1 (* Title: HOL/BNF/Tools/bnf_lfp.ML |
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2 Author: Dmitriy Traytel, TU Muenchen |
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3 Author: Andrei Popescu, TU Muenchen |
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4 Copyright 2012 |
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5 |
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6 Datatype construction. |
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7 *) |
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8 |
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9 signature BNF_LFP = |
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10 sig |
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11 val construct_lfp: mixfix list -> binding list -> binding list -> binding list list -> |
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12 binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list -> |
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13 local_theory -> BNF_FP_Util.fp_result * local_theory |
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14 end; |
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15 |
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16 structure BNF_LFP : BNF_LFP = |
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17 struct |
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18 |
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19 open BNF_Def |
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20 open BNF_Util |
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21 open BNF_Tactics |
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22 open BNF_Comp |
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23 open BNF_FP_Util |
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24 open BNF_FP_Def_Sugar |
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25 open BNF_LFP_Rec_Sugar |
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26 open BNF_LFP_Util |
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27 open BNF_LFP_Tactics |
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28 |
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29 (*all BNFs have the same lives*) |
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30 fun construct_lfp mixfixes map_bs rel_bs set_bss0 bs resBs (resDs, Dss) bnfs lthy = |
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31 let |
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32 val time = time lthy; |
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33 val timer = time (Timer.startRealTimer ()); |
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34 |
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35 val live = live_of_bnf (hd bnfs); |
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36 val n = length bnfs; (*active*) |
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37 val ks = 1 upto n; |
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38 val m = live - n; (*passive, if 0 don't generate a new BNF*) |
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39 |
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40 val note_all = Config.get lthy bnf_note_all; |
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41 val b_names = map Binding.name_of bs; |
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42 val b_name = mk_common_name b_names; |
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43 val b = Binding.name b_name; |
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44 val mk_internal_b = Binding.name #> Binding.prefix true b_name #> Binding.conceal; |
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45 fun mk_internal_bs name = |
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46 map (fn b => |
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47 Binding.prefix true b_name (Binding.prefix_name (name ^ "_") b) |> Binding.conceal) bs; |
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48 val external_bs = map2 (Binding.prefix false) b_names bs |
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49 |> note_all = false ? map Binding.conceal; |
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50 |
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51 (* TODO: check if m, n, etc., are sane *) |
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52 |
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53 val deads = fold (union (op =)) Dss resDs; |
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54 val names_lthy = fold Variable.declare_typ deads lthy; |
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55 val passives = map fst (subtract (op = o apsnd TFree) deads resBs); |
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56 |
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57 (* tvars *) |
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58 val (((((passiveAs, activeAs), passiveBs), activeBs), passiveCs), activeCs) = |
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59 names_lthy |
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60 |> variant_tfrees passives |
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61 ||>> mk_TFrees n |
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62 ||>> variant_tfrees passives |
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63 ||>> mk_TFrees n |
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64 ||>> variant_tfrees passives |
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65 ||>> mk_TFrees n |
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66 |> fst; |
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67 |
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68 val allAs = passiveAs @ activeAs; |
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69 val allBs' = passiveBs @ activeBs; |
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70 val Ass = replicate n allAs; |
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71 val allBs = passiveAs @ activeBs; |
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72 val Bss = replicate n allBs; |
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73 val allCs = passiveAs @ activeCs; |
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74 val allCs' = passiveBs @ activeCs; |
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75 val Css' = replicate n allCs'; |
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76 |
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77 (* types *) |
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78 val dead_poss = |
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79 map (fn x => if member (op =) deads (TFree x) then SOME (TFree x) else NONE) resBs; |
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80 fun mk_param NONE passive = (hd passive, tl passive) |
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81 | mk_param (SOME a) passive = (a, passive); |
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82 val mk_params = fold_map mk_param dead_poss #> fst; |
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83 |
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84 fun mk_FTs Ts = map2 (fn Ds => mk_T_of_bnf Ds Ts) Dss bnfs; |
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85 val (params, params') = `(map Term.dest_TFree) (mk_params passiveAs); |
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86 val FTsAs = mk_FTs allAs; |
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87 val FTsBs = mk_FTs allBs; |
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88 val FTsCs = mk_FTs allCs; |
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89 val ATs = map HOLogic.mk_setT passiveAs; |
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90 val BTs = map HOLogic.mk_setT activeAs; |
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91 val B'Ts = map HOLogic.mk_setT activeBs; |
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92 val B''Ts = map HOLogic.mk_setT activeCs; |
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93 val sTs = map2 (curry op -->) FTsAs activeAs; |
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94 val s'Ts = map2 (curry op -->) FTsBs activeBs; |
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95 val s''Ts = map2 (curry op -->) FTsCs activeCs; |
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96 val fTs = map2 (curry op -->) activeAs activeBs; |
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97 val inv_fTs = map2 (curry op -->) activeBs activeAs; |
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98 val self_fTs = map2 (curry op -->) activeAs activeAs; |
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99 val gTs = map2 (curry op -->) activeBs activeCs; |
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100 val all_gTs = map2 (curry op -->) allBs allCs'; |
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101 val prodBsAs = map2 (curry HOLogic.mk_prodT) activeBs activeAs; |
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102 val prodFTs = mk_FTs (passiveAs @ prodBsAs); |
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103 val prod_sTs = map2 (curry op -->) prodFTs activeAs; |
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104 |
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105 (* terms *) |
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106 val mapsAsAs = map4 mk_map_of_bnf Dss Ass Ass bnfs; |
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107 val mapsAsBs = map4 mk_map_of_bnf Dss Ass Bss bnfs; |
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108 val mapsBsAs = map4 mk_map_of_bnf Dss Bss Ass bnfs; |
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109 val mapsBsCs' = map4 mk_map_of_bnf Dss Bss Css' bnfs; |
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110 val mapsAsCs' = map4 mk_map_of_bnf Dss Ass Css' bnfs; |
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111 val map_fsts = map4 mk_map_of_bnf Dss (replicate n (passiveAs @ prodBsAs)) Bss bnfs; |
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112 val map_fsts_rev = map4 mk_map_of_bnf Dss Bss (replicate n (passiveAs @ prodBsAs)) bnfs; |
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113 fun mk_setss Ts = map3 mk_sets_of_bnf (map (replicate live) Dss) |
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114 (map (replicate live) (replicate n Ts)) bnfs; |
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115 val setssAs = mk_setss allAs; |
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116 val bd0s = map3 mk_bd_of_bnf Dss Ass bnfs; |
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117 val bds = |
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118 map3 (fn bd0 => fn Ds => fn bnf => mk_csum bd0 |
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119 (mk_card_of (HOLogic.mk_UNIV |
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120 (mk_T_of_bnf Ds (replicate live (fst (dest_relT (fastype_of bd0)))) bnf)))) |
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121 bd0s Dss bnfs; |
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122 val witss = map wits_of_bnf bnfs; |
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123 |
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124 val (((((((((((((((((((zs, zs'), As), Bs), Bs_copy), B's), B''s), ss), prod_ss), s's), s''s), |
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125 fs), fs_copy), inv_fs), self_fs), gs), all_gs), (xFs, xFs')), (yFs, yFs')), |
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126 names_lthy) = lthy |
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127 |> mk_Frees' "z" activeAs |
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128 ||>> mk_Frees "A" ATs |
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129 ||>> mk_Frees "B" BTs |
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130 ||>> mk_Frees "B" BTs |
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131 ||>> mk_Frees "B'" B'Ts |
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132 ||>> mk_Frees "B''" B''Ts |
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133 ||>> mk_Frees "s" sTs |
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134 ||>> mk_Frees "prods" prod_sTs |
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135 ||>> mk_Frees "s'" s'Ts |
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136 ||>> mk_Frees "s''" s''Ts |
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137 ||>> mk_Frees "f" fTs |
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138 ||>> mk_Frees "f" fTs |
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139 ||>> mk_Frees "f" inv_fTs |
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140 ||>> mk_Frees "f" self_fTs |
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141 ||>> mk_Frees "g" gTs |
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142 ||>> mk_Frees "g" all_gTs |
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143 ||>> mk_Frees' "x" FTsAs |
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144 ||>> mk_Frees' "y" FTsBs; |
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145 |
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146 val passive_UNIVs = map HOLogic.mk_UNIV passiveAs; |
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147 val active_UNIVs = map HOLogic.mk_UNIV activeAs; |
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148 val prod_UNIVs = map HOLogic.mk_UNIV prodBsAs; |
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149 val passive_ids = map HOLogic.id_const passiveAs; |
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150 val active_ids = map HOLogic.id_const activeAs; |
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151 val fsts = map fst_const prodBsAs; |
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152 |
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153 (* thms *) |
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154 val bd0_card_orders = map bd_card_order_of_bnf bnfs; |
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155 val bd0_Card_orders = map bd_Card_order_of_bnf bnfs; |
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156 val bd0_Cinfinites = map bd_Cinfinite_of_bnf bnfs; |
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157 val set_bd0ss = map set_bd_of_bnf bnfs; |
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158 |
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159 val bd_card_orders = |
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160 map (fn thm => @{thm card_order_csum} OF [thm, @{thm card_of_card_order_on}]) bd0_card_orders; |
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161 val bd_Card_order = @{thm Card_order_csum}; |
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162 val bd_Card_orders = replicate n bd_Card_order; |
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163 val bd_Cinfinites = map (fn thm => thm RS @{thm Cinfinite_csum1}) bd0_Cinfinites; |
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164 val bd_Cnotzeros = map (fn thm => thm RS @{thm Cinfinite_Cnotzero}) bd_Cinfinites; |
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165 val bd_Cinfinite = hd bd_Cinfinites; |
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166 val bd_Cnotzero = hd bd_Cnotzeros; |
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167 val set_bdss = |
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168 map2 (fn set_bd0s => fn bd0_Card_order => |
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169 map (fn thm => ctrans OF [thm, bd0_Card_order RS @{thm ordLeq_csum1}]) set_bd0s) |
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170 set_bd0ss bd0_Card_orders; |
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171 val in_bds = map in_bd_of_bnf bnfs; |
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172 val sym_map_comps = map (fn bnf => map_comp0_of_bnf bnf RS sym) bnfs; |
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173 val map_comps = map map_comp_of_bnf bnfs; |
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174 val map_cong0s = map map_cong0_of_bnf bnfs; |
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175 val map_id0s = map map_id0_of_bnf bnfs; |
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176 val map_ids = map map_id_of_bnf bnfs; |
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177 val set_mapss = map set_map_of_bnf bnfs; |
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178 val rel_mono_strongs = map rel_mono_strong_of_bnf bnfs; |
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179 val rel_OOs = map rel_OO_of_bnf bnfs; |
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180 |
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181 val timer = time (timer "Extracted terms & thms"); |
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182 |
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183 (* nonemptiness check *) |
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184 fun new_wit X (wit: nonemptiness_witness) = subset (op =) (#I wit, (0 upto m - 1) @ map snd X); |
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185 |
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186 val all = m upto m + n - 1; |
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187 |
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188 fun enrich X = map_filter (fn i => |
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189 (case find_first (fn (_, i') => i = i') X of |
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190 NONE => |
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191 (case find_index (new_wit X) (nth witss (i - m)) of |
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192 ~1 => NONE |
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193 | j => SOME (j, i)) |
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194 | SOME ji => SOME ji)) all; |
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195 val reachable = fixpoint (op =) enrich []; |
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196 val _ = (case subtract (op =) (map snd reachable) all of |
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197 [] => () |
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198 | i :: _ => error ("Cannot define empty datatype " ^ quote (Binding.name_of (nth bs (i - m))))); |
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199 |
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200 val wit_thms = flat (map2 (fn bnf => fn (j, _) => nth (wit_thmss_of_bnf bnf) j) bnfs reachable); |
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201 |
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202 val timer = time (timer "Checked nonemptiness"); |
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203 |
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204 (* derived thms *) |
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205 |
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206 (*map g1 ... gm g(m+1) ... g(m+n) (map id ... id f(m+1) ... f(m+n) x) = |
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207 map g1 ... gm (g(m+1) o f(m+1)) ... (g(m+n) o f(m+n)) x*) |
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208 fun mk_map_comp_id x mapAsBs mapBsCs mapAsCs map_comp0 = |
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209 let |
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210 val lhs = Term.list_comb (mapBsCs, all_gs) $ |
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211 (Term.list_comb (mapAsBs, passive_ids @ fs) $ x); |
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212 val rhs = Term.list_comb (mapAsCs, |
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213 take m all_gs @ map HOLogic.mk_comp (drop m all_gs ~~ fs)) $ x; |
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214 in |
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215 Goal.prove_sorry lthy [] [] |
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216 (fold_rev Logic.all (x :: fs @ all_gs) (mk_Trueprop_eq (lhs, rhs))) |
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217 (K (mk_map_comp_id_tac map_comp0)) |
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218 |> Thm.close_derivation |
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219 end; |
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220 |
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221 val map_comp_id_thms = map5 mk_map_comp_id xFs mapsAsBs mapsBsCs' mapsAsCs' map_comps; |
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222 |
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223 (*forall a : set(m+1) x. f(m+1) a = a; ...; forall a : set(m+n) x. f(m+n) a = a ==> |
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224 map id ... id f(m+1) ... f(m+n) x = x*) |
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225 fun mk_map_cong0L x mapAsAs sets map_cong0 map_id = |
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226 let |
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227 fun mk_prem set f z z' = HOLogic.mk_Trueprop |
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228 (mk_Ball (set $ x) (Term.absfree z' (HOLogic.mk_eq (f $ z, z)))); |
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229 val prems = map4 mk_prem (drop m sets) self_fs zs zs'; |
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230 val goal = mk_Trueprop_eq (Term.list_comb (mapAsAs, passive_ids @ self_fs) $ x, x); |
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231 in |
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232 Goal.prove_sorry lthy [] [] |
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233 (fold_rev Logic.all (x :: self_fs) (Logic.list_implies (prems, goal))) |
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234 (K (mk_map_cong0L_tac m map_cong0 map_id)) |
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235 |> Thm.close_derivation |
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236 end; |
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237 |
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238 val map_cong0L_thms = map5 mk_map_cong0L xFs mapsAsAs setssAs map_cong0s map_ids; |
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239 val in_mono'_thms = map (fn bnf => in_mono_of_bnf bnf OF (replicate m subset_refl)) bnfs; |
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240 val in_cong'_thms = map (fn bnf => in_cong_of_bnf bnf OF (replicate m refl)) bnfs; |
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241 |
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242 val timer = time (timer "Derived simple theorems"); |
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243 |
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244 (* algebra *) |
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245 |
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246 val alg_bind = mk_internal_b algN; |
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247 val alg_name = Binding.name_of alg_bind; |
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248 val alg_def_bind = (Thm.def_binding alg_bind, []); |
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249 |
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250 (*forall i = 1 ... n: (\<forall>x \<in> Fi_in A1 .. Am B1 ... Bn. si x \<in> Bi)*) |
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251 val alg_spec = |
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252 let |
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253 val algT = Library.foldr (op -->) (ATs @ BTs @ sTs, HOLogic.boolT); |
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254 |
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255 val ins = map3 mk_in (replicate n (As @ Bs)) setssAs FTsAs; |
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256 fun mk_alg_conjunct B s X x x' = |
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257 mk_Ball X (Term.absfree x' (HOLogic.mk_mem (s $ x, B))); |
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258 |
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259 val lhs = Term.list_comb (Free (alg_name, algT), As @ Bs @ ss); |
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260 val rhs = Library.foldr1 HOLogic.mk_conj (map5 mk_alg_conjunct Bs ss ins xFs xFs') |
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261 in |
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262 mk_Trueprop_eq (lhs, rhs) |
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263 end; |
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264 |
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265 val ((alg_free, (_, alg_def_free)), (lthy, lthy_old)) = |
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266 lthy |
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267 |> Specification.definition (SOME (alg_bind, NONE, NoSyn), (alg_def_bind, alg_spec)) |
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268 ||> `Local_Theory.restore; |
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269 |
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270 val phi = Proof_Context.export_morphism lthy_old lthy; |
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271 val alg = fst (Term.dest_Const (Morphism.term phi alg_free)); |
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272 val alg_def = Morphism.thm phi alg_def_free; |
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273 |
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274 fun mk_alg As Bs ss = |
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275 let |
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276 val args = As @ Bs @ ss; |
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277 val Ts = map fastype_of args; |
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278 val algT = Library.foldr (op -->) (Ts, HOLogic.boolT); |
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279 in |
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280 Term.list_comb (Const (alg, algT), args) |
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281 end; |
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282 |
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283 val alg_set_thms = |
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284 let |
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285 val alg_prem = HOLogic.mk_Trueprop (mk_alg As Bs ss); |
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286 fun mk_prem x set B = HOLogic.mk_Trueprop (mk_leq (set $ x) B); |
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287 fun mk_concl s x B = HOLogic.mk_Trueprop (HOLogic.mk_mem (s $ x, B)); |
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288 val premss = map2 ((fn x => fn sets => map2 (mk_prem x) sets (As @ Bs))) xFs setssAs; |
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289 val concls = map3 mk_concl ss xFs Bs; |
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290 val goals = map3 (fn x => fn prems => fn concl => |
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291 fold_rev Logic.all (x :: As @ Bs @ ss) |
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292 (Logic.list_implies (alg_prem :: prems, concl))) xFs premss concls; |
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293 in |
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294 map (fn goal => |
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295 Goal.prove_sorry lthy [] [] goal (K (mk_alg_set_tac alg_def)) |> Thm.close_derivation) |
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296 goals |
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297 end; |
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298 |
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299 fun mk_talg ATs BTs = mk_alg (map HOLogic.mk_UNIV ATs) (map HOLogic.mk_UNIV BTs); |
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300 |
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301 val talg_thm = |
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302 let |
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303 val goal = fold_rev Logic.all ss |
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304 (HOLogic.mk_Trueprop (mk_talg passiveAs activeAs ss)) |
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305 in |
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306 Goal.prove_sorry lthy [] [] goal |
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307 (K (stac alg_def 1 THEN CONJ_WRAP (K (EVERY' [rtac ballI, rtac UNIV_I] 1)) ss)) |
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308 |> Thm.close_derivation |
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309 end; |
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310 |
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311 val timer = time (timer "Algebra definition & thms"); |
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312 |
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313 val alg_not_empty_thms = |
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314 let |
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315 val alg_prem = |
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316 HOLogic.mk_Trueprop (mk_alg passive_UNIVs Bs ss); |
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317 val concls = map (HOLogic.mk_Trueprop o mk_not_empty) Bs; |
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318 val goals = |
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319 map (fn concl => |
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320 fold_rev Logic.all (Bs @ ss) (Logic.mk_implies (alg_prem, concl))) concls; |
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321 in |
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322 map2 (fn goal => fn alg_set => |
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323 Goal.prove_sorry lthy [] [] |
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324 goal (K (mk_alg_not_empty_tac lthy alg_set alg_set_thms wit_thms)) |
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325 |> Thm.close_derivation) |
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326 goals alg_set_thms |
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327 end; |
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328 |
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329 val timer = time (timer "Proved nonemptiness"); |
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330 |
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331 (* morphism *) |
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332 |
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333 val mor_bind = mk_internal_b morN; |
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334 val mor_name = Binding.name_of mor_bind; |
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335 val mor_def_bind = (Thm.def_binding mor_bind, []); |
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336 |
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337 (*fbetw) forall i = 1 ... n: (\<forall>x \<in> Bi. f x \<in> B'i)*) |
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338 (*mor) forall i = 1 ... n: (\<forall>x \<in> Fi_in UNIV ... UNIV B1 ... Bn. |
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339 f (s1 x) = s1' (Fi_map id ... id f1 ... fn x))*) |
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340 val mor_spec = |
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341 let |
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342 val morT = Library.foldr (op -->) (BTs @ sTs @ B'Ts @ s'Ts @ fTs, HOLogic.boolT); |
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343 |
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344 fun mk_fbetw f B1 B2 z z' = |
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345 mk_Ball B1 (Term.absfree z' (HOLogic.mk_mem (f $ z, B2))); |
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346 fun mk_mor sets mapAsBs f s s' T x x' = |
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347 mk_Ball (mk_in (passive_UNIVs @ Bs) sets T) |
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348 (Term.absfree x' (HOLogic.mk_eq (f $ (s $ x), s' $ |
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349 (Term.list_comb (mapAsBs, passive_ids @ fs) $ x)))); |
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350 val lhs = Term.list_comb (Free (mor_name, morT), Bs @ ss @ B's @ s's @ fs); |
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351 val rhs = HOLogic.mk_conj |
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352 (Library.foldr1 HOLogic.mk_conj (map5 mk_fbetw fs Bs B's zs zs'), |
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353 Library.foldr1 HOLogic.mk_conj |
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354 (map8 mk_mor setssAs mapsAsBs fs ss s's FTsAs xFs xFs')) |
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355 in |
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356 mk_Trueprop_eq (lhs, rhs) |
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357 end; |
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358 |
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359 val ((mor_free, (_, mor_def_free)), (lthy, lthy_old)) = |
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360 lthy |
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361 |> Specification.definition (SOME (mor_bind, NONE, NoSyn), (mor_def_bind, mor_spec)) |
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362 ||> `Local_Theory.restore; |
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363 |
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364 val phi = Proof_Context.export_morphism lthy_old lthy; |
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365 val mor = fst (Term.dest_Const (Morphism.term phi mor_free)); |
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366 val mor_def = Morphism.thm phi mor_def_free; |
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367 |
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368 fun mk_mor Bs1 ss1 Bs2 ss2 fs = |
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369 let |
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370 val args = Bs1 @ ss1 @ Bs2 @ ss2 @ fs; |
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371 val Ts = map fastype_of (Bs1 @ ss1 @ Bs2 @ ss2 @ fs); |
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372 val morT = Library.foldr (op -->) (Ts, HOLogic.boolT); |
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373 in |
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374 Term.list_comb (Const (mor, morT), args) |
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375 end; |
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376 |
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377 val (mor_image_thms, morE_thms) = |
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378 let |
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379 val prem = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs); |
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380 fun mk_image_goal f B1 B2 = fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs) |
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381 (Logic.mk_implies (prem, HOLogic.mk_Trueprop (mk_leq (mk_image f $ B1) B2))); |
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382 val image_goals = map3 mk_image_goal fs Bs B's; |
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383 fun mk_elim_prem sets x T = HOLogic.mk_Trueprop |
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384 (HOLogic.mk_mem (x, mk_in (passive_UNIVs @ Bs) sets T)); |
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385 fun mk_elim_goal sets mapAsBs f s s' x T = |
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386 fold_rev Logic.all (x :: Bs @ ss @ B's @ s's @ fs) |
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387 (Logic.list_implies ([prem, mk_elim_prem sets x T], |
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388 mk_Trueprop_eq (f $ (s $ x), s' $ Term.list_comb (mapAsBs, passive_ids @ fs @ [x])))); |
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389 val elim_goals = map7 mk_elim_goal setssAs mapsAsBs fs ss s's xFs FTsAs; |
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390 fun prove goal = |
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391 Goal.prove_sorry lthy [] [] goal (K (mk_mor_elim_tac mor_def)) |> Thm.close_derivation; |
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392 in |
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393 (map prove image_goals, map prove elim_goals) |
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394 end; |
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395 |
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396 val mor_incl_thm = |
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397 let |
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398 val prems = map2 (HOLogic.mk_Trueprop oo mk_leq) Bs Bs_copy; |
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399 val concl = HOLogic.mk_Trueprop (mk_mor Bs ss Bs_copy ss active_ids); |
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400 in |
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401 Goal.prove_sorry lthy [] [] |
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402 (fold_rev Logic.all (Bs @ ss @ Bs_copy) (Logic.list_implies (prems, concl))) |
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403 (K (mk_mor_incl_tac mor_def map_ids)) |
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404 |> Thm.close_derivation |
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405 end; |
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406 |
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407 val mor_comp_thm = |
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408 let |
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409 val prems = |
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410 [HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs), |
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411 HOLogic.mk_Trueprop (mk_mor B's s's B''s s''s gs)]; |
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412 val concl = |
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413 HOLogic.mk_Trueprop (mk_mor Bs ss B''s s''s (map2 (curry HOLogic.mk_comp) gs fs)); |
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414 in |
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415 Goal.prove_sorry lthy [] [] |
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416 (fold_rev Logic.all (Bs @ ss @ B's @ s's @ B''s @ s''s @ fs @ gs) |
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417 (Logic.list_implies (prems, concl))) |
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418 (K (mk_mor_comp_tac mor_def set_mapss map_comp_id_thms)) |
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419 |> Thm.close_derivation |
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420 end; |
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421 |
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422 val mor_inv_thm = |
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423 let |
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424 fun mk_inv_prem f inv_f B B' = HOLogic.mk_conj (mk_leq (mk_image inv_f $ B') B, |
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425 HOLogic.mk_conj (mk_inver inv_f f B, mk_inver f inv_f B')); |
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426 val prems = map HOLogic.mk_Trueprop |
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427 ([mk_mor Bs ss B's s's fs, |
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428 mk_alg passive_UNIVs Bs ss, |
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429 mk_alg passive_UNIVs B's s's] @ |
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430 map4 mk_inv_prem fs inv_fs Bs B's); |
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431 val concl = HOLogic.mk_Trueprop (mk_mor B's s's Bs ss inv_fs); |
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432 in |
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433 Goal.prove_sorry lthy [] [] |
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434 (fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs @ inv_fs) |
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435 (Logic.list_implies (prems, concl))) |
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436 (K (mk_mor_inv_tac alg_def mor_def set_mapss morE_thms map_comp_id_thms map_cong0L_thms)) |
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437 |> Thm.close_derivation |
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438 end; |
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439 |
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440 val mor_cong_thm = |
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441 let |
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442 val prems = map HOLogic.mk_Trueprop |
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443 (map2 (curry HOLogic.mk_eq) fs_copy fs @ [mk_mor Bs ss B's s's fs]) |
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444 val concl = HOLogic.mk_Trueprop (mk_mor Bs ss B's s's fs_copy); |
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445 in |
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446 Goal.prove_sorry lthy [] [] |
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447 (fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs @ fs_copy) |
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448 (Logic.list_implies (prems, concl))) |
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449 (K ((hyp_subst_tac lthy THEN' atac) 1)) |
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450 |> Thm.close_derivation |
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451 end; |
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452 |
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453 val mor_str_thm = |
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454 let |
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455 val maps = map2 (fn Ds => fn bnf => Term.list_comb |
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456 (mk_map_of_bnf Ds (passiveAs @ FTsAs) allAs bnf, passive_ids @ ss)) Dss bnfs; |
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457 in |
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458 Goal.prove_sorry lthy [] [] |
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459 (fold_rev Logic.all ss (HOLogic.mk_Trueprop |
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460 (mk_mor (map HOLogic.mk_UNIV FTsAs) maps active_UNIVs ss ss))) |
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461 (K (mk_mor_str_tac ks mor_def)) |
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462 |> Thm.close_derivation |
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463 end; |
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464 |
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465 val mor_convol_thm = |
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466 let |
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467 val maps = map3 (fn s => fn prod_s => fn mapx => |
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468 mk_convol (HOLogic.mk_comp (s, Term.list_comb (mapx, passive_ids @ fsts)), prod_s)) |
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469 s's prod_ss map_fsts; |
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470 in |
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471 Goal.prove_sorry lthy [] [] |
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472 (fold_rev Logic.all (s's @ prod_ss) (HOLogic.mk_Trueprop |
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473 (mk_mor prod_UNIVs maps (map HOLogic.mk_UNIV activeBs) s's fsts))) |
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474 (K (mk_mor_convol_tac ks mor_def)) |
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475 |> Thm.close_derivation |
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476 end; |
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477 |
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478 val mor_UNIV_thm = |
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479 let |
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480 fun mk_conjunct mapAsBs f s s' = HOLogic.mk_eq |
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481 (HOLogic.mk_comp (f, s), |
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482 HOLogic.mk_comp (s', Term.list_comb (mapAsBs, passive_ids @ fs))); |
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483 val lhs = mk_mor active_UNIVs ss (map HOLogic.mk_UNIV activeBs) s's fs; |
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484 val rhs = Library.foldr1 HOLogic.mk_conj (map4 mk_conjunct mapsAsBs fs ss s's); |
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485 in |
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486 Goal.prove_sorry lthy [] [] (fold_rev Logic.all (ss @ s's @ fs) (mk_Trueprop_eq (lhs, rhs))) |
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487 (K (mk_mor_UNIV_tac m morE_thms mor_def)) |
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488 |> Thm.close_derivation |
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489 end; |
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490 |
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491 val timer = time (timer "Morphism definition & thms"); |
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492 |
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493 (* isomorphism *) |
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494 |
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495 (*mor Bs1 ss1 Bs2 ss2 fs \<and> (\<exists>gs. mor Bs2 ss2 Bs1 ss1 fs \<and> |
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496 forall i = 1 ... n. (inver gs[i] fs[i] Bs1[i] \<and> inver fs[i] gs[i] Bs2[i]))*) |
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497 fun mk_iso Bs1 ss1 Bs2 ss2 fs gs = |
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498 let |
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499 val ex_inv_mor = list_exists_free gs |
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500 (HOLogic.mk_conj (mk_mor Bs2 ss2 Bs1 ss1 gs, |
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501 Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_conj) |
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502 (map3 mk_inver gs fs Bs1) (map3 mk_inver fs gs Bs2)))); |
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503 in |
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504 HOLogic.mk_conj (mk_mor Bs1 ss1 Bs2 ss2 fs, ex_inv_mor) |
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505 end; |
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506 |
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507 val iso_alt_thm = |
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508 let |
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509 val prems = map HOLogic.mk_Trueprop |
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510 [mk_alg passive_UNIVs Bs ss, |
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511 mk_alg passive_UNIVs B's s's] |
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512 val concl = mk_Trueprop_eq (mk_iso Bs ss B's s's fs inv_fs, |
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513 HOLogic.mk_conj (mk_mor Bs ss B's s's fs, |
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514 Library.foldr1 HOLogic.mk_conj (map3 mk_bij_betw fs Bs B's))); |
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515 in |
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516 Goal.prove_sorry lthy [] [] |
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517 (fold_rev Logic.all (Bs @ ss @ B's @ s's @ fs) (Logic.list_implies (prems, concl))) |
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518 (K (mk_iso_alt_tac mor_image_thms mor_inv_thm)) |
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519 |> Thm.close_derivation |
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520 end; |
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521 |
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522 val timer = time (timer "Isomorphism definition & thms"); |
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523 |
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524 (* algebra copies *) |
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525 |
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526 val (copy_alg_thm, ex_copy_alg_thm) = |
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527 let |
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528 val prems = map HOLogic.mk_Trueprop |
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529 (mk_alg passive_UNIVs Bs ss :: map3 mk_bij_betw inv_fs B's Bs); |
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530 val inver_prems = map HOLogic.mk_Trueprop |
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531 (map3 mk_inver inv_fs fs Bs @ map3 mk_inver fs inv_fs B's); |
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532 val all_prems = prems @ inver_prems; |
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533 fun mk_s f s mapT y y' = Term.absfree y' (f $ (s $ |
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534 (Term.list_comb (mapT, passive_ids @ inv_fs) $ y))); |
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535 |
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536 val alg = HOLogic.mk_Trueprop |
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537 (mk_alg passive_UNIVs B's (map5 mk_s fs ss mapsBsAs yFs yFs')); |
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538 val copy_str_thm = Goal.prove_sorry lthy [] [] |
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539 (fold_rev Logic.all (Bs @ ss @ B's @ inv_fs @ fs) |
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540 (Logic.list_implies (all_prems, alg))) |
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541 (K (mk_copy_str_tac set_mapss alg_def alg_set_thms)) |
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542 |> Thm.close_derivation; |
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543 |
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544 val iso = HOLogic.mk_Trueprop |
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545 (mk_iso B's (map5 mk_s fs ss mapsBsAs yFs yFs') Bs ss inv_fs fs_copy); |
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546 val copy_alg_thm = Goal.prove_sorry lthy [] [] |
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547 (fold_rev Logic.all (Bs @ ss @ B's @ inv_fs @ fs) |
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548 (Logic.list_implies (all_prems, iso))) |
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549 (K (mk_copy_alg_tac set_mapss alg_set_thms mor_def iso_alt_thm copy_str_thm)) |
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550 |> Thm.close_derivation; |
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551 |
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552 val ex = HOLogic.mk_Trueprop |
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553 (list_exists_free s's |
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554 (HOLogic.mk_conj (mk_alg passive_UNIVs B's s's, |
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555 mk_iso B's s's Bs ss inv_fs fs_copy))); |
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556 val ex_copy_alg_thm = Goal.prove_sorry lthy [] [] |
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557 (fold_rev Logic.all (Bs @ ss @ B's @ inv_fs @ fs) |
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558 (Logic.list_implies (prems, ex))) |
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559 (K (mk_ex_copy_alg_tac n copy_str_thm copy_alg_thm)) |
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560 |> Thm.close_derivation; |
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561 in |
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562 (copy_alg_thm, ex_copy_alg_thm) |
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563 end; |
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564 |
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565 val timer = time (timer "Copy thms"); |
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566 |
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567 |
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568 (* bounds *) |
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569 |
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570 val sum_Card_order = if n = 1 then bd_Card_order else @{thm Card_order_csum}; |
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571 val sum_Cnotzero = if n = 1 then bd_Cnotzero else bd_Cnotzero RS @{thm csum_Cnotzero1}; |
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572 val sum_Cinfinite = if n = 1 then bd_Cinfinite else bd_Cinfinite RS @{thm Cinfinite_csum1}; |
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573 fun mk_set_bd_sums i bd_Card_order bds = |
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574 if n = 1 then bds |
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575 else map (fn thm => bd_Card_order RS mk_ordLeq_csum n i thm) bds; |
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576 val set_bd_sumss = map3 mk_set_bd_sums ks bd_Card_orders set_bdss; |
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577 |
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578 fun mk_in_bd_sum i Co Cnz bd = |
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579 if n = 1 then bd |
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580 else Cnz RS ((Co RS mk_ordLeq_csum n i (Co RS @{thm ordLeq_refl})) RS |
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581 (bd RS @{thm ordLeq_transitive[OF _ cexp_mono2_Cnotzero[OF _ Card_order_csum]]})); |
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582 val in_bd_sums = map4 mk_in_bd_sum ks bd_Card_orders bd_Cnotzeros in_bds; |
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583 |
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584 val sum_bd = Library.foldr1 (uncurry mk_csum) bds; |
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585 val suc_bd = mk_cardSuc sum_bd; |
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586 val field_suc_bd = mk_Field suc_bd; |
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587 val suc_bdT = fst (dest_relT (fastype_of suc_bd)); |
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588 fun mk_Asuc_bd [] = mk_cexp ctwo suc_bd |
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589 | mk_Asuc_bd As = |
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590 mk_cexp (mk_csum (Library.foldr1 (uncurry mk_csum) (map mk_card_of As)) ctwo) suc_bd; |
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591 |
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592 val suc_bd_Card_order = if n = 1 then bd_Card_order RS @{thm cardSuc_Card_order} |
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593 else @{thm cardSuc_Card_order[OF Card_order_csum]}; |
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594 val suc_bd_Cinfinite = if n = 1 then bd_Cinfinite RS @{thm Cinfinite_cardSuc} |
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595 else bd_Cinfinite RS @{thm Cinfinite_cardSuc[OF Cinfinite_csum1]}; |
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596 val suc_bd_Cnotzero = suc_bd_Cinfinite RS @{thm Cinfinite_Cnotzero}; |
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597 val suc_bd_worel = suc_bd_Card_order RS @{thm Card_order_wo_rel} |
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598 val basis_Asuc = if m = 0 then @{thm ordLeq_refl[OF Card_order_ctwo]} |
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599 else @{thm ordLeq_csum2[OF Card_order_ctwo]}; |
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600 val Asuc_bd_Cinfinite = suc_bd_Cinfinite RS (basis_Asuc RS @{thm Cinfinite_cexp}); |
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601 |
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602 val suc_bd_Asuc_bd = @{thm ordLess_ordLeq_trans[OF ordLess_ctwo_cexp cexp_mono1]} OF |
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603 [suc_bd_Card_order, basis_Asuc, suc_bd_Card_order]; |
|
604 |
|
605 val Asuc_bdT = fst (dest_relT (fastype_of (mk_Asuc_bd As))); |
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606 val II_BTs = replicate n (HOLogic.mk_setT Asuc_bdT); |
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607 val II_sTs = map2 (fn Ds => fn bnf => |
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608 mk_T_of_bnf Ds (passiveAs @ replicate n Asuc_bdT) bnf --> Asuc_bdT) Dss bnfs; |
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609 |
|
610 val (((((((idxs, Asi_name), (idx, idx')), (jdx, jdx')), II_Bs), II_ss), Asuc_fs), |
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611 names_lthy) = names_lthy |
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612 |> mk_Frees "i" (replicate n suc_bdT) |
|
613 ||>> (fn ctxt => apfst the_single (mk_fresh_names ctxt 1 "Asi")) |
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614 ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "i") suc_bdT |
|
615 ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "j") suc_bdT |
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616 ||>> mk_Frees "IIB" II_BTs |
|
617 ||>> mk_Frees "IIs" II_sTs |
|
618 ||>> mk_Frees "f" (map (fn T => Asuc_bdT --> T) activeAs); |
|
619 |
|
620 val suc_bd_limit_thm = |
|
621 let |
|
622 val prem = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj |
|
623 (map (fn idx => HOLogic.mk_mem (idx, field_suc_bd)) idxs)); |
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624 fun mk_conjunct idx = HOLogic.mk_conj (mk_not_eq idx jdx, |
|
625 HOLogic.mk_mem (HOLogic.mk_prod (idx, jdx), suc_bd)); |
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626 val concl = HOLogic.mk_Trueprop (mk_Bex field_suc_bd |
|
627 (Term.absfree jdx' (Library.foldr1 HOLogic.mk_conj (map mk_conjunct idxs)))); |
|
628 in |
|
629 Goal.prove_sorry lthy [] [] |
|
630 (fold_rev Logic.all idxs (Logic.list_implies ([prem], concl))) |
|
631 (K (mk_bd_limit_tac n suc_bd_Cinfinite)) |
|
632 |> Thm.close_derivation |
|
633 end; |
|
634 |
|
635 val timer = time (timer "Bounds"); |
|
636 |
|
637 |
|
638 (* minimal algebra *) |
|
639 |
|
640 fun mk_minG Asi i k = mk_UNION (mk_underS suc_bd $ i) |
|
641 (Term.absfree jdx' (mk_nthN n (Asi $ jdx) k)); |
|
642 |
|
643 fun mk_minH_component As Asi i sets Ts s k = |
|
644 HOLogic.mk_binop @{const_name "sup"} |
|
645 (mk_minG Asi i k, mk_image s $ mk_in (As @ map (mk_minG Asi i) ks) sets Ts); |
|
646 |
|
647 fun mk_min_algs As ss = |
|
648 let |
|
649 val BTs = map (range_type o fastype_of) ss; |
|
650 val Ts = map (HOLogic.dest_setT o fastype_of) As @ BTs; |
|
651 val (Asi, Asi') = `Free (Asi_name, suc_bdT --> |
|
652 Library.foldr1 HOLogic.mk_prodT (map HOLogic.mk_setT BTs)); |
|
653 in |
|
654 mk_worec suc_bd (Term.absfree Asi' (Term.absfree idx' (HOLogic.mk_tuple |
|
655 (map4 (mk_minH_component As Asi idx) (mk_setss Ts) (mk_FTs Ts) ss ks)))) |
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656 end; |
|
657 |
|
658 val (min_algs_thms, min_algs_mono_thms, card_of_min_algs_thm, least_min_algs_thm) = |
|
659 let |
|
660 val i_field = HOLogic.mk_mem (idx, field_suc_bd); |
|
661 val min_algs = mk_min_algs As ss; |
|
662 val min_algss = map (fn k => mk_nthN n (min_algs $ idx) k) ks; |
|
663 |
|
664 val concl = HOLogic.mk_Trueprop |
|
665 (HOLogic.mk_eq (min_algs $ idx, HOLogic.mk_tuple |
|
666 (map4 (mk_minH_component As min_algs idx) setssAs FTsAs ss ks))); |
|
667 val goal = fold_rev Logic.all (idx :: As @ ss) |
|
668 (Logic.mk_implies (HOLogic.mk_Trueprop i_field, concl)); |
|
669 |
|
670 val min_algs_thm = Goal.prove_sorry lthy [] [] goal |
|
671 (K (mk_min_algs_tac suc_bd_worel in_cong'_thms)) |
|
672 |> Thm.close_derivation; |
|
673 |
|
674 val min_algs_thms = map (fn k => min_algs_thm RS mk_nthI n k) ks; |
|
675 |
|
676 fun mk_mono_goal min_alg = |
|
677 fold_rev Logic.all (As @ ss) (HOLogic.mk_Trueprop (mk_relChain suc_bd |
|
678 (Term.absfree idx' min_alg))); |
|
679 |
|
680 val monos = |
|
681 map2 (fn goal => fn min_algs => |
|
682 Goal.prove_sorry lthy [] [] goal (K (mk_min_algs_mono_tac lthy min_algs)) |
|
683 |> Thm.close_derivation) |
|
684 (map mk_mono_goal min_algss) min_algs_thms; |
|
685 |
|
686 val Asuc_bd = mk_Asuc_bd As; |
|
687 |
|
688 fun mk_card_conjunct min_alg = mk_ordLeq (mk_card_of min_alg) Asuc_bd; |
|
689 val card_conjunction = Library.foldr1 HOLogic.mk_conj (map mk_card_conjunct min_algss); |
|
690 val card_cT = certifyT lthy suc_bdT; |
|
691 val card_ct = certify lthy (Term.absfree idx' card_conjunction); |
|
692 |
|
693 val card_of = singleton (Proof_Context.export names_lthy lthy) |
|
694 (Goal.prove_sorry lthy [] [] |
|
695 (HOLogic.mk_Trueprop (HOLogic.mk_imp (i_field, card_conjunction))) |
|
696 (K (mk_min_algs_card_of_tac card_cT card_ct |
|
697 m suc_bd_worel min_algs_thms in_bd_sums |
|
698 sum_Card_order sum_Cnotzero suc_bd_Card_order suc_bd_Cinfinite suc_bd_Cnotzero |
|
699 suc_bd_Asuc_bd Asuc_bd_Cinfinite))) |
|
700 |> Thm.close_derivation; |
|
701 |
|
702 val least_prem = HOLogic.mk_Trueprop (mk_alg As Bs ss); |
|
703 val least_conjunction = Library.foldr1 HOLogic.mk_conj (map2 mk_leq min_algss Bs); |
|
704 val least_cT = certifyT lthy suc_bdT; |
|
705 val least_ct = certify lthy (Term.absfree idx' least_conjunction); |
|
706 |
|
707 val least = singleton (Proof_Context.export names_lthy lthy) |
|
708 (Goal.prove_sorry lthy [] [] |
|
709 (Logic.mk_implies (least_prem, |
|
710 HOLogic.mk_Trueprop (HOLogic.mk_imp (i_field, least_conjunction)))) |
|
711 (K (mk_min_algs_least_tac least_cT least_ct |
|
712 suc_bd_worel min_algs_thms alg_set_thms))) |
|
713 |> Thm.close_derivation; |
|
714 in |
|
715 (min_algs_thms, monos, card_of, least) |
|
716 end; |
|
717 |
|
718 val timer = time (timer "min_algs definition & thms"); |
|
719 |
|
720 val min_alg_binds = mk_internal_bs min_algN; |
|
721 fun min_alg_bind i = nth min_alg_binds (i - 1); |
|
722 fun min_alg_name i = Binding.name_of (min_alg_bind i); |
|
723 val min_alg_def_bind = rpair [] o Thm.def_binding o min_alg_bind; |
|
724 |
|
725 fun min_alg_spec i = |
|
726 let |
|
727 val min_algT = |
|
728 Library.foldr (op -->) (ATs @ sTs, HOLogic.mk_setT (nth activeAs (i - 1))); |
|
729 |
|
730 val lhs = Term.list_comb (Free (min_alg_name i, min_algT), As @ ss); |
|
731 val rhs = mk_UNION (field_suc_bd) |
|
732 (Term.absfree idx' (mk_nthN n (mk_min_algs As ss $ idx) i)); |
|
733 in |
|
734 mk_Trueprop_eq (lhs, rhs) |
|
735 end; |
|
736 |
|
737 val ((min_alg_frees, (_, min_alg_def_frees)), (lthy, lthy_old)) = |
|
738 lthy |
|
739 |> fold_map (fn i => Specification.definition |
|
740 (SOME (min_alg_bind i, NONE, NoSyn), (min_alg_def_bind i, min_alg_spec i))) ks |
|
741 |>> apsnd split_list o split_list |
|
742 ||> `Local_Theory.restore; |
|
743 |
|
744 val phi = Proof_Context.export_morphism lthy_old lthy; |
|
745 val min_algs = map (fst o Term.dest_Const o Morphism.term phi) min_alg_frees; |
|
746 val min_alg_defs = map (Morphism.thm phi) min_alg_def_frees; |
|
747 |
|
748 fun mk_min_alg As ss i = |
|
749 let |
|
750 val T = HOLogic.mk_setT (range_type (fastype_of (nth ss (i - 1)))) |
|
751 val args = As @ ss; |
|
752 val Ts = map fastype_of args; |
|
753 val min_algT = Library.foldr (op -->) (Ts, T); |
|
754 in |
|
755 Term.list_comb (Const (nth min_algs (i - 1), min_algT), args) |
|
756 end; |
|
757 |
|
758 val (alg_min_alg_thm, card_of_min_alg_thms, least_min_alg_thms, mor_incl_min_alg_thm) = |
|
759 let |
|
760 val min_algs = map (mk_min_alg As ss) ks; |
|
761 |
|
762 val goal = fold_rev Logic.all (As @ ss) (HOLogic.mk_Trueprop (mk_alg As min_algs ss)); |
|
763 val alg_min_alg = Goal.prove_sorry lthy [] [] goal |
|
764 (K (mk_alg_min_alg_tac m alg_def min_alg_defs suc_bd_limit_thm sum_Cinfinite |
|
765 set_bd_sumss min_algs_thms min_algs_mono_thms)) |
|
766 |> Thm.close_derivation; |
|
767 |
|
768 val Asuc_bd = mk_Asuc_bd As; |
|
769 fun mk_card_of_thm min_alg def = Goal.prove_sorry lthy [] [] |
|
770 (fold_rev Logic.all (As @ ss) |
|
771 (HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of min_alg) Asuc_bd))) |
|
772 (K (mk_card_of_min_alg_tac def card_of_min_algs_thm |
|
773 suc_bd_Card_order suc_bd_Asuc_bd Asuc_bd_Cinfinite)) |
|
774 |> Thm.close_derivation; |
|
775 |
|
776 val least_prem = HOLogic.mk_Trueprop (mk_alg As Bs ss); |
|
777 fun mk_least_thm min_alg B def = Goal.prove_sorry lthy [] [] |
|
778 (fold_rev Logic.all (As @ Bs @ ss) |
|
779 (Logic.mk_implies (least_prem, HOLogic.mk_Trueprop (mk_leq min_alg B)))) |
|
780 (K (mk_least_min_alg_tac def least_min_algs_thm)) |
|
781 |> Thm.close_derivation; |
|
782 |
|
783 val leasts = map3 mk_least_thm min_algs Bs min_alg_defs; |
|
784 |
|
785 val incl_prem = HOLogic.mk_Trueprop (mk_alg passive_UNIVs Bs ss); |
|
786 val incl_min_algs = map (mk_min_alg passive_UNIVs ss) ks; |
|
787 val incl = Goal.prove_sorry lthy [] [] |
|
788 (fold_rev Logic.all (Bs @ ss) |
|
789 (Logic.mk_implies (incl_prem, |
|
790 HOLogic.mk_Trueprop (mk_mor incl_min_algs ss Bs ss active_ids)))) |
|
791 (K (EVERY' (rtac mor_incl_thm :: map etac leasts) 1)) |
|
792 |> Thm.close_derivation; |
|
793 in |
|
794 (alg_min_alg, map2 mk_card_of_thm min_algs min_alg_defs, leasts, incl) |
|
795 end; |
|
796 |
|
797 val timer = time (timer "Minimal algebra definition & thms"); |
|
798 |
|
799 val II_repT = HOLogic.mk_prodT (HOLogic.mk_tupleT II_BTs, HOLogic.mk_tupleT II_sTs); |
|
800 val IIT_bind = mk_internal_b IITN; |
|
801 |
|
802 val ((IIT_name, (IIT_glob_info, IIT_loc_info)), lthy) = |
|
803 typedef (IIT_bind, params, NoSyn) |
|
804 (HOLogic.mk_UNIV II_repT) NONE (EVERY' [rtac exI, rtac UNIV_I] 1) lthy; |
|
805 |
|
806 val IIT = Type (IIT_name, params'); |
|
807 val Abs_IIT = Const (#Abs_name IIT_glob_info, II_repT --> IIT); |
|
808 val Rep_IIT = Const (#Rep_name IIT_glob_info, IIT --> II_repT); |
|
809 val Abs_IIT_inverse_thm = UNIV_I RS #Abs_inverse IIT_loc_info; |
|
810 |
|
811 val initT = IIT --> Asuc_bdT; |
|
812 val active_initTs = replicate n initT; |
|
813 val init_FTs = map2 (fn Ds => mk_T_of_bnf Ds (passiveAs @ active_initTs)) Dss bnfs; |
|
814 val init_fTs = map (fn T => initT --> T) activeAs; |
|
815 |
|
816 val (((((((iidx, iidx'), init_xs), (init_xFs, init_xFs')), |
|
817 init_fs), init_fs_copy), init_phis), names_lthy) = names_lthy |
|
818 |> yield_singleton (apfst (op ~~) oo mk_Frees' "i") IIT |
|
819 ||>> mk_Frees "ix" active_initTs |
|
820 ||>> mk_Frees' "x" init_FTs |
|
821 ||>> mk_Frees "f" init_fTs |
|
822 ||>> mk_Frees "f" init_fTs |
|
823 ||>> mk_Frees "P" (replicate n (mk_pred1T initT)); |
|
824 |
|
825 val II = HOLogic.mk_Collect (fst iidx', IIT, list_exists_free (II_Bs @ II_ss) |
|
826 (HOLogic.mk_conj (HOLogic.mk_eq (iidx, |
|
827 Abs_IIT $ (HOLogic.mk_prod (HOLogic.mk_tuple II_Bs, HOLogic.mk_tuple II_ss))), |
|
828 mk_alg passive_UNIVs II_Bs II_ss))); |
|
829 |
|
830 val select_Bs = map (mk_nthN n (HOLogic.mk_fst (Rep_IIT $ iidx))) ks; |
|
831 val select_ss = map (mk_nthN n (HOLogic.mk_snd (Rep_IIT $ iidx))) ks; |
|
832 |
|
833 val str_init_binds = mk_internal_bs str_initN; |
|
834 fun str_init_bind i = nth str_init_binds (i - 1); |
|
835 val str_init_name = Binding.name_of o str_init_bind; |
|
836 val str_init_def_bind = rpair [] o Thm.def_binding o str_init_bind; |
|
837 |
|
838 fun str_init_spec i = |
|
839 let |
|
840 val T = nth init_FTs (i - 1); |
|
841 val init_xF = nth init_xFs (i - 1) |
|
842 val select_s = nth select_ss (i - 1); |
|
843 val map = mk_map_of_bnf (nth Dss (i - 1)) |
|
844 (passiveAs @ active_initTs) (passiveAs @ replicate n Asuc_bdT) |
|
845 (nth bnfs (i - 1)); |
|
846 val map_args = passive_ids @ replicate n (mk_rapp iidx Asuc_bdT); |
|
847 val str_initT = T --> IIT --> Asuc_bdT; |
|
848 |
|
849 val lhs = Term.list_comb (Free (str_init_name i, str_initT), [init_xF, iidx]); |
|
850 val rhs = select_s $ (Term.list_comb (map, map_args) $ init_xF); |
|
851 in |
|
852 mk_Trueprop_eq (lhs, rhs) |
|
853 end; |
|
854 |
|
855 val ((str_init_frees, (_, str_init_def_frees)), (lthy, lthy_old)) = |
|
856 lthy |
|
857 |> fold_map (fn i => Specification.definition |
|
858 (SOME (str_init_bind i, NONE, NoSyn), (str_init_def_bind i, str_init_spec i))) ks |
|
859 |>> apsnd split_list o split_list |
|
860 ||> `Local_Theory.restore; |
|
861 |
|
862 val phi = Proof_Context.export_morphism lthy_old lthy; |
|
863 val str_inits = |
|
864 map (Term.subst_atomic_types (map (`(Morphism.typ phi)) params') o Morphism.term phi) |
|
865 str_init_frees; |
|
866 |
|
867 val str_init_defs = map (Morphism.thm phi) str_init_def_frees; |
|
868 |
|
869 val car_inits = map (mk_min_alg passive_UNIVs str_inits) ks; |
|
870 |
|
871 (*TODO: replace with instantiate? (problem: figure out right type instantiation)*) |
|
872 val alg_init_thm = Goal.prove_sorry lthy [] [] |
|
873 (HOLogic.mk_Trueprop (mk_alg passive_UNIVs car_inits str_inits)) |
|
874 (K (rtac alg_min_alg_thm 1)) |
|
875 |> Thm.close_derivation; |
|
876 |
|
877 val alg_select_thm = Goal.prove_sorry lthy [] [] |
|
878 (HOLogic.mk_Trueprop (mk_Ball II |
|
879 (Term.absfree iidx' (mk_alg passive_UNIVs select_Bs select_ss)))) |
|
880 (mk_alg_select_tac Abs_IIT_inverse_thm) |
|
881 |> Thm.close_derivation; |
|
882 |
|
883 val mor_select_thm = |
|
884 let |
|
885 val alg_prem = HOLogic.mk_Trueprop (mk_alg passive_UNIVs Bs ss); |
|
886 val i_prem = HOLogic.mk_Trueprop (HOLogic.mk_mem (iidx, II)); |
|
887 val mor_prem = HOLogic.mk_Trueprop (mk_mor select_Bs select_ss Bs ss Asuc_fs); |
|
888 val prems = [alg_prem, i_prem, mor_prem]; |
|
889 val concl = HOLogic.mk_Trueprop |
|
890 (mk_mor car_inits str_inits Bs ss |
|
891 (map (fn f => HOLogic.mk_comp (f, mk_rapp iidx Asuc_bdT)) Asuc_fs)); |
|
892 in |
|
893 Goal.prove_sorry lthy [] [] |
|
894 (fold_rev Logic.all (iidx :: Bs @ ss @ Asuc_fs) (Logic.list_implies (prems, concl))) |
|
895 (K (mk_mor_select_tac mor_def mor_cong_thm mor_comp_thm mor_incl_min_alg_thm alg_def |
|
896 alg_select_thm alg_set_thms set_mapss str_init_defs)) |
|
897 |> Thm.close_derivation |
|
898 end; |
|
899 |
|
900 val (init_ex_mor_thm, init_unique_mor_thms) = |
|
901 let |
|
902 val prem = HOLogic.mk_Trueprop (mk_alg passive_UNIVs Bs ss); |
|
903 val concl = HOLogic.mk_Trueprop |
|
904 (list_exists_free init_fs (mk_mor car_inits str_inits Bs ss init_fs)); |
|
905 val ex_mor = Goal.prove_sorry lthy [] [] |
|
906 (fold_rev Logic.all (Bs @ ss) (Logic.mk_implies (prem, concl))) |
|
907 (mk_init_ex_mor_tac Abs_IIT_inverse_thm ex_copy_alg_thm alg_min_alg_thm |
|
908 card_of_min_alg_thms mor_comp_thm mor_select_thm mor_incl_min_alg_thm) |
|
909 |> Thm.close_derivation; |
|
910 |
|
911 val prems = map2 (HOLogic.mk_Trueprop oo curry HOLogic.mk_mem) init_xs car_inits |
|
912 val mor_prems = map HOLogic.mk_Trueprop |
|
913 [mk_mor car_inits str_inits Bs ss init_fs, |
|
914 mk_mor car_inits str_inits Bs ss init_fs_copy]; |
|
915 fun mk_fun_eq f g x = HOLogic.mk_eq (f $ x, g $ x); |
|
916 val unique = HOLogic.mk_Trueprop |
|
917 (Library.foldr1 HOLogic.mk_conj (map3 mk_fun_eq init_fs init_fs_copy init_xs)); |
|
918 val unique_mor = Goal.prove_sorry lthy [] [] |
|
919 (fold_rev Logic.all (init_xs @ Bs @ ss @ init_fs @ init_fs_copy) |
|
920 (Logic.list_implies (prems @ mor_prems, unique))) |
|
921 (K (mk_init_unique_mor_tac m alg_def alg_init_thm least_min_alg_thms |
|
922 in_mono'_thms alg_set_thms morE_thms map_cong0s)) |
|
923 |> Thm.close_derivation; |
|
924 in |
|
925 (ex_mor, split_conj_thm unique_mor) |
|
926 end; |
|
927 |
|
928 val init_setss = mk_setss (passiveAs @ active_initTs); |
|
929 val active_init_setss = map (drop m) init_setss; |
|
930 val init_ins = map2 (fn sets => mk_in (passive_UNIVs @ car_inits) sets) init_setss init_FTs; |
|
931 |
|
932 fun mk_closed phis = |
|
933 let |
|
934 fun mk_conjunct phi str_init init_sets init_in x x' = |
|
935 let |
|
936 val prem = Library.foldr1 HOLogic.mk_conj |
|
937 (map2 (fn set => mk_Ball (set $ x)) init_sets phis); |
|
938 val concl = phi $ (str_init $ x); |
|
939 in |
|
940 mk_Ball init_in (Term.absfree x' (HOLogic.mk_imp (prem, concl))) |
|
941 end; |
|
942 in |
|
943 Library.foldr1 HOLogic.mk_conj |
|
944 (map6 mk_conjunct phis str_inits active_init_setss init_ins init_xFs init_xFs') |
|
945 end; |
|
946 |
|
947 val init_induct_thm = |
|
948 let |
|
949 val prem = HOLogic.mk_Trueprop (mk_closed init_phis); |
|
950 val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj |
|
951 (map2 mk_Ball car_inits init_phis)); |
|
952 in |
|
953 Goal.prove_sorry lthy [] [] |
|
954 (fold_rev Logic.all init_phis (Logic.mk_implies (prem, concl))) |
|
955 (K (mk_init_induct_tac m alg_def alg_init_thm least_min_alg_thms alg_set_thms)) |
|
956 |> Thm.close_derivation |
|
957 end; |
|
958 |
|
959 val timer = time (timer "Initiality definition & thms"); |
|
960 |
|
961 val ((T_names, (T_glob_infos, T_loc_infos)), lthy) = |
|
962 lthy |
|
963 |> fold_map3 (fn b => fn mx => fn car_init => |
|
964 typedef (Binding.conceal b, params, mx) car_init NONE |
|
965 (EVERY' [rtac ssubst, rtac @{thm ex_in_conv}, resolve_tac alg_not_empty_thms, |
|
966 rtac alg_init_thm] 1)) bs mixfixes car_inits |
|
967 |>> apsnd split_list o split_list; |
|
968 |
|
969 val Ts = map (fn name => Type (name, params')) T_names; |
|
970 fun mk_Ts passive = map (Term.typ_subst_atomic (passiveAs ~~ passive)) Ts; |
|
971 val Ts' = mk_Ts passiveBs; |
|
972 val Rep_Ts = map2 (fn info => fn T => Const (#Rep_name info, T --> initT)) T_glob_infos Ts; |
|
973 val Abs_Ts = map2 (fn info => fn T => Const (#Abs_name info, initT --> T)) T_glob_infos Ts; |
|
974 |
|
975 val type_defs = map #type_definition T_loc_infos; |
|
976 val Reps = map #Rep T_loc_infos; |
|
977 val Rep_casess = map #Rep_cases T_loc_infos; |
|
978 val Rep_injects = map #Rep_inject T_loc_infos; |
|
979 val Rep_inverses = map #Rep_inverse T_loc_infos; |
|
980 val Abs_inverses = map #Abs_inverse T_loc_infos; |
|
981 |
|
982 fun mk_inver_thm mk_tac rep abs X thm = |
|
983 Goal.prove_sorry lthy [] [] |
|
984 (HOLogic.mk_Trueprop (mk_inver rep abs X)) |
|
985 (K (EVERY' [rtac ssubst, rtac @{thm inver_def}, rtac ballI, mk_tac thm] 1)) |
|
986 |> Thm.close_derivation; |
|
987 |
|
988 val inver_Reps = map4 (mk_inver_thm rtac) Abs_Ts Rep_Ts (map HOLogic.mk_UNIV Ts) Rep_inverses; |
|
989 val inver_Abss = map4 (mk_inver_thm etac) Rep_Ts Abs_Ts car_inits Abs_inverses; |
|
990 |
|
991 val timer = time (timer "THE TYPEDEFs & Rep/Abs thms"); |
|
992 |
|
993 val UNIVs = map HOLogic.mk_UNIV Ts; |
|
994 val FTs = mk_FTs (passiveAs @ Ts); |
|
995 val FTs' = mk_FTs (passiveBs @ Ts'); |
|
996 fun mk_set_Ts T = passiveAs @ replicate n (HOLogic.mk_setT T); |
|
997 val setFTss = map (mk_FTs o mk_set_Ts) passiveAs; |
|
998 val FTs_setss = mk_setss (passiveAs @ Ts); |
|
999 val FTs'_setss = mk_setss (passiveBs @ Ts'); |
|
1000 val map_FT_inits = map2 (fn Ds => |
|
1001 mk_map_of_bnf Ds (passiveAs @ Ts) (passiveAs @ active_initTs)) Dss bnfs; |
|
1002 val fTs = map2 (curry op -->) Ts activeAs; |
|
1003 val foldT = Library.foldr1 HOLogic.mk_prodT (map2 (curry op -->) Ts activeAs); |
|
1004 val rec_sTs = map (Term.typ_subst_atomic (activeBs ~~ Ts)) prod_sTs; |
|
1005 val rec_maps = map (Term.subst_atomic_types (activeBs ~~ Ts)) map_fsts; |
|
1006 val rec_maps_rev = map (Term.subst_atomic_types (activeBs ~~ Ts)) map_fsts_rev; |
|
1007 val rec_fsts = map (Term.subst_atomic_types (activeBs ~~ Ts)) fsts; |
|
1008 val rec_UNIVs = map2 (HOLogic.mk_UNIV oo curry HOLogic.mk_prodT) Ts activeAs; |
|
1009 |
|
1010 val (((((((((Izs1, Izs1'), (Izs2, Izs2')), (xFs, xFs')), yFs), (AFss, AFss')), |
|
1011 (fold_f, fold_f')), fs), rec_ss), names_lthy) = names_lthy |
|
1012 |> mk_Frees' "z1" Ts |
|
1013 ||>> mk_Frees' "z2" Ts' |
|
1014 ||>> mk_Frees' "x" FTs |
|
1015 ||>> mk_Frees "y" FTs' |
|
1016 ||>> mk_Freess' "z" setFTss |
|
1017 ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "f") foldT |
|
1018 ||>> mk_Frees "f" fTs |
|
1019 ||>> mk_Frees "s" rec_sTs; |
|
1020 |
|
1021 val Izs = map2 retype_free Ts zs; |
|
1022 val phis = map2 retype_free (map mk_pred1T Ts) init_phis; |
|
1023 val phi2s = map2 retype_free (map2 mk_pred2T Ts Ts') init_phis; |
|
1024 |
|
1025 fun ctor_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctorN ^ "_"); |
|
1026 val ctor_name = Binding.name_of o ctor_bind; |
|
1027 val ctor_def_bind = rpair [] o Binding.conceal o Thm.def_binding o ctor_bind; |
|
1028 |
|
1029 fun ctor_spec i abs str map_FT_init x x' = |
|
1030 let |
|
1031 val ctorT = nth FTs (i - 1) --> nth Ts (i - 1); |
|
1032 |
|
1033 val lhs = Free (ctor_name i, ctorT); |
|
1034 val rhs = Term.absfree x' (abs $ (str $ |
|
1035 (Term.list_comb (map_FT_init, map HOLogic.id_const passiveAs @ Rep_Ts) $ x))); |
|
1036 in |
|
1037 mk_Trueprop_eq (lhs, rhs) |
|
1038 end; |
|
1039 |
|
1040 val ((ctor_frees, (_, ctor_def_frees)), (lthy, lthy_old)) = |
|
1041 lthy |
|
1042 |> fold_map6 (fn i => fn abs => fn str => fn mapx => fn x => fn x' => |
|
1043 Specification.definition |
|
1044 (SOME (ctor_bind i, NONE, NoSyn), (ctor_def_bind i, ctor_spec i abs str mapx x x'))) |
|
1045 ks Abs_Ts str_inits map_FT_inits xFs xFs' |
|
1046 |>> apsnd split_list o split_list |
|
1047 ||> `Local_Theory.restore; |
|
1048 |
|
1049 val phi = Proof_Context.export_morphism lthy_old lthy; |
|
1050 fun mk_ctors passive = |
|
1051 map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ (mk_params passive)) o |
|
1052 Morphism.term phi) ctor_frees; |
|
1053 val ctors = mk_ctors passiveAs; |
|
1054 val ctor's = mk_ctors passiveBs; |
|
1055 val ctor_defs = map (Morphism.thm phi) ctor_def_frees; |
|
1056 |
|
1057 val (mor_Rep_thm, mor_Abs_thm) = |
|
1058 let |
|
1059 val copy = alg_init_thm RS copy_alg_thm; |
|
1060 fun mk_bij inj Rep cases = @{thm bij_betwI'} OF [inj, Rep, cases]; |
|
1061 val bijs = map3 mk_bij Rep_injects Reps Rep_casess; |
|
1062 val mor_Rep = |
|
1063 Goal.prove_sorry lthy [] [] |
|
1064 (HOLogic.mk_Trueprop (mk_mor UNIVs ctors car_inits str_inits Rep_Ts)) |
|
1065 (mk_mor_Rep_tac ctor_defs copy bijs inver_Abss inver_Reps) |
|
1066 |> Thm.close_derivation; |
|
1067 |
|
1068 val inv = mor_inv_thm OF [mor_Rep, talg_thm, alg_init_thm]; |
|
1069 val mor_Abs = |
|
1070 Goal.prove_sorry lthy [] [] |
|
1071 (HOLogic.mk_Trueprop (mk_mor car_inits str_inits UNIVs ctors Abs_Ts)) |
|
1072 (K (mk_mor_Abs_tac inv inver_Abss inver_Reps)) |
|
1073 |> Thm.close_derivation; |
|
1074 in |
|
1075 (mor_Rep, mor_Abs) |
|
1076 end; |
|
1077 |
|
1078 val timer = time (timer "ctor definitions & thms"); |
|
1079 |
|
1080 val fold_fun = Term.absfree fold_f' |
|
1081 (mk_mor UNIVs ctors active_UNIVs ss (map (mk_nthN n fold_f) ks)); |
|
1082 val foldx = HOLogic.choice_const foldT $ fold_fun; |
|
1083 |
|
1084 fun fold_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctor_foldN ^ "_"); |
|
1085 val fold_name = Binding.name_of o fold_bind; |
|
1086 val fold_def_bind = rpair [] o Binding.conceal o Thm.def_binding o fold_bind; |
|
1087 |
|
1088 fun fold_spec i T AT = |
|
1089 let |
|
1090 val foldT = Library.foldr (op -->) (sTs, T --> AT); |
|
1091 |
|
1092 val lhs = Term.list_comb (Free (fold_name i, foldT), ss); |
|
1093 val rhs = mk_nthN n foldx i; |
|
1094 in |
|
1095 mk_Trueprop_eq (lhs, rhs) |
|
1096 end; |
|
1097 |
|
1098 val ((fold_frees, (_, fold_def_frees)), (lthy, lthy_old)) = |
|
1099 lthy |
|
1100 |> fold_map3 (fn i => fn T => fn AT => |
|
1101 Specification.definition |
|
1102 (SOME (fold_bind i, NONE, NoSyn), (fold_def_bind i, fold_spec i T AT))) |
|
1103 ks Ts activeAs |
|
1104 |>> apsnd split_list o split_list |
|
1105 ||> `Local_Theory.restore; |
|
1106 |
|
1107 val phi = Proof_Context.export_morphism lthy_old lthy; |
|
1108 val folds = map (Morphism.term phi) fold_frees; |
|
1109 val fold_names = map (fst o dest_Const) folds; |
|
1110 fun mk_folds passives actives = |
|
1111 map3 (fn name => fn T => fn active => |
|
1112 Const (name, Library.foldr (op -->) |
|
1113 (map2 (curry op -->) (mk_FTs (passives @ actives)) actives, T --> active))) |
|
1114 fold_names (mk_Ts passives) actives; |
|
1115 fun mk_fold Ts ss i = Term.list_comb (Const (nth fold_names (i - 1), Library.foldr (op -->) |
|
1116 (map fastype_of ss, nth Ts (i - 1) --> range_type (fastype_of (nth ss (i - 1))))), ss); |
|
1117 val fold_defs = map (Morphism.thm phi) fold_def_frees; |
|
1118 |
|
1119 val mor_fold_thm = |
|
1120 let |
|
1121 val ex_mor = talg_thm RS init_ex_mor_thm; |
|
1122 val mor_cong = mor_cong_thm OF (map (mk_nth_conv n) ks); |
|
1123 val mor_comp = mor_Rep_thm RS mor_comp_thm; |
|
1124 val cT = certifyT lthy foldT; |
|
1125 val ct = certify lthy fold_fun |
|
1126 in |
|
1127 singleton (Proof_Context.export names_lthy lthy) |
|
1128 (Goal.prove_sorry lthy [] [] |
|
1129 (HOLogic.mk_Trueprop (mk_mor UNIVs ctors active_UNIVs ss (map (mk_fold Ts ss) ks))) |
|
1130 (K (mk_mor_fold_tac cT ct fold_defs ex_mor (mor_comp RS mor_cong)))) |
|
1131 |> Thm.close_derivation |
|
1132 end; |
|
1133 |
|
1134 val ctor_fold_thms = map (fn morE => rule_by_tactic lthy |
|
1135 ((rtac CollectI THEN' CONJ_WRAP' (K (rtac @{thm subset_UNIV})) (1 upto m + n)) 1) |
|
1136 (mor_fold_thm RS morE)) morE_thms; |
|
1137 |
|
1138 val (fold_unique_mor_thms, fold_unique_mor_thm) = |
|
1139 let |
|
1140 val prem = HOLogic.mk_Trueprop (mk_mor UNIVs ctors active_UNIVs ss fs); |
|
1141 fun mk_fun_eq f i = HOLogic.mk_eq (f, mk_fold Ts ss i); |
|
1142 val unique = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_fun_eq fs ks)); |
|
1143 val unique_mor = Goal.prove_sorry lthy [] [] |
|
1144 (fold_rev Logic.all (ss @ fs) (Logic.mk_implies (prem, unique))) |
|
1145 (K (mk_fold_unique_mor_tac type_defs init_unique_mor_thms Reps |
|
1146 mor_comp_thm mor_Abs_thm mor_fold_thm)) |
|
1147 |> Thm.close_derivation; |
|
1148 in |
|
1149 `split_conj_thm unique_mor |
|
1150 end; |
|
1151 |
|
1152 val (ctor_fold_unique_thms, ctor_fold_unique_thm) = |
|
1153 `split_conj_thm (mk_conjIN n RS |
|
1154 (mor_UNIV_thm RS iffD2 RS fold_unique_mor_thm)) |
|
1155 |
|
1156 val fold_ctor_thms = |
|
1157 map (fn thm => (mor_incl_thm OF replicate n @{thm subset_UNIV}) RS thm RS sym) |
|
1158 fold_unique_mor_thms; |
|
1159 |
|
1160 val ctor_o_fold_thms = |
|
1161 let |
|
1162 val mor = mor_comp_thm OF [mor_fold_thm, mor_str_thm]; |
|
1163 in |
|
1164 map2 (fn unique => fn fold_ctor => |
|
1165 trans OF [mor RS unique, fold_ctor]) fold_unique_mor_thms fold_ctor_thms |
|
1166 end; |
|
1167 |
|
1168 val timer = time (timer "fold definitions & thms"); |
|
1169 |
|
1170 val map_ctors = map2 (fn Ds => fn bnf => |
|
1171 Term.list_comb (mk_map_of_bnf Ds (passiveAs @ FTs) (passiveAs @ Ts) bnf, |
|
1172 map HOLogic.id_const passiveAs @ ctors)) Dss bnfs; |
|
1173 |
|
1174 fun dtor_bind i = nth external_bs (i - 1) |> Binding.prefix_name (dtorN ^ "_"); |
|
1175 val dtor_name = Binding.name_of o dtor_bind; |
|
1176 val dtor_def_bind = rpair [] o Binding.conceal o Thm.def_binding o dtor_bind; |
|
1177 |
|
1178 fun dtor_spec i FT T = |
|
1179 let |
|
1180 val dtorT = T --> FT; |
|
1181 |
|
1182 val lhs = Free (dtor_name i, dtorT); |
|
1183 val rhs = mk_fold Ts map_ctors i; |
|
1184 in |
|
1185 mk_Trueprop_eq (lhs, rhs) |
|
1186 end; |
|
1187 |
|
1188 val ((dtor_frees, (_, dtor_def_frees)), (lthy, lthy_old)) = |
|
1189 lthy |
|
1190 |> fold_map3 (fn i => fn FT => fn T => |
|
1191 Specification.definition |
|
1192 (SOME (dtor_bind i, NONE, NoSyn), (dtor_def_bind i, dtor_spec i FT T))) ks FTs Ts |
|
1193 |>> apsnd split_list o split_list |
|
1194 ||> `Local_Theory.restore; |
|
1195 |
|
1196 val phi = Proof_Context.export_morphism lthy_old lthy; |
|
1197 fun mk_dtors params = |
|
1198 map (Term.subst_atomic_types (map (Morphism.typ phi) params' ~~ params) o Morphism.term phi) |
|
1199 dtor_frees; |
|
1200 val dtors = mk_dtors params'; |
|
1201 val dtor_defs = map (Morphism.thm phi) dtor_def_frees; |
|
1202 |
|
1203 val ctor_o_dtor_thms = map2 (fold_thms lthy o single) dtor_defs ctor_o_fold_thms; |
|
1204 |
|
1205 val dtor_o_ctor_thms = |
|
1206 let |
|
1207 fun mk_goal dtor ctor FT = |
|
1208 mk_Trueprop_eq (HOLogic.mk_comp (dtor, ctor), HOLogic.id_const FT); |
|
1209 val goals = map3 mk_goal dtors ctors FTs; |
|
1210 in |
|
1211 map5 (fn goal => fn dtor_def => fn foldx => fn map_comp_id => fn map_cong0L => |
|
1212 Goal.prove_sorry lthy [] [] goal |
|
1213 (K (mk_dtor_o_ctor_tac dtor_def foldx map_comp_id map_cong0L ctor_o_fold_thms)) |
|
1214 |> Thm.close_derivation) |
|
1215 goals dtor_defs ctor_fold_thms map_comp_id_thms map_cong0L_thms |
|
1216 end; |
|
1217 |
|
1218 val dtor_ctor_thms = map (fn thm => thm RS @{thm pointfree_idE}) dtor_o_ctor_thms; |
|
1219 val ctor_dtor_thms = map (fn thm => thm RS @{thm pointfree_idE}) ctor_o_dtor_thms; |
|
1220 |
|
1221 val bij_dtor_thms = |
|
1222 map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) ctor_o_dtor_thms dtor_o_ctor_thms; |
|
1223 val inj_dtor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_dtor_thms; |
|
1224 val surj_dtor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_dtor_thms; |
|
1225 val dtor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_dtor_thms; |
|
1226 val dtor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_dtor_thms; |
|
1227 val dtor_exhaust_thms = map (fn thm => thm RS exE) dtor_nchotomy_thms; |
|
1228 |
|
1229 val bij_ctor_thms = |
|
1230 map2 (fn thm1 => fn thm2 => @{thm o_bij} OF [thm1, thm2]) dtor_o_ctor_thms ctor_o_dtor_thms; |
|
1231 val inj_ctor_thms = map (fn thm => thm RS @{thm bij_is_inj}) bij_ctor_thms; |
|
1232 val surj_ctor_thms = map (fn thm => thm RS @{thm bij_is_surj}) bij_ctor_thms; |
|
1233 val ctor_nchotomy_thms = map (fn thm => thm RS @{thm surjD}) surj_ctor_thms; |
|
1234 val ctor_inject_thms = map (fn thm => thm RS @{thm inj_eq}) inj_ctor_thms; |
|
1235 val ctor_exhaust_thms = map (fn thm => thm RS exE) ctor_nchotomy_thms; |
|
1236 |
|
1237 val timer = time (timer "dtor definitions & thms"); |
|
1238 |
|
1239 val fst_rec_pair_thms = |
|
1240 let |
|
1241 val mor = mor_comp_thm OF [mor_fold_thm, mor_convol_thm]; |
|
1242 in |
|
1243 map2 (fn unique => fn fold_ctor => |
|
1244 trans OF [mor RS unique, fold_ctor]) fold_unique_mor_thms fold_ctor_thms |
|
1245 end; |
|
1246 |
|
1247 fun rec_bind i = nth external_bs (i - 1) |> Binding.prefix_name (ctor_recN ^ "_"); |
|
1248 val rec_name = Binding.name_of o rec_bind; |
|
1249 val rec_def_bind = rpair [] o Binding.conceal o Thm.def_binding o rec_bind; |
|
1250 |
|
1251 val rec_strs = |
|
1252 map3 (fn ctor => fn prod_s => fn mapx => |
|
1253 mk_convol (HOLogic.mk_comp (ctor, Term.list_comb (mapx, passive_ids @ rec_fsts)), prod_s)) |
|
1254 ctors rec_ss rec_maps; |
|
1255 |
|
1256 fun rec_spec i T AT = |
|
1257 let |
|
1258 val recT = Library.foldr (op -->) (rec_sTs, T --> AT); |
|
1259 |
|
1260 val lhs = Term.list_comb (Free (rec_name i, recT), rec_ss); |
|
1261 val rhs = HOLogic.mk_comp (snd_const (HOLogic.mk_prodT (T, AT)), mk_fold Ts rec_strs i); |
|
1262 in |
|
1263 mk_Trueprop_eq (lhs, rhs) |
|
1264 end; |
|
1265 |
|
1266 val ((rec_frees, (_, rec_def_frees)), (lthy, lthy_old)) = |
|
1267 lthy |
|
1268 |> fold_map3 (fn i => fn T => fn AT => |
|
1269 Specification.definition |
|
1270 (SOME (rec_bind i, NONE, NoSyn), (rec_def_bind i, rec_spec i T AT))) |
|
1271 ks Ts activeAs |
|
1272 |>> apsnd split_list o split_list |
|
1273 ||> `Local_Theory.restore; |
|
1274 |
|
1275 val phi = Proof_Context.export_morphism lthy_old lthy; |
|
1276 val recs = map (Morphism.term phi) rec_frees; |
|
1277 val rec_names = map (fst o dest_Const) recs; |
|
1278 fun mk_rec ss i = Term.list_comb (Const (nth rec_names (i - 1), Library.foldr (op -->) |
|
1279 (map fastype_of ss, nth Ts (i - 1) --> range_type (fastype_of (nth ss (i - 1))))), ss); |
|
1280 val rec_defs = map (Morphism.thm phi) rec_def_frees; |
|
1281 |
|
1282 val convols = map2 (fn T => fn i => mk_convol (HOLogic.id_const T, mk_rec rec_ss i)) Ts ks; |
|
1283 val ctor_rec_thms = |
|
1284 let |
|
1285 fun mk_goal i rec_s rec_map ctor x = |
|
1286 let |
|
1287 val lhs = mk_rec rec_ss i $ (ctor $ x); |
|
1288 val rhs = rec_s $ (Term.list_comb (rec_map, passive_ids @ convols) $ x); |
|
1289 in |
|
1290 fold_rev Logic.all (x :: rec_ss) (mk_Trueprop_eq (lhs, rhs)) |
|
1291 end; |
|
1292 val goals = map5 mk_goal ks rec_ss rec_maps_rev ctors xFs; |
|
1293 in |
|
1294 map2 (fn goal => fn foldx => |
|
1295 Goal.prove_sorry lthy [] [] goal (mk_rec_tac rec_defs foldx fst_rec_pair_thms) |
|
1296 |> Thm.close_derivation) |
|
1297 goals ctor_fold_thms |
|
1298 end; |
|
1299 |
|
1300 val rec_unique_mor_thm = |
|
1301 let |
|
1302 val id_fs = map2 (fn T => fn f => mk_convol (HOLogic.id_const T, f)) Ts fs; |
|
1303 val prem = HOLogic.mk_Trueprop (mk_mor UNIVs ctors rec_UNIVs rec_strs id_fs); |
|
1304 fun mk_fun_eq f i = HOLogic.mk_eq (f, mk_rec rec_ss i); |
|
1305 val unique = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_fun_eq fs ks)); |
|
1306 in |
|
1307 Goal.prove_sorry lthy [] [] |
|
1308 (fold_rev Logic.all (rec_ss @ fs) (Logic.mk_implies (prem, unique))) |
|
1309 (mk_rec_unique_mor_tac rec_defs fst_rec_pair_thms fold_unique_mor_thm) |
|
1310 |> Thm.close_derivation |
|
1311 end; |
|
1312 |
|
1313 val (ctor_rec_unique_thms, ctor_rec_unique_thm) = |
|
1314 `split_conj_thm (split_conj_prems n |
|
1315 (mor_UNIV_thm RS iffD2 RS rec_unique_mor_thm) |
|
1316 |> Local_Defs.unfold lthy (@{thms convol_o o_id id_o o_assoc[symmetric] fst_convol} @ |
|
1317 map_id0s @ sym_map_comps) OF replicate n @{thm arg_cong2[of _ _ _ _ convol, OF refl]}); |
|
1318 |
|
1319 val timer = time (timer "rec definitions & thms"); |
|
1320 |
|
1321 val (ctor_induct_thm, induct_params) = |
|
1322 let |
|
1323 fun mk_prem phi ctor sets x = |
|
1324 let |
|
1325 fun mk_IH phi set z = |
|
1326 let |
|
1327 val prem = HOLogic.mk_Trueprop (HOLogic.mk_mem (z, set $ x)); |
|
1328 val concl = HOLogic.mk_Trueprop (phi $ z); |
|
1329 in |
|
1330 Logic.all z (Logic.mk_implies (prem, concl)) |
|
1331 end; |
|
1332 |
|
1333 val IHs = map3 mk_IH phis (drop m sets) Izs; |
|
1334 val concl = HOLogic.mk_Trueprop (phi $ (ctor $ x)); |
|
1335 in |
|
1336 Logic.all x (Logic.list_implies (IHs, concl)) |
|
1337 end; |
|
1338 |
|
1339 val prems = map4 mk_prem phis ctors FTs_setss xFs; |
|
1340 |
|
1341 fun mk_concl phi z = phi $ z; |
|
1342 val concl = |
|
1343 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 mk_concl phis Izs)); |
|
1344 |
|
1345 val goal = Logic.list_implies (prems, concl); |
|
1346 in |
|
1347 (Goal.prove_sorry lthy [] [] |
|
1348 (fold_rev Logic.all (phis @ Izs) goal) |
|
1349 (K (mk_ctor_induct_tac lthy m set_mapss init_induct_thm morE_thms mor_Abs_thm |
|
1350 Rep_inverses Abs_inverses Reps)) |
|
1351 |> Thm.close_derivation, |
|
1352 rev (Term.add_tfrees goal [])) |
|
1353 end; |
|
1354 |
|
1355 val cTs = map (SOME o certifyT lthy o TFree) induct_params; |
|
1356 |
|
1357 val weak_ctor_induct_thms = |
|
1358 let fun insts i = (replicate (i - 1) TrueI) @ (asm_rl :: replicate (n - i) TrueI); |
|
1359 in map (fn i => (ctor_induct_thm OF insts i) RS mk_conjunctN n i) ks end; |
|
1360 |
|
1361 val (ctor_induct2_thm, induct2_params) = |
|
1362 let |
|
1363 fun mk_prem phi ctor ctor' sets sets' x y = |
|
1364 let |
|
1365 fun mk_IH phi set set' z1 z2 = |
|
1366 let |
|
1367 val prem1 = HOLogic.mk_Trueprop (HOLogic.mk_mem (z1, (set $ x))); |
|
1368 val prem2 = HOLogic.mk_Trueprop (HOLogic.mk_mem (z2, (set' $ y))); |
|
1369 val concl = HOLogic.mk_Trueprop (phi $ z1 $ z2); |
|
1370 in |
|
1371 fold_rev Logic.all [z1, z2] (Logic.list_implies ([prem1, prem2], concl)) |
|
1372 end; |
|
1373 |
|
1374 val IHs = map5 mk_IH phi2s (drop m sets) (drop m sets') Izs1 Izs2; |
|
1375 val concl = HOLogic.mk_Trueprop (phi $ (ctor $ x) $ (ctor' $ y)); |
|
1376 in |
|
1377 fold_rev Logic.all [x, y] (Logic.list_implies (IHs, concl)) |
|
1378 end; |
|
1379 |
|
1380 val prems = map7 mk_prem phi2s ctors ctor's FTs_setss FTs'_setss xFs yFs; |
|
1381 |
|
1382 fun mk_concl phi z1 z2 = phi $ z1 $ z2; |
|
1383 val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj |
|
1384 (map3 mk_concl phi2s Izs1 Izs2)); |
|
1385 fun mk_t phi (z1, z1') (z2, z2') = |
|
1386 Term.absfree z1' (HOLogic.mk_all (fst z2', snd z2', phi $ z1 $ z2)); |
|
1387 val cts = map3 (SOME o certify lthy ooo mk_t) phi2s (Izs1 ~~ Izs1') (Izs2 ~~ Izs2'); |
|
1388 val goal = Logic.list_implies (prems, concl); |
|
1389 in |
|
1390 (singleton (Proof_Context.export names_lthy lthy) |
|
1391 (Goal.prove_sorry lthy [] [] goal |
|
1392 (mk_ctor_induct2_tac cTs cts ctor_induct_thm weak_ctor_induct_thms)) |
|
1393 |> Thm.close_derivation, |
|
1394 rev (Term.add_tfrees goal [])) |
|
1395 end; |
|
1396 |
|
1397 val timer = time (timer "induction"); |
|
1398 |
|
1399 fun mk_ctor_map_DEADID_thm ctor_inject map_id0 = |
|
1400 trans OF [id_apply, iffD2 OF [ctor_inject, map_id0 RS sym]]; |
|
1401 |
|
1402 fun mk_ctor_Irel_DEADID_thm ctor_inject bnf = |
|
1403 trans OF [ctor_inject, rel_eq_of_bnf bnf RS @{thm predicate2_eqD} RS sym]; |
|
1404 |
|
1405 val IphiTs = map2 mk_pred2T passiveAs passiveBs; |
|
1406 val Ipsi1Ts = map2 mk_pred2T passiveAs passiveCs; |
|
1407 val Ipsi2Ts = map2 mk_pred2T passiveCs passiveBs; |
|
1408 val activephiTs = map2 mk_pred2T activeAs activeBs; |
|
1409 val activeIphiTs = map2 mk_pred2T Ts Ts'; |
|
1410 val (((((Iphis, Ipsi1s), Ipsi2s), activephis), activeIphis), names_lthy) = names_lthy |
|
1411 |> mk_Frees "R" IphiTs |
|
1412 ||>> mk_Frees "R" Ipsi1Ts |
|
1413 ||>> mk_Frees "Q" Ipsi2Ts |
|
1414 ||>> mk_Frees "S" activephiTs |
|
1415 ||>> mk_Frees "IR" activeIphiTs; |
|
1416 val rels = map2 (fn Ds => mk_rel_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs; |
|
1417 |
|
1418 (*register new datatypes as BNFs*) |
|
1419 val (timer, Ibnfs, (ctor_Imap_o_thms, ctor_Imap_thms), ctor_Iset_thmss', |
|
1420 ctor_Irel_thms, Ibnf_notes, lthy) = |
|
1421 if m = 0 then |
|
1422 (timer, replicate n DEADID_bnf, |
|
1423 map_split (`(mk_pointfree lthy)) (map2 mk_ctor_map_DEADID_thm ctor_inject_thms map_ids), |
|
1424 replicate n [], map2 mk_ctor_Irel_DEADID_thm ctor_inject_thms bnfs, [], lthy) |
|
1425 else let |
|
1426 val fTs = map2 (curry op -->) passiveAs passiveBs; |
|
1427 val uTs = map2 (curry op -->) Ts Ts'; |
|
1428 |
|
1429 val (((((fs, fs'), fs_copy), us), (ys, ys')), |
|
1430 names_lthy) = names_lthy |
|
1431 |> mk_Frees' "f" fTs |
|
1432 ||>> mk_Frees "f" fTs |
|
1433 ||>> mk_Frees "u" uTs |
|
1434 ||>> mk_Frees' "y" passiveAs; |
|
1435 |
|
1436 val map_FTFT's = map2 (fn Ds => |
|
1437 mk_map_of_bnf Ds (passiveAs @ Ts) (passiveBs @ Ts')) Dss bnfs; |
|
1438 fun mk_passive_maps ATs BTs Ts = |
|
1439 map2 (fn Ds => mk_map_of_bnf Ds (ATs @ Ts) (BTs @ Ts)) Dss bnfs; |
|
1440 fun mk_map_fold_arg fs Ts ctor fmap = |
|
1441 HOLogic.mk_comp (ctor, Term.list_comb (fmap, fs @ map HOLogic.id_const Ts)); |
|
1442 fun mk_map Ts fs Ts' ctors mk_maps = |
|
1443 mk_fold Ts (map2 (mk_map_fold_arg fs Ts') ctors (mk_maps Ts')); |
|
1444 val pmapsABT' = mk_passive_maps passiveAs passiveBs; |
|
1445 val fs_maps = map (mk_map Ts fs Ts' ctor's pmapsABT') ks; |
|
1446 |
|
1447 val ls = 1 upto m; |
|
1448 val setsss = map (mk_setss o mk_set_Ts) passiveAs; |
|
1449 |
|
1450 fun mk_col l T z z' sets = |
|
1451 let |
|
1452 fun mk_UN set = mk_Union T $ (set $ z); |
|
1453 in |
|
1454 Term.absfree z' |
|
1455 (mk_union (nth sets (l - 1) $ z, |
|
1456 Library.foldl1 mk_union (map mk_UN (drop m sets)))) |
|
1457 end; |
|
1458 |
|
1459 val colss = map5 (fn l => fn T => map3 (mk_col l T)) ls passiveAs AFss AFss' setsss; |
|
1460 val setss_by_range = map (fn cols => map (mk_fold Ts cols) ks) colss; |
|
1461 val setss_by_bnf = transpose setss_by_range; |
|
1462 |
|
1463 val set_bss = |
|
1464 map (flat o map2 (fn B => fn b => |
|
1465 if member (op =) resDs (TFree B) then [] else [b]) resBs) set_bss0; |
|
1466 |
|
1467 val ctor_witss = |
|
1468 let |
|
1469 val witss = map2 (fn Ds => fn bnf => mk_wits_of_bnf |
|
1470 (replicate (nwits_of_bnf bnf) Ds) |
|
1471 (replicate (nwits_of_bnf bnf) (passiveAs @ Ts)) bnf) Dss bnfs; |
|
1472 fun close_wit (I, wit) = fold_rev Term.absfree (map (nth ys') I) wit; |
|
1473 fun wit_apply (arg_I, arg_wit) (fun_I, fun_wit) = |
|
1474 (union (op =) arg_I fun_I, fun_wit $ arg_wit); |
|
1475 |
|
1476 fun gen_arg support i = |
|
1477 if i < m then [([i], nth ys i)] |
|
1478 else maps (mk_wit support (nth ctors (i - m)) (i - m)) (nth support (i - m)) |
|
1479 and mk_wit support ctor i (I, wit) = |
|
1480 let val args = map (gen_arg (nth_map i (remove (op =) (I, wit)) support)) I; |
|
1481 in |
|
1482 (args, [([], wit)]) |
|
1483 |-> fold (map_product wit_apply) |
|
1484 |> map (apsnd (fn t => ctor $ t)) |
|
1485 |> minimize_wits |
|
1486 end; |
|
1487 in |
|
1488 map3 (fn ctor => fn i => map close_wit o minimize_wits o maps (mk_wit witss ctor i)) |
|
1489 ctors (0 upto n - 1) witss |
|
1490 end; |
|
1491 |
|
1492 val (Ibnf_consts, lthy) = |
|
1493 fold_map8 (fn b => fn map_b => fn rel_b => fn set_bs => fn mapx => fn sets => fn wits => |
|
1494 fn T => fn lthy => |
|
1495 define_bnf_consts Dont_Inline (user_policy Note_Some lthy) (SOME deads) |
|
1496 map_b rel_b set_bs |
|
1497 ((((((b, T), fold_rev Term.absfree fs' mapx), sets), sum_bd), wits), NONE) lthy) |
|
1498 bs map_bs rel_bs set_bss fs_maps setss_by_bnf ctor_witss Ts lthy; |
|
1499 |
|
1500 val (_, Iconsts, Iconst_defs, mk_Iconsts) = split_list4 Ibnf_consts; |
|
1501 val (_, Isetss, Ibds_Ds, Iwitss_Ds, _) = split_list5 Iconsts; |
|
1502 val (Imap_defs, Iset_defss, Ibd_defs, Iwit_defss, Irel_defs) = split_list5 Iconst_defs; |
|
1503 val (mk_Imaps_Ds, mk_It_Ds, _, mk_Irels_Ds, _) = split_list5 mk_Iconsts; |
|
1504 |
|
1505 val Irel_unabs_defs = map (fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) Irel_defs; |
|
1506 val Iset_defs = flat Iset_defss; |
|
1507 |
|
1508 fun mk_Imaps As Bs = map (fn mk => mk deads As Bs) mk_Imaps_Ds; |
|
1509 fun mk_Isetss As = map2 (fn mk => fn Isets => map (mk deads As) Isets) mk_It_Ds Isetss; |
|
1510 val Ibds = map2 (fn mk => mk deads passiveAs) mk_It_Ds Ibds_Ds; |
|
1511 val Iwitss = |
|
1512 map2 (fn mk => fn Iwits => map (mk deads passiveAs o snd) Iwits) mk_It_Ds Iwitss_Ds; |
|
1513 fun mk_Irels As Bs = map (fn mk => mk deads As Bs) mk_Irels_Ds; |
|
1514 |
|
1515 val Imaps = mk_Imaps passiveAs passiveBs; |
|
1516 val fs_Imaps = map (fn m => Term.list_comb (m, fs)) Imaps; |
|
1517 val fs_copy_Imaps = map (fn m => Term.list_comb (m, fs_copy)) Imaps; |
|
1518 val (Isetss_by_range, Isetss_by_bnf) = `transpose (mk_Isetss passiveAs); |
|
1519 |
|
1520 val map_setss = map (fn T => map2 (fn Ds => |
|
1521 mk_map_of_bnf Ds (passiveAs @ Ts) (mk_set_Ts T)) Dss bnfs) passiveAs; |
|
1522 |
|
1523 val timer = time (timer "bnf constants for the new datatypes"); |
|
1524 |
|
1525 val (ctor_Imap_thms, ctor_Imap_o_thms) = |
|
1526 let |
|
1527 fun mk_goal fs_map map ctor ctor' = fold_rev Logic.all fs |
|
1528 (mk_Trueprop_eq (HOLogic.mk_comp (fs_map, ctor), |
|
1529 HOLogic.mk_comp (ctor', Term.list_comb (map, fs @ fs_Imaps)))); |
|
1530 val goals = map4 mk_goal fs_Imaps map_FTFT's ctors ctor's; |
|
1531 val maps = |
|
1532 map4 (fn goal => fn foldx => fn map_comp_id => fn map_cong0 => |
|
1533 Goal.prove_sorry lthy [] [] goal |
|
1534 (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Imap_defs THEN |
|
1535 mk_map_tac m n foldx map_comp_id map_cong0) |
|
1536 |> Thm.close_derivation) |
|
1537 goals ctor_fold_thms map_comp_id_thms map_cong0s; |
|
1538 in |
|
1539 `(map (fn thm => thm RS @{thm comp_eq_dest})) maps |
|
1540 end; |
|
1541 |
|
1542 val (ctor_Imap_unique_thms, ctor_Imap_unique_thm) = |
|
1543 let |
|
1544 fun mk_prem u map ctor ctor' = |
|
1545 mk_Trueprop_eq (HOLogic.mk_comp (u, ctor), |
|
1546 HOLogic.mk_comp (ctor', Term.list_comb (map, fs @ us))); |
|
1547 val prems = map4 mk_prem us map_FTFT's ctors ctor's; |
|
1548 val goal = |
|
1549 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj |
|
1550 (map2 (curry HOLogic.mk_eq) us fs_Imaps)); |
|
1551 val unique = Goal.prove_sorry lthy [] [] |
|
1552 (fold_rev Logic.all (us @ fs) (Logic.list_implies (prems, goal))) |
|
1553 (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Imap_defs THEN |
|
1554 mk_ctor_map_unique_tac ctor_fold_unique_thm sym_map_comps ctxt) |
|
1555 |> Thm.close_derivation; |
|
1556 in |
|
1557 `split_conj_thm unique |
|
1558 end; |
|
1559 |
|
1560 val timer = time (timer "map functions for the new datatypes"); |
|
1561 |
|
1562 val ctor_Iset_thmss = |
|
1563 let |
|
1564 fun mk_goal sets ctor set col map = |
|
1565 mk_Trueprop_eq (HOLogic.mk_comp (set, ctor), |
|
1566 HOLogic.mk_comp (col, Term.list_comb (map, passive_ids @ sets))); |
|
1567 val goalss = |
|
1568 map3 (fn sets => map4 (mk_goal sets) ctors sets) Isetss_by_range colss map_setss; |
|
1569 val setss = map (map2 (fn foldx => fn goal => |
|
1570 Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => |
|
1571 unfold_thms_tac ctxt Iset_defs THEN mk_set_tac foldx) |
|
1572 |> Thm.close_derivation) |
|
1573 ctor_fold_thms) goalss; |
|
1574 |
|
1575 fun mk_simp_goal pas_set act_sets sets ctor z set = |
|
1576 Logic.all z (mk_Trueprop_eq (set $ (ctor $ z), |
|
1577 mk_union (pas_set $ z, |
|
1578 Library.foldl1 mk_union (map2 (fn X => mk_UNION (X $ z)) act_sets sets)))); |
|
1579 val simp_goalss = |
|
1580 map2 (fn i => fn sets => |
|
1581 map4 (fn Fsets => mk_simp_goal (nth Fsets (i - 1)) (drop m Fsets) sets) |
|
1582 FTs_setss ctors xFs sets) |
|
1583 ls Isetss_by_range; |
|
1584 |
|
1585 val ctor_setss = map3 (fn i => map3 (fn set_nats => fn goal => fn set => |
|
1586 Goal.prove_sorry lthy [] [] goal |
|
1587 (K (mk_ctor_set_tac set (nth set_nats (i - 1)) (drop m set_nats))) |
|
1588 |> Thm.close_derivation) |
|
1589 set_mapss) ls simp_goalss setss; |
|
1590 in |
|
1591 ctor_setss |
|
1592 end; |
|
1593 |
|
1594 fun mk_set_thms ctor_set = (@{thm xt1(3)} OF [ctor_set, @{thm Un_upper1}]) :: |
|
1595 map (fn i => (@{thm xt1(3)} OF [ctor_set, @{thm Un_upper2}]) RS |
|
1596 (mk_Un_upper n i RS subset_trans) RSN |
|
1597 (2, @{thm UN_upper} RS subset_trans)) |
|
1598 (1 upto n); |
|
1599 val set_Iset_thmsss = transpose (map (map mk_set_thms) ctor_Iset_thmss); |
|
1600 |
|
1601 val timer = time (timer "set functions for the new datatypes"); |
|
1602 |
|
1603 val cxs = map (SOME o certify lthy) Izs; |
|
1604 val Isetss_by_range' = |
|
1605 map (map (Term.subst_atomic_types (passiveAs ~~ passiveBs))) Isetss_by_range; |
|
1606 |
|
1607 val Iset_Imap0_thmss = |
|
1608 let |
|
1609 fun mk_set_map0 f map z set set' = |
|
1610 HOLogic.mk_eq (mk_image f $ (set $ z), set' $ (map $ z)); |
|
1611 |
|
1612 fun mk_cphi f map z set set' = certify lthy |
|
1613 (Term.absfree (dest_Free z) (mk_set_map0 f map z set set')); |
|
1614 |
|
1615 val csetss = map (map (certify lthy)) Isetss_by_range'; |
|
1616 |
|
1617 val cphiss = map3 (fn f => fn sets => fn sets' => |
|
1618 (map4 (mk_cphi f) fs_Imaps Izs sets sets')) fs Isetss_by_range Isetss_by_range'; |
|
1619 |
|
1620 val inducts = map (fn cphis => |
|
1621 Drule.instantiate' cTs (map SOME cphis @ cxs) ctor_induct_thm) cphiss; |
|
1622 |
|
1623 val goals = |
|
1624 map3 (fn f => fn sets => fn sets' => |
|
1625 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj |
|
1626 (map4 (mk_set_map0 f) fs_Imaps Izs sets sets'))) |
|
1627 fs Isetss_by_range Isetss_by_range'; |
|
1628 |
|
1629 fun mk_tac induct = mk_set_nat_tac m (rtac induct) set_mapss ctor_Imap_thms; |
|
1630 val thms = |
|
1631 map5 (fn goal => fn csets => fn ctor_sets => fn induct => fn i => |
|
1632 singleton (Proof_Context.export names_lthy lthy) |
|
1633 (Goal.prove_sorry lthy [] [] goal (mk_tac induct csets ctor_sets i)) |
|
1634 |> Thm.close_derivation) |
|
1635 goals csetss ctor_Iset_thmss inducts ls; |
|
1636 in |
|
1637 map split_conj_thm thms |
|
1638 end; |
|
1639 |
|
1640 val Iset_bd_thmss = |
|
1641 let |
|
1642 fun mk_set_bd z bd set = mk_ordLeq (mk_card_of (set $ z)) bd; |
|
1643 |
|
1644 fun mk_cphi z set = certify lthy (Term.absfree (dest_Free z) (mk_set_bd z sum_bd set)); |
|
1645 |
|
1646 val cphiss = map (map2 mk_cphi Izs) Isetss_by_range; |
|
1647 |
|
1648 val inducts = map (fn cphis => |
|
1649 Drule.instantiate' cTs (map SOME cphis @ cxs) ctor_induct_thm) cphiss; |
|
1650 |
|
1651 val goals = |
|
1652 map (fn sets => |
|
1653 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj |
|
1654 (map3 mk_set_bd Izs Ibds sets))) Isetss_by_range; |
|
1655 |
|
1656 fun mk_tac induct = mk_set_bd_tac m (rtac induct) sum_Cinfinite set_bd_sumss; |
|
1657 val thms = |
|
1658 map4 (fn goal => fn ctor_sets => fn induct => fn i => |
|
1659 singleton (Proof_Context.export names_lthy lthy) |
|
1660 (Goal.prove_sorry lthy [] [] goal |
|
1661 (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt Ibd_defs THEN |
|
1662 mk_tac induct ctor_sets i ctxt)) |
|
1663 |> Thm.close_derivation) |
|
1664 goals ctor_Iset_thmss inducts ls; |
|
1665 in |
|
1666 map split_conj_thm thms |
|
1667 end; |
|
1668 |
|
1669 val Imap_cong0_thms = |
|
1670 let |
|
1671 fun mk_prem z set f g y y' = |
|
1672 mk_Ball (set $ z) (Term.absfree y' (HOLogic.mk_eq (f $ y, g $ y))); |
|
1673 |
|
1674 fun mk_map_cong0 sets z fmap gmap = |
|
1675 HOLogic.mk_imp |
|
1676 (Library.foldr1 HOLogic.mk_conj (map5 (mk_prem z) sets fs fs_copy ys ys'), |
|
1677 HOLogic.mk_eq (fmap $ z, gmap $ z)); |
|
1678 |
|
1679 fun mk_cphi sets z fmap gmap = |
|
1680 certify lthy (Term.absfree (dest_Free z) (mk_map_cong0 sets z fmap gmap)); |
|
1681 |
|
1682 val cphis = map4 mk_cphi Isetss_by_bnf Izs fs_Imaps fs_copy_Imaps; |
|
1683 |
|
1684 val induct = Drule.instantiate' cTs (map SOME cphis @ cxs) ctor_induct_thm; |
|
1685 |
|
1686 val goal = |
|
1687 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj |
|
1688 (map4 mk_map_cong0 Isetss_by_bnf Izs fs_Imaps fs_copy_Imaps)); |
|
1689 |
|
1690 val thm = singleton (Proof_Context.export names_lthy lthy) |
|
1691 (Goal.prove_sorry lthy [] [] goal |
|
1692 (mk_mcong_tac (rtac induct) set_Iset_thmsss map_cong0s ctor_Imap_thms)) |
|
1693 |> Thm.close_derivation; |
|
1694 in |
|
1695 split_conj_thm thm |
|
1696 end; |
|
1697 |
|
1698 val in_rels = map in_rel_of_bnf bnfs; |
|
1699 val in_Irels = map (fn def => trans OF [def, @{thm OO_Grp_alt}] RS @{thm predicate2_eqD}) |
|
1700 Irel_unabs_defs; |
|
1701 |
|
1702 val ctor_Iset_incl_thmss = map (map hd) set_Iset_thmsss; |
|
1703 val ctor_set_Iset_incl_thmsss = map (transpose o map tl) set_Iset_thmsss; |
|
1704 val ctor_Iset_thmss' = transpose ctor_Iset_thmss; |
|
1705 |
|
1706 val Irels = mk_Irels passiveAs passiveBs; |
|
1707 val Irelphis = map (fn rel => Term.list_comb (rel, Iphis)) Irels; |
|
1708 val relphis = map (fn rel => Term.list_comb (rel, Iphis @ Irelphis)) rels; |
|
1709 val Irelpsi1s = map (fn rel => Term.list_comb (rel, Ipsi1s)) (mk_Irels passiveAs passiveCs); |
|
1710 val Irelpsi2s = map (fn rel => Term.list_comb (rel, Ipsi2s)) (mk_Irels passiveCs passiveBs); |
|
1711 val Irelpsi12s = map (fn rel => |
|
1712 Term.list_comb (rel, map2 (curry mk_rel_compp) Ipsi1s Ipsi2s)) Irels; |
|
1713 |
|
1714 val ctor_Irel_thms = |
|
1715 let |
|
1716 fun mk_goal xF yF ctor ctor' Irelphi relphi = fold_rev Logic.all (xF :: yF :: Iphis) |
|
1717 (mk_Trueprop_eq (Irelphi $ (ctor $ xF) $ (ctor' $ yF), relphi $ xF $ yF)); |
|
1718 val goals = map6 mk_goal xFs yFs ctors ctor's Irelphis relphis; |
|
1719 in |
|
1720 map12 (fn i => fn goal => fn in_rel => fn map_comp0 => fn map_cong0 => |
|
1721 fn ctor_map => fn ctor_sets => fn ctor_inject => fn ctor_dtor => |
|
1722 fn set_map0s => fn ctor_set_incls => fn ctor_set_set_inclss => |
|
1723 Goal.prove_sorry lthy [] [] goal |
|
1724 (K (mk_ctor_rel_tac lthy in_Irels i in_rel map_comp0 map_cong0 ctor_map ctor_sets |
|
1725 ctor_inject ctor_dtor set_map0s ctor_set_incls ctor_set_set_inclss)) |
|
1726 |> Thm.close_derivation) |
|
1727 ks goals in_rels map_comps map_cong0s ctor_Imap_thms ctor_Iset_thmss' |
|
1728 ctor_inject_thms ctor_dtor_thms set_mapss ctor_Iset_incl_thmss |
|
1729 ctor_set_Iset_incl_thmsss |
|
1730 end; |
|
1731 |
|
1732 val le_Irel_OO_thm = |
|
1733 let |
|
1734 fun mk_le_Irel_OO Irelpsi1 Irelpsi2 Irelpsi12 Iz1 Iz2 = |
|
1735 HOLogic.mk_imp (mk_rel_compp (Irelpsi1, Irelpsi2) $ Iz1 $ Iz2, |
|
1736 Irelpsi12 $ Iz1 $ Iz2); |
|
1737 val goals = map5 mk_le_Irel_OO Irelpsi1s Irelpsi2s Irelpsi12s Izs1 Izs2; |
|
1738 |
|
1739 val cTs = map (SOME o certifyT lthy o TFree) induct2_params; |
|
1740 val cxs = map (SOME o certify lthy) (splice Izs1 Izs2); |
|
1741 fun mk_cphi z1 z2 goal = SOME (certify lthy (Term.absfree z1 (Term.absfree z2 goal))); |
|
1742 val cphis = map3 mk_cphi Izs1' Izs2' goals; |
|
1743 val induct = Drule.instantiate' cTs (cphis @ cxs) ctor_induct2_thm; |
|
1744 |
|
1745 val goal = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj goals); |
|
1746 in |
|
1747 singleton (Proof_Context.export names_lthy lthy) |
|
1748 (Goal.prove_sorry lthy [] [] goal |
|
1749 (mk_le_rel_OO_tac m induct ctor_nchotomy_thms ctor_Irel_thms rel_mono_strongs |
|
1750 rel_OOs)) |
|
1751 |> Thm.close_derivation |
|
1752 end; |
|
1753 |
|
1754 val timer = time (timer "helpers for BNF properties"); |
|
1755 |
|
1756 val map_id0_tacs = map (K o mk_map_id0_tac map_id0s) ctor_Imap_unique_thms; |
|
1757 val map_comp0_tacs = |
|
1758 map2 (K oo mk_map_comp0_tac map_comps ctor_Imap_thms) ctor_Imap_unique_thms ks; |
|
1759 val map_cong0_tacs = map (mk_map_cong0_tac m) Imap_cong0_thms; |
|
1760 val set_map0_tacss = map (map (K o mk_set_map0_tac)) (transpose Iset_Imap0_thmss); |
|
1761 val bd_co_tacs = replicate n (fn {context = ctxt, prems = _} => |
|
1762 unfold_thms_tac ctxt Ibd_defs THEN mk_bd_card_order_tac bd_card_orders); |
|
1763 val bd_cinf_tacs = replicate n (fn {context = ctxt, prems = _} => |
|
1764 unfold_thms_tac ctxt Ibd_defs THEN rtac (sum_Cinfinite RS conjunct1) 1); |
|
1765 val set_bd_tacss = map (map (fn thm => K (rtac thm 1))) (transpose Iset_bd_thmss); |
|
1766 val le_rel_OO_tacs = map (fn i => |
|
1767 K ((rtac @{thm predicate2I} THEN' etac (le_Irel_OO_thm RS mk_conjunctN n i RS mp)) 1)) ks; |
|
1768 |
|
1769 val rel_OO_Grp_tacs = map (fn def => K (rtac def 1)) Irel_unabs_defs; |
|
1770 |
|
1771 val tacss = map9 zip_axioms map_id0_tacs map_comp0_tacs map_cong0_tacs set_map0_tacss |
|
1772 bd_co_tacs bd_cinf_tacs set_bd_tacss le_rel_OO_tacs rel_OO_Grp_tacs; |
|
1773 |
|
1774 fun wit_tac {context = ctxt, prems = _} = unfold_thms_tac ctxt (flat Iwit_defss) THEN |
|
1775 mk_wit_tac ctxt n (flat ctor_Iset_thmss) (maps wit_thms_of_bnf bnfs); |
|
1776 |
|
1777 val (Ibnfs, lthy) = |
|
1778 fold_map5 (fn tacs => fn map_b => fn rel_b => fn set_bs => fn consts => fn lthy => |
|
1779 bnf_def Do_Inline (user_policy Note_Some) I tacs wit_tac (SOME deads) |
|
1780 map_b rel_b set_bs consts lthy |
|
1781 |> register_bnf (Local_Theory.full_name lthy b)) |
|
1782 tacss map_bs rel_bs set_bss |
|
1783 ((((((bs ~~ Ts) ~~ Imaps) ~~ Isetss_by_bnf) ~~ Ibds) ~~ Iwitss) ~~ map SOME Irels) |
|
1784 lthy; |
|
1785 |
|
1786 val timer = time (timer "registered new datatypes as BNFs"); |
|
1787 |
|
1788 val ls' = if m = 1 then [0] else ls |
|
1789 |
|
1790 val Ibnf_common_notes = |
|
1791 [(ctor_map_uniqueN, [ctor_Imap_unique_thm])] |
|
1792 |> map (fn (thmN, thms) => |
|
1793 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])); |
|
1794 |
|
1795 val Ibnf_notes = |
|
1796 [(ctor_mapN, map single ctor_Imap_thms), |
|
1797 (ctor_relN, map single ctor_Irel_thms), |
|
1798 (ctor_set_inclN, ctor_Iset_incl_thmss), |
|
1799 (ctor_set_set_inclN, map flat ctor_set_Iset_incl_thmsss)] @ |
|
1800 map2 (fn i => fn thms => (mk_ctor_setN i, map single thms)) ls' ctor_Iset_thmss |
|
1801 |> maps (fn (thmN, thmss) => |
|
1802 map2 (fn b => fn thms => |
|
1803 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) |
|
1804 bs thmss) |
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1805 in |
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1806 (timer, Ibnfs, (ctor_Imap_o_thms, ctor_Imap_thms), ctor_Iset_thmss', |
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1807 ctor_Irel_thms, Ibnf_common_notes @ Ibnf_notes, lthy) |
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1808 end; |
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1809 |
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1810 val ctor_fold_o_Imap_thms = mk_xtor_un_fold_o_map_thms Least_FP false m ctor_fold_unique_thm |
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1811 ctor_Imap_o_thms (map (mk_pointfree lthy) ctor_fold_thms) sym_map_comps map_cong0s; |
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1812 val ctor_rec_o_Imap_thms = mk_xtor_un_fold_o_map_thms Least_FP true m ctor_rec_unique_thm |
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1813 ctor_Imap_o_thms (map (mk_pointfree lthy) ctor_rec_thms) sym_map_comps map_cong0s; |
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1814 |
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1815 val Irels = if m = 0 then map HOLogic.eq_const Ts |
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1816 else map (mk_rel_of_bnf deads passiveAs passiveBs) Ibnfs; |
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1817 val Irel_induct_thm = |
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1818 mk_rel_xtor_co_induct_thm Least_FP rels activeIphis Irels Iphis xFs yFs ctors ctor's |
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1819 (mk_rel_induct_tac m ctor_induct2_thm ks ctor_Irel_thms rel_mono_strongs) lthy; |
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1820 |
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1821 val rels = map2 (fn Ds => mk_rel_of_bnf Ds allAs allBs') Dss bnfs; |
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1822 val ctor_fold_transfer_thms = |
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1823 mk_un_fold_transfer_thms Least_FP rels activephis Irels Iphis |
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1824 (mk_folds passiveAs activeAs) (mk_folds passiveBs activeBs) |
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1825 (mk_fold_transfer_tac m Irel_induct_thm (map map_transfer_of_bnf bnfs) ctor_fold_thms) |
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1826 lthy; |
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1827 |
|
1828 val timer = time (timer "relator induction"); |
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1829 |
|
1830 val common_notes = |
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1831 [(ctor_inductN, [ctor_induct_thm]), |
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1832 (ctor_induct2N, [ctor_induct2_thm]), |
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1833 (rel_inductN, [Irel_induct_thm]), |
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1834 (ctor_fold_transferN, ctor_fold_transfer_thms)] |
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1835 |> map (fn (thmN, thms) => |
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1836 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])); |
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1837 |
|
1838 val notes = |
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1839 [(ctor_dtorN, ctor_dtor_thms), |
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1840 (ctor_exhaustN, ctor_exhaust_thms), |
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1841 (ctor_foldN, ctor_fold_thms), |
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1842 (ctor_fold_uniqueN, ctor_fold_unique_thms), |
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1843 (ctor_rec_uniqueN, ctor_rec_unique_thms), |
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1844 (ctor_fold_o_mapN, ctor_fold_o_Imap_thms), |
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1845 (ctor_rec_o_mapN, ctor_rec_o_Imap_thms), |
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1846 (ctor_injectN, ctor_inject_thms), |
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1847 (ctor_recN, ctor_rec_thms), |
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1848 (dtor_ctorN, dtor_ctor_thms), |
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1849 (dtor_exhaustN, dtor_exhaust_thms), |
|
1850 (dtor_injectN, dtor_inject_thms)] |
|
1851 |> map (apsnd (map single)) |
|
1852 |> maps (fn (thmN, thmss) => |
|
1853 map2 (fn b => fn thms => |
|
1854 ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) |
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1855 bs thmss); |
|
1856 |
|
1857 (*FIXME: once the package exports all the necessary high-level characteristic theorems, |
|
1858 those should not only be concealed but rather not noted at all*) |
|
1859 val maybe_conceal_notes = note_all = false ? map (apfst (apfst Binding.conceal)); |
|
1860 in |
|
1861 timer; |
|
1862 ({Ts = Ts, bnfs = Ibnfs, ctors = ctors, dtors = dtors, xtor_co_iterss = transpose [folds, recs], |
|
1863 xtor_co_induct = ctor_induct_thm, dtor_ctors = dtor_ctor_thms, ctor_dtors = ctor_dtor_thms, |
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1864 ctor_injects = ctor_inject_thms, dtor_injects = dtor_inject_thms, |
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1865 xtor_map_thms = ctor_Imap_thms, xtor_set_thmss = ctor_Iset_thmss', |
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1866 xtor_rel_thms = ctor_Irel_thms, |
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1867 xtor_co_iter_thmss = transpose [ctor_fold_thms, ctor_rec_thms], |
|
1868 xtor_co_iter_o_map_thmss = transpose [ctor_fold_o_Imap_thms, ctor_rec_o_Imap_thms], |
|
1869 rel_xtor_co_induct_thm = Irel_induct_thm}, |
|
1870 lthy |> Local_Theory.notes (maybe_conceal_notes (common_notes @ notes @ Ibnf_notes)) |> snd) |
|
1871 end; |
|
1872 |
|
1873 val _ = |
|
1874 Outer_Syntax.local_theory @{command_spec "datatype_new"} "define new-style inductive datatypes" |
|
1875 (parse_co_datatype_cmd Least_FP construct_lfp); |
|
1876 |
|
1877 val _ = Outer_Syntax.local_theory @{command_spec "primrec_new"} |
|
1878 "define primitive recursive functions" |
|
1879 (Parse.fixes -- Parse_Spec.where_alt_specs >> (snd oo uncurry add_primrec_cmd)); |
|
1880 |
|
1881 end; |
|