1 | include "ASM/StatusProofsSplit.ma". |
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2 | |
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3 | include alias "arithmetics/nat.ma". |
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4 | include alias "basics/logic.ma". |
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5 | include alias "ASM/BitVectorTrie.ma". |
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6 | |
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7 | lemma fetch_many_singleton: |
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8 | ∀code_memory: BitVectorTrie Byte 16. |
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9 | ∀final_pc, start_pc: Word. |
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10 | ∀i: instruction. |
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11 | fetch_many code_memory final_pc start_pc [i] → |
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12 | 〈i, final_pc, ticks_of_instruction i〉 = fetch code_memory |
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13 | start_pc. |
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14 | #code_memory #final_pc #start_pc #i * #new_pc |
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15 | #fetch_many_assm whd in fetch_many_assm; |
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16 | cases (eq_bv_eq … fetch_many_assm) assumption |
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17 | qed. |
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18 | |
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19 | include alias "ASM/Vector.ma". |
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20 | include "ASM/Test.ma". |
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21 | |
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22 | lemma addressing_mode_ok_to_map_address_using_internal_pseudo_address_map: |
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23 | ∀M, cm, ps, sigma, x. |
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24 | ∀addr1: [[acc_a]]. |
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25 | addressing_mode_ok pseudo_assembly_program M cm ps addr1=true → |
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26 | map_address_using_internal_pseudo_address_map M sigma SFR_ACC_A x = x. |
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27 | #M #cm #ps #sigma #x #addr1 |
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28 | @(subaddressing_mode_elim … addr1) |
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29 | whd in ⊢ (??%? → ??%?); |
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30 | cases (\snd M) |
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31 | [1: |
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32 | // |
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33 | |2: |
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34 | #upper_lower #address normalize nodelta #absurd |
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35 | destruct(absurd) |
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36 | ] |
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37 | qed. |
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38 | |
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39 | lemma main_lemma_preinstruction: |
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40 | ∀M, M': internal_pseudo_address_map. |
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41 | ∀preamble: preamble. |
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42 | ∀instr_list: list labelled_instruction. |
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43 | ∀cm: pseudo_assembly_program. |
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44 | ∀EQcm: cm = 〈preamble, instr_list〉. |
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45 | ∀is_well_labelled_witness: is_well_labelled_p instr_list. |
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46 | ∀sigma: Word → Word. |
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47 | ∀policy: Word → bool. |
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48 | ∀sigma_policy_witness: sigma_policy_specification cm sigma policy. |
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49 | ∀ps: PseudoStatus cm. |
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50 | ∀ppc: Word. |
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51 | ∀program_counter_in_bounds_witness: nat_of_bitvector … ppc < |instr_list|. |
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52 | ∀EQppc: ppc = program_counter pseudo_assembly_program cm ps. |
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53 | ∀labels: label_map. |
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54 | ∀costs: BitVectorTrie costlabel 16. |
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55 | ∀create_label_cost_refl: create_label_cost_map instr_list = 〈labels, costs〉. |
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56 | ∀newppc: Word. |
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57 | ∀lookup_labels: Identifier → Word. |
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58 | ∀EQlookup_labels: lookup_labels = (λx. bitvector_of_nat 16 (lookup_def … labels x 0)). |
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59 | ∀lookup_datalabels: Identifier → Word. |
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60 | ∀EQlookup_datalabels: lookup_datalabels = (λx.lookup_def ASMTag Word (construct_datalabels preamble) x (zero 16)). |
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61 | ∀EQnewppc: newppc = add 16 ppc (bitvector_of_nat 16 1). |
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62 | ∀instr: preinstruction Identifier. |
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63 | ∀fetch_pseudo_refl: \fst (fetch_pseudo_instruction instr_list ppc program_counter_in_bounds_witness) = Instruction instr. |
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64 | ∀ticks: nat × nat. |
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65 | ∀EQticks: ticks = ticks_of0 〈preamble, instr_list〉 lookup_datalabels sigma policy ppc (Instruction instr). |
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66 | ∀addr_of: Identifier → PreStatus pseudo_assembly_program cm → BitVector 16. |
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67 | ∀EQaddr_of: addr_of = (λx:Identifier. λy:PreStatus pseudo_assembly_program cm. address_of_word_labels cm x). |
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68 | ∀s: PreStatus pseudo_assembly_program cm. |
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69 | ∀EQs: s = (set_program_counter pseudo_assembly_program cm ps (add 16 ppc (bitvector_of_nat 16 1))). |
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70 | ∀P: preinstruction Identifier → PseudoStatus cm → Prop. |
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71 | ∀EQP: P = (λinstr, s. sigma (add 16 ppc (bitvector_of_nat 16 1)) = add 16 (sigma ppc) |
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72 | (bitvector_of_nat 16 (\fst (assembly_1_pseudoinstruction lookup_labels sigma policy ppc |
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73 | lookup_datalabels (Instruction instr)))) → |
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74 | next_internal_pseudo_address_map0 ? cm addr_of (Instruction instr) M ps = Some internal_pseudo_address_map M' → |
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75 | fetch_many (load_code_memory (\fst (pi1 … (assembly cm sigma policy)))) (sigma (add 16 ppc (bitvector_of_nat 16 1))) (sigma (program_counter pseudo_assembly_program cm ps)) |
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76 | (expand_pseudo_instruction lookup_labels sigma policy (program_counter pseudo_assembly_program cm ps) lookup_datalabels (Instruction instr)) → |
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77 | ∃n: nat. execute n (code_memory_of_pseudo_assembly_program cm sigma policy) (status_of_pseudo_status M cm ps sigma policy) = |
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78 | status_of_pseudo_status M' cm s sigma policy). |
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79 | P instr (execute_1_preinstruction ticks Identifier pseudo_assembly_program cm addr_of instr s). |
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80 | (* XXX: takes about 45 minutes to type check! *) |
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81 | #M #M' #preamble #instr_list #cm #EQcm #is_well_labelled_witness #sigma #policy |
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82 | #sigma_policy_witness #ps #ppc #ppc_in_bounds_witness #EQppc #labels |
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83 | #costs #create_label_cost_refl #newppc #lookup_labels #EQlookup_labels |
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84 | #lookup_datalabels #EQlookup_datalabels #EQnewppc #instr #fetch_pseudo_refl |
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85 | #ticks #EQticks #addr_of #EQaddr_of #s #EQs #P #EQP |
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86 | (*#sigma_increment_commutation #maps_assm #fetch_many_assm *) |
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87 | letin a ≝ Identifier letin m ≝ pseudo_assembly_program |
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88 | cut (Σxxx:PseudoStatus cm. P instr (execute_1_preinstruction ticks a m cm addr_of instr s)) |
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89 | [2: * // ] |
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90 | @( |
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91 | let add_ticks1 ≝ λs: PreStatus m cm. set_clock ?? s (\fst ticks + clock ?? s) in |
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92 | let add_ticks2 ≝ λs: PreStatus m cm. set_clock ?? s (\snd ticks + clock ?? s) in |
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93 | match instr in preinstruction return λx. x = instr → Σs'.? with |
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94 | [ ADD addr1 addr2 ⇒ λinstr_refl. |
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95 | let s ≝ add_ticks1 s in |
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96 | let 〈result, flags〉 ≝ add_8_with_carry (get_arg_8 … s false addr1) |
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97 | (get_arg_8 … s false addr2) false in |
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98 | let cy_flag ≝ get_index' ? O ? flags in |
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99 | let ac_flag ≝ get_index' ? 1 ? flags in |
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100 | let ov_flag ≝ get_index' ? 2 ? flags in |
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101 | let s ≝ set_arg_8 … s ACC_A result in |
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102 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
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103 | | ADDC addr1 addr2 ⇒ λinstr_refl. |
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104 | let s ≝ add_ticks1 s in |
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105 | let old_cy_flag ≝ get_cy_flag ?? s in |
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106 | let 〈result, flags〉 ≝ add_8_with_carry (get_arg_8 … s false addr1) |
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107 | (get_arg_8 … s false addr2) old_cy_flag in |
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108 | let cy_flag ≝ get_index' ? O ? flags in |
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109 | let ac_flag ≝ get_index' ? 1 ? flags in |
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110 | let ov_flag ≝ get_index' ? 2 ? flags in |
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111 | let s ≝ set_arg_8 … s ACC_A result in |
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112 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
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113 | | SUBB addr1 addr2 ⇒ λinstr_refl. |
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114 | let s ≝ add_ticks1 s in |
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115 | let old_cy_flag ≝ get_cy_flag ?? s in |
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116 | let 〈result, flags〉 ≝ sub_8_with_carry (get_arg_8 … s false addr1) |
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117 | (get_arg_8 … s false addr2) old_cy_flag in |
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118 | let cy_flag ≝ get_index' ? O ? flags in |
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119 | let ac_flag ≝ get_index' ? 1 ? flags in |
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120 | let ov_flag ≝ get_index' ? 2 ? flags in |
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121 | let s ≝ set_arg_8 … s ACC_A result in |
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122 | set_flags … s cy_flag (Some Bit ac_flag) ov_flag |
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123 | | ANL addr ⇒ λinstr_refl. |
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124 | let s ≝ add_ticks1 s in |
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125 | match addr with |
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126 | [ inl l ⇒ |
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127 | match l with |
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128 | [ inl l' ⇒ |
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129 | let 〈addr1, addr2〉 ≝ l' in |
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130 | let and_val ≝ conjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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131 | set_arg_8 … s addr1 and_val |
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132 | | inr r ⇒ |
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133 | let 〈addr1, addr2〉 ≝ r in |
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134 | let and_val ≝ conjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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135 | set_arg_8 … s addr1 and_val |
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136 | ] |
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137 | | inr r ⇒ |
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138 | let 〈addr1, addr2〉 ≝ r in |
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139 | let and_val ≝ andb (get_cy_flag … s) (get_arg_1 … s addr2 true) in |
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140 | set_flags … s and_val (None ?) (get_ov_flag ?? s) |
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141 | ] |
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142 | | ORL addr ⇒ λinstr_refl. |
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143 | let s ≝ add_ticks1 s in |
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144 | match addr with |
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145 | [ inl l ⇒ |
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146 | match l with |
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147 | [ inl l' ⇒ |
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148 | let 〈addr1, addr2〉 ≝ l' in |
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149 | let or_val ≝ inclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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150 | set_arg_8 … s addr1 or_val |
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151 | | inr r ⇒ |
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152 | let 〈addr1, addr2〉 ≝ r in |
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153 | let or_val ≝ inclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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154 | set_arg_8 … s addr1 or_val |
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155 | ] |
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156 | | inr r ⇒ |
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157 | let 〈addr1, addr2〉 ≝ r in |
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158 | let or_val ≝ (get_cy_flag … s) ∨ (get_arg_1 … s addr2 true) in |
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159 | set_flags … s or_val (None ?) (get_ov_flag … s) |
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160 | ] |
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161 | | XRL addr ⇒ λinstr_refl. |
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162 | let s ≝ add_ticks1 s in |
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163 | match addr with |
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164 | [ inl l' ⇒ |
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165 | let 〈addr1, addr2〉 ≝ l' in |
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166 | let xor_val ≝ exclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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167 | set_arg_8 … s addr1 xor_val |
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168 | | inr r ⇒ |
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169 | let 〈addr1, addr2〉 ≝ r in |
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170 | let xor_val ≝ exclusive_disjunction_bv ? (get_arg_8 … s true addr1) (get_arg_8 … s true addr2) in |
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171 | set_arg_8 … s addr1 xor_val |
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172 | ] |
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173 | | INC addr ⇒ λinstr_refl. |
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174 | 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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175 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
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176 | let s' ≝ add_ticks1 s in |
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177 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true ACC_A) (bitvector_of_nat 8 1) in |
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178 | set_arg_8 … s' ACC_A result |
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179 | | REGISTER r ⇒ λregister: True. λEQaddr. |
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180 | let s' ≝ add_ticks1 s in |
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181 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (REGISTER r)) (bitvector_of_nat 8 1) in |
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182 | set_arg_8 … s' (REGISTER r) result |
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183 | | DIRECT d ⇒ λdirect: True. λEQaddr. |
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184 | let s' ≝ add_ticks1 s in |
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185 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (DIRECT d)) (bitvector_of_nat 8 1) in |
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186 | set_arg_8 … s' (DIRECT d) result |
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187 | | INDIRECT i ⇒ λindirect: True. λEQaddr. |
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188 | let s' ≝ add_ticks1 s in |
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189 | let 〈 carry, result 〉 ≝ half_add ? (get_arg_8 … s' true (INDIRECT i)) (bitvector_of_nat 8 1) in |
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190 | set_arg_8 … s' (INDIRECT i) result |
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191 | | DPTR ⇒ λdptr: True. λEQaddr. |
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192 | let s' ≝ add_ticks1 s in |
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193 | let 〈 carry, bl 〉 ≝ half_add ? (get_8051_sfr … s' SFR_DPL) (bitvector_of_nat 8 1) in |
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194 | let 〈 carry, bu 〉 ≝ full_add ? (get_8051_sfr … s' SFR_DPH) (zero 8) carry in |
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195 | let s ≝ set_8051_sfr … s' SFR_DPL bl in |
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196 | set_8051_sfr … s' SFR_DPH bu |
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197 | | _ ⇒ λother: False. ⊥ |
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198 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
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199 | | NOP ⇒ λinstr_refl. |
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200 | let s ≝ add_ticks2 s in |
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201 | s |
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202 | | DEC addr ⇒ λinstr_refl. |
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203 | let s ≝ add_ticks1 s in |
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204 | let 〈 result, flags 〉 ≝ sub_8_with_carry (get_arg_8 … s true addr) (bitvector_of_nat 8 1) false in |
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205 | set_arg_8 … s addr result |
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206 | | MUL addr1 addr2 ⇒ λinstr_refl. |
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207 | let s ≝ add_ticks1 s in |
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208 | let acc_a_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_A) in |
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209 | let acc_b_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_B) in |
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210 | let product ≝ acc_a_nat * acc_b_nat in |
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211 | let ov_flag ≝ product ≥ 256 in |
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212 | let low ≝ bitvector_of_nat 8 (product mod 256) in |
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213 | let high ≝ bitvector_of_nat 8 (product ÷ 256) in |
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214 | let s ≝ set_8051_sfr … s SFR_ACC_A low in |
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215 | set_8051_sfr … s SFR_ACC_B high |
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216 | | DIV addr1 addr2 ⇒ λinstr_refl. |
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217 | let s ≝ add_ticks1 s in |
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218 | let acc_a_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_A) in |
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219 | let acc_b_nat ≝ nat_of_bitvector 8 (get_8051_sfr … s SFR_ACC_B) in |
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220 | match acc_b_nat with |
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221 | [ O ⇒ set_flags … s false (None Bit) true |
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222 | | S o ⇒ |
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223 | let q ≝ bitvector_of_nat 8 (acc_a_nat ÷ (S o)) in |
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224 | let r ≝ bitvector_of_nat 8 (acc_a_nat mod 256) in |
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225 | let s ≝ set_8051_sfr … s SFR_ACC_A q in |
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226 | let s ≝ set_8051_sfr … s SFR_ACC_B r in |
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227 | set_flags … s false (None Bit) false |
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228 | ] |
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229 | | DA addr ⇒ λinstr_refl. |
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230 | let s ≝ add_ticks1 s in |
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231 | let 〈acc_nu, acc_nl〉 ≝ vsplit ? 4 4 (get_8051_sfr … s SFR_ACC_A) in |
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232 | if (gtb (nat_of_bitvector ? acc_nl) 9) ∨ (get_ac_flag … s) then |
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233 | let 〈result, flags〉 ≝ add_8_with_carry (get_8051_sfr … s SFR_ACC_A) (bitvector_of_nat 8 6) false in |
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234 | let cy_flag ≝ get_index' ? O ? flags in |
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235 | let 〈acc_nu', acc_nl'〉 ≝ vsplit ? 4 4 result in |
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236 | if (gtb (nat_of_bitvector ? acc_nu') 9) ∨ cy_flag then |
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237 | let 〈 carry, nu 〉 ≝ half_add ? acc_nu' (bitvector_of_nat 4 6) in |
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238 | let new_acc ≝ nu @@ acc_nl' in |
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239 | let s ≝ set_8051_sfr … s SFR_ACC_A new_acc in |
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240 | set_flags … s cy_flag (Some ? (get_ac_flag … s)) (get_ov_flag … s) |
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241 | else |
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242 | s |
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243 | else |
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244 | s |
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245 | | CLR addr ⇒ λinstr_refl. |
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246 | match addr return λx. bool_to_Prop (is_in … [[ acc_a; carry; bit_addr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
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247 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
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248 | let s ≝ add_ticks1 s in |
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249 | set_arg_8 … s ACC_A (zero 8) |
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250 | | CARRY ⇒ λcarry: True. λEQaddr. |
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251 | let s ≝ add_ticks1 s in |
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252 | set_arg_1 … s CARRY false |
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253 | | BIT_ADDR b ⇒ λbit_addr: True. λEQaddr. |
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254 | let s ≝ add_ticks1 s in |
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255 | set_arg_1 … s (BIT_ADDR b) false |
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256 | | _ ⇒ λother: False. ⊥ |
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257 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
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258 | | CPL addr ⇒ λinstr_refl. |
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259 | match addr return λx. bool_to_Prop (is_in … [[ acc_a; carry; bit_addr ]] x) → x = addr → Σs': PreStatus m cm. ? with |
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260 | [ ACC_A ⇒ λacc_a: True. λEQaddr. |
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261 | let s ≝ add_ticks1 s in |
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262 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
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263 | let new_acc ≝ negation_bv ? old_acc in |
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264 | set_8051_sfr … s SFR_ACC_A new_acc |
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265 | | CARRY ⇒ λcarry: True. λEQaddr. |
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266 | let s ≝ add_ticks1 s in |
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267 | let old_cy_flag ≝ get_arg_1 … s CARRY true in |
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268 | let new_cy_flag ≝ ¬old_cy_flag in |
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269 | set_arg_1 … s CARRY new_cy_flag |
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270 | | BIT_ADDR b ⇒ λbit_addr: True. λEQaddr. |
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271 | let s ≝ add_ticks1 s in |
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272 | let old_bit ≝ get_arg_1 … s (BIT_ADDR b) true in |
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273 | let new_bit ≝ ¬old_bit in |
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274 | set_arg_1 … s (BIT_ADDR b) new_bit |
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275 | | _ ⇒ λother: False. ? |
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276 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
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277 | | SETB b ⇒ λinstr_refl. |
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278 | let s ≝ add_ticks1 s in |
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279 | set_arg_1 … s b false |
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280 | | RL _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
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281 | let s ≝ add_ticks1 s in |
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282 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
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283 | let new_acc ≝ rotate_left … 1 old_acc in |
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284 | set_8051_sfr … s SFR_ACC_A new_acc |
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285 | | RR _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
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286 | let s ≝ add_ticks1 s in |
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287 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
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288 | let new_acc ≝ rotate_right … 1 old_acc in |
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289 | set_8051_sfr … s SFR_ACC_A new_acc |
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290 | | RLC _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
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291 | let s ≝ add_ticks1 s in |
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292 | let old_cy_flag ≝ get_cy_flag ?? s in |
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293 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
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294 | let new_cy_flag ≝ get_index' ? O ? old_acc in |
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295 | let new_acc ≝ shift_left … 1 old_acc old_cy_flag in |
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296 | let s ≝ set_arg_1 … s CARRY new_cy_flag in |
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297 | set_8051_sfr … s SFR_ACC_A new_acc |
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298 | | RRC _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
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299 | let s ≝ add_ticks1 s in |
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300 | let old_cy_flag ≝ get_cy_flag ?? s in |
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301 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
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302 | let new_cy_flag ≝ get_index' ? 7 ? old_acc in |
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303 | let new_acc ≝ shift_right … 1 old_acc old_cy_flag in |
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304 | let s ≝ set_arg_1 … s CARRY new_cy_flag in |
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305 | set_8051_sfr … s SFR_ACC_A new_acc |
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306 | | SWAP _ ⇒ λinstr_refl. (* DPM: always ACC_A *) |
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307 | let s ≝ add_ticks1 s in |
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308 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
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309 | let 〈nu,nl〉 ≝ vsplit ? 4 4 old_acc in |
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310 | let new_acc ≝ nl @@ nu in |
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311 | set_8051_sfr … s SFR_ACC_A new_acc |
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312 | | PUSH addr ⇒ λinstr_refl. |
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313 | match addr return λx. bool_to_Prop (is_in … [[ direct ]] x) → x = addr → Σs': PreStatus m cm. ? with |
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314 | [ DIRECT d ⇒ λdirect: True. λEQaddr. |
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315 | let s ≝ add_ticks1 s in |
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316 | let 〈carry, new_sp〉 ≝ half_add ? (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) in |
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317 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
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318 | write_at_stack_pointer … s d |
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319 | | _ ⇒ λother: False. ⊥ |
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320 | ] (subaddressing_modein … addr) (refl … (subaddressing_modeel … addr)) |
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321 | | POP addr ⇒ λinstr_refl. |
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322 | let s ≝ add_ticks1 s in |
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323 | let contents ≝ read_at_stack_pointer ?? s in |
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324 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
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325 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
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326 | set_arg_8 … s addr contents |
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327 | | XCH addr1 addr2 ⇒ λinstr_refl. |
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328 | let s ≝ add_ticks1 s in |
---|
329 | let old_addr ≝ get_arg_8 … s false addr2 in |
---|
330 | let old_acc ≝ get_8051_sfr … s SFR_ACC_A in |
---|
331 | let s ≝ set_8051_sfr … s SFR_ACC_A old_addr in |
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332 | set_arg_8 … s addr2 old_acc |
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333 | | XCHD addr1 addr2 ⇒ λinstr_refl. |
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334 | let s ≝ add_ticks1 s in |
---|
335 | let 〈acc_nu, acc_nl〉 ≝ vsplit … 4 4 (get_8051_sfr … s SFR_ACC_A) in |
---|
336 | let 〈arg_nu, arg_nl〉 ≝ vsplit … 4 4 (get_arg_8 … s false addr2) in |
---|
337 | let new_acc ≝ acc_nu @@ arg_nl in |
---|
338 | let new_arg ≝ arg_nu @@ acc_nl in |
---|
339 | let s ≝ set_8051_sfr ?? s SFR_ACC_A new_acc in |
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340 | set_arg_8 … s addr2 new_arg |
---|
341 | | RET ⇒ λinstr_refl. |
---|
342 | let s ≝ add_ticks1 s in |
---|
343 | let high_bits ≝ read_at_stack_pointer ?? s in |
---|
344 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
345 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
346 | let low_bits ≝ read_at_stack_pointer ?? s in |
---|
347 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
348 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
349 | let new_pc ≝ high_bits @@ low_bits in |
---|
350 | set_program_counter … s new_pc |
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351 | | RETI ⇒ λinstr_refl. |
---|
352 | let s ≝ add_ticks1 s in |
---|
353 | let high_bits ≝ read_at_stack_pointer ?? s in |
---|
354 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
355 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
356 | let low_bits ≝ read_at_stack_pointer ?? s in |
---|
357 | let 〈new_sp, flags〉 ≝ sub_8_with_carry (get_8051_sfr … s SFR_SP) (bitvector_of_nat 8 1) false in |
---|
358 | let s ≝ set_8051_sfr … s SFR_SP new_sp in |
---|
359 | let new_pc ≝ high_bits @@ low_bits in |
---|
360 | set_program_counter … s new_pc |
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361 | | MOVX addr ⇒ λinstr_refl. |
---|
362 | let s ≝ add_ticks1 s in |
---|
363 | (* DPM: only copies --- doesn't affect I/O *) |
---|
364 | match addr with |
---|
365 | [ inl l ⇒ |
---|
366 | let 〈addr1, addr2〉 ≝ l in |
---|
367 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
368 | | inr r ⇒ |
---|
369 | let 〈addr1, addr2〉 ≝ r in |
---|
370 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
371 | ] |
---|
372 | | MOV addr ⇒ λinstr_refl. |
---|
373 | let s ≝ add_ticks1 s in |
---|
374 | match addr with |
---|
375 | [ inl l ⇒ |
---|
376 | match l with |
---|
377 | [ inl l' ⇒ |
---|
378 | match l' with |
---|
379 | [ inl l'' ⇒ |
---|
380 | match l'' with |
---|
381 | [ inl l''' ⇒ |
---|
382 | match l''' with |
---|
383 | [ inl l'''' ⇒ |
---|
384 | let 〈addr1, addr2〉 ≝ l'''' in |
---|
385 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
386 | | inr r'''' ⇒ |
---|
387 | let 〈addr1, addr2〉 ≝ r'''' in |
---|
388 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
389 | ] |
---|
390 | | inr r''' ⇒ |
---|
391 | let 〈addr1, addr2〉 ≝ r''' in |
---|
392 | set_arg_8 … s addr1 (get_arg_8 … s false addr2) |
---|
393 | ] |
---|
394 | | inr r'' ⇒ |
---|
395 | let 〈addr1, addr2〉 ≝ r'' in |
---|
396 | set_arg_16 … s (get_arg_16 … s addr2) addr1 |
---|
397 | ] |
---|
398 | | inr r ⇒ |
---|
399 | let 〈addr1, addr2〉 ≝ r in |
---|
400 | set_arg_1 … s addr1 (get_arg_1 … s addr2 false) |
---|
401 | ] |
---|
402 | | inr r ⇒ |
---|
403 | let 〈addr1, addr2〉 ≝ r in |
---|
404 | set_arg_1 … s addr1 (get_arg_1 … s addr2 false) |
---|
405 | ] |
---|
406 | | JC addr ⇒ λinstr_refl. |
---|
407 | if get_cy_flag ?? s then |
---|
408 | let s ≝ add_ticks1 s in |
---|
409 | set_program_counter … s (addr_of addr s) |
---|
410 | else |
---|
411 | let s ≝ add_ticks2 s in |
---|
412 | s |
---|
413 | | JNC addr ⇒ λinstr_refl. |
---|
414 | if ¬(get_cy_flag ?? s) then |
---|
415 | let s ≝ add_ticks1 s in |
---|
416 | set_program_counter … s (addr_of addr s) |
---|
417 | else |
---|
418 | let s ≝ add_ticks2 s in |
---|
419 | s |
---|
420 | | JB addr1 addr2 ⇒ λinstr_refl. |
---|
421 | if get_arg_1 … s addr1 false then |
---|
422 | let s ≝ add_ticks1 s in |
---|
423 | set_program_counter … s (addr_of addr2 s) |
---|
424 | else |
---|
425 | let s ≝ add_ticks2 s in |
---|
426 | s |
---|
427 | | JNB addr1 addr2 ⇒ λinstr_refl. |
---|
428 | if ¬(get_arg_1 … s addr1 false) then |
---|
429 | let s ≝ add_ticks1 s in |
---|
430 | set_program_counter … s (addr_of addr2 s) |
---|
431 | else |
---|
432 | let s ≝ add_ticks2 s in |
---|
433 | s |
---|
434 | | JBC addr1 addr2 ⇒ λinstr_refl. |
---|
435 | let s ≝ set_arg_1 … s addr1 false in |
---|
436 | if get_arg_1 … s addr1 false then |
---|
437 | let s ≝ add_ticks1 s in |
---|
438 | set_program_counter … s (addr_of addr2 s) |
---|
439 | else |
---|
440 | let s ≝ add_ticks2 s in |
---|
441 | s |
---|
442 | | JZ addr ⇒ λinstr_refl. |
---|
443 | if eq_bv ? (get_8051_sfr … s SFR_ACC_A) (zero 8) then |
---|
444 | let s ≝ add_ticks1 s in |
---|
445 | set_program_counter … s (addr_of addr s) |
---|
446 | else |
---|
447 | let s ≝ add_ticks2 s in |
---|
448 | s |
---|
449 | | JNZ addr ⇒ λinstr_refl. |
---|
450 | if ¬(eq_bv ? (get_8051_sfr … s SFR_ACC_A) (zero 8)) then |
---|
451 | let s ≝ add_ticks1 s in |
---|
452 | set_program_counter … s (addr_of addr s) |
---|
453 | else |
---|
454 | let s ≝ add_ticks2 s in |
---|
455 | s |
---|
456 | | CJNE addr1 addr2 ⇒ λinstr_refl. |
---|
457 | match addr1 with |
---|
458 | [ inl l ⇒ |
---|
459 | let 〈addr1, addr2'〉 ≝ l in |
---|
460 | let new_cy ≝ ltb (nat_of_bitvector ? (get_arg_8 … s false addr1)) |
---|
461 | (nat_of_bitvector ? (get_arg_8 … s false addr2')) in |
---|
462 | if ¬(eq_bv ? (get_arg_8 … s false addr1) (get_arg_8 … s false addr2')) then |
---|
463 | let s ≝ add_ticks1 s in |
---|
464 | let s ≝ set_program_counter … s (addr_of addr2 s) in |
---|
465 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
466 | else |
---|
467 | let s ≝ add_ticks2 s in |
---|
468 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
469 | | inr r' ⇒ |
---|
470 | let 〈addr1, addr2'〉 ≝ r' in |
---|
471 | let new_cy ≝ ltb (nat_of_bitvector ? (get_arg_8 … s false addr1)) |
---|
472 | (nat_of_bitvector ? (get_arg_8 … s false addr2')) in |
---|
473 | if ¬(eq_bv ? (get_arg_8 … s false addr1) (get_arg_8 … s false addr2')) then |
---|
474 | let s ≝ add_ticks1 s in |
---|
475 | let s ≝ set_program_counter … s (addr_of addr2 s) in |
---|
476 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
477 | else |
---|
478 | let s ≝ add_ticks2 s in |
---|
479 | set_flags … s new_cy (None ?) (get_ov_flag ?? s) |
---|
480 | ] |
---|
481 | | DJNZ addr1 addr2 ⇒ λinstr_refl. |
---|
482 | let 〈result, flags〉 ≝ sub_8_with_carry (get_arg_8 … s true addr1) (bitvector_of_nat 8 1) false in |
---|
483 | let s ≝ set_arg_8 … s addr1 result in |
---|
484 | if ¬(eq_bv ? result (zero 8)) then |
---|
485 | let s ≝ add_ticks1 s in |
---|
486 | set_program_counter … s (addr_of addr2 s) |
---|
487 | else |
---|
488 | let s ≝ add_ticks2 s in |
---|
489 | s |
---|
490 | ] (refl … instr)) |
---|
491 | try cases other |
---|
492 | try assumption (*20s*) |
---|
493 | try (% @False) (*6s*) (* Bug exploited here to implement solve :-*) |
---|
494 | try (@(execute_1_technical … (subaddressing_modein …)) @I) (*66s*) |
---|
495 | whd in match execute_1_preinstruction; normalize nodelta |
---|
496 | |
---|
497 | (* [31,32: (* DJNZ *) |
---|
498 | (* XXX: work on the right hand side *) |
---|
499 | >p normalize nodelta >p1 normalize nodelta |
---|
500 | (* XXX: switch to the left hand side *) |
---|
501 | >EQP -P normalize nodelta |
---|
502 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
---|
503 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
504 | <EQppc in fetch_many_assm; |
---|
505 | whd in match (short_jump_cond ??); |
---|
506 | @pair_elim #sj_possible #disp |
---|
507 | @pair_elim #result #flags #sub16_refl |
---|
508 | @pair_elim #upper #lower #vsplit_refl |
---|
509 | inversion (get_index' bool ???) #get_index_refl' normalize nodelta |
---|
510 | #sj_possible_pair destruct(sj_possible_pair) |
---|
511 | >p1 normalize nodelta |
---|
512 | [1,3: |
---|
513 | >EQppc in ⊢ (% → ?); #fetch_many_assm %{1} |
---|
514 | >(sub16_with_carry_overflow … sub16_refl vsplit_refl get_index_refl') in fetch_many_assm; |
---|
515 | normalize nodelta in ⊢ (% → ?); #fetch_many_assm |
---|
516 | whd in ⊢ (??%?); |
---|
517 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
518 | lapply maps_assm whd in ⊢ (??%? → ?); |
---|
519 | inversion (addressing_mode_ok ?????) #addressing_mode_ok_refl normalize nodelta |
---|
520 | [2,4: #absurd destruct(absurd) ] @Some_Some_elim #Mrefl <Mrefl -M' |
---|
521 | (* XXX: work on the left hand side *) |
---|
522 | @(pair_replace ?????????? p) normalize nodelta |
---|
523 | [1,3: |
---|
524 | >EQs @eq_f3 [2,3,5,6: % ] >(get_arg_8_set_program_counter … true addr1) |
---|
525 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
526 | >(get_arg_8_set_program_counter … true addr1) |
---|
527 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
528 | @get_arg_8_pseudo_addressing_mode_ok assumption |
---|
529 | |2,4: |
---|
530 | >p1 normalize nodelta >EQs |
---|
531 | alias id "set_program_counter_status_of_pseudo_status" = "cic:/matita/cerco/ASM/Test/set_program_counter_status_of_pseudo_status.def(26)". |
---|
532 | >set_program_counter_status_of_pseudo_status |
---|
533 | whd in ⊢ (??%%); |
---|
534 | @split_eq_status |
---|
535 | [1,10: |
---|
536 | whd in ⊢ (??%%); >set_arg_8_set_program_counter |
---|
537 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
538 | >low_internal_ram_set_program_counter |
---|
539 | [1: |
---|
540 | >low_internal_ram_set_program_counter |
---|
541 | (* XXX: ??? *) |
---|
542 | |2: |
---|
543 | >low_internal_ram_set_clock |
---|
544 | (* XXX: ??? *) |
---|
545 | ] |
---|
546 | |2,11: |
---|
547 | whd in ⊢ (??%%); >set_arg_8_set_program_counter |
---|
548 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
549 | >high_internal_ram_set_program_counter |
---|
550 | [1: |
---|
551 | >high_internal_ram_set_program_counter |
---|
552 | (* XXX: ??? *) |
---|
553 | |2: |
---|
554 | >high_internal_ram_set_clock |
---|
555 | (* XXX: ??? *) |
---|
556 | ] |
---|
557 | |3,12: |
---|
558 | whd in ⊢ (??%%); >(external_ram_set_arg_8 ??? addr1) in ⊢ (???%); |
---|
559 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
560 | >(external_ram_set_arg_8 ??? addr1) |
---|
561 | [2,4: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] % |
---|
562 | |4,13: |
---|
563 | whd in ⊢ (??%%); >EQaddr_of normalize nodelta |
---|
564 | [1: |
---|
565 | >program_counter_set_program_counter |
---|
566 | >set_arg_8_set_program_counter |
---|
567 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
568 | >set_clock_set_program_counter >program_counter_set_program_counter |
---|
569 | change with (add ??? = ?) |
---|
570 | (* XXX: ??? *) |
---|
571 | |2: |
---|
572 | >set_arg_8_set_program_counter |
---|
573 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
574 | >program_counter_set_program_counter |
---|
575 | >set_arg_8_set_program_counter |
---|
576 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
577 | >set_clock_set_program_counter >program_counter_set_program_counter |
---|
578 | >sigma_increment_commutation <EQppc |
---|
579 | whd in match (assembly_1_pseudoinstruction ??????); |
---|
580 | whd in match (expand_pseudo_instruction ??????); |
---|
581 | (* XXX: ??? *) |
---|
582 | ] |
---|
583 | |5,14: |
---|
584 | whd in match (special_function_registers_8051 ???); |
---|
585 | [1: |
---|
586 | >special_function_registers_8051_set_program_counter |
---|
587 | >special_function_registers_8051_set_clock |
---|
588 | >set_arg_8_set_program_counter in ⊢ (???%); |
---|
589 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
590 | >special_function_registers_8051_set_program_counter |
---|
591 | >set_arg_8_set_program_counter |
---|
592 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
593 | >special_function_registers_8051_set_program_counter |
---|
594 | @special_function_registers_8051_set_arg_8 assumption |
---|
595 | |2: |
---|
596 | >special_function_registers_8051_set_clock |
---|
597 | >set_arg_8_set_program_counter |
---|
598 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
599 | >set_arg_8_set_program_counter |
---|
600 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
601 | >special_function_registers_8051_set_program_counter |
---|
602 | >special_function_registers_8051_set_program_counter |
---|
603 | @special_function_registers_8051_set_arg_8 assumption |
---|
604 | ] |
---|
605 | |6,15: |
---|
606 | whd in match (special_function_registers_8052 ???); |
---|
607 | whd in match (special_function_registers_8052 ???) in ⊢ (???%); |
---|
608 | [1: |
---|
609 | >set_arg_8_set_program_counter |
---|
610 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
611 | >set_arg_8_set_program_counter |
---|
612 | [2: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
613 | >special_function_registers_8052_set_program_counter |
---|
614 | >special_function_registers_8052_set_program_counter |
---|
615 | @special_function_registers_8052_set_arg_8 assumption |
---|
616 | |2: |
---|
617 | whd in ⊢ (??%%); |
---|
618 | >special_function_registers_8052_set_arg_8 in ⊢ (??%?); assumption |
---|
619 | ] |
---|
620 | (* XXX: we need special_function_registers_8052_set_arg_8 *) |
---|
621 | |7,16: |
---|
622 | whd in match (p1_latch ???); |
---|
623 | whd in match (p1_latch ???) in ⊢ (???%); |
---|
624 | (* XXX: we need p1_latch_8052_set_arg_8 *) |
---|
625 | |8,17: |
---|
626 | whd in match (p3_latch ???); |
---|
627 | whd in match (p3_latch ???) in ⊢ (???%); |
---|
628 | (* XXX: we need p3_latch_8052_set_arg_8 *) |
---|
629 | |9: |
---|
630 | >clock_set_clock |
---|
631 | >clock_set_program_counter in ⊢ (???%); >clock_set_clock |
---|
632 | >EQticks <instr_refl @eq_f2 |
---|
633 | [1: |
---|
634 | whd in ⊢ (??%%); whd in match (ticks_of0 ??????); |
---|
635 | |2: |
---|
636 | (* XXX: we need clock_set_arg_8 *) |
---|
637 | ] |
---|
638 | |18: |
---|
639 | ] |
---|
640 | ] |
---|
641 | (* XXX: switch to the right hand side *) |
---|
642 | normalize nodelta >EQs -s >EQticks -ticks |
---|
643 | cases (¬ eq_bv ???) normalize nodelta |
---|
644 | whd in ⊢ (??%%); |
---|
645 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
646 | @split_eq_status try % |
---|
647 | [1,2,3,19,20,21,28,29,30: |
---|
648 | cases daemon (* XXX: axioms as above *) |
---|
649 | |4,13,22,31: |
---|
650 | |5,14,23,32: |
---|
651 | |6,15,24,33: |
---|
652 | |7,16,25,34: |
---|
653 | |8,17,26,35: |
---|
654 | whd in ⊢ (??%%);maps_assm |
---|
655 | |
---|
656 | |9,18,27,36: |
---|
657 | whd in ⊢ (??%%); |
---|
658 | whd in match (ticks_of_instruction ?); <instr_refl |
---|
659 | cases daemon (* XXX: daemon in ticks_of0 stopping progression *) |
---|
660 | ] |
---|
661 | |2,4: |
---|
662 | >(? : eq_v bool 9 eq_b upper (zero 9) = false) |
---|
663 | [2, 4: |
---|
664 | cases daemon (* XXX: !!! *) |
---|
665 | ] |
---|
666 | normalize nodelta >EQppc |
---|
667 | * @(pose … (add 16 ??)) #intermediate_pc #EQintermediate_pc #fetch_refl |
---|
668 | * @(pose … (add 16 ??)) #intermediate_pc' #EQintermediate_pc' #fetch_refl' |
---|
669 | * @(pose … (add 16 ??)) #intermediate_pc'' #EQintermediate_pc'' #fetch_refl'' |
---|
670 | #fetch_many_assm whd in fetch_many_assm; %{2} |
---|
671 | change with (execute_1 ?? = ?) |
---|
672 | @(pose … (execute_1 ? (status_of_pseudo_status …))) |
---|
673 | #status_after_1 #EQstatus_after_1 |
---|
674 | <(?: ? = status_after_1) |
---|
675 | [3,6: |
---|
676 | >EQstatus_after_1 in ⊢ (???%); |
---|
677 | whd in ⊢ (???%); |
---|
678 | [1: |
---|
679 | <fetch_refl in ⊢ (???%); |
---|
680 | |2: |
---|
681 | <fetch_refl in ⊢ (???%); |
---|
682 | ] |
---|
683 | whd in ⊢ (???%); |
---|
684 | @(pair_replace ?????????? p) |
---|
685 | [1,3: |
---|
686 | cases daemon |
---|
687 | |2,4: |
---|
688 | normalize nodelta |
---|
689 | whd in match (addr_of_relative ????); |
---|
690 | cases (¬ eq_bv ???) normalize nodelta |
---|
691 | >set_clock_mk_Status_commutation |
---|
692 | whd in ⊢ (???%); |
---|
693 | change with (add ???) in match (\snd (half_add ???)); |
---|
694 | >set_arg_8_set_program_counter in ⊢ (???%); |
---|
695 | [2,4,6,8: /2 by is_in_subvector_is_in_supervector, subaddressing_modein, I/ ] |
---|
696 | >program_counter_set_program_counter in ⊢ (???%); |
---|
697 | >(?: add ? intermediate_pc (sign_extension (bitvector_of_nat ? 2)) = intermediate_pc') |
---|
698 | [2,4,6,8: |
---|
699 | >bitvector_of_nat_sign_extension_equivalence |
---|
700 | [1,3,5,7: |
---|
701 | >EQintermediate_pc' % |
---|
702 | |*: |
---|
703 | repeat @le_S_S @le_O_n |
---|
704 | ] |
---|
705 | ] |
---|
706 | [1,3: % ] |
---|
707 | ] |
---|
708 | |1,4: |
---|
709 | skip |
---|
710 | ] |
---|
711 | [3,4: |
---|
712 | -status_after_1 |
---|
713 | @(pose … (execute_1 ? (mk_PreStatus …))) |
---|
714 | #status_after_1 #EQstatus_after_1 |
---|
715 | <(?: ? = status_after_1) |
---|
716 | [3,6: |
---|
717 | >EQstatus_after_1 in ⊢ (???%); |
---|
718 | whd in ⊢ (???%); |
---|
719 | (* XXX: matita bug with patterns across multiple goals *) |
---|
720 | [1: |
---|
721 | <fetch_refl'' in ⊢ (???%); |
---|
722 | |2: |
---|
723 | <fetch_refl'' in ⊢ (???%); |
---|
724 | ] |
---|
725 | [2: % |1: whd in ⊢ (???%); % ] |
---|
726 | |1,4: |
---|
727 | skip |
---|
728 | ] |
---|
729 | -status_after_1 whd in ⊢ (??%?); |
---|
730 | (* XXX: switch to the right hand side *) |
---|
731 | normalize nodelta >EQs -s >EQticks -ticks |
---|
732 | normalize nodelta whd in ⊢ (??%%); |
---|
733 | ] |
---|
734 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
735 | @split_eq_status try % |
---|
736 | whd in ⊢ (??%%); |
---|
737 | cases daemon |
---|
738 | ] |
---|
739 | |30: (* CJNE *) |
---|
740 | (* XXX: work on the right hand side *) |
---|
741 | cases addr1 -addr1 #addr1 normalize nodelta |
---|
742 | cases addr1 -addr1 #addr1_l #addr1_r normalize nodelta |
---|
743 | (* XXX: switch to the left hand side *) |
---|
744 | >EQP -P normalize nodelta |
---|
745 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
---|
746 | |
---|
747 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
748 | <EQppc in fetch_many_assm; |
---|
749 | whd in match (short_jump_cond ??); |
---|
750 | @pair_elim #sj_possible #disp |
---|
751 | @pair_elim #result #flags #sub16_refl |
---|
752 | @pair_elim #upper #lower #vsplit_refl |
---|
753 | inversion (get_index' bool ???) #get_index_refl' normalize nodelta |
---|
754 | #sj_possible_pair destruct(sj_possible_pair) normalize nodelta |
---|
755 | [1,3: |
---|
756 | >EQppc in ⊢ (% → ?); #fetch_many_assm %{1} |
---|
757 | >(sub16_with_carry_overflow … sub16_refl vsplit_refl get_index_refl') in fetch_many_assm; |
---|
758 | normalize nodelta in ⊢ (% → ?); #fetch_many_assm |
---|
759 | whd in ⊢ (??%?); |
---|
760 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
761 | inversion (¬ (eq_bv ???)) in ⊢ (???%); #eq_bv_refl normalize nodelta |
---|
762 | lapply (refl_to_jmrefl ??? eq_bv_refl) -eq_bv_refl #eq_bv_refl |
---|
763 | @(if_then_else_replace ???????? eq_bv_refl) |
---|
764 | [1,3,5,7: |
---|
765 | cases daemon |
---|
766 | |2,4,6,8: |
---|
767 | (* XXX: switch to the right hand side *) |
---|
768 | normalize nodelta >EQs -s >EQticks -ticks |
---|
769 | whd in ⊢ (??%%); |
---|
770 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
771 | @split_eq_status try % |
---|
772 | [3,7,11,15: |
---|
773 | whd in ⊢ (??%?); |
---|
774 | [1,3: |
---|
775 | cases daemon |
---|
776 | |2,4: |
---|
777 | cases daemon |
---|
778 | ] |
---|
779 | ] |
---|
780 | cases daemon (* XXX *) |
---|
781 | ] |
---|
782 | |2,4: |
---|
783 | >(? : eq_v bool 9 eq_b upper (zero 9) = false) |
---|
784 | [2, 4: |
---|
785 | cases daemon (* XXX: !!! *) |
---|
786 | ] |
---|
787 | normalize nodelta >EQppc |
---|
788 | * @(pose … (add 16 ??)) #intermediate_pc #EQintermediate_pc #fetch_refl |
---|
789 | * @(pose … (add 16 ??)) #intermediate_pc' #EQintermediate_pc' #fetch_refl' |
---|
790 | * @(pose … (add 16 ??)) #intermediate_pc'' #EQintermediate_pc'' #fetch_refl'' |
---|
791 | #fetch_many_assm whd in fetch_many_assm; %{2} |
---|
792 | change with (execute_1 ?? = ?) |
---|
793 | @(pose … (execute_1 ? (status_of_pseudo_status …))) |
---|
794 | #status_after_1 #EQstatus_after_1 |
---|
795 | <(?: ? = status_after_1) |
---|
796 | [2,5: |
---|
797 | inversion (¬ (eq_bv ???)) #eq_bv_refl normalize nodelta |
---|
798 | |3,6: |
---|
799 | >EQstatus_after_1 in ⊢ (???%); |
---|
800 | whd in ⊢ (???%); |
---|
801 | [1: <fetch_refl in ⊢ (???%); |
---|
802 | |2: <fetch_refl in ⊢ (???%); |
---|
803 | ] |
---|
804 | whd in ⊢ (???%); |
---|
805 | inversion (¬ (eq_bv ???)) in ⊢ (???%); #eq_bv_refl normalize nodelta |
---|
806 | whd in ⊢ (???%); |
---|
807 | whd in match (addr_of_relative ????); |
---|
808 | change with (add ???) in match (\snd (half_add ???)); |
---|
809 | >set_clock_set_program_counter in ⊢ (???%); |
---|
810 | >program_counter_set_program_counter in ⊢ (???%); |
---|
811 | >(?: add ? intermediate_pc (sign_extension (bitvector_of_nat ? 2)) = intermediate_pc') |
---|
812 | [2,4,6,8: |
---|
813 | >bitvector_of_nat_sign_extension_equivalence |
---|
814 | [1,3,5,7: |
---|
815 | >EQintermediate_pc' % |
---|
816 | |*: |
---|
817 | repeat @le_S_S @le_O_n |
---|
818 | ] |
---|
819 | |1,5: |
---|
820 | % |
---|
821 | ] |
---|
822 | |1,4: skip |
---|
823 | ] |
---|
824 | [1,2,3,4: |
---|
825 | -status_after_1 |
---|
826 | @(pose … (execute_1 ? (mk_PreStatus …))) |
---|
827 | #status_after_1 #EQstatus_after_1 |
---|
828 | <(?: ? = status_after_1) |
---|
829 | [3,6,9,12: |
---|
830 | >EQstatus_after_1 in ⊢ (???%); |
---|
831 | whd in ⊢ (???%); |
---|
832 | (* XXX: matita bug with patterns across multiple goals *) |
---|
833 | [1: <fetch_refl'' in ⊢ (???%); |
---|
834 | |2: <fetch_refl'' in ⊢ (???%); |
---|
835 | |3: <fetch_refl'' in ⊢ (???%); |
---|
836 | |4: <fetch_refl'' in ⊢ (???%); |
---|
837 | ] % |
---|
838 | |1,4,7,10: |
---|
839 | skip |
---|
840 | ] |
---|
841 | -status_after_1 whd in ⊢ (??%?); |
---|
842 | (* XXX: switch to the right hand side *) |
---|
843 | normalize nodelta >EQs -s >EQticks -ticks |
---|
844 | whd in ⊢ (??%%); |
---|
845 | ] |
---|
846 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
847 | @split_eq_status try % |
---|
848 | cases daemon |
---|
849 | ] |
---|
850 | |17,19,21,23,25,27,29,16,18,20,22,24,26,28: (* JC, JNC, JB, JNB, JBC, JZ, JNZ (true cases last) *) |
---|
851 | (* XXX: work on the right hand side *) |
---|
852 | >p normalize nodelta |
---|
853 | (* XXX: switch to the left hand side *) |
---|
854 | >EQP -P normalize nodelta |
---|
855 | #sigma_increment_commutation #maps_assm #fetch_many_assm |
---|
856 | |
---|
857 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
858 | <EQppc in fetch_many_assm; |
---|
859 | whd in match (short_jump_cond ??); |
---|
860 | @pair_elim #sj_possible #disp |
---|
861 | @pair_elim #result #flags #sub16_refl |
---|
862 | @pair_elim #upper #lower #vsplit_refl |
---|
863 | inversion (get_index' bool ???) #get_index_refl' normalize nodelta |
---|
864 | #sj_possible_pair destruct(sj_possible_pair) normalize nodelta |
---|
865 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
866 | >EQppc in ⊢ (% → ?); #fetch_many_assm %{1} |
---|
867 | >(sub16_with_carry_overflow … sub16_refl vsplit_refl get_index_refl') in fetch_many_assm; |
---|
868 | normalize nodelta in ⊢ (% → ?); #fetch_many_assm |
---|
869 | whd in ⊢ (??%?); |
---|
870 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
871 | (* XXX: work on the left hand side *) |
---|
872 | @(if_then_else_replace ???????? p) normalize nodelta |
---|
873 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
874 | cases daemon |
---|
875 | ] |
---|
876 | (* XXX: switch to the right hand side *) |
---|
877 | normalize nodelta >EQs -s >EQticks -ticks |
---|
878 | whd in ⊢ (??%%); |
---|
879 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
880 | @split_eq_status try % |
---|
881 | cases daemon |
---|
882 | |2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
883 | >(? : eq_v bool 9 eq_b upper (zero 9) = false) |
---|
884 | [2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
885 | cases daemon (* XXX: !!! *) |
---|
886 | ] |
---|
887 | normalize nodelta >EQppc |
---|
888 | * @(pose … (add 16 ??)) #intermediate_pc #EQintermediate_pc #fetch_refl |
---|
889 | * @(pose … (add 16 ??)) #intermediate_pc' #EQintermediate_pc' #fetch_refl' |
---|
890 | * @(pose … (add 16 ??)) #intermediate_pc'' #EQintermediate_pc'' #fetch_refl'' |
---|
891 | #fetch_many_assm whd in fetch_many_assm; %{2} |
---|
892 | change with (execute_1 ?? = ?) |
---|
893 | @(pose … (execute_1 ? (status_of_pseudo_status …))) |
---|
894 | #status_after_1 #EQstatus_after_1 |
---|
895 | <(?: ? = status_after_1) |
---|
896 | [3,6,9,12,15,18,21,24,27,30,33,36,39,42: |
---|
897 | >EQstatus_after_1 in ⊢ (???%); |
---|
898 | whd in ⊢ (???%); |
---|
899 | [1: <fetch_refl in ⊢ (???%); |
---|
900 | |2: <fetch_refl in ⊢ (???%); |
---|
901 | |3: <fetch_refl in ⊢ (???%); |
---|
902 | |4: <fetch_refl in ⊢ (???%); |
---|
903 | |5: <fetch_refl in ⊢ (???%); |
---|
904 | |6: <fetch_refl in ⊢ (???%); |
---|
905 | |7: <fetch_refl in ⊢ (???%); |
---|
906 | |8: <fetch_refl in ⊢ (???%); |
---|
907 | |9: <fetch_refl in ⊢ (???%); |
---|
908 | |10: <fetch_refl in ⊢ (???%); |
---|
909 | |11: <fetch_refl in ⊢ (???%); |
---|
910 | |12: <fetch_refl in ⊢ (???%); |
---|
911 | |13: <fetch_refl in ⊢ (???%); |
---|
912 | |14: <fetch_refl in ⊢ (???%); |
---|
913 | ] |
---|
914 | whd in ⊢ (???%); |
---|
915 | @(if_then_else_replace ???????? p) |
---|
916 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
917 | cases daemon |
---|
918 | |2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
919 | normalize nodelta |
---|
920 | whd in match (addr_of_relative ????); |
---|
921 | >set_clock_mk_Status_commutation |
---|
922 | [9,10: |
---|
923 | (* XXX: demodulation not working in this case *) |
---|
924 | >program_counter_set_arg_1 in ⊢ (???%); |
---|
925 | >program_counter_set_program_counter in ⊢ (???%); |
---|
926 | |*: |
---|
927 | /demod/ |
---|
928 | ] |
---|
929 | whd in ⊢ (???%); |
---|
930 | change with (add ???) in match (\snd (half_add ???)); |
---|
931 | >(?: add ? intermediate_pc (sign_extension (bitvector_of_nat ? 2)) = intermediate_pc') |
---|
932 | [2,4,6,8,10,12,14,16,18,20,22,24,26,28: |
---|
933 | >bitvector_of_nat_sign_extension_equivalence |
---|
934 | [1,3,5,7,9,11,13,15,17,19,21,23,25,27: |
---|
935 | >EQintermediate_pc' % |
---|
936 | |*: |
---|
937 | repeat @le_S_S @le_O_n |
---|
938 | ] |
---|
939 | ] |
---|
940 | % |
---|
941 | ] |
---|
942 | |1,4,7,10,13,16,19,22,25,28,31,34,37,40: |
---|
943 | skip |
---|
944 | ] |
---|
945 | -status_after_1 |
---|
946 | @(pose … (execute_1 ? (mk_PreStatus …))) |
---|
947 | #status_after_1 #EQstatus_after_1 |
---|
948 | <(?: ? = status_after_1) |
---|
949 | [3,6,9,12,15,18,21,24,27,30,33,36,39,42: |
---|
950 | >EQstatus_after_1 in ⊢ (???%); |
---|
951 | whd in ⊢ (???%); |
---|
952 | (* XXX: matita bug with patterns across multiple goals *) |
---|
953 | [1: <fetch_refl'' in ⊢ (???%); |
---|
954 | |2: <fetch_refl' in ⊢ (???%); |
---|
955 | |3: <fetch_refl'' in ⊢ (???%); |
---|
956 | |4: <fetch_refl' in ⊢ (???%); |
---|
957 | |5: <fetch_refl'' in ⊢ (???%); |
---|
958 | |6: <fetch_refl' in ⊢ (???%); |
---|
959 | |7: <fetch_refl'' in ⊢ (???%); |
---|
960 | |8: <fetch_refl' in ⊢ (???%); |
---|
961 | |9: <fetch_refl'' in ⊢ (???%); |
---|
962 | |10: <fetch_refl' in ⊢ (???%); |
---|
963 | |11: <fetch_refl'' in ⊢ (???%); |
---|
964 | |12: <fetch_refl' in ⊢ (???%); |
---|
965 | |13: <fetch_refl'' in ⊢ (???%); |
---|
966 | |14: <fetch_refl' in ⊢ (???%); |
---|
967 | ] |
---|
968 | whd in ⊢ (???%); |
---|
969 | [9,10: |
---|
970 | |*: |
---|
971 | /demod/ |
---|
972 | ] % |
---|
973 | |1,4,7,10,13,16,19,22,25,28,31,34,37,40: |
---|
974 | skip |
---|
975 | ] |
---|
976 | -status_after_1 whd in ⊢ (??%?); |
---|
977 | (* XXX: switch to the right hand side *) |
---|
978 | normalize nodelta >EQs -s >EQticks -ticks |
---|
979 | whd in ⊢ (??%%); |
---|
980 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
981 | @split_eq_status try % |
---|
982 | [3,11,19,27,36,53,61: |
---|
983 | >program_counter_set_program_counter >set_clock_mk_Status_commutation |
---|
984 | [5: >program_counter_set_program_counter ] |
---|
985 | >EQaddr_of normalize nodelta |
---|
986 | whd in ⊢ (??%?); >EQlookup_labels normalize nodelta |
---|
987 | >EQcm change with (address_of_word_labels_code_mem ??) in match (address_of_word_labels ??); |
---|
988 | @eq_f lapply (create_label_cost_map_ok 〈preamble, instr_list〉) |
---|
989 | >create_label_cost_refl normalize nodelta #relevant @relevant |
---|
990 | whd in is_well_labelled_witness; @(is_well_labelled_witness … ppc … (Instruction … instr)) |
---|
991 | try assumption whd in match instruction_has_label; normalize nodelta |
---|
992 | <instr_refl normalize nodelta % |
---|
993 | |7,15,23,31,45,57,65: |
---|
994 | >set_clock_mk_Status_commutation >program_counter_set_program_counter |
---|
995 | whd in ⊢ (??%?); normalize nodelta |
---|
996 | >EQppc in fetch_many_assm; #fetch_many_assm |
---|
997 | [5: |
---|
998 | >program_counter_set_arg_1 >program_counter_set_program_counter |
---|
999 | ] |
---|
1000 | <(eq_bv_eq … fetch_many_assm) >EQintermediate_pc'' |
---|
1001 | <bitvector_of_nat_sign_extension_equivalence |
---|
1002 | [1,3,5,7,9,11,13: |
---|
1003 | whd in ⊢ (???%); cases (half_add ???) normalize // |
---|
1004 | |2,4,6,8,10,12,14: |
---|
1005 | @assembly1_lt_128 |
---|
1006 | @le_S_S @le_O_n |
---|
1007 | ] |
---|
1008 | |*: |
---|
1009 | cases daemon |
---|
1010 | ] |
---|
1011 | ] |
---|
1012 | |4,5,6,7,8,36,37,38,39,40,41,50: (* INC, CLR, CPL, PUSH *) |
---|
1013 | (* XXX: work on the right hand side *) |
---|
1014 | lapply (subaddressing_modein ???) |
---|
1015 | <EQaddr normalize nodelta #irrelevant |
---|
1016 | try (>p normalize nodelta) |
---|
1017 | try (>p1 normalize nodelta) |
---|
1018 | (* XXX: switch to the left hand side *) |
---|
1019 | >EQP -P normalize nodelta |
---|
1020 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
1021 | whd in ⊢ (??%?); |
---|
1022 | whd in match (expand_pseudo_instruction ??????) in fetch_many_assm; |
---|
1023 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
1024 | (* XXX: work on the left hand side *) |
---|
1025 | [1,2,3,4,5: |
---|
1026 | generalize in ⊢ (??(???(?%))?); |
---|
1027 | |6,7,8,9,10,11: |
---|
1028 | generalize in ⊢ (??(???(?%))?); |
---|
1029 | |12: |
---|
1030 | generalize in ⊢ (??(???(?%))?); |
---|
1031 | ] |
---|
1032 | <EQaddr normalize nodelta #irrelevant |
---|
1033 | try @(jmpair_as_replace ?????????? p) |
---|
1034 | [10: normalize nodelta try @(jmpair_as_replace ?????????? p1) ] |
---|
1035 | (* XXX: switch to the right hand side *) |
---|
1036 | normalize nodelta >EQs -s >EQticks -ticks |
---|
1037 | whd in ⊢ (??%%); |
---|
1038 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
1039 | try @split_eq_status try % whd in ⊢ (??%%); |
---|
1040 | cases daemon |
---|
1041 | |1,2,3,9,46,51,53,54,55: (* ADD, ADDC, SUBB, DEC, SWAP, POP, XCHD, RET, RETI *) |
---|
1042 | (* XXX: work on the right hand side *) |
---|
1043 | >p normalize nodelta |
---|
1044 | try (>p1 normalize nodelta) |
---|
1045 | (* XXX: switch to the left hand side *) |
---|
1046 | -instr_refl >EQP -P normalize nodelta |
---|
1047 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
1048 | whd in ⊢ (??%?); |
---|
1049 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
1050 | (* XXX: work on the left hand side *) |
---|
1051 | @(pair_replace ?????????? p) |
---|
1052 | [1,3,5,7,9,11,13,15,17: |
---|
1053 | >set_clock_set_program_counter >set_clock_mk_Status_commutation |
---|
1054 | >set_program_counter_mk_Status_commutation >clock_set_program_counter |
---|
1055 | cases daemon |
---|
1056 | |14,16,18: |
---|
1057 | normalize nodelta |
---|
1058 | @(pair_replace ?????????? p1) |
---|
1059 | [1,3,5: |
---|
1060 | >set_clock_mk_Status_commutation |
---|
1061 | cases daemon |
---|
1062 | ] |
---|
1063 | ] |
---|
1064 | (* XXX: switch to the right hand side *) |
---|
1065 | normalize nodelta >EQs -s >EQticks -ticks |
---|
1066 | whd in ⊢ (??%%); |
---|
1067 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
1068 | try @split_eq_status try % |
---|
1069 | cases daemon *) |
---|
1070 | [42,43,44,45,49,52,56: |
---|
1071 | |10: (* MUL *) |
---|
1072 | (* XXX: work on the right hand side *) |
---|
1073 | (* XXX: switch to the left hand side *) |
---|
1074 | >EQP -P normalize nodelta |
---|
1075 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
1076 | whd in maps_assm:(??%%); |
---|
1077 | inversion (addressing_mode_ok ?????) in maps_assm; #addressing_mode_ok_assm_1 |
---|
1078 | [2: normalize nodelta #absurd destruct(absurd) ] |
---|
1079 | inversion (addressing_mode_ok ?????) #addressing_mode_ok_assm_2 |
---|
1080 | [2: normalize nodelta #absurd destruct(absurd) ] |
---|
1081 | normalize nodelta @Some_Some_elim #Mrefl destruct(Mrefl) |
---|
1082 | whd in ⊢ (??%?); |
---|
1083 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm >EQs >EQticks <instr_refl |
---|
1084 | change with (set_8051_sfr ????? = ?) @set_8051_sfr_status_of_pseudo_status |
---|
1085 | [2: |
---|
1086 | whd in ⊢ (??%?); @eq_f2 try % @eq_f2 try % @eq_f2 @eq_f |
---|
1087 | @sym_eq |
---|
1088 | [1: |
---|
1089 | @(get_8051_sfr_status_of_pseudo_status … policy) |
---|
1090 | cases daemon (* XXX: need a lemma *) |
---|
1091 | |2: |
---|
1092 | @(get_8051_sfr_status_of_pseudo_status M' … policy) |
---|
1093 | @sym_eq @set_clock_status_of_pseudo_status [2: % ] |
---|
1094 | @sym_eq @set_program_counter_status_of_pseudo_status % |
---|
1095 | ] |
---|
1096 | ] |
---|
1097 | @sym_eq @set_8051_sfr_status_of_pseudo_status |
---|
1098 | [2: |
---|
1099 | >(addressing_mode_ok_to_map_address_using_internal_pseudo_address_map … addressing_mode_ok_assm_1) |
---|
1100 | @eq_f @eq_f2 try % @eq_f2 @eq_f |
---|
1101 | @sym_eq |
---|
1102 | [1: |
---|
1103 | @(get_8051_sfr_status_of_pseudo_status … policy) |
---|
1104 | cases daemon (* XXX: needs a lemma *) |
---|
1105 | |2: |
---|
1106 | @(get_8051_sfr_status_of_pseudo_status M' … policy) |
---|
1107 | @sym_eq @set_clock_status_of_pseudo_status [2: % ] |
---|
1108 | @sym_eq @set_program_counter_status_of_pseudo_status % |
---|
1109 | ] |
---|
1110 | ] |
---|
1111 | @sym_eq @set_clock_status_of_pseudo_status |
---|
1112 | [2: |
---|
1113 | @eq_f % |
---|
1114 | ] |
---|
1115 | @sym_eq @set_program_counter_status_of_pseudo_status % |
---|
1116 | |
---|
1117 | (* XXX: work on the left hand side *) |
---|
1118 | (* XXX: switch to the right hand side *) |
---|
1119 | normalize nodelta >EQs -s >EQticks -ticks |
---|
1120 | whd in ⊢ (??%%); |
---|
1121 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
1122 | cases daemon |
---|
1123 | |11,12: (* DIV *) |
---|
1124 | (* XXX: work on the right hand side *) |
---|
1125 | normalize nodelta in p; |
---|
1126 | >p normalize nodelta |
---|
1127 | (* XXX: switch to the left hand side *) |
---|
1128 | -instr_refl >EQP -P normalize nodelta |
---|
1129 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
1130 | whd in ⊢ (??%?); |
---|
1131 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
1132 | @(pose … (nat_of_bitvector 8 ?)) #pose_assm #pose_refl |
---|
1133 | >(?: pose_assm = 0) normalize nodelta |
---|
1134 | [2,4: |
---|
1135 | <p >pose_refl |
---|
1136 | cases daemon |
---|
1137 | |1,3: |
---|
1138 | (* XXX: switch to the right hand side *) |
---|
1139 | >EQs -s >EQticks -ticks |
---|
1140 | whd in ⊢ (??%%); |
---|
1141 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
1142 | @split_eq_status try % |
---|
1143 | cases daemon |
---|
1144 | ] |
---|
1145 | |13,14,15: (* DA *) |
---|
1146 | (* XXX: work on the right hand side *) |
---|
1147 | >p normalize nodelta |
---|
1148 | >p1 normalize nodelta |
---|
1149 | try (>p2 normalize nodelta |
---|
1150 | try (>p3 normalize nodelta |
---|
1151 | try (>p4 normalize nodelta |
---|
1152 | try (>p5 normalize nodelta)))) |
---|
1153 | (* XXX: switch to the left hand side *) |
---|
1154 | -instr_refl >EQP -P normalize nodelta |
---|
1155 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
1156 | whd in ⊢ (??%?); |
---|
1157 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
1158 | (* XXX: work on the left hand side *) |
---|
1159 | @(pair_replace ?????????? p) |
---|
1160 | [1,3,5: |
---|
1161 | /demod/ |
---|
1162 | cases daemon |
---|
1163 | |2,4,6: |
---|
1164 | @(if_then_else_replace ???????? p1) |
---|
1165 | [1,3,5: |
---|
1166 | cases daemon |
---|
1167 | |2,4: |
---|
1168 | normalize nodelta |
---|
1169 | @(pair_replace ?????????? p2) |
---|
1170 | [1,3: |
---|
1171 | cases daemon |
---|
1172 | |2,4: |
---|
1173 | normalize nodelta >p3 normalize nodelta |
---|
1174 | >p4 normalize nodelta try >p5 |
---|
1175 | ] |
---|
1176 | ] |
---|
1177 | (* XXX: switch to the right hand side *) |
---|
1178 | normalize nodelta >EQs -s >EQticks -ticks |
---|
1179 | whd in ⊢ (??%%); |
---|
1180 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
1181 | @split_eq_status try % |
---|
1182 | cases daemon |
---|
1183 | ] |
---|
1184 | |33,34,35,48: (* ANL, ORL, XRL, MOVX *) |
---|
1185 | (* XXX: work on the right hand side *) |
---|
1186 | cases addr #addr' normalize nodelta |
---|
1187 | [1,3: |
---|
1188 | cases addr' #addr'' normalize nodelta |
---|
1189 | ] |
---|
1190 | @pair_elim #lft #rgt #lft_rgt_refl >lft_rgt_refl normalize nodelta |
---|
1191 | (* XXX: switch to the left hand side *) |
---|
1192 | -instr_refl >EQP -P normalize nodelta |
---|
1193 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
1194 | whd in ⊢ (??%?); |
---|
1195 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
1196 | (* XXX: work on the left hand side *) |
---|
1197 | (* XXX: switch to the right hand side *) |
---|
1198 | normalize nodelta >EQs -s >EQticks -ticks |
---|
1199 | whd in ⊢ (??%%); |
---|
1200 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
1201 | cases daemon |
---|
1202 | |47: (* MOV *) |
---|
1203 | (* XXX: work on the right hand side *) |
---|
1204 | cases addr -addr #addr normalize nodelta |
---|
1205 | [1: |
---|
1206 | cases addr #addr normalize nodelta |
---|
1207 | [1: |
---|
1208 | cases addr #addr normalize nodelta |
---|
1209 | [1: |
---|
1210 | cases addr #addr normalize nodelta |
---|
1211 | [1: |
---|
1212 | cases addr #addr normalize nodelta |
---|
1213 | ] |
---|
1214 | ] |
---|
1215 | ] |
---|
1216 | ] |
---|
1217 | cases addr #lft #rgt normalize nodelta |
---|
1218 | (* XXX: switch to the left hand side *) |
---|
1219 | >EQP -P normalize nodelta |
---|
1220 | #sigma_increment_commutation #maps_assm #fetch_many_assm %{1} |
---|
1221 | whd in ⊢ (??%?); |
---|
1222 | <(fetch_many_singleton … fetch_many_assm) -fetch_many_assm whd in ⊢ (??%?); |
---|
1223 | (* XXX: work on the left hand side *) |
---|
1224 | (* XXX: switch to the right hand side *) |
---|
1225 | normalize nodelta >EQs -s >EQticks -ticks |
---|
1226 | whd in ⊢ (??%%); |
---|
1227 | (* XXX: finally, prove the equality using sigma commutation *) |
---|
1228 | cases daemon |
---|
1229 | ] |
---|
1230 | qed. |
---|