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.ma". *) |
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6 | include "Arithmetic.ma". |
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7 | include "BitVectorTrie.ma". |
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8 | |
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9 | ndefinition Time ≝ Nat. |
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10 | |
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11 | ninductive 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 | ninductive 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 | ninductive 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 | ndefinition 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 ⇒ Z |
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47 | | SFR_DPL ⇒ S Z |
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48 | | SFR_DPH ⇒ two |
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49 | | SFR_PCON ⇒ three |
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50 | | SFR_TCON ⇒ four |
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51 | | SFR_TMOD ⇒ five |
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52 | | SFR_TL0 ⇒ six |
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53 | | SFR_TL1 ⇒ seven |
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54 | | SFR_TH0 ⇒ eight |
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55 | | SFR_TH1 ⇒ nine |
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56 | | SFR_P1 ⇒ ten |
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57 | | SFR_SCON ⇒ eleven |
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58 | | SFR_SBUF ⇒ twelve |
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59 | | SFR_IE ⇒ thirteen |
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60 | | SFR_P3 ⇒ fourteen |
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61 | | SFR_IP ⇒ fifteen |
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62 | | SFR_PSW ⇒ sixteen |
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63 | | SFR_ACC_A ⇒ seventeen |
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64 | | SFR_ACC_B ⇒ eighteen |
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65 | ]. |
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66 | |
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67 | ninductive 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 | ndefinition 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 ⇒ Z |
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78 | | SFR_RCAP2L ⇒ S Z |
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79 | | SFR_RCAP2H ⇒ two |
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80 | | SFR_TL2 ⇒ three |
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81 | | SFR_TH2 ⇒ four |
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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 | nrecord Status: Type[0] ≝ |
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88 | { |
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89 | code_memory: BitVectorTrie Byte sixteen; |
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90 | low_internal_ram: BitVectorTrie Byte seven; |
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91 | high_internal_ram: BitVectorTrie Byte seven; |
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92 | external_ram: BitVectorTrie Byte sixteen; |
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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 nineteen; |
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97 | special_function_registers_8052: Vector Byte five; |
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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 | |
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103 | naxiom sfr8051_index_nineteen: |
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104 | ∀i: SFR8051. |
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105 | sfr_8051_index i < nineteen. |
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106 | |
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107 | naxiom sfr8052_index_five: |
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108 | ∀i: SFR8052. |
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109 | sfr_8052_index i < five. |
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110 | |
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111 | ndefinition get_8051_sfr ≝ |
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112 | λs: Status. |
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113 | λi: SFR8051. |
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114 | let sfr ≝ special_function_registers_8051 s in |
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115 | let index ≝ sfr_8051_index i in |
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116 | get_index … sfr index ?. |
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117 | napply (sfr8051_index_nineteen i). |
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118 | nqed. |
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119 | |
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120 | ndefinition get_8052_sfr ≝ |
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121 | λs: Status. |
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122 | λi: SFR8052. |
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123 | let sfr ≝ special_function_registers_8052 s in |
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124 | let index ≝ sfr_8052_index i in |
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125 | get_index … sfr index ?. |
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126 | napply (sfr8052_index_five i). |
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127 | nqed. |
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128 | |
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129 | ndefinition set_8051_sfr ≝ |
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130 | λs: Status. |
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131 | λi: SFR8051. |
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132 | λb: Byte. |
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133 | let index ≝ sfr_8051_index i in |
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134 | let old_code_memory ≝ code_memory s in |
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135 | let old_low_internal_ram ≝ low_internal_ram s in |
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136 | let old_high_internal_ram ≝ high_internal_ram s in |
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137 | let old_external_ram ≝ external_ram s in |
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138 | let old_program_counter ≝ program_counter s in |
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139 | let old_special_function_registers_8051 ≝ special_function_registers_8051 s in |
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140 | let old_special_function_registers_8052 ≝ special_function_registers_8052 s in |
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141 | let new_special_function_registers_8051 ≝ |
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142 | cic:/matita/ng/Vector/set_index.fix(0,3,2) Byte nineteen old_special_function_registers_8051 index b ? in |
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143 | mk_Status old_code_memory |
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144 | old_low_internal_ram |
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145 | old_high_internal_ram |
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146 | old_external_ram |
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147 | old_program_counter |
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148 | new_special_function_registers_8051 |
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149 | old_special_function_registers_8052. |
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150 | napply (sfr8051_index_nineteen i). |
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151 | nqed. |
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152 | |
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153 | ndefinition set_8052_sfr ≝ |
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154 | λs: Status. |
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155 | λi: SFR8052. |
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156 | λb: Byte. |
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157 | let index ≝ sfr_8052_index i in |
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158 | let old_code_memory ≝ code_memory s in |
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159 | let old_low_internal_ram ≝ low_internal_ram s in |
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160 | let old_high_internal_ram ≝ high_internal_ram s in |
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161 | let old_external_ram ≝ external_ram s in |
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162 | let old_program_counter ≝ program_counter s in |
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163 | let old_special_function_registers_8051 ≝ special_function_registers_8051 s in |
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164 | let old_special_function_registers_8052 ≝ special_function_registers_8052 s in |
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165 | let new_special_function_registers_8052 ≝ |
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166 | cic:/matita/ng/Vector/set_index.fix(0,3,2) Byte five old_special_function_registers_8052 index b ? in |
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167 | mk_Status old_code_memory |
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168 | old_low_internal_ram |
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169 | old_high_internal_ram |
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170 | old_external_ram |
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171 | old_program_counter |
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172 | old_special_function_registers_8051 |
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173 | new_special_function_registers_8052. |
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174 | napply (sfr8052_index_five i). |
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175 | nqed. |
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176 | |
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177 | ndefinition set_program_counter ≝ |
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178 | λs: Status. |
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179 | λw: Word. |
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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_special_function_registers_8051 ≝ special_function_registers_8051 s in |
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185 | let old_special_function_registers_8052 ≝ special_function_registers_8052 s in |
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186 | mk_Status old_code_memory |
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187 | old_low_internal_ram |
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188 | old_high_internal_ram |
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189 | old_external_ram |
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190 | w |
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191 | old_special_function_registers_8051 |
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192 | old_special_function_registers_8052. |
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193 | |
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194 | ndefinition set_code_memory ≝ |
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195 | λs: Status. |
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196 | λi: SFR8052. |
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197 | λr: BitVectorTrie Byte sixteen. |
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198 | let index ≝ sfr_8052_index i in |
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199 | let old_low_internal_ram ≝ low_internal_ram s in |
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200 | let old_high_internal_ram ≝ high_internal_ram s in |
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201 | let old_external_ram ≝ external_ram s in |
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202 | let old_program_counter ≝ program_counter s in |
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203 | let old_special_function_registers_8051 ≝ special_function_registers_8051 s in |
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204 | let old_special_function_registers_8052 ≝ special_function_registers_8052 s in |
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205 | mk_Status r |
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206 | old_low_internal_ram |
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207 | old_high_internal_ram |
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208 | old_external_ram |
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209 | old_program_counter |
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210 | old_special_function_registers_8051 |
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211 | old_special_function_registers_8052. |
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212 | |
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213 | ndefinition set_low_internal_ram ≝ |
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214 | λs: Status. |
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215 | λi: SFR8052. |
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216 | λr: BitVectorTrie Byte seven. |
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217 | let index ≝ sfr_8052_index i in |
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218 | let old_code_memory ≝ code_memory s in |
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219 | let old_high_internal_ram ≝ high_internal_ram s in |
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220 | let old_external_ram ≝ external_ram s in |
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221 | let old_program_counter ≝ program_counter s in |
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222 | let old_special_function_registers_8051 ≝ special_function_registers_8051 s in |
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223 | let old_special_function_registers_8052 ≝ special_function_registers_8052 s in |
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224 | mk_Status old_code_memory |
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225 | r |
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226 | old_high_internal_ram |
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227 | old_external_ram |
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228 | old_program_counter |
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229 | old_special_function_registers_8051 |
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230 | old_special_function_registers_8052. |
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231 | |
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232 | naxiom less_than_or_equal_monotone: |
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233 | ∀m, n: Nat. |
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234 | m ≤ n → S m ≤ S n. |
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235 | |
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236 | alias id "get_index" = "cic:/matita/ng/Vector/get_index.fix(0,3,2)". |
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237 | |
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238 | ndefinition get_cy_flag ≝ |
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239 | λs: Status. |
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240 | let sfr ≝ special_function_registers_8051 s in |
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241 | let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in |
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242 | get_index Bool eight psw Z ?. |
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243 | nnormalize. |
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244 | napply (less_than_or_equal_monotone ? ?). |
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245 | napply (less_than_or_equal_zero). |
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246 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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247 | napply (less_than_or_equal_zero). |
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248 | nqed. |
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249 | |
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250 | ndefinition get_ac_flag ≝ |
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251 | λs: Status. |
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252 | let sfr ≝ special_function_registers_8051 s in |
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253 | let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in |
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254 | get_index Bool eight psw (S Z) ?. |
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255 | nnormalize. |
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256 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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257 | napply (less_than_or_equal_zero). |
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258 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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259 | napply (less_than_or_equal_zero). |
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260 | nqed. |
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261 | |
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262 | ndefinition get_fo_flag ≝ |
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263 | λs: Status. |
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264 | let sfr ≝ special_function_registers_8051 s in |
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265 | let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in |
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266 | get_index Bool eight psw two ?. |
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267 | nnormalize. |
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268 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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269 | napply (less_than_or_equal_zero). |
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270 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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271 | napply (less_than_or_equal_zero). |
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272 | nqed. |
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273 | |
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274 | ndefinition get_rs1_flag ≝ |
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275 | λs: Status. |
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276 | let sfr ≝ special_function_registers_8051 s in |
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277 | let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in |
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278 | get_index Bool eight psw three ?. |
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279 | nnormalize. |
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280 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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281 | napply (less_than_or_equal_zero). |
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282 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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283 | napply (less_than_or_equal_zero). |
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284 | nqed. |
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285 | |
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286 | ndefinition get_rs0_flag ≝ |
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287 | λs: Status. |
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288 | let sfr ≝ special_function_registers_8051 s in |
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289 | let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in |
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290 | get_index Bool eight psw four ?. |
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291 | nnormalize. |
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292 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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293 | napply (less_than_or_equal_zero). |
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294 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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295 | napply (less_than_or_equal_zero). |
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296 | nqed. |
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297 | |
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298 | ndefinition get_ov_flag ≝ |
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299 | λs: Status. |
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300 | let sfr ≝ special_function_registers_8051 s in |
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301 | let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in |
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302 | get_index Bool eight psw five ?. |
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303 | nnormalize. |
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304 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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305 | napply (less_than_or_equal_zero). |
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306 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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307 | napply (less_than_or_equal_zero). |
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308 | nqed. |
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309 | |
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310 | ndefinition get_ud_flag ≝ |
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311 | λs: Status. |
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312 | let sfr ≝ special_function_registers_8051 s in |
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313 | let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in |
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314 | get_index Bool eight psw six ?. |
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315 | nnormalize. |
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316 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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317 | napply (less_than_or_equal_zero). |
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318 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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319 | napply (less_than_or_equal_zero). |
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320 | nqed. |
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321 | |
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322 | ndefinition get_p_flag ≝ |
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323 | λs: Status. |
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324 | let sfr ≝ special_function_registers_8051 s in |
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325 | let psw ≝ get_index Byte nineteen sfr (sfr_8051_index SFR_PSW) ? in |
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326 | get_index Bool eight psw seven ?. |
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327 | nnormalize. |
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328 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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329 | napply (less_than_or_equal_zero). |
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330 | nrepeat (napply (less_than_or_equal_monotone ? ?)). |
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331 | napply (less_than_or_equal_zero). |
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332 | nqed. |
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333 | |
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334 | ndefinition set_high_internal_ram ≝ |
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335 | λs: Status. |
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336 | λi: SFR8052. |
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337 | λr: BitVectorTrie Byte seven. |
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338 | let index ≝ sfr_8052_index i in |
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339 | let old_code_memory ≝ code_memory s in |
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340 | let old_low_internal_ram ≝ low_internal_ram s in |
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341 | let old_high_internal_ram ≝ high_internal_ram s in |
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342 | let old_external_ram ≝ external_ram s in |
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343 | let old_program_counter ≝ program_counter s in |
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344 | let old_special_function_registers_8051 ≝ special_function_registers_8051 s in |
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345 | let old_special_function_registers_8052 ≝ special_function_registers_8052 s in |
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346 | mk_Status old_code_memory |
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347 | old_low_internal_ram |
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348 | r |
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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 | |
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354 | ndefinition initialise_status ≝ |
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355 | let status ≝ mk_Status (Stub Byte sixteen) |
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356 | (Stub Byte seven) |
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357 | (Stub Byte seven) |
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358 | (Stub Byte sixteen) |
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359 | (zero sixteen) |
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360 | (replicate Byte nineteen (zero eight)) |
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361 | (replicate Byte five (zero eight)) |
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362 | (zero eight) |
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363 | (zero eight) in |
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364 | set_program_counter status (bitvector_of_nat sixteen seven). |
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365 | |
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366 | naxiom not_implemented: False. |
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367 | |
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368 | include "Arithmetic.ma". |
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369 | |
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370 | ndefinition get_bit_addressable_sfr ≝ |
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371 | λs: Status. |
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372 | λn: Nat. |
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373 | λb: BitVector n. |
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374 | λl: Bool. |
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375 | let address ≝ nat_of_bitvector … b in |
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376 | if (decidable_equality address one_hundred_and_twenty_eight) then |
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377 | ? |
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378 | else if (decidable_equality address one_hundred_and_forty_four) then |
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379 | if l then |
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380 | (p1_latch s) |
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381 | else |
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382 | (get_8051_sfr s SFR_P1) |
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383 | else if (decidable_equality address one_hundred_and_sixty) then |
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384 | ? |
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385 | else if (decidable_equality address one_hundred_and_seventy_six) then |
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386 | if l then |
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387 | (p3_latch s) |
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388 | else |
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389 | (get_8051_sfr s SFR_P3) |
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390 | else if (decidable_equality address one_hundred_and_fifty_three) then |
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391 | get_8051_sfr s SFR_SBUF |
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392 | else if (decidable_equality address one_hundred_and_thirty_eight) then |
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393 | get_8051_sfr s SFR_TL0 |
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394 | else if (decidable_equality address one_hundred_and_thirty_nine) then |
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395 | get_8051_sfr s SFR_TL1 |
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396 | else if (decidable_equality address one_hundred_and_forty) then |
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397 | get_8051_sfr s SFR_TH0 |
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398 | else if (decidable_equality address one_hundred_and_forty_one) then |
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399 | get_8051_sfr s SFR_TH1 |
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400 | else if (decidable_equality address two_hundred) then |
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401 | get_8052_sfr s SFR_T2CON |
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402 | else if (decidable_equality address two_hundred_and_two) then |
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403 | get_8052_sfr s SFR_RCAP2L |
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404 | else if (decidable_equality address two_hundred_and_three) then |
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405 | get_8052_sfr s SFR_RCAP2H |
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406 | else if (decidable_equality address two_hundred_and_four) then |
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407 | get_8052_sfr s SFR_TL2 |
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408 | else if (decidable_equality address two_hundred_and_five) then |
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409 | get_8052_sfr s SFR_TH2 |
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410 | else if (decidable_equality address one_hundred_and_thirty_five) then |
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411 | get_8051_sfr s SFR_PCON |
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412 | else if (decidable_equality address one_hundred_and_thirty_six) then |
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413 | get_8051_sfr s SFR_TCON |
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414 | else if (decidable_equality address one_hundred_and_thirty_seven) then |
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415 | get_8051_sfr s SFR_TMOD |
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416 | else if (decidable_equality address one_hundred_and_fifty_two) then |
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417 | get_8051_sfr s SFR_SCON |
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418 | else if (decidable_equality address one_hundred_and_sixty_eight) then |
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419 | get_8051_sfr s SFR_IE |
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420 | else if (decidable_equality address one_hundred_and_eighty_four) then |
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421 | get_8051_sfr s SFR_IP |
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422 | else if (decidable_equality address one_hundred_and_twenty_nine) then |
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423 | get_8051_sfr s SFR_SP |
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424 | else if (decidable_equality address one_hundred_and_thirty) then |
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425 | get_8051_sfr s SFR_DPL |
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426 | else if (decidable_equality address one_hundred_and_thirty_one) then |
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427 | get_8051_sfr s SFR_DPH |
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428 | else if (decidable_equality address two_hundred_and_eight) then |
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429 | get_8051_sfr s SFR_PSW |
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430 | else if (decidable_equality address two_hundred_and_twenty_four) then |
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431 | get_8051_sfr s SFR_ACC_A |
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432 | else if (decidable_equality address two_hundred_and_forty) then |
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433 | get_8051_sfr s SFR_ACC_B |
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434 | else |
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435 | ?. |
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436 | ncases not_implemented. |
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437 | nqed. |
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