1 | include "RTLabs/syntax.ma". |
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2 | include "RTL/RTL.ma". |
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3 | include "common/AssocList.ma". |
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4 | include "common/FrontEndOps.ma". |
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5 | include "common/Graphs.ma". |
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6 | include "joint/TranslateUtils.ma". |
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7 | include alias "ASM/BitVector.ma". |
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8 | include alias "arithmetics/nat.ma". |
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9 | |
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10 | let rec register_freshes (runiverse: universe RegisterTag) (n: nat) on n ≝ |
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11 | match n with |
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12 | [ O ⇒ 〈[],runiverse〉 |
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13 | | S n' ⇒ |
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14 | let 〈r,runiverse〉 ≝ fresh … runiverse in |
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15 | let 〈res,runiverse〉 ≝ register_freshes runiverse n' in |
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16 | 〈r::res,runiverse〉 ]. |
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17 | |
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18 | definition complete_regs ≝ |
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19 | λglobals. |
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20 | λdef. |
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21 | λsrcrs1. |
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22 | λsrcrs2. |
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23 | if leb (length … srcrs2) (length … srcrs1) then |
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24 | let 〈def, added_regs〉 ≝ fresh_regs rtl_params0 globals def (minus (length ? srcrs1) (length ? srcrs2)) in |
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25 | 〈〈srcrs1, srcrs2 @ added_regs〉, added_regs〉 |
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26 | else |
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27 | let 〈def, added_regs〉 ≝ fresh_regs rtl_params0 globals def (minus (length ? srcrs2) (length ? srcrs1)) in |
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28 | 〈〈srcrs1 @ added_regs, srcrs2〉, added_regs〉. |
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29 | |
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30 | lemma complete_regs_length: |
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31 | ∀globals,def,left,right. |
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32 | |\fst (\fst (complete_regs globals def left right))| = |\snd (\fst (complete_regs globals def left right))|. |
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33 | #globals #def #left #right |
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34 | whd in match complete_regs; normalize nodelta |
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35 | @leb_elim normalize nodelta #H |
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36 | [ generalize in match (fresh_regs_length rtl_params0 globals def (minus (length … left) (length … right))); |
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37 | | generalize in match (fresh_regs_length rtl_params0 globals def (minus (length … right) (length … left)));] |
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38 | cases (fresh_regs ????) #def' #fresh normalize >append_length |
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39 | generalize in match H; -H; |
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40 | generalize in match (length … left); generalize in match (length … right); generalize in match (length … fresh); |
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41 | [ /2/ | #x #y #z #H generalize in match (not_le_to_lt … H); -H #H #E >E >commutative_plus |
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42 | <plus_minus_m_m /2/ ] |
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43 | qed. |
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44 | |
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45 | definition size_of_sig_type ≝ |
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46 | λsig. |
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47 | match sig with |
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48 | [ ASTint isize sign ⇒ |
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49 | let isize' ≝ match isize with [ I8 ⇒ 8 | I16 ⇒ 16 | I32 ⇒ 32 ] in |
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50 | isize' ÷ (nat_of_bitvector ? int_size) |
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51 | | ASTfloat _ ⇒ ? (* dpm: not implemented *) |
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52 | | ASTptr rgn ⇒ nat_of_bitvector ? ptr_size |
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53 | ]. |
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54 | cases not_implemented; |
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55 | qed. |
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56 | |
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57 | inductive register_type: Type[0] ≝ |
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58 | | register_int: register → register_type |
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59 | | register_ptr: register → register → register_type. |
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60 | |
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61 | definition local_env ≝ identifier_map RegisterTag (list register). |
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62 | |
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63 | definition mem_local_env : register → local_env → bool ≝ |
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64 | λr,e. member … e r. |
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65 | |
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66 | definition add_local_env : register → list register → local_env → local_env ≝ |
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67 | λr,v,e. add … e r v. |
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68 | |
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69 | definition find_local_env : register → local_env → list register ≝ |
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70 | λr: register.λenv. lookup_def … env r []. |
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71 | |
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72 | definition initialize_local_env_internal ≝ |
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73 | λlenv_runiverse. |
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74 | λr_sig. |
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75 | let 〈lenv,runiverse〉 ≝ lenv_runiverse in |
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76 | let 〈r, sig〉 ≝ r_sig in |
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77 | let size ≝ size_of_sig_type sig in |
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78 | let 〈rs,runiverse〉 ≝ register_freshes runiverse size in |
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79 | 〈add_local_env r rs lenv,runiverse〉. |
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80 | |
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81 | definition initialize_local_env ≝ |
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82 | λruniverse. |
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83 | λregisters. |
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84 | λresult. |
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85 | let registers ≝ registers @ |
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86 | match result with |
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87 | [ None ⇒ [ ] |
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88 | | Some rt ⇒ [ rt ] |
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89 | ] |
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90 | in |
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91 | foldl … initialize_local_env_internal 〈empty_map …,runiverse〉 registers. |
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92 | |
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93 | definition map_list_local_env_internal ≝ |
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94 | λlenv,res,r. res @ (find_local_env r lenv). |
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95 | |
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96 | definition map_list_local_env ≝ |
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97 | λlenv,regs. foldl … (map_list_local_env_internal lenv) [ ] regs. |
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98 | |
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99 | definition make_addr ≝ |
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100 | λA. |
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101 | λlst: list A. |
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102 | λprf: 2 = length A lst. |
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103 | match lst return λx. 2 = |x| → A × A with |
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104 | [ nil ⇒ λlst_nil_prf. ? |
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105 | | cons hd tl ⇒ λprf. |
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106 | match tl return λx. 1 = |x| → A × A with |
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107 | [ nil ⇒ λtl_nil_prf. ? |
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108 | | cons hd' tl' ⇒ λtl_cons_prf. 〈hd, hd'〉 |
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109 | ] ? |
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110 | ] prf. |
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111 | [1: normalize in lst_nil_prf; |
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112 | destruct(lst_nil_prf) |
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113 | |2: normalize in prf; |
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114 | @injective_S |
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115 | assumption |
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116 | |3: normalize in tl_nil_prf; |
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117 | destruct(tl_nil_prf) |
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118 | ] |
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119 | qed. |
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120 | |
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121 | definition find_and_addr ≝ |
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122 | λr,lenv. make_addr ? (find_local_env r lenv). |
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123 | |
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124 | definition rtl_args ≝ |
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125 | λregs_list,lenv. flatten … (map … (λr. find_local_env r lenv) regs_list). |
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126 | |
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127 | definition translate_cst_int_internal ≝ |
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128 | λglobals,dest_lbl,r,i. sequential rtl_params_ globals (INT … r i) dest_lbl. |
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129 | |
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130 | definition split_into_bytes: |
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131 | ∀size. ∀int: bvint size. Σbytes: list Byte. |bytes| = size_intsize size ≝ |
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132 | λsize. |
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133 | match size return λsize.∀int: bvint size. Σbytes. |bytes| = size_intsize size with |
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134 | [ I8 ⇒ λint. ? | I16 ⇒ λint. ? | I32 ⇒ λint. ? ]. |
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135 | [ %[@[int]] // |
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136 | | %[@(let 〈h,l〉 ≝ vsplit ? 8 … int in [l;h])] cases (vsplit ????) // |
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137 | | %[@(let 〈h1,l〉 ≝ vsplit ? 8 … int in |
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138 | let 〈h2,l〉 ≝ vsplit ? 8 … l in |
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139 | let 〈h3,l〉 ≝ vsplit ? 8 … l in |
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140 | [l;h3;h2;h1])] |
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141 | cases (vsplit ????) #h1 #l normalize |
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142 | cases (vsplit ????) #h2 #l normalize |
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143 | cases (vsplit ????) // ] |
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144 | qed. |
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145 | |
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146 | lemma eqb_implies_eq: |
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147 | ∀m, n: nat. |
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148 | eqb m n = true → m = n. |
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149 | #M |
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150 | elim M |
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151 | [1: #N normalize |
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152 | cases N |
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153 | [1: normalize // |
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154 | |2: #M' normalize #HYP destruct(HYP) |
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155 | ] |
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156 | |2: #M' #IND_HYP #N |
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157 | normalize |
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158 | cases N |
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159 | [1: normalize #HYP destruct(HYP) |
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160 | |2: #M'' normalize #HYP |
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161 | @eq_f @(IND_HYP M'') |
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162 | assumption |
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163 | ] |
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164 | ] |
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165 | qed. |
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166 | |
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167 | definition translate_op: ∀globals. ? → list register → list register → list register → |
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168 | label → label → rtl_internal_function globals → rtl_internal_function globals ≝ |
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169 | λglobals: list ident. |
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170 | λop. |
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171 | λdestrs: list register. |
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172 | λsrcrs1: list register. |
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173 | λsrcrs2: list register. |
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174 | λstart_lbl: label. |
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175 | λdest_lbl: label. |
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176 | λdef: rtl_internal_function globals. |
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177 | match reduce_strong register register srcrs1 srcrs2 with |
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178 | [ mk_Sig reduced first_reduced_proof ⇒ |
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179 | let srcrsl_common ≝ \fst (\fst reduced) in |
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180 | let srcrsr_common ≝ \fst (\snd reduced) in |
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181 | let srcrsl_rest ≝ \snd (\fst reduced) in |
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182 | let srcrsr_rest ≝ \snd (\snd reduced) in |
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183 | let srcrs_rest ≝ srcrsl_rest @ srcrsr_rest in |
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184 | match reduce_strong register register destrs srcrsl_common with |
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185 | [ mk_Sig reduced second_reduced_proof ⇒ |
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186 | let destrs_common ≝ \fst (\fst reduced) in |
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187 | let destrs_rest ≝ \snd (\fst reduced) in |
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188 | match reduce_strong register register destrs_rest srcrs_rest with |
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189 | [ mk_Sig reduced third_reduced_proof ⇒ |
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190 | let destrs_cted ≝ \fst (\fst reduced) in |
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191 | let destrs_rest ≝ \snd (\fst reduced) in |
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192 | let srcrs_cted ≝ \fst (\snd reduced) in |
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193 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
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194 | let insts_init ≝ [ |
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195 | sequential … (CLEAR_CARRY …); |
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196 | sequential … (INT rtl_params_ globals tmpr (zero …)) |
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197 | ] in |
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198 | let f_add ≝ λdestr. λsrcr1. λsrcr2. sequential … (OP2 rtl_params_ globals op destr srcr1 srcr2) in |
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199 | let insts_add ≝ map3 ? ? ? ? f_add destrs_common srcrsl_common srcrsr_common ? ? in |
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200 | let f_add_cted ≝ λdestr. λsrcr. sequential … (OP2 rtl_params_ globals op destr srcr tmpr) in |
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201 | let insts_add_cted ≝ map2 … f_add_cted destrs_cted srcrs_cted ? in |
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202 | let f_rest ≝ λdestr. sequential … (OP2 rtl_params_ globals op destr tmpr tmpr) in |
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203 | let insts_rest ≝ map … f_rest destrs_rest in |
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204 | adds_graph rtl_params1 globals (insts_init @ insts_add @ insts_add_cted @ insts_rest) start_lbl dest_lbl def |
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205 | ] |
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206 | ] |
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207 | ]. |
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208 | [1: @third_reduced_proof |
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209 | |3: @first_reduced_proof |
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210 | |*: cases daemon (* XXX: some of these look like they may be false *) |
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211 | ] |
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212 | qed. |
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213 | |
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214 | (* Type safety in RTLabs has broken this for the moment... |
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215 | let rec translate_cst |
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216 | (globals: list ident) (cst: constant) (destrs: list register) |
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217 | (start_lbl: label) (dest_lbl: label) (def: rtl_internal_function globals) |
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218 | on cst: rtl_internal_function globals ≝ |
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219 | match cst with |
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220 | [ Ointconst size const ⇒ |
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221 | match destrs with |
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222 | [ nil ⇒ add_graph … start_lbl (GOTO … dest_lbl) def |
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223 | | _ ⇒ |
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224 | let size' ≝ size_intsize size in |
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225 | match eqb size' (|destrs|) return λx. (eqb size' (|destrs|)) = x → rtl_internal_function globals with |
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226 | [ true ⇒ λgood_case. |
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227 | match split_into_bytes size const with |
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228 | [ mk_Sig bytes bytes_length_proof ⇒ |
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229 | let mapped ≝ map2 … (λd. λb. (sequential … (INT rtl_params_ globals d b))) destrs bytes ? in |
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230 | adds_graph rtl_params1 globals mapped start_lbl dest_lbl def |
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231 | ] |
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232 | | false ⇒ λbad_case. ? |
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233 | ] (refl … (eqb size' (|destrs|))) |
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234 | ] |
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235 | | Ofloatconst float ⇒ ⊥ |
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236 | | Oaddrsymbol id offset ⇒ |
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237 | let 〈r1, r2〉 ≝ make_addr … destrs ? in |
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238 | let def ≝ add_graph rtl_params1 globals start_lbl (sequential … (ADDRESS rtl_params_ globals id ? r1 r2) dest_lbl) def in |
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239 | let def ≝ translate_op globals Addc [r1] [r1] [r2] start_lbl dest_lbl def in |
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240 | def |
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241 | | Oaddrstack offset ⇒ |
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242 | let 〈r1, r2〉 ≝ make_addr … destrs ? in |
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243 | let def ≝ add_graph rtl_params1 globals start_lbl (sequential … (extension rtl_params_ globals (rtl_st_ext_stack_address r1 r2)) dest_lbl) def in |
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244 | let def ≝ translate_op globals Addc [r1] [r1] [r2] start_lbl dest_lbl def in |
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245 | def |
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246 | ]. |
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247 | [1: >bytes_length_proof |
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248 | cut(size' = |destrs|) |
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249 | [1: @eqb_implies_eq |
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250 | assumption |
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251 | |2: #EQ_HYP |
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252 | <EQ_HYP % |
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253 | ] |
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254 | |2: cases daemon (* XXX: bad case where destrs is of the wrong length *) |
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255 | |3: cases not_implemented (* XXX: float, error_float in o'caml *) |
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256 | |*: cases daemon (* XXX: various proofs to be filled in *) |
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257 | ]. |
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258 | qed. |
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259 | |
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260 | definition translate_move_internal ≝ |
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261 | λglobals. |
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262 | λdestr: register. |
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263 | λsrcr: register. |
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264 | sequential rtl_params_ globals (MOVE … 〈destr,srcr〉). |
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265 | |
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266 | definition translate_move ≝ |
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267 | λglobals. |
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268 | λdestrs: list register. |
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269 | λsrcrs: list register. |
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270 | λstart_lbl: label. |
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271 | match reduce_strong register register destrs srcrs with |
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272 | [ mk_Sig crl_crr len_proof ⇒ |
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273 | let commonl ≝ \fst (\fst crl_crr) in |
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274 | let commonr ≝ \fst (\snd crl_crr) in |
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275 | let restl ≝ \snd (\fst crl_crr) in |
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276 | let restr ≝ \snd (\snd crl_crr) in |
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277 | let f_common ≝ translate_move_internal globals in |
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278 | let translate1 ≝ adds_graph rtl_params1 … (map2 … f_common commonl commonr ?) in |
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279 | let translate2 ≝ translate_cst … (Ointconst ? (repr I8 0)) restl in (* should this be 8? *) |
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280 | add_translates … [ translate1 ; translate2 ] start_lbl |
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281 | ]. |
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282 | @len_proof |
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283 | qed. |
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284 | |
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285 | let rec make |
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286 | (A: Type[0]) (elt: A) (n: nat) on n ≝ |
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287 | match n with |
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288 | [ O ⇒ [ ] |
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289 | | S n' ⇒ elt :: make A elt n' |
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290 | ]. |
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291 | |
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292 | lemma make_length: |
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293 | ∀A: Type[0]. |
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294 | ∀elt: A. |
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295 | ∀n: nat. |
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296 | n = length ? (make A elt n). |
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297 | #A #ELT #N |
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298 | elim N |
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299 | [ normalize % |
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300 | | #N #IH |
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301 | normalize <IH % |
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302 | ] |
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303 | qed. |
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304 | |
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305 | definition translate_cast_unsigned ≝ |
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306 | λglobals. |
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307 | λdestrs. |
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308 | λstart_lbl. |
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309 | λdest_lbl. |
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310 | λdef: joint_internal_function … (rtl_params globals). |
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311 | let 〈def, tmp_zero〉 ≝ fresh_reg … def in |
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312 | let zeros ≝ make … tmp_zero (length … destrs) in |
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313 | add_translates … [ |
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314 | adds_graph rtl_params1 … [ |
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315 | sequential rtl_params_ … (INT rtl_params_ ? tmp_zero (bitvector_of_nat ? 0)) |
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316 | ]; |
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317 | translate_move globals destrs zeros |
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318 | ] start_lbl dest_lbl def. |
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319 | |
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320 | definition translate_cast_signed: |
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321 | ∀globals: list ident. list register → ? → label → label → rtl_internal_function globals → rtl_internal_function globals ≝ |
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322 | λglobals: list ident. |
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323 | λdestrs. |
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324 | λsrcr. |
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325 | λstart_lbl. |
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326 | λdest_lbl. |
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327 | λdef. |
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328 | let 〈def, tmp_128〉 ≝ fresh_reg … def in |
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329 | let 〈def, tmp_255〉 ≝ fresh_reg … def in |
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330 | let 〈def, tmpr〉 ≝ fresh_reg … def in |
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331 | let 〈def, dummy〉 ≝ fresh_reg … def in |
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332 | let insts ≝ [ |
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333 | sequential … (INT rtl_params_ globals tmp_128 (bitvector_of_nat ? 128)); |
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334 | sequential … (OP2 rtl_params_ globals And tmpr tmp_128 srcr); |
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335 | sequential … (OPACCS rtl_params_ globals DivuModu tmpr dummy tmpr tmp_128); |
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336 | sequential … (INT rtl_params_ globals tmp_255 (bitvector_of_nat ? 255)); |
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337 | sequential … (OPACCS rtl_params_ globals Mul tmpr dummy tmpr tmp_255) |
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338 | ] |
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339 | in |
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340 | let srcrs ≝ make … tmpr (length … destrs) in |
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341 | add_translates rtl_params1 globals [ |
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342 | adds_graph rtl_params1 globals insts; |
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343 | translate_move globals destrs srcrs |
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344 | ] start_lbl dest_lbl def. |
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345 | |
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346 | definition translate_cast ≝ |
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347 | λglobals: list ident. |
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348 | λsrc_size: nat. |
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349 | λsrc_sign: signedness. |
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350 | λdest_size: nat. |
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351 | λdestrs: list register. |
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352 | λsrcrs: list register. |
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353 | match |srcrs| return λx. |srcrs| = x → ? with |
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354 | [ O ⇒ λzero_prf. adds_graph rtl_params1 globals [ ] |
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355 | | S n' ⇒ λsucc_prf. |
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356 | if ltb dest_size src_size then |
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357 | translate_move globals destrs srcrs |
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358 | else |
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359 | match reduce_strong register register destrs srcrs with |
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360 | [ mk_Sig crl len_proof ⇒ |
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361 | let commonl ≝ \fst (\fst crl) in |
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362 | let commonr ≝ \fst (\snd crl) in |
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363 | let restl ≝ \snd (\fst crl) in |
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364 | let restr ≝ \snd (\snd crl) in |
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365 | let insts_common ≝ translate_move globals commonl commonr in |
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366 | let sign_reg ≝ last_safe ? srcrs ? in |
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367 | let insts_sign ≝ |
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368 | match src_sign with |
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369 | [ Unsigned ⇒ translate_cast_unsigned globals restl |
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370 | | Signed ⇒ translate_cast_signed globals restl sign_reg |
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371 | ] |
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372 | in |
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373 | add_translates rtl_params1 globals [ insts_common; insts_sign ] |
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374 | ] |
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375 | ] (refl ? (|srcrs|)). |
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376 | >succ_prf // |
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377 | qed. |
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378 | |
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379 | definition translate_negint ≝ |
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380 | λglobals: list ident. |
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381 | λdestrs: list register. |
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382 | λsrcrs: list register. |
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383 | λstart_lbl: label. |
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384 | λdest_lbl: label. |
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385 | λdef: rtl_internal_function globals. |
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386 | λprf: |destrs| = |srcrs|. (* assert in caml code *) |
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387 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
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388 | let f_cmpl ≝ λdestr. λsrcr. sequential rtl_params_ globals (OP1 rtl_params1 globals Cmpl destr srcr) in |
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389 | let insts_cmpl ≝ map2 … f_cmpl destrs srcrs prf in |
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390 | let insts_init ≝ [ |
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391 | sequential … (SET_CARRY …); |
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392 | sequential … (INT rtl_params_ globals tmpr (zero ?)) |
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393 | ] in |
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394 | let f_add ≝ λdestr. sequential … (OP2 rtl_params_ globals Addc destr destr tmpr) in |
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395 | let insts_add ≝ map … f_add destrs in |
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396 | adds_graph rtl_params1 globals (insts_cmpl @ insts_init @ insts_add) start_lbl dest_lbl def. |
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397 | |
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398 | definition translate_notbool: ∀globals. list register → list register → label → label → rtl_internal_function globals → rtl_internal_function globals ≝ |
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399 | λglobals: list ident. |
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400 | λdestrs: list register. |
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401 | λsrcrs: list register. |
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402 | λstart_lbl: label. |
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403 | λdest_lbl: label. |
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404 | λdef: rtl_internal_function globals. |
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405 | match destrs with |
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406 | [ nil ⇒ add_graph rtl_params1 globals start_lbl (GOTO … start_lbl) def |
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407 | | cons destr destrs ⇒ |
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408 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
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409 | let 〈def, tmp_srcrs〉 ≝ fresh_regs rtl_params0 globals def (length ? srcrs) in |
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410 | let save_srcrs ≝ translate_move globals tmp_srcrs srcrs in |
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411 | let init_destr ≝ sequential … (INT rtl_params_ globals destr (bitvector_of_nat ? 1)) in |
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412 | let f ≝ λtmp_srcr. [ |
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413 | sequential … (CLEAR_CARRY rtl_params_ globals); |
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414 | sequential … (INT rtl_params_ globals tmpr (zero ?)); |
---|
415 | sequential … (OP2 rtl_params_ globals Sub tmpr tmpr tmp_srcr); |
---|
416 | sequential … (INT rtl_params_ globals tmpr (zero ?)); |
---|
417 | sequential … (OP2 rtl_params_ globals Addc tmpr tmpr tmpr); |
---|
418 | sequential … (OP2 rtl_params_ globals Xor destr destr tmpr) |
---|
419 | ] in |
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420 | let insts ≝ init_destr :: (flatten … (map … f tmp_srcrs)) in |
---|
421 | let epilogue ≝ translate_cst globals (Ointconst I8 (zero …)) destrs in |
---|
422 | add_translates rtl_params1 globals [ |
---|
423 | save_srcrs; adds_graph rtl_params1 globals insts; epilogue |
---|
424 | ] start_lbl dest_lbl def |
---|
425 | ]. |
---|
426 | |
---|
427 | (* TODO: examine this properly. This is a change from the O'caml code due |
---|
428 | to us dropping the explicit use of a cast destination size field. We |
---|
429 | instead infer the size of the cast's destination from the context. Is |
---|
430 | this correct? |
---|
431 | *) |
---|
432 | definition translate_op1 ≝ |
---|
433 | λglobals: list ident. |
---|
434 | λty, ty'. |
---|
435 | λop1: unary_operation ty ty'. |
---|
436 | λdestrs: list register. |
---|
437 | λsrcrs: list register. |
---|
438 | λprf: |destrs| = |srcrs|. |
---|
439 | λstart_lbl: label. |
---|
440 | λdest_lbl: label. |
---|
441 | λdef: rtl_internal_function globals. |
---|
442 | match op1 with |
---|
443 | [ Ocastint src_size src_sign _ _ ⇒ |
---|
444 | let dest_size ≝ |destrs| * 8 in |
---|
445 | let src_size ≝ bitsize_of_intsize src_size in |
---|
446 | translate_cast globals src_size src_sign dest_size destrs srcrs start_lbl dest_lbl def |
---|
447 | | Onegint _ _ ⇒ |
---|
448 | translate_negint globals destrs srcrs start_lbl dest_lbl def prf |
---|
449 | | Onotbool _ _ _ _ ⇒ |
---|
450 | translate_notbool globals destrs srcrs start_lbl dest_lbl def |
---|
451 | | Onotint _ _ ⇒ |
---|
452 | let f ≝ λdestr. λsrcr. sequential rtl_params_ globals (OP1 … Cmpl destr srcr) in |
---|
453 | let l ≝ map2 … f destrs srcrs prf in |
---|
454 | adds_graph rtl_params1 globals l start_lbl dest_lbl def |
---|
455 | | Optrofint _ _ r ⇒ |
---|
456 | translate_move globals destrs srcrs start_lbl dest_lbl def |
---|
457 | | Ointofptr _ _ r ⇒ |
---|
458 | translate_move globals destrs srcrs start_lbl dest_lbl def |
---|
459 | | Oid _ ⇒ |
---|
460 | translate_move globals destrs srcrs start_lbl dest_lbl def |
---|
461 | | _ ⇒ ? (* float operations implemented in runtime *) |
---|
462 | ]. |
---|
463 | cases not_implemented |
---|
464 | qed. |
---|
465 | |
---|
466 | let rec translate_mul1 |
---|
467 | (globals: list ident) (dummy: register) (tmpr: register) |
---|
468 | (destrs: list register) (srcrs1: list register) (srcr2: register) |
---|
469 | (start_lbl: label) |
---|
470 | on srcrs1 ≝ |
---|
471 | match destrs with |
---|
472 | [ nil ⇒ adds_graph rtl_params1 globals [ GOTO … ] start_lbl |
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473 | | cons destr tl ⇒ |
---|
474 | match tl with |
---|
475 | [ nil ⇒ |
---|
476 | match srcrs1 with |
---|
477 | [ nil ⇒ |
---|
478 | adds_graph rtl_params1 globals [ |
---|
479 | sequential … (INT rtl_params_ globals tmpr (zero …)); |
---|
480 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr) |
---|
481 | ] start_lbl |
---|
482 | | cons srcr1 tl' ⇒ |
---|
483 | adds_graph rtl_params1 globals [ |
---|
484 | sequential … (OPACCS rtl_params_ globals Mul tmpr dummy srcr2 srcr1); |
---|
485 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr) |
---|
486 | ] start_lbl |
---|
487 | ] |
---|
488 | | cons destr2 destrs ⇒ |
---|
489 | match srcrs1 with |
---|
490 | [ nil ⇒ |
---|
491 | add_translates rtl_params1 globals [ |
---|
492 | adds_graph rtl_params1 globals [ |
---|
493 | sequential … (INT rtl_params_ globals tmpr (zero …)); |
---|
494 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr); |
---|
495 | sequential … (OP2 rtl_params_ globals Addc destr2 tmpr tmpr) |
---|
496 | ]; |
---|
497 | translate_cst globals (Ointconst I8 (zero …)) destrs |
---|
498 | ] start_lbl |
---|
499 | | cons srcr1 srcrs1 ⇒ |
---|
500 | match destrs with |
---|
501 | [ nil ⇒ |
---|
502 | add_translates rtl_params1 globals [ |
---|
503 | adds_graph rtl_params1 globals [ |
---|
504 | sequential … (INT rtl_params_ globals tmpr (zero …)); |
---|
505 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr); |
---|
506 | sequential … (OP2 rtl_params_ globals Addc destr2 tmpr tmpr) |
---|
507 | ]; |
---|
508 | translate_cst globals (Ointconst I8 (zero ?)) destrs |
---|
509 | ] start_lbl |
---|
510 | | cons destr2 destrs ⇒ |
---|
511 | add_translates rtl_params1 globals [ |
---|
512 | adds_graph rtl_params1 globals [ |
---|
513 | sequential … (OPACCS rtl_params_ globals Mul tmpr destr2 srcr2 srcr1); |
---|
514 | sequential … (OP2 rtl_params_ globals Addc destr destr tmpr) |
---|
515 | ]; |
---|
516 | translate_mul1 globals dummy tmpr (destr2 :: destrs) srcrs1 srcr2 |
---|
517 | ] start_lbl |
---|
518 | ] |
---|
519 | ] |
---|
520 | ] |
---|
521 | ]. |
---|
522 | |
---|
523 | definition translate_muli ≝ |
---|
524 | λglobals: list ident. |
---|
525 | λdummy: register. |
---|
526 | λtmpr: register. |
---|
527 | λdestrs: list register. |
---|
528 | λtmp_destrs: list register. |
---|
529 | λsrcrs1: list register. |
---|
530 | λdummy_lbl: label. |
---|
531 | λi: nat. |
---|
532 | λi_prf: i ≤ |tmp_destrs|. |
---|
533 | λtranslates: list ?. |
---|
534 | λsrcr2i: register. |
---|
535 | let 〈tmp_destrs1, tmp_destrs2〉 ≝ vsplit … tmp_destrs i i_prf in |
---|
536 | let tmp_destrs2' ≝ |
---|
537 | match tmp_destrs2 with |
---|
538 | [ nil ⇒ [ ] |
---|
539 | | cons tmp_destr2 tmp_destrs2 ⇒ [ |
---|
540 | adds_graph rtl_params1 globals [ |
---|
541 | sequential rtl_params_ globals (CLEAR_CARRY …); |
---|
542 | sequential … (INT rtl_params_ globals tmp_destr2 (zero …)) |
---|
543 | ]; |
---|
544 | translate_mul1 globals dummy tmpr tmp_destrs2 srcrs1 srcr2i; |
---|
545 | translate_cst globals (Ointconst I8 (zero …)) tmp_destrs1; |
---|
546 | adds_graph rtl_params1 globals [ |
---|
547 | sequential rtl_params_ globals (CLEAR_CARRY …) |
---|
548 | ]; |
---|
549 | translate_op globals Addc destrs destrs tmp_destrs |
---|
550 | ] |
---|
551 | ] |
---|
552 | in |
---|
553 | translates @ tmp_destrs2'. |
---|
554 | |
---|
555 | let rec remove_n_first_internal |
---|
556 | (b: Type[0]) (n: nat) (the_list: list b) (i: nat) |
---|
557 | on the_list ≝ |
---|
558 | match the_list with |
---|
559 | [ nil ⇒ [ ] |
---|
560 | | cons hd tl ⇒ |
---|
561 | match eqb i n with |
---|
562 | [ true ⇒ the_list |
---|
563 | | false ⇒ remove_n_first_internal b n tl (S i) |
---|
564 | ] |
---|
565 | ]. |
---|
566 | |
---|
567 | definition remove_n_first ≝ |
---|
568 | λb: Type[0]. |
---|
569 | λn: nat. |
---|
570 | λthe_list: list b. |
---|
571 | remove_n_first_internal b n the_list 0. |
---|
572 | |
---|
573 | axiom plus_m_n_eq_o_to_lt_m_o: |
---|
574 | ∀m, n, o: nat. |
---|
575 | m + n = o → m ≤ o. |
---|
576 | |
---|
577 | include alias "arithmetics/nat.ma". |
---|
578 | |
---|
579 | axiom minus_m_n_Sp_to_minus_m_Sn_p: |
---|
580 | ∀m, n, p: nat. |
---|
581 | minus m n = S p → minus m (S n) = p. |
---|
582 | |
---|
583 | let rec foldi_strong_internal |
---|
584 | (a: Type[0]) (b: Type[0]) (reference: nat) (the_list: list b) |
---|
585 | (f: ∀j: nat. ∀proof: lt j (|the_list|). a → b → a) (seed: a) |
---|
586 | (counter: nat) (counter_proof: minus reference counter = |the_list|) |
---|
587 | on the_list: a ≝ |
---|
588 | match the_list return λx. the_list = x → (minus reference counter = |x|) → a with |
---|
589 | [ nil ⇒ λidentity. λbase_case. seed |
---|
590 | | cons hd tl ⇒ λidentity. λstep_case. |
---|
591 | let f' ≝ λj: nat. λproof: j < |tl|. f j ? in |
---|
592 | foldi_strong_internal a b reference tl f' (f counter ? seed hd) (S counter) ? |
---|
593 | ] (refl … the_list) counter_proof. |
---|
594 | [1: cases daemon (* XXX: to do *) |
---|
595 | |2: generalize in match counter_proof; |
---|
596 | >identity |
---|
597 | #HYP |
---|
598 | normalize in HYP:(???%); |
---|
599 | generalize in match (minus_m_n_Sp_to_minus_m_Sn_p reference counter (|tl|) HYP); |
---|
600 | #ASSM assumption |
---|
601 | |3: >identity |
---|
602 | normalize |
---|
603 | normalize in proof; |
---|
604 | generalize in match(le_S … proof); |
---|
605 | #HYP assumption |
---|
606 | ] |
---|
607 | qed. |
---|
608 | |
---|
609 | definition foldi_strong ≝ |
---|
610 | λa: Type[0]. |
---|
611 | λb: Type[0]. |
---|
612 | λthe_list: list b. |
---|
613 | λf: (∀i: nat. ∀proof: i < |the_list|. a → b → a). |
---|
614 | λseed: a. |
---|
615 | foldi_strong_internal a b (|the_list|) the_list f seed 0 ?. |
---|
616 | // |
---|
617 | qed. |
---|
618 | |
---|
619 | definition translate_mul ≝ |
---|
620 | λglobals: list ident. |
---|
621 | λdestrs: list register. |
---|
622 | λsrcrs1: list register. |
---|
623 | λsrcrs2: list register. |
---|
624 | λregs_proof: |destrs| = |srcrs2|. |
---|
625 | λstart_lbl: label. |
---|
626 | λdest_lbl: label. |
---|
627 | λdef: rtl_internal_function globals. |
---|
628 | let 〈def, dummy〉 ≝ fresh_reg rtl_params0 globals def in |
---|
629 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
---|
630 | match fresh_regs_strong rtl_params0 globals def (|destrs|) with |
---|
631 | [ mk_Sig def_tmp_destrs tmp_destrs_prf ⇒ |
---|
632 | let def ≝ \fst def_tmp_destrs in |
---|
633 | let tmp_destrs ≝ \snd def_tmp_destrs in |
---|
634 | let 〈def, fresh_srcrs1〉 ≝ fresh_regs rtl_params0 globals def (|srcrs1|) in |
---|
635 | let 〈def, fresh_srcrs2〉 ≝ fresh_regs rtl_params0 globals def (|srcrs2|) in |
---|
636 | let insts_init ≝ [ |
---|
637 | translate_move globals fresh_srcrs1 srcrs1; |
---|
638 | translate_move globals fresh_srcrs2 srcrs2; |
---|
639 | translate_cst globals (Ointconst I8 (zero …)) destrs |
---|
640 | ] |
---|
641 | in |
---|
642 | let f ≝ translate_muli globals dummy tmpr destrs tmp_destrs fresh_srcrs1 start_lbl in |
---|
643 | let f' ≝ λi. λi_proof: i < |srcrs2|. f i ? in |
---|
644 | let insts_mul ≝ foldi_strong … srcrs2 f' [ ] in |
---|
645 | add_translates rtl_params1 globals (insts_init @ insts_mul) start_lbl dest_lbl def |
---|
646 | ]. |
---|
647 | >tmp_destrs_prf |
---|
648 | >regs_proof |
---|
649 | /2/ |
---|
650 | qed. |
---|
651 | |
---|
652 | definition translate_divumodu8 ≝ |
---|
653 | λglobals: list ident. |
---|
654 | λorder: bool. |
---|
655 | λdestrs: list register. |
---|
656 | λsrcr1: register. |
---|
657 | λsrcr2: register. |
---|
658 | λstart_lbl: label. |
---|
659 | λdest_lbl: label. |
---|
660 | λdef: rtl_internal_function globals. |
---|
661 | match destrs with |
---|
662 | [ nil ⇒ add_graph rtl_params1 globals start_lbl (GOTO … dest_lbl) def |
---|
663 | | cons destr destrs ⇒ |
---|
664 | let 〈def, dummy〉 ≝ fresh_reg rtl_params0 globals def in |
---|
665 | let 〈destr1, destr2〉 ≝ match order with [ true ⇒ 〈destr, dummy〉 | _ ⇒ 〈dummy, destr〉 ] in |
---|
666 | let inst_div ≝ adds_graph rtl_params1 globals [ |
---|
667 | sequential rtl_params_ globals (OPACCS … DivuModu destr1 destr2 srcr1 srcr2) |
---|
668 | ] |
---|
669 | in |
---|
670 | let insts_rest ≝ translate_cst globals (Ointconst I8 (zero ?)) destrs in |
---|
671 | add_translates rtl_params1 globals [ inst_div; insts_rest ] start_lbl dest_lbl def |
---|
672 | ]. |
---|
673 | |
---|
674 | definition translate_ne: ∀globals: list ident. ? → ? → ? → ? → ? → ? → rtl_internal_function globals ≝ |
---|
675 | λglobals: list ident. |
---|
676 | λdestrs: list register. |
---|
677 | λsrcrs1: list register. |
---|
678 | λsrcrs2: list register. |
---|
679 | λstart_lbl: label. |
---|
680 | λdest_lbl: label. |
---|
681 | λdef: rtl_internal_function globals. |
---|
682 | match destrs with |
---|
683 | [ nil ⇒ add_graph rtl_params1 globals start_lbl (GOTO … dest_lbl) def |
---|
684 | | cons destr destrs ⇒ |
---|
685 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
---|
686 | let 〈def, tmp_zero〉 ≝ fresh_reg rtl_params0 globals def in |
---|
687 | let 〈def, tmp_srcrs1〉 ≝ fresh_regs rtl_params0 globals def (|srcrs1|) in |
---|
688 | let save_srcrs1 ≝ translate_move globals tmp_srcrs1 srcrs1 in |
---|
689 | let 〈def, tmp_srcrs2〉 ≝ fresh_regs rtl_params0 globals def (|srcrs2|) in |
---|
690 | let save_srcrs2 ≝ translate_move globals tmp_srcrs2 srcrs2 in |
---|
691 | match reduce_strong register register tmp_srcrs1 tmp_srcrs2 with |
---|
692 | [ mk_Sig crl their_proof ⇒ |
---|
693 | let commonl ≝ \fst (\fst crl) in |
---|
694 | let commonr ≝ \fst (\snd crl) in |
---|
695 | let restl ≝ \snd (\snd crl) in |
---|
696 | let restr ≝ \snd (\snd crl) in |
---|
697 | let rest ≝ restl @ restr in |
---|
698 | let inits ≝ [ |
---|
699 | sequential … (INT rtl_params_ globals destr (zero …)); |
---|
700 | sequential … (INT rtl_params_ globals tmp_zero (zero …)) |
---|
701 | ] |
---|
702 | in |
---|
703 | let f_common ≝ λtmp_srcr1. λtmp_srcr2. [ |
---|
704 | sequential … (CLEAR_CARRY …); |
---|
705 | sequential … (OP2 rtl_params_ globals Sub tmpr tmp_srcr1 tmp_srcr2); |
---|
706 | sequential … (OP2 rtl_params_ globals Or destr destr tmpr) |
---|
707 | ] |
---|
708 | in |
---|
709 | let insts_common ≝ flatten … (map2 … f_common commonl commonr ?) in |
---|
710 | let f_rest ≝ λtmp_srcr. [ |
---|
711 | sequential … (CLEAR_CARRY …); |
---|
712 | sequential … (OP2 rtl_params_ globals Sub tmpr tmp_zero tmp_srcr); |
---|
713 | sequential … (OP2 rtl_params_ globals Or destr destr tmpr) |
---|
714 | ] |
---|
715 | in |
---|
716 | let insts_rest ≝ flatten … (map … f_rest rest) in |
---|
717 | let insts ≝ inits @ insts_common @ insts_rest in |
---|
718 | let epilogue ≝ translate_cst globals (Ointconst I8 (zero …)) destrs in |
---|
719 | add_translates rtl_params1 globals [ |
---|
720 | save_srcrs1; save_srcrs2; adds_graph rtl_params1 globals insts; epilogue |
---|
721 | ] start_lbl dest_lbl def |
---|
722 | ] |
---|
723 | ]. |
---|
724 | @their_proof |
---|
725 | qed. |
---|
726 | |
---|
727 | definition translate_eq_reg ≝ |
---|
728 | λglobals: list ident. |
---|
729 | λtmp_zero: register. |
---|
730 | λtmp_one: register. |
---|
731 | λtmpr1: register. |
---|
732 | λtmpr2: register. |
---|
733 | λdestr: register. |
---|
734 | λdummy_lbl: label. |
---|
735 | λsrcr12: register × register. |
---|
736 | let 〈srcr1, srcr2〉 ≝ srcr12 in |
---|
737 | [ sequential … (CLEAR_CARRY …); |
---|
738 | sequential rtl_params_ globals (OP2 rtl_params_ globals Sub tmpr1 srcr1 srcr2); |
---|
739 | sequential … (OP2 rtl_params_ globals Addc tmpr1 tmp_zero tmp_zero); |
---|
740 | sequential … (OP2 rtl_params_ globals Sub tmpr2 srcr2 srcr1); |
---|
741 | sequential … (OP2 rtl_params_ globals Addc tmpr2 tmp_zero tmp_zero); |
---|
742 | sequential … (OP2 rtl_params_ globals Or tmpr1 tmpr1 tmpr2); |
---|
743 | sequential … (OP2 rtl_params_ globals Xor tmpr1 tmpr1 tmp_one); |
---|
744 | sequential … (OP2 rtl_params_ globals And destr destr tmpr1) ]. |
---|
745 | |
---|
746 | definition translate_eq_list ≝ |
---|
747 | λglobals: list ident. |
---|
748 | λtmp_zero: register. |
---|
749 | λtmp_one: register. |
---|
750 | λtmpr1: register. |
---|
751 | λtmpr2: register. |
---|
752 | λdestr: register. |
---|
753 | λleq: list (register × register). |
---|
754 | λdummy_lbl: label. |
---|
755 | let f ≝ translate_eq_reg globals tmp_zero tmp_one tmpr1 tmpr2 destr dummy_lbl in |
---|
756 | (sequential … (INT rtl_params_ globals destr (bitvector_of_nat ? 1))) :: |
---|
757 | flatten … (map … f leq). |
---|
758 | |
---|
759 | definition translate_atom ≝ |
---|
760 | λglobals: list ident. |
---|
761 | λtmp_zero: register. |
---|
762 | λtmp_one: register. |
---|
763 | λtmpr1: register. |
---|
764 | λtmpr2: register. |
---|
765 | λtmpr3: register. |
---|
766 | λdestr: register. |
---|
767 | λdummy_lbl: label. |
---|
768 | λleq: list (register × register). |
---|
769 | λsrcr1: register. |
---|
770 | λsrcr2: register. |
---|
771 | translate_eq_list globals tmp_zero tmp_one tmpr1 tmpr2 tmpr3 leq dummy_lbl @ |
---|
772 | [ sequential … (CLEAR_CARRY …); |
---|
773 | sequential … (OP2 rtl_params_ globals Sub tmpr1 srcr1 srcr2); |
---|
774 | sequential … (OP2 rtl_params_ globals Addc tmpr1 tmp_zero tmp_zero); |
---|
775 | sequential … (OP2 rtl_params_ globals And tmpr3 tmpr3 tmpr1); |
---|
776 | sequential … (OP2 rtl_params_ globals Or destr destr tmpr3) ]. |
---|
777 | |
---|
778 | definition translate_lt_main ≝ |
---|
779 | λglobals: list ident. |
---|
780 | λtmp_zero: register. |
---|
781 | λtmp_one: register. |
---|
782 | λtmpr1: register. |
---|
783 | λtmpr2: register. |
---|
784 | λtmpr3: register. |
---|
785 | λdestr: register. |
---|
786 | λdummy_lbl: label. |
---|
787 | λsrcrs1: list register. |
---|
788 | λsrcrs2: list register. |
---|
789 | λproof: |srcrs1| = |srcrs2|. |
---|
790 | let f ≝ λinsts_leq. λsrcr1. λsrcr2. |
---|
791 | let 〈insts, leq〉 ≝ insts_leq in |
---|
792 | let added_insts ≝ translate_atom globals tmp_zero tmp_one tmpr1 tmpr2 tmpr3 destr dummy_lbl leq srcr1 srcr2 in |
---|
793 | 〈insts @ added_insts, leq @ [〈srcr1, srcr2〉]〉 |
---|
794 | in |
---|
795 | \fst (fold_left2 … f 〈[ ], [ ]〉 srcrs1 srcrs2 proof). |
---|
796 | |
---|
797 | definition fresh_regs_strong: |
---|
798 | ∀globals. rtl_internal_function globals → ∀n: nat. Σfresh: (rtl_internal_function globals) × (list register). |\snd fresh| = n ≝ |
---|
799 | λglobals: list ident. |
---|
800 | λdef. |
---|
801 | λn. |
---|
802 | fresh_regs rtl_params0 globals def n. |
---|
803 | @fresh_regs_length |
---|
804 | qed. |
---|
805 | |
---|
806 | definition complete_regs_strong: |
---|
807 | ∀globals: list ident. rtl_internal_function globals → list register → list register → Σcomplete: (list register) × (list register) × (list register). |\fst (\fst complete)| = |\snd (\fst complete)| ≝ |
---|
808 | λglobals: list ident. |
---|
809 | λdef. |
---|
810 | λleft. |
---|
811 | λright. |
---|
812 | complete_regs globals def left right. |
---|
813 | @complete_regs_length |
---|
814 | qed. |
---|
815 | |
---|
816 | definition translate_lt ≝ |
---|
817 | λglobals: list ident. |
---|
818 | λdestrs: list register. |
---|
819 | λprf_destrs: 0 < |destrs|. |
---|
820 | λsrcrs1: list register. |
---|
821 | λsrcrs2: list register. |
---|
822 | λstart_lbl: label. |
---|
823 | λdest_lbl: label. |
---|
824 | λdef: rtl_internal_function globals. |
---|
825 | match destrs with |
---|
826 | [ nil ⇒ add_graph rtl_params1 globals start_lbl (GOTO … dest_lbl) def |
---|
827 | | _ ⇒ |
---|
828 | match fresh_regs_strong globals def (|destrs|) with |
---|
829 | [ mk_Sig def_tmp_destrs tmp_destrs_proof ⇒ |
---|
830 | let def ≝ \fst def_tmp_destrs in |
---|
831 | let tmp_destrs ≝ \snd def_tmp_destrs in |
---|
832 | let tmp_destr ≝ hd_safe ? tmp_destrs ? in |
---|
833 | let 〈def, tmp_zero〉 ≝ fresh_reg rtl_params1 globals def in |
---|
834 | let 〈def, tmp_one〉 ≝ fresh_reg rtl_params1 globals def in |
---|
835 | let 〈def, tmpr1〉 ≝ fresh_reg rtl_params1 globals def in |
---|
836 | let 〈def, tmpr2〉 ≝ fresh_reg rtl_params1 globals def in |
---|
837 | let 〈def, tmpr3〉 ≝ fresh_reg rtl_params1 globals def in |
---|
838 | match complete_regs_strong globals def srcrs1 srcrs2 with |
---|
839 | [ mk_Sig srcrs12_added srcrs12_proof ⇒ |
---|
840 | let srcrs1 ≝ \fst (\fst srcrs12_added) in |
---|
841 | let srcrs2 ≝ \snd (\fst srcrs12_added) in |
---|
842 | let added ≝ \snd srcrs12_added in |
---|
843 | let srcrs1' ≝ rev … srcrs1 in |
---|
844 | let srcrs2' ≝ rev … srcrs2 in |
---|
845 | let insts_init ≝ [ |
---|
846 | translate_cst globals (Ointconst I8 (zero ?)) tmp_destrs; |
---|
847 | translate_cst globals (Ointconst I8 (zero ?)) added; |
---|
848 | adds_graph rtl_params1 globals [ |
---|
849 | sequential rtl_params_ globals (INT rtl_params_ globals tmp_zero (zero …)); |
---|
850 | sequential rtl_params_ globals (INT rtl_params_ globals tmp_one (bitvector_of_nat … 1)) |
---|
851 | ] |
---|
852 | ] |
---|
853 | in |
---|
854 | let insts_main ≝ |
---|
855 | translate_lt_main globals tmp_zero tmp_one tmpr1 tmpr2 tmpr3 tmp_destr start_lbl srcrs1' srcrs2' ? in |
---|
856 | let insts_main ≝ [ adds_graph rtl_params1 globals insts_main ] in |
---|
857 | let insts_exit ≝ [ translate_move globals destrs tmp_destrs ] in |
---|
858 | add_translates rtl_params1 globals (insts_init @ insts_main @ insts_exit) start_lbl dest_lbl def |
---|
859 | ] |
---|
860 | ] |
---|
861 | ]. |
---|
862 | [2: >tmp_destrs_proof @prf_destrs |
---|
863 | |1: normalize nodelta |
---|
864 | generalize in match srcrs12_proof; |
---|
865 | #HYP >rev_length >rev_length @HYP |
---|
866 | ] |
---|
867 | qed. |
---|
868 | |
---|
869 | definition add_128_to_last ≝ |
---|
870 | λglobals: list ident. |
---|
871 | λtmp_128: register. |
---|
872 | λrs. |
---|
873 | λprf: 0 < |rs|. |
---|
874 | λstart_lbl: label. |
---|
875 | match rs with |
---|
876 | [ nil ⇒ adds_graph rtl_params1 globals [ ] start_lbl |
---|
877 | | _ ⇒ |
---|
878 | let r ≝ last_safe … rs prf in |
---|
879 | adds_graph rtl_params1 globals [ |
---|
880 | sequential rtl_params_ globals (OP2 rtl_params_ globals Add r r tmp_128) |
---|
881 | ] start_lbl |
---|
882 | ]. |
---|
883 | |
---|
884 | definition translate_lts ≝ |
---|
885 | λglobals: list ident. |
---|
886 | λdestrs: list register. |
---|
887 | λdestrs_prf: 0 < |destrs|. |
---|
888 | λsrcrs1: list register. |
---|
889 | λsrcrs2: list register. |
---|
890 | λsrcrs1_lt_prf: 0 < |srcrs1|. |
---|
891 | λsrcrs2_lt_prf: 0 < |srcrs2|. |
---|
892 | λstart_lbl: label. |
---|
893 | λdest_lbl: label. |
---|
894 | λdef: rtl_internal_function globals. |
---|
895 | match fresh_regs_strong globals def (|srcrs1|) with |
---|
896 | [ mk_Sig def_tmp_srcrs1 srcrs1_prf ⇒ |
---|
897 | let def ≝ \fst def_tmp_srcrs1 in |
---|
898 | let tmp_srcrs1 ≝ \snd def_tmp_srcrs1 in |
---|
899 | match fresh_regs_strong globals def (|srcrs2|) with |
---|
900 | [ mk_Sig def_tmp_srcrs2 srcrs2_prf ⇒ |
---|
901 | let def ≝ \fst def_tmp_srcrs2 in |
---|
902 | let tmp_srcrs2 ≝ \snd def_tmp_srcrs2 in |
---|
903 | let 〈def, tmp_128〉 ≝ fresh_reg rtl_params0 globals def in |
---|
904 | add_translates rtl_params1 globals [ |
---|
905 | translate_move globals tmp_srcrs1 srcrs1; |
---|
906 | translate_move globals tmp_srcrs2 srcrs2; |
---|
907 | adds_graph rtl_params1 globals [ |
---|
908 | sequential rtl_params_ globals (INT rtl_params_ globals tmp_128 (bitvector_of_nat ? 128)) |
---|
909 | ]; |
---|
910 | add_128_to_last globals tmp_128 tmp_srcrs1 ?; |
---|
911 | add_128_to_last globals tmp_128 tmp_srcrs2 ?; |
---|
912 | translate_lt globals destrs destrs_prf tmp_srcrs1 tmp_srcrs2 |
---|
913 | ] start_lbl dest_lbl def |
---|
914 | ] |
---|
915 | ]. |
---|
916 | [1: >srcrs1_prf @srcrs1_lt_prf |
---|
917 | |2: >srcrs2_prf @srcrs2_lt_prf |
---|
918 | ] |
---|
919 | qed. |
---|
920 | |
---|
921 | definition translate_op2 ≝ |
---|
922 | λglobals: list ident. |
---|
923 | λop2. |
---|
924 | λdestrs: list register. |
---|
925 | λdestrs_prf: 0 < |destrs|. |
---|
926 | λsrcrs1: list register. |
---|
927 | λsrcrs2: list register. |
---|
928 | λsrcrs2_destrs_prf: |srcrs2| = |destrs|. |
---|
929 | λsrcrs1_destrs_prf: |srcrs1| = |destrs|. |
---|
930 | λstart_lbl: label. |
---|
931 | λdest_lbl: label. |
---|
932 | λdef: rtl_internal_function globals. |
---|
933 | match op2 with |
---|
934 | [ Oadd ⇒ |
---|
935 | translate_op globals Addc destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
936 | | Oaddp ⇒ |
---|
937 | translate_op globals Addc destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
938 | | Osub ⇒ |
---|
939 | translate_op globals Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
940 | | Osubpi ⇒ |
---|
941 | translate_op globals Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
942 | | Osubpp sz ⇒ |
---|
943 | translate_op globals Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
944 | | Omul ⇒ |
---|
945 | translate_mul globals destrs srcrs1 srcrs2 ? start_lbl dest_lbl def |
---|
946 | | Odivu ⇒ |
---|
947 | match srcrs1 return λx. 0 < |x| → rtl_internal_function globals with |
---|
948 | [ cons hd tl ⇒ λcons_prf. |
---|
949 | match tl with |
---|
950 | [ nil ⇒ translate_divumodu8 globals true destrs hd (hd_safe register srcrs2 ?) start_lbl dest_lbl def |
---|
951 | | _ ⇒ ? (* not implemented *) |
---|
952 | ] |
---|
953 | | nil ⇒ λnil_absrd. ? |
---|
954 | ] ? |
---|
955 | | Omodu ⇒ |
---|
956 | match srcrs1 return λx. 0 < |x| → rtl_internal_function globals with |
---|
957 | [ cons hd tl ⇒ λcons_prf. |
---|
958 | match tl with |
---|
959 | [ nil ⇒ translate_divumodu8 globals false destrs hd (hd_safe register srcrs2 ?) start_lbl dest_lbl def |
---|
960 | | _ ⇒ ? (* not implemented *) |
---|
961 | ] |
---|
962 | | nil ⇒ λnil_absrd. ? |
---|
963 | ] ? |
---|
964 | | Oand ⇒ |
---|
965 | translate_op globals And destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
966 | | Oor ⇒ |
---|
967 | translate_op globals Or destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
968 | | Oxor ⇒ |
---|
969 | translate_op globals Xor destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
970 | | Ocmp c ⇒ |
---|
971 | match c with |
---|
972 | [ Ceq ⇒ |
---|
973 | add_translates rtl_params1 globals [ |
---|
974 | translate_ne globals destrs srcrs1 srcrs2; |
---|
975 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
976 | ] start_lbl dest_lbl def |
---|
977 | | Cne ⇒ translate_ne globals destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
978 | | Clt ⇒ translate_lts globals destrs destrs_prf srcrs1 srcrs2 ? ? start_lbl dest_lbl def |
---|
979 | | Cgt ⇒ translate_lts globals destrs destrs_prf srcrs2 srcrs1 ? ? start_lbl dest_lbl def |
---|
980 | | Cle ⇒ |
---|
981 | add_translates rtl_params1 globals [ |
---|
982 | translate_lts globals destrs destrs_prf srcrs2 srcrs1 ? ?; |
---|
983 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
984 | ] start_lbl dest_lbl def |
---|
985 | | Cge ⇒ |
---|
986 | add_translates rtl_params1 globals [ |
---|
987 | translate_lts globals destrs destrs_prf srcrs1 srcrs2 ? ?; |
---|
988 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
989 | ] start_lbl dest_lbl def |
---|
990 | ] |
---|
991 | | Ocmpu c ⇒ |
---|
992 | match c with |
---|
993 | [ Ceq ⇒ |
---|
994 | add_translates rtl_params1 globals [ |
---|
995 | translate_ne globals destrs srcrs1 srcrs2; |
---|
996 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
997 | ] start_lbl dest_lbl def |
---|
998 | | Cne ⇒ translate_ne globals destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
999 | | Clt ⇒ translate_lt globals destrs destrs_prf srcrs1 srcrs2 start_lbl dest_lbl def |
---|
1000 | | Cgt ⇒ translate_lt globals destrs destrs_prf srcrs2 srcrs1 start_lbl dest_lbl def |
---|
1001 | | Cle ⇒ |
---|
1002 | add_translates rtl_params1 globals [ |
---|
1003 | translate_lt globals destrs destrs_prf srcrs2 srcrs1; |
---|
1004 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
1005 | ] start_lbl dest_lbl def |
---|
1006 | | Cge ⇒ |
---|
1007 | add_translates rtl_params1 globals [ |
---|
1008 | translate_lt globals destrs destrs_prf srcrs1 srcrs2; |
---|
1009 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
1010 | ] start_lbl dest_lbl def |
---|
1011 | ] |
---|
1012 | | Ocmpp c ⇒ |
---|
1013 | match c with |
---|
1014 | [ Ceq ⇒ |
---|
1015 | add_translates rtl_params1 globals [ |
---|
1016 | translate_ne globals destrs srcrs1 srcrs2; |
---|
1017 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
1018 | ] start_lbl dest_lbl def |
---|
1019 | | Cne ⇒ translate_ne globals destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
1020 | | Clt ⇒ translate_lt globals destrs destrs_prf srcrs1 srcrs2 start_lbl dest_lbl def |
---|
1021 | | Cgt ⇒ translate_lt globals destrs destrs_prf srcrs2 srcrs1 start_lbl dest_lbl def |
---|
1022 | | Cle ⇒ |
---|
1023 | add_translates rtl_params1 globals [ |
---|
1024 | translate_lt globals destrs destrs_prf srcrs2 srcrs1; |
---|
1025 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
1026 | ] start_lbl dest_lbl def |
---|
1027 | | Cge ⇒ |
---|
1028 | add_translates rtl_params1 globals [ |
---|
1029 | translate_lt globals destrs destrs_prf srcrs1 srcrs2; |
---|
1030 | translate_op1 globals ?? (Onotbool (ASTint I8 Unsigned) I8 Unsigned I) destrs destrs (refl ? (|destrs|)) |
---|
1031 | ] start_lbl dest_lbl def |
---|
1032 | ] |
---|
1033 | | _ ⇒ ? (* assert false, implemented in run time or float op *) |
---|
1034 | ]. |
---|
1035 | [1: |
---|
1036 | @sym_eq |
---|
1037 | assumption |
---|
1038 | |3,8,19,22,24,25: |
---|
1039 | >srcrs1_destrs_prf |
---|
1040 | assumption |
---|
1041 | |4,9: |
---|
1042 | normalize in nil_absrd; |
---|
1043 | cases(not_le_Sn_O 0) |
---|
1044 | #HYP cases(HYP nil_absrd) |
---|
1045 | |5,10,20,21,23,26: |
---|
1046 | >srcrs2_destrs_prf |
---|
1047 | assumption |
---|
1048 | |*: |
---|
1049 | cases not_implemented (* XXX: yes, really *) |
---|
1050 | ] |
---|
1051 | qed. |
---|
1052 | |
---|
1053 | definition translate_cond: ∀globals: list ident. list register → label → label → label → rtl_internal_function globals → rtl_internal_function globals ≝ |
---|
1054 | λglobals: list ident. |
---|
1055 | λsrcrs: list register. |
---|
1056 | λstart_lbl: label. |
---|
1057 | λlbl_true: label. |
---|
1058 | λlbl_false: label. |
---|
1059 | λdef: rtl_internal_function globals. |
---|
1060 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
---|
1061 | let 〈tmp_lbl, def〉 ≝ fresh_label rtl_params1 globals def in |
---|
1062 | let init ≝ sequential rtl_params_ globals (INT rtl_params_ globals tmpr (zero …)) in |
---|
1063 | let f ≝ λsrcr. sequential rtl_params_ globals (OP2 rtl_params_ globals Or tmpr tmpr srcr) in |
---|
1064 | let def ≝ adds_graph rtl_params1 globals (init :: (map ? ? f srcrs)) start_lbl tmp_lbl def in |
---|
1065 | add_graph rtl_params1 globals tmp_lbl (sequential rtl_params_ globals (COND rtl_params_ globals tmpr lbl_true) lbl_false) def. |
---|
1066 | |
---|
1067 | definition translate_load ≝ |
---|
1068 | λglobals: list ident. |
---|
1069 | λaddr. |
---|
1070 | λaddr_prf: 2 = |addr|. |
---|
1071 | λdestrs: list register. |
---|
1072 | λstart_lbl: label. |
---|
1073 | λdest_lbl: label. |
---|
1074 | λdef: rtl_internal_function globals. |
---|
1075 | match fresh_regs_strong rtl_params0 globals def (|addr|) with |
---|
1076 | [ mk_Sig def_save_addr save_addr_prf ⇒ |
---|
1077 | let def ≝ \fst def_save_addr in |
---|
1078 | let save_addr ≝ \snd def_save_addr in |
---|
1079 | match fresh_regs_strong rtl_params0 globals def (|addr|) with |
---|
1080 | [ mk_Sig def_tmp_addr tmp_addr_prf ⇒ |
---|
1081 | let def ≝ \fst def_tmp_addr in |
---|
1082 | let tmp_addr ≝ \snd def_tmp_addr in |
---|
1083 | let 〈tmp_addr1, tmp_addr2〉 ≝ make_addr … tmp_addr ? in |
---|
1084 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
---|
1085 | let 〈def, dummy〉 ≝ fresh_reg rtl_params0 globals def in |
---|
1086 | let insts_save_addr ≝ translate_move globals save_addr addr in |
---|
1087 | let f ≝ λtranslates_off. λr. |
---|
1088 | let 〈translates, off〉 ≝ translates_off in |
---|
1089 | let translates ≝ translates @ [ |
---|
1090 | adds_graph rtl_params1 globals [ |
---|
1091 | sequential rtl_params_ globals (INT rtl_params_ globals tmpr off) |
---|
1092 | ]; |
---|
1093 | translate_op2 globals Oaddp tmp_addr ? save_addr [dummy; tmpr] ? ?; |
---|
1094 | adds_graph rtl_params1 globals [ |
---|
1095 | sequential rtl_params_ globals (LOAD rtl_params_ globals r tmp_addr1 tmp_addr2) |
---|
1096 | ] |
---|
1097 | ] |
---|
1098 | in |
---|
1099 | let 〈carry, result〉 ≝ half_add … off int_size in |
---|
1100 | 〈translates, result〉 |
---|
1101 | in |
---|
1102 | let 〈translates, ignore〉 ≝ foldl … f 〈[ ], (zero ?)〉 destrs in |
---|
1103 | add_translates rtl_params1 globals (insts_save_addr :: translates) start_lbl dest_lbl def |
---|
1104 | ] |
---|
1105 | ]. |
---|
1106 | [1: >tmp_addr_prf >save_addr_prf % |
---|
1107 | |2: >save_addr_prf >tmp_addr_prf |
---|
1108 | @addr_prf |
---|
1109 | |3: >tmp_addr_prf normalize |
---|
1110 | <addr_prf // |
---|
1111 | |4: >tmp_addr_prf assumption |
---|
1112 | ] |
---|
1113 | qed. |
---|
1114 | |
---|
1115 | definition translate_store ≝ |
---|
1116 | λglobals: list ident. |
---|
1117 | λaddr. |
---|
1118 | λaddr_prf: 2 = |addr|. |
---|
1119 | λsrcrs: list register. |
---|
1120 | λstart_lbl: label. |
---|
1121 | λdest_lbl: label. |
---|
1122 | λdef: rtl_internal_function globals. |
---|
1123 | match fresh_regs_strong rtl_params0 globals def (|addr|) with |
---|
1124 | [ mk_Sig def_tmp_addr tmp_addr_prf ⇒ |
---|
1125 | let def ≝ \fst def_tmp_addr in |
---|
1126 | let tmp_addr ≝ \snd def_tmp_addr in |
---|
1127 | let 〈tmp_addr1, tmp_addr2〉 ≝ make_addr … tmp_addr ? in |
---|
1128 | let 〈def, tmpr〉 ≝ fresh_reg rtl_params0 globals def in |
---|
1129 | let 〈def, dummy〉 ≝ fresh_reg rtl_params0 globals def in |
---|
1130 | let f ≝ λtranslate_off. λsrcr. |
---|
1131 | let 〈translates, off〉 ≝ translate_off in |
---|
1132 | let translates ≝ translates @ [ |
---|
1133 | adds_graph rtl_params1 globals [ |
---|
1134 | sequential rtl_params_ globals (INT rtl_params_ globals tmpr off) |
---|
1135 | ]; |
---|
1136 | translate_op2 globals Oaddp tmp_addr … addr [dummy; tmpr] ? ?; |
---|
1137 | adds_graph rtl_params1 globals [ |
---|
1138 | sequential rtl_params_ globals (STORE rtl_params_ globals tmp_addr1 tmp_addr2 srcr) |
---|
1139 | ] |
---|
1140 | ] |
---|
1141 | in |
---|
1142 | let 〈carry, result〉 ≝ half_add … off int_size in |
---|
1143 | 〈translates, result〉 |
---|
1144 | in |
---|
1145 | let 〈translates, ignore〉 ≝ foldl … f 〈[ ], zero …〉 srcrs in |
---|
1146 | add_translates rtl_params1 globals translates start_lbl dest_lbl def |
---|
1147 | ]. |
---|
1148 | [1: >tmp_addr_prf % |
---|
1149 | |2: >tmp_addr_prf normalize |
---|
1150 | <addr_prf // |
---|
1151 | |3: >tmp_addr_prf <addr_prf // |
---|
1152 | |4: >tmp_addr_prf @addr_prf |
---|
1153 | ] |
---|
1154 | qed. |
---|
1155 | |
---|
1156 | axiom fake_label: label. |
---|
1157 | |
---|
1158 | (* XXX: following conversation with CSC about the mix up in extension statements |
---|
1159 | and extension instructions in RTL, use fake_label in calls to |
---|
1160 | tailcall_* instructions. *) |
---|
1161 | definition translate_stmt ≝ |
---|
1162 | λglobals: list ident. |
---|
1163 | λlenv: local_env. |
---|
1164 | λlbl: label. |
---|
1165 | λstmt. |
---|
1166 | λdef: rtl_internal_function globals. |
---|
1167 | match stmt with |
---|
1168 | [ St_skip lbl' ⇒ add_graph … lbl (GOTO … lbl') def |
---|
1169 | | St_cost cost_lbl lbl' ⇒ add_graph rtl_params1 globals lbl (sequential rtl_params_ globals (COST_LABEL rtl_params_ globals cost_lbl) lbl') def |
---|
1170 | | St_const destr cst lbl' ⇒ |
---|
1171 | translate_cst globals cst (find_local_env destr lenv) lbl lbl' def |
---|
1172 | | St_op1 ty ty' op1 destr srcr lbl' ⇒ |
---|
1173 | translate_op1 globals ty ty' op1 (find_local_env destr lenv) (find_local_env srcr lenv) … lbl lbl' def |
---|
1174 | | St_op2 op2 destr srcr1 srcr2 lbl' ⇒ |
---|
1175 | translate_op2 globals op2 (find_local_env destr lenv) ? (find_local_env srcr1 lenv) (find_local_env srcr2 lenv) ? ? lbl lbl' def |
---|
1176 | (* XXX: should we be ignoring this? *) |
---|
1177 | | St_load ignore addr destr lbl' ⇒ |
---|
1178 | translate_load globals (find_local_env addr lenv) ? (find_local_env destr lenv) lbl lbl' def |
---|
1179 | (* XXX: should we be ignoring this? *) |
---|
1180 | | St_store ignore addr srcr lbl' ⇒ |
---|
1181 | translate_store globals (find_local_env addr lenv) ? (find_local_env srcr lenv) lbl lbl' def |
---|
1182 | | St_call_id f args retr lbl' ⇒ |
---|
1183 | match retr with |
---|
1184 | [ Some retr ⇒ |
---|
1185 | add_graph rtl_params1 globals lbl (sequential … (CALL_ID rtl_params1 globals f (rtl_args args lenv) (find_local_env retr lenv)) lbl') def |
---|
1186 | | None ⇒ add_graph rtl_params1 globals lbl (sequential … (CALL_ID rtl_params1 globals f (rtl_args args lenv) [ ]) lbl') def |
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1187 | ] |
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1188 | | St_call_ptr f args retr lbl' ⇒ |
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1189 | match retr with |
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1190 | [ None ⇒ |
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1191 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
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1192 | add_graph rtl_params1 globals lbl (sequential … (extension … (rtl_st_ext_call_ptr f1 f2 (rtl_args args lenv) [ ])) lbl') def |
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1193 | | Some retr ⇒ |
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1194 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
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1195 | add_graph rtl_params1 globals lbl (sequential … (extension … (rtl_st_ext_call_ptr f1 f2 (rtl_args args lenv) (find_local_env retr lenv))) lbl') def |
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1196 | ] |
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1197 | | St_tailcall_id f args ⇒ |
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1198 | add_graph rtl_params1 globals lbl (sequential rtl_params_ globals (extension rtl_params_ globals (rtl_st_ext_tailcall_id f (rtl_args args lenv))) fake_label) def |
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1199 | | St_tailcall_ptr f args ⇒ |
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1200 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
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1201 | add_graph rtl_params1 globals lbl (sequential rtl_params_ globals (extension rtl_params1 globals (rtl_st_ext_tailcall_ptr f1 f2 (rtl_args args lenv))) fake_label) def |
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1202 | | St_cond r lbl_true lbl_false ⇒ |
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1203 | translate_cond globals (find_local_env r lenv) lbl lbl_true lbl_false def |
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1204 | | St_jumptable r l ⇒ ? (* assert false: not implemented yet *) |
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1205 | | St_return ⇒ add_graph rtl_params1 globals lbl (RETURN …) def |
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1206 | ]. |
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1207 | [10: cases not_implemented (* jtable case *) |
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1208 | |*: cases daemon (* TODO: proofs regarding lengths of lists, examine! *) |
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1209 | ] |
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1210 | qed. |
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1211 | |
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1212 | (* XXX: we use a "hack" here to circumvent the proof obligations required to |
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1213 | create res, an empty internal_function record. we insert into our graph |
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1214 | the start and end nodes to ensure that they are in, and place dummy |
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1215 | skip instructions at these nodes. *) |
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1216 | definition translate_internal ≝ |
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1217 | λglobals: list ident. |
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1218 | λdef. |
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1219 | let runiverse ≝ f_reggen def in |
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1220 | let 〈lenv,runiverse〉 ≝ initialize_local_env runiverse |
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1221 | (f_params def @ f_locals def) (f_result def) in |
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1222 | let params ≝ map_list_local_env lenv (map … \fst (f_params def)) in |
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1223 | let locals ≝ map_list_local_env lenv (map … \fst (f_locals def)) in |
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1224 | let result ≝ |
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1225 | match (f_result def) with |
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1226 | [ None ⇒ [ ] |
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1227 | | Some r_typ ⇒ |
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1228 | let 〈r, typ〉 ≝ r_typ in |
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1229 | find_local_env r lenv |
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1230 | ] |
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1231 | in |
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1232 | let luniverse' ≝ f_labgen def in |
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1233 | let runiverse' ≝ runiverse in |
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1234 | let result' ≝ result in |
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1235 | let params' ≝ params in |
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1236 | let locals' ≝ locals in |
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1237 | let stack_size' ≝ f_stacksize def in |
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1238 | let entry' ≝ f_entry def in |
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1239 | let exit' ≝ f_exit def in |
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1240 | let graph' ≝ add LabelTag ? (empty_map LabelTag ?) entry' (GOTO rtl_params_ globals entry') in |
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1241 | let graph' ≝ add LabelTag ? graph' exit' (GOTO rtl_params_ globals exit') in |
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1242 | let res ≝ |
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1243 | mk_joint_internal_function … (rtl_params globals) luniverse' runiverse' result' params' |
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1244 | locals' stack_size' graph' ? ? in |
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1245 | foldi … (translate_stmt globals … lenv) (f_graph def) res. |
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1246 | [ % [@entry' | @graph_add_lookup @graph_add] |
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1247 | | % [@exit' | @graph_add]] |
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1248 | qed. |
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1249 | |
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1250 | (*CSC: here we are not doing any alignment on variables, like it is done in OCaml |
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1251 | because of CompCert heritage *) |
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1252 | definition rtlabs_to_rtl: RTLabs_program → rtl_program ≝ |
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1253 | λp. transform_program … p (transf_fundef … (translate_internal (prog_var_names …))). |
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1254 | |
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1255 | *) |
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1256 | axiom rtlabs_to_rtl: RTLabs_program → rtl_program. |
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1257 | |
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