1 | include "joint/semantics.ma". |
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2 | include alias "common/Identifiers.ma". |
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3 | include "utilities/hide.ma". |
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4 | include "ASM/BitVectorTrie.ma". |
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5 | |
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6 | record hw_register_env : Type[0] ≝ |
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7 | { reg_env : BitVectorTrie beval 6 |
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8 | ; other_bit : bebit |
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9 | }. |
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10 | |
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11 | definition empty_hw_register_env: hw_register_env ≝ |
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12 | mk_hw_register_env (Stub …) BBundef. |
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13 | |
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14 | include alias "ASM/BitVectorTrie.ma". |
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15 | |
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16 | definition hwreg_retrieve: hw_register_env → Register → beval ≝ |
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17 | λenv,r. lookup … (bitvector_of_register r) (reg_env env) BVundef. |
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18 | |
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19 | definition hwreg_store: Register → beval → hw_register_env → hw_register_env ≝ |
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20 | λr,v,env.mk_hw_register_env (insert … (bitvector_of_register r) v (reg_env env)) |
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21 | (other_bit env). |
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22 | |
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23 | definition hwreg_set_other : bebit → hw_register_env → hw_register_env ≝ |
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24 | λv,env.mk_hw_register_env (reg_env env) v. |
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25 | |
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26 | definition hwreg_retrieve_sp : hw_register_env → res xpointer ≝ |
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27 | λenv. |
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28 | let spl ≝ hwreg_retrieve env RegisterSPL in |
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29 | let sph ≝ hwreg_retrieve env RegisterSPH in |
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30 | ! ptr ← pointer_of_address 〈spl, sph〉 ; |
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31 | match ptype ptr return λx.ptype ptr = x → res xpointer with |
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32 | [ XData ⇒ λprf.return «ptr, prf» |
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33 | | _ ⇒ λ_.Error … [MSG BadPointer] |
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34 | ] (refl …). |
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35 | |
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36 | definition hwreg_store_sp : hw_register_env → xpointer → hw_register_env ≝ |
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37 | λenv,sp. |
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38 | let 〈spl, sph〉 ≝ beval_pair_of_pointer sp in |
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39 | hwreg_store RegisterSPH sph (hwreg_store RegisterSPL spl env). |
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40 | |
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41 | (*** Store/retrieve on pseudo-registers ***) |
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42 | include alias "common/Identifiers.ma". |
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43 | |
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44 | record reg_sp : Type[0] ≝ |
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45 | { reg_sp_env :> identifier_map RegisterTag beval |
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46 | ; stackp : xpointer |
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47 | }. |
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48 | |
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49 | axiom BadRegister : String. |
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50 | |
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51 | definition reg_store ≝ λreg,v,locals. update RegisterTag beval locals reg v. |
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52 | |
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53 | definition reg_retrieve : register_env beval → register → res beval ≝ |
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54 | λlocals,reg. opt_to_res … [MSG BadRegister; CTX ? reg] (lookup … locals reg). |
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55 | |
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56 | definition reg_sp_store ≝ λreg,v,locals. |
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57 | ! locals' ← reg_store reg v (reg_sp_env locals) ; |
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58 | return mk_reg_sp locals' (stackp locals). |
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59 | |
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60 | definition reg_sp_retrieve ≝ λlocals.reg_retrieve locals. |
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61 | |
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62 | (*** Store/retrieve on hardware registers ***) |
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63 | |
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64 | definition init_hw_register_env: xpointer → hw_register_env ≝ |
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65 | λsp.hwreg_store_sp empty_hw_register_env sp. |
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66 | |
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67 | (******************************** GRAPHS **************************************) |
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68 | |
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69 | definition make_sem_graph_params : |
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70 | ∀pars : unserialized_params. |
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71 | ∀g_pars : ∀F.sem_unserialized_params pars F. |
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72 | sem_params ≝ |
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73 | λpars,spars. |
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74 | let g_pars ≝ mk_graph_params pars in |
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75 | mk_sem_params |
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76 | g_pars |
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77 | (spars ?) |
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78 | (word_of_identifier ?) |
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79 | (an_identifier ?) |
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80 | ? (refl …). |
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81 | * #p % qed. |
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82 | |
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83 | (******************************** LINEAR **************************************) |
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84 | |
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85 | lemma succ_pos_of_nat_of_pos : ∀p.succ_pos_of_nat (nat_of_pos p) = succ p. |
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86 | @pos_elim [%] |
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87 | #p #IH >nat_possucc whd in ⊢ (??%?); >IH % qed. |
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88 | |
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89 | definition make_sem_lin_params : |
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90 | ∀pars : unserialized_params. |
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91 | (∀F.sem_unserialized_params pars F) → |
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92 | sem_params ≝ |
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93 | λpars,spars. |
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94 | let lin_pars ≝ mk_lin_params pars in |
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95 | mk_sem_params |
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96 | lin_pars |
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97 | (spars ?) |
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98 | succ_pos_of_nat |
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99 | (λp.pred (nat_of_pos p)) |
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100 | ??. |
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101 | [ #n >nat_succ_pos % |
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102 | | @pos_cases [%] #p >nat_possucc @succ_pos_of_nat_of_pos |
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103 | ] qed. |
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104 | |
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105 | |
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106 | |
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107 | |
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108 | lemma fetch_statement_eq : ∀p:sem_params.∀g. |
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109 | ∀ge : genv_t (joint_function p g).∀ptr : program_counter. |
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110 | ∀i,fn,s. |
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111 | fetch_internal_function … ge (pc_block ptr) = OK … 〈i, fn〉 → |
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112 | let pt ≝ point_of_pc … ptr in |
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113 | stmt_at … (joint_if_code … fn) pt = Some ? s → |
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114 | fetch_statement … ge ptr = OK … 〈i, fn, s〉. |
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115 | #p #g #ge #ptr #i #f #s #EQ1 #EQ2 |
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116 | whd in match fetch_statement; normalize nodelta >EQ1 >m_return_bind |
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117 | >EQ2 % |
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118 | qed. |
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119 | |
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120 | lemma fetch_statement_inv : ∀p:sem_params.∀g. |
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121 | ∀ge : genv_t (joint_function p g).∀ptr : program_counter. |
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122 | ∀i,fn,s. |
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123 | fetch_statement … ge ptr = OK … 〈i, fn, s〉 → |
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124 | fetch_internal_function … ge (pc_block ptr) = OK … 〈i, fn〉 ∧ |
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125 | let pt ≝ point_of_pc p ptr in |
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126 | stmt_at … (joint_if_code … fn) pt = Some ? s. |
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127 | #p #g #ge #ptr #i #fn #s #H |
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128 | elim (bind_inversion ????? H) * #i #f' * #EQ1 -H #H |
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129 | elim (bind_inversion ????? H) #s' * #H |
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130 | lapply (opt_eq_from_res ???? H) -H #EQ2 |
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131 | whd in ⊢ (??%%→?); #EQ destruct(EQ) %{EQ1 EQ2} |
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132 | qed. |
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133 | |
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