1 (* Title: HOL/BNF/Tools/bnf_fp.ML |
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2 Author: Dmitriy Traytel, TU Muenchen |
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3 Author: Jasmin Blanchette, TU Muenchen |
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4 Copyright 2012, 2013 |
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5 |
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6 Shared library for the datatype and codatatype constructions. |
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7 *) |
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8 |
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9 signature BNF_FP = |
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10 sig |
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11 type fp_result = |
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12 {bnfs: BNF_Def.bnf list, |
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13 ctors: term list, |
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14 dtors: term list, |
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15 folds: term list, |
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16 recs: term list, |
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17 induct: thm, |
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18 strong_induct: thm, |
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19 dtor_ctors: thm list, |
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20 ctor_dtors: thm list, |
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21 ctor_injects: thm list, |
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22 map_thms: thm list, |
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23 set_thmss: thm list list, |
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24 rel_thms: thm list, |
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25 fold_thms: thm list, |
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26 rec_thms: thm list} |
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27 |
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28 val fp_name_of_ctor: term -> string |
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29 val morph_fp_result: morphism -> fp_result -> fp_result |
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30 val eq_fp_result: fp_result * fp_result -> bool |
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31 |
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32 val time: Timer.real_timer -> string -> Timer.real_timer |
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33 |
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34 val IITN: string |
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35 val LevN: string |
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36 val algN: string |
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37 val behN: string |
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38 val bisN: string |
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39 val carTN: string |
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40 val caseN: string |
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41 val coN: string |
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42 val coinductN: string |
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43 val corecN: string |
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44 val ctorN: string |
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45 val ctor_dtorN: string |
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46 val ctor_dtor_corecN: string |
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47 val ctor_dtor_unfoldN: string |
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48 val ctor_exhaustN: string |
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49 val ctor_induct2N: string |
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50 val ctor_inductN: string |
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51 val ctor_injectN: string |
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52 val ctor_foldN: string |
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53 val ctor_fold_uniqueN: string |
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54 val ctor_mapN: string |
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55 val ctor_map_uniqueN: string |
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56 val ctor_recN: string |
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57 val ctor_rec_uniqueN: string |
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58 val ctor_relN: string |
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59 val ctor_set_inclN: string |
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60 val ctor_set_set_inclN: string |
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61 val ctor_srelN: string |
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62 val disc_unfoldN: string |
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63 val disc_unfold_iffN: string |
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64 val disc_corecN: string |
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65 val disc_corec_iffN: string |
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66 val dtorN: string |
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67 val dtor_coinductN: string |
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68 val dtor_corecN: string |
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69 val dtor_corec_uniqueN: string |
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70 val dtor_ctorN: string |
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71 val dtor_exhaustN: string |
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72 val dtor_injectN: string |
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73 val dtor_mapN: string |
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74 val dtor_map_coinductN: string |
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75 val dtor_map_strong_coinductN: string |
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76 val dtor_map_uniqueN: string |
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77 val dtor_relN: string |
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78 val dtor_set_inclN: string |
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79 val dtor_set_set_inclN: string |
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80 val dtor_srelN: string |
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81 val dtor_srel_coinductN: string |
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82 val dtor_srel_strong_coinductN: string |
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83 val dtor_strong_coinductN: string |
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84 val dtor_unfoldN: string |
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85 val dtor_unfold_uniqueN: string |
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86 val exhaustN: string |
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87 val foldN: string |
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88 val hsetN: string |
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89 val hset_recN: string |
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90 val inductN: string |
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91 val injectN: string |
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92 val isNodeN: string |
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93 val lsbisN: string |
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94 val mapN: string |
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95 val map_uniqueN: string |
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96 val min_algN: string |
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97 val morN: string |
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98 val nchotomyN: string |
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99 val recN: string |
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100 val rel_injectN: string |
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101 val rel_distinctN: string |
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102 val rvN: string |
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103 val sel_corecN: string |
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104 val set_inclN: string |
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105 val set_set_inclN: string |
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106 val sel_unfoldN: string |
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107 val setsN: string |
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108 val simpsN: string |
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109 val strTN: string |
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110 val str_initN: string |
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111 val strong_coinductN: string |
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112 val sum_bdN: string |
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113 val sum_bdTN: string |
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114 val unfoldN: string |
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115 val uniqueN: string |
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116 |
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117 (* TODO: Don't index set facts. Isabelle packages traditionally generate uniform names. *) |
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118 val mk_ctor_setN: int -> string |
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119 val mk_dtor_setN: int -> string |
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120 val mk_dtor_set_inductN: int -> string |
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121 val mk_set_inductN: int -> string |
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122 |
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123 val mk_common_name: string list -> string |
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124 |
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125 val split_conj_thm: thm -> thm list |
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126 val split_conj_prems: int -> thm -> thm |
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127 |
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128 val mk_sumTN: typ list -> typ |
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129 val mk_sumTN_balanced: typ list -> typ |
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130 |
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131 val id_const: typ -> term |
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132 |
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133 val Inl_const: typ -> typ -> term |
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134 val Inr_const: typ -> typ -> term |
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135 |
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136 val mk_Inl: typ -> term -> term |
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137 val mk_Inr: typ -> term -> term |
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138 val mk_InN: typ list -> term -> int -> term |
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139 val mk_InN_balanced: typ -> int -> term -> int -> term |
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140 val mk_sum_case: term * term -> term |
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141 val mk_sum_caseN: term list -> term |
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142 val mk_sum_caseN_balanced: term list -> term |
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143 |
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144 val dest_sumT: typ -> typ * typ |
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145 val dest_sumTN: int -> typ -> typ list |
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146 val dest_sumTN_balanced: int -> typ -> typ list |
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147 val dest_tupleT: int -> typ -> typ list |
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148 |
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149 val mk_Field: term -> term |
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150 val mk_If: term -> term -> term -> term |
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151 val mk_union: term * term -> term |
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152 |
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153 val mk_sumEN: int -> thm |
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154 val mk_sumEN_balanced: int -> thm |
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155 val mk_sumEN_tupled_balanced: int list -> thm |
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156 val mk_sum_casesN: int -> int -> thm |
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157 val mk_sum_casesN_balanced: int -> int -> thm |
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158 |
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159 val fixpoint: ('a * 'a -> bool) -> ('a list -> 'a list) -> 'a list -> 'a list |
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160 |
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161 val fp_bnf: (mixfix list -> (string * sort) list option -> binding list -> binding list -> |
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162 binding list -> binding list list -> typ list * typ list list -> BNF_Def.bnf list -> |
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163 local_theory -> 'a) -> |
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164 binding list -> mixfix list -> binding list -> binding list -> binding list list -> |
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165 (string * sort) list -> ((string * sort) * typ) list -> local_theory -> BNF_Def.bnf list * 'a |
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166 end; |
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167 |
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168 structure BNF_FP : BNF_FP = |
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169 struct |
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170 |
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171 open BNF_Comp |
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172 open BNF_Def |
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173 open BNF_Util |
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174 |
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175 type fp_result = |
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176 {bnfs: BNF_Def.bnf list, |
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177 ctors: term list, |
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178 dtors: term list, |
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179 folds: term list, |
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180 recs: term list, |
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181 induct: thm, |
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182 strong_induct: thm, |
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183 dtor_ctors: thm list, |
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184 ctor_dtors: thm list, |
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185 ctor_injects: thm list, |
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186 map_thms: thm list, |
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187 set_thmss: thm list list, |
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188 rel_thms: thm list, |
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189 fold_thms: thm list, |
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190 rec_thms: thm list}; |
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191 |
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192 val fp_name_of_ctor = fst o dest_Type o range_type o fastype_of; |
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193 |
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194 fun morph_fp_result phi {bnfs, ctors, dtors, folds, recs, induct, strong_induct, dtor_ctors, |
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195 ctor_dtors, ctor_injects, map_thms, set_thmss, rel_thms, fold_thms, rec_thms} = |
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196 {bnfs = map (morph_bnf phi) bnfs, |
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197 ctors = map (Morphism.term phi) ctors, |
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198 dtors = map (Morphism.term phi) dtors, |
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199 folds = map (Morphism.term phi) folds, |
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200 recs = map (Morphism.term phi) recs, |
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201 induct = Morphism.thm phi induct, |
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202 strong_induct = Morphism.thm phi strong_induct, |
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203 dtor_ctors = map (Morphism.thm phi) dtor_ctors, |
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204 ctor_dtors = map (Morphism.thm phi) ctor_dtors, |
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205 ctor_injects = map (Morphism.thm phi) ctor_injects, |
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206 map_thms = map (Morphism.thm phi) map_thms, |
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207 set_thmss = map (map (Morphism.thm phi)) set_thmss, |
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208 rel_thms = map (Morphism.thm phi) rel_thms, |
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209 fold_thms = map (Morphism.thm phi) fold_thms, |
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210 rec_thms = map (Morphism.thm phi) rec_thms}; |
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211 |
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212 fun eq_fp_result ({bnfs = bnfs1, ...} : fp_result, {bnfs = bnfs2, ...} : fp_result) = |
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213 eq_list eq_bnf (bnfs1, bnfs2); |
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214 |
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215 val timing = true; |
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216 fun time timer msg = (if timing |
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217 then warning (msg ^ ": " ^ ATP_Util.string_from_time (Timer.checkRealTimer timer)) |
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218 else (); Timer.startRealTimer ()); |
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219 |
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220 val preN = "pre_" |
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221 val rawN = "raw_" |
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222 |
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223 val coN = "co" |
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224 val unN = "un" |
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225 val algN = "alg" |
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226 val IITN = "IITN" |
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227 val foldN = "fold" |
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228 val unfoldN = unN ^ foldN |
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229 val uniqueN = "_unique" |
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230 val simpsN = "simps" |
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231 val ctorN = "ctor" |
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232 val dtorN = "dtor" |
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233 val ctor_foldN = ctorN ^ "_" ^ foldN |
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234 val dtor_unfoldN = dtorN ^ "_" ^ unfoldN |
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235 val ctor_fold_uniqueN = ctor_foldN ^ uniqueN |
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236 val dtor_unfold_uniqueN = dtor_unfoldN ^ uniqueN |
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237 val ctor_dtor_unfoldN = ctorN ^ "_" ^ dtor_unfoldN |
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238 val ctor_mapN = ctorN ^ "_" ^ mapN |
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239 val dtor_mapN = dtorN ^ "_" ^ mapN |
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240 val map_uniqueN = mapN ^ uniqueN |
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241 val ctor_map_uniqueN = ctorN ^ "_" ^ map_uniqueN |
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242 val dtor_map_uniqueN = dtorN ^ "_" ^ map_uniqueN |
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243 val min_algN = "min_alg" |
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244 val morN = "mor" |
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245 val bisN = "bis" |
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246 val lsbisN = "lsbis" |
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247 val sum_bdTN = "sbdT" |
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248 val sum_bdN = "sbd" |
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249 val carTN = "carT" |
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250 val strTN = "strT" |
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251 val isNodeN = "isNode" |
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252 val LevN = "Lev" |
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253 val rvN = "recover" |
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254 val behN = "beh" |
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255 val setsN = "sets" |
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256 val mk_ctor_setN = prefix (ctorN ^ "_") o mk_setN |
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257 val mk_dtor_setN = prefix (dtorN ^ "_") o mk_setN |
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258 fun mk_set_inductN i = mk_setN i ^ "_induct" |
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259 val mk_dtor_set_inductN = prefix (dtorN ^ "_") o mk_set_inductN |
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260 |
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261 val str_initN = "str_init" |
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262 val recN = "rec" |
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263 val corecN = coN ^ recN |
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264 val ctor_recN = ctorN ^ "_" ^ recN |
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265 val ctor_rec_uniqueN = ctor_recN ^ uniqueN |
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266 val dtor_corecN = dtorN ^ "_" ^ corecN |
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267 val dtor_corec_uniqueN = dtor_corecN ^ uniqueN |
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268 val ctor_dtor_corecN = ctorN ^ "_" ^ dtor_corecN |
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269 |
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270 val ctor_dtorN = ctorN ^ "_" ^ dtorN |
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271 val dtor_ctorN = dtorN ^ "_" ^ ctorN |
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272 val nchotomyN = "nchotomy" |
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273 val injectN = "inject" |
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274 val exhaustN = "exhaust" |
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275 val ctor_injectN = ctorN ^ "_" ^ injectN |
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276 val ctor_exhaustN = ctorN ^ "_" ^ exhaustN |
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277 val dtor_injectN = dtorN ^ "_" ^ injectN |
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278 val dtor_exhaustN = dtorN ^ "_" ^ exhaustN |
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279 val ctor_relN = ctorN ^ "_" ^ relN |
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280 val dtor_relN = dtorN ^ "_" ^ relN |
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281 val ctor_srelN = ctorN ^ "_" ^ srelN |
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282 val dtor_srelN = dtorN ^ "_" ^ srelN |
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283 val inductN = "induct" |
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284 val coinductN = coN ^ inductN |
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285 val ctor_inductN = ctorN ^ "_" ^ inductN |
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286 val ctor_induct2N = ctor_inductN ^ "2" |
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287 val dtor_map_coinductN = dtor_mapN ^ "_" ^ coinductN |
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288 val dtor_coinductN = dtorN ^ "_" ^ coinductN |
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289 val dtor_srel_coinductN = dtor_srelN ^ "_" ^ coinductN |
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290 val strong_coinductN = "strong_" ^ coinductN |
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291 val dtor_map_strong_coinductN = dtor_mapN ^ "_" ^ strong_coinductN |
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292 val dtor_strong_coinductN = dtorN ^ "_" ^ strong_coinductN |
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293 val dtor_srel_strong_coinductN = dtor_srelN ^ "_" ^ strong_coinductN |
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294 val hsetN = "Hset" |
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295 val hset_recN = hsetN ^ "_rec" |
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296 val set_inclN = "set_incl" |
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297 val ctor_set_inclN = ctorN ^ "_" ^ set_inclN |
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298 val dtor_set_inclN = dtorN ^ "_" ^ set_inclN |
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299 val set_set_inclN = "set_set_incl" |
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300 val ctor_set_set_inclN = ctorN ^ "_" ^ set_set_inclN |
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301 val dtor_set_set_inclN = dtorN ^ "_" ^ set_set_inclN |
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302 |
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303 val caseN = "case" |
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304 val discN = "disc" |
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305 val disc_unfoldN = discN ^ "_" ^ unfoldN |
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306 val disc_corecN = discN ^ "_" ^ corecN |
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307 val iffN = "_iff" |
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308 val disc_unfold_iffN = discN ^ "_" ^ unfoldN ^ iffN |
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309 val disc_corec_iffN = discN ^ "_" ^ corecN ^ iffN |
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310 val distinctN = "distinct" |
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311 val rel_distinctN = relN ^ "_" ^ distinctN |
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312 val injectN = "inject" |
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313 val rel_injectN = relN ^ "_" ^ injectN |
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314 val selN = "sel" |
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315 val sel_unfoldN = selN ^ "_" ^ unfoldN |
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316 val sel_corecN = selN ^ "_" ^ corecN |
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317 |
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318 val mk_common_name = space_implode "_"; |
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319 |
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320 fun dest_sumT (Type (@{type_name sum}, [T, T'])) = (T, T'); |
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321 |
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322 fun dest_sumTN 1 T = [T] |
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323 | dest_sumTN n (Type (@{type_name sum}, [T, T'])) = T :: dest_sumTN (n - 1) T'; |
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324 |
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325 val dest_sumTN_balanced = Balanced_Tree.dest dest_sumT; |
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326 |
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327 (* TODO: move something like this to "HOLogic"? *) |
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328 fun dest_tupleT 0 @{typ unit} = [] |
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329 | dest_tupleT 1 T = [T] |
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330 | dest_tupleT n (Type (@{type_name prod}, [T, T'])) = T :: dest_tupleT (n - 1) T'; |
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331 |
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332 val mk_sumTN = Library.foldr1 mk_sumT; |
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333 val mk_sumTN_balanced = Balanced_Tree.make mk_sumT; |
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334 |
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335 fun id_const T = Const (@{const_name id}, T --> T); |
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336 |
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337 fun Inl_const LT RT = Const (@{const_name Inl}, LT --> mk_sumT (LT, RT)); |
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338 fun mk_Inl RT t = Inl_const (fastype_of t) RT $ t; |
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339 |
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340 fun Inr_const LT RT = Const (@{const_name Inr}, RT --> mk_sumT (LT, RT)); |
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341 fun mk_Inr LT t = Inr_const LT (fastype_of t) $ t; |
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342 |
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343 fun mk_InN [_] t 1 = t |
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344 | mk_InN (_ :: Ts) t 1 = mk_Inl (mk_sumTN Ts) t |
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345 | mk_InN (LT :: Ts) t m = mk_Inr LT (mk_InN Ts t (m - 1)) |
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346 | mk_InN Ts t _ = raise (TYPE ("mk_InN", Ts, [t])); |
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347 |
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348 fun mk_InN_balanced sum_T n t k = |
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349 let |
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350 fun repair_types T (Const (s as @{const_name Inl}, _) $ t) = repair_inj_types T s fst t |
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351 | repair_types T (Const (s as @{const_name Inr}, _) $ t) = repair_inj_types T s snd t |
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352 | repair_types _ t = t |
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353 and repair_inj_types T s get t = |
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354 let val T' = get (dest_sumT T) in |
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355 Const (s, T' --> T) $ repair_types T' t |
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356 end; |
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357 in |
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358 Balanced_Tree.access {left = mk_Inl dummyT, right = mk_Inr dummyT, init = t} n k |
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359 |> repair_types sum_T |
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360 end; |
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361 |
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362 fun mk_sum_case (f, g) = |
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363 let |
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364 val fT = fastype_of f; |
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365 val gT = fastype_of g; |
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366 in |
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367 Const (@{const_name sum_case}, |
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368 fT --> gT --> mk_sumT (domain_type fT, domain_type gT) --> range_type fT) $ f $ g |
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369 end; |
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370 |
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371 val mk_sum_caseN = Library.foldr1 mk_sum_case; |
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372 val mk_sum_caseN_balanced = Balanced_Tree.make mk_sum_case; |
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373 |
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374 fun mk_If p t f = |
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375 let val T = fastype_of t; |
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376 in Const (@{const_name If}, HOLogic.boolT --> T --> T --> T) $ p $ t $ f end; |
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377 |
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378 fun mk_Field r = |
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379 let val T = fst (dest_relT (fastype_of r)); |
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380 in Const (@{const_name Field}, mk_relT (T, T) --> HOLogic.mk_setT T) $ r end; |
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381 |
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382 val mk_union = HOLogic.mk_binop @{const_name sup}; |
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383 |
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384 (*dangerous; use with monotonic, converging functions only!*) |
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385 fun fixpoint eq f X = if subset eq (f X, X) then X else fixpoint eq f (f X); |
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386 |
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387 (* stolen from "~~/src/HOL/Tools/Datatype/datatype_aux.ML" *) |
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388 fun split_conj_thm th = |
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389 ((th RS conjunct1) :: split_conj_thm (th RS conjunct2)) handle THM _ => [th]; |
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390 |
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391 fun split_conj_prems limit th = |
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392 let |
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393 fun split n i th = |
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394 if i = n then th else split n (i + 1) (conjI RSN (i, th)) handle THM _ => th; |
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395 in split limit 1 th end; |
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396 |
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397 fun mk_sumEN 1 = @{thm one_pointE} |
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398 | mk_sumEN 2 = @{thm sumE} |
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399 | mk_sumEN n = |
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400 (fold (fn i => fn thm => @{thm obj_sum_step} RSN (i, thm)) (2 upto n - 1) @{thm obj_sumE}) OF |
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401 replicate n (impI RS allI); |
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402 |
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403 fun mk_obj_sumEN_balanced n = |
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404 Balanced_Tree.make (fn (thm1, thm2) => thm1 RSN (1, thm2 RSN (2, @{thm obj_sumE_f}))) |
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405 (replicate n asm_rl); |
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406 |
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407 fun mk_sumEN_balanced' n all_impIs = mk_obj_sumEN_balanced n OF all_impIs RS @{thm obj_one_pointE}; |
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408 |
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409 fun mk_sumEN_balanced 1 = @{thm one_pointE} (*optimization*) |
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410 | mk_sumEN_balanced 2 = @{thm sumE} (*optimization*) |
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411 | mk_sumEN_balanced n = mk_sumEN_balanced' n (replicate n (impI RS allI)); |
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412 |
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413 fun mk_tupled_allIN 0 = @{thm unit_all_impI} |
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414 | mk_tupled_allIN 1 = @{thm impI[THEN allI]} |
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415 | mk_tupled_allIN 2 = @{thm prod_all_impI} (*optimization*) |
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416 | mk_tupled_allIN n = mk_tupled_allIN (n - 1) RS @{thm prod_all_impI_step}; |
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417 |
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418 fun mk_sumEN_tupled_balanced ms = |
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419 let val n = length ms in |
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420 if forall (curry (op =) 1) ms then mk_sumEN_balanced n |
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421 else mk_sumEN_balanced' n (map mk_tupled_allIN ms) |
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422 end; |
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423 |
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424 fun mk_sum_casesN 1 1 = refl |
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425 | mk_sum_casesN _ 1 = @{thm sum.cases(1)} |
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426 | mk_sum_casesN 2 2 = @{thm sum.cases(2)} |
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427 | mk_sum_casesN n k = trans OF [@{thm sum_case_step(2)}, mk_sum_casesN (n - 1) (k - 1)]; |
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428 |
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429 fun mk_sum_step base step thm = |
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430 if Thm.eq_thm_prop (thm, refl) then base else trans OF [step, thm]; |
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431 |
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432 fun mk_sum_casesN_balanced 1 1 = refl |
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433 | mk_sum_casesN_balanced n k = |
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434 Balanced_Tree.access {left = mk_sum_step @{thm sum.cases(1)} @{thm sum_case_step(1)}, |
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435 right = mk_sum_step @{thm sum.cases(2)} @{thm sum_case_step(2)}, init = refl} n k; |
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436 |
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437 (* FIXME: because of "@ lhss", the output could contain type variables that are not in the input; |
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438 also, "fp_sort" should put the "resBs" first and in the order in which they appear *) |
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439 fun fp_sort lhss NONE Ass = Library.sort (Term_Ord.typ_ord o pairself TFree) |
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440 (subtract (op =) lhss (fold (fold (insert (op =))) Ass [])) @ lhss |
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441 | fp_sort lhss (SOME resBs) Ass = |
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442 (subtract (op =) lhss (filter (fn T => exists (fn Ts => member (op =) Ts T) Ass) resBs)) @ lhss; |
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443 |
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444 fun mk_fp_bnf timer construct_fp resBs bs map_bs rel_bs set_bss sort lhss bnfs deadss livess |
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445 unfold_set lthy = |
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446 let |
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447 val name = mk_common_name (map Binding.name_of bs); |
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448 fun qualify i = |
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449 let val namei = name ^ nonzero_string_of_int i; |
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450 in Binding.qualify true namei end; |
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451 |
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452 val Ass = map (map dest_TFree) livess; |
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453 val resDs = (case resBs of NONE => [] | SOME Ts => fold (subtract (op =)) Ass Ts); |
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454 val Ds = fold (fold Term.add_tfreesT) deadss []; |
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455 |
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456 val _ = (case Library.inter (op =) Ds lhss of [] => () |
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457 | A :: _ => error ("Inadmissible type recursion (cannot take fixed point of dead type \ |
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458 \variable " ^ quote (Syntax.string_of_typ lthy (TFree A)) ^ ")")); |
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459 |
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460 val timer = time (timer "Construction of BNFs"); |
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461 |
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462 val ((kill_poss, _), (bnfs', (unfold_set', lthy'))) = |
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463 normalize_bnfs qualify Ass Ds sort bnfs unfold_set lthy; |
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464 |
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465 val Dss = map3 (append oo map o nth) livess kill_poss deadss; |
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466 |
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467 val ((bnfs'', deadss), lthy'') = |
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468 fold_map3 (seal_bnf unfold_set') (map (Binding.prefix_name preN) bs) Dss bnfs' lthy' |
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469 |>> split_list; |
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470 |
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471 val timer = time (timer "Normalization & sealing of BNFs"); |
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472 |
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473 val res = construct_fp resBs bs map_bs rel_bs set_bss (map TFree resDs, deadss) bnfs'' lthy''; |
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474 |
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475 val timer = time (timer "FP construction in total"); |
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476 in |
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477 timer; (bnfs'', res) |
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478 end; |
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479 |
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480 fun fp_bnf construct_fp bs mixfixes map_bs rel_bs set_bss resBs eqs lthy = |
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481 let |
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482 val timer = time (Timer.startRealTimer ()); |
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483 val (lhss, rhss) = split_list eqs; |
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484 val sort = fp_sort lhss (SOME resBs); |
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485 fun qualify b = Binding.qualify true (Binding.name_of (Binding.prefix_name rawN b)); |
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486 val ((bnfs, (Dss, Ass)), (unfold_set, lthy')) = apfst (apsnd split_list o split_list) |
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487 (fold_map2 (fn b => bnf_of_typ Smart_Inline (qualify b) sort) bs rhss |
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488 (empty_unfolds, lthy)); |
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489 in |
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490 mk_fp_bnf timer (construct_fp mixfixes) (SOME resBs) bs map_bs rel_bs set_bss sort lhss bnfs Dss |
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491 Ass unfold_set lthy' |
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492 end; |
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493 |
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494 end; |
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