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1 (* Title: HOL/Tools/Transfer/transfer.ML |
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2 Author: Brian Huffman, TU Muenchen |
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3 Author: Ondrej Kuncar, TU Muenchen |
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4 |
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5 Generic theorem transfer method. |
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6 *) |
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7 |
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8 signature TRANSFER = |
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9 sig |
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10 type pred_data |
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11 val rel_eq_onp: pred_data -> thm |
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12 |
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13 val bottom_rewr_conv: thm list -> conv |
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14 val top_rewr_conv: thm list -> conv |
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15 |
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16 val prep_conv: conv |
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17 val get_transfer_raw: Proof.context -> thm list |
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18 val get_relator_eq_item_net: Proof.context -> thm Item_Net.T |
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19 val get_relator_eq: Proof.context -> thm list |
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20 val get_sym_relator_eq: Proof.context -> thm list |
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21 val get_relator_eq_raw: Proof.context -> thm list |
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22 val get_relator_domain: Proof.context -> thm list |
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23 val morph_pred_data: morphism -> pred_data -> pred_data |
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24 val lookup_pred_data: Proof.context -> string -> pred_data option |
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25 val update_pred_data: string -> pred_data -> Context.generic -> Context.generic |
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26 val get_compound_lhs: Proof.context -> (term * thm) Item_Net.T |
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27 val get_compound_rhs: Proof.context -> (term * thm) Item_Net.T |
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28 val transfer_add: attribute |
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29 val transfer_del: attribute |
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30 val transfer_raw_add: thm -> Context.generic -> Context.generic |
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31 val transfer_raw_del: thm -> Context.generic -> Context.generic |
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32 val transferred_attribute: thm list -> attribute |
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33 val untransferred_attribute: thm list -> attribute |
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34 val prep_transfer_domain_thm: Proof.context -> thm -> thm |
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35 val transfer_domain_add: attribute |
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36 val transfer_domain_del: attribute |
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37 val transfer_rule_of_term: Proof.context -> bool -> term -> thm |
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38 val transfer_rule_of_lhs: Proof.context -> term -> thm |
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39 val eq_tac: Proof.context -> int -> tactic |
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40 val transfer_step_tac: Proof.context -> int -> tactic |
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41 val transfer_tac: bool -> Proof.context -> int -> tactic |
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42 val transfer_prover_tac: Proof.context -> int -> tactic |
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43 val gen_frees_tac: (string * typ) list -> Proof.context -> int -> tactic |
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44 val setup: theory -> theory |
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45 end |
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46 |
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47 structure Transfer : TRANSFER = |
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48 struct |
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49 |
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50 (** Theory Data **) |
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51 |
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52 val compound_xhs_empty_net = Item_Net.init (Thm.eq_thm_prop o pairself snd) (single o fst); |
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53 val rewr_rules = Item_Net.init Thm.eq_thm_prop (single o fst o HOLogic.dest_eq |
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54 o HOLogic.dest_Trueprop o Thm.concl_of); |
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55 |
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56 type pred_data = {rel_eq_onp: thm} |
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57 |
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58 val rel_eq_onp = #rel_eq_onp |
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59 |
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60 structure Data = Generic_Data |
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61 ( |
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62 type T = |
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63 { transfer_raw : thm Item_Net.T, |
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64 known_frees : (string * typ) list, |
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65 compound_lhs : (term * thm) Item_Net.T, |
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66 compound_rhs : (term * thm) Item_Net.T, |
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67 relator_eq : thm Item_Net.T, |
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68 relator_eq_raw : thm Item_Net.T, |
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69 relator_domain : thm Item_Net.T, |
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70 pred_data : pred_data Symtab.table } |
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71 val empty = |
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72 { transfer_raw = Thm.intro_rules, |
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73 known_frees = [], |
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74 compound_lhs = compound_xhs_empty_net, |
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75 compound_rhs = compound_xhs_empty_net, |
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76 relator_eq = rewr_rules, |
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77 relator_eq_raw = Thm.full_rules, |
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78 relator_domain = Thm.full_rules, |
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79 pred_data = Symtab.empty } |
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80 val extend = I |
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81 fun merge |
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82 ( { transfer_raw = t1, known_frees = k1, |
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83 compound_lhs = l1, |
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84 compound_rhs = c1, relator_eq = r1, |
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85 relator_eq_raw = rw1, relator_domain = rd1, |
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86 pred_data = pd1 }, |
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87 { transfer_raw = t2, known_frees = k2, |
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88 compound_lhs = l2, |
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89 compound_rhs = c2, relator_eq = r2, |
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90 relator_eq_raw = rw2, relator_domain = rd2, |
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91 pred_data = pd2 } ) = |
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92 { transfer_raw = Item_Net.merge (t1, t2), |
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93 known_frees = Library.merge (op =) (k1, k2), |
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94 compound_lhs = Item_Net.merge (l1, l2), |
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95 compound_rhs = Item_Net.merge (c1, c2), |
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96 relator_eq = Item_Net.merge (r1, r2), |
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97 relator_eq_raw = Item_Net.merge (rw1, rw2), |
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98 relator_domain = Item_Net.merge (rd1, rd2), |
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99 pred_data = Symtab.merge (K true) (pd1, pd2) } |
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100 ) |
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101 |
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102 fun get_transfer_raw ctxt = ctxt |
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103 |> (Item_Net.content o #transfer_raw o Data.get o Context.Proof) |
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104 |
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105 fun get_known_frees ctxt = ctxt |
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106 |> (#known_frees o Data.get o Context.Proof) |
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107 |
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108 fun get_compound_lhs ctxt = ctxt |
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109 |> (#compound_lhs o Data.get o Context.Proof) |
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110 |
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111 fun get_compound_rhs ctxt = ctxt |
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112 |> (#compound_rhs o Data.get o Context.Proof) |
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113 |
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114 fun get_relator_eq_item_net ctxt = (#relator_eq o Data.get o Context.Proof) ctxt |
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115 |
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116 fun get_relator_eq ctxt = ctxt |
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117 |> (Item_Net.content o #relator_eq o Data.get o Context.Proof) |
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118 |> map safe_mk_meta_eq |
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119 |
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120 fun get_sym_relator_eq ctxt = ctxt |
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121 |> (Item_Net.content o #relator_eq o Data.get o Context.Proof) |
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122 |> map (Thm.symmetric o safe_mk_meta_eq) |
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123 |
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124 fun get_relator_eq_raw ctxt = ctxt |
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125 |> (Item_Net.content o #relator_eq_raw o Data.get o Context.Proof) |
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126 |
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127 fun get_relator_domain ctxt = ctxt |
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128 |> (Item_Net.content o #relator_domain o Data.get o Context.Proof) |
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129 |
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130 fun get_pred_data ctxt = ctxt |
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131 |> (#pred_data o Data.get o Context.Proof) |
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132 |
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133 fun map_data f1 f2 f3 f4 f5 f6 f7 f8 |
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134 { transfer_raw, known_frees, compound_lhs, compound_rhs, |
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135 relator_eq, relator_eq_raw, relator_domain, pred_data } = |
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136 { transfer_raw = f1 transfer_raw, |
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137 known_frees = f2 known_frees, |
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138 compound_lhs = f3 compound_lhs, |
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139 compound_rhs = f4 compound_rhs, |
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140 relator_eq = f5 relator_eq, |
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141 relator_eq_raw = f6 relator_eq_raw, |
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142 relator_domain = f7 relator_domain, |
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143 pred_data = f8 pred_data } |
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144 |
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145 fun map_transfer_raw f = map_data f I I I I I I I |
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146 fun map_known_frees f = map_data I f I I I I I I |
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147 fun map_compound_lhs f = map_data I I f I I I I I |
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148 fun map_compound_rhs f = map_data I I I f I I I I |
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149 fun map_relator_eq f = map_data I I I I f I I I |
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150 fun map_relator_eq_raw f = map_data I I I I I f I I |
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151 fun map_relator_domain f = map_data I I I I I I f I |
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152 fun map_pred_data f = map_data I I I I I I I f |
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153 |
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154 fun add_transfer_thm thm = Data.map |
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155 (map_transfer_raw (Item_Net.update thm) o |
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156 map_compound_lhs |
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157 (case HOLogic.dest_Trueprop (Thm.concl_of thm) of |
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158 Const (@{const_name Rel}, _) $ _ $ (lhs as (_ $ _)) $ _ => |
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159 Item_Net.update (lhs, thm) |
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160 | _ => I) o |
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161 map_compound_rhs |
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162 (case HOLogic.dest_Trueprop (Thm.concl_of thm) of |
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163 Const (@{const_name Rel}, _) $ _ $ _ $ (rhs as (_ $ _)) => |
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164 Item_Net.update (rhs, thm) |
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165 | _ => I) o |
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166 map_known_frees (Term.add_frees (Thm.concl_of thm))) |
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167 |
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168 fun del_transfer_thm thm = Data.map |
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169 (map_transfer_raw (Item_Net.remove thm) o |
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170 map_compound_lhs |
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171 (case HOLogic.dest_Trueprop (Thm.concl_of thm) of |
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172 Const (@{const_name Rel}, _) $ _ $ (lhs as (_ $ _)) $ _ => |
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173 Item_Net.remove (lhs, thm) |
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174 | _ => I) o |
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175 map_compound_rhs |
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176 (case HOLogic.dest_Trueprop (Thm.concl_of thm) of |
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177 Const (@{const_name Rel}, _) $ _ $ _ $ (rhs as (_ $ _)) => |
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178 Item_Net.remove (rhs, thm) |
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179 | _ => I)) |
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180 |
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181 fun transfer_raw_add thm ctxt = add_transfer_thm thm ctxt |
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182 fun transfer_raw_del thm ctxt = del_transfer_thm thm ctxt |
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183 |
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184 (** Conversions **) |
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185 |
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186 fun bottom_rewr_conv rewrs = Conv.bottom_conv (K (Conv.try_conv (Conv.rewrs_conv rewrs))) @{context} |
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187 fun top_rewr_conv rewrs = Conv.top_conv (K (Conv.try_conv (Conv.rewrs_conv rewrs))) @{context} |
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188 |
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189 fun transfer_rel_conv conv = |
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190 Conv.concl_conv ~1 (HOLogic.Trueprop_conv (Conv.fun2_conv (Conv.arg_conv conv))) |
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191 |
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192 val Rel_rule = Thm.symmetric @{thm Rel_def} |
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193 |
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194 fun dest_funcT cT = |
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195 (case Thm.dest_ctyp cT of [T, U] => (T, U) |
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196 | _ => raise TYPE ("dest_funcT", [Thm.typ_of cT], [])) |
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197 |
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198 fun Rel_conv ct = |
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199 let val (cT, cT') = dest_funcT (Thm.ctyp_of_term ct) |
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200 val (cU, _) = dest_funcT cT' |
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201 in Drule.instantiate' [SOME cT, SOME cU] [SOME ct] Rel_rule end |
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202 |
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203 (* Conversion to preprocess a transfer rule *) |
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204 fun safe_Rel_conv ct = |
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205 Conv.try_conv (HOLogic.Trueprop_conv (Conv.fun_conv (Conv.fun_conv Rel_conv))) ct |
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206 |
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207 fun prep_conv ct = ( |
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208 Conv.implies_conv safe_Rel_conv prep_conv |
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209 else_conv |
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210 safe_Rel_conv |
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211 else_conv |
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212 Conv.all_conv) ct |
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213 |
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214 (** Replacing explicit equalities with is_equality premises **) |
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215 |
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216 fun mk_is_equality t = |
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217 Const (@{const_name is_equality}, Term.fastype_of t --> HOLogic.boolT) $ t |
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218 |
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219 val is_equality_lemma = |
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220 @{lemma "(!!R. is_equality R ==> PROP (P R)) == PROP (P (op =))" |
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221 by (unfold is_equality_def, rule, drule meta_spec, |
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222 erule meta_mp, rule refl, simp)} |
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223 |
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224 fun gen_abstract_equalities ctxt (dest : term -> term * (term -> term)) thm = |
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225 let |
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226 val thy = Thm.theory_of_thm thm |
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227 val prop = Thm.prop_of thm |
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228 val (t, mk_prop') = dest prop |
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229 (* Only consider "op =" at non-base types *) |
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230 fun is_eq (Const (@{const_name HOL.eq}, Type ("fun", [T, _]))) = |
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231 (case T of Type (_, []) => false | _ => true) |
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232 | is_eq _ = false |
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233 val add_eqs = Term.fold_aterms (fn t => if is_eq t then insert (op =) t else I) |
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234 val eq_consts = rev (add_eqs t []) |
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235 val eqTs = map (snd o dest_Const) eq_consts |
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236 val used = Term.add_free_names prop [] |
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237 val names = map (K "") eqTs |> Name.variant_list used |
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238 val frees = map Free (names ~~ eqTs) |
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239 val prems = map (HOLogic.mk_Trueprop o mk_is_equality) frees |
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240 val prop1 = mk_prop' (Term.subst_atomic (eq_consts ~~ frees) t) |
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241 val prop2 = fold Logic.all frees (Logic.list_implies (prems, prop1)) |
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242 val cprop = Thm.cterm_of thy prop2 |
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243 val equal_thm = Raw_Simplifier.rewrite ctxt false [is_equality_lemma] cprop |
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244 fun forall_elim thm = Thm.forall_elim_vars (Thm.maxidx_of thm + 1) thm |
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245 in |
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246 forall_elim (thm COMP (equal_thm COMP @{thm equal_elim_rule2})) |
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247 end |
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248 handle TERM _ => thm |
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249 |
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250 fun abstract_equalities_transfer ctxt thm = |
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251 let |
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252 fun dest prop = |
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253 let |
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254 val prems = Logic.strip_imp_prems prop |
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255 val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl prop) |
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256 val ((rel, x), y) = apfst Term.dest_comb (Term.dest_comb concl) |
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257 in |
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258 (rel, fn rel' => |
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259 Logic.list_implies (prems, HOLogic.mk_Trueprop (rel' $ x $ y))) |
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260 end |
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261 val contracted_eq_thm = |
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262 Conv.fconv_rule (transfer_rel_conv (bottom_rewr_conv (get_relator_eq ctxt))) thm |
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263 handle CTERM _ => thm |
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264 in |
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265 gen_abstract_equalities ctxt dest contracted_eq_thm |
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266 end |
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267 |
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268 fun abstract_equalities_relator_eq ctxt rel_eq_thm = |
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269 gen_abstract_equalities ctxt (fn x => (x, I)) |
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270 (rel_eq_thm RS @{thm is_equality_def [THEN iffD2]}) |
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271 |
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272 fun abstract_equalities_domain ctxt thm = |
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273 let |
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274 fun dest prop = |
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275 let |
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276 val prems = Logic.strip_imp_prems prop |
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277 val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl prop) |
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278 val ((eq, dom), y) = apfst Term.dest_comb (Term.dest_comb concl) |
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279 in |
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280 (dom, fn dom' => Logic.list_implies (prems, HOLogic.mk_Trueprop (eq $ dom' $ y))) |
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281 end |
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282 fun transfer_rel_conv conv = |
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283 Conv.concl_conv ~1 (HOLogic.Trueprop_conv (Conv.arg1_conv (Conv.arg_conv conv))) |
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284 val contracted_eq_thm = |
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285 Conv.fconv_rule (transfer_rel_conv (bottom_rewr_conv (get_relator_eq ctxt))) thm |
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286 in |
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287 gen_abstract_equalities ctxt dest contracted_eq_thm |
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288 end |
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289 |
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290 |
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291 (** Replacing explicit Domainp predicates with Domainp assumptions **) |
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292 |
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293 fun mk_Domainp_assm (T, R) = |
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294 HOLogic.mk_eq ((Const (@{const_name Domainp}, Term.fastype_of T --> Term.fastype_of R) $ T), R) |
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295 |
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296 val Domainp_lemma = |
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297 @{lemma "(!!R. Domainp T = R ==> PROP (P R)) == PROP (P (Domainp T))" |
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298 by (rule, drule meta_spec, |
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299 erule meta_mp, rule refl, simp)} |
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300 |
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301 fun fold_Domainp f (t as Const (@{const_name Domainp},_) $ (Var (_,_))) = f t |
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302 | fold_Domainp f (t $ u) = fold_Domainp f t #> fold_Domainp f u |
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303 | fold_Domainp f (Abs (_, _, t)) = fold_Domainp f t |
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304 | fold_Domainp _ _ = I |
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305 |
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306 fun subst_terms tab t = |
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307 let |
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308 val t' = Termtab.lookup tab t |
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309 in |
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310 case t' of |
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311 SOME t' => t' |
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312 | NONE => |
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313 (case t of |
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314 u $ v => (subst_terms tab u) $ (subst_terms tab v) |
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315 | Abs (a, T, t) => Abs (a, T, subst_terms tab t) |
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316 | t => t) |
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317 end |
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318 |
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319 fun gen_abstract_domains ctxt (dest : term -> term * (term -> term)) thm = |
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320 let |
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321 val thy = Thm.theory_of_thm thm |
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322 val prop = Thm.prop_of thm |
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323 val (t, mk_prop') = dest prop |
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324 val Domainp_tms = rev (fold_Domainp (fn t => insert op= t) t []) |
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325 val Domainp_Ts = map (snd o dest_funT o snd o dest_Const o fst o dest_comb) Domainp_tms |
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326 val used = Term.add_free_names t [] |
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327 val rels = map (snd o dest_comb) Domainp_tms |
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328 val rel_names = map (fst o fst o dest_Var) rels |
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329 val names = map (fn name => ("D" ^ name)) rel_names |> Name.variant_list used |
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330 val frees = map Free (names ~~ Domainp_Ts) |
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331 val prems = map (HOLogic.mk_Trueprop o mk_Domainp_assm) (rels ~~ frees); |
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332 val t' = subst_terms (fold Termtab.update (Domainp_tms ~~ frees) Termtab.empty) t |
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333 val prop1 = fold Logic.all frees (Logic.list_implies (prems, mk_prop' t')) |
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334 val prop2 = Logic.list_rename_params (rev names) prop1 |
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335 val cprop = Thm.cterm_of thy prop2 |
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336 val equal_thm = Raw_Simplifier.rewrite ctxt false [Domainp_lemma] cprop |
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337 fun forall_elim thm = Thm.forall_elim_vars (Thm.maxidx_of thm + 1) thm; |
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338 in |
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339 forall_elim (thm COMP (equal_thm COMP @{thm equal_elim_rule2})) |
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340 end |
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341 handle TERM _ => thm |
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342 |
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343 fun abstract_domains_transfer ctxt thm = |
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344 let |
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345 fun dest prop = |
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346 let |
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347 val prems = Logic.strip_imp_prems prop |
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348 val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl prop) |
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349 val ((rel, x), y) = apfst Term.dest_comb (Term.dest_comb concl) |
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350 in |
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351 (x, fn x' => |
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352 Logic.list_implies (prems, HOLogic.mk_Trueprop (rel $ x' $ y))) |
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353 end |
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354 in |
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355 gen_abstract_domains ctxt dest thm |
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356 end |
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357 |
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358 fun abstract_domains_relator_domain ctxt thm = |
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359 let |
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360 fun dest prop = |
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361 let |
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362 val prems = Logic.strip_imp_prems prop |
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363 val concl = HOLogic.dest_Trueprop (Logic.strip_imp_concl prop) |
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364 val ((rel, x), y) = apfst Term.dest_comb (Term.dest_comb concl) |
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365 in |
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366 (y, fn y' => |
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367 Logic.list_implies (prems, HOLogic.mk_Trueprop (rel $ x $ y'))) |
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368 end |
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369 in |
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370 gen_abstract_domains ctxt dest thm |
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371 end |
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372 |
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373 fun detect_transfer_rules thm = |
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374 let |
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375 fun is_transfer_rule tm = case (HOLogic.dest_Trueprop tm) of |
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376 (Const (@{const_name HOL.eq}, _)) $ ((Const (@{const_name Domainp}, _)) $ _) $ _ => false |
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377 | _ $ _ $ _ => true |
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378 | _ => false |
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379 fun safe_transfer_rule_conv ctm = |
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380 if is_transfer_rule (term_of ctm) then safe_Rel_conv ctm else Conv.all_conv ctm |
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381 in |
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382 Conv.fconv_rule (Conv.prems_conv ~1 safe_transfer_rule_conv) thm |
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383 end |
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384 |
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385 (** Adding transfer domain rules **) |
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386 |
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387 fun prep_transfer_domain_thm ctxt thm = |
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388 (abstract_equalities_domain ctxt o detect_transfer_rules) thm |
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389 |
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390 fun add_transfer_domain_thm thm ctxt = (add_transfer_thm o |
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391 prep_transfer_domain_thm (Context.proof_of ctxt)) thm ctxt |
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392 |
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393 fun del_transfer_domain_thm thm ctxt = (del_transfer_thm o |
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394 prep_transfer_domain_thm (Context.proof_of ctxt)) thm ctxt |
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395 |
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396 (** Transfer proof method **) |
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397 |
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398 val post_simps = |
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399 @{thms transfer_forall_eq [symmetric] |
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400 transfer_implies_eq [symmetric] transfer_bforall_unfold} |
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401 |
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402 fun gen_frees_tac keepers ctxt = SUBGOAL (fn (t, i) => |
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403 let |
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404 val keepers = keepers @ get_known_frees ctxt |
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405 val vs = rev (Term.add_frees t []) |
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406 val vs' = filter_out (member (op =) keepers) vs |
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407 in |
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408 Induct.arbitrary_tac ctxt 0 vs' i |
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409 end) |
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410 |
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411 fun mk_relT (T, U) = T --> U --> HOLogic.boolT |
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412 |
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413 fun mk_Rel t = |
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414 let val T = fastype_of t |
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415 in Const (@{const_name Transfer.Rel}, T --> T) $ t end |
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416 |
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417 fun transfer_rule_of_terms (prj : typ * typ -> typ) ctxt tab t u = |
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418 let |
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419 val thy = Proof_Context.theory_of ctxt |
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420 (* precondition: prj(T,U) must consist of only TFrees and type "fun" *) |
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421 fun rel (T as Type ("fun", [T1, T2])) (U as Type ("fun", [U1, U2])) = |
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422 let |
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423 val r1 = rel T1 U1 |
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424 val r2 = rel T2 U2 |
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425 val rT = fastype_of r1 --> fastype_of r2 --> mk_relT (T, U) |
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426 in |
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427 Const (@{const_name rel_fun}, rT) $ r1 $ r2 |
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428 end |
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429 | rel T U = |
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430 let |
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431 val (a, _) = dest_TFree (prj (T, U)) |
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432 in |
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433 Free (the (AList.lookup (op =) tab a), mk_relT (T, U)) |
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434 end |
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435 fun zip _ thms (Bound i) (Bound _) = (nth thms i, []) |
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436 | zip ctxt thms (Abs (x, T, t)) (Abs (y, U, u)) = |
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437 let |
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438 val ([x', y'], ctxt') = Variable.variant_fixes [x, y] ctxt |
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439 val prop = mk_Rel (rel T U) $ Free (x', T) $ Free (y', U) |
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440 val cprop = Thm.cterm_of thy (HOLogic.mk_Trueprop prop) |
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441 val thm0 = Thm.assume cprop |
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442 val (thm1, hyps) = zip ctxt' (thm0 :: thms) t u |
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443 val ((r1, x), y) = apfst Thm.dest_comb (Thm.dest_comb (Thm.dest_arg cprop)) |
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444 val r2 = Thm.dest_fun2 (Thm.dest_arg (cprop_of thm1)) |
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445 val (a1, (b1, _)) = apsnd dest_funcT (dest_funcT (ctyp_of_term r1)) |
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446 val (a2, (b2, _)) = apsnd dest_funcT (dest_funcT (ctyp_of_term r2)) |
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447 val tinsts = [SOME a1, SOME b1, SOME a2, SOME b2] |
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448 val insts = [SOME (Thm.dest_arg r1), SOME (Thm.dest_arg r2)] |
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449 val rule = Drule.instantiate' tinsts insts @{thm Rel_abs} |
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450 val thm2 = Thm.forall_intr x (Thm.forall_intr y (Thm.implies_intr cprop thm1)) |
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451 in |
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452 (thm2 COMP rule, hyps) |
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453 end |
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454 | zip ctxt thms (f $ t) (g $ u) = |
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455 let |
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456 val (thm1, hyps1) = zip ctxt thms f g |
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457 val (thm2, hyps2) = zip ctxt thms t u |
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458 in |
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459 (thm2 RS (thm1 RS @{thm Rel_app}), hyps1 @ hyps2) |
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460 end |
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461 | zip _ _ t u = |
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462 let |
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463 val T = fastype_of t |
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464 val U = fastype_of u |
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465 val prop = mk_Rel (rel T U) $ t $ u |
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466 val cprop = Thm.cterm_of thy (HOLogic.mk_Trueprop prop) |
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467 in |
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468 (Thm.assume cprop, [cprop]) |
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469 end |
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470 val r = mk_Rel (rel (fastype_of t) (fastype_of u)) |
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471 val goal = HOLogic.mk_Trueprop (r $ t $ u) |
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472 val rename = Thm.trivial (cterm_of thy goal) |
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473 val (thm, hyps) = zip ctxt [] t u |
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474 in |
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475 Drule.implies_intr_list hyps (thm RS rename) |
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476 end |
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477 |
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478 (* create a lambda term of the same shape as the given term *) |
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479 fun skeleton (is_atom : term -> bool) ctxt t = |
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480 let |
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481 fun dummy ctxt = |
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482 let |
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483 val (c, ctxt) = yield_singleton Variable.variant_fixes "a" ctxt |
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484 in |
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485 (Free (c, dummyT), ctxt) |
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486 end |
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487 fun go (Bound i) ctxt = (Bound i, ctxt) |
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488 | go (Abs (x, _, t)) ctxt = |
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489 let |
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490 val (t', ctxt) = go t ctxt |
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491 in |
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492 (Abs (x, dummyT, t'), ctxt) |
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493 end |
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494 | go (tu as (t $ u)) ctxt = |
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495 if is_atom tu andalso not (Term.is_open tu) then dummy ctxt else |
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496 let |
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497 val (t', ctxt) = go t ctxt |
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498 val (u', ctxt) = go u ctxt |
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499 in |
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500 (t' $ u', ctxt) |
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501 end |
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502 | go _ ctxt = dummy ctxt |
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503 in |
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504 go t ctxt |> fst |> Syntax.check_term ctxt |> |
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505 map_types (map_type_tfree (fn (a, _) => TFree (a, @{sort type}))) |
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506 end |
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507 |
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508 (** Monotonicity analysis **) |
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509 |
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510 (* TODO: Put extensible table in theory data *) |
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511 val monotab = |
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512 Symtab.make |
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513 [(@{const_name transfer_implies}, [~1, 1]), |
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514 (@{const_name transfer_forall}, [1])(*, |
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515 (@{const_name implies}, [~1, 1]), |
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516 (@{const_name All}, [1])*)] |
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517 |
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518 (* |
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519 Function bool_insts determines the set of boolean-relation variables |
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520 that can be instantiated to implies, rev_implies, or iff. |
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521 |
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522 Invariants: bool_insts p (t, u) requires that |
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523 u :: _ => _ => ... => bool, and |
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524 t is a skeleton of u |
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525 *) |
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526 fun bool_insts p (t, u) = |
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527 let |
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528 fun strip2 (t1 $ t2, u1 $ u2, tus) = |
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529 strip2 (t1, u1, (t2, u2) :: tus) |
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530 | strip2 x = x |
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531 fun or3 ((a, b, c), (x, y, z)) = (a orelse x, b orelse y, c orelse z) |
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532 fun go Ts p (Abs (_, T, t), Abs (_, _, u)) tab = go (T :: Ts) p (t, u) tab |
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533 | go Ts p (t, u) tab = |
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534 let |
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535 val (a, _) = dest_TFree (Term.body_type (Term.fastype_of1 (Ts, t))) |
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536 val (_, tf, tus) = strip2 (t, u, []) |
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537 val ps_opt = case tf of Const (c, _) => Symtab.lookup monotab c | _ => NONE |
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538 val tab1 = |
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539 case ps_opt of |
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540 SOME ps => |
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541 let |
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542 val ps' = map (fn x => p * x) (take (length tus) ps) |
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543 in |
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544 fold I (map2 (go Ts) ps' tus) tab |
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545 end |
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546 | NONE => tab |
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547 val tab2 = Symtab.make [(a, (p >= 0, p <= 0, is_none ps_opt))] |
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548 in |
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549 Symtab.join (K or3) (tab1, tab2) |
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550 end |
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551 val tab = go [] p (t, u) Symtab.empty |
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552 fun f (a, (true, false, false)) = SOME (a, @{const implies}) |
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553 | f (a, (false, true, false)) = SOME (a, @{const rev_implies}) |
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554 | f (a, (true, true, _)) = SOME (a, HOLogic.eq_const HOLogic.boolT) |
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555 | f _ = NONE |
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556 in |
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557 map_filter f (Symtab.dest tab) |
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558 end |
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559 |
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560 fun retrieve_terms t net = map fst (Item_Net.retrieve net t) |
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561 |
|
562 fun matches_list ctxt term = |
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563 is_some o find_first (fn pat => Pattern.matches (Proof_Context.theory_of ctxt) (pat, term)) |
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564 |
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565 fun transfer_rule_of_term ctxt equiv t : thm = |
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566 let |
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567 val compound_rhs = get_compound_rhs ctxt |
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568 fun is_rhs t = compound_rhs |> retrieve_terms t |> matches_list ctxt t |
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569 val s = skeleton is_rhs ctxt t |
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570 val frees = map fst (Term.add_frees s []) |
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571 val tfrees = map fst (Term.add_tfrees s []) |
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572 fun prep a = "R" ^ Library.unprefix "'" a |
|
573 val (rnames, ctxt') = Variable.variant_fixes (map prep tfrees) ctxt |
|
574 val tab = tfrees ~~ rnames |
|
575 fun prep a = the (AList.lookup (op =) tab a) |
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576 val thm = transfer_rule_of_terms fst ctxt' tab s t |
|
577 val binsts = bool_insts (if equiv then 0 else 1) (s, t) |
|
578 val cbool = @{ctyp bool} |
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579 val relT = @{typ "bool => bool => bool"} |
|
580 val idx = Thm.maxidx_of thm + 1 |
|
581 val thy = Proof_Context.theory_of ctxt |
|
582 fun tinst (a, _) = (ctyp_of thy (TVar ((a, idx), @{sort type})), cbool) |
|
583 fun inst (a, t) = (cterm_of thy (Var (Name.clean_index (prep a, idx), relT)), cterm_of thy t) |
|
584 in |
|
585 thm |
|
586 |> Thm.generalize (tfrees, rnames @ frees) idx |
|
587 |> Thm.instantiate (map tinst binsts, map inst binsts) |
|
588 end |
|
589 |
|
590 fun transfer_rule_of_lhs ctxt t : thm = |
|
591 let |
|
592 val compound_lhs = get_compound_lhs ctxt |
|
593 fun is_lhs t = compound_lhs |> retrieve_terms t |> matches_list ctxt t |
|
594 val s = skeleton is_lhs ctxt t |
|
595 val frees = map fst (Term.add_frees s []) |
|
596 val tfrees = map fst (Term.add_tfrees s []) |
|
597 fun prep a = "R" ^ Library.unprefix "'" a |
|
598 val (rnames, ctxt') = Variable.variant_fixes (map prep tfrees) ctxt |
|
599 val tab = tfrees ~~ rnames |
|
600 fun prep a = the (AList.lookup (op =) tab a) |
|
601 val thm = transfer_rule_of_terms snd ctxt' tab t s |
|
602 val binsts = bool_insts 1 (s, t) |
|
603 val cbool = @{ctyp bool} |
|
604 val relT = @{typ "bool => bool => bool"} |
|
605 val idx = Thm.maxidx_of thm + 1 |
|
606 val thy = Proof_Context.theory_of ctxt |
|
607 fun tinst (a, _) = (ctyp_of thy (TVar ((a, idx), @{sort type})), cbool) |
|
608 fun inst (a, t) = (cterm_of thy (Var (Name.clean_index (prep a, idx), relT)), cterm_of thy t) |
|
609 in |
|
610 thm |
|
611 |> Thm.generalize (tfrees, rnames @ frees) idx |
|
612 |> Thm.instantiate (map tinst binsts, map inst binsts) |
|
613 end |
|
614 |
|
615 fun eq_rules_tac eq_rules = TRY o REPEAT_ALL_NEW (resolve_tac eq_rules) |
|
616 THEN_ALL_NEW rtac @{thm is_equality_eq} |
|
617 |
|
618 fun eq_tac ctxt = eq_rules_tac (get_relator_eq_raw ctxt) |
|
619 |
|
620 fun transfer_step_tac ctxt = (REPEAT_ALL_NEW (resolve_tac (get_transfer_raw ctxt)) |
|
621 THEN_ALL_NEW (DETERM o eq_rules_tac (get_relator_eq_raw ctxt))) |
|
622 |
|
623 fun transfer_tac equiv ctxt i = |
|
624 let |
|
625 val pre_simps = @{thms transfer_forall_eq transfer_implies_eq} |
|
626 val start_rule = |
|
627 if equiv then @{thm transfer_start} else @{thm transfer_start'} |
|
628 val rules = get_transfer_raw ctxt |
|
629 val eq_rules = get_relator_eq_raw ctxt |
|
630 (* allow unsolved subgoals only for standard transfer method, not for transfer' *) |
|
631 val end_tac = if equiv then K all_tac else K no_tac |
|
632 val err_msg = "Transfer failed to convert goal to an object-logic formula" |
|
633 fun main_tac (t, i) = |
|
634 rtac start_rule i THEN |
|
635 (rtac (transfer_rule_of_term ctxt equiv (HOLogic.dest_Trueprop t)) |
|
636 THEN_ALL_NEW |
|
637 (SOLVED' (REPEAT_ALL_NEW (resolve_tac rules) THEN_ALL_NEW (DETERM o eq_rules_tac eq_rules)) |
|
638 ORELSE' end_tac)) (i + 1) |
|
639 handle TERM (_, ts) => raise TERM (err_msg, ts) |
|
640 in |
|
641 EVERY |
|
642 [rewrite_goal_tac ctxt pre_simps i THEN |
|
643 SUBGOAL main_tac i, |
|
644 (* FIXME: rewrite_goal_tac does unwanted eta-contraction *) |
|
645 rewrite_goal_tac ctxt post_simps i, |
|
646 Goal.norm_hhf_tac ctxt i] |
|
647 end |
|
648 |
|
649 fun transfer_prover_tac ctxt = SUBGOAL (fn (t, i) => |
|
650 let |
|
651 val rhs = (snd o Term.dest_comb o HOLogic.dest_Trueprop) t |
|
652 val rule1 = transfer_rule_of_term ctxt false rhs |
|
653 val rules = get_transfer_raw ctxt |
|
654 val eq_rules = get_relator_eq_raw ctxt |
|
655 val expand_eq_in_rel = transfer_rel_conv (top_rewr_conv [@{thm rel_fun_eq[symmetric,THEN eq_reflection]}]) |
|
656 in |
|
657 EVERY |
|
658 [CONVERSION prep_conv i, |
|
659 rtac @{thm transfer_prover_start} i, |
|
660 ((rtac rule1 ORELSE' (CONVERSION expand_eq_in_rel THEN' rtac rule1)) |
|
661 THEN_ALL_NEW |
|
662 (REPEAT_ALL_NEW (resolve_tac rules) THEN_ALL_NEW (DETERM o eq_rules_tac eq_rules))) (i+1), |
|
663 rtac @{thm refl} i] |
|
664 end) |
|
665 |
|
666 (** Transfer attribute **) |
|
667 |
|
668 fun transferred ctxt extra_rules thm = |
|
669 let |
|
670 val start_rule = @{thm transfer_start} |
|
671 val start_rule' = @{thm transfer_start'} |
|
672 val rules = extra_rules @ get_transfer_raw ctxt |
|
673 val eq_rules = get_relator_eq_raw ctxt |
|
674 val err_msg = "Transfer failed to convert goal to an object-logic formula" |
|
675 val pre_simps = @{thms transfer_forall_eq transfer_implies_eq} |
|
676 val thm1 = Drule.forall_intr_vars thm |
|
677 val instT = rev (Term.add_tvars (Thm.full_prop_of thm1) []) |
|
678 |> map (fn v as ((a, _), S) => (v, TFree (a, S))) |
|
679 val thm2 = thm1 |
|
680 |> Thm.certify_instantiate (instT, []) |
|
681 |> Raw_Simplifier.rewrite_rule ctxt pre_simps |
|
682 val ctxt' = Variable.declare_names (Thm.full_prop_of thm2) ctxt |
|
683 val t = HOLogic.dest_Trueprop (Thm.concl_of thm2) |
|
684 val rule = transfer_rule_of_lhs ctxt' t |
|
685 val tac = |
|
686 resolve_tac [thm2 RS start_rule', thm2 RS start_rule] 1 THEN |
|
687 (rtac rule |
|
688 THEN_ALL_NEW |
|
689 (SOLVED' (REPEAT_ALL_NEW (resolve_tac rules) |
|
690 THEN_ALL_NEW (DETERM o eq_rules_tac eq_rules)))) 1 |
|
691 handle TERM (_, ts) => raise TERM (err_msg, ts) |
|
692 val thm3 = Goal.prove_internal ctxt' [] @{cpat "Trueprop ?P"} (K tac) |
|
693 val tnames = map (fst o dest_TFree o snd) instT |
|
694 in |
|
695 thm3 |
|
696 |> Raw_Simplifier.rewrite_rule ctxt' post_simps |
|
697 |> Simplifier.norm_hhf ctxt' |
|
698 |> Drule.generalize (tnames, []) |
|
699 |> Drule.zero_var_indexes |
|
700 end |
|
701 (* |
|
702 handle THM _ => thm |
|
703 *) |
|
704 |
|
705 fun untransferred ctxt extra_rules thm = |
|
706 let |
|
707 val start_rule = @{thm untransfer_start} |
|
708 val rules = extra_rules @ get_transfer_raw ctxt |
|
709 val eq_rules = get_relator_eq_raw ctxt |
|
710 val err_msg = "Transfer failed to convert goal to an object-logic formula" |
|
711 val pre_simps = @{thms transfer_forall_eq transfer_implies_eq} |
|
712 val thm1 = Drule.forall_intr_vars thm |
|
713 val instT = rev (Term.add_tvars (Thm.full_prop_of thm1) []) |
|
714 |> map (fn v as ((a, _), S) => (v, TFree (a, S))) |
|
715 val thm2 = thm1 |
|
716 |> Thm.certify_instantiate (instT, []) |
|
717 |> Raw_Simplifier.rewrite_rule ctxt pre_simps |
|
718 val ctxt' = Variable.declare_names (Thm.full_prop_of thm2) ctxt |
|
719 val t = HOLogic.dest_Trueprop (Thm.concl_of thm2) |
|
720 val rule = transfer_rule_of_term ctxt' true t |
|
721 val tac = |
|
722 rtac (thm2 RS start_rule) 1 THEN |
|
723 (rtac rule |
|
724 THEN_ALL_NEW |
|
725 (SOLVED' (REPEAT_ALL_NEW (resolve_tac rules) |
|
726 THEN_ALL_NEW (DETERM o eq_rules_tac eq_rules)))) 1 |
|
727 handle TERM (_, ts) => raise TERM (err_msg, ts) |
|
728 val thm3 = Goal.prove_internal ctxt' [] @{cpat "Trueprop ?P"} (K tac) |
|
729 val tnames = map (fst o dest_TFree o snd) instT |
|
730 in |
|
731 thm3 |
|
732 |> Raw_Simplifier.rewrite_rule ctxt' post_simps |
|
733 |> Simplifier.norm_hhf ctxt' |
|
734 |> Drule.generalize (tnames, []) |
|
735 |> Drule.zero_var_indexes |
|
736 end |
|
737 |
|
738 (** Methods and attributes **) |
|
739 |
|
740 val free = Args.context -- Args.term >> (fn (_, Free v) => v | (ctxt, t) => |
|
741 error ("Bad free variable: " ^ Syntax.string_of_term ctxt t)) |
|
742 |
|
743 val fixing = Scan.optional (Scan.lift (Args.$$$ "fixing" -- Args.colon) |
|
744 |-- Scan.repeat free) [] |
|
745 |
|
746 fun transfer_method equiv : (Proof.context -> Proof.method) context_parser = |
|
747 fixing >> (fn vs => fn ctxt => |
|
748 SIMPLE_METHOD' (gen_frees_tac vs ctxt THEN' transfer_tac equiv ctxt)) |
|
749 |
|
750 val transfer_prover_method : (Proof.context -> Proof.method) context_parser = |
|
751 Scan.succeed (fn ctxt => SIMPLE_METHOD' (transfer_prover_tac ctxt)) |
|
752 |
|
753 (* Attribute for transfer rules *) |
|
754 |
|
755 fun prep_rule ctxt = |
|
756 abstract_domains_transfer ctxt o abstract_equalities_transfer ctxt o Conv.fconv_rule prep_conv |
|
757 |
|
758 val transfer_add = |
|
759 Thm.declaration_attribute (fn thm => fn ctxt => |
|
760 (add_transfer_thm o prep_rule (Context.proof_of ctxt)) thm ctxt) |
|
761 |
|
762 val transfer_del = |
|
763 Thm.declaration_attribute (fn thm => fn ctxt => |
|
764 (del_transfer_thm o prep_rule (Context.proof_of ctxt)) thm ctxt) |
|
765 |
|
766 val transfer_attribute = |
|
767 Attrib.add_del transfer_add transfer_del |
|
768 |
|
769 (* Attributes for transfer domain rules *) |
|
770 |
|
771 val transfer_domain_add = Thm.declaration_attribute add_transfer_domain_thm |
|
772 |
|
773 val transfer_domain_del = Thm.declaration_attribute del_transfer_domain_thm |
|
774 |
|
775 val transfer_domain_attribute = |
|
776 Attrib.add_del transfer_domain_add transfer_domain_del |
|
777 |
|
778 (* Attributes for transferred rules *) |
|
779 |
|
780 fun transferred_attribute thms = Thm.rule_attribute |
|
781 (fn context => transferred (Context.proof_of context) thms) |
|
782 |
|
783 fun untransferred_attribute thms = Thm.rule_attribute |
|
784 (fn context => untransferred (Context.proof_of context) thms) |
|
785 |
|
786 val transferred_attribute_parser = |
|
787 Attrib.thms >> transferred_attribute |
|
788 |
|
789 val untransferred_attribute_parser = |
|
790 Attrib.thms >> untransferred_attribute |
|
791 |
|
792 fun morph_pred_data phi {rel_eq_onp} = {rel_eq_onp = Morphism.thm phi rel_eq_onp} |
|
793 |
|
794 fun lookup_pred_data ctxt type_name = Symtab.lookup (get_pred_data ctxt) type_name |
|
795 |> Option.map (morph_pred_data (Morphism.transfer_morphism (Proof_Context.theory_of ctxt))) |
|
796 |
|
797 fun update_pred_data type_name qinfo ctxt = |
|
798 Data.map (map_pred_data (Symtab.update (type_name, qinfo))) ctxt |
|
799 |
|
800 (* Theory setup *) |
|
801 |
|
802 val relator_eq_setup = |
|
803 let |
|
804 val name = @{binding relator_eq} |
|
805 fun add_thm thm context = context |
|
806 |> Data.map (map_relator_eq (Item_Net.update thm)) |
|
807 |> Data.map (map_relator_eq_raw |
|
808 (Item_Net.update (abstract_equalities_relator_eq (Context.proof_of context) thm))) |
|
809 fun del_thm thm context = context |
|
810 |> Data.map (map_relator_eq (Item_Net.remove thm)) |
|
811 |> Data.map (map_relator_eq_raw |
|
812 (Item_Net.remove (abstract_equalities_relator_eq (Context.proof_of context) thm))) |
|
813 val add = Thm.declaration_attribute add_thm |
|
814 val del = Thm.declaration_attribute del_thm |
|
815 val text = "declaration of relator equality rule (used by transfer method)" |
|
816 val content = Item_Net.content o #relator_eq o Data.get |
|
817 in |
|
818 Attrib.setup name (Attrib.add_del add del) text |
|
819 #> Global_Theory.add_thms_dynamic (name, content) |
|
820 end |
|
821 |
|
822 val relator_domain_setup = |
|
823 let |
|
824 val name = @{binding relator_domain} |
|
825 fun add_thm thm context = |
|
826 let |
|
827 val thm = abstract_domains_relator_domain (Context.proof_of context) thm |
|
828 in |
|
829 context |> Data.map (map_relator_domain (Item_Net.update thm)) |> add_transfer_domain_thm thm |
|
830 end |
|
831 fun del_thm thm context = |
|
832 let |
|
833 val thm = abstract_domains_relator_domain (Context.proof_of context) thm |
|
834 in |
|
835 context |> Data.map (map_relator_domain (Item_Net.remove thm)) |> del_transfer_domain_thm thm |
|
836 end |
|
837 val add = Thm.declaration_attribute add_thm |
|
838 val del = Thm.declaration_attribute del_thm |
|
839 val text = "declaration of relator domain rule (used by transfer method)" |
|
840 val content = Item_Net.content o #relator_domain o Data.get |
|
841 in |
|
842 Attrib.setup name (Attrib.add_del add del) text |
|
843 #> Global_Theory.add_thms_dynamic (name, content) |
|
844 end |
|
845 |
|
846 val setup = |
|
847 relator_eq_setup |
|
848 #> relator_domain_setup |
|
849 #> Attrib.setup @{binding transfer_rule} transfer_attribute |
|
850 "transfer rule for transfer method" |
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851 #> Global_Theory.add_thms_dynamic |
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852 (@{binding transfer_raw}, Item_Net.content o #transfer_raw o Data.get) |
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853 #> Attrib.setup @{binding transfer_domain_rule} transfer_domain_attribute |
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854 "transfer domain rule for transfer method" |
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855 #> Attrib.setup @{binding transferred} transferred_attribute_parser |
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856 "raw theorem transferred to abstract theorem using transfer rules" |
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857 #> Attrib.setup @{binding untransferred} untransferred_attribute_parser |
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858 "abstract theorem transferred to raw theorem using transfer rules" |
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859 #> Global_Theory.add_thms_dynamic |
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860 (@{binding relator_eq_raw}, Item_Net.content o #relator_eq_raw o Data.get) |
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861 #> Method.setup @{binding transfer} (transfer_method true) |
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862 "generic theorem transfer method" |
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863 #> Method.setup @{binding transfer'} (transfer_method false) |
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864 "generic theorem transfer method" |
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865 #> Method.setup @{binding transfer_prover} transfer_prover_method |
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866 "for proving transfer rules" |
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867 |
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868 end |