1 | include "ASM/Util.ma". |
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2 | include "utilities/BitVectorTrieSet.ma". |
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3 | include "utilities/IdentifierTools.ma". |
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4 | include "LIN/LIN.ma". |
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5 | |
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6 | let rec association (i: Identifier) (l: list (Identifier × nat)) |
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7 | on l: member i (eq_bv ?) (map ? ? (fst ? ?) l) → nat ≝ |
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8 | match l return λl. member i (eq_bv ?) (map ? ? (fst ? ?) l) → nat with |
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9 | [ nil ⇒ λabsd. ? |
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10 | | cons hd tl ⇒ |
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11 | λprf: member i (eq_bv ?) (map ? ? (fst ? ?) (cons ? hd tl)). |
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12 | (match eq_bv ? (\fst hd) i return λb. eq_bv ? (\fst hd) i = b → nat with |
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13 | [ true ⇒ λeq_prf. \snd hd |
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14 | | false ⇒ λeq_prf. association i tl ? |
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15 | ]) (refl ? (eq_bv ? (\fst hd) i)) |
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16 | ]. |
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17 | [ cases absd |
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18 | | cases prf |
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19 | [ > eq_prf |
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20 | # H |
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21 | cases H |
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22 | | # H |
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23 | assumption |
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24 | ] |
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25 | ] |
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26 | qed. |
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27 | |
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28 | definition statement_labels ≝ |
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29 | λg: list Identifier. |
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30 | λs: LINStatement g. |
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31 | let 〈label, instr〉 ≝ s in |
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32 | let generated ≝ |
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33 | match instr with |
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34 | [ LIN_St_Sequential instr' _ ⇒ |
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35 | match instr' with |
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36 | [ Joint_Instr_Goto lbl ⇒ set_insert ? lbl (set_empty ?) |
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37 | | Joint_Instr_CostLabel lbl ⇒ set_insert ? lbl (set_empty ?) |
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38 | | Joint_Instr_CondAcc lbl ⇒ set_insert ? lbl (set_empty ?) |
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39 | | _ ⇒ set_empty ? |
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40 | ] |
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41 | | LIN_St_Return ⇒ set_empty ? |
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42 | ] in |
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43 | match label with |
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44 | [ None ⇒ generated |
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45 | | Some lbl ⇒ set_insert ? lbl generated |
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46 | ]. |
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47 | |
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48 | definition function_labels_internal ≝ |
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49 | λglobals: list Identifier. |
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50 | λlabels: BitVectorTrieSet ?. |
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51 | λstatement: LINStatement globals. |
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52 | set_union ? labels (statement_labels globals statement). |
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53 | |
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54 | (* dpm: A = Identifier *) |
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55 | definition function_labels: ∀A. ∀globals. ∀f. BitVectorTrieSet ? ≝ |
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56 | λA: Type[0]. |
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57 | λglobals: list Identifier. |
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58 | λf: A × (LINFunctionDefinition globals). |
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59 | let 〈ignore, fun_def〉 ≝ f in |
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60 | match fun_def return λ_. BitVectorTrieSet ? with |
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61 | [ LIN_Fu_Internal stmts ⇒ |
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62 | foldl ? ? (function_labels_internal globals) (set_empty ?) stmts |
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63 | | LIN_Fu_External _ ⇒ set_empty ? |
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64 | ]. |
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65 | |
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66 | definition program_labels_internal: ∀A. ∀globals. ∀labels. ∀funct. BitVectorTrieSet ? ≝ |
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67 | λA: Type[0]. |
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68 | λglobals: list Identifier. |
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69 | λlabels: BitVectorTrieSet ?. |
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70 | λfunct: A × (LINFunctionDefinition globals). |
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71 | set_union ? labels (function_labels ? globals funct). |
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72 | |
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73 | definition program_labels ≝ |
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74 | λprogram. |
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75 | foldl ? ? (program_labels_internal ? (map ? ? (fst ? ?) (LIN_Pr_vars program))) |
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76 | (set_empty ?) (LIN_Pr_funs program). |
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77 | |
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78 | definition data_of_int ≝ λbv. DATA bv. |
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79 | definition data16_of_int ≝ λbv. DATA16 (bitvector_of_nat 16 bv). |
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80 | definition accumulator_address ≝ DIRECT (bitvector_of_nat 8 224). |
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81 | |
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82 | axiom ImplementedInRuntime: False. |
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83 | |
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84 | definition translate_statements ≝ |
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85 | λglobals: list (Identifier × nat). |
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86 | λglobals_old: list Identifier. |
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87 | λprf: ∀i: Identifier. member i (eq_bv ?) globals_old → member i (eq_bv ?) (map ? ? (fst ? ?) globals). |
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88 | λstatement: LINStatement globals_old. |
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89 | 〈\fst statement, match \snd statement with |
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90 | [ LIN_St_Return ⇒ [ Instruction (RET ?) ] |
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91 | | LIN_St_Sequential instr _⇒ |
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92 | match instr with |
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93 | [ Joint_Instr_Goto lbl ⇒ [ Jmp lbl ] |
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94 | | Joint_Instr_Comment _ ⇒ [ ] |
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95 | | Joint_Instr_CostLabel lbl ⇒ [ Cost lbl ] |
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96 | | Joint_Instr_Pop ⇒ [ Instruction (POP ? accumulator_address) ] |
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97 | | Joint_Instr_Push ⇒ [ Instruction (PUSH ? accumulator_address) ] |
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98 | | Joint_Instr_ClearCarry ⇒ [ Instruction (CLR ? CARRY) ] |
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99 | | Joint_Instr_CallId f ⇒ [ Call f ] |
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100 | | Joint_Instr_OpAccs accs ⇒ |
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101 | match accs with |
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102 | [ Mul ⇒ [ Instruction (MUL ? ACC_A ACC_B) ] |
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103 | | Divu ⇒ [ Instruction (DIV ? ACC_A ACC_B) ] |
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104 | | Modu ⇒ ? |
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105 | ] |
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106 | | Joint_Instr_Op1 op1 ⇒ |
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107 | match op1 with |
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108 | [ Cmpl ⇒ [ Instruction (CPL ? ACC_A) ] |
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109 | | Inc ⇒ [ Instruction (INC ? ACC_A) ] |
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110 | ] |
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111 | | Joint_Instr_Op2 op2 reg ⇒ |
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112 | match op2 with |
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113 | [ Add ⇒ |
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114 | let reg' ≝ register_address reg in |
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115 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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116 | direct; |
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117 | register ]] x) → ? with |
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118 | [ ACC_A ⇒ λacc_a: True. |
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119 | [ Instruction (ADD ? ACC_A accumulator_address) ] |
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120 | | DIRECT d ⇒ λdirect1: True. |
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121 | [ Instruction (ADD ? ACC_A (DIRECT d)) ] |
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122 | | REGISTER r ⇒ λregister1: True. |
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123 | [ Instruction (ADD ? ACC_A (REGISTER r)) ] |
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124 | | _ ⇒ λother: False. ⊥ |
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125 | ] (subaddressing_modein … reg') |
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126 | | Addc ⇒ |
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127 | let reg' ≝ register_address reg in |
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128 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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129 | direct; |
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130 | register ]] x) → ? with |
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131 | [ ACC_A ⇒ λacc_a: True. |
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132 | [ Instruction (ADDC ? ACC_A accumulator_address) ] |
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133 | | DIRECT d ⇒ λdirect2: True. |
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134 | [ Instruction (ADDC ? ACC_A (DIRECT d)) ] |
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135 | | REGISTER r ⇒ λregister2: True. |
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136 | [ Instruction (ADDC ? ACC_A (REGISTER r)) ] |
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137 | | _ ⇒ λother: False. ⊥ |
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138 | ] (subaddressing_modein … reg') |
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139 | | Sub ⇒ |
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140 | let reg' ≝ register_address reg in |
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141 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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142 | direct; |
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143 | register ]] x) → ? with |
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144 | [ ACC_A ⇒ λacc_a: True. |
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145 | [ Instruction (SUBB ? ACC_A accumulator_address) ] |
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146 | | DIRECT d ⇒ λdirect3: True. |
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147 | [ Instruction (SUBB ? ACC_A (DIRECT d)) ] |
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148 | | REGISTER r ⇒ λregister3: True. |
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149 | [ Instruction (SUBB ? ACC_A (REGISTER r)) ] |
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150 | | _ ⇒ λother: False. ⊥ |
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151 | ] (subaddressing_modein … reg') |
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152 | | And ⇒ |
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153 | let reg' ≝ register_address reg in |
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154 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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155 | direct; |
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156 | register ]] x) → ? with |
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157 | [ ACC_A ⇒ λacc_a: True. |
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158 | [ Instruction (NOP ?) ] |
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159 | | DIRECT d ⇒ λdirect4: True. |
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160 | [ Instruction (ANL ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉))) ] |
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161 | | REGISTER r ⇒ λregister4: True. |
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162 | [ Instruction (ANL ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉))) ] |
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163 | | _ ⇒ λother: False. ⊥ |
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164 | ] (subaddressing_modein … reg') |
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165 | | Or ⇒ |
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166 | let reg' ≝ register_address reg in |
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167 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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168 | direct; |
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169 | register ]] x) → ? with |
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170 | [ ACC_A ⇒ λacc_a: True. |
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171 | [ Instruction (NOP ?) ] |
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172 | | DIRECT d ⇒ λdirect5: True. |
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173 | [ Instruction (ORL ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉))) ] |
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174 | | REGISTER r ⇒ λregister5: True. |
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175 | [ Instruction (ORL ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉))) ] |
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176 | | _ ⇒ λother: False. ⊥ |
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177 | ] (subaddressing_modein … reg') |
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178 | | Xor ⇒ |
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179 | let reg' ≝ register_address reg in |
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180 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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181 | direct; |
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182 | register ]] x) → ? with |
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183 | [ ACC_A ⇒ λacc_a: True. |
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184 | [ Instruction (XRL ? (inr ? ? 〈accumulator_address, ACC_A〉)) ] |
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185 | | DIRECT d ⇒ λdirect6: True. |
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186 | [ Instruction (XRL ? (inl ? ? 〈ACC_A, DIRECT d〉)) ] |
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187 | | REGISTER r ⇒ λregister6: True. |
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188 | [ Instruction (XRL ? (inl ? ? 〈ACC_A, REGISTER r〉)) ] |
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189 | | _ ⇒ λother: False. ⊥ |
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190 | ] (subaddressing_modein … reg') |
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191 | ] |
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192 | | Joint_Instr_Int reg byte ⇒ |
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193 | let reg' ≝ register_address reg in |
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194 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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195 | direct; |
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196 | register ]] x) → ? with |
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197 | [ REGISTER r ⇒ λregister7: True. |
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198 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈REGISTER r, (data_of_int byte)〉)))))) ] |
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199 | | ACC_A ⇒ λacc: True. |
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200 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, (data_of_int byte)〉)))))) ] |
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201 | | DIRECT d ⇒ λdirect7: True. |
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202 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈DIRECT d, (data_of_int byte)〉))))) ] |
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203 | | _ ⇒ λother: False. ⊥ |
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204 | ] (subaddressing_modein … reg') |
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205 | | Joint_Instr_FromAcc reg ⇒ |
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206 | let reg' ≝ register_address reg in |
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207 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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208 | direct; |
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209 | register ]] x) → ? with |
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210 | [ REGISTER r ⇒ λregister8: True. |
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211 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈REGISTER r, ACC_A〉)))))) ] |
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212 | | ACC_A ⇒ λacc: True. |
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213 | [ Instruction (NOP ?) ] |
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214 | | DIRECT d ⇒ λdirect8: True. |
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215 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈DIRECT d, ACC_A〉))))) ] |
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216 | | _ ⇒ λother: False. ⊥ |
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217 | ] (subaddressing_modein … reg') |
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218 | | Joint_Instr_ToAcc reg ⇒ |
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219 | let reg' ≝ register_address reg in |
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220 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
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221 | direct; |
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222 | register ]] x) → ? with |
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223 | [ REGISTER r ⇒ λregister9: True. |
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224 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉)))))) ] |
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225 | | DIRECT d ⇒ λdirect9: True. |
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226 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉)))))) ] |
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227 | | ACC_A ⇒ λacc_a: True. |
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228 | [ Instruction (NOP ?) ] |
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229 | | _ ⇒ λother: False. ⊥ |
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230 | ] (subaddressing_modein … reg') |
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231 | | Joint_Instr_Load ⇒ [ Instruction (MOVX ? (inl ? ? 〈ACC_A, EXT_INDIRECT_DPTR〉)) ] |
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232 | | Joint_Instr_Store ⇒ [ Instruction (MOVX ? (inr ? ? 〈EXT_INDIRECT_DPTR, ACC_A〉)) ] |
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233 | | Joint_Instr_Address addr proof ⇒ |
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234 | let look ≝ association addr globals (prf ? proof) in |
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235 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inr ? ? (〈DPTR, (data16_of_int look)〉))))) ] |
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236 | | Joint_Instr_CondAcc lbl ⇒ |
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237 | (* dpm: this should be handled in translate_code! *) |
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238 | [ WithLabel (JNZ ? lbl) ] |
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239 | ] |
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240 | ]〉. |
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241 | try assumption |
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242 | try @ I |
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243 | cases ImplementedInRuntime |
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244 | qed. |
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245 | |
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246 | definition translate_code ≝ |
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247 | λglobals: list (Identifier × nat). |
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248 | λglobals_old: list Identifier. |
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249 | λprf. |
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250 | λcode: list (LINStatement globals_old). |
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251 | flatten ? (map ? ? (translate_statements globals globals_old prf) code). |
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252 | |
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253 | definition translate_fun_def ≝ |
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254 | λglobals.λglobals_old.λprf. |
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255 | λid_def. |
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256 | let 〈id, def〉 ≝ id_def in |
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257 | match def with |
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258 | [ LIN_Fu_Internal code ⇒ (Label id) :: (translate_code globals globals_old prf code) |
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259 | | _ ⇒ [ ] |
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260 | ]. |
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261 | |
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262 | definition translate_functs ≝ |
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263 | λglobals. |
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264 | λglobals_old. |
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265 | λprf. |
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266 | λexit_label. |
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267 | λmain. |
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268 | λfuncts. |
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269 | let preamble ≝ |
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270 | match main with |
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271 | [ None ⇒ [ ] |
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272 | | Some main' ⇒ [ Call main' ; Label exit_label ; Jmp exit_label ] |
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273 | ] in |
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274 | preamble @ (flatten ? (map ? ? (translate_fun_def globals globals_old prf) functs)). |
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275 | |
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276 | definition globals_addr_internal ≝ |
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277 | λres_offset. |
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278 | λx_size: Identifier × nat. |
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279 | let 〈res, offset〉 ≝ res_offset in |
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280 | let 〈x, size〉 ≝ x_size in |
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281 | 〈〈x, offset〉 :: res, offset + size〉. |
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282 | |
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283 | definition globals_addr ≝ |
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284 | λl. |
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285 | \fst (foldl ? ? globals_addr_internal 〈[ ], 0〉 l). |
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286 | |
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287 | (* dpm: plays the role of the string "_exit" in the O'caml source *) |
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288 | axiom identifier_prefix: Identifier. |
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289 | |
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290 | (* |
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291 | definition translate ≝ |
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292 | λp. |
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293 | let prog_lbls ≝ program_labels p in |
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294 | let exit_label ≝ fresh_prefix prog_lbls identifier_prefix in |
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295 | let global_addr ≝ globals_addr (LIN_Pr_vars p) in |
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296 | 〈global_addr, translate_functs global_addr (map ? ? (fst ? ?) (LIN_Pr_vars p)) ? exit_label (LIN_Pr_main p) (LIN_Pr_funs p)〉. |
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297 | *) |
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