
---|
534 | |
---|
535 | definition get_bit_addressable_sfr ≝ |
---|
536 | λM: Type[0]. |
---|
537 | λs: PreStatus M. |
---|
538 | λn: nat. |
---|
539 | λb: BitVector n. |
---|
540 | λl: bool. |
---|
541 | let address ≝ nat_of_bitvector … b in |
---|
542 | if (eqb address 128) then |
---|
543 | ? |
---|
544 | else if (eqb address 144) then |
---|
545 | if l then |
---|
546 | (p1_latch ? s) |
---|
547 | else |
---|
548 | (get_8051_sfr ? s SFR_P1) |
---|
549 | else if (eqb address 160) then |
---|
550 | ? |
---|
551 | else if (eqb address 176) then |
---|
552 | if l then |
---|
553 | (p3_latch ? s) |
---|
554 | else |
---|
555 | (get_8051_sfr ? s SFR_P3) |
---|
556 | else if (eqb address 153) then |
---|
557 | get_8051_sfr ? s SFR_SBUF |
---|
558 | else if (eqb address 138) then |
---|
559 | get_8051_sfr ? s SFR_TL0 |
---|
560 | else if (eqb address 139) then |
---|
561 | get_8051_sfr ? s SFR_TL1 |
---|
562 | else if (eqb address 140) then |
---|
563 | get_8051_sfr ? s SFR_TH0 |
---|
564 | else if (eqb address 141) then |
---|
565 | get_8051_sfr ? s SFR_TH1 |
---|
566 | else if (eqb address 200) then |
---|
567 | get_8052_sfr ? s SFR_T2CON |
---|
568 | else if (eqb address 202) then |
---|
569 | get_8052_sfr ? s SFR_RCAP2L |
---|
570 | else if (eqb address 203) then |
---|
571 | get_8052_sfr ? s SFR_RCAP2H |
---|
572 | else if (eqb address 204) then |
---|
573 | get_8052_sfr ? s SFR_TL2 |
---|
574 | else if (eqb address 205) then |
---|
575 | get_8052_sfr ? s SFR_TH2 |
---|
576 | else if (eqb address 135) then |
---|
577 | get_8051_sfr ? s SFR_PCON |
---|
578 | else if (eqb address 136) then |
---|
579 | get_8051_sfr ? s SFR_TCON |
---|
580 | else if (eqb address 137) then |
---|
581 | get_8051_sfr ? s SFR_TMOD |
---|
582 | else if (eqb address 152) then |
---|
583 | get_8051_sfr ? s SFR_SCON |
---|
584 | else if (eqb address 168) then |
---|
585 | get_8051_sfr ? s SFR_IE |
---|
586 | else if (eqb address 184) then |
---|
587 | get_8051_sfr ? s SFR_IP |
---|
588 | else if (eqb address 129) then |
---|
589 | get_8051_sfr ? s SFR_SP |
---|
590 | else if (eqb address 130) then |
---|
591 | get_8051_sfr ? s SFR_DPL |
---|
592 | else if (eqb address 131) then |
---|
593 | get_8051_sfr ? s SFR_DPH |
---|
594 | else if (eqb address 208) then |
---|
595 | get_8051_sfr ? s SFR_PSW |
---|
596 | else if (eqb address 224) then |
---|
597 | get_8051_sfr ? s SFR_ACC_A |
---|
598 | else if (eqb address 240) then |
---|
599 | get_8051_sfr ? s SFR_ACC_B |
---|
600 | else |
---|
601 | ?. |
---|
602 | cases not_implemented |
---|
603 | qed. |
---|
604 | |
---|
605 | definition set_bit_addressable_sfr ≝ |
---|
606 | λM: Type[0]. |
---|
607 | λs: PreStatus M. |
---|
608 | λb: Byte. |
---|
609 | λv: Byte. |
---|
610 | let address ≝ nat_of_bitvector … b in |
---|
611 | if (eqb address 128) then |
---|
612 | ? |
---|
613 | else if (eqb address 144) then |
---|
614 | let status_1 ≝ set_8051_sfr ? s SFR_P1 v in |
---|
615 | let status_2 ≝ set_p1_latch ? s v in |
---|
616 | status_2 |
---|
617 | else if (eqb address 160) then |
---|
618 | ? |
---|
619 | else if (eqb address 176) then |
---|
620 | let status_1 ≝ set_8051_sfr ? s SFR_P3 v in |
---|
621 | let status_2 ≝ set_p3_latch ? s v in |
---|
622 | status_2 |
---|
623 | else if (eqb address 153) then |
---|
624 | set_8051_sfr ? s SFR_SBUF v |
---|
625 | else if (eqb address 138) then |
---|
626 | set_8051_sfr ? s SFR_TL0 v |
---|
627 | else if (eqb address 139) then |
---|
628 | set_8051_sfr ? s SFR_TL1 v |
---|
629 | else if (eqb address 140) then |
---|
630 | set_8051_sfr ? s SFR_TH0 v |
---|
631 | else if (eqb address 141) then |
---|
632 | set_8051_sfr ? s SFR_TH1 v |
---|
633 | else if (eqb address 200) then |
---|
634 | set_8052_sfr ? s SFR_T2CON v |
---|
635 | else if (eqb address 202) then |
---|
636 | set_8052_sfr ? s SFR_RCAP2L v |
---|
637 | else if (eqb address 203) then |
---|
638 | set_8052_sfr ? s SFR_RCAP2H v |
---|
639 | else if (eqb address 204) then |
---|
640 | set_8052_sfr ? s SFR_TL2 v |
---|
641 | else if (eqb address 205) then |
---|
642 | set_8052_sfr ? s SFR_TH2 v |
---|
643 | else if (eqb address 135) then |
---|
644 | set_8051_sfr ? s SFR_PCON v |
---|
645 | else if (eqb address 136) then |
---|
646 | set_8051_sfr ? s SFR_TCON v |
---|
647 | else if (eqb address 137) then |
---|
648 | set_8051_sfr ? s SFR_TMOD v |
---|
649 | else if (eqb address 152) then |
---|
650 | set_8051_sfr ? s SFR_SCON v |
---|
651 | else if (eqb address 168) then |
---|
652 | set_8051_sfr ? s SFR_IE v |
---|
653 | else if (eqb address 184) then |
---|
654 | set_8051_sfr ? s SFR_IP v |
---|
655 | else if (eqb address 129) then |
---|
656 | set_8051_sfr ? s SFR_SP v |
---|
657 | else if (eqb address 130) then |
---|
658 | set_8051_sfr ? s SFR_DPL v |
---|
659 | else if (eqb address 131) then |
---|
660 | set_8051_sfr ? s SFR_DPH v |
---|
661 | else if (eqb address 208) then |
---|
662 | set_8051_sfr ? s SFR_PSW v |
---|
663 | else if (eqb address 224) then |
---|
664 | set_8051_sfr ? s SFR_ACC_A v |
---|
665 | else if (eqb address 240) then |
---|
666 | set_8051_sfr ? s SFR_ACC_B v |
---|
667 | else |
---|
668 | ?. |
---|
669 | cases not_implemented |
---|
670 | qed. |
---|
671 | |
---|
672 | definition bit_address_of_register ≝ |
---|
673 | λM: Type[0]. |
---|
674 | λs: PreStatus M. |
---|
675 | λr: BitVector 3. |
---|
676 | let b ≝ get_index_v … r O ? in |
---|
677 | let c ≝ get_index_v … r 1 ? in |
---|
678 | let d ≝ get_index_v … r 2 ? in |
---|
679 | let 〈 un, ln 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_PSW) in |
---|
680 | let 〈 r1, r0 〉 ≝ 〈 get_index_v … 4 un 2 ?, get_index_v … 4 un 3 ? 〉 in |
---|
681 | let offset ≝ |
---|
682 | if ¬r1 ∧ ¬r0 then |
---|
683 | O |
---|
684 | else if ¬r1 ∧ r0 then |
---|
685 | 8 |
---|
686 | else if r1 ∧ r0 then |
---|
687 | 24 |
---|
688 | else |
---|
689 | 16 |
---|
690 | in |
---|
691 | bitvector_of_nat 7 (offset + (nat_of_bitvector ? [[ false ; b ; c ; d ]])). |
---|
692 | [1,2,3,4,5: |
---|
693 | normalize |
---|
694 | repeat (@ le_S_S) |
---|
695 | @ le_O_n; |
---|
696 | ] |
---|
697 | qed. |
---|
698 | |
---|
699 | definition get_register ≝ |
---|
700 | λM: Type[0]. |
---|
701 | λs: PreStatus M. |
---|
702 | λr: BitVector 3. |
---|
703 | let address ≝ bit_address_of_register ? s r in |
---|
704 | lookup ?? address (low_internal_ram ? s) (zero 8). |
---|
705 | |
---|
706 | definition set_register ≝ |
---|
707 | λM: Type[0]. |
---|
708 | λs: PreStatus M. |
---|
709 | λr: BitVector 3. |
---|
710 | λv: Byte. |
---|
711 | let address ≝ bit_address_of_register ? s r in |
---|
712 | let old_low_internal_ram ≝ low_internal_ram ? s in |
---|
713 | let new_low_internal_ram ≝ insert … address v old_low_internal_ram in |
---|
714 | set_low_internal_ram ? s new_low_internal_ram. |
---|
715 | |
---|
716 | definition read_at_stack_pointer ≝ |
---|
717 | λM: Type[0]. |
---|
718 | λs: PreStatus M. |
---|
719 | let 〈 nu, nl 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_SP) in |
---|
720 | let m ≝ get_index_v … nu O ? in |
---|
721 | let r1 ≝ get_index_v … nu 1 ? in |
---|
722 | let r2 ≝ get_index_v … nu 2 ? in |
---|
723 | let r3 ≝ get_index_v … nu 3 ? in |
---|
724 | let address ≝ [[ r1 ; r2 ; r3 ]] @@ nl in |
---|
725 | let memory ≝ |
---|
726 | if m then |
---|
727 | (low_internal_ram ? s) |
---|
728 | else |
---|
729 | (high_internal_ram ? s) |
---|
730 | in |
---|
731 | lookup … address memory (zero 8). |
---|
732 | [1,2,3,4: |
---|
733 | normalize |
---|
734 | repeat (@ le_S_S) |
---|
735 | @ le_O_n |
---|
736 | ] |
---|
737 | qed. |
---|
738 | |
---|
739 | definition write_at_stack_pointer ≝ |
---|
740 | λM: Type[0]. |
---|
741 | λs: PreStatus M. |
---|
742 | λv: Byte. |
---|
743 | let 〈 nu, nl 〉 ≝ split … 4 4 (get_8051_sfr ? s SFR_SP) in |
---|
744 | let bit_zero ≝ get_index_v… nu O ? in |
---|
745 | let bit_1 ≝ get_index_v… nu 1 ? in |
---|
746 | let bit_2 ≝ get_index_v… nu 2 ? in |
---|
747 | let bit_3 ≝ get_index_v… nu 3 ? in |
---|
748 | if bit_zero then |
---|
749 | let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl) |
---|
750 | v (low_internal_ram ? s) in |
---|
751 | set_low_internal_ram ? s memory |
---|
752 | else |
---|
753 | let memory ≝ insert … ([[ bit_1 ; bit_2 ; bit_3 ]] @@ nl) |
---|
754 | v (high_internal_ram ? s) in |
---|
755 | set_high_internal_ram ? s memory. |
---|
756 | [1,2,3,4: |
---|
757 | normalize |
---|
758 | repeat (@ le_S_S) |
---|
759 | @ le_O_n |
---|
760 | ] |
---|
761 | qed. |
---|
762 | |
---|
763 | definition set_arg_16: ∀M: Type[0]. PreStatus M → Word → [[ dptr ]] → PreStatus M ≝ |
---|
764 | λM. |
---|
765 | λs. |
---|
766 | λv. |
---|
767 | λa. |
---|
768 | match a return λx. bool_to_Prop (is_in ? [[ dptr ]] x) → ? with |
---|
769 | [ DPTR ⇒ λ_:True. |
---|
770 | let 〈 bu, bl 〉 ≝ split … 8 8 v in |
---|
771 | let status ≝ set_8051_sfr ? s SFR_DPH bu in |
---|
772 | let status ≝ set_8051_sfr ? status SFR_DPL bl in |
---|
773 | status |
---|
774 | | _ ⇒ λK. |
---|
775 | match K in False with |
---|
776 | [ |
---|
777 | ] |
---|
778 | ] (subaddressing_modein … a). |
---|
779 | |
---|
780 | definition get_arg_16: ∀M: Type[0]. PreStatus M → [[ data16 ]] → Word ≝ |
---|
781 | λm, s, a. |
---|
782 | match a return λx. bool_to_Prop (is_in ? [[ data16 ]] x) → ? with |
---|
783 | [ DATA16 d ⇒ λ_:True. d |
---|
784 | | _ ⇒ λK. |
---|
785 | match K in False with |
---|
786 | [ |
---|
787 | ] |
---|
788 | ] (subaddressing_modein … a). |
---|
789 | |
---|
790 | definition get_arg_8: ∀M: Type[0]. PreStatus M → bool → [[ direct ; indirect ; registr ; |
---|
791 | acc_a ; acc_b ; data ; acc_dptr ; |
---|
792 | acc_pc ; ext_indirect ; |
---|
793 | ext_indirect_dptr ]] → Byte ≝ |
---|
794 | λm, s, l, a. |
---|
795 | match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; registr ; |
---|
796 | acc_a ; acc_b ; data ; acc_dptr ; |
---|
797 | acc_pc ; ext_indirect ; |
---|
798 | ext_indirect_dptr ]] x) → ? with |
---|
799 | [ ACC_A ⇒ λacc_a: True. get_8051_sfr ? s SFR_ACC_A |
---|
800 | | ACC_B ⇒ λacc_b: True. get_8051_sfr ? s SFR_ACC_B |
---|
801 | | DATA d ⇒ λdata: True. d |
---|
802 | | REGISTER r ⇒ λregister: True. get_register ? s r |
---|
803 | | EXT_INDIRECT_DPTR ⇒ |
---|
804 | λext_indirect_dptr: True. |
---|
805 | let address ≝ (get_8051_sfr ? s SFR_DPH) @@ (get_8051_sfr ? s SFR_DPL) in |
---|
806 | lookup ? 16 address (external_ram ? s) (zero 8) |
---|
807 | | EXT_INDIRECT e ⇒ |
---|
808 | λext_indirect: True. |
---|
809 | let address ≝ get_register ? s [[ false; false; e ]] in |
---|
810 | let padded_address ≝ pad 8 8 address in |
---|
811 | lookup ? 16 padded_address (external_ram ? s) (zero 8) |
---|
812 | | ACC_DPTR ⇒ |
---|
813 | λacc_dptr: True. |
---|
814 | let dptr ≝ (get_8051_sfr ? s SFR_DPH) @@ (get_8051_sfr ? s SFR_DPL) in |
---|
815 | let padded_acc ≝ pad 8 8 (get_8051_sfr ? s SFR_ACC_A) in |
---|
816 | let 〈 carry, address 〉 ≝ half_add 16 dptr padded_acc in |
---|
817 | lookup ? 16 address (external_ram ? s) (zero 8) |
---|
818 | | ACC_PC ⇒ |
---|
819 | λacc_pc: True. |
---|
820 | let padded_acc ≝ pad 8 8 (get_8051_sfr ? s SFR_ACC_A) in |
---|
821 | let 〈 carry, address 〉 ≝ half_add 16 (program_counter ? s) padded_acc in |
---|
822 | lookup ? 16 address (external_ram ? s) (zero 8) |
---|
823 | | DIRECT d ⇒ |
---|
824 | λdirect: True. |
---|
825 | let 〈 nu, nl 〉 ≝ split ? 4 4 d in |
---|
826 | let bit_one ≝ get_index_v ? ? nu 0 ? in |
---|
827 | let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in |
---|
828 | match bit_one with |
---|
829 | [ false ⇒ |
---|
830 | let address ≝ three_bits @@ nl in |
---|
831 | lookup ? 7 address (low_internal_ram ? s) (zero 8) |
---|
832 | | true ⇒ get_bit_addressable_sfr ? s 8 d l |
---|
833 | ] |
---|
834 | | INDIRECT i ⇒ |
---|
835 | λindirect: True. |
---|
836 | let 〈 nu, nl 〉 ≝ split ? 4 4 (get_register ? s [[ false; false; i]]) in |
---|
837 | let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in |
---|
838 | let bit_1 ≝ get_index_v ?? bit_one_v O ? in |
---|
839 | match bit_1 with |
---|
840 | [ false ⇒ |
---|
841 | lookup ? 7 (three_bits @@ nl) (low_internal_ram ? s) (zero 8) |
---|
842 | | true ⇒ |
---|
843 | lookup ? 7 (three_bits @@ nl) (high_internal_ram ? s) (zero 8) |
---|
844 | ] |
---|
845 | | _ ⇒ λother. |
---|
846 | match other in False with [ ] |
---|
847 | ] (subaddressing_modein … a). |
---|
848 | [1,2: |
---|
849 | normalize |
---|
850 | repeat (@ le_S_S) |
---|
851 | @ le_O_n |
---|
852 | ] |
---|
853 | qed. |
---|
854 | |
---|
855 | definition set_arg_8: ∀M: Type[0]. PreStatus M → [[ direct ; indirect ; registr ; |
---|
856 | acc_a ; acc_b ; ext_indirect ; |
---|
857 | ext_indirect_dptr ]] → Byte → PreStatus M ≝ |
---|
858 | λm, s, a, v. |
---|
859 | match a return λx. bool_to_Prop (is_in ? [[ direct ; indirect ; registr ; |
---|
860 | acc_a ; acc_b ; ext_indirect ; |
---|
861 | ext_indirect_dptr ]] x) → ? with |
---|
862 | [ DIRECT d ⇒ |
---|
863 | λdirect: True. |
---|
864 | let 〈 nu, nl 〉 ≝ split … 4 4 d in |
---|
865 | let bit_one ≝ get_index_v ? ? nu 0 ? in |
---|
866 | let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in |
---|
867 | match bit_one with |
---|
868 | [ true ⇒ set_bit_addressable_sfr ? s d v |
---|
869 | | false ⇒ |
---|
870 | let memory ≝ insert ? 7 (three_bits @@ nl) v (low_internal_ram ? s) in |
---|
871 | set_low_internal_ram ? s memory |
---|
872 | ] |
---|
873 | | INDIRECT i ⇒ |
---|
874 | λindirect: True. |
---|
875 | let register ≝ get_register ? s [[ false; false; i ]] in |
---|
876 | let 〈nu, nl〉 ≝ split ? 4 4 register in |
---|
877 | let bit_1 ≝ get_index_v … nu 0 ? in |
---|
878 | let 〈ignore, three_bits〉 ≝ split ? 1 3 nu in |
---|
879 | match bit_1 with |
---|
880 | [ false ⇒ |
---|
881 | let memory ≝ insert … (three_bits @@ nl) v (low_internal_ram ? s) in |
---|
882 | set_low_internal_ram ? s memory |
---|
883 | | true ⇒ |
---|
884 | let memory ≝ insert … (three_bits @@ nl) v (high_internal_ram ? s) in |
---|
885 | set_high_internal_ram ? s memory |
---|
886 | ] |
---|
887 | | REGISTER r ⇒ λregister: True. set_register ? s r v |
---|
888 | | ACC_A ⇒ λacc_a: True. set_8051_sfr ? s SFR_ACC_A v |
---|
889 | | ACC_B ⇒ λacc_b: True. set_8051_sfr ? s SFR_ACC_B v |
---|
890 | | EXT_INDIRECT e ⇒ |
---|
891 | λext_indirect: True. |
---|
892 | let address ≝ get_register ? s [[ false; false; e ]] in |
---|
893 | let padded_address ≝ pad 8 8 address in |
---|
894 | let memory ≝ insert ? 16 padded_address v (external_ram ? s) in |
---|
895 | set_external_ram ? s memory |
---|
896 | | EXT_INDIRECT_DPTR ⇒ |
---|
897 | λext_indirect_dptr: True. |
---|
898 | let address ≝ (get_8051_sfr ? s SFR_DPH) @@ (get_8051_sfr ? s SFR_DPL) in |
---|
899 | let memory ≝ insert ? 16 address v (external_ram ? s) in |
---|
900 | set_external_ram ? s memory |
---|
901 | | _ ⇒ |
---|
902 | λother: False. |
---|
903 | match other in False with [ ] |
---|
904 | ] (subaddressing_modein … a). |
---|
905 | [1,2,3,4: |
---|
906 | normalize |
---|
907 | repeat (@ le_S_S) |
---|
908 | @ le_O_n |
---|
909 | ] |
---|
910 | qed. |
---|
911 | |
---|
912 | theorem modulus_less_than: |
---|
913 | ∀m,n: nat. (m mod (S n)) < S n. |
---|
914 | #n #m |
---|
915 | normalize |
---|
916 | @ le_S_S |
---|
917 | lapply (le_n n) |
---|
918 | generalize in ⊢ (?%? → ?(??%?)?) |
---|
919 | elim n in ⊢ (∀_:?. ??% → ?(?%??)?) |
---|
920 | [ normalize |
---|
921 | #n |
---|
922 | @ (less_than_or_equal_b_elim n m) |
---|
923 | normalize |
---|
924 | [ // |
---|
925 | | #H #K |
---|
926 | inversion K |
---|
927 | [ # H1 |
---|
928 | < H1 |
---|
929 | // |
---|
930 | | #x #H1 #H2 #H3 |
---|
931 | destruct |
---|
932 | ] |
---|
933 | ] |
---|
934 | | normalize |
---|
935 | # y # H1 # n # H2 |
---|
936 | @ (less_than_or_equal_b_elim n m) |
---|
937 | normalize |
---|
938 | [ // |
---|
939 | | # K |
---|
940 | @ H1 |
---|
941 | cut (n ≤ S y → n - S m ≤ y) |
---|
942 | /2/ |
---|
943 | cases n |
---|
944 | normalize |
---|
945 | // |
---|
946 | # x # K1 |
---|
947 | lapply (le_S_S_to_le … K1) |
---|
948 | generalize in match m |
---|
949 | elim x |
---|
950 | normalize |
---|
951 | // |
---|
952 | # w1 # H # m |
---|
953 | cases m |
---|
954 | normalize |
---|
955 | // |
---|
956 | # q # K2 |
---|
957 | apply H |
---|
958 | /3/ |
---|
959 | ] |
---|
960 | ] |
---|
961 | qed. |
---|
962 | |
---|
963 | definition get_arg_1: ∀M: Type[0]. PreStatus M → [[ bit_addr ; n_bit_addr ; carry ]] → |
---|
964 | bool → bool ≝ |
---|
965 | λm, s, a, l. |
---|
966 | match a return λx. bool_to_Prop (is_in ? [[ bit_addr ; |
---|
967 | n_bit_addr ; |
---|
968 | carry ]] x) → ? with |
---|
969 | [ BIT_ADDR b ⇒ |
---|
970 | λbit_addr: True. |
---|
971 | let 〈 nu, nl 〉 ≝ split … 4 4 b in |
---|
972 | let bit_1 ≝ get_index_v ? ? nu 0 ? in |
---|
973 | let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in |
---|
974 | match bit_1 with |
---|
975 | [ true ⇒ |
---|
976 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
977 | let d ≝ address ÷ 8 in |
---|
978 | let m ≝ address mod 8 in |
---|
979 | let trans ≝ bitvector_of_nat 8 ((d * 8) + 128) in |
---|
980 | let sfr ≝ get_bit_addressable_sfr ? s ? trans l in |
---|
981 | get_index_v … sfr m ? |
---|
982 | | false ⇒ |
---|
983 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
984 | let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in |
---|
985 | let t ≝ lookup … 7 address' (low_internal_ram ? s) (zero 8) in |
---|
986 | get_index_v … t (modulus address 8) ? |
---|
987 | ] |
---|
988 | | N_BIT_ADDR n ⇒ |
---|
989 | λn_bit_addr: True. |
---|
990 | let 〈 nu, nl 〉 ≝ split … 4 4 n in |
---|
991 | let bit_1 ≝ get_index_v ? ? nu 0 ? in |
---|
992 | let 〈 bit_one_v, three_bits 〉 ≝ split ? 1 3 nu in |
---|
993 | match bit_1 with |
---|
994 | [ true ⇒ |
---|
995 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
996 | let d ≝ address ÷ 8 in |
---|
997 | let m ≝ address mod 8 in |
---|
998 | let trans ≝ bitvector_of_nat 8 ((d * 8) + 128) in |
---|
999 | let sfr ≝ get_bit_addressable_sfr ? s ? trans l in |
---|
1000 | ¬(get_index_v … sfr m ?) |
---|
1001 | | false ⇒ |
---|
1002 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
1003 | let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in |
---|
1004 | let trans ≝ lookup ? 7 address' (low_internal_ram ? s) (zero 8) in |
---|
1005 | ¬(get_index_v … trans (modulus address 8) ?) |
---|
1006 | ] |
---|
1007 | | CARRY ⇒ λcarry: True. get_cy_flag ? s |
---|
1008 | | _ ⇒ λother. |
---|
1009 | match other in False with [ ] |
---|
1010 | ] (subaddressing_modein … a). |
---|
1011 | [3,6: |
---|
1012 | normalize |
---|
1013 | repeat (@ le_S_S) |
---|
1014 | @ le_O_n |
---|
1015 | |1,2,4,5: |
---|
1016 | apply modulus_less_than |
---|
1017 | ] |
---|
1018 | qed. |
---|
1019 | |
---|
1020 | definition set_arg_1: ∀M: Type[0]. PreStatus M → [[ bit_addr ; carry ]] → |
---|
1021 | Bit → PreStatus M ≝ |
---|
1022 | λm, s, a, v. |
---|
1023 | match a return λx. bool_to_Prop (is_in ? [[ bit_addr ; carry ]] x) → ? with |
---|
1024 | [ BIT_ADDR b ⇒ λbit_addr: True. |
---|
1025 | let 〈 nu, nl 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_PSW) in |
---|
1026 | let bit_1 ≝ get_index_v … nu 0 ? in |
---|
1027 | let 〈 ignore, three_bits 〉 ≝ split ? 1 3 nu in |
---|
1028 | match bit_1 with |
---|
1029 | [ true ⇒ |
---|
1030 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
1031 | let d ≝ address ÷ 8 in |
---|
1032 | let m ≝ address mod 8 in |
---|
1033 | let t ≝ bitvector_of_nat 8 ((d * 8) + 128) in |
---|
1034 | let sfr ≝ get_bit_addressable_sfr ? s ? t true in |
---|
1035 | let new_sfr ≝ set_index … sfr m v ? in |
---|
1036 | set_bit_addressable_sfr ? s new_sfr t |
---|
1037 | | false ⇒ |
---|
1038 | let address ≝ nat_of_bitvector … (three_bits @@ nl) in |
---|
1039 | let address' ≝ bitvector_of_nat 7 ((address ÷ 8) + 32) in |
---|
1040 | let t ≝ lookup ? 7 address' (low_internal_ram ? s) (zero 8) in |
---|
1041 | let n_bit ≝ set_index … t (modulus address 8) v ? in |
---|
1042 | let memory ≝ insert ? 7 address' n_bit (low_internal_ram ? s) in |
---|
1043 | set_low_internal_ram ? s memory |
---|
1044 | ] |
---|
1045 | | CARRY ⇒ |
---|
1046 | λcarry: True. |
---|
1047 | let 〈 nu, nl 〉 ≝ split ? 4 4 (get_8051_sfr ? s SFR_PSW) in |
---|
1048 | let bit_1 ≝ get_index_v… nu 1 ? in |
---|
1049 | let bit_2 ≝ get_index_v… nu 2 ? in |
---|
1050 | let bit_3 ≝ get_index_v… nu 3 ? in |
---|
1051 | let new_psw ≝ [[ v; bit_1 ; bit_2; bit_3 ]] @@ nl in |
---|
1052 | set_8051_sfr ? s SFR_PSW new_psw |
---|
1053 | | _ ⇒ |
---|
1054 | λother: False. |
---|
1055 | match other in False with |
---|
1056 | [ ] |
---|
1057 | ] (subaddressing_modein … a). |
---|
1058 | [1,2,3,6: |
---|
1059 | normalize |
---|
1060 | repeat (@ le_S_S) |
---|
1061 | @ le_O_n |
---|
1062 | |4,5: |
---|
1063 | @ modulus_less_than |
---|
1064 | ] |
---|
1065 | qed. |
---|
1066 | |
---|
1067 | definition load_code_memory ≝ |
---|
1068 | fold_left_i … ( |
---|
1069 | λi, mem, v. |
---|
1070 | insert … (bitvector_of_nat … i) v mem) (Stub Byte 16). |
---|
1071 | |
---|
1072 | definition load ≝ |
---|
1073 | λl. |
---|
1074 | λstatus. |
---|
1075 | set_code_memory (BitVectorTrie Word 16) ? status (load_code_memory l). |
---|
1076 | |
---|
1077 | definition fetch_pseudo_instruction: list labelled_instruction → Word → (pseudo_instruction × Word) ≝ |
---|
1078 | λcode_mem. |
---|
1079 | λpc: Word. |
---|
1080 | let 〈lbl, instr〉 ≝ nth (nat_of_bitvector ? pc) … code_mem ? in |
---|
1081 | let 〈flags, new_pc〉 ≝ half_add ? pc (bitvector_of_nat ? 1) in |
---|
1082 | 〈instr, new_pc〉. |
---|
1083 | cases not_implemented. |
---|
1084 | qed. |
---|
1085 | |
---|
1086 | lemma snd_fetch_pseudo_instruction: |
---|
1087 | ∀l,ppc. \snd (fetch_pseudo_instruction l ppc) = \snd (half_add ? ppc (bitvector_of_nat ? 1)). |
---|
1088 | #l #ppc whd in ⊢ (??%?) whd in ⊢ (?? match % with [_ ⇒ ?]?) @pair_elim' |
---|
1089 | #lft #rgt @pair_elim' #x #y #_ @pair_elim' #a #b #_ normalize #H |
---|
1090 | generalize in match (pair_destruct_2 ????? H) normalize #K >K % |
---|
1091 | qed. |
---|
1092 | |
---|
1093 | definition instruction_matches_identifier ≝ |
---|
1094 | λy: Identifier. |
---|
1095 | λx: labelled_instruction. |
---|
1096 | match \fst x with |
---|
1097 | [ None ⇒ false |
---|
1098 | | Some x ⇒ eq_identifier ? x y |
---|
1099 | ]. |
---|
1100 | |
---|
1101 | let rec does_not_occur (id:Identifier) (l:list labelled_instruction) on l: bool ≝ |
---|
1102 | match l with |
---|
1103 | [ nil ⇒ true |
---|
1104 | | cons hd tl ⇒ notb (instruction_matches_identifier id hd) ∧ does_not_occur id tl]. |
---|
1105 | |
---|
1106 | lemma does_not_occur_None: |
---|
1107 | ∀id,i,list_instr. |
---|
1108 | does_not_occur id (list_instr@[〈None …,i〉]) = |
---|
1109 | does_not_occur id list_instr. |
---|
1110 | #id #i #list_instr elim list_instr |
---|
1111 | [ % | #hd #tl #IH whd in ⊢ (??%%) >IH %] |
---|
1112 | qed. |
---|
1113 | |
---|
1114 | lemma does_not_occur_Some: |
---|
1115 | ∀id,id',i,list_instr. |
---|
1116 | eq_identifier ? id' id = false → |
---|
1117 | does_not_occur id (list_instr@[〈Some ? id',i〉]) = |
---|
1118 | does_not_occur id list_instr. |
---|
1119 | #id #id' #i #list_instr elim list_instr |
---|
1120 | [ #H normalize in H ⊢ %; >H % |
---|
1121 | | * #x #i' #tl #IH #H whd in ⊢ (??%%) >(IH H) %] |
---|
1122 | qed. |
---|
1123 | |
---|
1124 | lemma does_not_occur_absurd: |
---|
1125 | ∀id,i,list_instr. |
---|
1126 | does_not_occur id (list_instr@[〈Some ? id,i〉]) = false. |
---|
1127 | #id #i #list_instr elim list_instr |
---|
1128 | [ normalize change with (if (if eq_identifier ??? then ? else ?) then ? else ? = ?) |
---|
1129 | >eq_identifier_refl % |
---|
1130 | | * #x #i' #tl #IH whd in ⊢ (??%%) >IH cases (notb ?) %] |
---|
1131 | qed. |
---|
1132 | |
---|
1133 | |
---|
1134 | let rec occurs_exactly_once (id:Identifier) (l:list labelled_instruction) on l : bool ≝ |
---|
1135 | match l with |
---|
1136 | [ nil ⇒ false |
---|
1137 | | cons hd tl ⇒ |
---|
1138 | if instruction_matches_identifier id hd then |
---|
1139 | does_not_occur id tl |
---|
1140 | else |
---|
1141 | occurs_exactly_once id tl ]. |
---|
1142 | |
---|
1143 | lemma occurs_exactly_once_None: |
---|
1144 | ∀id,i,list_instr. |
---|
1145 | occurs_exactly_once id (list_instr@[〈None …,i〉]) = |
---|
1146 | occurs_exactly_once id list_instr. |
---|
1147 | #id #i #list_instr elim list_instr |
---|
1148 | [ % | #hd #tl #IH whd in ⊢ (??%%) >IH >does_not_occur_None %] |
---|
1149 | qed. |
---|
1150 | |
---|
1151 | lemma occurs_exactly_once_Some: |
---|
1152 | ∀id,id',i,prefix. |
---|
1153 | occurs_exactly_once id (prefix@[〈Some ? id',i〉]) → eq_identifier ? id' id ∨ occurs_exactly_once id prefix. |
---|
1154 | #id #id' #i #prefix elim prefix |
---|
1155 | [ whd in ⊢ (?% → ?) |
---|
1156 | change in ⊢ (?(match % with [_ ⇒ ? | _ ⇒ ?]) → ?) with (eq_identifier ? id' id) |
---|
1157 | @eq_identifier_elim normalize nodelta; /2/ |
---|
1158 | | *; #he #i' #tl #IH whd in ⊢ (?% → ?) whd in ⊢ (?(match % with [_ ⇒ ? | _ ⇒ ?]) → ?) |
---|
1159 | cases he; normalize nodelta |
---|
1160 | [ #H @ (IH H) |
---|
1161 | | #x whd in ⊢ (? → ?(??%)) change in match (instruction_matches_identifier ??) with (eq_identifier ? x id) |
---|
1162 | @eq_identifier_elim #E normalize nodelta |
---|
1163 | [ destruct @eq_identifier_elim normalize nodelta; |
---|
1164 | /2/ #H >does_not_occur_Some /2/ |
---|
1165 | | #H @IH @H]]] |
---|
1166 | qed. |
---|
1167 | |
---|
1168 | lemma occurs_exactly_once_Some_stronger: |
---|
1169 | ∀id,id',i,prefix. |
---|
1170 | occurs_exactly_once id (prefix@[〈Some ? id',i〉]) → |
---|
1171 | (eq_identifier ? id' id ∧ does_not_occur id prefix) ∨ |
---|
1172 | (¬eq_identifier ? id' id ∧ occurs_exactly_once id prefix). |
---|
1173 | #id #id' #i #prefix elim prefix |
---|
1174 | [ whd in ⊢ (?% → ?) change in ⊢ (?(match % with [_ ⇒ ?| _ ⇒ ?]) → ?) with (eq_identifier ???) |
---|
1175 | @eq_identifier_elim #E |
---|
1176 | [ normalize // |
---|
1177 | | normalize #H @⊥ @H |
---|
1178 | ] |
---|
1179 | | *; #he #i' #tl #IH whd in ⊢ (?% → ?) whd in ⊢ (?(match % with [_ ⇒ ? | _ ⇒ ?]) → ?) |
---|
1180 | cases he; normalize nodelta |
---|
1181 | [ #H @ (IH H) |
---|
1182 | | #x @eq_identifier_elim #Heq |
---|
1183 | [ @eq_identifier_elim normalize nodelta |
---|
1184 | [ #H >H >does_not_occur_absurd #Hf @⊥ @Hf |
---|
1185 | | #H >(does_not_occur_Some) |
---|
1186 | [ #H2 whd in match (does_not_occur ??) |
---|
1187 | change in match (instruction_matches_identifier ??) with (eq_identifier ???) |
---|
1188 | >Heq >eq_identifier_refl normalize nodelta |
---|
1189 | @orb_elim normalize nodelta whd in match (occurs_exactly_once ??) |
---|
1190 | change in match (instruction_matches_identifier ??) with (eq_identifier ???) |
---|
1191 | >eq_identifier_refl |
---|
1192 | normalize nodelta @H2 |
---|
1193 | | /2/ |
---|
1194 | ] |
---|
1195 | ] |
---|
1196 | | normalize nodelta #H lapply (IH H) -IH -H; |
---|
1197 | @eq_identifier_elim #Heq2 |
---|
1198 | #Hor @orb_elim |
---|
1199 | [ <Heq2 in Hor; #Hor normalize in Hor; |
---|
1200 | whd in match (does_not_occur ??) change in match (instruction_matches_identifier ??) with (eq_identifier ???) |
---|
1201 | >eq_identifier_false // normalize nodelta |
---|
1202 | cases (does_not_occur id' tl) in Hor; normalize nodelta // |
---|
1203 | | normalize nodelta whd in match (occurs_exactly_once ??) |
---|
1204 | change in match (instruction_matches_identifier ??) with (eq_identifier ???) |
---|
1205 | >eq_identifier_false // |
---|
1206 | ] |
---|
1207 | ] |
---|
1208 | ] |
---|
1209 | ] |
---|
1210 | qed. |
---|
1211 | |
---|
1212 | let rec index_of_internal (A: Type[0]) (pred: A → bool) (l: list A) (acc: nat) on l: nat ≝ |
---|
1213 | match l with |
---|
1214 | [ nil ⇒ ? |
---|
1215 | | cons hd tl ⇒ |
---|
1216 | if pred hd then |
---|
1217 | acc |
---|
1218 | else |
---|
1219 | index_of_internal A pred tl (S acc) |
---|
1220 | ]. |
---|
1221 | cases not_implemented. |
---|
1222 | qed. |
---|
1223 | |
---|
1224 | |
---|
1225 | definition index_of ≝ |
---|
1226 | λA. |
---|
1227 | λeq. |
---|
1228 | λl. |
---|
1229 | index_of_internal A eq l 0. |
---|
1230 | |
---|
1231 | lemma index_of_internal_None: ∀i,id,instr_list,n. |
---|
1232 | occurs_exactly_once id (instr_list@[〈None …,i〉]) → |
---|
1233 | index_of_internal ? (instruction_matches_identifier id) instr_list n = |
---|
1234 | index_of_internal ? (instruction_matches_identifier id) (instr_list@[〈None …,i〉]) n. |
---|
1235 | #i #id #instr_list elim instr_list |
---|
1236 | [ #n #abs whd in abs; cases abs |
---|
1237 | | #hd #tl #IH #n whd in ⊢ (% → ??%%); whd in ⊢ (match % with [_ ⇒ ? | _ ⇒ ?] → ?) |
---|
1238 | cases (instruction_matches_identifier id hd) whd in ⊢ (match % with [_ ⇒ ? | _ ⇒ ?] → ??%%) |
---|
1239 | [ #H % |
---|
1240 | | #H @IH whd in H; cases (occurs_exactly_once ??) in H ⊢ % |
---|
1241 | [ #_ % | #abs cases abs ]]] |
---|
1242 | qed. |
---|
1243 | |
---|
1244 | lemma index_of_internal_Some_miss: ∀i,id,id'. |
---|
1245 | eq_identifier ? id' id = false → |
---|
1246 | ∀instr_list,n. |
---|
1247 | occurs_exactly_once id (instr_list@[〈Some ? id',i〉]) → |
---|
1248 | index_of_internal ? (instruction_matches_identifier id) instr_list n = |
---|
1249 | index_of_internal ? (instruction_matches_identifier id) (instr_list@[〈Some ? id',i〉]) n. |
---|
1250 | #i #id #id' #EQ #instr_list #n #H generalize in match (occurs_exactly_once_Some … H) in ⊢ ?; >EQ |
---|
1251 | change with (occurs_exactly_once ?? → ?) generalize in match n; -n H; elim instr_list |
---|
1252 | [ #n #abs cases abs |
---|
1253 | | #hd #tl #IH #n whd in ⊢ (?% → ??%%) cases (instruction_matches_identifier id hd) normalize nodelta; |
---|
1254 | [ // | #K @IH //]] |
---|
1255 | qed. |
---|
1256 | |
---|
1257 | lemma index_of_internal_Some_hit: ∀i,id. |
---|
1258 | ∀instr_list,n. |
---|
1259 | occurs_exactly_once id (instr_list@[〈Some ? id,i〉]) → |
---|
1260 | index_of_internal ? (instruction_matches_identifier id) (instr_list@[〈Some ? id,i〉]) n |
---|
1261 | = |instr_list| + n. |
---|
1262 | #i #id #instr_list elim instr_list |
---|
1263 | [ #n #_ whd in ⊢ (??%%) change with (if eq_identifier … id id then ? else ? = ?) >eq_identifier_refl % |
---|
1264 | | #hd #tl #IH #n whd in ⊢ (?% → ??%%) cases (instruction_matches_identifier id hd) normalize nodelta; |
---|
1265 | [ >does_not_occur_absurd #abs cases abs | #H >plus_n_Sm applyS (IH (S n)) //]] |
---|
1266 | qed. |
---|
1267 | |
---|
1268 | definition address_of_word_labels_code_mem ≝ |
---|
1269 | λcode_mem. |
---|
1270 | λid: Identifier. |
---|
1271 | bitvector_of_nat 16 (index_of ? (instruction_matches_identifier id) code_mem). |
---|
1272 | |
---|
1273 | lemma address_of_word_labels_code_mem_None: ∀i,id,instr_list. |
---|
1274 | occurs_exactly_once id (instr_list@[〈None …,i〉]) → |
---|
1275 | address_of_word_labels_code_mem instr_list id = |
---|
1276 | address_of_word_labels_code_mem (instr_list@[〈None …,i〉]) id. |
---|
1277 | #i #id #instr_list #H whd in ⊢ (??%%) whd in ⊢ (??(??%?)(??%?)) |
---|
1278 | >(index_of_internal_None … H) % |
---|
1279 | qed. |
---|
1280 | |
---|
1281 | lemma address_of_word_labels_code_mem_Some_miss: ∀i,id,id',instr_list. |
---|
1282 | eq_identifier ? id' id = false → |
---|
1283 | occurs_exactly_once id (instr_list@[〈Some ? id',i〉]) → |
---|
1284 | address_of_word_labels_code_mem instr_list id = |
---|
1285 | address_of_word_labels_code_mem (instr_list@[〈Some … id',i〉]) id. |
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1286 | #i #id #id' #instr_list #EQ #H whd in ⊢ (??%%) whd in ⊢ (??(??%?)(??%?)) |
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1287 | >(index_of_internal_Some_miss … H) [ @refl | // ] |
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1288 | qed. |
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1289 | |
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1290 | lemma address_of_word_labels_code_mem_Some_hit: ∀i,id,instr_list. |
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1291 | occurs_exactly_once id (instr_list@[〈Some ? id,i〉]) → |
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1292 | address_of_word_labels_code_mem (instr_list@[〈Some … id,i〉]) id |
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1293 | = bitvector_of_nat … (|instr_list|). |
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1294 | #i #id #instr_list #H whd in ⊢ (??%%) whd in ⊢ (??(??%?)?) |
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1295 | >(index_of_internal_Some_hit … H) <plus_n_O @refl |
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1296 | qed. |
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1297 | |
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1298 | definition address_of_word_labels ≝ |
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1299 | λps: PseudoStatus. |
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1300 | λid: Identifier. |
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1301 | address_of_word_labels_code_mem (\snd (code_memory ? ps)) id. |
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1302 | |
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1303 | definition construct_datalabels ≝ |
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1304 | λpreamble. |
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1305 | \fst (foldl ((identifier_map ASMTag Word) × nat) ? ( |
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1306 | λt. λpreamble. |
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1307 | let 〈datalabels, addr〉 ≝ t in |
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1308 | let 〈name, size〉 ≝ preamble in |
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1309 | let addr_16 ≝ bitvector_of_nat 16 addr in |
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1310 | 〈add ? ? datalabels name addr_16, addr + size〉) |
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1311 | 〈empty_map …, 0〉 preamble). |
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