1 | include "joint/joint_semantics.ma". |
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2 | include "common/StructuredTraces.ma". |
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3 | |
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4 | record evaluation_params : Type[1] ≝ |
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5 | { globals: list ident |
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6 | ; sparams:> sem_params |
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7 | ; ev_genv: genv sparams globals |
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8 | (* ; io_env : state sparams → ∀o:io_out.res (io_in o) *) |
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9 | }. |
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10 | |
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11 | record prog_params : Type[1] ≝ |
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12 | { prog_spars : sem_params |
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13 | ; prog : joint_program prog_spars |
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14 | ; stack_sizes : ident → option ℕ |
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15 | (* ; prog_io : state prog_spars → ∀o.res (io_in o) *) |
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16 | }. |
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17 | |
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18 | lemma map_Exists : ∀A,B,f,P,l.Exists B P (map A B f l) → Exists ? (λx.P (f x)) l. |
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19 | #A #B #f #P #l elim l -l [*] |
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20 | #hd #tl #IH * |
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21 | [ #Phd %1{Phd} |
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22 | | #Ptl %2{(IH Ptl)} |
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23 | ] |
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24 | qed. |
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25 | |
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26 | lemma Exists_In : ∀A,P,l.Exists A P l → ∃x.In A l x ∧ P x. |
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27 | #A #P #l elim l -l [*] #hd #tl #IH * |
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28 | [ #Phd %{hd} %{Phd} %1 % |
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29 | | #Ptl elim (IH Ptl) #x * #H1 #H2 %{x} %{H2} %2{H1} |
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30 | ] |
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31 | qed. |
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32 | |
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33 | lemma In_Exists : ∀A,P,l,x.In A l x → P x → Exists A P l. |
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34 | #A #P #l elim l -l [ #x *] #hd #tl #IH #x * |
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35 | [ #EQ >EQ #H %1{H} |
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36 | | #Intl #Px %2{(IH … Intl Px)} |
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37 | ] |
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38 | qed. |
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39 | |
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40 | lemma Exists_mp : ∀A,P,Q,l.(∀x.P x → Q x) → Exists A P l → Exists A Q l. |
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41 | #A #P #Q #l #H elim l -l [*] #hd #tl #IH * #G [ %1 | %2 ] /2/ qed. |
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42 | |
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43 | definition make_global : prog_params → evaluation_params |
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44 | ≝ |
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45 | λpars. |
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46 | let p ≝ prog pars in |
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47 | let spars ≝ prog_spars pars in |
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48 | let genv ≝ globalenv_noinit ? p in |
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49 | let get_pc_lbl ≝ λid,lbl. |
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50 | ! bl ← block_of_funct_id … spars genv id ; |
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51 | pc_of_label … genv bl lbl in |
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52 | mk_evaluation_params |
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53 | (prog_var_names … p) |
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54 | spars |
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55 | (mk_genv_gen ?? genv ? (stack_sizes pars) get_pc_lbl) |
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56 | (* (prog_io pars) *). |
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57 | #s #H |
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58 | elim (find_symbol_exists … p s ?) |
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59 | [ #bl #EQ >EQ % #ABS destruct(ABS)|*:] |
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60 | @Exists_append_r |
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61 | @(Exists_mp … H) // |
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62 | qed. |
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63 | |
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64 | coercion prog_params_to_ev_params : ∀p : prog_params.evaluation_params |
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65 | ≝ make_global on _p : prog_params to evaluation_params. |
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66 | |
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67 | definition make_initial_state : |
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68 | ∀pars: prog_params.res (state_pc pars) ≝ |
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69 | λpars.let p ≝ prog pars in |
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70 | let sem_globals : evaluation_params ≝ pars in |
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71 | let ge ≝ ev_genv sem_globals in |
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72 | let m0 ≝ alloc_mem … p in |
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73 | let 〈m,spb〉 as H ≝ alloc … m0 0 external_ram_size in |
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74 | let globals_size ≝ globals_stacksize … p in |
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75 | (* stack pointer should start at 2^16 - |globals|, right? |
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76 | first call to main shuold bring it to 2^16 - |globals| - |main stack| |
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77 | Also, on words 2^16 - |globals| = - |globals| *) |
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78 | let spp : xpointer ≝ |
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79 | «mk_pointer spb (mk_offset (bitvector_of_Z 16 (-globals_size))), |
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80 | pi2 … spb» in |
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81 | (* let ispp : xpointer ≝ mk_pointer ispb (mk_offset (bitvector_of_nat ? 47)) in *) |
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82 | let main ≝ prog_main … p in |
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83 | let st0 ≝ mk_state pars (Some ? (empty_framesT …)) empty_is (BBbit false) (empty_regsT … spp) m in |
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84 | (* use exit_pc as ra and call_dest_for_main as dest *) |
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85 | let st0' ≝ mk_state_pc … (set_sp … spp st0) exit_pc exit_pc in |
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86 | ! st0_no_pc ← save_frame ?? sem_globals ID (call_dest_for_main … pars) st0' ; |
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87 | let st0'' ≝ set_no_pc … st0_no_pc st0' in |
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88 | ! bl ← block_of_call … ge (inl … main) st0''; |
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89 | ! 〈i, fn〉 ← fetch_function … ge bl ; |
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90 | match fn with |
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91 | [ Internal ifn ⇒ |
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92 | ! st' ← eval_internal_call … ge i ifn (call_args_for_main … pars) st0'' ; |
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93 | let pc' ≝ pc_of_point … bl (joint_if_entry … ifn) in |
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94 | return mk_state_pc … st' pc' exit_pc |
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95 | | External _ ⇒ Error … [MSG BadMain; CTX ? main] (* External main not supported: why? *) |
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96 | ]. |
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97 | cases m0 in H; #m1 #m2 #m3 #H |
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98 | whd in H:(???%); destruct whd in ⊢(??%?); @Zleb_elim_Type0 // #abs @⊥ |
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99 | @(absurd … (irreflexive_Zlt …)) % #I cases (I OZ) /3 by Zlt_to_Zle_to_Zlt/ |
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100 | qed. |
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101 | |
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102 | definition joint_classify_step : |
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103 | ∀p : evaluation_params.joint_step p (globals … p) → status_class ≝ |
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104 | λp,stmt. |
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105 | match stmt with |
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106 | [ CALL f args dest ⇒ cl_call |
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107 | | COND _ _ ⇒ cl_jump |
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108 | | _ ⇒ cl_other |
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109 | ]. |
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110 | |
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111 | definition joint_classify_final : |
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112 | ∀p : evaluation_params.joint_fin_step p → status_class ≝ |
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113 | λp,stmt. |
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114 | match stmt with |
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115 | [ GOTO _ ⇒ cl_other |
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116 | | RETURN ⇒ cl_return |
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117 | | TAILCALL _ f args ⇒ cl_tailcall |
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118 | ]. |
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119 | |
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120 | definition joint_classify : |
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121 | ∀p : evaluation_params.state_pc p → status_class ≝ |
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122 | λp,st. |
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123 | match fetch_statement … (ev_genv p) (pc … st) with |
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124 | [ OK i_fn_s ⇒ |
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125 | match \snd i_fn_s with |
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126 | [ sequential s _ ⇒ joint_classify_step p s |
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127 | | final s ⇒ joint_classify_final p s |
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128 | | FCOND _ _ _ _ ⇒ cl_jump |
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129 | ] |
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130 | | _ ⇒ cl_other |
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131 | ]. |
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132 | |
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133 | lemma joint_classify_call : ∀p : evaluation_params.∀st. |
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134 | joint_classify p st = cl_call → |
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135 | ∃i_f,f',args,dest,next. |
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136 | fetch_statement … (ev_genv p) (pc … st) = |
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137 | OK ? 〈i_f, sequential … (CALL … f' args dest) next〉. |
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138 | #p #st |
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139 | whd in match joint_classify; normalize nodelta |
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140 | inversion (fetch_statement … (ev_genv p) (pc … st)) |
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141 | [2: #e #_ whd in ⊢ (??%?→?); #ABS destruct(ABS) ] |
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142 | * #i_f * |
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143 | [2,3: [ * [ #lbl | | #fl #f #args ] | #fl #a #ltrue #lfalse ] #_ |
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144 | normalize nodelta normalize in ⊢ (%→?); #ABS destruct |
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145 | ] |
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146 | * [ #c | #f' #args #dest | #a #lbl | #s ] #nxt #fetch normalize nodelta |
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147 | normalize in ⊢ (%→?); #EQ destruct |
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148 | %[|%[|%[|%[|%[| %]]]]] |
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149 | qed. |
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150 | |
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151 | definition joint_after_ret : ∀p:evaluation_params. |
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152 | (Σs : state_pc p.joint_classify p s = cl_call) → state_pc p → Prop ≝ |
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153 | λp,s1,s2. |
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154 | match fetch_statement … (ev_genv p) (pc … s1) with |
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155 | [ OK x ⇒ |
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156 | match \snd x with |
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157 | [ sequential s next ⇒ |
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158 | last_pop … s2 = pc … s1 ∧ |
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159 | pc … s2 = succ_pc p (pc … s1) next |
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160 | | _ ⇒ False (* never happens *) |
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161 | ] |
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162 | | _ ⇒ False (* never happens *) |
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163 | ]. |
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164 | |
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165 | definition joint_call_ident : ∀p:evaluation_params. |
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166 | state_pc p → ident ≝ |
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167 | (* this is a definition without a dummy ident : |
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168 | λp,st. |
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169 | match ? |
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170 | return λx. |
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171 | !〈f, s〉 ← fetch_statement ? p … (ev_genv p) (pc … st) ; |
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172 | match s with |
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173 | [ sequential s next ⇒ |
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174 | match s with |
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175 | [ CALL f' args dest ⇒ function_of_call … (ev_genv p) st f' |
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176 | | _ ⇒ Error … [ ] |
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177 | ] |
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178 | | _ ⇒ Error … [ ] |
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179 | ] = x → ? with |
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180 | [ OK v ⇒ λ_.v |
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181 | | Error e ⇒ λABS.⊥ |
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182 | ] (refl …). |
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183 | @hide_prf |
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184 | elim (joint_classify_call … (pi2 … st)) |
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185 | #f *#f' *#args *#dest *#next *#fn *#fd ** #EQ1 #EQ2 #EQ3 |
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186 | lapply ABS -ABS |
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187 | >EQ1 >m_return_bind normalize nodelta >EQ2 #ABS destruct(ABS) |
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188 | qed. *) |
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189 | (* with a dummy ident (which is never used as seen above in the commented script) |
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190 | I think handling of the function is easier *) |
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191 | λp,st. |
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192 | let dummy : ident ≝ an_identifier ? one in (* used where it cannot ever happen *) |
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193 | match fetch_statement … (ev_genv p) (pc … st) with |
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194 | [ OK x ⇒ |
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195 | match \snd x with |
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196 | [ sequential s next ⇒ |
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197 | match s with |
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198 | [ CALL f' args dest ⇒ |
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199 | match |
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200 | (! bl ← block_of_call … (ev_genv p) f' st; |
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201 | fetch_internal_function … (ev_genv p) bl) with |
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202 | [ OK i_f ⇒ \fst i_f |
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203 | | _ ⇒ dummy |
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204 | ] |
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205 | | _ ⇒ dummy |
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206 | ] |
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207 | | _ ⇒ dummy |
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208 | ] |
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209 | | _ ⇒ dummy |
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210 | ]. |
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211 | |
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212 | definition joint_tailcall_ident : ∀p:evaluation_params. |
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213 | state_pc p → ident ≝ |
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214 | λp,st. |
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215 | let dummy : ident ≝ an_identifier ? one in (* used where it cannot ever happen *) |
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216 | match fetch_statement … (ev_genv p) (pc … st) with |
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217 | [ OK x ⇒ |
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218 | match \snd x with |
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219 | [ final s ⇒ |
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220 | match s with |
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221 | [ TAILCALL _ f' args ⇒ |
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222 | match |
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223 | (! bl ← block_of_call … (ev_genv p) f' st; |
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224 | fetch_internal_function … (ev_genv p) bl) with |
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225 | [ OK i_f ⇒ \fst i_f |
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226 | | _ ⇒ dummy |
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227 | ] |
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228 | | _ ⇒ dummy |
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229 | ] |
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230 | | _ ⇒ dummy |
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231 | ] |
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232 | | _ ⇒ dummy |
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233 | ]. |
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234 | |
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235 | definition pcDeq ≝ mk_DeqSet program_counter eq_program_counter ?. |
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236 | *#p1 #EQ1 * #p2 #EQ2 @eq_program_counter_elim |
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237 | [ #EQ destruct % #H % |
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238 | | * #NEQ % #ABS destruct elim (NEQ ?) % |
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239 | ] |
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240 | qed. |
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241 | |
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242 | (* |
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243 | let rec io_evaluate O I X (env : ∀o.res (I o)) (c : IO O I X) on c : res X ≝ |
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244 | match c with |
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245 | [ Value x ⇒ OK … x |
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246 | | Interact o f ⇒ |
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247 | ! i ← env o ; |
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248 | io_evaluate O I X env (f i) |
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249 | | Wrong e ⇒ Error … e |
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250 | ]. |
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251 | *) |
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252 | |
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253 | definition cost_label_of_stmt : |
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254 | ∀p : evaluation_params.joint_statement p (globals p) → option costlabel ≝ |
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255 | λp,s.match s with |
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256 | [ sequential s _ ⇒ |
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257 | match s with |
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258 | [ COST_LABEL lbl ⇒ Some ? lbl |
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259 | | _ ⇒ None ? |
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260 | ] |
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261 | | _ ⇒ None ? |
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262 | ]. |
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263 | |
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264 | definition joint_label_of_pc ≝ |
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265 | λp : evaluation_params. |
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266 | (λpc. |
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267 | match fetch_statement … (ev_genv p) pc with |
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268 | [ OK fn_stmt ⇒ cost_label_of_stmt … (\snd fn_stmt) |
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269 | | _ ⇒ None ? |
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270 | ]). |
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271 | |
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272 | definition joint_abstract_status : |
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273 | ∀p : prog_params. |
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274 | abstract_status ≝ |
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275 | λp. |
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276 | mk_abstract_status |
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277 | (* as_status ≝ *) (state_pc p) |
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278 | (* as_execute ≝ *) |
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279 | (λs1,s2.eval_state … (ev_genv p) s1 = return s2) |
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280 | (* (* as_init ≝ *) (make_initial_state p) *) |
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281 | (* as_pc ≝ *) pcDeq |
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282 | (* as_pc_of ≝ *) (pc …) |
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283 | (* as_classify ≝ *) (joint_classify p) |
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284 | (* as_label_of_pc ≝ *) (joint_label_of_pc p) |
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285 | (* as_after_return ≝ *) (joint_after_ret p) |
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286 | (* as_result ≝ *) (is_final p (globals ?) (ev_genv p) exit_pc) |
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287 | (* as_call_ident ≝ *) (λst.joint_call_ident p st) |
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288 | (* as_tailcall_ident ≝ *) (λst.joint_tailcall_ident p st). |
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289 | |
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290 | (* alternative definition with integrated prog_params constructor *) |
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291 | definition joint_status : |
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292 | ∀p : sem_params. |
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293 | joint_program p → (ident → option ℕ) → abstract_status ≝ |
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294 | λp,prog,stacksizes.joint_abstract_status (mk_prog_params p prog stacksizes). |
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