[789] | 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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[1071] | 4 | include "common/FrontEndOps.ma". |
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[789] | 5 | include "common/Graphs.ma". |
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| 6 | |
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| 7 | definition add_graph ≝ |
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[793] | 8 | λl: label. |
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[789] | 9 | λstmt. |
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[793] | 10 | λp. |
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| 11 | let rtl_if_luniverse' ≝ rtl_if_luniverse p in |
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| 12 | let rtl_if_runiverse' ≝ rtl_if_runiverse p in |
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| 13 | let rtl_if_result' ≝ rtl_if_result p in |
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| 14 | let rtl_if_params' ≝ rtl_if_params p in |
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| 15 | let rtl_if_locals' ≝ rtl_if_locals p in |
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| 16 | let rtl_if_stacksize' ≝ rtl_if_stacksize p in |
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| 17 | let rtl_if_graph' ≝ add ? ? (rtl_if_graph p) l stmt in |
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| 18 | let rtl_if_entry' ≝ rtl_if_entry p in |
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| 19 | let rtl_if_exit' ≝ rtl_if_exit p in |
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[1068] | 20 | mk_rtl_internal_function rtl_if_luniverse' rtl_if_runiverse' |
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[793] | 21 | rtl_if_params' rtl_if_params' rtl_if_locals' |
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[1071] | 22 | rtl_if_stacksize' rtl_if_graph' ? ?. |
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| 23 | [1: cases(rtl_if_entry') |
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[1073] | 24 | #LABEL #HYP % |
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[1071] | 25 | [1: @LABEL |
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| 26 | |2: cases(HYP) |
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[1077] | 27 | generalize in match (graph_add_lookup ? (rtl_if_graph p) LABEL stmt l); |
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| 28 | normalize nodelta; |
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[1073] | 29 | /2/ |
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[1071] | 30 | ] |
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[1073] | 31 | |2: cases(rtl_if_exit') |
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| 32 | #LABEL #HYP % |
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| 33 | [1: @LABEL |
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| 34 | |2: cases(HYP) |
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[1077] | 35 | generalize in match (graph_add_lookup ? (rtl_if_graph p) LABEL stmt l); |
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| 36 | normalize nodelta; |
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[1073] | 37 | /2/ |
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| 38 | ] |
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| 39 | ] |
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| 40 | qed. |
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[789] | 41 | |
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[1057] | 42 | definition fresh_label: rtl_internal_function → rtl_internal_function × label ≝ |
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[789] | 43 | λdef. |
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[1057] | 44 | let 〈lbl, new_univ〉 ≝ fresh LabelTag (rtl_if_luniverse def) in |
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| 45 | let locals ≝ rtl_if_locals def in |
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| 46 | let rtl_if_luniverse' ≝ new_univ in |
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| 47 | let rtl_if_runiverse' ≝ rtl_if_runiverse def in |
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| 48 | let rtl_if_result' ≝ rtl_if_result def in |
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| 49 | let rtl_if_params' ≝ rtl_if_params def in |
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| 50 | let rtl_if_locals' ≝ rtl_if_locals def in |
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| 51 | let rtl_if_stacksize' ≝ rtl_if_stacksize def in |
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| 52 | let rtl_if_graph' ≝ rtl_if_graph def in |
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| 53 | let rtl_if_entry' ≝ rtl_if_entry def in |
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| 54 | let rtl_if_exit' ≝ rtl_if_exit def in |
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| 55 | 〈mk_rtl_internal_function |
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[1068] | 56 | rtl_if_luniverse' rtl_if_runiverse' rtl_if_result' |
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[1057] | 57 | rtl_if_params' rtl_if_locals' rtl_if_stacksize' rtl_if_graph' |
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| 58 | rtl_if_entry' rtl_if_exit', lbl〉. |
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[789] | 59 | |
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[1047] | 60 | axiom register_fresh: universe RegisterTag → register. |
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[789] | 61 | |
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[1047] | 62 | definition fresh_reg: rtl_internal_function → rtl_internal_function × register ≝ |
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| 63 | λdef. |
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| 64 | let r ≝ register_fresh (rtl_if_runiverse def) in |
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| 65 | let locals ≝ r :: rtl_if_locals def in |
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| 66 | let rtl_if_luniverse' ≝ rtl_if_luniverse def in |
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| 67 | let rtl_if_runiverse' ≝ rtl_if_runiverse def in |
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| 68 | let rtl_if_result' ≝ rtl_if_result def in |
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| 69 | let rtl_if_params' ≝ rtl_if_params def in |
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| 70 | let rtl_if_locals' ≝ locals in |
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| 71 | let rtl_if_stacksize' ≝ rtl_if_stacksize def in |
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| 72 | let rtl_if_graph' ≝ rtl_if_graph def in |
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| 73 | let rtl_if_entry' ≝ rtl_if_entry def in |
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| 74 | let rtl_if_exit' ≝ rtl_if_exit def in |
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| 75 | 〈mk_rtl_internal_function |
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[1068] | 76 | rtl_if_luniverse' rtl_if_runiverse' rtl_if_result' |
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[1047] | 77 | rtl_if_params' rtl_if_locals' rtl_if_stacksize' rtl_if_graph' |
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| 78 | rtl_if_entry' rtl_if_exit', r〉. |
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| 79 | |
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[793] | 80 | let rec fresh_regs (def: rtl_internal_function) (n: nat) on n ≝ |
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[789] | 81 | match n with |
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| 82 | [ O ⇒ 〈def, [ ]〉 |
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| 83 | | S n ⇒ |
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| 84 | let 〈def, res〉 ≝ fresh_regs def n in |
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| 85 | let 〈def, r〉 ≝ fresh_reg def in |
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| 86 | 〈def, r :: res〉 |
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| 87 | ]. |
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| 88 | |
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[1063] | 89 | axiom fresh_regs_length: |
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| 90 | ∀def: rtl_internal_function. |
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| 91 | ∀n: nat. |
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| 92 | |(\snd (fresh_regs def n))| = n. |
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| 93 | |
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[789] | 94 | definition addr_regs ≝ |
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| 95 | λregs. |
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| 96 | match regs with |
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| 97 | [ cons hd tl ⇒ |
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| 98 | match tl with |
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| 99 | [ cons hd' tl' ⇒ Some (register × register) 〈hd, hd'〉 |
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| 100 | | nil ⇒ None (register × register) |
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| 101 | ] |
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[1047] | 102 | | nil ⇒ None (register × register) (* registers are not an address *) |
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[789] | 103 | ]. |
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| 104 | |
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[1047] | 105 | let rec register_freshes (runiverse: universe RegisterTag) (n: nat) on n ≝ |
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| 106 | match n with |
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| 107 | [ O ⇒ [ ] |
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| 108 | | S n' ⇒ register_fresh runiverse :: (register_freshes runiverse n') |
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| 109 | ]. |
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| 110 | |
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| 111 | definition choose_rest ≝ |
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| 112 | λA: Type[0]. |
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| 113 | λleft, right: list A. |
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[1061] | 114 | λprfl: 0 < |left|. |
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| 115 | λprfr: 0 < |right|. |
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| 116 | match left return λx. 0 < |x| → list A with |
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| 117 | [ nil ⇒ λnil_prf. |
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| 118 | match right return λx. 0 < |x| → list A with |
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| 119 | [ nil ⇒ λnil_nil_absrd. ? |
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| 120 | | _ ⇒ λnil_cons_prf. right |
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| 121 | ] prfr |
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| 122 | | _ ⇒ λcons_prf. right |
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| 123 | ] prfl. |
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| 124 | normalize in nil_prf; |
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| 125 | cases(not_le_Sn_O 0) |
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| 126 | #HYP |
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| 127 | cases(HYP nil_prf) |
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| 128 | qed. |
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[1047] | 129 | |
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| 130 | definition complete_regs ≝ |
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| 131 | λdef. |
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| 132 | λsrcrs1. |
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| 133 | λsrcrs2. |
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| 134 | let nb_added ≝ abs ((length ? srcrs1) - (length ? srcrs2)) in |
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| 135 | let 〈def, added_regs〉 ≝ fresh_regs def nb_added in |
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| 136 | if gtb nb_added 0 then |
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| 137 | 〈〈srcrs1, srcrs2 @ added_regs〉, added_regs〉 |
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| 138 | else |
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| 139 | 〈〈srcrs1 @ added_regs, srcrs2〉, added_regs〉. |
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| 140 | |
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[1064] | 141 | (* obvious, but proof doesn't look easy! *) |
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| 142 | axiom complete_regs_length: |
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| 143 | ∀def. |
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| 144 | ∀left. |
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| 145 | ∀right. |
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| 146 | |\fst (\fst (complete_regs def left right))| = |\snd (\fst (complete_regs def left right))|. |
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| 147 | |
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[1053] | 148 | definition size_of_sig_type ≝ |
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[1052] | 149 | λsig. |
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| 150 | match sig with |
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[1047] | 151 | [ ASTint isize sign ⇒ |
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[1053] | 152 | let isize' ≝ match isize with [ I8 ⇒ 8 | I16 ⇒ 16 | I32 ⇒ 32 ] in |
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| 153 | isize' ÷ (nat_of_bitvector ? int_size) |
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| 154 | | ASTfloat _ ⇒ ? (* dpm: not implemented *) |
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| 155 | | ASTptr rgn ⇒ nat_of_bitvector ? ptr_size |
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[1047] | 156 | ]. |
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[1053] | 157 | cases not_implemented; |
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[1052] | 158 | qed. |
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[1047] | 159 | |
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[789] | 160 | inductive register_type: Type[0] ≝ |
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| 161 | | register_int: register → register_type |
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| 162 | | register_ptr: register → register → register_type. |
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| 163 | |
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[1052] | 164 | definition local_env ≝ BitVectorTrie (list register). |
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[789] | 165 | |
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[1052] | 166 | definition mem_local_env ≝ |
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| 167 | λr: register. |
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| 168 | match r with |
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| 169 | [ an_identifier w ⇒ member (list register) 16 w |
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| 170 | ]. |
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| 171 | |
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| 172 | definition add_local_env ≝ |
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| 173 | λr: register. |
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| 174 | match r with |
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| 175 | [ an_identifier w ⇒ insert (list register) 16 w |
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| 176 | ]. |
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| 177 | |
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| 178 | definition find_local_env ≝ |
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| 179 | λr: register. |
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| 180 | λbvt. |
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| 181 | match r with |
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| 182 | [ an_identifier w ⇒ lookup (list register) 16 w bvt [ ] |
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| 183 | ]. |
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| 184 | |
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[789] | 185 | definition initialize_local_env_internal ≝ |
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| 186 | λruniverse. |
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| 187 | λlenv. |
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[1053] | 188 | λr_sig. |
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| 189 | let 〈r, sig〉 ≝ r_sig in |
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| 190 | let size ≝ size_of_sig_type sig in |
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| 191 | let rs ≝ register_freshes runiverse size in |
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| 192 | add_local_env r rs lenv. |
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[789] | 193 | |
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| 194 | definition initialize_local_env ≝ |
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| 195 | λruniverse. |
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| 196 | λregisters. |
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[1053] | 197 | λresult. |
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[1050] | 198 | let registers ≝ registers @ |
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| 199 | match result with |
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| 200 | [ None ⇒ [ ] |
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| 201 | | Some rt ⇒ [ rt ] |
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| 202 | ] |
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| 203 | in |
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[1053] | 204 | foldl ? ? (initialize_local_env_internal runiverse) (Stub …) registers. |
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[1050] | 205 | |
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| 206 | definition map_list_local_env_internal ≝ |
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| 207 | λlenv. |
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| 208 | λres. |
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| 209 | λr. |
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| 210 | res @ (find_local_env r lenv). |
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| 211 | |
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| 212 | definition map_list_local_env ≝ |
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| 213 | λlenv. |
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| 214 | λregs. |
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[1053] | 215 | foldl ? ? (map_list_local_env_internal lenv) [ ] regs. |
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[1050] | 216 | |
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[1053] | 217 | definition make_addr ≝ |
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| 218 | λA. |
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| 219 | λlst: list A. |
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[1066] | 220 | λprf: 2 ≤ length A lst. |
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| 221 | match lst return λx. 2 ≤ |x| → A × A with |
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[1053] | 222 | [ nil ⇒ λlst_nil_prf. ? |
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| 223 | | cons hd tl ⇒ λprf. |
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[1066] | 224 | match tl return λx. 1 ≤ |x| → A × A with |
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[1053] | 225 | [ nil ⇒ λtl_nil_prf. ? |
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| 226 | | cons hd' tl' ⇒ λtl_cons_prf. 〈hd, hd'〉 |
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| 227 | ] ? |
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| 228 | ] prf. |
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| 229 | [1: normalize in lst_nil_prf; |
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[1066] | 230 | cases(not_le_Sn_O 1); |
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| 231 | #HYP cases(HYP lst_nil_prf) |
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[1053] | 232 | |2: normalize in prf; |
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[1066] | 233 | @le_S_S_to_le |
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| 234 | assumption |
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[1053] | 235 | |3: normalize in tl_nil_prf; |
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[1066] | 236 | cases(not_le_Sn_O 0) |
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| 237 | #HYP cases(HYP tl_nil_prf) |
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[1053] | 238 | ] |
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| 239 | qed. |
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[1050] | 240 | |
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[789] | 241 | definition find_and_addr ≝ |
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| 242 | λr. |
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| 243 | λlenv. |
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[1053] | 244 | make_addr ? (find_local_env r lenv). |
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[789] | 245 | |
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| 246 | definition rtl_args ≝ |
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| 247 | λregs_list. |
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| 248 | λlenv. |
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[1053] | 249 | flatten ? (map ? ? ( |
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| 250 | λr. find_local_env r lenv) regs_list). |
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[789] | 251 | |
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| 252 | definition change_label ≝ |
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| 253 | λlbl. |
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[793] | 254 | λstmt: rtl_statement. |
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[789] | 255 | match stmt with |
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| 256 | [ rtl_st_skip _ ⇒ rtl_st_skip lbl |
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| 257 | | rtl_st_cost cost_lbl _ ⇒ rtl_st_cost cost_lbl lbl |
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| 258 | | rtl_st_addr r1 r2 id _ ⇒ rtl_st_addr r1 r2 id lbl |
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| 259 | | rtl_st_stack_addr r1 r2 _ ⇒ rtl_st_stack_addr r1 r2 lbl |
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| 260 | | rtl_st_int r i _ ⇒ rtl_st_int r i lbl |
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| 261 | | rtl_st_move r1 r2 _ ⇒ rtl_st_move r1 r2 lbl |
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[1060] | 262 | | rtl_st_opaccs opaccs d s1 s2 s3 _ ⇒ rtl_st_opaccs opaccs d s1 s2 s3 lbl |
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[789] | 263 | | rtl_st_op1 op1 d s _ ⇒ rtl_st_op1 op1 d s lbl |
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| 264 | | rtl_st_op2 op2 d s1 s2 _ ⇒ rtl_st_op2 op2 d s1 s2 lbl |
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| 265 | | rtl_st_load d a1 a2 _ ⇒ rtl_st_load d a1 a2 lbl |
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| 266 | | rtl_st_store a1 a2 s _ ⇒ rtl_st_store a1 a2 s lbl |
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| 267 | | rtl_st_call_id f a r _ ⇒ rtl_st_call_id f a r lbl |
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| 268 | | rtl_st_call_ptr f1 f2 a r _ ⇒ rtl_st_call_ptr f1 f2 a r lbl |
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| 269 | | rtl_st_tailcall_id f a ⇒ rtl_st_tailcall_id f a |
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| 270 | | rtl_st_tailcall_ptr f1 f2 a ⇒ rtl_st_tailcall_ptr f1 f2 a |
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[1066] | 271 | | rtl_st_cond r l1 l2 ⇒ rtl_st_cond r l1 l2 |
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[1060] | 272 | | rtl_st_clear_carry l ⇒ rtl_st_clear_carry lbl |
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| 273 | | rtl_st_set_carry l ⇒ rtl_st_set_carry lbl |
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[1068] | 274 | | rtl_st_return ⇒ rtl_st_return |
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[789] | 275 | ]. |
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| 276 | |
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[1053] | 277 | (* Ack! Should generating a fresh label ever fail? This seems to be a side-effect |
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| 278 | of implementing everything as a bitvector, which is bounded. If we implemented |
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| 279 | labels as unbounded nats then this function will never fail. |
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| 280 | *) |
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[1057] | 281 | (* Fixed with changes to label generation. |
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| 282 | *) |
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[793] | 283 | let rec adds_graph (stmt_list: ?) (start_lbl: label) (dest_lbl: label) (def: rtl_internal_function) ≝ |
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[789] | 284 | match stmt_list with |
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[1057] | 285 | [ nil ⇒ def |
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[789] | 286 | | cons hd tl ⇒ |
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| 287 | match tl with |
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[1057] | 288 | [ nil ⇒ add_graph start_lbl (change_label dest_lbl hd) def |
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[793] | 289 | | cons hd' tl' ⇒ |
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[1057] | 290 | let 〈new_def, tmp_lbl〉 ≝ fresh_label def in |
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| 291 | let stmt ≝ change_label tmp_lbl hd in |
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| 292 | let def ≝ add_graph start_lbl stmt new_def in |
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| 293 | adds_graph tl tmp_lbl dest_lbl new_def |
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[789] | 294 | ] |
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| 295 | ]. |
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[1053] | 296 | |
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[793] | 297 | let rec add_translates (translate_list: ?) (start_lbl: label) (dest_lbl: label) |
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| 298 | (def: ?) on translate_list ≝ |
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| 299 | match translate_list with |
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[1057] | 300 | [ nil ⇒ def |
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[793] | 301 | | cons hd tl ⇒ |
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| 302 | match tl with |
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[795] | 303 | [ nil ⇒ hd start_lbl dest_lbl def |
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[793] | 304 | | cons hd' tl' ⇒ |
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[1057] | 305 | let 〈new_def, tmp_lbl〉 ≝ fresh_label def in |
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| 306 | let applied ≝ hd start_lbl tmp_lbl new_def in |
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| 307 | add_translates tl tmp_lbl dest_lbl applied |
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[793] | 308 | ] |
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| 309 | ]. |
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[789] | 310 | |
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[1057] | 311 | definition translate_cst_int_internal ≝ |
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| 312 | λdest_lbl. |
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| 313 | λr. |
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| 314 | λi. |
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| 315 | rtl_st_int r i dest_lbl. |
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| 316 | |
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[1059] | 317 | axiom translate_cst: |
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| 318 | ∀cst: constant. |
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| 319 | ∀destrs: list register. |
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| 320 | ∀start_lbl: label. |
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| 321 | ∀dest_lbl: label. |
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| 322 | ∀def: rtl_internal_function. |
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| 323 | rtl_internal_function. |
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[793] | 324 | |
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[1059] | 325 | definition translate_move_internal ≝ |
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| 326 | λstart_lbl: label. |
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| 327 | λdestr: register. |
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| 328 | λsrcr: register. |
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| 329 | rtl_st_move destr srcr start_lbl. |
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[1057] | 330 | |
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[1059] | 331 | definition translate_move ≝ |
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| 332 | λdestrs: list register. |
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| 333 | λsrcrs: list register. |
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| 334 | λstart_lbl: label. |
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[1071] | 335 | match reduce_strong register register destrs srcrs with |
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[1060] | 336 | [ dp crl_crr len_proof ⇒ |
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| 337 | let commonl ≝ \fst (\fst crl_crr) in |
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| 338 | let commonr ≝ \fst (\snd crl_crr) in |
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| 339 | let restl ≝ \snd (\fst crl_crr) in |
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| 340 | let restr ≝ \snd (\snd crl_crr) in |
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| 341 | let f_common ≝ translate_move_internal start_lbl in |
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| 342 | let translate1 ≝ adds_graph (map2 … f_common commonl commonr ?) in |
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| 343 | let translate2 ≝ translate_cst (Ointconst ? (repr I8 0)) restl in (* should this be 8? *) |
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| 344 | add_translates [ translate1 ; translate2 ] start_lbl |
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| 345 | ]. |
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| 346 | @len_proof |
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| 347 | qed. |
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| 348 | |
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| 349 | let rec make |
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| 350 | (A: Type[0]) (elt: A) (n: nat) on n ≝ |
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| 351 | match n with |
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| 352 | [ O ⇒ [ ] |
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| 353 | | S n' ⇒ elt :: make A elt n' |
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| 354 | ]. |
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| 355 | |
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| 356 | lemma make_length: |
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| 357 | ∀A: Type[0]. |
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| 358 | ∀elt: A. |
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| 359 | ∀n: nat. |
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| 360 | n = length ? (make A elt n). |
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| 361 | #A #ELT #N |
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| 362 | elim N |
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| 363 | [ normalize % |
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| 364 | | #N #IH |
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| 365 | normalize <IH % |
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| 366 | ] |
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| 367 | qed. |
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| 368 | |
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| 369 | definition translate_cast_unsigned ≝ |
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| 370 | λdestrs. |
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| 371 | λstart_lbl. |
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| 372 | λdest_lbl. |
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| 373 | λdef. |
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| 374 | let 〈def, tmp_zero〉 ≝ fresh_reg def in |
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| 375 | let zeros ≝ make ? tmp_zero (length ? destrs) in |
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| 376 | add_translates [ |
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| 377 | adds_graph [ |
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| 378 | rtl_st_int tmp_zero (bitvector_of_nat ? 0) start_lbl |
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| 379 | ]; |
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| 380 | translate_move destrs zeros |
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| 381 | ] start_lbl dest_lbl def. |
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| 382 | |
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| 383 | definition translate_cast_signed ≝ |
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| 384 | λdestrs. |
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| 385 | λsrcr. |
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| 386 | λstart_lbl. |
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| 387 | λdest_lbl. |
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| 388 | λdef. |
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| 389 | let 〈def, tmp_128〉 ≝ fresh_reg def in |
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| 390 | let 〈def, tmp_255〉 ≝ fresh_reg def in |
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| 391 | let 〈def, tmpr〉 ≝ fresh_reg def in |
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| 392 | let 〈def, dummy〉 ≝ fresh_reg def in |
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| 393 | let insts ≝ [ |
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| 394 | rtl_st_int tmp_128 (bitvector_of_nat ? 128) start_lbl; |
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| 395 | rtl_st_op2 And tmpr tmp_128 srcr start_lbl; |
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| 396 | rtl_st_opaccs DivuModu tmpr dummy tmpr tmp_128 start_lbl; |
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| 397 | rtl_st_int tmp_255 (bitvector_of_nat ? 255) start_lbl; |
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| 398 | rtl_st_opaccs Mul tmpr dummy tmpr tmp_255 start_lbl |
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| 399 | ] in |
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| 400 | let srcrs ≝ make ? tmpr (length ? destrs) in |
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| 401 | add_translates [ |
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| 402 | adds_graph insts; |
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| 403 | translate_move destrs srcrs |
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| 404 | ] start_lbl dest_lbl def. |
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| 405 | |
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| 406 | definition translate_cast ≝ |
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| 407 | λsrc_size. |
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| 408 | λsrc_sign. |
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| 409 | λdest_size. |
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| 410 | λdestrs. |
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| 411 | λsrcrs. |
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[1066] | 412 | match |srcrs| return λx. |srcrs| = x → ? with |
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[1060] | 413 | [ O ⇒ λzero_prf. adds_graph [ ] |
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| 414 | | S n' ⇒ λsucc_prf. |
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| 415 | if ltb dest_size src_size then |
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| 416 | translate_move destrs srcrs |
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| 417 | else |
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[1071] | 418 | match reduce_strong register register destrs srcrs with |
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[1060] | 419 | [ dp crl len_proof ⇒ |
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| 420 | let commonl ≝ \fst (\fst crl) in |
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| 421 | let commonr ≝ \fst (\snd crl) in |
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| 422 | let restl ≝ \snd (\fst crl) in |
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| 423 | let restr ≝ \snd (\snd crl) in |
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| 424 | let insts_common ≝ translate_move commonl commonr in |
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| 425 | let sign_reg ≝ last_safe ? srcrs ? in |
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| 426 | let insts_sign ≝ |
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| 427 | match src_sign with |
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| 428 | [ Unsigned ⇒ translate_cast_unsigned restl |
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| 429 | | Signed ⇒ translate_cast_signed restl sign_reg |
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| 430 | ] |
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| 431 | in |
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| 432 | add_translates [ insts_common; insts_sign ] |
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| 433 | ] |
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| 434 | ] (refl ? (|srcrs|)). |
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| 435 | >succ_prf // |
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| 436 | qed. |
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| 437 | |
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| 438 | definition translate_negint ≝ |
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| 439 | λdestrs. |
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| 440 | λsrcrs. |
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| 441 | λstart_lbl. |
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| 442 | λdest_lbl. |
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| 443 | λdef. |
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| 444 | λprf: | destrs | = | srcrs |. (* assert in caml code *) |
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| 445 | let 〈def, tmpr〉 ≝ fresh_reg def in |
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| 446 | let f_cmpl ≝ λdestr. λsrcr. rtl_st_op1 Cmpl destr srcr start_lbl in |
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| 447 | let insts_cmpl ≝ map2 ? ? ? f_cmpl destrs srcrs prf in |
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| 448 | let insts_init ≝ [ |
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| 449 | rtl_st_set_carry start_lbl; |
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| 450 | rtl_st_int tmpr (zero ?) start_lbl |
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| 451 | ] in |
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| 452 | let f_add ≝ λdestr. rtl_st_op2 Addc destr destr tmpr start_lbl in |
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| 453 | let insts_add ≝ map … f_add destrs in |
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| 454 | adds_graph (insts_cmpl @ insts_init @ insts_add) start_lbl dest_lbl def. |
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| 455 | |
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| 456 | definition translate_notbool ≝ |
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| 457 | λdestrs. |
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| 458 | λsrcrs. |
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| 459 | λstart_lbl. |
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| 460 | λdest_lbl. |
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| 461 | λdef. |
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| 462 | match destrs with |
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| 463 | [ nil ⇒ add_graph start_lbl (rtl_st_skip dest_lbl) def |
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| 464 | | cons destr destrs ⇒ |
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| 465 | let 〈def, tmpr〉 ≝ fresh_reg def in |
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| 466 | let 〈def, tmp_srcrs〉 ≝ fresh_regs def (length ? srcrs) in |
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| 467 | let save_srcrs ≝ translate_move tmp_srcrs srcrs in |
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| 468 | let init_destr ≝ rtl_st_int destr (bitvector_of_nat ? 1) start_lbl in |
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| 469 | let f ≝ λtmp_srcr. [ |
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| 470 | rtl_st_clear_carry start_lbl; |
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| 471 | rtl_st_int tmpr (zero ?) start_lbl; |
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| 472 | rtl_st_op2 Sub tmpr tmpr tmp_srcr start_lbl; |
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| 473 | rtl_st_int tmpr (zero ?) start_lbl; |
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| 474 | rtl_st_op2 Addc tmpr tmpr tmpr start_lbl; |
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| 475 | rtl_st_op2 Xor destr destr tmpr start_lbl |
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| 476 | ] in |
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| 477 | let insts ≝ init_destr :: (flatten ? (map … f tmp_srcrs)) in |
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| 478 | let epilogue ≝ translate_cst (Ointconst I8 (bitvector_of_nat ? 0)) destrs in |
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| 479 | add_translates [ |
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| 480 | save_srcrs; adds_graph insts; epilogue |
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| 481 | ] start_lbl dest_lbl def |
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| 482 | ]. |
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| 483 | |
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[1066] | 484 | (* TODO: examine this properly. This is a change from the O'caml code due |
---|
| 485 | to us dropping the explicit use of a cast destination size field. We |
---|
| 486 | instead infer the size of the cast's destination from the context. Is |
---|
| 487 | this correct? |
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| 488 | *) |
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[1064] | 489 | definition translate_op1 ≝ |
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[1066] | 490 | λop1: unary_operation. |
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[1064] | 491 | λdestrs: list register. |
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| 492 | λsrcrs: list register. |
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[1062] | 493 | λprf: |destrs| = |srcrs|. |
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[1064] | 494 | λstart_lbl: label. |
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| 495 | λdest_lbl: label. |
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| 496 | λdef: rtl_internal_function. |
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[1060] | 497 | match op1 with |
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[1066] | 498 | [ Ocastint src_sign src_size ⇒ |
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| 499 | let dest_size ≝ |destrs| * 8 in |
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| 500 | let src_size ≝ bitsize_of_intsize src_size in |
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[1060] | 501 | translate_cast src_size src_sign dest_size destrs srcrs start_lbl dest_lbl def |
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[1066] | 502 | | Onegint ⇒ |
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[1060] | 503 | translate_negint destrs srcrs start_lbl dest_lbl def prf |
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[1066] | 504 | | Onotbool ⇒ |
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[1060] | 505 | translate_notbool destrs srcrs start_lbl dest_lbl def |
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[1066] | 506 | | Onotint ⇒ |
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[1060] | 507 | let f ≝ λdestr. λsrcr. rtl_st_op1 Cmpl destr srcr start_lbl in |
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| 508 | let l ≝ map2 … f destrs srcrs prf in |
---|
| 509 | adds_graph l start_lbl dest_lbl def |
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[1066] | 510 | | Optrofint r ⇒ |
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[1060] | 511 | translate_move destrs srcrs start_lbl dest_lbl def |
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[1066] | 512 | | Ointofptr r ⇒ |
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[1060] | 513 | translate_move destrs srcrs start_lbl dest_lbl def |
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[1066] | 514 | | Oid ⇒ |
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[1060] | 515 | translate_move destrs srcrs start_lbl dest_lbl def |
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[1066] | 516 | | _ ⇒ ? (* float operations implemented in runtime *) |
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[1060] | 517 | ]. |
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[1066] | 518 | cases not_implemented |
---|
| 519 | qed. |
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[1061] | 520 | |
---|
| 521 | definition translate_op ≝ |
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| 522 | λop. |
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| 523 | λdestrs. |
---|
| 524 | λsrcrs1. |
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| 525 | λsrcrs2. |
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| 526 | λstart_lbl. |
---|
| 527 | λdest_lbl. |
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| 528 | λdef. |
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[1071] | 529 | match reduce_strong register register srcrs1 srcrs2 with |
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[1061] | 530 | [ dp reduced first_reduced_proof ⇒ |
---|
| 531 | let srcrsl_common ≝ \fst (\fst reduced) in |
---|
| 532 | let srcrsr_common ≝ \fst (\snd reduced) in |
---|
| 533 | let srcrsl_rest ≝ \snd (\fst reduced) in |
---|
| 534 | let srcrsr_rest ≝ \snd (\snd reduced) in |
---|
| 535 | let srcrs_rest ≝ choose_rest ? srcrsl_rest srcrsr_rest ? ? in |
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[1071] | 536 | match reduce_strong register register destrs srcrsl_common with |
---|
[1061] | 537 | [ dp reduced second_reduced_proof ⇒ |
---|
| 538 | let destrs_common ≝ \fst (\fst reduced) in |
---|
| 539 | let destrs_rest ≝ \snd (\fst reduced) in |
---|
[1071] | 540 | match reduce_strong register register destrs_rest srcrs_rest with |
---|
[1061] | 541 | [ dp reduced third_reduced_proof ⇒ |
---|
| 542 | let destrs_cted ≝ \fst (\fst reduced) in |
---|
| 543 | let destrs_rest ≝ \snd (\fst reduced) in |
---|
| 544 | let srcrs_cted ≝ \fst (\snd reduced) in |
---|
| 545 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
| 546 | let insts_init ≝ [ |
---|
| 547 | rtl_st_clear_carry start_lbl; |
---|
| 548 | rtl_st_int tmpr (zero ?) start_lbl |
---|
| 549 | ] in |
---|
| 550 | let f_add ≝ λdestr. λsrcr1. λsrcr2. rtl_st_op2 op destr srcr1 srcr2 start_lbl in |
---|
| 551 | let insts_add ≝ map3 … f_add destrs_common srcrsl_common srcrsr_common ? ? in |
---|
| 552 | let f_add_cted ≝ λdestr. λsrcr. rtl_st_op2 op destr srcr tmpr start_lbl in |
---|
| 553 | let insts_add_cted ≝ map2 ? ? ? f_add_cted destrs_cted srcrs_cted ? in |
---|
| 554 | let f_rest ≝ λdestr. rtl_st_op2 op destr tmpr tmpr start_lbl in |
---|
| 555 | let insts_rest ≝ map … f_rest destrs_rest in |
---|
| 556 | adds_graph (insts_init @ insts_add @ insts_add_cted @ insts_rest) start_lbl dest_lbl def |
---|
| 557 | ] |
---|
| 558 | ] |
---|
| 559 | ]. |
---|
[1066] | 560 | [1: @third_reduced_proof |
---|
| 561 | |3: @first_reduced_proof |
---|
| 562 | |*: cases daemon (* TODO *) |
---|
| 563 | ] |
---|
[1062] | 564 | qed. |
---|
[1057] | 565 | |
---|
[1062] | 566 | let rec translate_mul1 |
---|
| 567 | (dummy: register) (tmpr: register) (destrs: list register) |
---|
| 568 | (srcrs1: list register) (srcr2: register) (start_lbl: label) |
---|
| 569 | on srcrs1 ≝ |
---|
| 570 | match destrs with |
---|
| 571 | [ nil ⇒ adds_graph [ rtl_st_skip start_lbl ] start_lbl |
---|
| 572 | | cons destr tl ⇒ |
---|
| 573 | match tl with |
---|
| 574 | [ nil ⇒ |
---|
| 575 | match srcrs1 with |
---|
| 576 | [ nil ⇒ |
---|
| 577 | adds_graph [ |
---|
| 578 | rtl_st_int tmpr (zero ?) start_lbl; |
---|
| 579 | rtl_st_op2 Addc destr destr tmpr start_lbl |
---|
| 580 | ] start_lbl |
---|
| 581 | | cons srcr1 tl' ⇒ |
---|
| 582 | adds_graph [ |
---|
| 583 | rtl_st_opaccs Mul tmpr dummy srcr2 srcr1 start_lbl; |
---|
| 584 | rtl_st_op2 Addc destr destr tmpr start_lbl |
---|
| 585 | ] start_lbl |
---|
| 586 | ] |
---|
| 587 | | cons destr2 destrs ⇒ |
---|
| 588 | match srcrs1 with |
---|
| 589 | [ nil ⇒ |
---|
| 590 | add_translates [ |
---|
| 591 | adds_graph [ |
---|
| 592 | rtl_st_int tmpr (zero ?) start_lbl; |
---|
| 593 | rtl_st_op2 Addc destr destr tmpr start_lbl; |
---|
| 594 | rtl_st_op2 Addc destr2 tmpr tmpr start_lbl |
---|
| 595 | ]; |
---|
| 596 | translate_cst (Ointconst I8 (zero ?)) destrs |
---|
| 597 | ] start_lbl |
---|
| 598 | | cons srcr1 srcrs1 ⇒ |
---|
| 599 | match destrs with |
---|
| 600 | [ nil ⇒ |
---|
| 601 | add_translates [ |
---|
| 602 | adds_graph [ |
---|
| 603 | rtl_st_int tmpr (zero ?) start_lbl; |
---|
| 604 | rtl_st_op2 Addc destr destr tmpr start_lbl; |
---|
| 605 | rtl_st_op2 Addc destr2 tmpr tmpr start_lbl |
---|
| 606 | ]; |
---|
| 607 | translate_cst (Ointconst I8 (zero ?)) destrs |
---|
| 608 | ] start_lbl |
---|
| 609 | | cons destr2 destrs ⇒ |
---|
| 610 | add_translates [ |
---|
| 611 | adds_graph [ |
---|
| 612 | rtl_st_opaccs Mul tmpr destr2 srcr2 srcr1 start_lbl; |
---|
| 613 | rtl_st_op2 Addc destr destr tmpr start_lbl |
---|
| 614 | ]; |
---|
| 615 | translate_mul1 dummy tmpr (destr2 :: destrs) srcrs1 srcr2 |
---|
| 616 | ] start_lbl |
---|
| 617 | ] |
---|
| 618 | ] |
---|
| 619 | ] |
---|
| 620 | ]. |
---|
| 621 | |
---|
| 622 | definition translate_muli ≝ |
---|
| 623 | λdummy: register. |
---|
| 624 | λtmpr: register. |
---|
| 625 | λdestrs: list register. |
---|
| 626 | λtmp_destrs: list register. |
---|
| 627 | λsrcrs1: list register. |
---|
| 628 | λdummy_lbl: label. |
---|
| 629 | λi: nat. |
---|
[1063] | 630 | λi_prf. |
---|
| 631 | λtranslates: list ?. |
---|
| 632 | λsrcr2i: register. |
---|
| 633 | let 〈tmp_destrs1, tmp_destrs2〉 ≝ split ? tmp_destrs i i_prf in |
---|
| 634 | let tmp_destrs2' ≝ |
---|
| 635 | match tmp_destrs2 with |
---|
| 636 | [ nil ⇒ [ ] |
---|
| 637 | | cons tmp_destr2 tmp_destrs2 ⇒ [ |
---|
| 638 | adds_graph [ |
---|
| 639 | rtl_st_clear_carry dummy_lbl; |
---|
| 640 | rtl_st_int tmp_destr2 (zero ?) dummy_lbl |
---|
| 641 | ]; |
---|
| 642 | translate_mul1 dummy tmpr tmp_destrs2 srcrs1 srcr2i; |
---|
| 643 | translate_cst (Ointconst I8 (zero ?)) tmp_destrs1; |
---|
| 644 | adds_graph [ |
---|
| 645 | rtl_st_clear_carry dummy_lbl |
---|
| 646 | ]; |
---|
[1066] | 647 | translate_op Addc destrs destrs tmp_destrs |
---|
[1063] | 648 | ] |
---|
| 649 | ] |
---|
| 650 | in |
---|
| 651 | translates @ tmp_destrs2'. |
---|
[1062] | 652 | |
---|
[1064] | 653 | axiom translate_mul: |
---|
| 654 | ∀destrs: list register. |
---|
| 655 | ∀srcrs1: list register. |
---|
| 656 | ∀srcrs2: list register. |
---|
| 657 | ∀start_lbl: label. |
---|
| 658 | ∀dest_lbl: label. |
---|
| 659 | ∀def: rtl_internal_function. |
---|
| 660 | rtl_internal_function. |
---|
| 661 | |
---|
| 662 | (* |
---|
[1063] | 663 | definition translate_mul ≝ |
---|
| 664 | λdestrs: list register. |
---|
| 665 | λsrcrs1: list register. |
---|
| 666 | λsrcrs2: list register. |
---|
| 667 | λstart_lbl: label. |
---|
| 668 | λdest_lbl: label. |
---|
| 669 | λdef: rtl_internal_function. |
---|
| 670 | let 〈def, dummy〉 ≝ fresh_reg def in |
---|
| 671 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
| 672 | let 〈def, tmp_destrs〉 ≝ fresh_regs def (|destrs|) in |
---|
| 673 | let 〈def, fresh_srcrs1〉 ≝ fresh_regs def (|srcrs1|) in |
---|
| 674 | let 〈def, fresh_srcrs2〉 ≝ fresh_regs def (|srcrs2|) in |
---|
| 675 | let insts_init ≝ [ |
---|
| 676 | translate_move fresh_srcrs1 srcrs1; |
---|
| 677 | translate_move fresh_srcrs2 srcrs2; |
---|
| 678 | translate_cst (Ointconst I8 (zero ?)) destrs |
---|
| 679 | ] |
---|
| 680 | in |
---|
| 681 | let f ≝ λi. translate_muli dummy tmpr destrs tmp_destrs ? fresh_srcrs1 start_lbl i ? in |
---|
| 682 | let insts_mul ≝ foldi ? ? [ ] srcrs2 in ?. [5: check insts_init. |
---|
| 683 | add_translates (insts_init @ insts_mul) start_lbl dest_lbl def. |
---|
[1064] | 684 | *) |
---|
[1062] | 685 | |
---|
[1064] | 686 | definition translate_divumodu8 ≝ |
---|
| 687 | λorder: bool. |
---|
| 688 | λdestrs: list register. |
---|
| 689 | λsrcr1: register. |
---|
| 690 | λsrcr2: register. |
---|
| 691 | λstart_lbl: label. |
---|
| 692 | λdest_lbl: label. |
---|
| 693 | λdef: rtl_internal_function. |
---|
| 694 | match destrs with |
---|
| 695 | [ nil ⇒ add_graph start_lbl (rtl_st_skip dest_lbl) def |
---|
| 696 | | cons destr destrs ⇒ |
---|
| 697 | let 〈def, dummy〉 ≝ fresh_reg def in |
---|
| 698 | let 〈destr1, destr2〉 ≝ match order with [ true ⇒ 〈destr, dummy〉 | _ ⇒ 〈dummy, destr〉 ] in |
---|
| 699 | let inst_div ≝ adds_graph [ |
---|
| 700 | rtl_st_opaccs DivuModu destr1 destr2 srcr1 srcr2 start_lbl |
---|
| 701 | ] |
---|
| 702 | in |
---|
| 703 | let insts_rest ≝ translate_cst (Ointconst I8 (zero ?)) destrs in |
---|
| 704 | add_translates [ inst_div; insts_rest ] start_lbl dest_lbl def |
---|
| 705 | ]. |
---|
[1063] | 706 | |
---|
[1064] | 707 | definition translate_ne: ? → ? → ? → ? → ? → ? → rtl_internal_function ≝ |
---|
| 708 | λdestrs: list register. |
---|
| 709 | λsrcrs1: list register. |
---|
| 710 | λsrcrs2: list register. |
---|
| 711 | λstart_lbl: label. |
---|
| 712 | λdest_lbl: label. |
---|
| 713 | λdef: rtl_internal_function. |
---|
| 714 | match destrs with |
---|
| 715 | [ nil ⇒ add_graph start_lbl (rtl_st_skip dest_lbl) def |
---|
| 716 | | cons destr destrs ⇒ |
---|
| 717 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
| 718 | let 〈def, tmp_zero〉 ≝ fresh_reg def in |
---|
| 719 | let 〈def, tmp_srcrs1〉 ≝ fresh_regs def (|srcrs1|) in |
---|
| 720 | let save_srcrs1 ≝ translate_move tmp_srcrs1 srcrs1 in |
---|
| 721 | let 〈def, tmp_srcrs2〉 ≝ fresh_regs def (|srcrs2|) in |
---|
| 722 | let save_srcrs2 ≝ translate_move tmp_srcrs2 srcrs2 in |
---|
[1071] | 723 | match reduce_strong register register tmp_srcrs1 tmp_srcrs2 with |
---|
[1064] | 724 | [ dp crl their_proof ⇒ |
---|
| 725 | let commonl ≝ \fst (\fst crl) in |
---|
| 726 | let commonr ≝ \fst (\snd crl) in |
---|
| 727 | let restl ≝ \snd (\snd crl) in |
---|
| 728 | let restr ≝ \snd (\snd crl) in |
---|
| 729 | let rest ≝ choose_rest ? restl restr ? ? in |
---|
| 730 | let inits ≝ [ |
---|
| 731 | rtl_st_int destr (zero ?) start_lbl; |
---|
| 732 | rtl_st_int tmp_zero (zero ?) start_lbl |
---|
| 733 | ] |
---|
| 734 | in |
---|
| 735 | let f_common ≝ λtmp_srcr1. λtmp_srcr2. [ |
---|
| 736 | rtl_st_clear_carry start_lbl; |
---|
| 737 | rtl_st_op2 Sub tmpr tmp_srcr1 tmp_srcr2 start_lbl; |
---|
| 738 | rtl_st_op2 Or destr destr tmpr start_lbl |
---|
| 739 | ] |
---|
| 740 | in |
---|
| 741 | let insts_common ≝ flatten ? (map2 … f_common commonl commonr ?) in |
---|
| 742 | let f_rest ≝ λtmp_srcr. [ |
---|
| 743 | rtl_st_clear_carry start_lbl; |
---|
| 744 | rtl_st_op2 Sub tmpr tmp_zero tmp_srcr start_lbl; |
---|
| 745 | rtl_st_op2 Or destr destr tmpr start_lbl |
---|
| 746 | ] |
---|
| 747 | in |
---|
| 748 | let insts_rest ≝ flatten ? (map ? ? f_rest rest) in |
---|
| 749 | let insts ≝ inits @ insts_common @ insts_rest in |
---|
| 750 | let epilogue ≝ translate_cst (Ointconst I8 (zero ?)) destrs in |
---|
| 751 | add_translates [ |
---|
| 752 | save_srcrs1; save_srcrs2; adds_graph insts; epilogue |
---|
| 753 | ] start_lbl dest_lbl def |
---|
| 754 | ] |
---|
| 755 | ]. |
---|
| 756 | [1: @their_proof |
---|
| 757 | |*: cases not_implemented (* choose rest requires non-emptiness proofs but |
---|
| 758 | these appear impossible to obtain, similar proof |
---|
| 759 | to above *) |
---|
| 760 | ] |
---|
| 761 | qed. |
---|
| 762 | |
---|
| 763 | definition translate_eq_reg ≝ |
---|
| 764 | λtmp_zero: register. |
---|
| 765 | λtmp_one: register. |
---|
| 766 | λtmpr1: register. |
---|
| 767 | λtmpr2: register. |
---|
| 768 | λdestr: register. |
---|
| 769 | λdummy_lbl: label. |
---|
| 770 | λsrcr12: register × register. |
---|
| 771 | let 〈srcr1, srcr2〉 ≝ srcr12 in |
---|
| 772 | [ rtl_st_clear_carry dummy_lbl; |
---|
| 773 | rtl_st_op2 Sub tmpr1 srcr1 srcr2 dummy_lbl; |
---|
| 774 | rtl_st_op2 Addc tmpr1 tmp_zero tmp_zero dummy_lbl; |
---|
| 775 | rtl_st_op2 Sub tmpr2 srcr2 srcr1 dummy_lbl; |
---|
| 776 | rtl_st_op2 Addc tmpr2 tmp_zero tmp_zero dummy_lbl; |
---|
| 777 | rtl_st_op2 Or tmpr1 tmpr1 tmpr2 dummy_lbl; |
---|
| 778 | rtl_st_op2 Xor tmpr1 tmpr1 tmp_one dummy_lbl; |
---|
| 779 | rtl_st_op2 And destr destr tmpr1 dummy_lbl ]. |
---|
| 780 | |
---|
| 781 | definition translate_eq_list ≝ |
---|
| 782 | λtmp_zero: register. |
---|
| 783 | λtmp_one: register. |
---|
| 784 | λtmpr1: register. |
---|
| 785 | λtmpr2: register. |
---|
| 786 | λdestr: register. |
---|
| 787 | λleq: list (register × register). |
---|
| 788 | λdummy_lbl: label. |
---|
| 789 | let f ≝ translate_eq_reg tmp_zero tmp_one tmpr1 tmpr2 destr dummy_lbl in |
---|
| 790 | (rtl_st_int destr (bitvector_of_nat ? 1) dummy_lbl) :: |
---|
| 791 | flatten ? (map ? ? f leq). |
---|
| 792 | |
---|
| 793 | definition translate_atom ≝ |
---|
| 794 | λtmp_zero: register. |
---|
| 795 | λtmp_one: register. |
---|
| 796 | λtmpr1: register. |
---|
| 797 | λtmpr2: register. |
---|
| 798 | λtmpr3: register. |
---|
| 799 | λdestr: register. |
---|
| 800 | λdummy_lbl: label. |
---|
| 801 | λleq: list (register × register). |
---|
| 802 | λsrcr1: register. |
---|
| 803 | λsrcr2: register. |
---|
| 804 | translate_eq_list tmp_zero tmp_one tmpr1 tmpr2 tmpr3 leq dummy_lbl @ |
---|
| 805 | [ rtl_st_clear_carry dummy_lbl; |
---|
| 806 | rtl_st_op2 Sub tmpr1 srcr1 srcr2 dummy_lbl; |
---|
| 807 | rtl_st_op2 Addc tmpr1 tmp_zero tmp_zero dummy_lbl; |
---|
| 808 | rtl_st_op2 And tmpr3 tmpr3 tmpr1 dummy_lbl; |
---|
| 809 | rtl_st_op2 Or destr destr tmpr3 dummy_lbl ]. |
---|
| 810 | |
---|
| 811 | definition translate_lt_main ≝ |
---|
| 812 | λtmp_zero: register. |
---|
| 813 | λtmp_one: register. |
---|
| 814 | λtmpr1: register. |
---|
| 815 | λtmpr2: register. |
---|
| 816 | λtmpr3: register. |
---|
| 817 | λdestr: register. |
---|
| 818 | λdummy_lbl: label. |
---|
| 819 | λsrcrs1: list register. |
---|
| 820 | λsrcrs2: list register. |
---|
| 821 | λproof: |srcrs1| = |srcrs2|. |
---|
| 822 | let f ≝ λinsts_leq. λsrcr1. λsrcr2. |
---|
| 823 | let 〈insts, leq〉 ≝ insts_leq in |
---|
| 824 | let added_insts ≝ translate_atom tmp_zero tmp_one tmpr1 tmpr2 tmpr3 destr dummy_lbl leq srcr1 srcr2 in |
---|
| 825 | 〈insts @ added_insts, leq @ [〈srcr1, srcr2〉]〉 |
---|
| 826 | in |
---|
| 827 | \fst (fold_left2 ? ? ? f 〈[ ], [ ]〉 srcrs1 srcrs2 proof). |
---|
| 828 | |
---|
| 829 | definition fresh_regs_strong: |
---|
| 830 | rtl_internal_function → ∀n: nat. Σfresh: rtl_internal_function × (list register). |\snd fresh| = n ≝ |
---|
| 831 | λdef. |
---|
| 832 | λn. |
---|
| 833 | fresh_regs def n. |
---|
| 834 | @fresh_regs_length |
---|
| 835 | qed. |
---|
| 836 | |
---|
| 837 | definition complete_regs_strong: |
---|
| 838 | rtl_internal_function → list register → list register → Σcomplete: (list register) × (list register) × (list register). |\fst (\fst complete)| = |\snd (\fst complete)| ≝ |
---|
| 839 | λdef. |
---|
| 840 | λleft. |
---|
| 841 | λright. |
---|
| 842 | complete_regs def left right. |
---|
| 843 | @complete_regs_length |
---|
| 844 | qed. |
---|
| 845 | |
---|
| 846 | definition translate_lt ≝ |
---|
| 847 | λdestrs: list register. |
---|
| 848 | λprf_destrs: lt 0 (|destrs|). |
---|
| 849 | λsrcrs1: list register. |
---|
| 850 | λsrcrs2: list register. |
---|
| 851 | λstart_lbl: label. |
---|
| 852 | λdest_lbl: label. |
---|
| 853 | λdef: rtl_internal_function. |
---|
| 854 | match destrs with |
---|
| 855 | [ nil ⇒ add_graph start_lbl (rtl_st_skip dest_lbl) def |
---|
| 856 | | _ ⇒ |
---|
| 857 | match fresh_regs_strong def (|destrs|) with |
---|
| 858 | [ dp def_tmp_destrs tmp_destrs_proof ⇒ |
---|
| 859 | let def ≝ \fst def_tmp_destrs in |
---|
| 860 | let tmp_destrs ≝ \snd def_tmp_destrs in |
---|
| 861 | let tmp_destr ≝ hd_safe ? tmp_destrs ? in |
---|
| 862 | let 〈def, tmp_zero〉 ≝ fresh_reg def in |
---|
| 863 | let 〈def, tmp_one〉 ≝ fresh_reg def in |
---|
| 864 | let 〈def, tmpr1〉 ≝ fresh_reg def in |
---|
| 865 | let 〈def, tmpr2〉 ≝ fresh_reg def in |
---|
| 866 | let 〈def, tmpr3〉 ≝ fresh_reg def in |
---|
| 867 | match complete_regs_strong def srcrs1 srcrs2 with |
---|
| 868 | [ dp srcrs12_added srcrs12_proof ⇒ |
---|
| 869 | let srcrs1 ≝ \fst (\fst srcrs12_added) in |
---|
| 870 | let srcrs2 ≝ \snd (\fst srcrs12_added) in |
---|
| 871 | let added ≝ \snd srcrs12_added in |
---|
| 872 | let srcrs1' ≝ rev ? srcrs1 in |
---|
| 873 | let srcrs2' ≝ rev ? srcrs2 in |
---|
| 874 | let insts_init ≝ [ |
---|
| 875 | translate_cst (Ointconst I8 (zero ?)) tmp_destrs; |
---|
| 876 | translate_cst (Ointconst I8 (zero ?)) added; |
---|
| 877 | adds_graph [ |
---|
| 878 | rtl_st_int tmp_zero (zero ?) start_lbl; |
---|
| 879 | rtl_st_int tmp_one (bitvector_of_nat ? 1) start_lbl |
---|
| 880 | ] |
---|
| 881 | ] |
---|
| 882 | in |
---|
| 883 | let insts_main ≝ |
---|
| 884 | translate_lt_main tmp_zero tmp_one tmpr1 tmpr2 tmpr3 tmp_destr start_lbl srcrs1' srcrs2' ? in |
---|
| 885 | let insts_main ≝ [ adds_graph insts_main ] in |
---|
| 886 | let insts_exit ≝ [ translate_move destrs tmp_destrs ] in |
---|
| 887 | add_translates (insts_init @ insts_main @ insts_exit) start_lbl dest_lbl def |
---|
| 888 | ] |
---|
| 889 | ] |
---|
| 890 | ]. |
---|
| 891 | [2: >tmp_destrs_proof @prf_destrs |
---|
| 892 | |1: normalize nodelta |
---|
| 893 | generalize in match srcrs12_proof |
---|
| 894 | #HYP >rev_length >rev_length @HYP |
---|
| 895 | ] |
---|
| 896 | qed. |
---|
| 897 | |
---|
| 898 | definition add_128_to_last ≝ |
---|
| 899 | λtmp_128: register. |
---|
| 900 | λrs. |
---|
| 901 | λprf: 0 < |rs|. |
---|
| 902 | λstart_lbl: label. |
---|
| 903 | match rs with |
---|
| 904 | [ nil ⇒ adds_graph [ ] start_lbl |
---|
| 905 | | _ ⇒ |
---|
| 906 | let r ≝ last_safe ? rs prf in |
---|
| 907 | adds_graph [ |
---|
| 908 | rtl_st_op2 Add r r tmp_128 start_lbl |
---|
| 909 | ] start_lbl |
---|
| 910 | ]. |
---|
| 911 | |
---|
| 912 | definition translate_lts ≝ |
---|
| 913 | λdestrs: list register. |
---|
| 914 | λdestrs_prf: lt 0 (|destrs|). |
---|
| 915 | λsrcrs1: list register. |
---|
| 916 | λsrcrs2: list register. |
---|
| 917 | λsrcrs1_lt_prf: 0 < |srcrs1|. |
---|
[1066] | 918 | λsrcrs2_lt_prf: 0 < |srcrs2|. |
---|
[1064] | 919 | λstart_lbl: label. |
---|
| 920 | λdest_lbl: label. |
---|
| 921 | λdef: rtl_internal_function. |
---|
| 922 | match fresh_regs_strong def (|srcrs1|) with |
---|
| 923 | [ dp def_tmp_srcrs1 srcrs1_prf ⇒ |
---|
| 924 | let def ≝ \fst def_tmp_srcrs1 in |
---|
| 925 | let tmp_srcrs1 ≝ \snd def_tmp_srcrs1 in |
---|
| 926 | match fresh_regs_strong def (|srcrs2|) with |
---|
| 927 | [ dp def_tmp_srcrs2 srcrs2_prf ⇒ |
---|
| 928 | let def ≝ \fst def_tmp_srcrs2 in |
---|
| 929 | let tmp_srcrs2 ≝ \snd def_tmp_srcrs2 in |
---|
| 930 | let 〈def, tmp_128〉 ≝ fresh_reg def in |
---|
| 931 | add_translates [ |
---|
| 932 | translate_move tmp_srcrs1 srcrs1; |
---|
| 933 | translate_move tmp_srcrs2 srcrs2; |
---|
| 934 | adds_graph [ |
---|
| 935 | rtl_st_int tmp_128 (bitvector_of_nat ? 128) start_lbl |
---|
| 936 | ]; |
---|
| 937 | add_128_to_last tmp_128 tmp_srcrs1 ?; |
---|
| 938 | add_128_to_last tmp_128 tmp_srcrs2 ?; |
---|
[1066] | 939 | translate_lt destrs destrs_prf tmp_srcrs1 tmp_srcrs2 |
---|
[1064] | 940 | ] start_lbl dest_lbl def |
---|
| 941 | ] |
---|
| 942 | ]. |
---|
[1066] | 943 | [1: >srcrs1_prf @srcrs1_lt_prf |
---|
| 944 | |2: >srcrs2_prf @srcrs2_lt_prf |
---|
[1064] | 945 | ] |
---|
| 946 | qed. |
---|
| 947 | |
---|
| 948 | definition translate_op2 ≝ |
---|
| 949 | λop2. |
---|
| 950 | λdestrs: list register. |
---|
| 951 | λdestrs_prf: lt 0 (|destrs|). |
---|
| 952 | λsrcrs1: list register. |
---|
| 953 | λsrcrs2: list register. |
---|
[1066] | 954 | λsrcrs1_prf: lt 0 (|srcrs1|). (* can this be relaxed? i think it can |
---|
| 955 | but we need more dep. typ. in modu/divu |
---|
| 956 | cases *) |
---|
| 957 | λsrcrs2_prf: lt 0 (|srcrs2|). |
---|
[1064] | 958 | λstart_lbl: label. |
---|
| 959 | λdest_lbl: label. |
---|
| 960 | λdef: rtl_internal_function. |
---|
| 961 | match op2 with |
---|
[1066] | 962 | [ Oadd ⇒ |
---|
| 963 | translate_op Addc destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 964 | | Oaddp ⇒ |
---|
| 965 | translate_op Addc destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 966 | | Osub ⇒ |
---|
| 967 | translate_op Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 968 | | Osubpi ⇒ |
---|
| 969 | translate_op Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 970 | | Osubpp sz ⇒ |
---|
| 971 | translate_op Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 972 | | Omul ⇒ |
---|
| 973 | translate_mul destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 974 | | Odivu ⇒ |
---|
| 975 | match srcrs1 return λx. 0 < |x| → rtl_internal_function with |
---|
| 976 | [ cons hd tl ⇒ λcons_prf. |
---|
| 977 | match tl with |
---|
| 978 | [ nil ⇒ translate_divumodu8 true destrs hd (hd_safe register srcrs2 ?) start_lbl dest_lbl def |
---|
| 979 | | _ ⇒ ? (* not implemented *) |
---|
| 980 | ] |
---|
| 981 | | nil ⇒ λnil_absrd. ? |
---|
| 982 | ] srcrs1_prf |
---|
| 983 | | Omodu ⇒ |
---|
| 984 | match srcrs1 return λx. 0 < |x| → rtl_internal_function with |
---|
| 985 | [ cons hd tl ⇒ λcons_prf. |
---|
| 986 | match tl with |
---|
| 987 | [ nil ⇒ translate_divumodu8 false destrs hd (hd_safe register srcrs2 ?) start_lbl dest_lbl def |
---|
| 988 | | _ ⇒ ? (* not implemented *) |
---|
| 989 | ] |
---|
| 990 | | nil ⇒ λnil_absrd. ? |
---|
| 991 | ] srcrs1_prf |
---|
| 992 | | Oand ⇒ |
---|
| 993 | translate_op And destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 994 | | Oor ⇒ |
---|
| 995 | translate_op Or destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 996 | | Oxor ⇒ |
---|
| 997 | translate_op Xor destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 998 | | Ocmp c ⇒ |
---|
[1064] | 999 | match c with |
---|
[1066] | 1000 | [ Ceq ⇒ |
---|
[1064] | 1001 | add_translates [ |
---|
[1066] | 1002 | translate_ne destrs srcrs1 srcrs2; |
---|
| 1003 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
[1064] | 1004 | ] start_lbl dest_lbl def |
---|
[1066] | 1005 | | Cne ⇒ translate_ne destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 1006 | | Clt ⇒ translate_lts destrs destrs_prf srcrs1 srcrs2 ? ? start_lbl dest_lbl def |
---|
| 1007 | | Cgt ⇒ translate_lts destrs destrs_prf srcrs2 srcrs1 ? ? start_lbl dest_lbl def |
---|
| 1008 | | Cle ⇒ |
---|
[1064] | 1009 | add_translates [ |
---|
[1066] | 1010 | translate_lts destrs destrs_prf srcrs2 srcrs1 ? ?; |
---|
| 1011 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
[1064] | 1012 | ] start_lbl dest_lbl def |
---|
[1066] | 1013 | | Cge ⇒ |
---|
[1064] | 1014 | add_translates [ |
---|
[1066] | 1015 | translate_lts destrs destrs_prf srcrs1 srcrs2 ? ?; |
---|
| 1016 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
[1064] | 1017 | ] start_lbl dest_lbl def |
---|
| 1018 | ] |
---|
[1066] | 1019 | | Ocmpu c ⇒ |
---|
| 1020 | match c with |
---|
| 1021 | [ Ceq ⇒ |
---|
| 1022 | add_translates [ |
---|
| 1023 | translate_ne destrs srcrs1 srcrs2; |
---|
| 1024 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
| 1025 | ] start_lbl dest_lbl def |
---|
| 1026 | | Cne ⇒ translate_ne destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 1027 | | Clt ⇒ translate_lt destrs destrs_prf srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 1028 | | Cgt ⇒ translate_lt destrs destrs_prf srcrs2 srcrs1 start_lbl dest_lbl def |
---|
| 1029 | | Cle ⇒ |
---|
| 1030 | add_translates [ |
---|
| 1031 | translate_lt destrs destrs_prf srcrs2 srcrs1; |
---|
| 1032 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
| 1033 | ] start_lbl dest_lbl def |
---|
| 1034 | | Cge ⇒ |
---|
| 1035 | add_translates [ |
---|
| 1036 | translate_lt destrs destrs_prf srcrs1 srcrs2; |
---|
| 1037 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
| 1038 | ] start_lbl dest_lbl def |
---|
| 1039 | ] |
---|
| 1040 | | Ocmpp c ⇒ |
---|
| 1041 | match c with |
---|
| 1042 | [ Ceq ⇒ |
---|
| 1043 | add_translates [ |
---|
| 1044 | translate_ne destrs srcrs1 srcrs2; |
---|
| 1045 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
| 1046 | ] start_lbl dest_lbl def |
---|
| 1047 | | Cne ⇒ translate_ne destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 1048 | | Clt ⇒ translate_lt destrs destrs_prf srcrs1 srcrs2 start_lbl dest_lbl def |
---|
| 1049 | | Cgt ⇒ translate_lt destrs destrs_prf srcrs2 srcrs1 start_lbl dest_lbl def |
---|
| 1050 | | Cle ⇒ |
---|
| 1051 | add_translates [ |
---|
| 1052 | translate_lt destrs destrs_prf srcrs2 srcrs1; |
---|
| 1053 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
| 1054 | ] start_lbl dest_lbl def |
---|
| 1055 | | Cge ⇒ |
---|
| 1056 | add_translates [ |
---|
| 1057 | translate_lt destrs destrs_prf srcrs1 srcrs2; |
---|
| 1058 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
| 1059 | ] start_lbl dest_lbl def |
---|
| 1060 | ] |
---|
| 1061 | | _ ⇒ ? (* assert false, implemented in run time or float op *) |
---|
| 1062 | ]. |
---|
| 1063 | [ 2,6: normalize in nil_absrd; |
---|
| 1064 | cases(not_le_Sn_O 0) |
---|
| 1065 | #HYP cases(HYP nil_absrd) |
---|
| 1066 | | 3,7,12,17,13,15,18,19,20,21,14,16: |
---|
| 1067 | assumption |
---|
| 1068 | | *: cases not_implemented (* yes, really *) |
---|
| 1069 | ] |
---|
| 1070 | qed. |
---|
| 1071 | |
---|
| 1072 | definition translate_cond ≝ |
---|
| 1073 | λsrcrs: list register. |
---|
| 1074 | λstart_lbl: label. |
---|
| 1075 | λlbl_true: label. |
---|
| 1076 | λlbl_false: label. |
---|
| 1077 | λdef: rtl_internal_function. |
---|
| 1078 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
| 1079 | let 〈def, tmp_lbl〉 ≝ fresh_label def in |
---|
| 1080 | let init ≝ rtl_st_int tmpr (zero ?) start_lbl in |
---|
| 1081 | let f ≝ λsrcr. rtl_st_op2 Or tmpr tmpr srcr start_lbl in |
---|
| 1082 | let def ≝ adds_graph (init :: (map … f srcrs)) start_lbl tmp_lbl def in |
---|
| 1083 | add_graph tmp_lbl (rtl_st_cond tmpr lbl_true lbl_false) def. |
---|
| 1084 | |
---|
| 1085 | definition translate_load ≝ |
---|
| 1086 | λaddr. |
---|
| 1087 | λaddr_prf: 2 ≤ |addr|. |
---|
| 1088 | λdestrs: list register. |
---|
| 1089 | λstart_lbl: label. |
---|
| 1090 | λdest_lbl: label. |
---|
| 1091 | λdef: rtl_internal_function. |
---|
| 1092 | match fresh_regs_strong def (|addr|) with |
---|
| 1093 | [ dp def_save_addr save_addr_prf ⇒ |
---|
| 1094 | let def ≝ \fst def_save_addr in |
---|
| 1095 | let save_addr ≝ \snd def_save_addr in |
---|
| 1096 | match fresh_regs_strong def (|addr|) with |
---|
| 1097 | [ dp def_tmp_addr tmp_addr_prf ⇒ |
---|
| 1098 | let def ≝ \fst def_tmp_addr in |
---|
| 1099 | let tmp_addr ≝ \snd def_tmp_addr in |
---|
| 1100 | let 〈tmp_addr1, tmp_addr2〉 ≝ make_addr ? tmp_addr ? in |
---|
| 1101 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
| 1102 | let insts_save_addr ≝ translate_move save_addr addr in |
---|
| 1103 | let f ≝ λtranslates_off. λr. |
---|
| 1104 | let 〈translates, off〉 ≝ translates_off in |
---|
| 1105 | let translates ≝ translates @ [ |
---|
| 1106 | adds_graph [ |
---|
| 1107 | rtl_st_int tmpr off start_lbl |
---|
| 1108 | ]; |
---|
| 1109 | translate_op2 Oaddp tmp_addr ? save_addr [tmpr] ? ?; |
---|
| 1110 | adds_graph [ |
---|
| 1111 | rtl_st_load r tmp_addr1 tmp_addr2 dest_lbl |
---|
| 1112 | ] |
---|
| 1113 | ] |
---|
| 1114 | in |
---|
| 1115 | let 〈carry, result〉 ≝ half_add ? off int_size in |
---|
| 1116 | 〈translates, result〉 |
---|
| 1117 | in |
---|
| 1118 | let 〈translates, ignore〉 ≝ foldl ? ? f 〈[ ], (zero ?)〉 destrs in |
---|
| 1119 | add_translates (insts_save_addr :: translates) start_lbl dest_lbl def |
---|
| 1120 | ] |
---|
| 1121 | ]. |
---|
| 1122 | [1: normalize // |
---|
| 1123 | |2: >save_addr_prf normalize |
---|
| 1124 | @(transitive_le 1 2 (|addr|)) // |
---|
| 1125 | |3: >tmp_addr_prf normalize |
---|
| 1126 | @(transitive_le 1 2 (|addr|)) // |
---|
| 1127 | |*: >tmp_addr_prf assumption |
---|
| 1128 | ] |
---|
| 1129 | qed. |
---|
| 1130 | |
---|
| 1131 | definition translate_store ≝ |
---|
| 1132 | λaddr. |
---|
| 1133 | λaddr_prf: 2 ≤ |addr|. |
---|
| 1134 | λsrcrs: list register. |
---|
| 1135 | λstart_lbl: label. |
---|
| 1136 | λdest_lbl: label. |
---|
| 1137 | λdef: rtl_internal_function. |
---|
| 1138 | match fresh_regs_strong def (|addr|) with |
---|
| 1139 | [ dp def_tmp_addr tmp_addr_prf ⇒ |
---|
| 1140 | let def ≝ \fst def_tmp_addr in |
---|
| 1141 | let tmp_addr ≝ \snd def_tmp_addr in |
---|
| 1142 | let 〈tmp_addr1, tmp_addr2〉 ≝ make_addr ? tmp_addr ? in |
---|
| 1143 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
| 1144 | let f ≝ λtranslate_off. λsrcr. |
---|
| 1145 | let 〈translates, off〉 ≝ translate_off in |
---|
| 1146 | let translates ≝ translates @ [ |
---|
| 1147 | adds_graph [ |
---|
| 1148 | rtl_st_int tmpr off start_lbl |
---|
| 1149 | ]; |
---|
| 1150 | translate_op2 Oaddp tmp_addr ? addr [tmpr] ? ?; |
---|
| 1151 | adds_graph [ |
---|
| 1152 | rtl_st_store tmp_addr1 tmp_addr2 srcr dest_lbl |
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| 1153 | ] |
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| 1154 | ] |
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| 1155 | in |
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| 1156 | let 〈carry, result〉 ≝ half_add ? off int_size in |
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| 1157 | 〈translates, result〉 |
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| 1158 | in |
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| 1159 | let 〈translates, ignore〉 ≝ foldl ? ? f 〈[ ], zero ?〉 srcrs in |
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| 1160 | add_translates translates start_lbl dest_lbl def |
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| 1161 | ]. |
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| 1162 | [1: normalize // |
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| 1163 | |2: >tmp_addr_prf normalize |
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| 1164 | @(transitive_le 1 2 (|addr|)) // |
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| 1165 | |3: >tmp_addr_prf normalize |
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| 1166 | @(transitive_le 1 2 (|addr|)) // |
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| 1167 | |*: >tmp_addr_prf assumption |
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| 1168 | ] |
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| 1169 | qed. |
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| 1170 | |
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| 1171 | definition translate_stmt ≝ |
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| 1172 | λlenv. |
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| 1173 | λlbl: label. |
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| 1174 | λstmt. |
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| 1175 | λdef: rtl_internal_function. |
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| 1176 | match stmt with |
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| 1177 | [ St_skip lbl' ⇒ add_graph lbl (rtl_st_skip lbl') def |
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| 1178 | | St_cost cost_lbl lbl' ⇒ add_graph lbl (rtl_st_cost cost_lbl lbl') def |
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| 1179 | | St_const destr cst lbl' ⇒ |
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| 1180 | translate_cst cst (find_local_env destr lenv) lbl lbl' def |
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| 1181 | | St_op1 op1 destr srcr lbl' ⇒ |
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| 1182 | translate_op1 op1 (find_local_env destr lenv) (find_local_env srcr lenv) ? lbl lbl' def |
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| 1183 | | St_op2 op2 destr srcr1 srcr2 lbl' ⇒ |
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| 1184 | translate_op2 op2 (find_local_env destr lenv) ? (find_local_env srcr1 lenv) (find_local_env srcr2 lenv) ? ? lbl lbl' def |
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| 1185 | | St_load ignore addr destr lbl' ⇒ |
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| 1186 | translate_load (find_local_env addr lenv) ? (find_local_env destr lenv) lbl lbl' def |
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| 1187 | | St_store ignore addr srcr lbl' ⇒ |
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| 1188 | translate_store (find_local_env addr lenv) ? (find_local_env srcr lenv) lbl lbl' def |
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| 1189 | | St_call_id f args retr lbl' ⇒ |
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| 1190 | match retr with |
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| 1191 | [ Some retr ⇒ |
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| 1192 | add_graph lbl (rtl_st_call_id f (rtl_args args lenv) (find_local_env retr lenv) lbl') def |
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| 1193 | | None ⇒ add_graph lbl (rtl_st_call_id f (rtl_args args lenv) [ ] lbl') def |
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| 1194 | ] |
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| 1195 | | St_call_ptr f args retr lbl' ⇒ |
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| 1196 | match retr with |
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| 1197 | [ None ⇒ |
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| 1198 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
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| 1199 | add_graph lbl (rtl_st_call_ptr f1 f2 (rtl_args args lenv) [ ] lbl') def |
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| 1200 | | Some retr ⇒ |
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| 1201 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
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| 1202 | add_graph lbl (rtl_st_call_ptr f1 f2 (rtl_args args lenv) (find_local_env retr lenv) lbl') def |
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| 1203 | ] |
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| 1204 | | St_tailcall_id f args ⇒ |
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| 1205 | add_graph lbl (rtl_st_tailcall_id f (rtl_args args lenv)) def |
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| 1206 | | St_tailcall_ptr f args ⇒ |
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| 1207 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
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| 1208 | add_graph lbl (rtl_st_tailcall_ptr f1 f2 (rtl_args args lenv)) def |
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| 1209 | | St_cond r lbl_true lbl_false ⇒ |
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| 1210 | translate_cond (find_local_env r lenv) lbl lbl_true lbl_false def |
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| 1211 | | St_jumptable r l ⇒ ? (* assert false: not implemented yet *) |
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[1068] | 1212 | | St_return ⇒ add_graph lbl rtl_st_return def |
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[1064] | 1213 | ]. |
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[1067] | 1214 | [10: cases not_implemented (* jtable case *) |
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| 1215 | |*: cases daemon (* TODO: proofs regarding lengths of lists, examine! *) |
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| 1216 | ] |
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| 1217 | qed. |
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[1064] | 1218 | |
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[1073] | 1219 | (* XXX: we use a "hack" here to circumvent the proof obligations required to |
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| 1220 | create res, an empty internal_function record. we insert into our graph |
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| 1221 | the start and end nodes to ensure that they are in, and place dummy |
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| 1222 | skip instructions at these nodes. *) |
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[1067] | 1223 | definition translate_internal ≝ |
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| 1224 | λdef. |
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| 1225 | let runiverse ≝ f_reggen def in |
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| 1226 | let lenv ≝ initialize_local_env runiverse |
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[1068] | 1227 | (f_params def @ f_locals def) (f_result def) in |
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| 1228 | let params ≝ map_list_local_env lenv (map ? ? \fst (f_params def)) in |
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| 1229 | let locals ≝ map_list_local_env lenv (map ? ? \fst (f_locals def)) in |
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[1149] | 1230 | let result ≝ |
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[1068] | 1231 | match (f_result def) with |
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| 1232 | [ None ⇒ [ ] |
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| 1233 | | Some r_typ ⇒ |
---|
| 1234 | let 〈r, typ〉 ≝ r_typ in |
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| 1235 | find_local_env r lenv |
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[1053] | 1236 | ] |
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[1068] | 1237 | in |
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| 1238 | let luniverse' ≝ f_labgen def in |
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| 1239 | let runiverse' ≝ runiverse in |
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| 1240 | let result' ≝ result in |
---|
| 1241 | let params' ≝ params in |
---|
| 1242 | let locals' ≝ locals in |
---|
| 1243 | let stack_size' ≝ f_stacksize def in |
---|
| 1244 | let entry' ≝ f_entry def in |
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| 1245 | let exit' ≝ f_exit def in |
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[1073] | 1246 | let graph' ≝ add ? ? (empty_map ? ?) entry' (rtl_st_skip entry') in |
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| 1247 | let graph' ≝ add ? ? graph' exit' (rtl_st_skip exit') in |
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[1068] | 1248 | let res ≝ |
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| 1249 | mk_rtl_internal_function luniverse' runiverse' result' params' |
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[1073] | 1250 | locals' stack_size' graph' ? ? in |
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[1077] | 1251 | foldi ? ? ? (translate_stmt lenv) (f_graph def) res. |
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[1073] | 1252 | [1: % |
---|
| 1253 | [1: @entry' |
---|
| 1254 | |2: normalize nodelta; |
---|
| 1255 | @graph_add_lookup |
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[1077] | 1256 | @graph_add |
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[1073] | 1257 | ] |
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| 1258 | |2: % |
---|
| 1259 | [1: @exit' |
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[1077] | 1260 | |2: normalize nodelta; |
---|
| 1261 | @graph_add |
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[1073] | 1262 | ] |
---|
| 1263 | ] |
---|
| 1264 | qed. |
---|
[1053] | 1265 | |
---|
[1068] | 1266 | definition translate_fun_def ≝ |
---|
| 1267 | λfdef: fundef internal_function. |
---|
| 1268 | match fdef with |
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| 1269 | [ Internal f ⇒ Internal ? (translate_internal f) |
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| 1270 | | External e ⇒ External ? e |
---|
[1053] | 1271 | ]. |
---|
| 1272 | |
---|
[1077] | 1273 | (* XXX: change, we need to propagate the region information, not ignore it *) |
---|
[1068] | 1274 | definition init_data_to_nat ≝ |
---|
| 1275 | λi: init_data. |
---|
| 1276 | match i with |
---|
| 1277 | [ Init_int8 i8 ⇒ 8 |
---|
| 1278 | | Init_int16 i16 ⇒ 16 |
---|
| 1279 | | Init_int32 i32 ⇒ 32 |
---|
| 1280 | | Init_float32 f32 ⇒ 32 |
---|
| 1281 | | Init_float64 f64 ⇒ 64 |
---|
| 1282 | | Init_space s ⇒ s |
---|
| 1283 | | Init_null r ⇒ 0 |
---|
| 1284 | | Init_addrof r i o ⇒ 8 (* XXX: not at all sure about this one *) |
---|
[1053] | 1285 | ]. |
---|
| 1286 | |
---|
[1068] | 1287 | definition translate ≝ |
---|
[1224] | 1288 | λp: program (λ_.fundef internal_function) nat. |
---|
[1068] | 1289 | let f_funct ≝ λid_fun_def. |
---|
| 1290 | let 〈id, fun_def〉 ≝ id_fun_def in |
---|
[1224] | 1291 | 〈id, translate_fun_def fun_def〉 in |
---|
| 1292 | (*CSC: bug here: we are throwing away the regions doing no checks at all *) |
---|
| 1293 | let vars' ≝ map … (λx. let 〈id,reg,n〉 ≝ x in 〈id,n〉) (prog_vars … p) in |
---|
[1068] | 1294 | let functs' ≝ map ? ? f_funct (prog_funct ? ? p) in |
---|
| 1295 | let main' ≝ prog_main ? ? p in |
---|
| 1296 | mk_rtl_program vars' functs' (Some ? main'). |
---|