1 | (* Operations common to the Cminor and RTLabs front end stages. *) |
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2 | |
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3 | (* Adapted from CompCert's Cminor.ma: *) |
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4 | |
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5 | (* *********************************************************************) |
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6 | (* *) |
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7 | (* The Compcert verified compiler *) |
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8 | (* *) |
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9 | (* Xavier Leroy, INRIA Paris-Rocquencourt *) |
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10 | (* *) |
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11 | (* Copyright Institut National de Recherche en Informatique et en *) |
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12 | (* Automatique. All rights reserved. This file is distributed *) |
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13 | (* under the terms of the GNU General Public License as published by *) |
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14 | (* the Free Software Foundation, either version 2 of the License, or *) |
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15 | (* (at your option) any later version. This file is also distributed *) |
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16 | (* under the terms of the INRIA Non-Commercial License Agreement. *) |
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17 | (* *) |
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18 | (* *********************************************************************) |
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19 | |
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20 | include "common/Values.ma". |
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21 | |
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22 | inductive constant : Type[0] ≝ |
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23 | | Ointconst: ∀sz. bvint sz → constant (**r integer constant *) |
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24 | | Ofloatconst: float → constant (**r floating-point constant *) |
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25 | | Oaddrsymbol: ident → nat → constant (**r address of the symbol plus the offset *) |
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26 | | Oaddrstack: nat → constant. (**r stack pointer plus the given offset *) |
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27 | |
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28 | inductive unary_operation : Type[0] ≝ |
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29 | | Ocastint: intsize → signedness → unary_operation (**r 8-bit zero extension *) |
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30 | | Onegint: unary_operation (**r integer opposite *) |
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31 | | Onotbool: unary_operation (**r boolean negation *) |
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32 | | Onotint: unary_operation (**r bitwise complement *) |
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33 | | Onegf: unary_operation (**r float opposite *) |
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34 | | Oabsf: unary_operation (**r float absolute value *) |
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35 | | Osingleoffloat: unary_operation (**r float truncation *) |
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36 | | Ointoffloat: intsize → unary_operation (**r signed integer to float *) |
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37 | | Ointuoffloat: intsize → unary_operation (**r unsigned integer to float *) |
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38 | | Ofloatofint: unary_operation (**r float to signed integer *) |
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39 | | Ofloatofintu: unary_operation (**r float to unsigned integer *) |
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40 | | Oid: unary_operation (**r identity (used to move between registers *) |
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41 | | Optrofint: region → unary_operation (**r int to pointer with given representation *) |
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42 | | Ointofptr: intsize → unary_operation. (**r pointer to int *) |
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43 | |
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44 | inductive binary_operation : Type[0] ≝ |
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45 | | Oadd: binary_operation (**r integer addition *) |
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46 | | Osub: binary_operation (**r integer subtraction *) |
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47 | | Omul: binary_operation (**r integer multiplication *) |
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48 | | Odiv: binary_operation (**r integer signed division *) |
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49 | | Odivu: binary_operation (**r integer unsigned division *) |
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50 | | Omod: binary_operation (**r integer signed modulus *) |
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51 | | Omodu: binary_operation (**r integer unsigned modulus *) |
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52 | | Oand: binary_operation (**r bitwise ``and'' *) |
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53 | | Oor: binary_operation (**r bitwise ``or'' *) |
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54 | | Oxor: binary_operation (**r bitwise ``xor'' *) |
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55 | | Oshl: binary_operation (**r left shift *) |
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56 | | Oshr: binary_operation (**r right signed shift *) |
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57 | | Oshru: binary_operation (**r right unsigned shift *) |
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58 | | Oaddf: binary_operation (**r float addition *) |
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59 | | Osubf: binary_operation (**r float subtraction *) |
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60 | | Omulf: binary_operation (**r float multiplication *) |
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61 | | Odivf: binary_operation (**r float division *) |
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62 | | Ocmp: comparison -> binary_operation (**r integer signed comparison *) |
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63 | | Ocmpu: comparison -> binary_operation (**r integer unsigned comparison *) |
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64 | | Ocmpf: comparison -> binary_operation (**r float comparison *) |
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65 | | Oaddp: binary_operation (**r add an integer to a pointer *) |
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66 | | Osubpi: binary_operation (**r subtract int from a pointers *) |
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67 | | Osubpp: intsize → binary_operation (**r subtract two pointers *) |
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68 | | Ocmpp: comparison → binary_operation. (**r compare pointers *) |
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69 | |
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70 | |
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71 | (* * Evaluation of constants and operator applications. |
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72 | [None] is returned when the computation is undefined, e.g. |
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73 | if arguments are of the wrong types, or in case of an integer division |
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74 | by zero. *) |
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75 | |
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76 | definition eval_constant : (ident → option block) → block → constant → option val ≝ |
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77 | λfind_symbol,sp,cst. |
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78 | match cst with |
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79 | [ Ointconst sz n ⇒ Some ? (Vint sz n) |
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80 | | Ofloatconst n ⇒ Some ? (Vfloat n) |
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81 | | Oaddrsymbol s ofs ⇒ |
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82 | match find_symbol s with |
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83 | [ None ⇒ None ? |
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84 | | Some b ⇒ Some ? (Vptr Any b (match b with [ mk_block r id ⇒ universal_compat r id ]) (shift_offset ? zero_offset (repr I16 ofs))) |
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85 | ] |
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86 | | Oaddrstack ofs ⇒ |
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87 | Some ? (Vptr Any sp ? (shift_offset ? zero_offset (repr I16 ofs))) |
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88 | ]. cases sp // qed. |
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89 | |
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90 | definition eval_unop : unary_operation → val → option val ≝ |
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91 | λop,arg. |
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92 | match op with |
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93 | [ Ocastint sz sg ⇒ |
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94 | match sg with |
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95 | [ Unsigned ⇒ Some ? (zero_ext sz arg) |
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96 | | Signed ⇒ Some ? (sign_ext sz arg) |
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97 | ] |
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98 | | Onegint ⇒ match arg with [ Vint sz1 n1 ⇒ Some ? (Vint sz1 (two_complement_negation ? n1)) | _ ⇒ None ? ] |
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99 | | Onotbool ⇒ match arg with [ Vint sz1 n1 ⇒ Some ? (of_bool (eq_bv ? n1 (zero ?))) |
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100 | | Vptr _ _ _ _ ⇒ Some ? Vfalse |
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101 | | Vnull _ ⇒ Some ? Vtrue |
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102 | | _ ⇒ None ? |
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103 | ] |
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104 | | Onotint ⇒ match arg with [ Vint sz1 n1 ⇒ Some ? (Vint sz1 (exclusive_disjunction_bv ? n1 (mone ?))) | _ ⇒ None ? ] |
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105 | | Onegf ⇒ match arg with [ Vfloat f1 ⇒ Some ? (Vfloat (Fneg f1)) | _ ⇒ None ? ] |
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106 | | Oabsf ⇒ match arg with [ Vfloat f1 ⇒ Some ? (Vfloat (Fabs f1)) | _ ⇒ None ? ] |
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107 | | Osingleoffloat ⇒ Some ? (singleoffloat arg) |
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108 | | Ointoffloat sz ⇒ match arg with [ Vfloat f1 ⇒ Some ? (Vint sz (intoffloat ? f1)) | _ ⇒ None ? ] |
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109 | | Ointuoffloat sz ⇒ match arg with [ Vfloat f1 ⇒ Some ? (Vint sz (intuoffloat ? f1)) | _ ⇒ None ? ] |
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110 | | Ofloatofint ⇒ match arg with [ Vint sz1 n1 ⇒ Some ? (Vfloat (floatofint ? n1)) | _ ⇒ None ? ] |
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111 | | Ofloatofintu ⇒ match arg with [ Vint sz1 n1 ⇒ Some ? (Vfloat (floatofintu ? n1)) | _ ⇒ None ? ] |
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112 | | Oid ⇒ Some ? arg (* XXX should we restricted the values allowed? *) |
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113 | (* Only conversion of null pointers is specified. *) |
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114 | | Optrofint r ⇒ match arg with [ Vint sz1 n1 ⇒ if eq_bv ? n1 (zero ?) then Some ? (Vnull r) else None ? | _ ⇒ None ? ] |
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115 | | Ointofptr sz ⇒ match arg with [ Vnull _ ⇒ Some ? (Vint sz (zero ?)) | _ ⇒ None ? ] |
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116 | ]. |
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117 | |
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118 | (* I think this is duplicated somewhere else *) |
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119 | definition eval_compare_mismatch : comparison → option val ≝ |
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120 | λc. match c with [ Ceq ⇒ Some ? Vfalse | Cne ⇒ Some ? Vtrue | _ ⇒ None ? ]. |
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121 | |
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122 | (* Individual operations, adapted from Values. These differ in that they |
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123 | implement the plain Cminor/RTLabs operations (e.g., with separate addition |
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124 | for ints,floats and pointers) and use option rather than Vundef. The ones |
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125 | in Value are probably not needed. *) |
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126 | |
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127 | definition ev_add ≝ λv1,v2: val. |
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128 | match v1 with |
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129 | [ Vint sz1 n1 ⇒ match v2 with |
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130 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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131 | (λn1. Some ? (Vint ? (addition_n ? n1 n2))) |
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132 | (None ?) |
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133 | | _ ⇒ None ? ] |
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134 | | _ ⇒ None ? ]. |
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135 | |
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136 | definition ev_sub ≝ λv1,v2: val. |
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137 | match v1 with |
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138 | [ Vint sz1 n1 ⇒ match v2 with |
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139 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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140 | (λn1. Some ? (Vint ? (subtraction ? n1 n2))) |
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141 | (None ?) |
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142 | | _ ⇒ None ? ] |
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143 | | _ ⇒ None ? ]. |
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144 | |
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145 | (* NB: requires arguments to be presented pointer first. *) |
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146 | definition ev_addp ≝ λv1,v2: val. |
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147 | match v1 with |
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148 | [ Vptr r b1 p ofs1 ⇒ match v2 with |
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149 | [ Vint sz2 n2 ⇒ Some ? (Vptr r b1 p (shift_offset ? ofs1 n2)) |
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150 | | _ ⇒ None ? ] |
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151 | | Vnull r ⇒ match v2 with |
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152 | [ Vint sz2 n2 ⇒ if eq_bv ? n2 (zero ?) then Some ? (Vnull r) else None ? |
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153 | | _ ⇒ None ? |
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154 | ] |
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155 | | _ ⇒ None ? ]. |
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156 | |
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157 | definition ev_subpi ≝ λv1,v2: val. |
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158 | match v1 with |
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159 | [ Vptr r1 b1 p1 ofs1 ⇒ match v2 with |
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160 | [ Vint sz2 n2 ⇒ Some ? (Vptr r1 b1 p1 (neg_shift_offset ? ofs1 n2)) |
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161 | | _ ⇒ None ? ] |
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162 | | Vnull r ⇒ match v2 with [ Vint sz2 n2 ⇒ if eq_bv ? n2 (zero ?) then Some ? (Vnull r) else None ? | _ ⇒ None ? ] |
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163 | | _ ⇒ None ? ]. |
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164 | |
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165 | definition ev_subpp ≝ λsz. λv1,v2: val. |
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166 | match v1 with |
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167 | [ Vptr r1 b1 p1 ofs1 ⇒ match v2 with |
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168 | [ Vptr r2 b2 p2 ofs2 ⇒ |
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169 | if eq_block b1 b2 then Some ? (Vint sz (sub_offset ? ofs1 ofs2)) else None ? |
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170 | | _ ⇒ None ? ] |
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171 | | Vnull r ⇒ match v2 with [ Vnull r' ⇒ Some ? (Vint sz (zero ?)) | _ ⇒ None ? ] |
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172 | | _ ⇒ None ? ]. |
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173 | |
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174 | definition ev_mul ≝ λv1, v2: val. |
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175 | match v1 with |
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176 | [ Vint sz1 n1 ⇒ match v2 with |
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177 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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178 | (λn1. Some ? (Vint ? (\snd (split … (multiplication ? n1 n2))))) |
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179 | (None ?) |
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180 | | _ ⇒ None ? ] |
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181 | | _ ⇒ None ? ]. |
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182 | |
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183 | definition ev_divs ≝ λv1, v2: val. |
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184 | match v1 with |
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185 | [ Vint sz1 n1 ⇒ match v2 with |
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186 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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187 | (λn1. option_map ?? (Vint ?) (division_s ? n1 n2)) |
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188 | (None ?) |
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189 | | _ ⇒ None ? ] |
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190 | | _ ⇒ None ? ]. |
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191 | |
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192 | definition ev_mods ≝ λv1, v2: val. |
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193 | match v1 with |
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194 | [ Vint sz1 n1 ⇒ match v2 with |
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195 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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196 | (λn1. option_map ?? (Vint ?) (modulus_s ? n1 n2)) |
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197 | (None ?) |
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198 | | _ ⇒ None ? |
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199 | ] |
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200 | | _ ⇒ None ? |
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201 | ]. |
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202 | |
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203 | definition ev_divu ≝ λv1, v2: val. |
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204 | match v1 with |
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205 | [ Vint sz1 n1 ⇒ match v2 with |
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206 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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207 | (λn1. option_map ?? (Vint ?) (division_u ? n1 n2)) |
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208 | (None ?) |
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209 | | _ ⇒ None ? |
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210 | ] |
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211 | | _ ⇒ None ? |
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212 | ]. |
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213 | |
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214 | definition ev_modu ≝ λv1, v2: val. |
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215 | match v1 with |
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216 | [ Vint sz1 n1 ⇒ match v2 with |
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217 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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218 | (λn1. option_map ?? (Vint ?) (modulus_u ? n1 n2)) |
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219 | (None ?) |
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220 | | _ ⇒ None ? |
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221 | ] |
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222 | | _ ⇒ None ? |
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223 | ]. |
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224 | |
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225 | definition ev_and ≝ λv1, v2: val. |
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226 | match v1 with |
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227 | [ Vint sz1 n1 ⇒ match v2 with |
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228 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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229 | (λn1. Some ? (Vint ? (conjunction_bv ? n1 n2))) |
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230 | (None ?) |
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231 | | _ ⇒ None ? ] |
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232 | | _ ⇒ None ? ]. |
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233 | |
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234 | definition ev_or ≝ λv1, v2: val. |
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235 | match v1 with |
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236 | [ Vint sz1 n1 ⇒ match v2 with |
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237 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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238 | (λn1. Some ? (Vint ? (inclusive_disjunction_bv ? n1 n2))) |
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239 | (None ?) |
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240 | | _ ⇒ None ? ] |
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241 | | _ ⇒ None ? ]. |
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242 | |
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243 | definition ev_xor ≝ λv1, v2: val. |
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244 | match v1 with |
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245 | [ Vint sz1 n1 ⇒ match v2 with |
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246 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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247 | (λn1. Some ? (Vint ? (exclusive_disjunction_bv ? n1 n2))) |
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248 | (None ?) |
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249 | | _ ⇒ None ? ] |
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250 | | _ ⇒ None ? ]. |
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251 | |
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252 | definition ev_shl ≝ λv1, v2: val. |
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253 | match v1 with |
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254 | [ Vint sz1 n1 ⇒ match v2 with |
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255 | [ Vint sz2 n2 ⇒ |
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256 | if lt_u ? n2 (bitvector_of_nat … (bitsize_of_intsize sz1)) |
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257 | then Some ? (Vint sz1 (shift_left ?? (nat_of_bitvector … n2) n1 false)) |
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258 | else None ? |
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259 | | _ ⇒ None ? ] |
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260 | | _ ⇒ None ? ]. |
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261 | |
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262 | definition ev_shr ≝ λv1, v2: val. |
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263 | match v1 with |
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264 | [ Vint sz1 n1 ⇒ match v2 with |
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265 | [ Vint sz2 n2 ⇒ |
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266 | if lt_u ? n2 (bitvector_of_nat … (bitsize_of_intsize sz1)) |
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267 | then Some ? (Vint sz1 (shift_right ?? (nat_of_bitvector … n2) n1 (head' … n1))) |
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268 | else None ? |
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269 | | _ ⇒ None ? ] |
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270 | | _ ⇒ None ? ]. |
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271 | |
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272 | definition ev_shru ≝ λv1, v2: val. |
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273 | match v1 with |
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274 | [ Vint sz1 n1 ⇒ match v2 with |
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275 | [ Vint sz2 n2 ⇒ |
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276 | if lt_u ? n2 (bitvector_of_nat … (bitsize_of_intsize sz1)) |
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277 | then Some ? (Vint sz1 (shift_right ?? (nat_of_bitvector … n2) n1 false)) |
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278 | else None ? |
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279 | | _ ⇒ None ? ] |
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280 | | _ ⇒ None ? ]. |
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281 | |
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282 | definition ev_addf ≝ λv1,v2: val. |
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283 | match v1 with |
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284 | [ Vfloat f1 ⇒ match v2 with |
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285 | [ Vfloat f2 ⇒ Some ? (Vfloat (Fadd f1 f2)) |
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286 | | _ ⇒ None ? ] |
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287 | | _ ⇒ None ? ]. |
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288 | |
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289 | definition ev_subf ≝ λv1,v2: val. |
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290 | match v1 with |
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291 | [ Vfloat f1 ⇒ match v2 with |
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292 | [ Vfloat f2 ⇒ Some ? (Vfloat (Fsub f1 f2)) |
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293 | | _ ⇒ None ? ] |
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294 | | _ ⇒ None ? ]. |
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295 | |
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296 | definition ev_mulf ≝ λv1,v2: val. |
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297 | match v1 with |
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298 | [ Vfloat f1 ⇒ match v2 with |
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299 | [ Vfloat f2 ⇒ Some ? (Vfloat (Fmul f1 f2)) |
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300 | | _ ⇒ None ? ] |
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301 | | _ ⇒ None ? ]. |
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302 | |
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303 | definition ev_divf ≝ λv1,v2: val. |
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304 | match v1 with |
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305 | [ Vfloat f1 ⇒ match v2 with |
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306 | [ Vfloat f2 ⇒ Some ? (Vfloat (Fdiv f1 f2)) |
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307 | | _ ⇒ None ? ] |
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308 | | _ ⇒ None ? ]. |
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309 | |
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310 | definition ev_cmp_match : comparison → option val ≝ λc. |
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311 | match c with |
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312 | [ Ceq ⇒ Some ? Vtrue |
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313 | | Cne ⇒ Some ? Vfalse |
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314 | | _ ⇒ None ? |
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315 | ]. |
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316 | |
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317 | definition ev_cmp_mismatch : comparison → option val ≝ λc. |
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318 | match c with |
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319 | [ Ceq ⇒ Some ? Vfalse |
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320 | | Cne ⇒ Some ? Vtrue |
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321 | | _ ⇒ None ? |
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322 | ]. |
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323 | |
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324 | definition ev_cmp ≝ λc: comparison. λv1,v2: val. |
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325 | match v1 with |
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326 | [ Vint sz1 n1 ⇒ match v2 with |
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327 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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328 | (λn1. Some ? (of_bool (cmp_int ? c n1 n2))) |
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329 | (None ?) |
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330 | | _ ⇒ None ? ] |
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331 | | _ ⇒ None ? ]. |
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332 | |
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333 | definition ev_cmpp ≝ λc: comparison. λv1,v2: val. |
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334 | match v1 with |
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335 | [ Vptr r1 b1 p1 ofs1 ⇒ match v2 with |
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336 | [ Vptr r2 b2 p2 ofs2 ⇒ |
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337 | if eq_block b1 b2 |
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338 | then Some ? (of_bool (cmp_offset c ofs1 ofs2)) |
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339 | else ev_cmp_mismatch c |
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340 | | Vnull r2 ⇒ ev_cmp_mismatch c |
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341 | | _ ⇒ None ? ] |
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342 | | Vnull r1 ⇒ match v2 with |
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343 | [ Vptr _ _ _ _ ⇒ ev_cmp_mismatch c |
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344 | | Vnull r2 ⇒ ev_cmp_match c |
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345 | | _ ⇒ None ? |
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346 | ] |
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347 | | _ ⇒ None ? ]. |
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348 | |
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349 | (* TODO: check this, it isn't the cmpu used elsewhere *) |
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350 | definition ev_cmpu ≝ λc: comparison. λv1,v2: val. |
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351 | match v1 with |
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352 | [ Vint sz1 n1 ⇒ match v2 with |
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353 | [ Vint sz2 n2 ⇒ intsize_eq_elim ? sz1 sz2 ? n1 |
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354 | (λn1. Some ? (of_bool (cmpu_int ? c n1 n2))) |
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355 | (None ?) |
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356 | | _ ⇒ None ? ] |
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357 | | _ ⇒ None ? ]. |
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358 | |
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359 | definition ev_cmpf ≝ λc: comparison. λv1,v2: val. |
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360 | match v1 with |
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361 | [ Vfloat f1 ⇒ match v2 with |
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362 | [ Vfloat f2 ⇒ Some ? (of_bool (Fcmp c f1 f2)) |
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363 | | _ ⇒ None ? ] |
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364 | | _ ⇒ None ? ]. |
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365 | |
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366 | definition eval_binop : binary_operation → val → val → option val ≝ |
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367 | λop. |
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368 | match op with |
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369 | [ Oadd ⇒ ev_add |
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370 | | Osub ⇒ ev_sub |
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371 | | Omul ⇒ ev_mul |
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372 | | Odiv ⇒ ev_divs |
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373 | | Odivu ⇒ ev_divu |
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374 | | Omod ⇒ ev_mods |
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375 | | Omodu ⇒ ev_modu |
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376 | | Oand ⇒ ev_and |
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377 | | Oor ⇒ ev_or |
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378 | | Oxor ⇒ ev_xor |
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379 | | Oshl ⇒ ev_shl |
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380 | | Oshr ⇒ ev_shr |
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381 | | Oshru ⇒ ev_shru |
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382 | | Oaddf ⇒ ev_addf |
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383 | | Osubf ⇒ ev_subf |
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384 | | Omulf ⇒ ev_mulf |
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385 | | Odivf ⇒ ev_divf |
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386 | | Ocmp c ⇒ ev_cmp c |
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387 | | Ocmpu c ⇒ ev_cmpu c |
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388 | | Ocmpf c ⇒ ev_cmpf c |
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389 | | Oaddp ⇒ ev_addp |
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390 | | Osubpi ⇒ ev_subpi |
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391 | | Osubpp sz ⇒ ev_subpp sz |
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392 | | Ocmpp c ⇒ ev_cmpp c |
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393 | ]. |
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394 | |
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