1 | |
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2 | (* Replace initialisation of global variables with equivalent Cminor code. *) |
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3 | |
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4 | include "Cminor/syntax.ma". |
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5 | include "common/Globalenvs.ma". |
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6 | |
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7 | (* XXX having to specify the return type in the match is annoying. *) |
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8 | definition init_expr : init_data → option (𝚺t:typ. expr t) ≝ |
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9 | λinit. |
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10 | match init return λ_.option (𝚺t:typ. expr t) with |
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11 | [ Init_int8 i ⇒ Some ? (mk_DPair ?? (ASTint I8 Unsigned) (Cst ? (Ointconst I8 i))) |
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12 | | Init_int16 i ⇒ Some ? (mk_DPair ?? (ASTint I16 Unsigned) (Cst ? (Ointconst I16 i))) |
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13 | | Init_int32 i ⇒ Some ? (mk_DPair ?? (ASTint I32 Unsigned) (Cst ? (Ointconst I32 i))) |
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14 | | Init_float32 f ⇒ Some ? (mk_DPair ?? (ASTfloat F32) (Cst ? (Ofloatconst f))) |
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15 | | Init_float64 f ⇒ Some ? (mk_DPair ?? (ASTfloat F64) (Cst ? (Ofloatconst f))) |
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16 | | Init_space n ⇒ None ? |
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17 | | Init_null r ⇒ Some ? (mk_DPair ?? (ASTptr r) (Op1 (ASTint I8 Unsigned) ? (Optrofint ?? r) (Cst ? (Ointconst I8 (zero ?))))) |
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18 | | Init_addrof r id off ⇒ Some ? (mk_DPair ?? (ASTptr r) (Cst ? (Oaddrsymbol id off))) |
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19 | ]. |
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20 | |
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21 | (* None of the additional code introduces locals or labels. *) |
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22 | definition stmt_inv : stmt → Prop ≝ |
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23 | stmt_P (λs. stmt_vars (λ_.λ_.False) s ∧ stmt_labels (λ_.False) s). |
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24 | |
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25 | discriminator option. |
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26 | discriminator DPair. |
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27 | |
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28 | (* Produces a few extra skips - hopefully the compiler will optimise these |
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29 | away. *) |
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30 | |
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31 | definition init_datum : ident → region → init_data → nat (*offset*) → Σs:stmt. stmt_inv s ≝ |
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32 | λid,r,init,off. |
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33 | match init_expr init with |
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34 | [ None ⇒ St_skip |
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35 | | Some x ⇒ |
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36 | match x with [ mk_DPair t e ⇒ |
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37 | St_store t r (Cst ? (Oaddrsymbol id off)) e |
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38 | ] |
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39 | ]. |
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40 | % // |
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41 | cases init in p; [ 8: #a #b ] #c #p normalize in p; |
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42 | destruct;/2/ |
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43 | qed. |
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44 | |
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45 | definition init_var : ident → region → list init_data → Σs:stmt. stmt_inv s ≝ |
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46 | λid,r,init. |
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47 | \snd (foldr ?? |
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48 | (λdatum,os. |
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49 | let 〈off,s〉 ≝ os in |
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50 | 〈off + (size_init_data datum), St_seq (init_datum id r datum off) s〉) |
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51 | 〈0, mk_Sig ? (λx.stmt_inv x) St_skip ?〉 init). |
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52 | [ % // |
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53 | | elim init |
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54 | [ % // |
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55 | | #h #t #IH whd in ⊢ (?(???%)); @breakup_pair whd in ⊢ (?%); % [ % [ % // | @(pi2 … (init_datum …)) ] | @IH ] |
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56 | ] qed. |
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57 | |
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58 | definition init_vars : list (ident × region × (list init_data)) → Σs:stmt. stmt_inv s ≝ |
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59 | λvars. foldr ? (Σs:stmt. stmt_inv s) |
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60 | (λvar,s. mk_Sig ? (λx.stmt_inv x ) (St_seq s (init_var (\fst (\fst var)) (\snd (\fst var)) (\snd var))) ?) (mk_Sig ? (λx.stmt_inv x ) St_skip (conj ?? I I)) vars. |
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61 | % [ % [ % // | @(pi2 … s) ] | @(pi2 … (init_var …)) ] |
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62 | qed. |
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63 | |
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64 | lemma no_labels : ∀s. stmt_inv s → labels_of s = [ ]. |
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65 | #s elim s // |
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66 | [ #s1 #s2 #IH1 #IH2 * * * #_ #_ #H1 #H2 whd in ⊢ (??%?); |
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67 | >(IH1 H1) >(IH2 H2) @refl |
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68 | | #sz #sg #e #s1 #s2 #IH1 #IH2 * * * #_ #_ #H1 #H2 whd in ⊢ (??%?); |
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69 | >(IH1 H1) >(IH2 H2) @refl |
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70 | | #s #IH * * #_ #_ #H @(IH H) |
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71 | | #s #IH * * #_ #_ #H @(IH H) |
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72 | | #l #s #IH * * #_ * |
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73 | | #l #s #IH * * #_ #_ #H @(IH H) |
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74 | ] qed. |
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75 | |
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76 | definition add_statement : ident → (Σs:stmt. stmt_inv s) → |
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77 | list (ident × (fundef internal_function)) → |
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78 | list (ident × (fundef internal_function)) ≝ |
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79 | λid,s. match s with [ mk_Sig s H ⇒ |
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80 | map ?? |
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81 | (λidf. |
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82 | let 〈id',f'〉 ≝ idf in |
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83 | match ident_eq id id' with |
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84 | [ inl _ ⇒ |
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85 | match f' with |
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86 | [ Internal f ⇒ 〈id, Internal ? (mk_internal_function |
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87 | (f_return f) |
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88 | (f_params f) |
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89 | (f_vars f) |
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90 | (f_distinct f) |
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91 | (f_stacksize f) |
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92 | (St_seq s (f_body f)) |
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93 | ?)〉 |
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94 | | External f ⇒ 〈id, External ? f〉 (* Error ? *) |
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95 | ] |
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96 | | inr _ ⇒ 〈id',f'〉 ]) ]. |
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97 | % |
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98 | [ % [ % // | |
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99 | @(stmt_P_mp … H) #s * #V #L % |
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100 | [ @(stmt_vars_mp … V) #i #t * |
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101 | | @(stmt_labels_mp … L) #l * |
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102 | ] |
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103 | ] |
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104 | | whd in ⊢ (?(λ_.??(?(λ_.???%)?))?); >(no_labels … H) @(f_inv f) |
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105 | ] qed. |
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106 | |
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107 | definition empty_vars : list (ident × region × (list init_data)) → |
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108 | list (ident × region × nat) ≝ |
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109 | map ?? (λv. 〈〈\fst (\fst v), \snd (\fst v)〉, |
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110 | size_init_data_list (\snd v)〉). |
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111 | |
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112 | definition replace_init : Cminor_program → Cminor_noinit_program ≝ |
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113 | λp. |
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114 | mk_program ?? |
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115 | (empty_vars (prog_vars ?? p)) |
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116 | (add_statement (prog_main ?? p) (init_vars (prog_vars ?? p)) (prog_funct ?? p)) |
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117 | (prog_main ?? p). |
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