1 (* Title: HOL/Tools/datatype.ML |
1 (* Title: HOL/Tools/datatype.ML |
2 Author: Stefan Berghofer, TU Muenchen |
2 Author: Stefan Berghofer, TU Muenchen |
3 |
3 |
4 Datatype package for Isabelle/HOL. |
4 Datatype package interface for Isabelle/HOL. |
5 *) |
5 *) |
6 |
6 |
7 signature DATATYPE = |
7 signature DATATYPE = |
8 sig |
8 sig |
9 include DATATYPE_COMMON |
9 include DATATYPE_DATA |
10 val derive_datatype_props : config -> string list -> string list option |
10 include DATATYPE_REP_PROOFS |
11 -> descr list -> (string * sort) list -> thm -> thm list list -> thm list list |
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12 -> theory -> string list * theory |
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13 val rep_datatype : config -> (string list -> Proof.context -> Proof.context) |
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14 -> string list option -> term list -> theory -> Proof.state |
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15 val rep_datatype_cmd : string list option -> string list -> theory -> Proof.state |
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16 val get_info : theory -> string -> info option |
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17 val the_info : theory -> string -> info |
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18 val the_descr : theory -> string list |
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19 -> descr * (string * sort) list * string list |
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20 * string * (string list * string list) * (typ list * typ list) |
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21 val the_spec : theory -> string -> (string * sort) list * (string * typ list) list |
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22 val all_distincts : theory -> typ list -> thm list list |
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23 val get_constrs : theory -> string -> (string * typ) list option |
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24 val get_all : theory -> info Symtab.table |
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25 val info_of_constr : theory -> string * typ -> info option |
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26 val info_of_case : theory -> string -> info option |
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27 val interpretation : (config -> string list -> theory -> theory) -> theory -> theory |
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28 val make_case : Proof.context -> DatatypeCase.config -> string list -> term -> |
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29 (term * term) list -> term * (term * (int * bool)) list |
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30 val strip_case : Proof.context -> bool -> term -> (term * (term * term) list) option |
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31 val read_typ: theory -> string -> (string * sort) list -> typ * (string * sort) list |
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32 val cert_typ: theory -> typ -> (string * sort) list -> typ * (string * sort) list |
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33 val mk_case_names_induct: descr -> attribute |
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34 val setup: theory -> theory |
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35 end; |
11 end; |
36 |
12 |
37 structure Datatype : DATATYPE = |
13 structure Datatype = |
38 struct |
14 struct |
39 |
15 |
40 open DatatypeAux; |
16 open Datatype_Data; |
41 |
17 open DatatypeRepProofs; |
42 (** theory data **) |
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43 |
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44 (* data management *) |
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45 |
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46 structure DatatypesData = Theory_Data |
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47 ( |
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48 type T = |
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49 {types: info Symtab.table, |
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50 constrs: (string * info) list Symtab.table, |
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51 cases: info Symtab.table}; |
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52 |
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53 val empty = |
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54 {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty}; |
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55 val extend = I; |
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56 fun merge |
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57 ({types = types1, constrs = constrs1, cases = cases1}, |
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58 {types = types2, constrs = constrs2, cases = cases2}) : T = |
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59 {types = Symtab.merge (K true) (types1, types2), |
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60 constrs = Symtab.join (K (AList.merge (op =) (K true))) (constrs1, constrs2), |
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61 cases = Symtab.merge (K true) (cases1, cases2)}; |
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62 ); |
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63 |
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64 val get_all = #types o DatatypesData.get; |
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65 val get_info = Symtab.lookup o get_all; |
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66 |
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67 fun the_info thy name = |
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68 (case get_info thy name of |
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69 SOME info => info |
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70 | NONE => error ("Unknown datatype " ^ quote name)); |
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71 |
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72 fun info_of_constr thy (c, T) = |
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73 let |
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74 val tab = Symtab.lookup_list ((#constrs o DatatypesData.get) thy) c; |
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75 val hint = case strip_type T of (_, Type (tyco, _)) => SOME tyco | _ => NONE; |
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76 val default = if null tab then NONE |
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77 else SOME (snd (Library.last_elem tab)) |
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78 (*conservative wrt. overloaded constructors*); |
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79 in case hint |
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80 of NONE => default |
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81 | SOME tyco => case AList.lookup (op =) tab tyco |
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82 of NONE => default (*permissive*) |
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83 | SOME info => SOME info |
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84 end; |
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85 |
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86 val info_of_case = Symtab.lookup o #cases o DatatypesData.get; |
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87 |
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88 fun register (dt_infos : (string * info) list) = |
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89 DatatypesData.map (fn {types, constrs, cases} => |
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90 {types = types |> fold Symtab.update dt_infos, |
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91 constrs = constrs |> fold (fn (constr, dtname_info) => |
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92 Symtab.map_default (constr, []) (cons dtname_info)) |
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93 (maps (fn (dtname, info as {descr, index, ...}) => |
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94 map (rpair (dtname, info) o fst) |
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95 (#3 (the (AList.lookup op = descr index)))) dt_infos), |
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96 cases = cases |> fold Symtab.update |
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97 (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos)}); |
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98 |
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99 |
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100 (* complex queries *) |
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101 |
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102 fun the_spec thy dtco = |
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103 let |
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104 val info as { descr, index, sorts = raw_sorts, ... } = the_info thy dtco; |
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105 val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr index; |
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106 val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v)) |
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107 o DatatypeAux.dest_DtTFree) dtys; |
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108 val cos = map |
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109 (fn (co, tys) => (co, map (DatatypeAux.typ_of_dtyp descr sorts) tys)) raw_cos; |
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110 in (sorts, cos) end; |
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111 |
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112 fun the_descr thy (raw_tycos as raw_tyco :: _) = |
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113 let |
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114 val info = the_info thy raw_tyco; |
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115 val descr = #descr info; |
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116 |
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117 val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr (#index info); |
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118 val vs = map ((fn v => (v, (the o AList.lookup (op =) (#sorts info)) v)) |
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119 o dest_DtTFree) dtys; |
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120 |
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121 fun is_DtTFree (DtTFree _) = true |
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122 | is_DtTFree _ = false |
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123 val k = find_index (fn (_, (_, dTs, _)) => not (forall is_DtTFree dTs)) descr; |
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124 val protoTs as (dataTs, _) = chop k descr |
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125 |> (pairself o map) (fn (_, (tyco, dTs, _)) => (tyco, map (typ_of_dtyp descr vs) dTs)); |
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126 |
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127 val tycos = map fst dataTs; |
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128 val _ = if eq_set (op =) (tycos, raw_tycos) then () |
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129 else error ("Type constructors " ^ commas (map quote raw_tycos) |
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130 ^ " do not belong exhaustively to one mutual recursive datatype"); |
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131 |
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132 val (Ts, Us) = (pairself o map) Type protoTs; |
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133 |
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134 val names = map Long_Name.base_name (the_default tycos (#alt_names info)); |
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135 val (auxnames, _) = Name.make_context names |
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136 |> fold_map (yield_singleton Name.variants o name_of_typ) Us; |
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137 val prefix = space_implode "_" names; |
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138 |
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139 in (descr, vs, tycos, prefix, (names, auxnames), (Ts, Us)) end; |
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140 |
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141 fun all_distincts thy Ts = |
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142 let |
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143 fun add_tycos (Type (tyco, Ts)) = insert (op =) tyco #> fold add_tycos Ts |
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144 | add_tycos _ = I; |
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145 val tycos = fold add_tycos Ts []; |
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146 in map_filter (Option.map #distinct o get_info thy) tycos end; |
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147 |
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148 fun get_constrs thy dtco = |
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149 case try (the_spec thy) dtco |
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150 of SOME (sorts, cos) => |
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151 let |
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152 fun subst (v, sort) = TVar ((v, 0), sort); |
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153 fun subst_ty (TFree v) = subst v |
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154 | subst_ty ty = ty; |
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155 val dty = Type (dtco, map subst sorts); |
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156 fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty); |
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157 in SOME (map mk_co cos) end |
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158 | NONE => NONE; |
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159 |
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160 |
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161 |
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162 (** various auxiliary **) |
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163 |
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164 (* prepare datatype specifications *) |
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165 |
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166 fun read_typ thy str sorts = |
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167 let |
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168 val ctxt = ProofContext.init thy |
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169 |> fold (Variable.declare_typ o TFree) sorts; |
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170 val T = Syntax.read_typ ctxt str; |
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171 in (T, Term.add_tfreesT T sorts) end; |
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172 |
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173 fun cert_typ sign raw_T sorts = |
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174 let |
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175 val T = Type.no_tvars (Sign.certify_typ sign raw_T) |
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176 handle TYPE (msg, _, _) => error msg; |
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177 val sorts' = Term.add_tfreesT T sorts; |
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178 val _ = |
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179 case duplicates (op =) (map fst sorts') of |
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180 [] => () |
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181 | dups => error ("Inconsistent sort constraints for " ^ commas dups) |
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182 in (T, sorts') end; |
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183 |
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184 |
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185 (* case names *) |
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186 |
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187 local |
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188 |
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189 fun dt_recs (DtTFree _) = [] |
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190 | dt_recs (DtType (_, dts)) = maps dt_recs dts |
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191 | dt_recs (DtRec i) = [i]; |
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192 |
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193 fun dt_cases (descr: descr) (_, args, constrs) = |
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194 let |
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195 fun the_bname i = Long_Name.base_name (#1 (the (AList.lookup (op =) descr i))); |
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196 val bnames = map the_bname (distinct (op =) (maps dt_recs args)); |
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197 in map (fn (c, _) => space_implode "_" (Long_Name.base_name c :: bnames)) constrs end; |
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198 |
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199 fun induct_cases descr = |
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200 DatatypeProp.indexify_names (maps (dt_cases descr) (map #2 descr)); |
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201 |
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202 fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i)); |
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203 |
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204 in |
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205 |
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206 fun mk_case_names_induct descr = Rule_Cases.case_names (induct_cases descr); |
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207 |
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208 fun mk_case_names_exhausts descr new = |
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209 map (Rule_Cases.case_names o exhaust_cases descr o #1) |
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210 (filter (fn ((_, (name, _, _))) => member (op =) new name) descr); |
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211 |
18 |
212 end; |
19 end; |
213 |
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214 |
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215 (* translation rules for case *) |
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216 |
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217 fun make_case ctxt = DatatypeCase.make_case |
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218 (info_of_constr (ProofContext.theory_of ctxt)) ctxt; |
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219 |
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220 fun strip_case ctxt = DatatypeCase.strip_case |
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221 (info_of_case (ProofContext.theory_of ctxt)); |
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222 |
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223 fun add_case_tr' case_names thy = |
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224 Sign.add_advanced_trfuns ([], [], |
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225 map (fn case_name => |
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226 let val case_name' = Sign.const_syntax_name thy case_name |
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227 in (case_name', DatatypeCase.case_tr' info_of_case case_name') |
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228 end) case_names, []) thy; |
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229 |
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230 val trfun_setup = |
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231 Sign.add_advanced_trfuns ([], |
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232 [("_case_syntax", DatatypeCase.case_tr true info_of_constr)], |
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233 [], []); |
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234 |
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235 |
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236 |
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237 (** document antiquotation **) |
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238 |
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239 val _ = ThyOutput.antiquotation "datatype" Args.tyname |
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240 (fn {source = src, context = ctxt, ...} => fn dtco => |
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241 let |
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242 val thy = ProofContext.theory_of ctxt; |
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243 val (vs, cos) = the_spec thy dtco; |
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244 val ty = Type (dtco, map TFree vs); |
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245 fun pretty_typ_bracket (ty as Type (_, _ :: _)) = |
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246 Pretty.enclose "(" ")" [Syntax.pretty_typ ctxt ty] |
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247 | pretty_typ_bracket ty = |
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248 Syntax.pretty_typ ctxt ty; |
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249 fun pretty_constr (co, tys) = |
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250 (Pretty.block o Pretty.breaks) |
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251 (Syntax.pretty_term ctxt (Const (co, tys ---> ty)) :: |
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252 map pretty_typ_bracket tys); |
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253 val pretty_datatype = |
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254 Pretty.block |
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255 (Pretty.command "datatype" :: Pretty.brk 1 :: |
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256 Syntax.pretty_typ ctxt ty :: |
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257 Pretty.str " =" :: Pretty.brk 1 :: |
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258 flat (separate [Pretty.brk 1, Pretty.str "| "] |
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259 (map (single o pretty_constr) cos))); |
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260 in ThyOutput.output (ThyOutput.maybe_pretty_source (K pretty_datatype) src [()]) end); |
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261 |
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262 |
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263 |
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264 (** abstract theory extensions relative to a datatype characterisation **) |
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265 |
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266 structure Datatype_Interpretation = Interpretation |
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267 (type T = config * string list val eq: T * T -> bool = eq_snd op =); |
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268 fun interpretation f = Datatype_Interpretation.interpretation (uncurry f); |
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269 |
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270 fun make_dt_info alt_names descr sorts induct inducts rec_names rec_rewrites |
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271 (index, (((((((((((_, (tname, _, _))), inject), distinct), |
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272 exhaust), nchotomy), case_name), case_rewrites), case_cong), weak_case_cong), |
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273 (split, split_asm))) = |
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274 (tname, |
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275 {index = index, |
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276 alt_names = alt_names, |
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277 descr = descr, |
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278 sorts = sorts, |
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279 inject = inject, |
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280 distinct = distinct, |
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281 induct = induct, |
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282 inducts = inducts, |
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283 exhaust = exhaust, |
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284 nchotomy = nchotomy, |
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285 rec_names = rec_names, |
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286 rec_rewrites = rec_rewrites, |
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287 case_name = case_name, |
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288 case_rewrites = case_rewrites, |
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289 case_cong = case_cong, |
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290 weak_case_cong = weak_case_cong, |
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291 split = split, |
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292 split_asm = split_asm}); |
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293 |
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294 fun derive_datatype_props config dt_names alt_names descr sorts |
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295 induct inject distinct thy1 = |
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296 let |
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297 val thy2 = thy1 |> Theory.checkpoint; |
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298 val flat_descr = flat descr; |
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299 val new_type_names = map Long_Name.base_name (the_default dt_names alt_names); |
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300 val _ = message config ("Deriving properties for datatype(s) " ^ commas_quote new_type_names); |
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301 |
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302 val (exhaust, thy3) = DatatypeAbsProofs.prove_casedist_thms config new_type_names |
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303 descr sorts induct (mk_case_names_exhausts flat_descr dt_names) thy2; |
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304 val (nchotomys, thy4) = DatatypeAbsProofs.prove_nchotomys config new_type_names |
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305 descr sorts exhaust thy3; |
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306 val ((rec_names, rec_rewrites), thy5) = DatatypeAbsProofs.prove_primrec_thms |
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307 config new_type_names descr sorts (#inject o the o Symtab.lookup (get_all thy4)) |
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308 inject (distinct, all_distincts thy2 (get_rec_types flat_descr sorts)) |
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309 induct thy4; |
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310 val ((case_rewrites, case_names), thy6) = DatatypeAbsProofs.prove_case_thms |
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311 config new_type_names descr sorts rec_names rec_rewrites thy5; |
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312 val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names |
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313 descr sorts nchotomys case_rewrites thy6; |
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314 val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names |
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315 descr sorts thy7; |
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316 val (splits, thy9) = DatatypeAbsProofs.prove_split_thms |
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317 config new_type_names descr sorts inject distinct exhaust case_rewrites thy8; |
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318 |
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319 val inducts = Project_Rule.projections (ProofContext.init thy2) induct; |
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320 val dt_infos = map_index |
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321 (make_dt_info alt_names flat_descr sorts induct inducts rec_names rec_rewrites) |
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322 (hd descr ~~ inject ~~ distinct ~~ exhaust ~~ nchotomys ~~ |
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323 case_names ~~ case_rewrites ~~ case_congs ~~ weak_case_congs ~~ splits); |
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324 val dt_names = map fst dt_infos; |
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325 val prfx = Binding.qualify true (space_implode "_" new_type_names); |
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326 val simps = flat (inject @ distinct @ case_rewrites) @ rec_rewrites; |
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327 val named_rules = flat (map_index (fn (index, tname) => |
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328 [((Binding.empty, [nth inducts index]), [Induct.induct_type tname]), |
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329 ((Binding.empty, [nth exhaust index]), [Induct.cases_type tname])]) dt_names); |
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330 val unnamed_rules = map (fn induct => |
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331 ((Binding.empty, [induct]), [Rule_Cases.inner_rule, Induct.induct_type ""])) |
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332 (drop (length dt_names) inducts); |
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333 in |
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334 thy9 |
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335 |> PureThy.add_thmss ([((prfx (Binding.name "simps"), simps), []), |
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336 ((prfx (Binding.name "inducts"), inducts), []), |
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337 ((prfx (Binding.name "splits"), maps (fn (x, y) => [x, y]) splits), []), |
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338 ((Binding.empty, flat case_rewrites @ flat distinct @ rec_rewrites), |
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339 [Simplifier.simp_add]), |
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340 ((Binding.empty, rec_rewrites), [Code.add_default_eqn_attribute]), |
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341 ((Binding.empty, flat inject), [iff_add]), |
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342 ((Binding.empty, map (fn th => th RS notE) (flat distinct)), |
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343 [Classical.safe_elim NONE]), |
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344 ((Binding.empty, weak_case_congs), [Simplifier.attrib (op addcongs)])] |
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345 @ named_rules @ unnamed_rules) |
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346 |> snd |
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347 |> add_case_tr' case_names |
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348 |> register dt_infos |
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349 |> Datatype_Interpretation.data (config, dt_names) |
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350 |> pair dt_names |
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351 end; |
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352 |
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353 |
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354 |
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355 (** declare existing type as datatype **) |
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356 |
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357 fun prove_rep_datatype config dt_names alt_names descr sorts |
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358 raw_inject half_distinct raw_induct thy1 = |
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359 let |
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360 val raw_distinct = (map o maps) (fn thm => [thm, thm RS not_sym]) half_distinct; |
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361 val new_type_names = map Long_Name.base_name (the_default dt_names alt_names); |
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362 val (((inject, distinct), [induct]), thy2) = |
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363 thy1 |
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364 |> store_thmss "inject" new_type_names raw_inject |
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365 ||>> store_thmss "distinct" new_type_names raw_distinct |
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366 ||> Sign.add_path (space_implode "_" new_type_names) |
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367 ||>> PureThy.add_thms [((Binding.name "induct", raw_induct), [mk_case_names_induct descr])] |
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368 ||> Sign.restore_naming thy1; |
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369 in |
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370 thy2 |
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371 |> derive_datatype_props config dt_names alt_names [descr] sorts |
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372 induct inject distinct |
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373 end; |
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374 |
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375 fun gen_rep_datatype prep_term config after_qed alt_names raw_ts thy = |
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376 let |
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377 fun constr_of_term (Const (c, T)) = (c, T) |
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378 | constr_of_term t = |
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379 error ("Not a constant: " ^ Syntax.string_of_term_global thy t); |
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380 fun no_constr (c, T) = error ("Bad constructor: " |
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381 ^ Sign.extern_const thy c ^ "::" |
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382 ^ Syntax.string_of_typ_global thy T); |
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383 fun type_of_constr (cT as (_, T)) = |
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384 let |
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385 val frees = OldTerm.typ_tfrees T; |
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386 val (tyco, vs) = ((apsnd o map) (dest_TFree) o dest_Type o snd o strip_type) T |
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387 handle TYPE _ => no_constr cT |
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388 val _ = if has_duplicates (eq_fst (op =)) vs then no_constr cT else (); |
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389 val _ = if length frees <> length vs then no_constr cT else (); |
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390 in (tyco, (vs, cT)) end; |
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391 |
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392 val raw_cs = AList.group (op =) (map (type_of_constr o constr_of_term o prep_term thy) raw_ts); |
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393 val _ = case map_filter (fn (tyco, _) => |
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394 if Symtab.defined (get_all thy) tyco then SOME tyco else NONE) raw_cs |
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395 of [] => () |
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396 | tycos => error ("Type(s) " ^ commas (map quote tycos) |
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397 ^ " already represented inductivly"); |
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398 val raw_vss = maps (map (map snd o fst) o snd) raw_cs; |
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399 val ms = case distinct (op =) (map length raw_vss) |
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400 of [n] => 0 upto n - 1 |
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401 | _ => error ("Different types in given constructors"); |
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402 fun inter_sort m = map (fn xs => nth xs m) raw_vss |
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403 |> Library.foldr1 (Sorts.inter_sort (Sign.classes_of thy)) |
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404 val sorts = map inter_sort ms; |
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405 val vs = Name.names Name.context Name.aT sorts; |
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406 |
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407 fun norm_constr (raw_vs, (c, T)) = (c, map_atyps |
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408 (TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T); |
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409 |
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410 val cs = map (apsnd (map norm_constr)) raw_cs; |
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411 val dtyps_of_typ = map (dtyp_of_typ (map (rpair (map fst vs) o fst) cs)) |
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412 o fst o strip_type; |
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413 val dt_names = map fst cs; |
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414 |
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415 fun mk_spec (i, (tyco, constr)) = (i, (tyco, |
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416 map (DtTFree o fst) vs, |
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417 (map o apsnd) dtyps_of_typ constr)) |
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418 val descr = map_index mk_spec cs; |
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419 val injs = DatatypeProp.make_injs [descr] vs; |
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420 val half_distincts = map snd (DatatypeProp.make_distincts [descr] vs); |
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421 val ind = DatatypeProp.make_ind [descr] vs; |
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422 val rules = (map o map o map) Logic.close_form [[[ind]], injs, half_distincts]; |
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423 |
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424 fun after_qed' raw_thms = |
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425 let |
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426 val [[[raw_induct]], raw_inject, half_distinct] = |
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427 unflat rules (map Drule.zero_var_indexes_list raw_thms); |
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428 (*FIXME somehow dubious*) |
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429 in |
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430 ProofContext.theory_result |
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431 (prove_rep_datatype config dt_names alt_names descr vs |
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432 raw_inject half_distinct raw_induct) |
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433 #-> after_qed |
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434 end; |
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435 in |
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436 thy |
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437 |> ProofContext.init |
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438 |> Proof.theorem_i NONE after_qed' ((map o map) (rpair []) (flat rules)) |
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439 end; |
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440 |
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441 val rep_datatype = gen_rep_datatype Sign.cert_term; |
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442 val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global default_config (K I); |
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443 |
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444 |
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445 |
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446 (** package setup **) |
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447 |
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448 (* setup theory *) |
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449 |
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450 val setup = |
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451 trfun_setup #> |
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452 Datatype_Interpretation.init; |
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453 |
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454 |
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455 (* outer syntax *) |
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456 |
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457 local |
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458 |
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459 structure P = OuterParse and K = OuterKeyword |
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460 |
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461 in |
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462 |
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463 val _ = |
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464 OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_goal |
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465 (Scan.option (P.$$$ "(" |-- Scan.repeat1 P.name --| P.$$$ ")") -- Scan.repeat1 P.term |
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466 >> (fn (alt_names, ts) => Toplevel.print |
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467 o Toplevel.theory_to_proof (rep_datatype_cmd alt_names ts))); |
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468 |
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469 end; |
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470 |
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471 end; |
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