1 | (* Memory model used in the dynamic semantics of the back-end intermediate |
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2 | languages. Inspired by common/Mem.ma, adapted from Compcert *) |
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3 | |
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4 | (* * This file develops the memory model that is used in the dynamic |
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5 | semantics of all the languages used in the compiler. |
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6 | It defines a type [mem] of memory states, the following 4 basic |
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7 | operations over memory states, and their properties: |
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8 | - [load]: read a memory chunk at a given address; |
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9 | - [store]: store a memory chunk at a given address; |
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10 | - [alloc]: allocate a fresh memory block; |
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11 | - [free]: invalidate a memory block. |
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12 | *) |
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13 | |
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14 | include "common/ByteValues.ma". |
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15 | include "common/GenMem.ma". |
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16 | |
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17 | definition bemem ≝ mem. |
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18 | |
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19 | definition is_addressable : region → bool ≝ λr.match r with |
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20 | [ XData ⇒ true | Code ⇒ true | _ ⇒ false ]. |
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21 | |
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22 | |
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23 | definition is_address : (beval × beval) → Prop ≝ λa. |
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24 | ∃p : Σp.bool_to_Prop (is_addressable (ptype p)).∃p0,p1. |
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25 | \fst a = BVptr p p0 ∧ part_no … p0 = 0 ∧ |
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26 | \snd a = BVptr p p1 ∧ part_no … p1 = 1. |
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27 | |
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28 | definition is_addressb : (beval × beval) → bool ≝ λa. |
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29 | match a with |
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30 | [ mk_Prod a0 a1 ⇒ |
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31 | match a0 with |
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32 | [ BVptr p0 part0 ⇒ |
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33 | is_addressable (ptype p0) ∧ eqb part0 0 ∧ |
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34 | match a1 with |
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35 | [ BVptr p1 part1 ⇒ |
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36 | eq_pointer p0 p1 ∧ eqb part1 1 |
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37 | | _ ⇒ false |
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38 | ] |
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39 | | _ ⇒ false |
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40 | ] |
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41 | ]. |
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42 | |
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43 | lemma is_addressb_elim : ∀P : bool → Prop.∀a : beval × beval. |
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44 | (is_address a → P true) → (¬is_address a → P false) → P (is_addressb a). |
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45 | #P * * |
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46 | [4:|*: [|#b0|(*#r0*)#part0] #a1 #_ #Pfalse @Pfalse % * #x * #p0 * #p1 *** #EQ destruct(EQ)] |
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47 | #p0 #part0 #a1 |
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48 | whd in match is_addressb; normalize nodelta |
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49 | elim (true_or_false_Prop (is_addressable (ptype p0))) |
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50 | #H >H |
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51 | [ @(eqb_elim part0 0) #Heq |
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52 | [ cases a1 [|#b0|(*#r0*)#part0|#p1#part1] whd in match (?∧?); |
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53 | [4: @eq_pointer_elim #Heq' |
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54 | [ @(eqb_elim part1 1) #Heq'' |
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55 | [ #Ptrue #_ @Ptrue destruct |
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56 | %{p1} [assumption] %{part0} %{part1} |
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57 | % [ % [ % ]] try % assumption |
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58 | ] |
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59 | ] |
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60 | ] |
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61 | ] |
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62 | ] |
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63 | #_ #Pfalse @Pfalse % ** #p0' #H' * #part0' * #part1' *** |
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64 | #H0 #H1 #H2 #H3 destruct /2 by absurd/ |
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65 | qed. |
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66 | |
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67 | (* CSC: only pointers to XRAM or code memory ATM *) |
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68 | definition address ≝ beval × beval. |
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69 | definition safe_address ≝ Sig address is_address. |
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70 | unification hint 0 ≔ ; |
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71 | P ≟ Prod beval beval |
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72 | (*------------------*)⊢ |
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73 | safe_address ≡ Sig P is_address. |
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74 | |
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75 | definition eq_address: address → address → bool ≝ |
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76 | λaddr1,addr2. |
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77 | eq_beval (\fst addr1) (\fst addr2) ∧ eq_beval (\snd addr1) (\snd addr2). |
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78 | |
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79 | definition pointer_of_address: address → res pointer ≝ |
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80 | λp. let 〈v1,v2〉 ≝ p in pointer_of_bevals [v1;v2]. |
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81 | |
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82 | definition pointer_of_address_safe : safe_address → pointer ≝ |
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83 | λp.match \fst p return λx.\fst p = x → ? with |
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84 | [ BVptr ptr _ ⇒ λ_.ptr |
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85 | | _ ⇒ λabs.⊥ |
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86 | ] (refl …). |
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87 | lapply abs -abs cases p |
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88 | * #a0 #a1 * #x * #p0 * #p1 *** #H0 #H1 #H2 #H3 #H4 |
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89 | destruct(H0 H4) |
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90 | qed. |
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91 | (* For full 8051 memory spaces |
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92 | definition pointer_compat' ≝ λb,r. |
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93 | match b with |
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94 | [ mk_block r' z ⇒ |
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95 | if eq_region r' r then True |
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96 | else |
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97 | match r with |
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98 | [ Any ⇒ True |
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99 | | XData ⇒ match r' with |
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100 | [ PData ⇒ True |
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101 | | _ ⇒ False |
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102 | ] |
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103 | | _ ⇒ False |
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104 | ] |
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105 | ]. |
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106 | |
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107 | lemma pointer_compat_to_ind : ∀b,r.pointer_compat' b r → pointer_compat b r. |
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108 | ** #z ** // |
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109 | qed. |
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110 | |
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111 | lemma pointer_compat_from_ind : ∀b,r.pointer_compat b r → pointer_compat' b r. |
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112 | #b #r #H inversion H |
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113 | [ #s #id #EQ1 #EQ2 #EQ3 whd >reflexive_eq_region % |
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114 | | #id #EQ1 #EQ2 #EQ3 % |
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115 | | #r #id #EQ1 #EQ2 #EQ3 whd @eq_region_elim #EQ4 destruct(EQ4) % |
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116 | ] |
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117 | qed. |
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118 | *) |
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119 | lemma pointer_of_address_is_safe : ∀a : safe_address.pointer_of_address a = OK … (pointer_of_address_safe a). |
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120 | ** #a0 #a1 ***** #z #o |
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121 | #Hr |
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122 | (* |
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123 | ** #a0 #a1 ***** #r #z #Hr #o * lapply (pointer_compat_from_ind ?? Hr) |
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124 | cases r in Hr ⊢ %; #Hr * |
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125 | *) |
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126 | ** #part0 #H0 ** #part1 #H1 *** #EQa0 #EQpart0 #EQa1 #EQpart1 |
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127 | destruct normalize |
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128 | @eqZb_elim [2,4,6: * #ABS elim (ABS (refl …))] |
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129 | @eqZb_elim [2,4,6: * #ABS elim (ABS (refl …))] |
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130 | #_ #_ normalize % |
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131 | qed. |
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132 | |
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133 | definition address_of_pointer : pointer → res address ≝ beval_pair_of_pointer. |
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134 | |
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135 | example address_of_pointer_OK_to_safe : |
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136 | ∀p,a.address_of_pointer p = OK … a → is_address a. |
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137 | #p |
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138 | lapply (refl … p) |
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139 | generalize in match p in ⊢ (???%→%); *(***) |
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140 | whd in match (address_of_pointer ?); |
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141 | #b (*#H*) #o #EQp * #a0 #a1 |
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142 | normalize #EQ destruct(EQ) |
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143 | %{p} >EQp [ cases (block_region b) // | % [2: % [2: % [ % [ % ] ] ] ] % |
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144 | (* |
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145 | %{p} >EQp [1,3: %] |
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146 | % [2,4: % [2,4: % [1,3: % [1,3: %]]]] % |
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147 | *) |
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148 | qed. |
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149 | |
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150 | definition safe_address_of_pointer: pointer → res safe_address ≝ λp. |
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151 | do a as EQ ← address_of_pointer p ; return «a ,address_of_pointer_OK_to_safe ?? EQ». |
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152 | |
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153 | lemma address_of_pointer_is_safe : |
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154 | ∀p.address_of_pointer p = ! a ← safe_address_of_pointer p ; return (a : address). |
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155 | #p normalize % qed. |
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156 | (* |
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157 | ****#z #H |
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158 | lapply (pointer_compat_from_ind ?? H) * #o |
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159 | normalize % |
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160 | qed.*) |
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161 | |
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162 | definition code_pointer_of_address: address → res (Σp:pointer. ptype p = Code) ≝ |
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163 | code_pointer_of_beval_pair. |
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164 | |
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165 | definition address_of_code_pointer: (Σp:pointer. ptype p = Code) → address ≝ beval_pair_of_code_pointer. |
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166 | |
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167 | definition safe_address_of_code_pointer: (Σp:pointer. ptype p = Code) → safe_address ≝ address_of_code_pointer. |
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168 | cases H -H * #b #o normalize cases b * #z #EQ destruct |
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169 | %{«mk_pointer (mk_block Code z) o,I»} |
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170 | % [2: % [2: % [ % [ % ]]]] % |
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171 | qed. |
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172 | (* |
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173 | cases H -H * #r #b #H #o #EQ destruct(EQ) normalize lapply H |
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174 | lapply (pointer_compat_from_ind … H) -H cases b * #z * #H |
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175 | %{«mk_pointer ? (mk_block Code z) H o,I»} |
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176 | % [2: % [2: % [ % [ % ]] % |]|] |
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177 | qed.*) |
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178 | |
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179 | (* Paolo: why only code pointers and not XRAM too? *) |
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180 | definition addr_add: address → nat → res address ≝ |
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181 | λaddr,n. |
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182 | do ptr ← code_pointer_of_address addr ; |
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183 | OK … (address_of_code_pointer (shift_pointer 16 ptr (bitvector_of_nat … n))). |
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184 | normalize cases ptr #p #E @E |
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185 | qed. |
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186 | |
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187 | definition safe_addr_add: safe_address → nat → res safe_address ≝ |
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188 | λaddr,n. |
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189 | do ptr ← code_pointer_of_address addr ; |
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190 | OK … (safe_address_of_code_pointer (shift_pointer 16 ptr (bitvector_of_nat … n))). |
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191 | normalize cases ptr #p #E @E |
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192 | qed. |
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193 | |
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194 | definition addr_sub: address → nat → res address ≝ |
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195 | λaddr,n. |
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196 | do ptr ← code_pointer_of_address addr ; |
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197 | OK … (address_of_code_pointer (neg_shift_pointer 16 ptr (bitvector_of_nat … n))). |
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198 | normalize cases ptr #p #E @E |
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199 | qed. |
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200 | |
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201 | definition safe_addr_sub: safe_address → nat → res safe_address ≝ |
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202 | λaddr,n. |
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203 | do ptr ← code_pointer_of_address addr ; |
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204 | OK … (safe_address_of_code_pointer (neg_shift_pointer 16 ptr (bitvector_of_nat … n))). |
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205 | normalize cases ptr #p #E @E |
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206 | qed. |
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