1 | include "joint/SemanticUtils.ma". |
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2 | (* |
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3 | include "utilities/lists.ma". |
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4 | include "common/Errors.ma". |
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5 | include "common/Globalenvs.ma". |
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6 | include "common/IO.ma". |
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7 | include "common/SmallstepExec.ma". |
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8 | *) |
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9 | include "RTL/RTL.ma". (* CSC: syntax.ma in RTLabs *) |
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10 | include alias "common/Identifiers.ma". |
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11 | include alias "ASM/Util.ma". |
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12 | |
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13 | record frame: Type[0] ≝ |
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14 | { fr_ret_regs: list register |
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15 | ; fr_pc: address |
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16 | ; fr_sp: pointer |
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17 | ; fr_carry: beval |
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18 | ; fr_regs: register_env beval |
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19 | }. |
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20 | |
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21 | definition rtl_more_sem_params: more_sem_params rtl_params_ := |
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22 | mk_more_sem_params rtl_params_ |
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23 | (list frame) (register_env beval) graph_succ_p |
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24 | reg_store reg_retrieve reg_store reg_retrieve reg_store reg_retrieve |
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25 | reg_store reg_retrieve reg_store reg_retrieve |
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26 | (λlocals,dest_src. |
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27 | do v ← reg_retrieve locals (\snd dest_src) ; |
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28 | reg_store (\fst dest_src) v locals) |
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29 | pointer_of_label. |
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30 | definition rtl_sem_params: sem_params ≝ mk_sem_params … rtl_more_sem_params. |
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31 | |
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32 | definition rtl_init_locals : |
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33 | list register → register_env beval → register_env beval ≝ |
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34 | λlocals,env. |
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35 | foldl ?? (λlenv,reg. add … lenv reg BVundef) env locals. |
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36 | |
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37 | (*CSC: could we use here a dependent type to avoid the Error case? *) |
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38 | axiom EmptyStack: String. |
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39 | axiom OutOfBounds: String. |
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40 | |
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41 | (*CSC: we could use a dependent type here: the list of return values should have |
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42 | the same length of the list of return registers that store the values. This |
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43 | saves the OutOfBounds exception *) |
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44 | definition rtl_pop_frame: list beval → state … rtl_sem_params → res (state … rtl_sem_params) ≝ |
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45 | λret_vals,st. |
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46 | let frms ≝ st_frms ? st in |
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47 | match frms with |
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48 | [ nil ⇒ Error ? [MSG EmptyStack] |
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49 | | cons hd tl ⇒ |
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50 | do st ← |
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51 | mfold_left_i ?? |
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52 | (λi.λst.λreg. |
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53 | do v ← opt_to_res ? [MSG OutOfBounds] (nth_opt … i ret_vals) ; |
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54 | greg_store rtl_sem_params reg v st) |
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55 | (OK … st) (fr_ret_regs hd) ; |
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56 | OK … |
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57 | (set_frms rtl_sem_params tl |
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58 | (set_regs rtl_sem_params (fr_regs hd) |
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59 | (set_sp … (fr_sp hd) |
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60 | (set_pc … (fr_pc hd) |
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61 | (set_carry … (fr_carry hd) |
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62 | (set_m … (free … (m … st) (pblock (sp … st))) st)))))) ]. |
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63 | |
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64 | definition rtl_save_frame: |
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65 | nat → list register → list register → list register → state … rtl_sem_params → res (state … rtl_sem_params) ≝ |
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66 | λstacksize,formal_arg_regs,actual_arg_regs,retregs,st. |
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67 | let 〈mem,b〉 ≝ alloc … (m … st) 0 stacksize XData in |
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68 | do new_regs ← |
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69 | mfold_left2 … |
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70 | (λlenv,dest,src. |
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71 | do v ← greg_retrieve … st src ; |
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72 | OK … (add … lenv dest v)) |
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73 | (OK … (empty_map …)) formal_arg_regs actual_arg_regs ; |
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74 | OK … |
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75 | (set_frms rtl_sem_params |
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76 | (mk_frame retregs (pc … st) (sp … st) (carry … st) (regs … st) :: (st_frms … st)) |
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77 | (set_regs rtl_sem_params new_regs |
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78 | (set_m … mem |
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79 | (set_sp … (mk_pointer XData b ? (mk_offset 0)) st)))). |
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80 | cases daemon (*CSC: XXXX easy lemma on alloc to be turned into a dependent type*) |
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81 | qed. |
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82 | |
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83 | definition rtl_more_sem_params1 : more_sem_params1 … rtl_params1 ≝ |
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84 | mk_more_sem_params1 ? rtl_params1 rtl_more_sem_params |
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85 | rtl_init_locals rtl_pop_frame rtl_save_frame. |
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86 | |
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87 | (*CSC: XXXXX, for is_final only *) |
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88 | axiom rtl_fetch_result: state rtl_sem_params → res (list beval). |
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89 | (* let ret_vals ≝ map … (λreg.greg_retrieve rtl_sem_params st reg) ret_val_regs in |
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90 | *) |
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91 | |
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92 | (*CSC: XXXX, for external functions only*) |
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93 | axiom rtl_fetch_external_args: external_function → state rtl_sem_params → res (list val). |
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94 | axiom rtl_set_result: list val → state rtl_sem_params → res (state rtl_sem_params). |
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95 | |
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96 | definition rtl_exec_extended: |
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97 | ∀globals. genv globals (rtl_params globals) → |
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98 | rtl_statement_extension → label → state rtl_sem_params → |
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99 | IO io_out io_in (trace × (state rtl_sem_params)) ≝ |
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100 | λglobals,ge,stm,l,st. |
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101 | match stm with |
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102 | [ rtl_st_ext_stack_address dreg1 dreg2 ⇒ |
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103 | let sp ≝ sp ? st in |
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104 | ! 〈dpl,dph〉 ← beval_pair_of_pointer sp ; |
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105 | ! st ← greg_store rtl_sem_params dreg1 dpl st ; |
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106 | ! st ← greg_store rtl_sem_params dreg2 dph st ; |
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107 | ret ? 〈E0, goto … l st〉 |
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108 | | rtl_st_ext_call_ptr _ _ _ _ ⇒ ? |
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109 | | rtl_st_ext_tailcall_id id regs ⇒ ? |
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110 | | rtl_st_ext_tailcall_ptr _ _ _ ⇒ ? |
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111 | ]. |
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112 | [1,2,3: cases not_implemented ] (*CSC: tailcalls and pointer calls not implemented ATM *) |
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113 | qed. |
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114 | |
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115 | definition rtl_more_sem_params2: ∀globals. more_sem_params2 … (rtl_params globals) ≝ |
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116 | λglobals. |
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117 | mk_more_sem_params2 … rtl_more_sem_params1 |
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118 | (graph_fetch_statement …) rtl_fetch_result rtl_fetch_external_args rtl_set_result |
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119 | (rtl_exec_extended …). |
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120 | |
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121 | definition rtl_fullexec ≝ |
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122 | joint_fullexec … (λp. rtl_more_sem_params2 (prog_var_names … p)). |
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123 | |
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124 | (* |
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125 | (* CSC: external functions never fail (??) and always return something of the |
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126 | size of one register, both in the frontend and in the backend. |
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127 | Is this reasonable??? In OCaml it always return a list, but in the frontend |
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128 | only the head is kept (or Undef if the list is empty) ??? *) |
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129 | |
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130 | (* CSC: carries are values and booleans are not values; so we use integers. |
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131 | But why using values at all? To have undef? *) |
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132 | (* CSC: ???????????? *) |
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133 | axiom smerge: val → val → res val. |
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134 | (* CSC: ???????????? In OCaml: IntValue.Int32.merge |
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135 | Note also that the translation can fail; so it should be a res int! *) |
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136 | axiom smerge2: list val → int. |
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137 | (* CSC: I have a byte, I need a value, but it is complex to do so *) |
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138 | axiom val_of_Byte: Byte → val. |
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139 | axiom Byte_of_val: val → res Byte. |
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140 | (* Map from the front-end memory model to the back-end memory model *) |
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141 | axiom represent_block: block → val × val. |
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142 | (* CSC: fixed size chunk *) |
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143 | axiom chunk: memory_chunk. |
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144 | |
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145 | definition genv ≝ (genv_t Genv) (fundef rtl_internal_function). |
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146 | |
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147 | (* CSC: added carry *) |
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148 | record frame : Type[0] ≝ |
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149 | { func : rtl_internal_function |
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150 | ; locals : register_env val |
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151 | ; next : label |
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152 | ; sp : block |
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153 | ; retdst : list register |
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154 | ; carry : val |
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155 | }. |
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156 | |
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157 | (* CSC: added carry *) |
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158 | definition adv : label → frame → frame ≝ |
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159 | λl,f. mk_frame (func f) (locals f) l (sp f) (retdst f) (carry f). |
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160 | |
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161 | inductive state : Type[0] ≝ |
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162 | | State : |
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163 | ∀ f : frame. |
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164 | ∀ fs : list frame. |
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165 | ∀ m : mem. |
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166 | state |
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167 | | Callstate : |
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168 | ∀ fd : fundef rtl_internal_function. |
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169 | ∀args : list val. |
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170 | ∀ dst : list register. (* CSC: changed from option to list *) |
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171 | ∀ stk : list frame. |
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172 | ∀ m : mem. |
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173 | state |
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174 | | Returnstate : |
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175 | (* CSC: the two lists should have the same length, but this is |
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176 | enforced only by the semantics *) |
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177 | ∀ rtv : list val. (* CSC: changed from option to list *) |
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178 | ∀ dst : list register. (* CSC: changed from option to list *) |
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179 | ∀ stk : list frame. |
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180 | ∀ m : mem. |
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181 | state. |
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182 | |
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183 | definition mem_of_state : state → mem ≝ |
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184 | λs. match s with [ State _ _ m ⇒ m | Callstate _ _ _ _ m ⇒ m | Returnstate _ _ _ m ⇒ m ]. |
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185 | |
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186 | definition build_state ≝ λf.λfs.λm.λn. State (adv n f) fs m. |
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187 | |
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188 | (* CSC: modified to take in input a list of registers (untyped) *) |
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189 | definition init_locals : list register → register_env val ≝ |
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190 | foldr ?? (λid,en. add RegisterTag val en id Vundef) (empty_map ??). |
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191 | |
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192 | definition reg_store ≝ |
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193 | λreg,v,locals. |
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194 | update RegisterTag val locals reg v. |
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195 | |
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196 | axiom WrongNumberOfParameters : String. |
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197 | |
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198 | (* CSC: modified to take in input a list of registers (untyped) *) |
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199 | let rec params_store (rs:list register) (vs:list val) (locals : register_env val) : res (register_env val) ≝ |
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200 | match rs with |
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201 | [ nil ⇒ match vs with [ nil ⇒ OK ? locals | _ ⇒ Error ? (msg WrongNumberOfParameters)] |
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202 | | cons r rst ⇒ match vs with [ nil ⇒ Error ? (msg WrongNumberOfParameters) | cons v vst ⇒ |
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203 | let locals' ≝ add RegisterTag val locals r v in |
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204 | params_store rst vst locals' |
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205 | ] ]. |
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206 | |
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207 | axiom BadRegister : String. |
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208 | |
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209 | definition reg_retrieve : register_env ? → register → res val ≝ |
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210 | λlocals,reg. opt_to_res … [MSG BadRegister; CTX ? reg] (lookup ?? locals reg). |
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211 | |
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212 | axiom FailedOp : String. |
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213 | axiom MissingSymbol : String. |
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214 | |
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215 | axiom MissingStatement : String. |
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216 | axiom FailedConstant : String. |
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217 | axiom FailedLoad : String. |
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218 | axiom FailedStore : String. |
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219 | axiom BadFunction : String. |
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220 | axiom BadJumpTable : String. |
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221 | axiom BadJumpValue : String. |
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222 | axiom FinalState : String. |
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223 | axiom ReturnMismatch : String. |
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224 | |
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225 | definition eval_statement : genv → state → IO io_out io_in (trace × state) ≝ |
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226 | λge,st. |
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227 | match st with |
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228 | [ State f fs m ⇒ |
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229 | ! s ← opt_to_io … [MSG MissingStatement; CTX ? (next f)] (lookup ?? (rtl_if_graph (func f)) (next f)); |
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230 | match s with |
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231 | [ rtl_st_skip l ⇒ ret ? 〈E0, build_state f fs m l〉 |
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232 | | rtl_st_cost cl l ⇒ ret ? 〈Echarge cl, build_state f fs m l〉 |
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233 | | rtl_st_load addrl addrh dst l ⇒ (* CSC: pairs of regs vs reg *) |
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234 | ! vaddrh ← reg_retrieve (locals f) addrh; |
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235 | ! vaddrl ← reg_retrieve (locals f) addrl; |
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236 | ! vaddr ← smerge vaddrl vaddrh; |
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237 | ! v ← opt_to_res … (msg FailedLoad) (loadv chunk m vaddr); |
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238 | ! locals ← reg_store dst v (locals f); |
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239 | ret ? 〈E0, State (mk_frame (func f) locals l (sp f) (retdst f) (carry f)) fs m〉 |
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240 | | rtl_st_store addrl addrh src l ⇒ (* CSC: pairs of regs vs reg *) |
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241 | ! vaddrh ← reg_retrieve (locals f) addrh; |
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242 | ! vaddrl ← reg_retrieve (locals f) addrl; |
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243 | ! vaddr ← smerge vaddrl vaddrh; |
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244 | ! v ← reg_retrieve (locals f) src; |
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245 | ! m' ← opt_to_res … (msg FailedStore) (storev chunk m vaddr v); |
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246 | ret ? 〈E0, build_state f fs m' l〉 |
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247 | | rtl_st_call_id id args dst l ⇒ |
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248 | ! b ← opt_to_res … [MSG MissingSymbol; CTX ? id] (find_symbol ?? ge id); |
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249 | ! fd ← opt_to_res … [MSG BadFunction; CTX ? id] (find_funct_ptr ?? ge b); |
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250 | ! vs ← mmap ?? (reg_retrieve (locals f)) args; |
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251 | ret ? 〈E0, Callstate fd vs dst (adv l f::fs) m〉 |
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252 | | rtl_st_call_ptr lfrs hfrs args dst l ⇒ (* CSC: pairs of regs vs reg *) |
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253 | ! hfv ← reg_retrieve (locals f) hfrs; |
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254 | ! lfv ← reg_retrieve (locals f) lfrs; |
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255 | ! fv ← smerge lfv hfv; |
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256 | ! fd ← opt_to_res … (msg BadFunction) (find_funct ?? ge fv); |
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257 | ! vs ← mmap ?? (reg_retrieve (locals f)) args; |
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258 | ret ? 〈E0, Callstate fd vs dst (adv l f::fs) m〉 |
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259 | | rtl_st_tailcall_id id args ⇒ |
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260 | ! b ← opt_to_res … [MSG MissingSymbol; CTX ? id] (find_symbol ?? ge id); |
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261 | ! fd ← opt_to_res … [MSG BadFunction; CTX ? id] (find_funct_ptr ?? ge b); |
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262 | ! vs ← mmap ?? (reg_retrieve (locals f)) args; |
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263 | ret ? 〈E0, Callstate fd vs (retdst f) fs (free m (sp f))〉 |
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264 | | rtl_st_tailcall_ptr lfrs hfrs args ⇒ (* CSC: pairs of regs vs reg *) |
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265 | ! hfv ← reg_retrieve (locals f) hfrs; |
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266 | ! lfv ← reg_retrieve (locals f) lfrs; |
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267 | ! fv ← smerge lfv hfv; |
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268 | ! fd ← opt_to_res … (msg BadFunction) (find_funct ?? ge fv); |
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269 | ! vs ← mmap ?? (reg_retrieve (locals f)) args; |
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270 | ret ? 〈E0, Callstate fd vs (retdst f) fs (free m (sp f))〉 |
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271 | | rtl_st_return ⇒ |
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272 | (* CSC: rtl_if_result/f_result; list vs option *) |
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273 | let dest ≝ rtl_if_result (func f) in |
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274 | ! v ← mmap … (reg_retrieve (locals f)) dest; |
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275 | ret ? 〈E0, Returnstate v (retdst f) fs (free m (sp f))〉 |
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276 | | rtl_st_cond src ltrue lfalse ⇒ |
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277 | ! v ← reg_retrieve (locals f) src; |
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278 | ! b ← eval_bool_of_val v; |
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279 | ret ? 〈E0, build_state f fs m (if b then ltrue else lfalse)〉 |
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280 | (* CSC: mismatch between the memory models and failures for the next two opx *) |
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281 | | rtl_st_op1 op dst src l ⇒ |
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282 | ! v ← reg_retrieve (locals f) src; |
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283 | ! v ← Byte_of_val v; |
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284 | let v' ≝ val_of_Byte (op1 eval op v) in |
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285 | ! locals ← reg_store dst v' (locals f); |
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286 | ret ? 〈E0, State (mk_frame (func f) locals l (sp f) (retdst f) (carry f)) fs m〉 |
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287 | | rtl_st_op2 op dst src1 src2 l ⇒ |
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288 | ! v1 ← reg_retrieve (locals f) src1; |
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289 | ! v1 ← Byte_of_val v1; |
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290 | ! v2 ← reg_retrieve (locals f) src2; |
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291 | ! v2 ← Byte_of_val v2; |
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292 | ! carry ← eval_bool_of_val (carry f); |
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293 | let 〈v',carry〉 ≝ op2 eval carry op v1 v2 in |
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294 | let v' ≝ val_of_Byte v' in |
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295 | let carry ≝ of_bool carry in |
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296 | ! locals ← reg_store dst v' (locals f); |
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297 | ret ? 〈E0, State (mk_frame (func f) locals l (sp f) (retdst f) carry) fs m〉 |
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298 | |
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299 | (* CSC: Removed: St_jumptable *) |
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300 | (* CSC: Added: *) |
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301 | |
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302 | (* CSC: St_const splitted into rtl_st_int, rtl_st_addr and rt_st_stack_addr; *) |
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303 | | rtl_st_addr ldest hdest id l ⇒ |
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304 | ! addr ← opt_to_res … [MSG MissingSymbol; CTX … id] (find_symbol ?? ge id); |
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305 | let 〈laddr,haddr〉 ≝ represent_block addr in |
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306 | ! locals ← reg_store ldest laddr (locals f); |
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307 | ! locals ← reg_store hdest haddr locals; |
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308 | ret ? 〈E0, State (mk_frame (func f) locals l (sp f) (retdst f) (carry f)) fs m〉 |
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309 | | rtl_st_stack_addr ldest hdest l ⇒ |
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310 | let 〈laddr,haddr〉 ≝ represent_block (sp f) in |
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311 | ! locals ← reg_store ldest laddr (locals f); |
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312 | ! locals ← reg_store hdest haddr locals; |
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313 | ret ? 〈E0, State (mk_frame (func f) locals l (sp f) (retdst f) (carry f)) fs m〉 |
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314 | | rtl_st_int dest v l ⇒ |
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315 | ! locals ← reg_store dest (val_of_Byte v) (locals f); |
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316 | ret ? 〈E0, State (mk_frame (func f) locals l (sp f) (retdst f) (carry f)) fs m〉 |
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317 | |
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318 | (* CSC: St_op1 splitted into rtl_st_op1 and rtl_st_move *) |
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319 | | rtl_st_move dst src l ⇒ |
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320 | ! v ← reg_retrieve (locals f) src; |
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321 | ! locals ← reg_store dst v (locals f); |
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322 | ret ? 〈E0, State (mk_frame (func f) locals l (sp f) (retdst f) (carry f)) fs m〉 |
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323 | (* CSC: St_op2 splitted into rtl_st_op2 and rtl_st_opaccs *) |
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324 | | rtl_st_opaccs op dacc dbacc sacc sbacc l ⇒ |
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325 | ! v1 ← reg_retrieve (locals f) sacc; |
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326 | ! v1 ← Byte_of_val v1; |
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327 | ! v2 ← reg_retrieve (locals f) sbacc; |
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328 | ! v2 ← Byte_of_val v2; |
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329 | let 〈v1',v2'〉 ≝ opaccs eval op v1 v2 in |
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330 | let v1' ≝ val_of_Byte v1' in |
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331 | let v2' ≝ val_of_Byte v2' in |
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332 | ! locals ← reg_store dacc v1' (locals f); |
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333 | ! locals ← reg_store dbacc v2' locals; |
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334 | ret ? 〈E0, State (mk_frame (func f) locals l (sp f) (retdst f) (carry f)) fs m〉 |
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335 | |
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336 | | rtl_st_clear_carry l ⇒ |
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337 | ret ? 〈E0, State (mk_frame (func f) (locals f) l (sp f) (retdst f) Vfalse) fs m〉 |
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338 | | rtl_st_set_carry l ⇒ |
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339 | ret ? 〈E0, State (mk_frame (func f) (locals f) l (sp f) (retdst f) Vtrue) fs m〉 |
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340 | ] |
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341 | | Callstate fd params dst fs m ⇒ |
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342 | match fd with |
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343 | [ Internal fn ⇒ |
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344 | ! locals ← params_store (rtl_if_params fn) params (init_locals (rtl_if_locals fn)); |
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345 | let 〈m', sp〉 ≝ alloc m 0 (rtl_if_stacksize fn) Any in |
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346 | (* CSC: added carry *) |
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347 | ret ? 〈E0, State (mk_frame fn locals (rtl_if_entry fn) sp dst Vundef) fs m'〉 |
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348 | | External fn ⇒ |
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349 | ! evargs ← check_eventval_list params (sig_args (ef_sig fn)); |
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350 | ! evres ← do_io (ef_id fn) evargs (proj_sig_res (ef_sig fn)); |
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351 | (* CSC: return type changed from option to list *) |
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352 | (* CSC: XXX bug here; I think I should split it into Byte-long |
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353 | components; instead I am making a singleton out of it *) |
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354 | ret ? 〈Eextcall (ef_id fn) evargs (mk_eventval ? evres), Returnstate [mk_val ? evres] dst fs m〉 |
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355 | ] |
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356 | | Returnstate v dst fs m ⇒ |
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357 | match fs with |
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358 | [ nil ⇒ Error ? (msg FinalState) (* Already in final state *) |
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359 | | cons f fs' ⇒ |
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360 | ! locals ← |
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361 | mfold_left2 ??? |
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362 | (λlocals,dst,v. reg_store dst v locals) (OK ? (locals f)) dst v; |
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363 | ret ? 〈E0, State (mk_frame (func f) locals (next f) (sp f) (retdst f) (carry f)) fs' m〉 |
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364 | ] |
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365 | ]. |
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366 | |
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367 | axiom WrongReturnValueType: String. |
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368 | |
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369 | definition is_final : state → option ((*CSC: why not res*) int) ≝ |
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370 | λs. match s with |
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371 | [ State _ _ _ ⇒ None ? |
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372 | | Callstate _ _ _ _ _ ⇒ None ? |
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373 | | Returnstate v _ fs _ ⇒ |
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374 | match fs with |
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375 | [ nil ⇒ Some ? (smerge2 v) |
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376 | | _ ⇒ None ? ]]. |
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377 | (* |
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378 | definition RTL_exec : execstep io_out io_in ≝ |
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379 | mk_execstep … ? is_final mem_of_state eval_statement. |
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380 | *) |
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381 | (* CSC: XXX the program type does not fit with the globalenv and init_mem |
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382 | definition make_initial_state : rtl_program → res (genv × state) ≝ |
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383 | λp. |
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384 | do ge ← globalenv Genv ?? p; |
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385 | do m ← init_mem Genv ?? p; |
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386 | let main ≝ rtl_pr_main ?? p in |
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387 | do b ← opt_to_res ? [MSG MissingSymbol; CTX ? main] (find_symbol ? ? ge main); |
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388 | do f ← opt_to_res ? [MSG BadFunction; CTX ? main] (find_funct_ptr ? ? ge b); |
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389 | OK ? 〈ge,Callstate f (nil ?) [ ] (nil ?) m〉. |
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390 | |
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391 | definition RTL_fullexec : fullexec io_out io_in ≝ |
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392 | mk_fullexec … RTL_exec ? make_initial_state. |
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393 | *) |
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394 | *) |
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