1 | include "Clight/Csyntax.ma". |
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2 | |
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3 | (* Label freedom *) |
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4 | |
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5 | let rec expr_label_free (e:expr) : bool ≝ |
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6 | match e with |
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7 | [ Expr e' _ ⇒ |
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8 | match e' with |
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9 | [ Ederef e1 ⇒ expr_label_free e1 |
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10 | | Eaddrof e1 ⇒ expr_label_free e1 |
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11 | | Eunop _ e1 ⇒ expr_label_free e1 |
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12 | | Ebinop _ e1 e2 ⇒ expr_label_free e1 ∧ expr_label_free e2 |
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13 | | Ecast _ e1 ⇒ expr_label_free e1 |
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14 | | Econdition e1 e2 e3 ⇒ expr_label_free e1 ∧ expr_label_free e2 ∧ expr_label_free e3 |
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15 | | Eandbool e1 e2 ⇒ expr_label_free e1 ∧ expr_label_free e2 |
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16 | | Eorbool e1 e2 ⇒ expr_label_free e1 ∧ expr_label_free e2 |
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17 | | Efield e1 _ ⇒ expr_label_free e1 |
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18 | | Ecost _ _ ⇒ false |
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19 | | _ ⇒ true |
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20 | ] |
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21 | ]. |
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22 | |
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23 | let rec statement_label_free (s:statement) : bool ≝ |
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24 | match s with |
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25 | [ Sassign e1 e2 ⇒ expr_label_free e1 ∧ expr_label_free e2 |
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26 | | Scall oe e1 es ⇒ option_map_def … expr_label_free true oe ∧ expr_label_free e1 ∧ all … expr_label_free es |
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27 | | Ssequence s1 s2 ⇒ statement_label_free s1 ∧ statement_label_free s2 |
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28 | | Sifthenelse e1 s1 s2 ⇒ expr_label_free e1 ∧ statement_label_free s1 ∧ statement_label_free s2 |
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29 | | Swhile e1 s1 cl ⇒ expr_label_free e1 ∧ statement_label_free s1 ∧ match cl with [ None ⇒ true | _ ⇒ false ] |
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30 | | Sdowhile e1 s1 ⇒ expr_label_free e1 ∧ statement_label_free s1 |
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31 | | Sfor s1 e1 s2 s3 ⇒ statement_label_free s1 ∧ expr_label_free e1 ∧ statement_label_free s2 ∧ statement_label_free s3 |
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32 | | Sreturn oe ⇒ option_map_def … expr_label_free true oe |
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33 | | Sswitch e1 ls ⇒ expr_label_free e1 ∧ labeled_statements_label_free ls |
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34 | | Slabel _ s1 ⇒ statement_label_free s1 |
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35 | | Scost _ _ ⇒ false |
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36 | | _ ⇒ true |
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37 | ] and labeled_statements_label_free (ls:labeled_statements) : bool ≝ |
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38 | match ls with |
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39 | [ LSdefault s1 ⇒ statement_label_free s1 |
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40 | | LScase _ _ s1 ls1 ⇒ statement_label_free s1 ∧ labeled_statements_label_free ls1 |
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41 | ]. |
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42 | |
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43 | definition clight_fundef_label_free : ident × clight_fundef → bool ≝ |
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44 | λifd. match \snd ifd with |
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45 | [ CL_Internal f ⇒ statement_label_free (fn_body f) |
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46 | | _ ⇒ true |
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47 | ]. |
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48 | |
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49 | definition clight_label_free : clight_program → bool ≝ |
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50 | λp. all ? clight_fundef_label_free (prog_funct ?? p). |
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51 | |
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52 | (* Adding labels *) |
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53 | |
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54 | definition add_cost_before : statement → universe CostTag → statement × (universe CostTag) ≝ |
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55 | λs,gen. |
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56 | let 〈l,gen〉 ≝ fresh … gen in |
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57 | 〈Scost l s, gen〉. |
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58 | |
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59 | definition add_cost_after : statement → universe CostTag → statement × (universe CostTag) ≝ |
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60 | λs,gen. |
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61 | let 〈l,gen〉 ≝ fresh … gen in |
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62 | 〈Ssequence s (Scost l Sskip), gen〉. |
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63 | |
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64 | definition add_cost_expr : expr → universe CostTag → expr × (universe CostTag) ≝ |
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65 | λe,gen. |
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66 | let 〈l,gen〉 ≝ fresh … gen in |
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67 | 〈Expr (Ecost l e) (typeof e), gen〉. |
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68 | |
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69 | definition const_int : nat → expr ≝ |
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70 | λn. Expr (Econst_int ? (repr I32 n)) (Tint I32 Signed). |
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71 | |
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72 | let rec label_expr (e:expr) (costgen:universe CostTag) |
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73 | on e : expr × (universe CostTag) ≝ |
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74 | match e with |
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75 | [ Expr ed ty ⇒ let 〈ed,costgen〉 ≝ label_expr_descr ed costgen ty in |
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76 | 〈Expr ed ty, costgen〉 |
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77 | ] |
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78 | and label_expr_descr (e:expr_descr) (costgen:universe CostTag) (ty:type) |
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79 | on e : expr_descr × (universe CostTag) ≝ |
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80 | match e with |
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81 | [ Ederef e' ⇒ |
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82 | let 〈e',costgen〉 ≝ label_expr e' costgen in |
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83 | 〈Ederef e', costgen〉 |
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84 | | Eaddrof e' ⇒ |
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85 | let 〈e',costgen〉 ≝ label_expr e' costgen in |
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86 | 〈Eaddrof e', costgen〉 |
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87 | | Eunop op e' ⇒ |
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88 | let 〈e',costgen〉 ≝ label_expr e' costgen in |
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89 | 〈Eunop op e', costgen〉 |
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90 | | Ebinop op e1 e2 ⇒ |
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91 | let 〈e1,costgen〉 ≝ label_expr e1 costgen in |
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92 | let 〈e2,costgen〉 ≝ label_expr e2 costgen in |
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93 | 〈Ebinop op e1 e2, costgen〉 |
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94 | | Ecast ty e' ⇒ |
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95 | let 〈e',costgen〉 ≝ label_expr e' costgen in |
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96 | 〈Ecast ty e', costgen〉 |
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97 | | Econdition e' e1 e2 ⇒ |
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98 | let 〈e',costgen〉 ≝ label_expr e' costgen in |
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99 | let 〈e1,costgen〉 ≝ label_expr e1 costgen in |
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100 | let 〈e1,costgen〉 ≝ add_cost_expr e1 costgen in |
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101 | let 〈e2,costgen〉 ≝ label_expr e2 costgen in |
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102 | let 〈e2,costgen〉 ≝ add_cost_expr e2 costgen in |
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103 | 〈Econdition e' e1 e2, costgen〉 |
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104 | (* andbool and orbool are changed to conditionals to capture their |
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105 | short-circuiting cost difference; note that we have to return 0 or 1 *) |
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106 | | Eandbool e1 e2 ⇒ |
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107 | let 〈e1,costgen〉 ≝ label_expr e1 costgen in |
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108 | let 〈e2,costgen〉 ≝ label_expr e2 costgen in |
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109 | let 〈e2,costgen〉 ≝ add_cost_expr (Expr (Econdition e2 (const_int 1) (const_int 0)) ty) costgen in |
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110 | let 〈ef,costgen〉 ≝ add_cost_expr (const_int 0) costgen in |
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111 | 〈Econdition e1 e2 ef, costgen〉 |
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112 | | Eorbool e1 e2 ⇒ |
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113 | let 〈e1,costgen〉 ≝ label_expr e1 costgen in |
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114 | let 〈et,costgen〉 ≝ add_cost_expr (const_int 1) costgen in |
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115 | let 〈e2,costgen〉 ≝ label_expr e2 costgen in |
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116 | let 〈e2,costgen〉 ≝ add_cost_expr (Expr (Econdition e2 (const_int 1) (const_int 0)) ty) costgen in |
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117 | 〈Econdition e1 et e2, costgen〉 |
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118 | |
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119 | | Efield e' id ⇒ |
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120 | let 〈e',costgen〉 ≝ label_expr e' costgen in |
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121 | 〈Efield e' id, costgen〉 |
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122 | (* The prototype asserts on preexisting cost labels, but I'd quite like to |
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123 | keep them. *) |
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124 | | Ecost l e' ⇒ |
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125 | let 〈e',costgen〉 ≝ label_expr e' costgen in |
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126 | 〈Ecost l e', costgen〉 |
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127 | |
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128 | (* The remaining expressions don't have subexpressions. *) |
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129 | | _ ⇒ 〈e,costgen〉 |
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130 | ]. |
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131 | |
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132 | let rec label_exprs (l:list expr) (costgen:universe CostTag) |
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133 | on l : list expr × (universe CostTag) ≝ |
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134 | match l with |
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135 | [ nil ⇒ 〈nil ?,costgen〉 |
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136 | | cons e es ⇒ |
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137 | let 〈e,costgen〉 ≝ label_expr e costgen in |
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138 | let 〈es,costgen〉 ≝ label_exprs es costgen in |
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139 | 〈e::es,costgen〉 |
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140 | ]. |
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141 | |
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142 | definition label_opt_expr ≝ |
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143 | λoe,costgen. match oe with |
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144 | [ None ⇒ 〈None ?, costgen〉 |
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145 | | Some e ⇒ let 〈e,costgen〉 ≝ label_expr e costgen in 〈Some ? e,costgen〉 |
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146 | ]. |
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147 | |
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148 | definition ensure_label : option costlabel → universe CostTag → costlabel × (universe CostTag) ≝ |
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149 | λo,u. |
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150 | match o with |
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151 | [ Some cl ⇒ 〈cl,u〉 |
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152 | | None ⇒ fresh … u |
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153 | ]. |
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154 | |
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155 | |
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156 | let rec label_statement (s:statement) (costgen:universe CostTag) |
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157 | on s : statement × (universe CostTag) ≝ |
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158 | match s with |
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159 | [ Sskip ⇒ 〈Sskip,costgen〉 |
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160 | | Sassign e1 e2 ⇒ |
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161 | let 〈e1,costgen〉 ≝ label_expr e1 costgen in |
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162 | let 〈e2,costgen〉 ≝ label_expr e2 costgen in |
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163 | 〈Sassign e1 e2, costgen〉 |
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164 | | Scall e_ret e_fn e_args ⇒ |
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165 | let 〈e_ret,costgen〉 ≝ label_opt_expr e_ret costgen in |
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166 | let 〈e_fn,costgen〉 ≝ label_expr e_fn costgen in |
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167 | let 〈e_args,costgen〉 ≝ label_exprs e_args costgen in |
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168 | 〈Scall e_ret e_fn e_args, costgen〉 |
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169 | | Ssequence s1 s2 ⇒ |
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170 | let 〈s1,costgen〉 ≝ label_statement s1 costgen in |
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171 | let 〈s2,costgen〉 ≝ label_statement s2 costgen in |
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172 | 〈Ssequence s1 s2, costgen〉 |
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173 | | Sifthenelse e s1 s2 ⇒ |
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174 | let 〈e,costgen〉 ≝ label_expr e costgen in |
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175 | let 〈s1,costgen〉 ≝ label_statement s1 costgen in |
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176 | let 〈s1,costgen〉 ≝ add_cost_before s1 costgen in |
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177 | let 〈s2,costgen〉 ≝ label_statement s2 costgen in |
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178 | let 〈s2,costgen〉 ≝ add_cost_before s2 costgen in |
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179 | 〈Sifthenelse e s1 s2, costgen〉 |
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180 | | Swhile e s' cl ⇒ |
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181 | let 〈e,costgen〉 ≝ label_expr e costgen in |
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182 | let 〈s',costgen〉 ≝ label_statement s' costgen in |
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183 | let 〈s',costgen〉 ≝ add_cost_before s' costgen in |
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184 | let 〈after,costgen〉 ≝ ensure_label cl costgen in |
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185 | 〈Swhile e s' (Some ? after), costgen〉 |
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186 | | Sdowhile e s' ⇒ |
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187 | let 〈e,costgen〉 ≝ label_expr e costgen in |
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188 | let 〈s',costgen〉 ≝ label_statement s' costgen in |
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189 | let 〈s',costgen〉 ≝ add_cost_before s' costgen in |
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190 | let 〈s,costgen〉 ≝ add_cost_after (Sdowhile e s') costgen in |
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191 | 〈s,costgen〉 |
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192 | | Sfor s1 e s2 s3 ⇒ |
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193 | let 〈e,costgen〉 ≝ label_expr e costgen in |
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194 | let 〈s1,costgen〉 ≝ label_statement s1 costgen in |
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195 | let 〈s2,costgen〉 ≝ label_statement s2 costgen in |
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196 | let 〈s3,costgen〉 ≝ label_statement s3 costgen in |
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197 | let 〈s3,costgen〉 ≝ add_cost_before s3 costgen in |
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198 | let 〈s,costgen〉 ≝ add_cost_after (Sfor s1 e s2 s3) costgen in |
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199 | 〈s,costgen〉 |
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200 | | Sbreak ⇒ 〈Sbreak,costgen〉 |
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201 | | Scontinue ⇒ 〈Scontinue,costgen〉 |
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202 | | Sreturn opt_e ⇒ |
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203 | let 〈opt_e,costgen〉 ≝ label_opt_expr opt_e costgen in |
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204 | 〈Sreturn opt_e,costgen〉 |
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205 | | Sswitch e ls ⇒ |
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206 | let 〈e,costgen〉 ≝ label_expr e costgen in |
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207 | let 〈ls,costgen〉 ≝ label_lstatements ls costgen in |
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208 | 〈Sswitch e ls, costgen〉 |
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209 | | Slabel l s' ⇒ |
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210 | let 〈s',costgen〉 ≝ label_statement s' costgen in |
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211 | let 〈s',costgen〉 ≝ add_cost_before s' costgen in |
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212 | 〈Slabel l s', costgen〉 |
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213 | | Sgoto l ⇒ 〈Sgoto l, costgen〉 |
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214 | |
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215 | (* The prototype asserts on preexisting cost labels, but I'd quite like to |
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216 | keep them. *) |
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217 | | Scost l s' ⇒ |
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218 | let 〈s',costgen〉 ≝ label_statement s' costgen in |
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219 | 〈Scost l s', costgen〉 |
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220 | ] |
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221 | and label_lstatements (ls:labeled_statements) (costgen:universe CostTag) |
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222 | on ls : labeled_statements × (universe CostTag) ≝ |
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223 | match ls with |
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224 | [ LSdefault s ⇒ |
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225 | let 〈s,costgen〉 ≝ label_statement s costgen in |
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226 | let 〈s,costgen〉 ≝ add_cost_before s costgen in |
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227 | 〈LSdefault s, costgen〉 |
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228 | | LScase sz i s ls' ⇒ |
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229 | let 〈s,costgen〉 ≝ label_statement s costgen in |
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230 | let 〈s,costgen〉 ≝ add_cost_before s costgen in |
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231 | let 〈ls',costgen〉 ≝ label_lstatements ls' costgen in |
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232 | 〈LScase sz i s ls', costgen〉 |
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233 | ]. |
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234 | |
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235 | definition label_function : universe CostTag → function → function × (universe CostTag) ≝ |
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236 | λcostgen,f. |
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237 | let 〈body,costgen〉 ≝ label_statement (fn_body f) costgen in |
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238 | let 〈body,costgen〉 ≝ add_cost_before body costgen in |
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239 | 〈mk_function (fn_return f) (fn_params f) (fn_vars f) body, costgen〉. |
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240 | |
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241 | definition label_fundef : universe CostTag → clight_fundef → clight_fundef × (universe CostTag) ≝ |
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242 | λgen,f. match f with |
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243 | [ CL_Internal f ⇒ |
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244 | let 〈f',gen'〉 ≝ label_function gen f in |
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245 | 〈CL_Internal f', gen'〉 |
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246 | | CL_External id args ty ⇒ 〈CL_External id args ty, gen〉 |
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247 | ]. |
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248 | |
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249 | |
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250 | |
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251 | definition clight_label : clight_program → clight_program × costlabel ≝ |
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252 | λp. |
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253 | let costgen ≝ new_universe CostTag in |
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254 | let 〈init_cost, costgen〉 ≝ fresh … costgen in |
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255 | 〈\fst (transform_program_gen … costgen p (λ_.label_fundef)), init_cost〉. |
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