1 (* Title: HOL/Tools/datatype_package.ML |
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2 Author: Stefan Berghofer, TU Muenchen |
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3 |
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4 Datatype package for Isabelle/HOL. |
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5 *) |
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6 |
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7 signature DATATYPE_PACKAGE = |
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8 sig |
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9 val quiet_mode : bool ref |
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10 val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table |
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11 val print_datatypes : theory -> unit |
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12 val get_datatype : theory -> string -> DatatypeAux.datatype_info option |
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13 val the_datatype : theory -> string -> DatatypeAux.datatype_info |
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14 val datatype_of_constr : theory -> string -> DatatypeAux.datatype_info option |
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15 val datatype_of_case : theory -> string -> DatatypeAux.datatype_info option |
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16 val the_datatype_spec : theory -> string -> (string * sort) list * (string * typ list) list |
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17 val get_datatype_constrs : theory -> string -> (string * typ) list option |
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18 val construction_interpretation : theory |
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19 -> {atom : typ -> 'a, dtyp : string -> 'a, rtyp : string * typ list -> 'a list -> 'a} |
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20 -> (string * sort) list -> string list |
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21 -> (string * (string * 'a list) list) list |
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22 * ((string * typ list) * (string * 'a list) list) list |
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23 val distinct_simproc : simproc |
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24 val make_case : Proof.context -> bool -> string list -> term -> |
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25 (term * term) list -> term * (term * (int * bool)) list |
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26 val strip_case : Proof.context -> bool -> term -> (term * (term * term) list) option |
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27 val read_typ: theory -> |
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28 (typ list * (string * sort) list) * string -> typ list * (string * sort) list |
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29 val interpretation : (string list -> theory -> theory) -> theory -> theory |
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30 val rep_datatype : ({distinct : thm list list, |
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31 inject : thm list list, |
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32 exhaustion : thm list, |
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33 rec_thms : thm list, |
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34 case_thms : thm list list, |
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35 split_thms : (thm * thm) list, |
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36 induction : thm, |
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37 simps : thm list} -> Proof.context -> Proof.context) -> string list option -> term list |
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38 -> theory -> Proof.state; |
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39 val rep_datatype_cmd : string list option -> string list -> theory -> Proof.state; |
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40 val add_datatype : bool -> bool -> string list -> (string list * binding * mixfix * |
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41 (binding * typ list * mixfix) list) list -> theory -> |
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42 {distinct : thm list list, |
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43 inject : thm list list, |
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44 exhaustion : thm list, |
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45 rec_thms : thm list, |
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46 case_thms : thm list list, |
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47 split_thms : (thm * thm) list, |
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48 induction : thm, |
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49 simps : thm list} * theory |
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50 val add_datatype_cmd : bool -> string list -> (string list * binding * mixfix * |
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51 (binding * string list * mixfix) list) list -> theory -> |
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52 {distinct : thm list list, |
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53 inject : thm list list, |
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54 exhaustion : thm list, |
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55 rec_thms : thm list, |
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56 case_thms : thm list list, |
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57 split_thms : (thm * thm) list, |
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58 induction : thm, |
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59 simps : thm list} * theory |
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60 val setup: theory -> theory |
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61 end; |
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62 |
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63 structure DatatypePackage : DATATYPE_PACKAGE = |
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64 struct |
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65 |
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66 open DatatypeAux; |
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67 |
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68 val quiet_mode = quiet_mode; |
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69 |
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70 |
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71 (* theory data *) |
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72 |
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73 structure DatatypesData = TheoryDataFun |
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74 ( |
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75 type T = |
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76 {types: datatype_info Symtab.table, |
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77 constrs: datatype_info Symtab.table, |
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78 cases: datatype_info Symtab.table}; |
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79 |
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80 val empty = |
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81 {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty}; |
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82 val copy = I; |
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83 val extend = I; |
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84 fun merge _ |
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85 ({types = types1, constrs = constrs1, cases = cases1}, |
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86 {types = types2, constrs = constrs2, cases = cases2}) = |
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87 {types = Symtab.merge (K true) (types1, types2), |
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88 constrs = Symtab.merge (K true) (constrs1, constrs2), |
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89 cases = Symtab.merge (K true) (cases1, cases2)}; |
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90 ); |
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91 |
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92 val get_datatypes = #types o DatatypesData.get; |
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93 val map_datatypes = DatatypesData.map; |
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94 |
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95 fun print_datatypes thy = |
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96 Pretty.writeln (Pretty.strs ("datatypes:" :: |
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97 map #1 (NameSpace.extern_table (Sign.type_space thy, get_datatypes thy)))); |
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98 |
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99 |
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100 (** theory information about datatypes **) |
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101 |
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102 fun put_dt_infos (dt_infos : (string * datatype_info) list) = |
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103 map_datatypes (fn {types, constrs, cases} => |
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104 {types = fold Symtab.update dt_infos types, |
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105 constrs = fold Symtab.default (*conservative wrt. overloaded constructors*) |
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106 (maps (fn (_, info as {descr, index, ...}) => map (rpair info o fst) |
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107 (#3 (the (AList.lookup op = descr index)))) dt_infos) constrs, |
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108 cases = fold Symtab.update |
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109 (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos) |
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110 cases}); |
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111 |
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112 val get_datatype = Symtab.lookup o get_datatypes; |
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113 |
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114 fun the_datatype thy name = (case get_datatype thy name of |
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115 SOME info => info |
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116 | NONE => error ("Unknown datatype " ^ quote name)); |
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117 |
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118 val datatype_of_constr = Symtab.lookup o #constrs o DatatypesData.get; |
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119 val datatype_of_case = Symtab.lookup o #cases o DatatypesData.get; |
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120 |
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121 fun get_datatype_descr thy dtco = |
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122 get_datatype thy dtco |
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123 |> Option.map (fn info as { descr, index, ... } => |
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124 (info, (((fn SOME (_, dtys, cos) => (dtys, cos)) o AList.lookup (op =) descr) index))); |
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125 |
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126 fun the_datatype_spec thy dtco = |
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127 let |
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128 val info as { descr, index, sorts = raw_sorts, ... } = the_datatype thy dtco; |
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129 val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr index; |
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130 val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v)) |
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131 o DatatypeAux.dest_DtTFree) dtys; |
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132 val cos = map |
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133 (fn (co, tys) => (co, map (DatatypeAux.typ_of_dtyp descr sorts) tys)) raw_cos; |
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134 in (sorts, cos) end; |
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135 |
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136 fun get_datatype_constrs thy dtco = |
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137 case try (the_datatype_spec thy) dtco |
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138 of SOME (sorts, cos) => |
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139 let |
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140 fun subst (v, sort) = TVar ((v, 0), sort); |
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141 fun subst_ty (TFree v) = subst v |
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142 | subst_ty ty = ty; |
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143 val dty = Type (dtco, map subst sorts); |
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144 fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty); |
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145 in SOME (map mk_co cos) end |
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146 | NONE => NONE; |
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147 |
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148 fun construction_interpretation thy { atom, dtyp, rtyp } sorts tycos = |
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149 let |
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150 val descr = (#descr o the_datatype thy o hd) tycos; |
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151 val k = length tycos; |
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152 val descr_of = the o AList.lookup (op =) descr; |
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153 val typ_of_dtyp = typ_of_dtyp descr sorts; |
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154 fun interpT (dT as DtTFree _) = atom (typ_of_dtyp dT) |
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155 | interpT (dT as DtType (tyco, dTs)) = |
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156 let |
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157 val Ts = map typ_of_dtyp dTs; |
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158 in if is_rec_type dT |
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159 then rtyp (tyco, Ts) (map interpT dTs) |
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160 else atom (Type (tyco, Ts)) |
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161 end |
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162 | interpT (DtRec l) = if l < k then (dtyp o #1 o descr_of) l |
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163 else let |
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164 val (tyco, dTs, _) = descr_of l; |
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165 val Ts = map typ_of_dtyp dTs; |
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166 in rtyp (tyco, Ts) (map interpT dTs) end; |
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167 fun interpC (c, dTs) = (c, map interpT dTs); |
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168 fun interpD (_, (tyco, _, cs)) = (tyco, map interpC cs); |
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169 fun interpR (_, (tyco, dTs, cs)) = ((tyco, map typ_of_dtyp dTs), map interpC cs); |
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170 in chop k descr |> (apfst o map) interpD |> (apsnd o map) interpR end; |
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171 |
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172 |
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173 |
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174 (** induct method setup **) |
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175 |
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176 (* case names *) |
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177 |
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178 local |
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179 |
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180 fun dt_recs (DtTFree _) = [] |
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181 | dt_recs (DtType (_, dts)) = maps dt_recs dts |
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182 | dt_recs (DtRec i) = [i]; |
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183 |
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184 fun dt_cases (descr: descr) (_, args, constrs) = |
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185 let |
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186 fun the_bname i = Long_Name.base_name (#1 (the (AList.lookup (op =) descr i))); |
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187 val bnames = map the_bname (distinct (op =) (maps dt_recs args)); |
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188 in map (fn (c, _) => space_implode "_" (Long_Name.base_name c :: bnames)) constrs end; |
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189 |
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190 |
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191 fun induct_cases descr = |
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192 DatatypeProp.indexify_names (maps (dt_cases descr) (map #2 descr)); |
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193 |
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194 fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i)); |
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195 |
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196 in |
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197 |
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198 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr); |
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199 |
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200 fun mk_case_names_exhausts descr new = |
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201 map (RuleCases.case_names o exhaust_cases descr o #1) |
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202 (filter (fn ((_, (name, _, _))) => member (op =) new name) descr); |
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203 |
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204 end; |
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205 |
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206 fun add_rules simps case_thms rec_thms inject distinct |
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207 weak_case_congs cong_att = |
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208 PureThy.add_thmss [((Binding.name "simps", simps), []), |
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209 ((Binding.empty, flat case_thms @ |
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210 flat distinct @ rec_thms), [Simplifier.simp_add]), |
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211 ((Binding.empty, rec_thms), [Code.add_default_eqn_attribute]), |
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212 ((Binding.empty, flat inject), [iff_add]), |
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213 ((Binding.empty, map (fn th => th RS notE) (flat distinct)), [Classical.safe_elim NONE]), |
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214 ((Binding.empty, weak_case_congs), [cong_att])] |
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215 #> snd; |
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216 |
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217 |
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218 (* add_cases_induct *) |
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219 |
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220 fun add_cases_induct infos induction thy = |
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221 let |
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222 val inducts = ProjectRule.projections (ProofContext.init thy) induction; |
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223 |
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224 fun named_rules (name, {index, exhaustion, ...}: datatype_info) = |
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225 [((Binding.empty, nth inducts index), [Induct.induct_type name]), |
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226 ((Binding.empty, exhaustion), [Induct.cases_type name])]; |
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227 fun unnamed_rule i = |
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228 ((Binding.empty, nth inducts i), [Thm.kind_internal, Induct.induct_type ""]); |
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229 in |
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230 thy |> PureThy.add_thms |
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231 (maps named_rules infos @ |
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232 map unnamed_rule (length infos upto length inducts - 1)) |> snd |
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233 |> PureThy.add_thmss [((Binding.name "inducts", inducts), [])] |> snd |
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234 end; |
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235 |
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236 |
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237 |
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238 (**** simplification procedure for showing distinctness of constructors ****) |
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239 |
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240 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T) |
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241 | stripT p = p; |
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242 |
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243 fun stripC (i, f $ x) = stripC (i + 1, f) |
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244 | stripC p = p; |
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245 |
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246 val distinctN = "constr_distinct"; |
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247 |
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248 fun distinct_rule thy ss tname eq_t = case #distinct (the_datatype thy tname) of |
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249 FewConstrs thms => Goal.prove (Simplifier.the_context ss) [] [] eq_t (K |
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250 (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1, |
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251 atac 2, resolve_tac thms 1, etac FalseE 1])) |
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252 | ManyConstrs (thm, simpset) => |
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253 let |
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254 val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] = |
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255 map (PureThy.get_thm (ThyInfo.the_theory "Datatype" thy)) |
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256 ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]; |
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257 in |
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258 Goal.prove (Simplifier.the_context ss) [] [] eq_t (K |
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259 (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1, |
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260 full_simp_tac (Simplifier.inherit_context ss simpset) 1, |
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261 REPEAT (dresolve_tac [In0_inject, In1_inject] 1), |
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262 eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1, |
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263 etac FalseE 1])) |
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264 end; |
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265 |
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266 fun distinct_proc thy ss (t as Const ("op =", _) $ t1 $ t2) = |
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267 (case (stripC (0, t1), stripC (0, t2)) of |
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268 ((i, Const (cname1, T1)), (j, Const (cname2, T2))) => |
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269 (case (stripT (0, T1), stripT (0, T2)) of |
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270 ((i', Type (tname1, _)), (j', Type (tname2, _))) => |
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271 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then |
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272 (case (get_datatype_descr thy) tname1 of |
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273 SOME (_, (_, constrs)) => let val cnames = map fst constrs |
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274 in if cname1 mem cnames andalso cname2 mem cnames then |
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275 SOME (distinct_rule thy ss tname1 |
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276 (Logic.mk_equals (t, Const ("False", HOLogic.boolT)))) |
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277 else NONE |
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278 end |
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279 | NONE => NONE) |
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280 else NONE |
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281 | _ => NONE) |
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282 | _ => NONE) |
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283 | distinct_proc _ _ _ = NONE; |
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284 |
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285 val distinct_simproc = |
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286 Simplifier.simproc @{theory HOL} distinctN ["s = t"] distinct_proc; |
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287 |
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288 val dist_ss = HOL_ss addsimprocs [distinct_simproc]; |
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289 |
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290 val simproc_setup = |
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291 Simplifier.map_simpset (fn ss => ss addsimprocs [distinct_simproc]); |
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292 |
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293 |
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294 (**** translation rules for case ****) |
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295 |
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296 fun make_case ctxt = DatatypeCase.make_case |
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297 (datatype_of_constr (ProofContext.theory_of ctxt)) ctxt; |
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298 |
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299 fun strip_case ctxt = DatatypeCase.strip_case |
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300 (datatype_of_case (ProofContext.theory_of ctxt)); |
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301 |
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302 fun add_case_tr' case_names thy = |
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303 Sign.add_advanced_trfuns ([], [], |
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304 map (fn case_name => |
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305 let val case_name' = Sign.const_syntax_name thy case_name |
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306 in (case_name', DatatypeCase.case_tr' datatype_of_case case_name') |
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307 end) case_names, []) thy; |
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308 |
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309 val trfun_setup = |
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310 Sign.add_advanced_trfuns ([], |
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311 [("_case_syntax", DatatypeCase.case_tr true datatype_of_constr)], |
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312 [], []); |
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313 |
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314 |
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315 (* prepare types *) |
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316 |
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317 fun read_typ thy ((Ts, sorts), str) = |
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318 let |
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319 val ctxt = ProofContext.init thy |
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320 |> fold (Variable.declare_typ o TFree) sorts; |
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321 val T = Syntax.read_typ ctxt str; |
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322 in (Ts @ [T], Term.add_tfreesT T sorts) end; |
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323 |
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324 fun cert_typ sign ((Ts, sorts), raw_T) = |
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325 let |
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326 val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle |
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327 TYPE (msg, _, _) => error msg; |
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328 val sorts' = Term.add_tfreesT T sorts; |
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329 in (Ts @ [T], |
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330 case duplicates (op =) (map fst sorts') of |
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331 [] => sorts' |
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332 | dups => error ("Inconsistent sort constraints for " ^ commas dups)) |
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333 end; |
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334 |
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335 |
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336 (**** make datatype info ****) |
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337 |
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338 fun make_dt_info alt_names descr sorts induct reccomb_names rec_thms |
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339 (((((((((i, (_, (tname, _, _))), case_name), case_thms), |
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340 exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) = |
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341 (tname, |
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342 {index = i, |
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343 alt_names = alt_names, |
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344 descr = descr, |
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345 sorts = sorts, |
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346 rec_names = reccomb_names, |
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347 rec_rewrites = rec_thms, |
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348 case_name = case_name, |
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349 case_rewrites = case_thms, |
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350 induction = induct, |
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351 exhaustion = exhaustion_thm, |
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352 distinct = distinct_thm, |
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353 inject = inject, |
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354 nchotomy = nchotomy, |
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355 case_cong = case_cong, |
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356 weak_case_cong = weak_case_cong}); |
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357 |
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358 structure DatatypeInterpretation = InterpretationFun(type T = string list val eq = op =); |
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359 val interpretation = DatatypeInterpretation.interpretation; |
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360 |
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361 |
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362 (******************* definitional introduction of datatypes *******************) |
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363 |
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364 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info |
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365 case_names_induct case_names_exhausts thy = |
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366 let |
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367 val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names); |
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368 |
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369 val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |> |
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370 DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts |
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371 types_syntax constr_syntax case_names_induct; |
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372 |
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373 val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr |
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374 sorts induct case_names_exhausts thy2; |
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375 val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms |
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376 flat_names new_type_names descr sorts dt_info inject dist_rewrites |
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377 (Simplifier.theory_context thy3 dist_ss) induct thy3; |
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378 val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms |
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379 flat_names new_type_names descr sorts reccomb_names rec_thms thy4; |
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380 val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names |
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381 descr sorts inject dist_rewrites casedist_thms case_thms thy6; |
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382 val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names |
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383 descr sorts casedist_thms thy7; |
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384 val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names |
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385 descr sorts nchotomys case_thms thy8; |
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386 val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names |
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387 descr sorts thy9; |
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388 |
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389 val dt_infos = map |
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390 (make_dt_info (SOME new_type_names) (flat descr) sorts induct reccomb_names rec_thms) |
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391 ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~ |
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392 casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs); |
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393 |
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394 val simps = flat (distinct @ inject @ case_thms) @ rec_thms; |
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395 |
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396 val thy12 = |
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397 thy10 |
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398 |> add_case_tr' case_names |
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399 |> Sign.add_path (space_implode "_" new_type_names) |
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400 |> add_rules simps case_thms rec_thms inject distinct |
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401 weak_case_congs (Simplifier.attrib (op addcongs)) |
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402 |> put_dt_infos dt_infos |
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403 |> add_cases_induct dt_infos induct |
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404 |> Sign.parent_path |
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405 |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd |
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406 |> DatatypeInterpretation.data (map fst dt_infos); |
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407 in |
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408 ({distinct = distinct, |
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409 inject = inject, |
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410 exhaustion = casedist_thms, |
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411 rec_thms = rec_thms, |
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412 case_thms = case_thms, |
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413 split_thms = split_thms, |
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414 induction = induct, |
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415 simps = simps}, thy12) |
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416 end; |
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417 |
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418 |
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419 (*********************** declare existing type as datatype *********************) |
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420 |
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421 fun prove_rep_datatype alt_names new_type_names descr sorts induct inject half_distinct thy = |
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422 let |
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423 val ((_, [induct']), _) = |
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424 Variable.importT_thms [induct] (Variable.thm_context induct); |
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425 |
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426 fun err t = error ("Ill-formed predicate in induction rule: " ^ |
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427 Syntax.string_of_term_global thy t); |
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428 |
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429 fun get_typ (t as _ $ Var (_, Type (tname, Ts))) = |
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430 ((tname, map (fst o dest_TFree) Ts) handle TERM _ => err t) |
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431 | get_typ t = err t; |
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432 val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induct'))); |
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433 |
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434 val dt_info = get_datatypes thy; |
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435 |
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436 val distinct = (map o maps) (fn thm => [thm, thm RS not_sym]) half_distinct; |
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437 val (case_names_induct, case_names_exhausts) = |
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438 (mk_case_names_induct descr, mk_case_names_exhausts descr (map #1 dtnames)); |
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439 |
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440 val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names); |
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441 |
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442 val (casedist_thms, thy2) = thy |> |
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443 DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induct |
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444 case_names_exhausts; |
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445 val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms |
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446 false new_type_names [descr] sorts dt_info inject distinct |
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447 (Simplifier.theory_context thy2 dist_ss) induct thy2; |
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448 val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false |
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449 new_type_names [descr] sorts reccomb_names rec_thms thy3; |
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450 val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms |
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451 new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4; |
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452 val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names |
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453 [descr] sorts casedist_thms thy5; |
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454 val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names |
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455 [descr] sorts nchotomys case_thms thy6; |
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456 val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names |
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457 [descr] sorts thy7; |
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458 |
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459 val ((_, [induct']), thy10) = |
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460 thy8 |
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461 |> store_thmss "inject" new_type_names inject |
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462 ||>> store_thmss "distinct" new_type_names distinct |
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463 ||> Sign.add_path (space_implode "_" new_type_names) |
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464 ||>> PureThy.add_thms [((Binding.name "induct", induct), [case_names_induct])]; |
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465 |
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466 val dt_infos = map (make_dt_info alt_names descr sorts induct' reccomb_names rec_thms) |
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467 ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~ |
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468 map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs); |
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469 |
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470 val simps = flat (distinct @ inject @ case_thms) @ rec_thms; |
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471 |
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472 val thy11 = |
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473 thy10 |
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474 |> add_case_tr' case_names |
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475 |> add_rules simps case_thms rec_thms inject distinct |
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476 weak_case_congs (Simplifier.attrib (op addcongs)) |
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477 |> put_dt_infos dt_infos |
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478 |> add_cases_induct dt_infos induct' |
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479 |> Sign.parent_path |
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480 |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |
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481 |> snd |
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482 |> DatatypeInterpretation.data (map fst dt_infos); |
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483 in |
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484 ({distinct = distinct, |
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485 inject = inject, |
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486 exhaustion = casedist_thms, |
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487 rec_thms = rec_thms, |
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488 case_thms = case_thms, |
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489 split_thms = split_thms, |
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490 induction = induct', |
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491 simps = simps}, thy11) |
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492 end; |
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493 |
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494 fun gen_rep_datatype prep_term after_qed alt_names raw_ts thy = |
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495 let |
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496 fun constr_of_term (Const (c, T)) = (c, T) |
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497 | constr_of_term t = |
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498 error ("Not a constant: " ^ Syntax.string_of_term_global thy t); |
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499 fun no_constr (c, T) = error ("Bad constructor: " |
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500 ^ Sign.extern_const thy c ^ "::" |
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501 ^ Syntax.string_of_typ_global thy T); |
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502 fun type_of_constr (cT as (_, T)) = |
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503 let |
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504 val frees = OldTerm.typ_tfrees T; |
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505 val (tyco, vs) = ((apsnd o map) (dest_TFree) o dest_Type o snd o strip_type) T |
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506 handle TYPE _ => no_constr cT |
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507 val _ = if has_duplicates (eq_fst (op =)) vs then no_constr cT else (); |
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508 val _ = if length frees <> length vs then no_constr cT else (); |
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509 in (tyco, (vs, cT)) end; |
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510 |
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511 val raw_cs = AList.group (op =) (map (type_of_constr o constr_of_term o prep_term thy) raw_ts); |
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512 val _ = case map_filter (fn (tyco, _) => |
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513 if Symtab.defined (get_datatypes thy) tyco then SOME tyco else NONE) raw_cs |
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514 of [] => () |
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515 | tycos => error ("Type(s) " ^ commas (map quote tycos) |
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516 ^ " already represented inductivly"); |
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517 val raw_vss = maps (map (map snd o fst) o snd) raw_cs; |
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518 val ms = case distinct (op =) (map length raw_vss) |
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519 of [n] => 0 upto n - 1 |
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520 | _ => error ("Different types in given constructors"); |
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521 fun inter_sort m = map (fn xs => nth xs m) raw_vss |
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522 |> Library.foldr1 (Sorts.inter_sort (Sign.classes_of thy)) |
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523 val sorts = map inter_sort ms; |
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524 val vs = Name.names Name.context Name.aT sorts; |
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525 |
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526 fun norm_constr (raw_vs, (c, T)) = (c, map_atyps |
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527 (TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T); |
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528 |
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529 val cs = map (apsnd (map norm_constr)) raw_cs; |
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530 val dtyps_of_typ = map (dtyp_of_typ (map (rpair (map fst vs) o fst) cs)) |
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531 o fst o strip_type; |
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532 val new_type_names = map Long_Name.base_name (the_default (map fst cs) alt_names); |
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533 |
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534 fun mk_spec (i, (tyco, constr)) = (i, (tyco, |
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535 map (DtTFree o fst) vs, |
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536 (map o apsnd) dtyps_of_typ constr)) |
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537 val descr = map_index mk_spec cs; |
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538 val injs = DatatypeProp.make_injs [descr] vs; |
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539 val half_distincts = map snd (DatatypeProp.make_distincts [descr] vs); |
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540 val ind = DatatypeProp.make_ind [descr] vs; |
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541 val rules = (map o map o map) Logic.close_form [[[ind]], injs, half_distincts]; |
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542 |
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543 fun after_qed' raw_thms = |
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544 let |
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545 val [[[induct]], injs, half_distincts] = |
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546 unflat rules (map Drule.zero_var_indexes_list raw_thms); |
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547 (*FIXME somehow dubious*) |
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548 in |
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549 ProofContext.theory_result |
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550 (prove_rep_datatype alt_names new_type_names descr vs induct injs half_distincts) |
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551 #-> after_qed |
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552 end; |
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553 in |
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554 thy |
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555 |> ProofContext.init |
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556 |> Proof.theorem_i NONE after_qed' ((map o map) (rpair []) (flat rules)) |
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557 end; |
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558 |
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559 val rep_datatype = gen_rep_datatype Sign.cert_term; |
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560 val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global (K I); |
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561 |
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562 |
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563 |
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564 (******************************** add datatype ********************************) |
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565 |
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566 fun gen_add_datatype prep_typ err flat_names new_type_names dts thy = |
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567 let |
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568 val _ = Theory.requires thy "Datatype" "datatype definitions"; |
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569 |
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570 (* this theory is used just for parsing *) |
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571 |
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572 val tmp_thy = thy |> |
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573 Theory.copy |> |
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574 Sign.add_types (map (fn (tvs, tname, mx, _) => |
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575 (tname, length tvs, mx)) dts); |
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576 |
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577 val (tyvars, _, _, _)::_ = dts; |
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578 val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) => |
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579 let val full_tname = Sign.full_name tmp_thy (Binding.map_name (Syntax.type_name mx) tname) |
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580 in (case duplicates (op =) tvs of |
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581 [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx)) |
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582 else error ("Mutually recursive datatypes must have same type parameters") |
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583 | dups => error ("Duplicate parameter(s) for datatype " ^ quote (Binding.str_of tname) ^ |
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584 " : " ^ commas dups)) |
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585 end) dts); |
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586 |
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587 val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of |
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588 [] => () | dups => error ("Duplicate datatypes: " ^ commas dups)); |
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589 |
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590 fun prep_dt_spec ((tvs, tname, mx, constrs), tname') (dts', constr_syntax, sorts, i) = |
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591 let |
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592 fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') = |
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593 let |
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594 val (cargs', sorts'') = Library.foldl (prep_typ tmp_thy) (([], sorts'), cargs); |
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595 val _ = (case fold (curry OldTerm.add_typ_tfree_names) cargs' [] \\ tvs of |
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596 [] => () |
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597 | vs => error ("Extra type variables on rhs: " ^ commas vs)) |
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598 in (constrs @ [((if flat_names then Sign.full_name tmp_thy else |
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599 Sign.full_name_path tmp_thy tname') |
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600 (Binding.map_name (Syntax.const_name mx') cname), |
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601 map (dtyp_of_typ new_dts) cargs')], |
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602 constr_syntax' @ [(cname, mx')], sorts'') |
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603 end handle ERROR msg => cat_error msg |
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604 ("The error above occured in constructor " ^ quote (Binding.str_of cname) ^ |
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605 " of datatype " ^ quote (Binding.str_of tname)); |
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606 |
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607 val (constrs', constr_syntax', sorts') = |
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608 fold prep_constr constrs ([], [], sorts) |
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609 |
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610 in |
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611 case duplicates (op =) (map fst constrs') of |
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612 [] => |
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613 (dts' @ [(i, (Sign.full_name tmp_thy (Binding.map_name (Syntax.type_name mx) tname), |
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614 map DtTFree tvs, constrs'))], |
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615 constr_syntax @ [constr_syntax'], sorts', i + 1) |
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616 | dups => error ("Duplicate constructors " ^ commas dups ^ |
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617 " in datatype " ^ quote (Binding.str_of tname)) |
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618 end; |
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619 |
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620 val (dts', constr_syntax, sorts', i) = |
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621 fold prep_dt_spec (dts ~~ new_type_names) ([], [], [], 0); |
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622 val sorts = sorts' @ (map (rpair (Sign.defaultS tmp_thy)) (tyvars \\ map fst sorts')); |
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623 val dt_info = get_datatypes thy; |
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624 val (descr, _) = unfold_datatypes tmp_thy dts' sorts dt_info dts' i; |
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625 val _ = check_nonempty descr handle (exn as Datatype_Empty s) => |
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626 if err then error ("Nonemptiness check failed for datatype " ^ s) |
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627 else raise exn; |
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628 |
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629 val descr' = flat descr; |
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630 val case_names_induct = mk_case_names_induct descr'; |
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631 val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts); |
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632 in |
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633 add_datatype_def |
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634 flat_names new_type_names descr sorts types_syntax constr_syntax dt_info |
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635 case_names_induct case_names_exhausts thy |
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636 end; |
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637 |
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638 val add_datatype = gen_add_datatype cert_typ; |
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639 val add_datatype_cmd = gen_add_datatype read_typ true; |
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640 |
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641 |
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642 |
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643 (** package setup **) |
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644 |
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645 (* setup theory *) |
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646 |
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647 val setup = |
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648 DatatypeRepProofs.distinctness_limit_setup #> |
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649 simproc_setup #> |
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650 trfun_setup #> |
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651 DatatypeInterpretation.init; |
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652 |
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653 |
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654 (* outer syntax *) |
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655 |
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656 local structure P = OuterParse and K = OuterKeyword in |
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657 |
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658 val datatype_decl = |
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659 Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.binding -- P.opt_infix -- |
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660 (P.$$$ "=" |-- P.enum1 "|" (P.binding -- Scan.repeat P.typ -- P.opt_mixfix)); |
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661 |
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662 fun mk_datatype args = |
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663 let |
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664 val names = map |
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665 (fn ((((NONE, _), t), _), _) => Binding.name_of t | ((((SOME t, _), _), _), _) => t) args; |
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666 val specs = map (fn ((((_, vs), t), mx), cons) => |
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667 (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args; |
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668 in snd o add_datatype_cmd false names specs end; |
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669 |
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670 val _ = |
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671 OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl |
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672 (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype)); |
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673 |
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674 val _ = |
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675 OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_goal |
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676 (Scan.option (P.$$$ "(" |-- Scan.repeat1 P.name --| P.$$$ ")") -- Scan.repeat1 P.term |
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677 >> (fn (alt_names, ts) => Toplevel.print |
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678 o Toplevel.theory_to_proof (rep_datatype_cmd alt_names ts))); |
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679 |
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680 end; |
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681 |
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682 |
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683 (* document antiquotation *) |
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684 |
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685 val _ = ThyOutput.antiquotation "datatype" Args.tyname |
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686 (fn {source = src, context = ctxt, ...} => fn dtco => |
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687 let |
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688 val thy = ProofContext.theory_of ctxt; |
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689 val (vs, cos) = the_datatype_spec thy dtco; |
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690 val ty = Type (dtco, map TFree vs); |
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691 fun pretty_typ_bracket (ty as Type (_, _ :: _)) = |
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692 Pretty.enclose "(" ")" [Syntax.pretty_typ ctxt ty] |
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693 | pretty_typ_bracket ty = |
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694 Syntax.pretty_typ ctxt ty; |
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695 fun pretty_constr (co, tys) = |
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696 (Pretty.block o Pretty.breaks) |
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697 (Syntax.pretty_term ctxt (Const (co, tys ---> ty)) :: |
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698 map pretty_typ_bracket tys); |
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699 val pretty_datatype = |
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700 Pretty.block |
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701 (Pretty.command "datatype" :: Pretty.brk 1 :: |
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702 Syntax.pretty_typ ctxt ty :: |
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703 Pretty.str " =" :: Pretty.brk 1 :: |
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704 flat (separate [Pretty.brk 1, Pretty.str "| "] |
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705 (map (single o pretty_constr) cos))); |
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706 in ThyOutput.output (ThyOutput.maybe_pretty_source (K pretty_datatype) src [()]) end); |
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707 |
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708 end; |
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709 |
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