1 | include "ASM/AssemblyProof.ma". |
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2 | include alias "arithmetics/nat.ma". |
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3 | include alias "basics/logic.ma". |
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4 | |
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5 | lemma set_arg_16_mk_Status_commutation: |
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6 | ∀M: Type[0]. |
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7 | ∀cm: M. |
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8 | ∀s: PreStatus M cm. |
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9 | ∀w: Word. |
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10 | ∀d: [[dptr]]. |
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11 | set_arg_16 M cm s w d = |
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12 | mk_PreStatus M cm |
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13 | (low_internal_ram … s) |
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14 | (high_internal_ram … s) |
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15 | (external_ram … s) |
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16 | (program_counter … s) |
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17 | (special_function_registers_8051 … (set_arg_16 M cm s w d)) |
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18 | (special_function_registers_8052 … s) |
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19 | (p1_latch … s) |
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20 | (p3_latch … s) |
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21 | (clock … s). |
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22 | #M #cm #s #w #d |
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23 | whd in match set_arg_16; normalize nodelta |
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24 | whd in match set_arg_16'; normalize nodelta |
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25 | @(subaddressing_mode_elim … [[dptr]] … [[dptr]]) [1: // ] |
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26 | cases (split bool 8 8 w) #bu #bl normalize nodelta |
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27 | whd in match set_8051_sfr; normalize nodelta % |
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28 | qed. |
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29 | |
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30 | lemma set_program_counter_mk_Status_commutation: |
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31 | ∀M: Type[0]. |
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32 | ∀cm: M. |
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33 | ∀s: PreStatus M cm. |
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34 | ∀w: Word. |
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35 | set_program_counter M cm s w = |
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36 | mk_PreStatus M cm |
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37 | (low_internal_ram … s) |
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38 | (high_internal_ram … s) |
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39 | (external_ram … s) |
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40 | w |
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41 | (special_function_registers_8051 … s) |
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42 | (special_function_registers_8052 … s) |
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43 | (p1_latch … s) |
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44 | (p3_latch … s) |
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45 | (clock … s). |
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46 | // |
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47 | qed. |
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48 | |
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49 | lemma set_clock_mk_Status_commutation: |
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50 | ∀M: Type[0]. |
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51 | ∀cm: M. |
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52 | ∀s: PreStatus M cm. |
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53 | ∀c: nat. |
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54 | set_clock M cm s c = |
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55 | mk_PreStatus M cm |
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56 | (low_internal_ram … s) |
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57 | (high_internal_ram … s) |
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58 | (external_ram … s) |
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59 | (program_counter … s) |
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60 | (special_function_registers_8051 … s) |
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61 | (special_function_registers_8052 … s) |
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62 | (p1_latch … s) |
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63 | (p3_latch … s) |
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64 | c. |
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65 | // |
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66 | qed. |
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67 | |
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68 | lemma get_8051_sfr_set_clock: |
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69 | ∀M: Type[0]. |
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70 | ∀cm: M. |
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71 | ∀s: PreStatus M cm. |
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72 | ∀sfr: SFR8051. |
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73 | ∀t: Time. |
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74 | get_8051_sfr M cm (set_clock M cm s t) sfr = |
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75 | get_8051_sfr M cm s sfr. |
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76 | #M #cm #s #sfr #t % |
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77 | qed. |
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78 | |
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79 | lemma special_function_registers_8051_set_arg_16: |
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80 | ∀M, M': Type[0]. |
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81 | ∀cm: M. |
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82 | ∀cm': M'. |
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83 | ∀s: PreStatus M cm. |
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84 | ∀s': PreStatus M' cm'. |
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85 | ∀w, w': Word. |
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86 | ∀d, d': [[dptr]]. |
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87 | special_function_registers_8051 ?? s = special_function_registers_8051 … s' → |
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88 | w = w' → |
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89 | special_function_registers_8051 ?? (set_arg_16 … s w d) = |
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90 | special_function_registers_8051 ?? (set_arg_16 M' cm' s' w' d'). |
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91 | #M #M' #cm #cm' #s #s' #w #w' |
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92 | @list_addressing_mode_tags_elim_prop try % |
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93 | @list_addressing_mode_tags_elim_prop try % |
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94 | #EQ1 #EQ2 <EQ2 normalize cases (split bool 8 8 w) #b1 #b2 normalize <EQ1 % |
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95 | qed. |
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96 | |
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97 | lemma None_Some_elim: ∀P:Prop. ∀A,a. None A = Some A a → P. |
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98 | #P #A #a #abs destruct |
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99 | qed. |
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100 | |
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101 | (* |
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102 | lemma pi1_let_commute: |
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103 | ∀A,B,C,P. ∀c:A × B. ∀t: Σc:C.P c. |
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104 | pi1 … (let 〈x1,y1〉 ≝ c in t) = (let 〈x1,y1〉 ≝ c in pi1 … t). |
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105 | #A #B #C #P * #a #b * // |
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106 | qed. |
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107 | |
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108 | lemma pi1_let_as_commute: |
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109 | ∀A,B,C,P. ∀c:A × B. ∀t: Σc:C.P c. |
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110 | pi1 … (let 〈x1,y1〉 as H ≝ c in t) = |
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111 | (let 〈x1,y1〉 as H ≝ c in pi1 … t). |
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112 | #A #B #C #P * #a #b * // |
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113 | qed. |
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114 | |
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115 | lemma tech_pi1_let_as_commute: |
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116 | ∀A,B,C,P. ∀f. ∀c,c':A × B. |
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117 | ∀t: ∀a,b. 〈a,b〉=c → Σc:C.P c. |
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118 | ∀t': ∀a,b. 〈a,b〉=c' → Σc:C.P c. |
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119 | c=c' → (∀x,y,H,H'.t x y H = f (pi1 … (t' x y H'))) → |
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120 | pi1 … (let 〈x1,y1〉 as H ≝ c in t x1 y1 H) = |
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121 | f (pi1 … (let 〈x1,y1〉 as H ≝ c' in t' x1 y1 H)). |
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122 | #A #B #C #P #f * #a #b * #a' #b' #t #t' #EQ1 destruct normalize /2/ |
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123 | qed. |
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124 | *) |
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125 | |
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126 | include alias "arithmetics/nat.ma". |
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127 | include alias "basics/logic.ma". |
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128 | include alias "ASM/BitVectorTrie.ma". |
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129 | |
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130 | lemma pair_replace: |
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131 | ∀A,B,T:Type[0].∀P:T → Prop. ∀t. ∀a,b.∀c,c': A × B. c'=c → c ≃ 〈a,b〉 → |
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132 | P (t a b) → P (let 〈a',b'〉 ≝ c' in t a' b'). |
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133 | #A #B #T #P #t #a #b * #x #y * #x' #y' #H1 #H2 destruct // |
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134 | qed. |
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135 | |
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136 | lemma pair_as_replace: |
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137 | ∀A,B,T:Type[0].∀P:T → Prop. ∀a:A. ∀b:B.∀c,c': A × B. ∀t: ∀a,b. 〈a, b〉 = c' → T. ∀EQc: c'= c. |
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138 | c ≃ 〈a,b〉 → |
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139 | P (let 〈a, b〉 as H ≝ c in t a b ?) → P (let 〈a',b'〉 as H ≝ c' in t a' b' H). |
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140 | [2: |
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141 | >EQc assumption |
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142 | |1: |
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143 | #A #B #T #P #a #b * #x #y * #x' #y' #t #H1 #H2 destruct // |
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144 | ] |
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145 | qed. |
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146 | |
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147 | lemma if_then_else_replace: |
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148 | ∀T: Type[0]. |
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149 | ∀P: T → Prop. |
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150 | ∀t1, t2: T. |
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151 | ∀c, c', c'': bool. |
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152 | c' = c → c ≃ c'' → P (if c'' then t1 else t2) → P (if c' then t1 else t2). |
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153 | #T #P #t1 #t2 #c #c' #c'' #c_refl #c_refl' destruct #assm |
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154 | assumption |
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155 | qed. |
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156 | |
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157 | lemma main_lemma_preinstruction: |
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158 | ∀M,M': internal_pseudo_address_map. |
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159 | ∀preamble : preamble. ∀instr_list : list labelled_instruction. |
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160 | ∀cm: pseudo_assembly_program. |
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161 | ∀EQcm: cm = 〈preamble,instr_list〉. |
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162 | ∀sigma : Word→Word. ∀policy : Word→bool. |
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163 | ∀sigma_policy_witness : sigma_policy_specification cm sigma policy. |
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164 | ∀ps : PseudoStatus cm. |
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165 | ∀ppc : Word. |
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166 | ∀EQppc : ppc=program_counter pseudo_assembly_program cm ps. |
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167 | ∀labels : label_map. |
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168 | ∀costs : BitVectorTrie costlabel 16. |
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169 | ∀create_label_cost_refl : create_label_cost_map instr_list=〈labels,costs〉. |
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170 | ∀assembled : list Byte. |
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171 | ∀costs' : BitVectorTrie costlabel 16. |
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172 | ∀assembly_refl : assembly 〈preamble,instr_list〉 sigma policy=〈assembled,costs'〉. |
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173 | ∀EQassembled : assembled=\fst (assembly cm sigma policy). |
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174 | ∀newppc : Word. |
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175 | ∀lookup_labels : Identifier→Word. |
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176 | ∀EQlookup_labels : lookup_labels = (λx:Identifier.sigma (address_of_word_labels_code_mem instr_list x)). |
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177 | ∀lookup_datalabels : identifier ASMTag→Word. |
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178 | ∀ EQlookup_datalabels : lookup_datalabels = (λx.lookup_def ASMTag Word (construct_datalabels preamble) x (zero 16)). |
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179 | ∀EQnewppc : newppc=add 16 ppc (bitvector_of_nat 16 1). |
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180 | ∀instr: preinstruction Identifier. |
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181 | ∀ticks. |
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182 | ∀EQticks: ticks = ticks_of0 〈preamble,instr_list〉 sigma policy ppc (Instruction instr). |
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183 | ∀addr_of. |
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184 | ∀EQaddr_of: addr_of = (λx:Identifier |
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185 | .λy:PreStatus pseudo_assembly_program cm |
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186 | .address_of_word_labels cm x). |
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187 | ∀s. |
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188 | ∀EQs: s = (set_program_counter pseudo_assembly_program cm ps |
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189 | (add 16 ppc (bitvector_of_nat 16 1))). |
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190 | ∀P. |
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191 | ∀EQP: |
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192 | P = (λs. |
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193 | execute (|expand_relative_jump lookup_labels sigma ppc instr|) |
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194 | (code_memory_of_pseudo_assembly_program cm sigma |
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195 | policy) |
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196 | (status_of_pseudo_status M cm ps sigma policy) |
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197 | =status_of_pseudo_status M' cm s sigma policy). |
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198 | sigma (add 16 ppc (bitvector_of_nat 16 1)) |
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199 | =add 16 (sigma ppc) |
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200 | (bitvector_of_nat 16 |
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201 | (\fst (assembly_1_pseudoinstruction lookup_labels sigma policy ppc |
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202 | lookup_datalabels (Instruction instr)))) |
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203 | →next_internal_pseudo_address_map0 pseudo_assembly_program (Instruction instr) |
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204 | M cm ps |
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205 | =Some internal_pseudo_address_map M' |
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206 | →fetch_many (load_code_memory assembled) |
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207 | (sigma (add 16 ppc (bitvector_of_nat 16 1))) (sigma ppc) |
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208 | (expand_pseudo_instruction lookup_labels sigma policy ppc lookup_datalabels |
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209 | (Instruction instr)) |
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210 | →P (execute_1_preinstruction ticks Identifier pseudo_assembly_program cm |
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211 | addr_of instr s). |
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212 | #M #M' #preamble #instr_list #cm #EQcm #sigma #policy #sigma_policy_witness #ps #ppc #EQppc #labels |
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213 | #costs #create_label_cost_refl #assembled #costs' #assembly_refl #EQassembled #newppc |
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214 | #lookup_labels #EQlookup_labels #lookup_datalabels #EQlookup_datalabels #EQnewppc #instr |
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215 | #ticks #EQticks #addr_of #EQaddr_of #s #EQs #P #EQP |
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216 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
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217 | letin a ≝ Identifier letin m ≝ pseudo_assembly_program |
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218 | cut (Σxxx:PseudoStatus cm. P (execute_1_preinstruction ticks a m cm addr_of instr s)) |
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219 | [2: * // ] |
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220 | @( |
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221 | let add_ticks1 ≝ λs: PreStatus m cm. set_clock ?? s (\fst ticks + clock ?? s) in |
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222 | let add_ticks2 ≝ λs: PreStatus m cm. set_clock ?? s (\snd ticks + clock ?? s) in |
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223 | match instr in preinstruction return λx. x = instr → Σs'.? with |
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224 | [ ADD addr1 addr2 ⇒ λinstr_refl. |
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225 | let s ≝ add_ticks1 s in |
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226 | let 〈result, flags〉 ≝ add_8_with_carry (get_arg_8 … s false addr1) |
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227 | (get_arg_8 … s false addr2) false in |
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228 | let cy_flag ≝ get_index' ? O ? flags in |
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229 | let ac_flag ≝ get_index' ? 1 ? flags in |
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230 | let ov_flag ≝ get_index' ? 2 ? flags in |
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231 | let s ≝ set_arg_8 … s ACC_A result in |
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232 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
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233 | | ADDC addr1 addr2 ⇒ λinstr_refl. |
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234 | let s ≝ add_ticks1 s in |
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235 | let old_cy_flag ≝ get_cy_flag ?? s in |
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236 | let 〈result, flags〉 ≝ add_8_with_carry (get_arg_8 … s false addr1) |
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237 | (get_arg_8 … s false addr2) old_cy_flag in |
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238 | let cy_flag ≝ get_index' ? O ? flags in |
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239 | let ac_flag ≝ get_index' ? 1 ? flags in |
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240 | let ov_flag ≝ get_index' ? 2 ? flags in |
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241 | let s ≝ set_arg_8 … s ACC_A result in |
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242 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
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243 | | SUBB addr1 addr2 ⇒ λinstr_refl. |
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244 | let s ≝ add_ticks1 s in |
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245 | let old_cy_flag ≝ get_cy_flag ?? s in |
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246 | let 〈result, flags〉 ≝ sub_8_with_carry (get_arg_8 … s false addr1) |
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247 | (get_arg_8 … s false addr2) old_cy_flag in |
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248 | let cy_flag ≝ get_index' ? O ? flags in |
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249 | let ac_flag ≝ get_index' ? 1 ? flags in |
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250 | let ov_flag ≝ get_index' ? 2 ? flags in |
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251 | let s ≝ set_arg_8 … s ACC_A result in |
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252 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
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253 | | ANL addr ⇒ λinstr_refl. |
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254 | let s ≝ add_ticks1 s in |
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255 | match addr with |
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256 | [ inl l ⇒ |
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257 | match l with |
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258 | [ inl l' ⇒ |
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259 | let 〈addr1, addr2〉 ≝ l' in |
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260 | let and_val ≝ conjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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261 | set_arg_8 … s addr1 and_val |
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262 | | inr r ⇒ |
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263 | let 〈addr1, addr2〉 ≝ r in |
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264 | let and_val ≝ conjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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265 | set_arg_8 … s addr1 and_val |
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266 | ] |
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267 | | inr r ⇒ |
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268 | let 〈addr1, addr2〉 ≝ r in |
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269 | let and_val ≝ andb (get_cy_flag … s) (get_arg_1 … s addr2 true) in |
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270 | set_flags … s and_val (None ?) (get_ov_flag ?? s) |
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271 | ] |
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272 | | ORL addr ⇒ λinstr_refl. |
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273 | let s ≝ add_ticks1 s in |
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274 | match addr with |
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275 | [ inl l ⇒ |
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276 | match l with |
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277 | [ inl l' ⇒ |
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278 | let 〈addr1, addr2〉 ≝ l' in |
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279 | let or_val ≝ inclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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280 | set_arg_8 … s addr1 or_val |
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281 | | inr r ⇒ |
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282 | let 〈addr1, addr2〉 ≝ r in |
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283 | let or_val ≝ inclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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284 | set_arg_8 … s addr1 or_val |
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285 | ] |
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286 | | inr r ⇒ |
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287 | let 〈addr1, addr2〉 ≝ r in |
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288 | let or_val ≝ (get_cy_flag … s) ∨ (get_arg_1 … s addr2 true) in |
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289 | set_flags … s or_val (None ?) (get_ov_flag … s) |
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290 | ] |
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291 | | XRL addr ⇒ λinstr_refl. |
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292 | let s ≝ add_ticks1 s in |
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293 | match addr with |
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294 | [ inl l' ⇒ |
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295 | let 〈addr1, addr2〉 ≝ l' in |
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296 | let xor_val ≝ exclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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297 | set_arg_8 … s addr1 xor_val |
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298 | | inr r ⇒ |
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299 | let 〈addr1, addr2〉 ≝ r in |
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300 | let xor_val ≝ exclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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301 | set_arg_8 … s addr1 xor_val |
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302 | ] |
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303 | | INC addr ⇒ λinstr_refl. |
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304 | match addr return λx. bool_to_Prop (is_in … [[ acc_a;registr;direct;indirect;dptr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
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305 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
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306 | let s' ≝ add_ticks1 s in |
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307 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true ACC_A) (bitvector_of_nat 8 1) in |
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308 | set_arg_8 … s' ACC_A result |
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309 | | REGISTER r ⇒ λregister: True. λEQaddr. |
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310 | let s' ≝ add_ticks1 s in |
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311 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (REGISTER r)) (bitvector_of_nat 8 1) in |
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312 | set_arg_8 … s' (REGISTER r) result |
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313 | | DIRECT d ⇒ λdirect: True. λEQaddr. |
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314 | let s' ≝ add_ticks1 s in |
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315 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (DIRECT d)) (bitvector_of_nat 8 1) in |
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316 | set_arg_8 … s' (DIRECT d) result |
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317 | | INDIRECT i ⇒ λindirect: True. λEQaddr. |
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318 | let s' ≝ add_ticks1 s in |
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319 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (INDIRECT i)) (bitvector_of_nat 8 1) in |
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320 | set_arg_8 … s' (INDIRECT i) result |
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321 | | DPTR ⇒ λdptr: True. λEQaddr. |
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322 | let s' ≝ add_ticks1 s in |
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323 | let 〈 carry, bl 〉 ≝ half_add ? (get_8051_sfr … s' SFR_DPL) (bitvector_of_nat 8 1) in |
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324 | let 〈 carry, bu 〉 ≝ full_add ? (get_8051_sfr … s' SFR_DPH) (zero 8) carry in |
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325 | let s ≝ set_8051_sfr … s' SFR_DPL bl in |
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326 | set_8051_sfr … s' SFR_DPH bu |
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327 | | _ ⇒ λother: False. ⊥ |
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328 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
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329 | | NOP ⇒ λinstr_refl. |
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330 | let s ≝ add_ticks2 s in |
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331 | s |
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332 | | DEC addr ⇒ λinstr_refl. |
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333 | let s ≝ add_ticks1 s in |
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334 | let 〈 result, flags 〉 ≝ sub_8_with_carry (get_arg_8 … s true addr) (bitvector_of_nat 8 1) false in |
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335 | set_arg_8 … s addr result |
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336 | | MUL addr1 addr2 ⇒ λinstr_refl. |
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337 | let s ≝ add_ticks1 s in |
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338 | let acc_a_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_A) in |
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339 | let acc_b_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_B) in |
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340 | let product ≝ acc_a_nat * acc_b_nat in |
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341 | let ov_flag ≝ product ≥ 256 in |
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342 | let low ≝ bitvector_of_nat 8 (product mod 256) in |
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343 | let high ≝ bitvector_of_nat 8 (product ÷ 256) in |
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344 | let s ≝ set_8051_sfr … s SFR_ACC_A low in |
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345 | set_8051_sfr … s SFR_ACC_B high |
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346 | | DIV addr1 addr2 ⇒ λinstr_refl. |
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347 | let s ≝ add_ticks1 s in |
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348 | let acc_a_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_A) in |
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349 | let acc_b_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_B) in |
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350 | match acc_b_nat with |
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351 | [ O ⇒ set_flags … s false (None Bit) true |
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352 | | S o ⇒ |
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353 | let q ≝ bitvector_of_nat 8 (acc_a_nat ÷ (S o)) in |
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354 | let r ≝ bitvector_of_nat 8 (acc_a_nat mod 256) in |
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355 | let s ≝ set_8051_sfr … s SFR_ACC_A q in |
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356 | let s ≝ set_8051_sfr … s SFR_ACC_B r in |
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357 | set_flags … s false (None Bit) false |
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358 | ] |
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359 | | DA addr ⇒ λinstr_refl. |
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360 | let s ≝ add_ticks1 s in |
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361 | let 〈acc_nu, acc_nl〉 ≝ split ? 4 4 (get_8051_sfr … s SFR_ACC_A) in |
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362 | if (gtb (nat_of_bitvector ? acc_nl) 9) ∨ (get_ac_flag … s) then |
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363 | let 〈result, flags〉 ≝ add_8_with_carry (get_8051_sfr … s SFR_ACC_A) (bitvector_of_nat 8 6) false in |
---|
364 | let cy_flag ≝ get_index' ? O ? flags in |
---|
365 | let 〈acc_nu', acc_nl'〉 ≝ split ? 4 4 result in |
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366 | if (gtb (nat_of_bitvector ? acc_nu') 9) ∨ cy_flag then |
---|
367 | let 〈 carry, nu 〉 ≝ half_add ? acc_nu' (bitvector_of_nat 4 6) in |
---|
368 | let new_acc ≝ nu @@ acc_nl' in |
---|
369 | let s ≝ set_8051_sfr … s SFR_ACC_A new_acc in |
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370 | set_flags … s cy_flag (Some ? (get_ac_flag … s)) (get_ov_flag … s) |
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371 | else |
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372 | s |
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373 | else |
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374 | s |
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375 | | CLR addr ⇒ λinstr_refl. |
---|
376 | match addr return λx. bool_to_Prop (is_in … [[ acc_a; carry; bit_addr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
377 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
---|
378 | let s ≝ add_ticks1 s in |
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379 | set_arg_8 … s ACC_A (zero 8) |
---|
380 | | CARRY ⇒ λcarry: True. λEQaddr. |
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381 | let s ≝ add_ticks1 s in |
---|
382 | set_arg_1 … s CARRY false |
---|
383 | | BIT_ADDR b ⇒ λbit_addr: True. λEQaddr. |
---|
384 | let s ≝ add_ticks1 s in |
---|
385 | set_arg_1 … s (BIT_ADDR b) false |
---|
386 | | _ ⇒ λother: False. ⊥ |
---|
387 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
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388 | | CPL addr ⇒ λinstr_refl. |
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389 | match addr return λx. bool_to_Prop (is_in … [[ acc_a; carry; bit_addr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
390 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
---|
391 | let s ≝ add_ticks1 s in |
---|
392 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
393 | let new_acc ≝ negation_bv ? old_acc in |
---|
394 | set_8051_sfr … s SFR_ACC_A new_acc |
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395 | | CARRY ⇒ λcarry: True. λEQaddr. |
---|
396 | let s ≝ add_ticks1 s in |
---|
397 | let old_cy_flag ≝ get_arg_1 … s CARRY true in |
---|
398 | let new_cy_flag ≝ ¬old_cy_flag in |
---|
399 | set_arg_1 … s CARRY new_cy_flag |
---|
400 | | BIT_ADDR b ⇒ λbit_addr: True. λEQaddr. |
---|
401 | let s ≝ add_ticks1 s in |
---|
402 | let old_bit ≝ get_arg_1 … s (BIT_ADDR b) true in |
---|
403 | let new_bit ≝ ¬old_bit in |
---|
404 | set_arg_1 … s (BIT_ADDR b) new_bit |
---|
405 | | _ ⇒ λother: False. ? |
---|
406 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
---|
407 | | SETB b ⇒ λinstr_refl. |
---|
408 | let s ≝ add_ticks1 s in |
---|
409 | set_arg_1 … s b false |
---|
410 | | RL _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
411 | let s ≝ add_ticks1 s in |
---|
412 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
413 | let new_acc ≝ rotate_left … 1 old_acc in |
---|
414 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
415 | | RR _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
416 | let s ≝ add_ticks1 s in |
---|
417 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
418 | let new_acc ≝ rotate_right … 1 old_acc in |
---|
419 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
420 | | RLC _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
421 | let s ≝ add_ticks1 s in |
---|
422 | let old_cy_flag ≝ get_cy_flag ?? s in |
---|
423 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
424 | let new_cy_flag ≝ get_index' ? O ? old_acc in |
---|
425 | let new_acc ≝ shift_left … 1 old_acc old_cy_flag in |
---|
426 | let s ≝ set_arg_1 … s CARRY new_cy_flag in |
---|
427 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
428 | | RRC _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
429 | let s ≝ add_ticks1 s in |
---|
430 | let old_cy_flag ≝ get_cy_flag ?? s in |
---|
431 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
432 | let new_cy_flag ≝ get_index' ? 7 ? old_acc in |
---|
433 | let new_acc ≝ shift_right … 1 old_acc old_cy_flag in |
---|
434 | let s ≝ set_arg_1 … s CARRY new_cy_flag in |
---|
435 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
436 | | SWAP _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
---|
437 | let s ≝ add_ticks1 s in |
---|
438 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
439 | let 〈nu,nl〉 ≝ split ? 4 4 old_acc in |
---|
440 | let new_acc ≝ nl @@ nu in |
---|
441 | set_8051_sfr … s SFR_ACC_A new_acc |
---|
442 | | PUSH addr ⇒ λinstr_refl. |
---|
443 | match addr return λx. bool_to_Prop (is_in … [[ direct ]] x) → x = addr → Σs': PreStatus m cm. ? with |
---|
444 | [ DIRECT d ⇒ λdirect: True. λEQaddr. |
---|
445 | let s ≝ add_ticks1 s in |
---|
446 | let 〈carry, new_sp〉 ≝ half_add ? (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) in |
---|
447 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
448 | write_at_stack_pointer … s d |
---|
449 | | _ ⇒ λother: False. ⊥ |
---|
450 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
---|
451 | | POP addr ⇒ λinstr_refl. |
---|
452 | let s ≝ add_ticks1 s in |
---|
453 | let contents ≝ read_at_stack_pointer ?? s in |
---|
454 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
455 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
456 | set_arg_8 … s addr contents |
---|
457 | | XCH addr1 addr2 ⇒ λinstr_refl. |
---|
458 | let s ≝ add_ticks1 s in |
---|
459 | let old_addr ≝ get_arg_8 … s false addr2 in |
---|
460 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
461 | let s ≝ set_8051_sfr … s SFR_ACC_A old_addr in |
---|
462 | set_arg_8 … s addr2 old_acc |
---|
463 | | XCHD addr1 addr2 ⇒ λinstr_refl. |
---|
464 | let s ≝ add_ticks1 s in |
---|
465 | let 〈acc_nu, acc_nl〉 ≝ split … 4 4 (get_8051_sfr … s SFR_ACC_A) in |
---|
466 | let 〈arg_nu, arg_nl〉 ≝ split … 4 4 (get_arg_8 … s false addr2) in |
---|
467 | let new_acc ≝ acc_nu @@ arg_nl in |
---|
468 | let new_arg ≝ arg_nu @@ acc_nl in |
---|
469 | let s ≝ set_8051_sfr ?? s SFR_ACC_A new_acc in |
---|
470 | set_arg_8 … s addr2 new_arg |
---|
471 | | RET ⇒ λinstr_refl. |
---|
472 | let s ≝ add_ticks1 s in |
---|
473 | let high_bits ≝ read_at_stack_pointer ?? s in |
---|
474 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
475 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
476 | let low_bits ≝ read_at_stack_pointer ?? s in |
---|
477 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
478 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
479 | let new_pc ≝ high_bits @@ low_bits in |
---|
480 | set_program_counter … s new_pc |
---|
481 | | RETI ⇒ λinstr_refl. |
---|
482 | let s ≝ add_ticks1 s in |
---|
483 | let high_bits ≝ read_at_stack_pointer ?? s in |
---|
484 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
485 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
486 | let low_bits ≝ read_at_stack_pointer ?? s in |
---|
487 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
488 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
489 | let new_pc ≝ high_bits @@ low_bits in |
---|
490 | set_program_counter … s new_pc |
---|
491 | | MOVX addr ⇒ λinstr_refl. |
---|
492 | let s ≝ add_ticks1 s in |
---|
493 | (* DPM: only copies --- doesn't affect I/O *) |
---|
494 | match addr with |
---|
495 | [ inl l ⇒ |
---|
496 | let 〈addr1, addr2〉 ≝ l in |
---|
497 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
498 | | inr r ⇒ |
---|
499 | let 〈addr1, addr2〉 ≝ r in |
---|
500 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
501 | ] |
---|
502 | | MOV addr ⇒ λinstr_refl. |
---|
503 | let s ≝ add_ticks1 s in |
---|
504 | match addr with |
---|
505 | [ inl l ⇒ |
---|
506 | match l with |
---|
507 | [ inl l' ⇒ |
---|
508 | match l' with |
---|
509 | [ inl l'' ⇒ |
---|
510 | match l'' with |
---|
511 | [ inl l''' ⇒ |
---|
512 | match l''' with |
---|
513 | [ inl l'''' ⇒ |
---|
514 | let 〈addr1, addr2〉 ≝ l'''' in |
---|
515 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
516 | | inr r'''' ⇒ |
---|
517 | let 〈addr1, addr2〉 ≝ r'''' in |
---|
518 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
519 | ] |
---|
520 | | inr r''' ⇒ |
---|
521 | let 〈addr1, addr2〉 ≝ r''' in |
---|
522 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
523 | ] |
---|
524 | | inr r'' ⇒ |
---|
525 | let 〈addr1, addr2〉 ≝ r'' in |
---|
526 | set_arg_16 … s (get_arg_16 … s addr2) addr1 |
---|
527 | ] |
---|
528 | | inr r ⇒ |
---|
529 | let 〈addr1, addr2〉 ≝ r in |
---|
530 | set_arg_1 … s addr1 (get_arg_1 … s addr2 false) |
---|
531 | ] |
---|
532 | | inr r ⇒ |
---|
533 | let 〈addr1, addr2〉 ≝ r in |
---|
534 | set_arg_1 … s addr1 (get_arg_1 … s addr2 false) |
---|
535 | ] |
---|
536 | | JC addr ⇒ λinstr_refl. |
---|
537 | if get_cy_flag ?? s then |
---|
538 | let s ≝ add_ticks1 s in |
---|
539 | set_program_counter … s (addr_of addr s) |
---|
540 | else |
---|
541 | let s ≝ add_ticks2 s in |
---|
542 | s |
---|
543 | | JNC addr ⇒ λinstr_refl. |
---|
544 | if ¬(get_cy_flag ?? s) then |
---|
545 | let s ≝ add_ticks1 s in |
---|
546 | set_program_counter … s (addr_of addr s) |
---|
547 | else |
---|
548 | let s ≝ add_ticks2 s in |
---|
549 | s |
---|
550 | | JB addr1 addr2 ⇒ λinstr_refl. |
---|
551 | if get_arg_1 … s addr1 false then |
---|
552 | let s ≝ add_ticks1 s in |
---|
553 | set_program_counter … s (addr_of addr2 s) |
---|
554 | else |
---|
555 | let s ≝ add_ticks2 s in |
---|
556 | s |
---|
557 | | JNB addr1 addr2 ⇒ λinstr_refl. |
---|
558 | if ¬(get_arg_1 … s addr1 false) then |
---|
559 | let s ≝ add_ticks1 s in |
---|
560 | set_program_counter … s (addr_of addr2 s) |
---|
561 | else |
---|
562 | let s ≝ add_ticks2 s in |
---|
563 | s |
---|
564 | | JBC addr1 addr2 ⇒ λinstr_refl. |
---|
565 | let s ≝ set_arg_1 … s addr1 false in |
---|
566 | if get_arg_1 … s addr1 false then |
---|
567 | let s ≝ add_ticks1 s in |
---|
568 | set_program_counter … s (addr_of addr2 s) |
---|
569 | else |
---|
570 | let s ≝ add_ticks2 s in |
---|
571 | s |
---|
572 | | JZ addr ⇒ λinstr_refl. |
---|
573 | if eq_bv ? (get_8051_sfr … s SFR_ACC_A) (zero 8) then |
---|
574 | let s ≝ add_ticks1 s in |
---|
575 | set_program_counter … s (addr_of addr s) |
---|
576 | else |
---|
577 | let s ≝ add_ticks2 s in |
---|
578 | s |
---|
579 | | JNZ addr ⇒ λinstr_refl. |
---|
580 | if ¬(eq_bv ? (get_8051_sfr … s SFR_ACC_A) (zero 8)) then |
---|
581 | let s ≝ add_ticks1 s in |
---|
582 | set_program_counter … s (addr_of addr s) |
---|
583 | else |
---|
584 | let s ≝ add_ticks2 s in |
---|
585 | s |
---|
586 | | CJNE addr1 addr2 ⇒ λinstr_refl. |
---|
587 | match addr1 with |
---|
588 | [ inl l ⇒ |
---|
589 | let 〈addr1, addr2'〉 ≝ l in |
---|
590 | let new_cy ≝ ltb (nat_of_bitvector ? (get_arg_8 … s false addr1)) |
---|
591 | (nat_of_bitvector ? (get_arg_8 … s false addr2')) in |
---|
592 | if ¬(eq_bv ? (get_arg_8 … s false addr1) (get_arg_8 … s false addr2')) then |
---|
593 | let s ≝ add_ticks1 s in |
---|
594 | let s ≝ set_program_counter … s (addr_of addr2 s) in |
---|
595 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
596 | else |
---|
597 | let s ≝ add_ticks2 s in |
---|
598 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
599 | | inr r' ⇒ |
---|
600 | let 〈addr1, addr2'〉 ≝ r' in |
---|
601 | let new_cy ≝ ltb (nat_of_bitvector ? (get_arg_8 … s false addr1)) |
---|
602 | (nat_of_bitvector ? (get_arg_8 … s false addr2')) in |
---|
603 | if ¬(eq_bv ? (get_arg_8 … s false addr1) (get_arg_8 … s false addr2')) then |
---|
604 | let s ≝ add_ticks1 s in |
---|
605 | let s ≝ set_program_counter … s (addr_of addr2 s) in |
---|
606 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
607 | else |
---|
608 | let s ≝ add_ticks2 s in |
---|
609 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
610 | ] |
---|
611 | | DJNZ addr1 addr2 ⇒ λinstr_refl. |
---|
612 | let 〈result, flags〉 ≝ sub_8_with_carry (get_arg_8 … s true addr1) (bitvector_of_nat 8 1) false in |
---|
613 | let s ≝ set_arg_8 … s addr1 result in |
---|
614 | if ¬(eq_bv ? result (zero 8)) then |
---|
615 | let s ≝ add_ticks1 s in |
---|
616 | set_program_counter … s (addr_of addr2 s) |
---|
617 | else |
---|
618 | let s ≝ add_ticks2 s in |
---|
619 | s |
---|
620 | ] (refl … instr)) |
---|
621 | try (cases(other)) |
---|
622 | try assumption (*20s*) |
---|
623 | try (% @False) (*6s*) (* Bug exploited here to implement solve :-*) |
---|
624 | try ( |
---|
625 | @(execute_1_technical … (subaddressing_modein …)) |
---|
626 | @I |
---|
627 | ) (*66s*) |
---|
628 | whd in match execute_1_preinstruction; normalize nodelta |
---|
629 | [4,5,6,7,8,36,37,38,39,40,41,50: (* INC, CLR, CPL, PUSH *) |
---|
630 | lapply (subaddressing_modein ???) |
---|
631 | <EQaddr normalize nodelta #irrelevant |
---|
632 | try (>p normalize nodelta) |
---|
633 | try (>p1 normalize nodelta) |
---|
634 | (* XXX: start work on the left hand side *) |
---|
635 | >EQP <instr_refl normalize nodelta whd in ⊢ (??%?); |
---|
636 | (* XXX: work on fetch_many *) |
---|
637 | <instr_refl in fetch_many_assm; whd in ⊢ (% → ?); >EQassembled |
---|
638 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
639 | whd in match (program_counter ?? (status_of_pseudo_status M cm ps sigma policy)); |
---|
640 | <EQppc cases (fetch ??) * #instr' #newpc #ticks' normalize nodelta * * |
---|
641 | #eq_instr #EQticks' #fetch_many_assm whd in fetch_many_assm; |
---|
642 | >(eq_bv_eq … fetch_many_assm) -newpc |
---|
643 | >(eq_instruction_to_eq … eq_instr) -instr' whd in ⊢ (??%?); |
---|
644 | (* XXX: work on sigma commutation *) |
---|
645 | <instr_refl in sigma_increment_commutation; #sigma_increment_commutation |
---|
646 | (* XXX: work on ticks (of all kinds) *) |
---|
647 | >EQticks' -ticks' <instr_refl in EQticks; #EQticks >EQticks |
---|
648 | (* XXX: work on both sides *) |
---|
649 | [1,2,3,4,5: |
---|
650 | generalize in ⊢ (??(???(?%))?); |
---|
651 | |6,7,8,9,10,11: |
---|
652 | generalize in ⊢ (??(???(?%))?); |
---|
653 | |12: |
---|
654 | generalize in ⊢ (??(???(?%))?); |
---|
655 | ] |
---|
656 | <EQaddr normalize nodelta #irrelevant |
---|
657 | [1: |
---|
658 | @(pair_as_replace ??? (λx. pi1 ?? x = ?) ???? (λx. λy. λ_. half_add ???) ? p) |
---|
659 | |
---|
660 | (* XXX: removes status 's' *) |
---|
661 | normalize nodelta >EQs -s -ticks |
---|
662 | whd in ⊢ (??%%); |
---|
663 | (* XXX: simplify the left hand side *) |
---|
664 | |
---|
665 | (* XXX: work on both sides *) |
---|
666 | |1,2,3,9,51,53,54,55: (* ADD, ADDC, SUBB, DEC, POP, XCHD, RET, RETI *) |
---|
667 | (* XXX: simplify the right hand side *) |
---|
668 | >p normalize nodelta |
---|
669 | try (>p1 normalize nodelta) |
---|
670 | (* XXX: start work on the left hand side *) |
---|
671 | >EQP <instr_refl normalize nodelta whd in ⊢ (??%?); |
---|
672 | (* XXX: work on fetch_many *) |
---|
673 | <instr_refl in fetch_many_assm; whd in ⊢ (% → ?); >EQassembled |
---|
674 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
675 | whd in match (program_counter ?? (status_of_pseudo_status M cm ps sigma policy)); |
---|
676 | <EQppc cases (fetch ??) * #instr' #newpc #ticks' normalize nodelta * * |
---|
677 | #eq_instr #EQticks' #fetch_many_assm whd in fetch_many_assm; |
---|
678 | >(eq_bv_eq … fetch_many_assm) -newpc |
---|
679 | >(eq_instruction_to_eq … eq_instr) -instr' whd in ⊢ (??%?); |
---|
680 | (* XXX: work on sigma commutation *) |
---|
681 | <instr_refl in sigma_increment_commutation; #sigma_increment_commutation |
---|
682 | (* XXX: work on ticks (of all kinds) *) |
---|
683 | >EQticks' -ticks' <instr_refl in EQticks; #EQticks >EQticks |
---|
684 | (* XXX: simplify the left hand side *) |
---|
685 | @(pair_replace ?????????? p) |
---|
686 | [1,3,5,7,9,11,13,15: |
---|
687 | cases daemon |
---|
688 | |12,14,16: |
---|
689 | normalize nodelta |
---|
690 | @(pair_replace ?????????? p1) |
---|
691 | [1,3,5: |
---|
692 | cases daemon |
---|
693 | ] |
---|
694 | ] |
---|
695 | (* XXX: removes status 's' *) |
---|
696 | normalize nodelta >EQs -s -ticks |
---|
697 | whd in ⊢ (??%%); |
---|
698 | (* XXX: work on both sides *) |
---|
699 | cases daemon (* |
---|
700 | @split_eq_status try % |
---|
701 | [*: whd in ⊢ (??%%); >set_clock_mk_Status_commutation |
---|
702 | whd in match (set_flags ??????); |
---|
703 | (* CSC: TO BE COMPLETED *) |
---|
704 | ] *) |
---|
705 | |10,42,43,44,45,49,52,56: (* MUL *) |
---|
706 | (* XXX: simplify the right hand side *) |
---|
707 | (* XXX: start work on the left hand side *) |
---|
708 | >EQP <instr_refl normalize nodelta whd in ⊢ (??%?); |
---|
709 | (* XXX: work on fetch_many *) |
---|
710 | <instr_refl in fetch_many_assm; whd in ⊢ (% → ?); >EQassembled |
---|
711 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
712 | whd in match (program_counter ?? (status_of_pseudo_status M cm ps sigma policy)); |
---|
713 | <EQppc cases (fetch ??) * #instr' #newpc #ticks' normalize nodelta * * |
---|
714 | #eq_instr #EQticks' #fetch_many_assm whd in fetch_many_assm; |
---|
715 | >(eq_bv_eq … fetch_many_assm) -newpc |
---|
716 | >(eq_instruction_to_eq … eq_instr) -instr' whd in ⊢ (??%?); |
---|
717 | (* XXX: work on sigma commutation *) |
---|
718 | <instr_refl in sigma_increment_commutation; #sigma_increment_commutation |
---|
719 | (* XXX: work on ticks (of all kinds) *) |
---|
720 | >EQticks' -ticks' <instr_refl in EQticks; #EQticks >EQticks |
---|
721 | (* XXX: removes status 's' *) |
---|
722 | normalize nodelta >EQs -s -ticks |
---|
723 | whd in ⊢ (??%%); |
---|
724 | (* XXX: work on both sides *) |
---|
725 | (* @split_eq_status try % *) |
---|
726 | cases daemon |
---|
727 | |11,12: (* DIV *) |
---|
728 | normalize nodelta in p; |
---|
729 | >p normalize nodelta |
---|
730 | >EQP <instr_refl normalize nodelta whd in ⊢ (??%?); |
---|
731 | (* XXX: work on fetch_many *) |
---|
732 | <instr_refl in fetch_many_assm; whd in ⊢ (% → ?); >EQassembled |
---|
733 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
734 | whd in match (program_counter ?? (status_of_pseudo_status M cm ps sigma policy)); |
---|
735 | <EQppc cases (fetch ??) * #instr' #newpc #ticks' normalize nodelta * * |
---|
736 | #eq_instr #EQticks' #fetch_many_assm whd in fetch_many_assm; |
---|
737 | >(eq_bv_eq … fetch_many_assm) -newpc |
---|
738 | >(eq_instruction_to_eq … eq_instr) -instr' whd in ⊢ (??%?); |
---|
739 | (* XXX: work on sigma commutation *) |
---|
740 | <instr_refl in sigma_increment_commutation; #sigma_increment_commutation |
---|
741 | (* XXX: work on ticks (of all kinds) *) |
---|
742 | >EQticks' -ticks' <instr_refl in EQticks; #EQticks >EQticks |
---|
743 | (* XXX: work on both sides *) |
---|
744 | @(pose … (nat_of_bitvector 8 ?)) #pose_assm #pose_refl |
---|
745 | >(?: pose_assm = 0) |
---|
746 | [2,4: |
---|
747 | <p >pose_refl |
---|
748 | cases daemon |
---|
749 | |1,3: |
---|
750 | (* XXX: removes status 's' *) |
---|
751 | normalize nodelta >EQs -s -ticks |
---|
752 | whd in ⊢ (??%%); |
---|
753 | (* XXX: work on both sides *) |
---|
754 | @split_eq_status try % |
---|
755 | cases daemon |
---|
756 | ] |
---|
757 | |13,14,15: (* DA *) |
---|
758 | >p normalize nodelta |
---|
759 | >p1 normalize nodelta |
---|
760 | try (>p2 normalize nodelta |
---|
761 | try (>p3 normalize nodelta |
---|
762 | try (>p4 normalize nodelta |
---|
763 | try (>p5 normalize nodelta)))) |
---|
764 | >EQP <instr_refl normalize nodelta whd in ⊢ (??%?); |
---|
765 | (* XXX: work on fetch_many *) |
---|
766 | <instr_refl in fetch_many_assm; whd in ⊢ (% → ?); >EQassembled |
---|
767 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
768 | whd in match (program_counter ?? (status_of_pseudo_status M cm ps sigma policy)); |
---|
769 | <EQppc cases (fetch ??) * #instr' #newpc #ticks' normalize nodelta * * |
---|
770 | #eq_instr #EQticks' #fetch_many_assm whd in fetch_many_assm; |
---|
771 | >(eq_bv_eq … fetch_many_assm) -newpc |
---|
772 | >(eq_instruction_to_eq … eq_instr) -instr' whd in ⊢ (??%?); |
---|
773 | (* XXX: work on sigma commutation *) |
---|
774 | <instr_refl in sigma_increment_commutation; #sigma_increment_commutation |
---|
775 | (* XXX: work on ticks (of all kinds) *) |
---|
776 | >EQticks' -ticks' <instr_refl in EQticks; #EQticks >EQticks |
---|
777 | (* XXX: work on both sides *) |
---|
778 | @(pair_replace ?????????? p) |
---|
779 | [1,3,5: |
---|
780 | cases daemon |
---|
781 | |2,4,6: |
---|
782 | @(if_then_else_replace ???????? p1) |
---|
783 | [1,3,5: |
---|
784 | cases daemon |
---|
785 | |2,4: |
---|
786 | normalize nodelta |
---|
787 | @(pair_replace ?????????? p2) |
---|
788 | [1,3: |
---|
789 | cases daemon |
---|
790 | |2,4: |
---|
791 | normalize nodelta >p3 normalize nodelta |
---|
792 | >p4 normalize nodelta try >p5 |
---|
793 | ] |
---|
794 | ] |
---|
795 | (* XXX: removes status 's' *) |
---|
796 | normalize nodelta >EQs -s -ticks |
---|
797 | whd in ⊢ (??%%); |
---|
798 | (* XXX: work on both sides *) |
---|
799 | @split_eq_status try % |
---|
800 | cases daemon |
---|
801 | ] |
---|
802 | |33,34,35: (* ANL, ORL, XRL *) |
---|
803 | (* XXX: simplify the right hand side *) |
---|
804 | [1,2,3: |
---|
805 | inversion addr #addr' #EQaddr normalize nodelta |
---|
806 | [1,3: |
---|
807 | inversion addr' #addr'' #EQaddr' normalize nodelta |
---|
808 | ] |
---|
809 | ] |
---|
810 | @pair_elim #lft #rgt #lft_rgt_refl normalize nodelta |
---|
811 | (* XXX: start work on the left hand side *) |
---|
812 | >EQP <instr_refl normalize nodelta whd in ⊢ (??%?); |
---|
813 | (* XXX: work on fetch_many *) |
---|
814 | <instr_refl in fetch_many_assm; whd in ⊢ (% → ?); >EQassembled |
---|
815 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
816 | whd in match (program_counter ?? (status_of_pseudo_status M cm ps sigma policy)); |
---|
817 | <EQppc cases (fetch ??) * #instr' #newpc #ticks' normalize nodelta * * |
---|
818 | #eq_instr #EQticks' #fetch_many_assm whd in fetch_many_assm; |
---|
819 | >(eq_bv_eq … fetch_many_assm) -newpc |
---|
820 | >(eq_instruction_to_eq … eq_instr) -instr' whd in ⊢ (??%?); |
---|
821 | (* XXX: work on sigma commutation *) |
---|
822 | <instr_refl in sigma_increment_commutation; #sigma_increment_commutation |
---|
823 | (* XXX: work on ticks (of all kinds) *) |
---|
824 | >EQticks' -ticks' <instr_refl in EQticks; #EQticks >EQticks |
---|
825 | (* XXX: simplify the left hand side *) |
---|
826 | >EQaddr normalize nodelta try (>EQaddr' normalize nodelta) |
---|
827 | >lft_rgt_refl normalize nodelta |
---|
828 | (* XXX: removes status 's' *) |
---|
829 | normalize nodelta >EQs -s -ticks |
---|
830 | whd in ⊢ (??%%); |
---|
831 | (* XXX: work on both sides *) |
---|
832 | cases daemon |
---|
833 | | |
---|
834 | qed. |
---|
835 | (* |
---|
836 | |
---|
837 | |
---|
838 | @list_addressing_mode_tags_elim_prop try % whd |
---|
839 | @list_addressing_mode_tags_elim_prop try % whd #arg |
---|
840 | (* XXX: we first work on sigma_increment_commutation *) |
---|
841 | #sigma_increment_commutation |
---|
842 | normalize in match (assembly_1_pseudoinstruction ??????) in sigma_increment_commutation; |
---|
843 | (* XXX: we work on the maps *) |
---|
844 | whd in ⊢ (??%? → ?); |
---|
845 | try (change with (if ? then ? else ? = ? → ?) |
---|
846 | cases (addressing_mode_ok ????? ∧ addressing_mode_ok ?????) normalize nodelta) |
---|
847 | #H try @(None_Some_elim ??? H) @(Some_Some_elim ????? H) #map_refl_assm <map_refl_assm |
---|
848 | (* XXX: we assume the fetch_many hypothesis *) |
---|
849 | #fetch_many_assm |
---|
850 | (* XXX: we give the existential *) |
---|
851 | %{1} |
---|
852 | whd in match (execute_1_pseudo_instruction0 ?????); |
---|
853 | (* XXX: work on the left hand side of the equality *) |
---|
854 | whd in ⊢ (??%?); whd in match (program_counter ???); <EQppc |
---|
855 | (* XXX: execute fetches some more *) |
---|
856 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
857 | whd in fetch_many_assm; |
---|
858 | >EQassembled in fetch_many_assm; |
---|
859 | cases (fetch ??) * #instr #newpc #ticks normalize nodelta * * |
---|
860 | #eq_instr #EQticks whd in EQticks:(???%); >EQticks |
---|
861 | #fetch_many_assm whd in fetch_many_assm; |
---|
862 | lapply (eq_bv_eq … fetch_many_assm) -fetch_many_assm #EQnewpc |
---|
863 | >(eq_instruction_to_eq … eq_instr) -instr |
---|
864 | [ @(pose … (pi1 … (execute_1_preinstruction' …))) #lhs #EQlhs |
---|
865 | @(pose … |
---|
866 | (λlhs. status_of_pseudo_status M 〈preamble,instr_list〉 lhs sigma policy)) |
---|
867 | #Pl #EQPl |
---|
868 | cut (∀A,B:Type[0].∀f,f':A → B.∀x. f=f' → f x = f' x) [2: #eq_f_g_to_eq |
---|
869 | lapply (λy.eq_f_g_to_eq ???? y EQPl) #XX <(XX lhs) -XX >EQlhs -lhs |
---|
870 | whd in ⊢ (??%?); whd in ⊢ (??(???%)(?(???%))); |
---|
871 | @pair_elim |
---|
872 | >tech_pi1_let_as_commute |
---|
873 | |
---|
874 | *) |
---|
875 | |
---|
876 | |
---|
877 | theorem main_thm: |
---|
878 | ∀M. |
---|
879 | ∀M'. |
---|
880 | ∀program: pseudo_assembly_program. |
---|
881 | ∀sigma: Word → Word. |
---|
882 | ∀policy: Word → bool. |
---|
883 | ∀sigma_policy_specification_witness: sigma_policy_specification program sigma policy. |
---|
884 | ∀ps: PseudoStatus program. |
---|
885 | next_internal_pseudo_address_map M program ps = Some … M' → |
---|
886 | ∃n. execute n … (status_of_pseudo_status M … ps sigma policy) = |
---|
887 | status_of_pseudo_status M' … |
---|
888 | (execute_1_pseudo_instruction (ticks_of program sigma policy) program ps) sigma policy. |
---|
889 | #M #M' * #preamble #instr_list #sigma #policy #sigma_policy_witness #ps |
---|
890 | change with (next_internal_pseudo_address_map0 ????? = ? → ?) |
---|
891 | @(pose … (program_counter ?? ps)) #ppc #EQppc |
---|
892 | generalize in match (fetch_assembly_pseudo2 〈preamble,instr_list〉 sigma policy sigma_policy_witness ppc) in ⊢ ?; |
---|
893 | @pair_elim #labels #costs #create_label_cost_refl normalize nodelta |
---|
894 | @pair_elim #assembled #costs' #assembly_refl normalize nodelta |
---|
895 | lapply (pair_destruct_1 ????? (sym_eq ??? assembly_refl)) #EQassembled |
---|
896 | @pair_elim #pi #newppc #fetch_pseudo_refl normalize nodelta |
---|
897 | @(pose … (λx. sigma (address_of_word_labels_code_mem instr_list x))) #lookup_labels #EQlookup_labels |
---|
898 | @(pose … (λx. lookup_def … (construct_datalabels preamble) x (zero 16))) #lookup_datalabels #EQlookup_datalabels |
---|
899 | whd in match execute_1_pseudo_instruction; normalize nodelta |
---|
900 | whd in match ticks_of; normalize nodelta <EQppc >fetch_pseudo_refl normalize nodelta |
---|
901 | lapply (snd_fetch_pseudo_instruction instr_list ppc) >fetch_pseudo_refl #EQnewppc >EQnewppc |
---|
902 | lapply (snd_assembly_1_pseudoinstruction_ok 〈preamble,instr_list〉 … sigma policy sigma_policy_witness … ppc pi … EQlookup_labels EQlookup_datalabels ?) |
---|
903 | [1: >fetch_pseudo_refl % ] |
---|
904 | #assm1 #assm2 #assm3 generalize in match assm2; generalize in match assm3; |
---|
905 | generalize in match assm1; -assm1 -assm2 -assm3 |
---|
906 | normalize nodelta |
---|
907 | cases pi |
---|
908 | [2,3: |
---|
909 | #arg |
---|
910 | (* XXX: we first work on sigma_increment_commutation *) |
---|
911 | #sigma_increment_commutation |
---|
912 | normalize in match (assembly_1_pseudoinstruction ??????) in sigma_increment_commutation; |
---|
913 | (* XXX: we work on the maps *) |
---|
914 | whd in ⊢ (??%? → ?); @Some_Some_elim #map_refl_assm <map_refl_assm |
---|
915 | (* XXX: we assume the fetch_many hypothesis *) |
---|
916 | #fetch_many_assm |
---|
917 | (* XXX: we give the existential *) |
---|
918 | %{0} |
---|
919 | whd in match (execute_1_pseudo_instruction0 ?????); |
---|
920 | (* XXX: work on the left hand side of the equality *) |
---|
921 | whd in ⊢ (??%?); |
---|
922 | @split_eq_status // |
---|
923 | [1,2: /demod/ >EQnewppc >sigma_increment_commutation <add_zero % (*CSC: auto not working, why? *) ] |
---|
924 | |6: (* Mov *) |
---|
925 | #arg1 #arg2 |
---|
926 | (* XXX: we first work on sigma_increment_commutation *) |
---|
927 | #sigma_increment_commutation |
---|
928 | normalize in match (assembly_1_pseudoinstruction ??????) in sigma_increment_commutation; |
---|
929 | (* XXX: we work on the maps *) |
---|
930 | whd in ⊢ (??%? → ?); @Some_Some_elim #map_refl_assm <map_refl_assm |
---|
931 | (* XXX: we assume the fetch_many hypothesis *) |
---|
932 | #fetch_many_assm |
---|
933 | (* XXX: we give the existential *) |
---|
934 | %{1} |
---|
935 | whd in match (execute_1_pseudo_instruction0 ?????); |
---|
936 | (* XXX: work on the left hand side of the equality *) |
---|
937 | whd in ⊢ (??%?); whd in match (program_counter ???); <EQppc |
---|
938 | (* XXX: execute fetches some more *) |
---|
939 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
940 | whd in fetch_many_assm; |
---|
941 | >EQassembled in fetch_many_assm; |
---|
942 | cases (fetch ??) * #instr #newpc #ticks normalize nodelta * * |
---|
943 | #eq_instr #EQticks whd in EQticks:(???%); >EQticks |
---|
944 | #fetch_many_assm whd in fetch_many_assm; |
---|
945 | lapply (eq_bv_eq … fetch_many_assm) -fetch_many_assm #EQnewpc |
---|
946 | >(eq_instruction_to_eq … eq_instr) -instr whd in ⊢ (??%?); |
---|
947 | (* XXX: now we start to work on the mk_PreStatus equality *) |
---|
948 | (* XXX: lhs *) |
---|
949 | change with (set_arg_16 ????? = ?) |
---|
950 | >set_program_counter_mk_Status_commutation |
---|
951 | >set_clock_mk_Status_commutation |
---|
952 | >set_arg_16_mk_Status_commutation |
---|
953 | (* XXX: rhs *) |
---|
954 | change with (? = status_of_pseudo_status ?? (set_arg_16 ?????) ??) |
---|
955 | >set_program_counter_mk_Status_commutation |
---|
956 | >set_clock_mk_Status_commutation |
---|
957 | >set_arg_16_mk_Status_commutation in ⊢ (???%); |
---|
958 | (* here we are *) |
---|
959 | @split_eq_status // |
---|
960 | [1: |
---|
961 | assumption |
---|
962 | |2: |
---|
963 | @special_function_registers_8051_set_arg_16 |
---|
964 | [2: >EQlookup_datalabels % |
---|
965 | |1: // |
---|
966 | ] |
---|
967 | ] |
---|
968 | |1: (* Instruction *) -pi; #instr |
---|
969 | @(main_lemma_preinstruction M M' preamble instr_list … (refl …) … sigma_policy_witness |
---|
970 | … EQppc … create_label_cost_refl … assembly_refl EQassembled … EQlookup_labels … |
---|
971 | EQlookup_datalabels EQnewppc instr … (refl …) … (refl …) … (refl …) … (refl …)) |
---|
972 | |4,5: cases daemon |
---|
973 | ] |
---|
974 | qed. |
---|
975 | (* |
---|
976 | * |
---|
977 | [1,2,3: (* ADD, ADDC, SUBB *) |
---|
978 | @list_addressing_mode_tags_elim_prop try % whd |
---|
979 | @list_addressing_mode_tags_elim_prop try % whd #arg |
---|
980 | (* XXX: we first work on sigma_increment_commutation *) |
---|
981 | #sigma_increment_commutation |
---|
982 | normalize in match (assembly_1_pseudoinstruction ??????) in sigma_increment_commutation; |
---|
983 | (* XXX: we work on the maps *) |
---|
984 | whd in ⊢ (??%? → ?); |
---|
985 | try (change with (if ? then ? else ? = ? → ?) |
---|
986 | cases (addressing_mode_ok ????? ∧ addressing_mode_ok ?????) normalize nodelta) |
---|
987 | #H try @(None_Some_elim ??? H) @(Some_Some_elim ????? H) #map_refl_assm <map_refl_assm |
---|
988 | (* XXX: we assume the fetch_many hypothesis *) |
---|
989 | #fetch_many_assm |
---|
990 | (* XXX: we give the existential *) |
---|
991 | %{1} |
---|
992 | whd in match (execute_1_pseudo_instruction0 ?????); |
---|
993 | (* XXX: work on the left hand side of the equality *) |
---|
994 | whd in ⊢ (??%?); whd in match (program_counter ???); <EQppc |
---|
995 | (* XXX: execute fetches some more *) |
---|
996 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
997 | whd in fetch_many_assm; |
---|
998 | >EQassembled in fetch_many_assm; |
---|
999 | cases (fetch ??) * #instr #newpc #ticks normalize nodelta * * |
---|
1000 | #eq_instr #EQticks whd in EQticks:(???%); >EQticks |
---|
1001 | #fetch_many_assm whd in fetch_many_assm; |
---|
1002 | lapply (eq_bv_eq … fetch_many_assm) -fetch_many_assm #EQnewpc |
---|
1003 | >(eq_instruction_to_eq … eq_instr) -instr |
---|
1004 | [ @(pose … (pi1 … (execute_1_preinstruction' …))) #lhs #EQlhs |
---|
1005 | @(pose … |
---|
1006 | (λlhs. status_of_pseudo_status M 〈preamble,instr_list〉 lhs sigma policy)) |
---|
1007 | #Pl #EQPl |
---|
1008 | cut (∀A,B:Type[0].∀f,f':A → B.∀x. f=f' → f x = f' x) [2: #eq_f_g_to_eq |
---|
1009 | lapply (λy.eq_f_g_to_eq ???? y EQPl) #XX <(XX lhs) -XX >EQlhs -lhs |
---|
1010 | whd in ⊢ (??%?); whd in ⊢ (??(???%)(?(???%))); |
---|
1011 | @pair_elim |
---|
1012 | >tech_pi1_let_as_commute |
---|
1013 | |
---|
1014 | |
---|
1015 | whd in ⊢ (??%?); |
---|
1016 | [ @(pose … (execute_1_preinstruction' ???????)) |
---|
1017 | #lhs whd in ⊢ (???% → ?); #EQlhs |
---|
1018 | @(pose … (execute_1_preinstruction' ???????)) |
---|
1019 | #rhs whd in ⊢ (???% → ?); #EQrhs |
---|
1020 | |
---|
1021 | |
---|
1022 | CSC: delirium |
---|
1023 | |
---|
1024 | >EQlhs -EQlhs >EQrhs -EQrhs |
---|
1025 | cases (add_8_with_carry ???) #bits1 #bits2 whd in ⊢ (??%%); |
---|
1026 | |
---|
1027 | lapply (refl ? (execute_1_preinstruction' ???????)); |
---|
1028 | [ whd in match (execute_1_preinstruction' ???????); |
---|
1029 | |
---|
1030 | whd in ⊢ (??%?); |
---|
1031 | [ whd in ⊢ (??(???%)%); |
---|
1032 | whd in match (execute_1_preinstruction' ???????); |
---|
1033 | cases (add_8_with_carry ???) #bits1 #bits2 whd in ⊢ (??%?); |
---|
1034 | @pair_elim #result #flags #Heq1 |
---|
1035 | whd in match execute_1_preinstruction'; normalize nodelta |
---|
1036 | (* XXX: now we start to work on the mk_PreStatus equality *) |
---|
1037 | whd in ⊢ (??%?); |
---|
1038 | |
---|
1039 | |
---|
1040 | |
---|
1041 | [1,2,3: (* ADD, ADDC, SUBB *) #arg1 #arg2 |
---|
1042 | (* XXX: we take up the hypotheses *) |
---|
1043 | #sigma_increment_commutation #next_map_assm #fetch_many_assm |
---|
1044 | (* XXX: we give the existential *) |
---|
1045 | %{1} |
---|
1046 | whd in match (execute_1_pseudo_instruction0 ?????); |
---|
1047 | whd in ⊢ (??%?); whd in match (program_counter ???); <EQppc |
---|
1048 | whd in match code_memory_of_pseudo_assembly_program; normalize nodelta |
---|
1049 | (* XXX: fetching of the instruction *) |
---|
1050 | whd in fetch_many_assm; |
---|
1051 | >EQassembled in fetch_many_assm; |
---|
1052 | cases (fetch ??) * #instr #newpc #ticks normalize nodelta * * |
---|
1053 | #eq_instr #EQticks whd in EQticks:(???%); >EQticks |
---|
1054 | #fetch_many_assm whd in fetch_many_assm; |
---|
1055 | lapply (eq_bv_eq … fetch_many_assm) -fetch_many_assm #EQnewpc |
---|
1056 | >(eq_instruction_to_eq … eq_instr) -instr |
---|
1057 | (* XXX: now we start to work on the mk_PreStatus equality *) |
---|
1058 | whd in ⊢ (??%?); |
---|
1059 | check execute_1_preinstruction |
---|
1060 | |
---|
1061 | |
---|
1062 | #MAP #H1 #H2 #EQ %[1,3,5:@1] |
---|
1063 | normalize in H1; generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?) |
---|
1064 | change in ⊢ (? → ??%?) with (execute_1_0 ??) |
---|
1065 | cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta; |
---|
1066 | * * #H2a #H2b whd in ⊢ (% → ?) #H2c |
---|
1067 | >H2b >(eq_instruction_to_eq … H2a) |
---|
1068 | generalize in match EQ; -EQ; whd in ⊢ (???% → ??%?); generalize in match MAP; -MAP; |
---|
1069 | @(list_addressing_mode_tags_elim_prop … arg1) whd try % -arg1; |
---|
1070 | @(list_addressing_mode_tags_elim_prop … arg2) whd try % -arg2; #ARG2 |
---|
1071 | normalize nodelta; #MAP; |
---|
1072 | [1: change in ⊢ (? → %) with |
---|
1073 | ((let 〈result,flags〉 ≝ |
---|
1074 | add_8_with_carry |
---|
1075 | (get_arg_8 ? ps false ACC_A) |
---|
1076 | (get_arg_8 ? |
---|
1077 | (set_low_internal_ram ? ps (low_internal_ram_of_pseudo_low_internal_ram M (low_internal_ram … ps))) |
---|
1078 | false (DIRECT ARG2)) |
---|
1079 | ? in ?) = ?) |
---|
1080 | [2,3: %] |
---|
1081 | change in ⊢ (???% → ?) with |
---|
1082 | (let 〈result,flags〉 ≝ add_8_with_carry ?(*(get_arg_8 ? ps false ACC_A)*) ?? in ?) |
---|
1083 | >get_arg_8_set_clock |
---|
1084 | [1,2: cases (addressing_mode_ok ???? ∧ addressing_mode_ok ????) in MAP ⊢ ? |
---|
1085 | [2,4: #abs @⊥ normalize in abs; destruct (abs) |
---|
1086 | |*:whd in ⊢ (??%? → ?) #H <(option_destruct_Some ??? H)] |
---|
1087 | [ change in ⊢ (? → %) with |
---|
1088 | ((let 〈result,flags〉 ≝ |
---|
1089 | add_8_with_carry |
---|
1090 | (get_arg_8 ? ps false ACC_A) |
---|
1091 | (get_arg_8 ? |
---|
1092 | (set_low_internal_ram ? ps (low_internal_ram_of_pseudo_low_internal_ram M (low_internal_ram … ps))) |
---|
1093 | false (DIRECT ARG2)) |
---|
1094 | ? in ?) = ?) |
---|
1095 | >get_arg_8_set_low_internal_ram |
---|
1096 | |
---|
1097 | cases (add_8_with_carry ???) |
---|
1098 | |
---|
1099 | [1,2,3,4,5,6,7,8: cases (add_8_with_carry ???) |*: cases (sub_8_with_carry ???)] |
---|
1100 | #result #flags |
---|
1101 | #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) % |
---|
1102 | |
---|
1103 | |
---|
1104 | |4: (* Jmp *) #label whd in ⊢ (??%? → ???% → ?); |
---|
1105 | @Some_Some_elim #MAP cases (pol ?) normalize nodelta |
---|
1106 | [3: (* long *) #EQ3 @(Some_Some_elim ????? EQ3) #EQ3' |
---|
1107 | whd in match eject normalize nodelta >EQ3' in ⊢ (% → ?) whd in ⊢ (% → ?) |
---|
1108 | @pair_elim' * #instr #newppc' #ticks #EQ4 |
---|
1109 | * * #H2a #H2b whd in ⊢ (% → ?) #H2 |
---|
1110 | >H2b >(eq_instruction_to_eq … H2a) |
---|
1111 | #EQ %[@1] |
---|
1112 | <MAP >(eq_bv_eq … H2) >EQ |
---|
1113 | whd in ⊢ (??%?) >EQ4 whd in ⊢ (??%?) |
---|
1114 | cases ps in EQ4; #A1 #A2 #A3 #A4 #A5 #A6 #A7 #A8 #A9 #A10 #XXX >XXX % |
---|
1115 | whd in ⊢ (??%?) |
---|
1116 | whd in ⊢ (??(match ?%? with [_ ⇒ ?])?) |
---|
1117 | cases ps in EQ0 ⊢ %; #A1 #A2 #A3 #A4 #A5 #A6 #A7 #A8 #A9 #A10 #XXXX >XXXX % |
---|
1118 | |5: (* Call *) #label #MAP |
---|
1119 | generalize in match (option_destruct_Some ??? MAP) -MAP; #MAP <MAP -MAP; |
---|
1120 | whd in ⊢ (???% → ?) cases (pol ?) normalize nodelta; |
---|
1121 | [ (* short *) #abs @⊥ destruct (abs) |
---|
1122 | |3: (* long *) #H1 #H2 #EQ %[@1] |
---|
1123 | (* normalize in H1; !!!*) generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?) |
---|
1124 | change in ⊢ (? → ??%?) with (execute_1_0 ??) |
---|
1125 | cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta; |
---|
1126 | * * #H2a #H2b whd in ⊢ (% → ?) #H2c |
---|
1127 | >H2b >(eq_instruction_to_eq … H2a) |
---|
1128 | generalize in match EQ; -EQ; |
---|
1129 | whd in ⊢ (???% → ??%?); |
---|
1130 | generalize in match (refl … (half_add 8 (get_8051_sfr ? ps SFR_SP) (bitvector_of_nat ? 1))) cases (half_add ???) in ⊢ (??%? → %) #carry #new_sp #EQ1 normalize nodelta; |
---|
1131 | >(eq_bv_eq … H2c) |
---|
1132 | change with |
---|
1133 | ((?=let 〈ppc_bu,ppc_bl〉 ≝ split bool 8 8 newppc in ?) → |
---|
1134 | (let 〈pc_bu,pc_bl〉 ≝ split bool 8 8 (sigma 〈preamble,instr_list〉 pol newppc) in ?)=?) |
---|
1135 | generalize in match (refl … (split … 8 8 newppc)) cases (split bool 8 8 newppc) in ⊢ (??%? → %) #ppc_bu #ppc_bl #EQppc |
---|
1136 | generalize in match (refl … (split … 8 8 (sigma 〈preamble,instr_list〉 pol newppc))) cases (split bool 8 8 (sigma 〈preamble,instr_list〉 pol newppc)) in ⊢ (??%? → %) #pc_bu #pc_bl #EQpc normalize nodelta; |
---|
1137 | >get_8051_sfr_write_at_stack_pointer >get_8051_sfr_write_at_stack_pointer |
---|
1138 | >get_8051_sfr_set_8051_sfr >get_8051_sfr_set_8051_sfr |
---|
1139 | generalize in match (refl … (half_add ? new_sp (bitvector_of_nat ? 1))) cases (half_add ???) in ⊢ (??%? → %) #carry' #new_sp' #EQ2 normalize nodelta; |
---|
1140 | #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) |
---|
1141 | @split_eq_status; |
---|
1142 | [ >code_memory_write_at_stack_pointer whd in ⊢ (??%?) |
---|
1143 | >code_memory_write_at_stack_pointer % |
---|
1144 | | >set_program_counter_set_low_internal_ram |
---|
1145 | >set_clock_set_low_internal_ram |
---|
1146 | @low_internal_ram_write_at_stack_pointer |
---|
1147 | [ >EQ0 @pol | % | % |
---|
1148 | | @( … EQ1) |
---|
1149 | | @(pair_destruct_2 … EQ2) |
---|
1150 | | >(pair_destruct_1 ????? EQpc) |
---|
1151 | >(pair_destruct_2 ????? EQpc) |
---|
1152 | @split_elim #x #y #H <H -x y H; |
---|
1153 | >(pair_destruct_1 ????? EQppc) |
---|
1154 | >(pair_destruct_2 ????? EQppc) |
---|
1155 | @split_elim #x #y #H <H -x y H; |
---|
1156 | >EQ0 % ] |
---|
1157 | | >set_low_internal_ram_set_high_internal_ram |
---|
1158 | >set_program_counter_set_high_internal_ram |
---|
1159 | >set_clock_set_high_internal_ram |
---|
1160 | @high_internal_ram_write_at_stack_pointer |
---|
1161 | [ >EQ0 @pol | % | % |
---|
1162 | | @(pair_destruct_2 … EQ1) |
---|
1163 | | @(pair_destruct_2 … EQ2) |
---|
1164 | | >(pair_destruct_1 ????? EQpc) |
---|
1165 | >(pair_destruct_2 ????? EQpc) |
---|
1166 | @split_elim #x #y #H <H -x y H; |
---|
1167 | >(pair_destruct_1 ????? EQppc) |
---|
1168 | >(pair_destruct_2 ????? EQppc) |
---|
1169 | @split_elim #x #y #H <H -x y H; |
---|
1170 | >EQ0 % ] |
---|
1171 | | >external_ram_write_at_stack_pointer whd in ⊢ (??%?) |
---|
1172 | >external_ram_write_at_stack_pointer whd in ⊢ (???%) |
---|
1173 | >external_ram_write_at_stack_pointer whd in ⊢ (???%) |
---|
1174 | >external_ram_write_at_stack_pointer % |
---|
1175 | | change with (? = sigma ?? (address_of_word_labels_code_mem (\snd (code_memory ? ps)) ?)) |
---|
1176 | >EQ0 % |
---|
1177 | | >special_function_registers_8051_write_at_stack_pointer whd in ⊢ (??%?) |
---|
1178 | >special_function_registers_8051_write_at_stack_pointer whd in ⊢ (???%) |
---|
1179 | >special_function_registers_8051_write_at_stack_pointer whd in ⊢ (???%) |
---|
1180 | >special_function_registers_8051_write_at_stack_pointer % |
---|
1181 | | >special_function_registers_8052_write_at_stack_pointer whd in ⊢ (??%?) |
---|
1182 | >special_function_registers_8052_write_at_stack_pointer whd in ⊢ (???%) |
---|
1183 | >special_function_registers_8052_write_at_stack_pointer whd in ⊢ (???%) |
---|
1184 | >special_function_registers_8052_write_at_stack_pointer % |
---|
1185 | | >p1_latch_write_at_stack_pointer whd in ⊢ (??%?) |
---|
1186 | >p1_latch_write_at_stack_pointer whd in ⊢ (???%) |
---|
1187 | >p1_latch_write_at_stack_pointer whd in ⊢ (???%) |
---|
1188 | >p1_latch_write_at_stack_pointer % |
---|
1189 | | >p3_latch_write_at_stack_pointer whd in ⊢ (??%?) |
---|
1190 | >p3_latch_write_at_stack_pointer whd in ⊢ (???%) |
---|
1191 | >p3_latch_write_at_stack_pointer whd in ⊢ (???%) |
---|
1192 | >p3_latch_write_at_stack_pointer % |
---|
1193 | | >clock_write_at_stack_pointer whd in ⊢ (??%?) |
---|
1194 | >clock_write_at_stack_pointer whd in ⊢ (???%) |
---|
1195 | >clock_write_at_stack_pointer whd in ⊢ (???%) |
---|
1196 | >clock_write_at_stack_pointer %] |
---|
1197 | (*| (* medium *) #H1 #H2 #EQ %[@1] generalize in match H1; -H1; |
---|
1198 | @pair_elim' #fst_5_addr #rest_addr #EQ1 |
---|
1199 | @pair_elim' #fst_5_pc #rest_pc #EQ2 |
---|
1200 | generalize in match (refl … (eq_bv … fst_5_addr fst_5_pc)) |
---|
1201 | cases (eq_bv ???) in ⊢ (??%? → %) normalize nodelta; #EQ3 #TEQ [2: destruct (TEQ)] |
---|
1202 | generalize in match (option_destruct_Some ??? TEQ) -TEQ; #K1 >K1 in H2; whd in ⊢ (% → ?) |
---|
1203 | change in ⊢ (? →??%?) with (execute_1_0 ??) |
---|
1204 | @pair_elim' * #instr #newppc' #ticks #EQn |
---|
1205 | * * #H2a #H2b whd in ⊢ (% → ?) #H2c >H2b >(eq_instruction_to_eq … H2a) whd in ⊢ (??%?) |
---|
1206 | generalize in match EQ; -EQ; normalize nodelta; >(eq_bv_eq … H2c) |
---|
1207 | @pair_elim' #carry #new_sp change with (half_add ? (get_8051_sfr ? ps ?) ? = ? → ?) #EQ4 |
---|
1208 | @split_elim' #pc_bu #pc_bl >program_counter_set_8051_sfr XXX change with (newppc = ?) #EQ5 |
---|
1209 | @pair_elim' #carry' #new_sp' #EQ6 normalize nodelta; #EQx >EQx -EQx; |
---|
1210 | change in ⊢ (??(match ????% with [_ ⇒ ?])?) with (sigma … newppc) |
---|
1211 | @split_elim' #pc_bu' #pc_bl' #EQ7 change with (newppc' = ? → ?) |
---|
1212 | >get_8051_sfr_set_8051_sfr |
---|
1213 | |
---|
1214 | whd in EQ:(???%) ⊢ ? >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) whd in ⊢ (??%?) |
---|
1215 | change with ((let 〈pc_bu,pc_bl〉 ≝ split bool 8 8 (sigma 〈preamble,instr_list〉 newppc) in ?)=?) |
---|
1216 | generalize in match (refl … (split bool 8 8 (sigma 〈preamble,instr_list〉 newppc))) |
---|
1217 | cases (split ????) in ⊢ (??%? → %) #pc_bu #pc_bl normalize nodelta; #EQ4 |
---|
1218 | generalize in match (refl … (split bool 4 4 pc_bu)) |
---|
1219 | cases (split ????) in ⊢ (??%? → %) #nu #nl normalize nodelta; #EQ5 |
---|
1220 | generalize in match (refl … (split bool 3 8 rest_addr)) |
---|
1221 | cases (split ????) in ⊢ (??%? → %) #relevant1 #relevant2 normalize nodelta; #EQ6 |
---|
1222 | change with ((let 〈carry,new_pc〉 ≝ half_add ? (sigma … newppc) ? in ?) = ?) |
---|
1223 | generalize in match |
---|
1224 | (refl … |
---|
1225 | (half_add 16 (sigma 〈preamble,instr_list〉 newppc) |
---|
1226 | ((nu@@get_index' bool 0 3 nl:::relevant1)@@relevant2))) |
---|
1227 | cases (half_add ???) in ⊢ (??%? → %) #carry #new_pc normalize nodelta; #EQ7 |
---|
1228 | @split_eq_status try % |
---|
1229 | [ change with (? = sigma ? (address_of_word_labels ps label)) |
---|
1230 | (* ARITHMETICS, BUT THE GOAL SEEMS FALSE *) |
---|
1231 | | whd in ⊢ (??%%) whd in ⊢ (??(?%?)?) whd in ⊢ (??(?(match ?(?%)? with [_ ⇒ ?])?)?) |
---|
1232 | @(bitvector_3_elim_prop … (\fst (split bool 3 8 rest_addr))) %]] *)] |
---|
1233 | |4: (* Jmp *) #label #MAP |
---|
1234 | generalize in match (option_destruct_Some ??? MAP) -MAP; #MAP >MAP -MAP; |
---|
1235 | whd in ⊢ (???% → ?) cases (pol ?) normalize nodelta; |
---|
1236 | [3: (* long *) #H1 #H2 #EQ %[@1] |
---|
1237 | (* normalize in H1; !!!*) generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?) |
---|
1238 | change in ⊢ (? → ??%?) with (execute_1_0 ??) |
---|
1239 | cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta; |
---|
1240 | * * #H2a #H2b whd in ⊢ (% → ?) #H2c |
---|
1241 | >H2b >(eq_instruction_to_eq … H2a) |
---|
1242 | generalize in match EQ; -EQ; |
---|
1243 | #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) |
---|
1244 | cases ps in EQ0 ⊢ %; #A1 #A2 #A3 #A4 #A5 #A6 #A7 #A8 #A9 #A10 #XXXX >XXXX % |
---|
1245 | |1: (* short *) #H1 #H2 #EQ %[@1] generalize in match H1; -H1; |
---|
1246 | generalize in match |
---|
1247 | (refl ? |
---|
1248 | (sub_16_with_carry |
---|
1249 | (sigma 〈preamble,instr_list〉 pol (program_counter … ps)) |
---|
1250 | (sigma 〈preamble,instr_list〉 pol (address_of_word_labels_code_mem instr_list label)) |
---|
1251 | false)) |
---|
1252 | cases (sub_16_with_carry ???) in ⊢ (??%? → %); #results #flags normalize nodelta; |
---|
1253 | generalize in match (refl … (split … 8 8 results)) cases (split ????) in ⊢ (??%? → %) #upper #lower normalize nodelta; |
---|
1254 | generalize in match (refl … (eq_bv … upper (zero 8))) cases (eq_bv ???) in ⊢ (??%? → %) normalize nodelta; |
---|
1255 | #EQ1 #EQ2 #EQ3 #H1 [2: @⊥ destruct (H1)] |
---|
1256 | generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?) |
---|
1257 | change in ⊢ (? → ??%?) with (execute_1_0 ??) |
---|
1258 | cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta; |
---|
1259 | * * #H2a #H2b whd in ⊢ (% → ?) #H2c |
---|
1260 | >H2b >(eq_instruction_to_eq … H2a) |
---|
1261 | generalize in match EQ; -EQ; |
---|
1262 | whd in ⊢ (???% → ?); |
---|
1263 | #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) |
---|
1264 | change with ((let 〈carry,new_pc〉 ≝ half_add ? (sigma ???) ? in ?) = ?) |
---|
1265 | generalize in match (refl … (half_add 16 (sigma 〈preamble,instr_list〉 pol newppc) (sign_extension lower))) |
---|
1266 | cases (half_add ???) in ⊢ (??%? → %) #carry #newpc normalize nodelta #EQ4 |
---|
1267 | @split_eq_status try % change with (newpc = sigma ?? (address_of_word_labels ps label)) |
---|
1268 | (* ARITHMETICS, BUT THE GOAL SEEMS FALSE *) |
---|
1269 | | (* medium *) #H1 #H2 #EQ %[@1] generalize in match H1; -H1; |
---|
1270 | generalize in match |
---|
1271 | (refl … |
---|
1272 | (split … 5 11 (sigma 〈preamble,instr_list〉 pol (address_of_word_labels_code_mem instr_list label)))) |
---|
1273 | cases (split ????) in ⊢ (??%? → %) #fst_5_addr #rest_addr normalize nodelta; #EQ1 |
---|
1274 | generalize in match |
---|
1275 | (refl … |
---|
1276 | (split … 5 11 (sigma 〈preamble,instr_list〉 pol (program_counter … ps)))) |
---|
1277 | cases (split ????) in ⊢ (??%? → %) #fst_5_pc #rest_pc normalize nodelta; #EQ2 |
---|
1278 | generalize in match (refl … (eq_bv … fst_5_addr fst_5_pc)) |
---|
1279 | cases (eq_bv ???) in ⊢ (??%? → %) normalize nodelta; #EQ3 #TEQ [2: destruct (TEQ)] |
---|
1280 | generalize in match (option_destruct_Some ??? TEQ) -TEQ; #K1 >K1 in H2; whd in ⊢ (% → ?) |
---|
1281 | change in ⊢ (? →??%?) with (execute_1_0 ??) |
---|
1282 | cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta; |
---|
1283 | * * #H2a #H2b whd in ⊢ (% → ?) #H2c |
---|
1284 | >H2b >(eq_instruction_to_eq … H2a) |
---|
1285 | generalize in match EQ; -EQ; |
---|
1286 | whd in ⊢ (???% → ?); |
---|
1287 | #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) whd in ⊢ (??%?) |
---|
1288 | change with ((let 〈pc_bu,pc_bl〉 ≝ split bool 8 8 (sigma 〈preamble,instr_list〉 pol newppc) in ?)=?) |
---|
1289 | generalize in match (refl … (split bool 8 8 (sigma 〈preamble,instr_list〉 pol newppc))) |
---|
1290 | cases (split ????) in ⊢ (??%? → %) #pc_bu #pc_bl normalize nodelta; #EQ4 |
---|
1291 | generalize in match (refl … (split bool 4 4 pc_bu)) |
---|
1292 | cases (split ????) in ⊢ (??%? → %) #nu #nl normalize nodelta; #EQ5 |
---|
1293 | generalize in match (refl … (split bool 3 8 rest_addr)) |
---|
1294 | cases (split ????) in ⊢ (??%? → %) #relevant1 #relevant2 normalize nodelta; #EQ6 |
---|
1295 | change with ((let 〈carry,new_pc〉 ≝ half_add ? (sigma … newppc) ? in ?) = ?) |
---|
1296 | generalize in match |
---|
1297 | (refl … |
---|
1298 | (half_add 16 (sigma 〈preamble,instr_list〉 pol newppc) |
---|
1299 | ((nu@@get_index' bool 0 3 nl:::relevant1)@@relevant2))) |
---|
1300 | cases (half_add ???) in ⊢ (??%? → %) #carry #new_pc normalize nodelta; #EQ7 |
---|
1301 | @split_eq_status try % |
---|
1302 | [ change with (? = sigma ?? (address_of_word_labels ps label)) |
---|
1303 | (* ARITHMETICS, BUT THE GOAL SEEMS FALSE *) |
---|
1304 | | whd in ⊢ (??%%) whd in ⊢ (??(?%?)?) whd in ⊢ (??(?(match ?(?%)? with [_ ⇒ ?])?)?) |
---|
1305 | @(bitvector_3_elim_prop … (\fst (split bool 3 8 rest_addr))) %]] |
---|
1306 | | (* Instruction *) -pi; whd in ⊢ (? → ??%? → ?) *; normalize nodelta; |
---|
1307 | [1,2,3: (* ADD, ADDC, SUBB *) #arg1 #arg2 #MAP #H1 #H2 #EQ %[1,3,5:@1] |
---|
1308 | normalize in H1; generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?) |
---|
1309 | change in ⊢ (? → ??%?) with (execute_1_0 ??) |
---|
1310 | cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 pol (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta; |
---|
1311 | * * #H2a #H2b whd in ⊢ (% → ?) #H2c |
---|
1312 | >H2b >(eq_instruction_to_eq … H2a) |
---|
1313 | generalize in match EQ; -EQ; whd in ⊢ (???% → ??%?); generalize in match MAP; -MAP; |
---|
1314 | @(list_addressing_mode_tags_elim_prop … arg1) whd try % -arg1; |
---|
1315 | @(list_addressing_mode_tags_elim_prop … arg2) whd try % -arg2; #ARG2 |
---|
1316 | normalize nodelta; #MAP; |
---|
1317 | [1: change in ⊢ (? → %) with |
---|
1318 | ((let 〈result,flags〉 ≝ |
---|
1319 | add_8_with_carry |
---|
1320 | (get_arg_8 ? ps false ACC_A) |
---|
1321 | (get_arg_8 ? |
---|
1322 | (set_low_internal_ram ? ps (low_internal_ram_of_pseudo_low_internal_ram M (low_internal_ram … ps))) |
---|
1323 | false (DIRECT ARG2)) |
---|
1324 | ? in ?) = ?) |
---|
1325 | [2,3: %] |
---|
1326 | change in ⊢ (???% → ?) with |
---|
1327 | (let 〈result,flags〉 ≝ add_8_with_carry ?(*(get_arg_8 ? ps false ACC_A)*) ?? in ?) |
---|
1328 | >get_arg_8_set_clock |
---|
1329 | [1,2: cases (addressing_mode_ok ???? ∧ addressing_mode_ok ????) in MAP ⊢ ? |
---|
1330 | [2,4: #abs @⊥ normalize in abs; destruct (abs) |
---|
1331 | |*:whd in ⊢ (??%? → ?) #H <(option_destruct_Some ??? H)] |
---|
1332 | [ change in ⊢ (? → %) with |
---|
1333 | ((let 〈result,flags〉 ≝ |
---|
1334 | add_8_with_carry |
---|
1335 | (get_arg_8 ? ps false ACC_A) |
---|
1336 | (get_arg_8 ? |
---|
1337 | (set_low_internal_ram ? ps (low_internal_ram_of_pseudo_low_internal_ram M (low_internal_ram … ps))) |
---|
1338 | false (DIRECT ARG2)) |
---|
1339 | ? in ?) = ?) |
---|
1340 | >get_arg_8_set_low_internal_ram |
---|
1341 | |
---|
1342 | cases (add_8_with_carry ???) |
---|
1343 | |
---|
1344 | [1,2,3,4,5,6,7,8: cases (add_8_with_carry ???) |*: cases (sub_8_with_carry ???)] |
---|
1345 | #result #flags |
---|
1346 | #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) % |
---|
1347 | | (* INC *) #arg1 #H1 #H2 #EQ %[@1] |
---|
1348 | normalize in H1; generalize in match (option_destruct_Some ??? H1) #K1 >K1 in H2; whd in ⊢ (% → ?) |
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1349 | change in ⊢ (? → ??%?) with (execute_1_0 ??) |
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1350 | cases (fetch (load_code_memory assembled) (sigma 〈preamble,instr_list〉 (program_counter … ps))) * #instr #newppc' #ticks normalize nodelta; |
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1351 | * * #H2a #H2b whd in ⊢ (% → ?) #H2c |
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1352 | >H2b >(eq_instruction_to_eq … H2a) |
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1353 | generalize in match EQ; -EQ; whd in ⊢ (???% → ??%?); |
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1354 | @(list_addressing_mode_tags_elim_prop … arg1) whd try % -arg1; normalize nodelta; [1,2,3: #ARG] |
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1355 | [1,2,3,4: cases (half_add ???) #carry #result |
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1356 | | cases (half_add ???) #carry #bl normalize nodelta; |
---|
1357 | cases (full_add ????) #carry' #bu normalize nodelta ] |
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1358 | #EQ >EQ -EQ; normalize nodelta; >(eq_bv_eq … H2c) -newppc'; |
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1359 | [5: % |
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1360 | |1: <(set_arg_8_set_code_memory 0 [[direct]] ? ? ? (set_clock pseudo_assembly_program |
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1361 | (set_program_counter pseudo_assembly_program ps newppc) |
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1362 | (\fst (ticks_of0 〈preamble,instr_list〉 |
---|
1363 | (program_counter pseudo_assembly_program ps) |
---|
1364 | (Instruction (INC Identifier (DIRECT ARG)))) |
---|
1365 | +clock pseudo_assembly_program |
---|
1366 | (set_program_counter pseudo_assembly_program ps newppc))) (load_code_memory assembled) result (DIRECT ARG)) |
---|
1367 | [2,3: // ] |
---|
1368 | <(set_arg_8_set_program_counter 0 [[direct]] ? ? ? ? ?) [2://] |
---|
1369 | whd in ⊢ (??%%) |
---|
1370 | cases (split bool 4 4 ARG) |
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1371 | #nu' #nl' |
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1372 | normalize nodelta |
---|
1373 | cases (split bool 1 3 nu') |
---|
1374 | #bit_1' #ignore' |
---|
1375 | normalize nodelta |
---|
1376 | cases (get_index_v bool 4 nu' ? ?) |
---|
1377 | [ normalize nodelta (* HERE *) whd in ⊢ (??%%) % |
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1378 | | |
---|
1379 | ] |
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1380 | cases daemon (* EASY CASES TO BE COMPLETED *) |
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1381 | qed. |
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1382 | *) |
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