1 | include "ASM/Util.ma". |
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2 | include "utilities/BitVectorTrieSet.ma". |
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3 | include "LIN/LIN.ma". |
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4 | include "ASM/ASM.ma". |
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5 | |
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6 | definition register_address: Register → [[ acc_a; direct; registr ]] ≝ |
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7 | λr: Register. |
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8 | match r with |
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9 | [ Register00 ⇒ REGISTER [[ false; false; false ]] |
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10 | | Register01 ⇒ REGISTER [[ false; false; true ]] |
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11 | | Register02 ⇒ REGISTER [[ false; true; false ]] |
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12 | | Register03 ⇒ REGISTER [[ false; true; true ]] |
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13 | | Register04 ⇒ REGISTER [[ true; false; false ]] |
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14 | | Register05 ⇒ REGISTER [[ true; false; true ]] |
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15 | | Register06 ⇒ REGISTER [[ true; true; false ]] |
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16 | | Register07 ⇒ REGISTER [[ true; true; true ]] |
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17 | | RegisterA ⇒ ACC_A |
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18 | | RegisterB ⇒ DIRECT (bitvector_of_nat 8 240) |
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19 | | RegisterDPL ⇒ DIRECT (bitvector_of_nat 8 82) |
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20 | | RegisterDPH ⇒ DIRECT (bitvector_of_nat 8 83) |
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21 | | _ ⇒ DIRECT (bitvector_of_nat 8 (nat_of_register r)) |
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22 | ]. @I qed. |
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23 | |
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24 | (* TODO: |
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25 | this should translate back end immediates (which rely on beval) to ASM |
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26 | byte immediates. How should it work? surely needs arguments for instantiation |
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27 | of blocks. If it's too much a fuss, we can go back to byte immediates in the |
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28 | back end. *) |
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29 | definition asm_byte_of_beval : beval → Byte ≝ |
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30 | λb.match b with |
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31 | [ BVByte b ⇒ b |
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32 | | BVundef ⇒ (* any will do *) zero_byte |
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33 | | BVnonzero ⇒ (* any will do *) maximum 7 @@ [[ true ]] |
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34 | | BVnull _ ⇒ zero_byte (* is it correct? *) |
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35 | | BVptr b p o ⇒ ? |
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36 | ]. |
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37 | cases daemon qed. |
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38 | |
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39 | definition arg_address : hdw_argument → [[ acc_a ; direct ; registr ; data ]] ≝ |
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40 | λa.match a with |
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41 | [ Reg r ⇒ register_address r |
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42 | | Imm bv ⇒ DATA (asm_byte_of_beval bv) |
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43 | ]. |
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44 | cases a #x [2: normalize //] normalize nodelta |
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45 | elim (register_address ?) #rslt @is_in_subvector_is_in_supervector @I |
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46 | qed. |
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47 | |
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48 | let rec association (i: ident) (l: list (ident × nat)) |
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49 | on l: member i (eq_identifier ?) (map ? ? (fst ? ?) l) → nat ≝ |
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50 | match l return λl. member i (eq_identifier ?) (map ? ? (fst ? ?) l) → nat with |
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51 | [ nil ⇒ λabsd. ? |
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52 | | cons hd tl ⇒ |
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53 | λprf: member i (eq_identifier ?) (map ? ? (fst ? ?) (cons ? hd tl)). |
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54 | (match eq_identifier ? (\fst hd) i return λb. eq_identifier ? (\fst hd) i = b → nat with |
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55 | [ true ⇒ λeq_prf. \snd hd |
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56 | | false ⇒ λeq_prf. association i tl ? |
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57 | ]) (refl ? (eq_identifier ? (\fst hd) i)) |
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58 | ]. |
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59 | [ cases absd |
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60 | | cases prf |
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61 | [ > eq_prf |
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62 | # H |
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63 | cases H |
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64 | | # H |
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65 | assumption |
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66 | ] |
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67 | ] |
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68 | qed. |
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69 | |
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70 | definition lin_statement ≝ λg.labelled_obj LabelTag (joint_statement LIN g). |
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71 | |
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72 | definition statement_labels ≝ |
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73 | λg: list ident. |
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74 | λs: lin_statement g. |
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75 | let 〈label, instr〉 ≝ s in |
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76 | let generated ≝ |
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77 | match instr with |
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78 | [ sequential instr' _ ⇒ |
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79 | match instr' with |
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80 | [ step_seq instr'' ⇒ |
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81 | match instr'' with |
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82 | [ COST_LABEL lbl ⇒ { (toASM_ident ? lbl) } |
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83 | | _ ⇒ ∅ |
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84 | ] |
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85 | | COND acc_a_reg lbl ⇒ { (toASM_ident ? lbl) } |
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86 | ] |
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87 | | final instr' ⇒ |
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88 | match instr' with |
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89 | [ GOTO lbl ⇒ {(toASM_ident ? lbl)} |
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90 | | _ ⇒ ∅ |
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91 | ] |
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92 | ] |
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93 | in |
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94 | match label with |
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95 | [ None ⇒ generated |
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96 | | Some lbl ⇒ add_set ? generated (toASM_ident ? lbl) |
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97 | ]. |
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98 | |
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99 | definition function_labels_internal ≝ |
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100 | λglobals: list ident. |
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101 | λlabels: identifier_set ?. |
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102 | λstatement: lin_statement globals. |
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103 | labels ∪ (statement_labels globals statement). |
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104 | |
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105 | (* dpm: A = Identifier *) |
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106 | definition function_labels: ∀A. ∀globals. ∀f. identifier_set ? ≝ |
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107 | λA: Type[0]. |
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108 | λglobals: list ident. |
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109 | λf: A × (joint_function LIN globals). |
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110 | let 〈ignore, fun_def〉 ≝ f in |
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111 | match fun_def return λ_. identifier_set ? with |
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112 | [ Internal stmts ⇒ |
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113 | foldl ? ? (function_labels_internal globals) ∅ (joint_if_code ?? stmts) |
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114 | | External _ ⇒ ∅ |
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115 | ]. |
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116 | |
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117 | definition program_labels_internal: ∀A. ∀globals. ∀labels. ∀funct. identifier_set ? ≝ |
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118 | λA: Type[0]. |
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119 | λglobals: list ident. |
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120 | λlabels: identifier_set ?. |
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121 | λfunct: A × (joint_function LIN globals). |
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122 | labels ∪ (function_labels ? globals funct). |
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123 | |
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124 | (* CSC: here we are silently throwing away the region information *) |
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125 | definition program_labels ≝ |
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126 | λprogram: lin_program. |
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127 | foldl … (program_labels_internal … (map … (λx. fst … (fst … x)) (prog_vars … program))) |
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128 | ∅ (prog_funct … program). |
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129 | |
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130 | definition data_of_int ≝ λbv. DATA bv. |
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131 | definition data16_of_int ≝ λbv. DATA16 (bitvector_of_nat 16 bv). |
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132 | definition accumulator_address ≝ DIRECT (bitvector_of_nat 8 224). |
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133 | |
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134 | (* TODO: check and change to free bit *) |
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135 | definition asm_other_bit ≝ BIT_ADDR (zero_byte). |
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136 | |
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137 | definition translate_statements ≝ |
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138 | λglobals: list (ident × nat). |
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139 | λglobals_old: list ident. |
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140 | λprf: ∀i: ident. member i (eq_identifier ?) globals_old → member i (eq_identifier ?) (map ? ? (fst ? ?) globals). |
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141 | λstatement: joint_statement LIN globals_old. |
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142 | match statement with |
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143 | [ final instr ⇒ |
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144 | match instr with |
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145 | [ GOTO lbl ⇒ Jmp (toASM_ident ? lbl) |
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146 | | RETURN ⇒ Instruction (RET ?) |
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147 | | tailcall abs ⇒ match abs in void with [ ] |
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148 | ] |
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149 | | sequential instr _ ⇒ |
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150 | match instr with |
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151 | [ step_seq instr' ⇒ |
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152 | match instr' with |
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153 | [ extension_seq ext ⇒ |
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154 | match ext with |
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155 | [ SAVE_CARRY ⇒ |
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156 | Instruction (MOV ? (inr ?? 〈asm_other_bit, CARRY〉)) |
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157 | | RESTORE_CARRY ⇒ |
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158 | Instruction (MOV ? (inl ?? (inr ?? 〈CARRY, asm_other_bit〉))) |
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159 | ] |
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160 | | COMMENT comment ⇒ Comment comment |
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161 | | COST_LABEL lbl ⇒ Cost lbl |
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162 | | POP _ ⇒ Instruction (POP ? accumulator_address) |
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163 | | PUSH _ ⇒ Instruction (PUSH ? accumulator_address) |
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164 | | CLEAR_CARRY ⇒ Instruction (CLR ? CARRY) |
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165 | | CALL_ID f _ _ ⇒ Call (toASM_ident ? f) |
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166 | | extension_call abs ⇒ match abs in void with [ ] |
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167 | | OPACCS accs _ _ _ _ ⇒ |
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168 | match accs with |
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169 | [ Mul ⇒ Instruction (MUL ? ACC_A ACC_B) |
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170 | | DivuModu ⇒ Instruction (DIV ? ACC_A ACC_B) |
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171 | ] |
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172 | | OP1 op1 _ _ ⇒ |
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173 | match op1 with |
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174 | [ Cmpl ⇒ Instruction (CPL ? ACC_A) |
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175 | | Inc ⇒ Instruction (INC ? ACC_A) |
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176 | | Rl ⇒ Instruction (RL ? ACC_A) |
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177 | ] |
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178 | | OP2 op2 _ _ reg ⇒ |
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179 | match op2 with |
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180 | [ Add ⇒ |
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181 | let reg' ≝ arg_address reg in |
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182 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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183 | direct; |
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184 | registr; |
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185 | data ]] x) → ? with |
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186 | [ ACC_A ⇒ λacc_a: True. |
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187 | Instruction (ADD ? ACC_A accumulator_address) |
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188 | | DIRECT d ⇒ λdirect1: True. |
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189 | Instruction (ADD ? ACC_A (DIRECT d)) |
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190 | | REGISTER r ⇒ λregister1: True. |
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191 | Instruction (ADD ? ACC_A (REGISTER r)) |
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192 | | DATA b ⇒ λdata : True. |
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193 | Instruction (ADD ? ACC_A (DATA b)) |
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194 | | _ ⇒ Ⓧ |
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195 | ] (subaddressing_modein … reg') |
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196 | | Addc ⇒ |
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197 | let reg' ≝ arg_address reg in |
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198 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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199 | direct; |
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200 | registr; |
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201 | data ]] x) → ? with |
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202 | [ ACC_A ⇒ λacc_a: True. |
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203 | Instruction (ADDC ? ACC_A accumulator_address) |
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204 | | DIRECT d ⇒ λdirect2: True. |
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205 | Instruction (ADDC ? ACC_A (DIRECT d)) |
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206 | | REGISTER r ⇒ λregister2: True. |
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207 | Instruction (ADDC ? ACC_A (REGISTER r)) |
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208 | | DATA b ⇒ λdata : True. |
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209 | Instruction (ADDC ? ACC_A (DATA b)) |
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210 | | _ ⇒ Ⓧ |
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211 | ] (subaddressing_modein … reg') |
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212 | | Sub ⇒ |
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213 | let reg' ≝ arg_address reg in |
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214 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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215 | direct; |
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216 | registr; |
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217 | data ]] x) → ? with |
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218 | [ ACC_A ⇒ λacc_a: True. |
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219 | Instruction (SUBB ? ACC_A accumulator_address) |
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220 | | DIRECT d ⇒ λdirect3: True. |
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221 | Instruction (SUBB ? ACC_A (DIRECT d)) |
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222 | | REGISTER r ⇒ λregister3: True. |
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223 | Instruction (SUBB ? ACC_A (REGISTER r)) |
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224 | | DATA b ⇒ λdata : True. |
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225 | Instruction (SUBB ? ACC_A (DATA b)) |
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226 | | _ ⇒ Ⓧ |
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227 | ] (subaddressing_modein … reg') |
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228 | | And ⇒ |
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229 | let reg' ≝ arg_address reg in |
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230 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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231 | direct; |
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232 | registr; |
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233 | data ]] x) → ? with |
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234 | [ ACC_A ⇒ λacc_a: True. |
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235 | Instruction (NOP ?) |
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236 | | DIRECT d ⇒ λdirect4: True. |
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237 | Instruction (ANL ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉))) |
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238 | | REGISTER r ⇒ λregister4: True. |
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239 | Instruction (ANL ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉))) |
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240 | | DATA b ⇒ λdata : True. |
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241 | Instruction (ANL ? (inl ? ? (inl ? ? 〈ACC_A, DATA b〉))) |
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242 | | _ ⇒ Ⓧ |
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243 | ] (subaddressing_modein … reg') |
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244 | | Or ⇒ |
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245 | let reg' ≝ arg_address reg in |
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246 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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247 | direct; |
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248 | registr ; data ]] x) → ? with |
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249 | [ ACC_A ⇒ λacc_a: True. |
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250 | Instruction (NOP ?) |
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251 | | DIRECT d ⇒ λdirect5: True. |
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252 | Instruction (ORL ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉))) |
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253 | | REGISTER r ⇒ λregister5: True. |
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254 | Instruction (ORL ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉))) |
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255 | | DATA b ⇒ λdata : True. |
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256 | Instruction (ORL ? (inl ? ? (inl ? ? 〈ACC_A, DATA b〉))) |
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257 | | _ ⇒ Ⓧ |
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258 | ] (subaddressing_modein … reg') |
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259 | | Xor ⇒ |
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260 | let reg' ≝ arg_address reg in |
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261 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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262 | direct; |
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263 | registr ; data ]] x) → ? with |
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264 | [ ACC_A ⇒ λacc_a: True. |
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265 | Instruction (XRL ? (inr ? ? 〈accumulator_address, ACC_A〉)) |
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266 | | DIRECT d ⇒ λdirect6: True. |
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267 | Instruction (XRL ? (inl ? ? 〈ACC_A, DIRECT d〉)) |
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268 | | REGISTER r ⇒ λregister6: True. |
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269 | Instruction (XRL ? (inl ? ? 〈ACC_A, REGISTER r〉)) |
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270 | | DATA b ⇒ λdata : True. |
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271 | Instruction (XRL ? (inl ? ? 〈ACC_A, DATA b〉)) |
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272 | | _ ⇒ Ⓧ |
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273 | ] (subaddressing_modein … reg') |
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274 | ] |
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275 | | LOAD _ _ _ ⇒ Instruction (MOVX ? (inl ? ? 〈ACC_A, EXT_INDIRECT_DPTR〉)) |
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276 | | STORE _ _ _ ⇒ Instruction (MOVX ? (inr ? ? 〈EXT_INDIRECT_DPTR, ACC_A〉)) |
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277 | | ADDRESS addr proof _ _ ⇒ |
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278 | let look ≝ association addr globals (prf ? proof) in |
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279 | Instruction (MOV ? (inl ? ? (inl ? ? (inr ? ? (〈DPTR, (data16_of_int look)〉))))) |
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280 | | SET_CARRY ⇒ |
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281 | Instruction (SETB ? CARRY) |
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282 | | MOVE regs ⇒ |
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283 | match regs with |
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284 | [ to_acc _ reg ⇒ |
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285 | let reg' ≝ register_address reg in |
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286 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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287 | direct; |
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288 | registr ]] x) → ? with |
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289 | [ REGISTER r ⇒ λregister9: True. |
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290 | Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉)))))) |
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291 | | DIRECT d ⇒ λdirect9: True. |
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292 | Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉)))))) |
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293 | | ACC_A ⇒ λacc_a: True. |
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294 | Instruction (NOP ?) |
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295 | | _ ⇒ λother: False. ⊥ |
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296 | ] (subaddressing_modein … reg') |
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297 | | from_acc reg _ ⇒ |
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298 | let reg' ≝ register_address reg in |
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299 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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300 | direct; |
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301 | registr ]] x) → ? with |
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302 | [ REGISTER r ⇒ λregister8: True. |
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303 | Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈REGISTER r, ACC_A〉)))))) |
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304 | | ACC_A ⇒ λacc: True. |
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305 | Instruction (NOP ?) |
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306 | | DIRECT d ⇒ λdirect8: True. |
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307 | Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈DIRECT d, ACC_A〉))))) |
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308 | | _ ⇒ λother: False. ⊥ |
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309 | ] (subaddressing_modein … reg') |
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310 | | int_to_reg reg bv ⇒ |
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311 | let b ≝ asm_byte_of_beval bv in |
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312 | let reg' ≝ register_address reg in |
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313 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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314 | direct; |
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315 | registr ]] x) → ? with |
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316 | [ REGISTER r ⇒ λregister7: True. |
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317 | Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈REGISTER r, DATA b〉)))))) |
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318 | | ACC_A ⇒ λacc: True. |
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319 | Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, DATA b〉)))))) |
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320 | | DIRECT d ⇒ λdirect7: True. |
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321 | Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈DIRECT d, DATA b〉))))) |
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322 | | _ ⇒ λother: False. ⊥ |
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323 | ] (subaddressing_modein … reg') |
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324 | | int_to_acc _ bv ⇒ |
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325 | let b ≝ asm_byte_of_beval bv in |
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326 | Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, DATA b〉)))))) |
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327 | ] |
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328 | ] |
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329 | | COND _ lbl ⇒ |
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330 | (* dpm: this should be handled in translate_code! *) |
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331 | Instruction (JNZ ? (toASM_ident ? lbl)) |
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332 | ] |
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333 | ]. |
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334 | try assumption |
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335 | try @ I |
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336 | qed. |
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337 | |
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338 | (*CSC: XXXXXXXXXXX looks bad: what invariant is needed here? *) |
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339 | definition ident_of_label: label → Identifier ≝ |
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340 | toASM_ident LabelTag. |
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341 | |
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342 | definition build_translated_statement ≝ |
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343 | λglobals. |
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344 | λglobals_old. |
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345 | λprf. |
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346 | λstatement: lin_statement globals_old. |
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347 | 〈option_map … ident_of_label (\fst statement), translate_statements globals globals_old prf (\snd statement)〉. |
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348 | |
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349 | definition translate_code ≝ |
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350 | λglobals: list (ident × nat). |
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351 | λglobals_old: list ident. |
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352 | λprf. |
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353 | λcode: list (lin_statement globals_old). |
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354 | map ? ? (build_translated_statement globals globals_old prf) code. |
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355 | |
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356 | definition translate_fun_def ≝ |
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357 | λglobals: list (ident × nat). |
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358 | λglobals_old. |
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359 | λprf. |
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360 | λid_def. |
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361 | let 〈id, def〉 ≝ id_def in |
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362 | match def with |
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363 | [ Internal int ⇒ |
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364 | let code ≝ joint_if_code LIN globals_old int in |
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365 | match translate_code globals globals_old prf code with |
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366 | [ nil ⇒ ⊥ |
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367 | | cons hd tl ⇒ |
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368 | let rest ≝ 〈Some ? (toASM_ident SymbolTag id), \snd hd〉 :: tl in |
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369 | map ? ? ( |
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370 | λr. |
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371 | match fst ? ? r with |
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372 | [ Some id' ⇒ 〈Some ? (toASM_ident ? id'), snd ? ? r〉 |
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373 | | None ⇒ 〈None ?, \snd r〉 |
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374 | ]) rest |
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375 | ] |
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376 | | External _ ⇒ [ ] |
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377 | ]. |
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378 | cases daemon (*CSC: XXX will be fixed by an invariant later *) |
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379 | qed. |
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380 | |
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381 | include "common/Identifiers.ma". |
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382 | |
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383 | let rec flatten_fun_defs |
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384 | (globals: list (ident × nat)) (globals_old: list ident) (prf: ?) (initial_pc: nat) |
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385 | (the_list: list ((identifier SymbolTag) × (fundef (joint_internal_function LIN globals_old)))) |
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386 | on the_list: ((list (option Identifier × pseudo_instruction)) × (identifier_map ? nat)) ≝ |
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387 | match the_list return λx. ((list (option Identifier × pseudo_instruction)) × (identifier_map ? nat)) with |
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388 | [ cons hd tl ⇒ |
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389 | let fun_def ≝ \snd hd in |
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390 | let fun_id ≝ \fst hd in |
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391 | let translated ≝ translate_fun_def globals globals_old prf hd in |
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392 | let size_translated ≝ | translated | in |
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393 | let 〈tail_trans, tail_map〉 ≝ flatten_fun_defs globals globals_old prf (initial_pc + size_translated) tl in |
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394 | let new_hd ≝ translated @ tail_trans in |
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395 | let new_map ≝ add ? ? tail_map fun_id initial_pc in |
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396 | 〈new_hd, new_map〉 |
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397 | | nil ⇒ 〈[ ], empty_map …〉 |
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398 | ]. |
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399 | |
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400 | definition translate_functs ≝ |
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401 | λglobals. |
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402 | λglobals_old. |
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403 | λprf. |
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404 | λexit_label. |
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405 | λmain. |
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406 | λfuncts. |
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407 | let preamble ≝ [ 〈None ?, Call main〉 ; 〈Some ? exit_label, Jmp exit_label〉 ] in |
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408 | let 〈flattened, map〉 ≝ flatten_fun_defs globals globals_old prf 6 (* Size of preamble above *) functs in |
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409 | 〈preamble @ flattened, map〉. |
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410 | |
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411 | (*CSC: region silently thrown away here *) |
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412 | definition globals_addr ≝ |
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413 | λl. |
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414 | let globals_addr_internal ≝ |
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415 | λres_offset. |
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416 | λx_size: ident × region × nat. |
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417 | let 〈res, offset〉 ≝ res_offset in |
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418 | let 〈x, region, size〉 ≝ x_size in |
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419 | 〈〈x, offset〉 :: res, offset + size〉 |
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420 | in |
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421 | \fst (foldl ? ? globals_addr_internal 〈[ ], 0〉 l). |
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422 | |
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423 | (* dpm: plays the role of the string "_exit" in the O'caml source *) |
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424 | axiom identifier_prefix: Identifier. |
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425 | (*CSC: XXXXXXX wrong anyway since labels from different functions can now |
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426 | clash with each other and with names of functions *) |
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427 | axiom fresh_prefix: identifier_set ASMTag → Identifier → Identifier. |
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428 | |
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429 | (* dpm: fresh prefix stuff needs unifying with brian *) |
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430 | definition lin_to_asm : lin_program → pseudo_assembly_program ≝ |
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431 | λp. |
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432 | let prog_lbls ≝ program_labels … p in |
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433 | let exit_label ≝ fresh_prefix prog_lbls identifier_prefix in |
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434 | let global_addr ≝ globals_addr (prog_vars … p) in |
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435 | let global_addr' ≝ map … (λx_off. let 〈x,off〉 ≝ x_off in 〈toASM_ident ? x, bitvector_of_nat 16 off〉) global_addr in |
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436 | let 〈translated, funct_map〉 ≝ translate_functs global_addr (prog_var_names … p) ? exit_label (toASM_ident … (prog_main … p)) (prog_funct … p) in |
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437 | 〈〈funct_map, global_addr'〉, translated〉. |
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438 | #i normalize nodelta -global_addr' -global_addr -exit_label -prog_lbls; |
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439 | normalize in match prog_var_names; normalize nodelta |
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440 | elim (prog_vars … p) // |
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441 | #hd #tl #IH whd in ⊢ (% → %); |
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442 | whd in match globals_addr; normalize nodelta |
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443 | whd in match (foldl ???? (hd::tl)); normalize nodelta |
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444 | cases hd * #id #reg #size normalize nodelta |
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445 | cases daemon (*CSC: provable using a pair of lemmas over foldl *) |
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446 | qed. |
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