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1 (* Title: HOL/BNF/Tools/bnf_fp_def_sugar.ML |
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2 Author: Jasmin Blanchette, TU Muenchen |
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3 Copyright 2012 |
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4 |
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5 Sugared datatype and codatatype constructions. |
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6 *) |
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7 |
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8 signature BNF_FP_DEF_SUGAR = |
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9 sig |
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10 val datatypes: bool -> |
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11 (mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list -> |
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12 BNF_Def.BNF list -> local_theory -> BNF_FP.fp_result * local_theory) -> |
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13 (bool * bool) * ((((typ * sort) list * binding) * mixfix) * ((((binding * binding) * |
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14 (binding * typ) list) * (binding * term) list) * mixfix) list) list -> |
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15 local_theory -> local_theory |
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16 val parse_datatype_cmd: bool -> |
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17 (mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list -> |
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18 BNF_Def.BNF list -> local_theory -> BNF_FP.fp_result * local_theory) -> |
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19 (local_theory -> local_theory) parser |
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20 end; |
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21 |
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22 structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR = |
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23 struct |
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24 |
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25 open BNF_Util |
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26 open BNF_Wrap |
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27 open BNF_Def |
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28 open BNF_FP |
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29 open BNF_FP_Def_Sugar_Tactics |
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30 |
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31 (* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A") *) |
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32 fun quasi_unambiguous_case_names names = |
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33 let |
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34 val ps = map (`Long_Name.base_name) names; |
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35 val dups = Library.duplicates (op =) (map fst ps); |
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36 fun underscore s = |
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37 let val ss = space_explode Long_Name.separator s in |
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38 space_implode "_" (drop (length ss - 2) ss) |
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39 end; |
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40 in |
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41 map (fn (base, full) => if member (op =) dups base then underscore full else base) ps |
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42 end; |
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43 |
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44 val mp_conj = @{thm mp_conj}; |
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45 |
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46 val simp_attrs = @{attributes [simp]}; |
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47 val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs; |
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48 |
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49 fun split_list4 xs = (map #1 xs, map #2 xs, map #3 xs, map #4 xs); |
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50 |
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51 fun resort_tfree S (TFree (s, _)) = TFree (s, S); |
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52 |
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53 fun typ_subst inst (T as Type (s, Ts)) = |
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54 (case AList.lookup (op =) inst T of |
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55 NONE => Type (s, map (typ_subst inst) Ts) |
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56 | SOME T' => T') |
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57 | typ_subst inst T = the_default T (AList.lookup (op =) inst T); |
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58 |
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59 fun variant_types ss Ss ctxt = |
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60 let |
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61 val (tfrees, _) = |
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62 fold_map2 (fn s => fn S => Name.variant s #> apfst (rpair S)) ss Ss (Variable.names_of ctxt); |
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63 val ctxt' = fold (Variable.declare_constraints o Logic.mk_type o TFree) tfrees ctxt; |
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64 in (tfrees, ctxt') end; |
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65 |
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66 val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs)); |
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67 |
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68 fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs)); |
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69 fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs; |
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70 fun mk_uncurried2_fun f xss = |
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71 mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); |
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72 |
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73 fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) = |
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74 Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1)); |
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75 |
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76 fun flip_rels lthy n thm = |
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77 let |
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78 val Rs = Term.add_vars (prop_of thm) []; |
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79 val Rs' = rev (drop (length Rs - n) Rs); |
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80 val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs'; |
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81 in |
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82 Drule.cterm_instantiate cRs thm |
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83 end; |
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84 |
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85 fun mk_ctor_or_dtor get_T Ts t = |
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86 let val Type (_, Ts0) = get_T (fastype_of t) in |
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87 Term.subst_atomic_types (Ts0 ~~ Ts) t |
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88 end; |
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89 |
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90 val mk_ctor = mk_ctor_or_dtor range_type; |
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91 val mk_dtor = mk_ctor_or_dtor domain_type; |
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92 |
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93 fun mk_rec_like lfp Ts Us t = |
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94 let |
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95 val (bindings, body) = strip_type (fastype_of t); |
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96 val (f_Us, prebody) = split_last bindings; |
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97 val Type (_, Ts0) = if lfp then prebody else body; |
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98 val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us); |
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99 in |
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100 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t |
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101 end; |
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102 |
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103 fun mk_map live Ts Us t = |
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104 let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in |
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105 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t |
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106 end; |
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107 |
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108 fun mk_rel live Ts Us t = |
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109 let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in |
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110 Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t |
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111 end; |
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112 |
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113 fun liveness_of_fp_bnf n bnf = |
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114 (case T_of_bnf bnf of |
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115 Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts |
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116 | _ => replicate n false); |
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117 |
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118 fun tick u f = Term.lambda u (HOLogic.mk_prod (u, f $ u)); |
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119 |
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120 fun tack z_name (c, u) f = |
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121 let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in |
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122 Term.lambda z (mk_sum_case (Term.lambda u u, Term.lambda c (f $ c)) $ z) |
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123 end; |
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124 |
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125 fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; |
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126 |
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127 fun merge_type_arg T T' = if T = T' then T else cannot_merge_types (); |
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128 |
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129 fun merge_type_args (As, As') = |
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130 if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types (); |
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131 |
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132 fun reassoc_conjs thm = |
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133 reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]}) |
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134 handle THM _ => thm; |
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135 |
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136 fun type_args_constrained_of (((cAs, _), _), _) = cAs; |
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137 fun type_binding_of (((_, b), _), _) = b; |
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138 fun mixfix_of ((_, mx), _) = mx; |
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139 fun ctr_specs_of (_, ctr_specs) = ctr_specs; |
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140 |
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141 fun disc_of ((((disc, _), _), _), _) = disc; |
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142 fun ctr_of ((((_, ctr), _), _), _) = ctr; |
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143 fun args_of (((_, args), _), _) = args; |
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144 fun defaults_of ((_, ds), _) = ds; |
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145 fun ctr_mixfix_of (_, mx) = mx; |
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146 |
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147 fun define_datatypes prepare_constraint prepare_typ prepare_term lfp construct_fp |
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148 (wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 = |
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149 let |
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150 (* TODO: sanity checks on arguments *) |
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151 (* TODO: integration with function package ("size") *) |
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152 |
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153 val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes" |
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154 else (); |
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155 |
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156 fun qualify mandatory fp_b_name = |
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157 Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix); |
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158 |
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159 val nn = length specs; |
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160 val fp_bs = map type_binding_of specs; |
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161 val fp_b_names = map Binding.name_of fp_bs; |
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162 val fp_common_name = mk_common_name fp_b_names; |
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163 |
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164 fun prepare_type_arg (ty, c) = |
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165 let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in |
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166 TFree (s, prepare_constraint no_defs_lthy0 c) |
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167 end; |
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168 |
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169 val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs; |
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170 val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0; |
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171 val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0; |
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172 |
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173 val (((Bs0, Cs), Xs), no_defs_lthy) = |
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174 no_defs_lthy0 |
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175 |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As |
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176 |> mk_TFrees (length unsorted_As) |
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177 ||>> mk_TFrees nn |
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178 ||>> apfst (map TFree) o |
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179 variant_types (map (prefix "'") fp_b_names) (replicate nn HOLogic.typeS); |
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180 |
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181 (* TODO: cleaner handling of fake contexts, without "background_theory" *) |
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182 (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a |
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183 locale and shadows an existing global type*) |
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184 val fake_thy = |
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185 Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy |
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186 (type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs; |
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187 val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy; |
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188 |
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189 fun mk_fake_T b = |
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190 Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), |
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191 unsorted_As); |
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192 |
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193 val fake_Ts = map mk_fake_T fp_bs; |
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194 |
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195 val mixfixes = map mixfix_of specs; |
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196 |
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197 val _ = (case duplicates Binding.eq_name fp_bs of [] => () |
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198 | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); |
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199 |
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200 val ctr_specss = map ctr_specs_of specs; |
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201 |
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202 val disc_bindingss = map (map disc_of) ctr_specss; |
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203 val ctr_bindingss = |
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204 map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss; |
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205 val ctr_argsss = map (map args_of) ctr_specss; |
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206 val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; |
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207 |
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208 val sel_bindingsss = map (map (map fst)) ctr_argsss; |
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209 val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; |
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210 val raw_sel_defaultsss = map (map defaults_of) ctr_specss; |
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211 |
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212 val (As :: _) :: fake_ctr_Tsss = |
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213 burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0); |
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214 |
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215 val _ = (case duplicates (op =) unsorted_As of [] => () |
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216 | A :: _ => error ("Duplicate type parameter " ^ |
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217 quote (Syntax.string_of_typ no_defs_lthy A))); |
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218 |
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219 val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; |
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220 val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of |
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221 [] => () |
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222 | A' :: _ => error ("Extra type variable on right-hand side: " ^ |
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223 quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); |
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224 |
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225 fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) = |
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226 s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ |
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227 quote (Syntax.string_of_typ fake_lthy T))) |
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228 | eq_fpT_check _ _ = false; |
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229 |
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230 fun freeze_fp (T as Type (s, Us)) = |
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231 (case find_index (eq_fpT_check T) fake_Ts of |
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232 ~1 => Type (s, map freeze_fp Us) |
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233 | kk => nth Xs kk) |
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234 | freeze_fp T = T; |
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235 |
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236 val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss; |
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237 val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs; |
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238 |
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239 val fp_eqs = |
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240 map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsXs; |
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241 |
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242 (* TODO: clean up list *) |
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243 val (pre_bnfs, ((fp_bnfs as any_fp_bnf :: _, dtors0, ctors0, fp_folds0, fp_recs0, fp_induct, |
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244 fp_strong_induct, dtor_ctors, ctor_dtors, ctor_injects, fp_map_thms, fp_set_thmss, |
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245 fp_rel_thms, fp_fold_thms, fp_rec_thms), lthy)) = |
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246 fp_bnf construct_fp fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0; |
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247 |
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248 val timer = time (Timer.startRealTimer ()); |
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249 |
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250 fun add_nesty_bnf_names Us = |
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251 let |
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252 fun add (Type (s, Ts)) ss = |
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253 let val (needs, ss') = fold_map add Ts ss in |
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254 if exists I needs then (true, insert (op =) s ss') else (false, ss') |
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255 end |
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256 | add T ss = (member (op =) Us T, ss); |
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257 in snd oo add end; |
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258 |
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259 fun nesty_bnfs Us = |
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260 map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssXs []); |
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261 |
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262 val nesting_bnfs = nesty_bnfs As; |
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263 val nested_bnfs = nesty_bnfs Xs; |
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264 |
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265 val pre_map_defs = map map_def_of_bnf pre_bnfs; |
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266 val pre_set_defss = map set_defs_of_bnf pre_bnfs; |
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267 val pre_rel_defs = map rel_def_of_bnf pre_bnfs; |
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268 val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs; |
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269 val nesting_map_ids = map map_id_of_bnf nesting_bnfs; |
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270 val nesting_set_natural's = maps set_natural'_of_bnf nesting_bnfs; |
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271 |
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272 val live = live_of_bnf any_fp_bnf; |
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273 |
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274 val Bs = |
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275 map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A) |
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276 (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0; |
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277 |
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278 val B_ify = Term.typ_subst_atomic (As ~~ Bs); |
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279 |
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280 val ctors = map (mk_ctor As) ctors0; |
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281 val dtors = map (mk_dtor As) dtors0; |
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282 |
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283 val fpTs = map (domain_type o fastype_of) dtors; |
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284 |
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285 val exists_fp_subtype = exists_subtype (member (op =) fpTs); |
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286 |
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287 val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs; |
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288 val ns = map length ctr_Tsss; |
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289 val kss = map (fn n => 1 upto n) ns; |
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290 val mss = map (map length) ctr_Tsss; |
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291 val Css = map2 replicate ns Cs; |
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292 |
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293 val fp_folds as any_fp_fold :: _ = map (mk_rec_like lfp As Cs) fp_folds0; |
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294 val fp_recs as any_fp_rec :: _ = map (mk_rec_like lfp As Cs) fp_recs0; |
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295 |
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296 val fp_fold_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_fold))); |
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297 val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_rec))); |
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298 |
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299 val (((fold_only as (gss, _, _), rec_only as (hss, _, _)), |
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300 (zs, cs, cpss, unfold_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))), |
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301 names_lthy0) = |
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302 if lfp then |
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303 let |
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304 val y_Tsss = |
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305 map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type) |
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306 ns mss fp_fold_fun_Ts; |
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307 val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css; |
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308 |
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309 val ((gss, ysss), lthy) = |
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310 lthy |
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311 |> mk_Freess "f" g_Tss |
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312 ||>> mk_Freesss "x" y_Tsss; |
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313 val yssss = map (map (map single)) ysss; |
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314 |
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315 fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) = |
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316 if member (op =) Cs U then Us else [T] |
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317 | dest_rec_prodT T = [T]; |
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318 |
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319 val z_Tssss = |
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320 map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o |
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321 dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts; |
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322 val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css; |
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323 |
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324 val hss = map2 (map2 retype_free) h_Tss gss; |
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325 val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss; |
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326 val (zssss_tl, lthy) = |
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327 lthy |
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328 |> mk_Freessss "y" (map (map (map tl)) z_Tssss); |
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329 val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl; |
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330 in |
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331 ((((gss, g_Tss, yssss), (hss, h_Tss, zssss)), |
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332 ([], [], [], (([], []), ([], [])), (([], []), ([], [])))), lthy) |
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333 end |
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334 else |
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335 let |
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336 (*avoid "'a itself" arguments in coiterators and corecursors*) |
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337 val mss' = map (fn [0] => [1] | ms => ms) mss; |
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338 |
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339 val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs; |
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340 |
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341 fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss); |
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342 |
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343 fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss |
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344 | flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) = |
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345 p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss; |
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346 |
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347 fun mk_types maybe_dest_sumT fun_Ts = |
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348 let |
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349 val f_sum_prod_Ts = map range_type fun_Ts; |
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350 val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts; |
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351 val f_Tssss = |
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352 map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT)) |
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353 Cs mss' f_prod_Tss; |
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354 val q_Tssss = |
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355 map (map (map (fn [_] => [] | [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss; |
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356 val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss; |
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357 in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end; |
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358 |
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359 val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_fold_fun_Ts; |
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360 |
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361 val ((((Free (z, _), cs), pss), gssss), lthy) = |
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362 lthy |
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363 |> yield_singleton (mk_Frees "z") dummyT |
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364 ||>> mk_Frees "a" Cs |
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365 ||>> mk_Freess "p" p_Tss |
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366 ||>> mk_Freessss "g" g_Tssss; |
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367 val rssss = map (map (map (fn [] => []))) r_Tssss; |
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368 |
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369 fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) = |
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370 if member (op =) Cs U then Us else [T] |
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371 | dest_corec_sumT T = [T]; |
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372 |
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373 val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts; |
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374 |
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375 val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss; |
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376 val ((sssss, hssss_tl), lthy) = |
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377 lthy |
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378 |> mk_Freessss "q" s_Tssss |
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379 ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss); |
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380 val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl; |
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381 |
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382 val cpss = map2 (fn c => map (fn p => p $ c)) cs pss; |
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383 |
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384 fun mk_preds_getters_join [] [cf] = cf |
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385 | mk_preds_getters_join [cq] [cf, cf'] = |
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386 mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf'); |
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387 |
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388 fun mk_terms qssss fssss = |
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389 let |
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390 val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss; |
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391 val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss; |
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392 val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss; |
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393 val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss; |
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394 in (pfss, cqfsss) end; |
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395 in |
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396 (((([], [], []), ([], [], [])), |
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397 ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)), |
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398 (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss)))), lthy) |
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399 end; |
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400 |
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401 fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor), |
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402 fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs), |
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403 pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings), |
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404 ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy = |
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405 let |
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406 val fp_b_name = Binding.name_of fp_b; |
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407 |
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408 val dtorT = domain_type (fastype_of ctor); |
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409 val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss; |
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410 val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts; |
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411 val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss; |
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412 |
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413 val (((((w, fs), xss), yss), u'), names_lthy) = |
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414 no_defs_lthy |
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415 |> yield_singleton (mk_Frees "w") dtorT |
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416 ||>> mk_Frees "f" case_Ts |
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417 ||>> mk_Freess "x" ctr_Tss |
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418 ||>> mk_Freess "y" (map (map B_ify) ctr_Tss) |
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419 ||>> yield_singleton Variable.variant_fixes fp_b_name; |
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420 |
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421 val u = Free (u', fpT); |
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422 |
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423 val tuple_xs = map HOLogic.mk_tuple xss; |
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424 val tuple_ys = map HOLogic.mk_tuple yss; |
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425 |
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426 val ctr_rhss = |
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427 map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $ |
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428 mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs; |
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429 |
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430 val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b); |
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431 |
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432 val case_rhs = |
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433 fold_rev Term.lambda (fs @ [u]) |
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434 (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u)); |
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435 |
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436 val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy |
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437 |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => |
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438 Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) |
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439 (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) |
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440 ||> `Local_Theory.restore; |
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441 |
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442 val phi = Proof_Context.export_morphism lthy lthy'; |
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443 |
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444 val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; |
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445 val ctr_defs' = |
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446 map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs; |
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447 val case_def = Morphism.thm phi raw_case_def; |
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448 |
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449 val ctrs0 = map (Morphism.term phi) raw_ctrs; |
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450 val casex0 = Morphism.term phi raw_case; |
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451 |
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452 val ctrs = map (mk_ctr As) ctrs0; |
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453 |
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454 fun wrap lthy = |
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455 let |
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456 fun exhaust_tac {context = ctxt, ...} = |
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457 let |
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458 val ctor_iff_dtor_thm = |
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459 let |
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460 val goal = |
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461 fold_rev Logic.all [w, u] |
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462 (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w))); |
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463 in |
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464 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
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465 mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT]) |
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466 (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor) |
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467 |> Thm.close_derivation |
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468 |> Morphism.thm phi |
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469 end; |
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470 |
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471 val sumEN_thm' = |
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472 unfold_thms lthy @{thms all_unit_eq} |
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473 (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] |
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474 (mk_sumEN_balanced n)) |
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475 |> Morphism.thm phi; |
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476 in |
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477 mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm' |
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478 end; |
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479 |
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480 val inject_tacss = |
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481 map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} => |
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482 mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs; |
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483 |
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484 val half_distinct_tacss = |
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485 map (map (fn (def, def') => fn {context = ctxt, ...} => |
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486 mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs)); |
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487 |
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488 val case_tacs = |
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489 map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => |
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490 mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs; |
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491 |
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492 val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; |
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493 |
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494 val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss |
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495 in |
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496 wrap_datatype tacss (((wrap_opts, ctrs0), casex0), (disc_bindings, (sel_bindingss, |
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497 sel_defaultss))) lthy |
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498 end; |
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499 |
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500 fun derive_maps_sets_rels (wrap_res, lthy) = |
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501 let |
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502 val rel_flip = rel_flip_of_bnf fp_bnf; |
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503 val nones = replicate live NONE; |
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504 |
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505 val ctor_cong = |
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506 if lfp then Drule.dummy_thm |
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507 else cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor)] arg_cong; |
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508 |
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509 fun mk_cIn ify = |
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510 certify lthy o (not lfp ? curry (op $) (map_types ify ctor)) oo |
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511 mk_InN_balanced (ify ctr_sum_prod_T) n; |
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512 |
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513 val cxIns = map2 (mk_cIn I) tuple_xs ks; |
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514 val cyIns = map2 (mk_cIn B_ify) tuple_ys ks; |
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515 |
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516 fun mk_map_thm ctr_def' xs cxIn = |
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517 fold_thms lthy [ctr_def'] |
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518 (unfold_thms lthy (pre_map_def :: |
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519 (if lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map) |
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520 (cterm_instantiate_pos (nones @ [SOME cxIn]) |
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521 (if lfp then fp_map_thm else fp_map_thm RS ctor_cong))) |
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522 |> singleton (Proof_Context.export names_lthy no_defs_lthy); |
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523 |
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524 fun mk_set_thm fp_set_thm ctr_def' xs cxIn = |
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525 fold_thms lthy [ctr_def'] |
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526 (unfold_thms lthy (pre_set_defs @ nested_set_natural's @ nesting_set_natural's @ |
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527 (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_set) |
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528 (cterm_instantiate_pos [SOME cxIn] fp_set_thm)) |
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529 |> singleton (Proof_Context.export names_lthy no_defs_lthy); |
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530 |
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531 fun mk_set_thms fp_set_thm = map3 (mk_set_thm fp_set_thm) ctr_defs' xss cxIns; |
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532 |
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533 val map_thms = map3 mk_map_thm ctr_defs' xss cxIns; |
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534 val set_thmss = map mk_set_thms fp_set_thms; |
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535 |
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536 val rel_infos = (ctr_defs' ~~ xss ~~ cxIns, ctr_defs' ~~ yss ~~ cyIns); |
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537 |
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538 fun mk_rel_thm postproc ctr_defs' xs cxIn ys cyIn = |
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539 fold_thms lthy ctr_defs' |
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540 (unfold_thms lthy (pre_rel_def :: (if lfp then [] else [dtor_ctor]) @ |
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541 sum_prod_thms_rel) |
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542 (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm)) |
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543 |> postproc |
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544 |> singleton (Proof_Context.export names_lthy no_defs_lthy); |
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545 |
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546 fun mk_rel_inject_thm (((ctr_def', xs), cxIn), ((_, ys), cyIn)) = |
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547 mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] xs cxIn ys cyIn; |
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548 |
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549 val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos); |
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550 |
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551 fun mk_half_rel_distinct_thm (((xctr_def', xs), cxIn), ((yctr_def', ys), cyIn)) = |
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552 mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def'] |
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553 xs cxIn ys cyIn; |
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554 |
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555 fun mk_other_half_rel_distinct_thm thm = |
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556 flip_rels lthy live thm RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2); |
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557 |
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558 val half_rel_distinct_thmss = |
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559 map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos); |
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560 val other_half_rel_distinct_thmss = |
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561 map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss; |
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562 val (rel_distinct_thms, _) = |
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563 join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss; |
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564 |
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565 val notes = |
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566 [(mapN, map_thms, code_simp_attrs), |
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567 (rel_distinctN, rel_distinct_thms, code_simp_attrs), |
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568 (rel_injectN, rel_inject_thms, code_simp_attrs), |
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569 (setsN, flat set_thmss, code_simp_attrs)] |
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570 |> filter_out (null o #2) |
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571 |> map (fn (thmN, thms, attrs) => |
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572 ((qualify true fp_b_name (Binding.name thmN), attrs), [(thms, [])])); |
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573 in |
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574 (wrap_res, lthy |> Local_Theory.notes notes |> snd) |
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575 end; |
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576 |
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577 fun define_fold_rec no_defs_lthy = |
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578 let |
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579 val fpT_to_C = fpT --> C; |
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580 |
|
581 fun generate_rec_like (suf, fp_rec_like, (fss, f_Tss, xssss)) = |
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582 let |
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583 val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C; |
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584 val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b); |
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585 val spec = |
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586 mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)), |
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587 Term.list_comb (fp_rec_like, |
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588 map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss)); |
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589 in (binding, spec) end; |
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590 |
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591 val rec_like_infos = |
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592 [(foldN, fp_fold, fold_only), |
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593 (recN, fp_rec, rec_only)]; |
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594 |
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595 val (bindings, specs) = map generate_rec_like rec_like_infos |> split_list; |
|
596 |
|
597 val ((csts, defs), (lthy', lthy)) = no_defs_lthy |
|
598 |> apfst split_list o fold_map2 (fn b => fn spec => |
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599 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) |
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600 #>> apsnd snd) bindings specs |
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601 ||> `Local_Theory.restore; |
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602 |
|
603 val phi = Proof_Context.export_morphism lthy lthy'; |
|
604 |
|
605 val [fold_def, rec_def] = map (Morphism.thm phi) defs; |
|
606 |
|
607 val [foldx, recx] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts; |
|
608 in |
|
609 ((foldx, recx, fold_def, rec_def), lthy) |
|
610 end; |
|
611 |
|
612 fun define_unfold_corec no_defs_lthy = |
|
613 let |
|
614 val B_to_fpT = C --> fpT; |
|
615 |
|
616 fun mk_preds_getterss_join c n cps sum_prod_T cqfss = |
|
617 Term.lambda c (mk_IfN sum_prod_T cps |
|
618 (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n))); |
|
619 |
|
620 fun generate_corec_like (suf, fp_rec_like, ((pfss, cqfsss), (f_sum_prod_Ts, |
|
621 pf_Tss))) = |
|
622 let |
|
623 val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT; |
|
624 val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b); |
|
625 val spec = |
|
626 mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)), |
|
627 Term.list_comb (fp_rec_like, |
|
628 map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss)); |
|
629 in (binding, spec) end; |
|
630 |
|
631 val corec_like_infos = |
|
632 [(unfoldN, fp_fold, unfold_only), |
|
633 (corecN, fp_rec, corec_only)]; |
|
634 |
|
635 val (bindings, specs) = map generate_corec_like corec_like_infos |> split_list; |
|
636 |
|
637 val ((csts, defs), (lthy', lthy)) = no_defs_lthy |
|
638 |> apfst split_list o fold_map2 (fn b => fn spec => |
|
639 Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) |
|
640 #>> apsnd snd) bindings specs |
|
641 ||> `Local_Theory.restore; |
|
642 |
|
643 val phi = Proof_Context.export_morphism lthy lthy'; |
|
644 |
|
645 val [unfold_def, corec_def] = map (Morphism.thm phi) defs; |
|
646 |
|
647 val [unfold, corec] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts; |
|
648 in |
|
649 ((unfold, corec, unfold_def, corec_def), lthy) |
|
650 end; |
|
651 |
|
652 val define_rec_likes = if lfp then define_fold_rec else define_unfold_corec; |
|
653 |
|
654 fun massage_res ((wrap_res, rec_like_res), lthy) = |
|
655 (((ctrs, xss, ctr_defs, wrap_res), rec_like_res), lthy); |
|
656 in |
|
657 (wrap #> (live > 0 ? derive_maps_sets_rels) ##>> define_rec_likes #> massage_res, lthy') |
|
658 end; |
|
659 |
|
660 fun wrap_types_and_more (wrap_types_and_mores, lthy) = |
|
661 fold_map I wrap_types_and_mores lthy |
|
662 |>> apsnd split_list4 o apfst split_list4 o split_list; |
|
663 |
|
664 fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) = |
|
665 let |
|
666 val bnf = the (bnf_of lthy s); |
|
667 val live = live_of_bnf bnf; |
|
668 val mapx = mk_map live Ts Us (map_of_bnf bnf); |
|
669 val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx))); |
|
670 in Term.list_comb (mapx, map build_arg TUs') end; |
|
671 |
|
672 (* TODO: Add map, sets, rel simps *) |
|
673 val mk_simp_thmss = |
|
674 map3 (fn (_, _, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn fold_likes => |
|
675 injects @ distincts @ cases @ rec_likes @ fold_likes); |
|
676 |
|
677 fun derive_induct_fold_rec_thms_for_types (((ctrss, xsss, ctr_defss, wrap_ress), (folds, recs, |
|
678 fold_defs, rec_defs)), lthy) = |
|
679 let |
|
680 val (((ps, ps'), us'), names_lthy) = |
|
681 lthy |
|
682 |> mk_Frees' "P" (map mk_pred1T fpTs) |
|
683 ||>> Variable.variant_fixes fp_b_names; |
|
684 |
|
685 val us = map2 (curry Free) us' fpTs; |
|
686 |
|
687 fun mk_sets_nested bnf = |
|
688 let |
|
689 val Type (T_name, Us) = T_of_bnf bnf; |
|
690 val lives = lives_of_bnf bnf; |
|
691 val sets = sets_of_bnf bnf; |
|
692 fun mk_set U = |
|
693 (case find_index (curry (op =) U) lives of |
|
694 ~1 => Term.dummy |
|
695 | i => nth sets i); |
|
696 in |
|
697 (T_name, map mk_set Us) |
|
698 end; |
|
699 |
|
700 val setss_nested = map mk_sets_nested nested_bnfs; |
|
701 |
|
702 val (induct_thms, induct_thm) = |
|
703 let |
|
704 fun mk_set Ts t = |
|
705 let val Type (_, Ts0) = domain_type (fastype_of t) in |
|
706 Term.subst_atomic_types (Ts0 ~~ Ts) t |
|
707 end; |
|
708 |
|
709 fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) = |
|
710 (case find_index (curry (op =) T) fpTs of |
|
711 ~1 => |
|
712 (case AList.lookup (op =) setss_nested T_name of |
|
713 NONE => [] |
|
714 | SOME raw_sets0 => |
|
715 let |
|
716 val (Ts, raw_sets) = |
|
717 split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0)); |
|
718 val sets = map (mk_set Ts0) raw_sets; |
|
719 val (ys, names_lthy') = names_lthy |> mk_Frees s Ts; |
|
720 val xysets = map (pair x) (ys ~~ sets); |
|
721 val ppremss = map (mk_raw_prem_prems names_lthy') ys; |
|
722 in |
|
723 flat (map2 (map o apfst o cons) xysets ppremss) |
|
724 end) |
|
725 | kk => [([], (kk + 1, x))]) |
|
726 | mk_raw_prem_prems _ _ = []; |
|
727 |
|
728 fun close_prem_prem xs t = |
|
729 fold_rev Logic.all (map Free (drop (nn + length xs) |
|
730 (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t; |
|
731 |
|
732 fun mk_prem_prem xs (xysets, (j, x)) = |
|
733 close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) => |
|
734 HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets, |
|
735 HOLogic.mk_Trueprop (nth ps (j - 1) $ x))); |
|
736 |
|
737 fun mk_raw_prem phi ctr ctr_Ts = |
|
738 let |
|
739 val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts; |
|
740 val pprems = maps (mk_raw_prem_prems names_lthy') xs; |
|
741 in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end; |
|
742 |
|
743 fun mk_prem (xs, raw_pprems, concl) = |
|
744 fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl)); |
|
745 |
|
746 val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss; |
|
747 |
|
748 val goal = |
|
749 Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss, |
|
750 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us))); |
|
751 |
|
752 val kksss = map (map (map (fst o snd) o #2)) raw_premss; |
|
753 |
|
754 val ctor_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss); |
|
755 |
|
756 val thm = |
|
757 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
758 mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' |
|
759 nested_set_natural's pre_set_defss) |
|
760 |> singleton (Proof_Context.export names_lthy lthy) |
|
761 |> Thm.close_derivation; |
|
762 in |
|
763 `(conj_dests nn) thm |
|
764 end; |
|
765 |
|
766 val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss); |
|
767 |
|
768 val (fold_thmss, rec_thmss) = |
|
769 let |
|
770 val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; |
|
771 val gfolds = map (lists_bmoc gss) folds; |
|
772 val hrecs = map (lists_bmoc hss) recs; |
|
773 |
|
774 fun mk_goal fss frec_like xctr f xs fxs = |
|
775 fold_rev (fold_rev Logic.all) (xs :: fss) |
|
776 (mk_Trueprop_eq (frec_like $ xctr, Term.list_comb (f, fxs))); |
|
777 |
|
778 fun build_rec_like frec_likes maybe_tick (T, U) = |
|
779 if T = U then |
|
780 id_const T |
|
781 else |
|
782 (case find_index (curry (op =) T) fpTs of |
|
783 ~1 => build_map (build_rec_like frec_likes maybe_tick) T U |
|
784 | kk => maybe_tick (nth us kk) (nth frec_likes kk)); |
|
785 |
|
786 fun mk_U maybe_mk_prodT = |
|
787 typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs); |
|
788 |
|
789 fun intr_rec_likes frec_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) = |
|
790 if member (op =) fpTs T then |
|
791 maybe_cons x [build_rec_like frec_likes (K I) (T, mk_U (K I) T) $ x] |
|
792 else if exists_fp_subtype T then |
|
793 [build_rec_like frec_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x] |
|
794 else |
|
795 [x]; |
|
796 |
|
797 val gxsss = map (map (maps (intr_rec_likes gfolds (K I) (K I) (K I)))) xsss; |
|
798 val hxsss = |
|
799 map (map (maps (intr_rec_likes hrecs cons tick (curry HOLogic.mk_prodT)))) xsss; |
|
800 |
|
801 val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss; |
|
802 val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss; |
|
803 |
|
804 val fold_tacss = |
|
805 map2 (map o mk_rec_like_tac pre_map_defs nesting_map_ids fold_defs) fp_fold_thms |
|
806 ctr_defss; |
|
807 val rec_tacss = |
|
808 map2 (map o mk_rec_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms |
|
809 ctr_defss; |
|
810 |
|
811 fun prove goal tac = |
|
812 Skip_Proof.prove lthy [] [] goal (tac o #context) |
|
813 |> Thm.close_derivation; |
|
814 in |
|
815 (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss) |
|
816 end; |
|
817 |
|
818 val simp_thmss = mk_simp_thmss wrap_ress rec_thmss fold_thmss; |
|
819 |
|
820 val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases)); |
|
821 fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name)); |
|
822 |
|
823 val common_notes = |
|
824 (if nn > 1 then [(inductN, [induct_thm], [induct_case_names_attr])] else []) |
|
825 |> map (fn (thmN, thms, attrs) => |
|
826 ((qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])])); |
|
827 |
|
828 val notes = |
|
829 [(foldN, fold_thmss, K code_simp_attrs), |
|
830 (inductN, map single induct_thms, |
|
831 fn T_name => [induct_case_names_attr, induct_type_attr T_name]), |
|
832 (recN, rec_thmss, K code_simp_attrs), |
|
833 (simpsN, simp_thmss, K [])] |
|
834 |> maps (fn (thmN, thmss, attrs) => |
|
835 map3 (fn fp_b_name => fn Type (T_name, _) => fn thms => |
|
836 ((qualify true fp_b_name (Binding.name thmN), attrs T_name), |
|
837 [(thms, [])])) fp_b_names fpTs thmss); |
|
838 in |
|
839 lthy |> Local_Theory.notes (common_notes @ notes) |> snd |
|
840 end; |
|
841 |
|
842 fun derive_coinduct_unfold_corec_thms_for_types (((ctrss, _, ctr_defss, wrap_ress), (unfolds, |
|
843 corecs, unfold_defs, corec_defs)), lthy) = |
|
844 let |
|
845 val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs; |
|
846 |
|
847 val discss = map (map (mk_disc_or_sel As) o #1) wrap_ress; |
|
848 val selsss = map (map (map (mk_disc_or_sel As)) o #2) wrap_ress; |
|
849 val exhaust_thms = map #3 wrap_ress; |
|
850 val disc_thmsss = map #7 wrap_ress; |
|
851 val discIss = map #8 wrap_ress; |
|
852 val sel_thmsss = map #9 wrap_ress; |
|
853 |
|
854 val (((rs, us'), vs'), names_lthy) = |
|
855 lthy |
|
856 |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs) |
|
857 ||>> Variable.variant_fixes fp_b_names |
|
858 ||>> Variable.variant_fixes (map (suffix "'") fp_b_names); |
|
859 |
|
860 val us = map2 (curry Free) us' fpTs; |
|
861 val udiscss = map2 (map o rapp) us discss; |
|
862 val uselsss = map2 (map o map o rapp) us selsss; |
|
863 |
|
864 val vs = map2 (curry Free) vs' fpTs; |
|
865 val vdiscss = map2 (map o rapp) vs discss; |
|
866 val vselsss = map2 (map o map o rapp) vs selsss; |
|
867 |
|
868 val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) = |
|
869 let |
|
870 val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs; |
|
871 val uv_eqs = map2 (curry HOLogic.mk_eq) us vs; |
|
872 val strong_rs = |
|
873 map4 (fn u => fn v => fn uvr => fn uv_eq => |
|
874 fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs; |
|
875 |
|
876 fun build_rel_step build_arg (Type (s, Ts)) = |
|
877 let |
|
878 val bnf = the (bnf_of lthy s); |
|
879 val live = live_of_bnf bnf; |
|
880 val rel = mk_rel live Ts Ts (rel_of_bnf bnf); |
|
881 val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel))); |
|
882 in Term.list_comb (rel, map build_arg Ts') end; |
|
883 |
|
884 fun build_rel rs' T = |
|
885 (case find_index (curry (op =) T) fpTs of |
|
886 ~1 => |
|
887 if exists_fp_subtype T then build_rel_step (build_rel rs') T |
|
888 else HOLogic.eq_const T |
|
889 | kk => nth rs' kk); |
|
890 |
|
891 fun build_rel_app rs' usel vsel = |
|
892 fold rapp [usel, vsel] (build_rel rs' (fastype_of usel)); |
|
893 |
|
894 fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels = |
|
895 (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @ |
|
896 (if null usels then |
|
897 [] |
|
898 else |
|
899 [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc], |
|
900 Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]); |
|
901 |
|
902 fun mk_prem_concl rs' n udiscs uselss vdiscs vselss = |
|
903 Library.foldr1 HOLogic.mk_conj |
|
904 (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss)) |
|
905 handle List.Empty => @{term True}; |
|
906 |
|
907 fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss = |
|
908 fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr, |
|
909 HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss))); |
|
910 |
|
911 val concl = |
|
912 HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj |
|
913 (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v))) |
|
914 uvrs us vs)); |
|
915 |
|
916 fun mk_goal rs' = |
|
917 Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss, |
|
918 concl); |
|
919 |
|
920 val goal = mk_goal rs; |
|
921 val strong_goal = mk_goal strong_rs; |
|
922 |
|
923 fun prove dtor_coinduct' goal = |
|
924 Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => |
|
925 mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors |
|
926 exhaust_thms ctr_defss disc_thmsss sel_thmsss) |
|
927 |> singleton (Proof_Context.export names_lthy lthy) |
|
928 |> Thm.close_derivation; |
|
929 |
|
930 fun postproc nn thm = |
|
931 Thm.permute_prems 0 nn |
|
932 (if nn = 1 then thm RS mp |
|
933 else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm) |
|
934 |> Drule.zero_var_indexes |
|
935 |> `(conj_dests nn); |
|
936 in |
|
937 (postproc nn (prove fp_induct goal), postproc nn (prove fp_strong_induct strong_goal)) |
|
938 end; |
|
939 |
|
940 fun mk_maybe_not pos = not pos ? HOLogic.mk_not; |
|
941 |
|
942 val z = the_single zs; |
|
943 val gunfolds = map (lists_bmoc pgss) unfolds; |
|
944 val hcorecs = map (lists_bmoc phss) corecs; |
|
945 |
|
946 val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) = |
|
947 let |
|
948 fun mk_goal pfss c cps fcorec_like n k ctr m cfs' = |
|
949 fold_rev (fold_rev Logic.all) ([c] :: pfss) |
|
950 (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps, |
|
951 mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs')))); |
|
952 |
|
953 fun build_corec_like fcorec_likes maybe_tack (T, U) = |
|
954 if T = U then |
|
955 id_const T |
|
956 else |
|
957 (case find_index (curry (op =) U) fpTs of |
|
958 ~1 => build_map (build_corec_like fcorec_likes maybe_tack) T U |
|
959 | kk => maybe_tack (nth cs kk, nth us kk) (nth fcorec_likes kk)); |
|
960 |
|
961 fun mk_U maybe_mk_sumT = |
|
962 typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs); |
|
963 |
|
964 fun intr_corec_likes fcorec_likes maybe_mk_sumT maybe_tack cqf = |
|
965 let val T = fastype_of cqf in |
|
966 if exists_subtype (member (op =) Cs) T then |
|
967 build_corec_like fcorec_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf |
|
968 else |
|
969 cqf |
|
970 end; |
|
971 |
|
972 val crgsss' = map (map (map (intr_corec_likes gunfolds (K I) (K I)))) crgsss; |
|
973 val cshsss' = |
|
974 map (map (map (intr_corec_likes hcorecs (curry mk_sumT) (tack z)))) cshsss; |
|
975 |
|
976 val unfold_goalss = |
|
977 map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss'; |
|
978 val corec_goalss = |
|
979 map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss'; |
|
980 |
|
981 val unfold_tacss = |
|
982 map3 (map oo mk_corec_like_tac unfold_defs nesting_map_ids) fp_fold_thms pre_map_defs |
|
983 ctr_defss; |
|
984 val corec_tacss = |
|
985 map3 (map oo mk_corec_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs |
|
986 ctr_defss; |
|
987 |
|
988 fun prove goal tac = |
|
989 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation; |
|
990 |
|
991 val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss; |
|
992 val corec_thmss = |
|
993 map2 (map2 prove) corec_goalss corec_tacss |
|
994 |> map (map (unfold_thms lthy @{thms sum_case_if})); |
|
995 |
|
996 val unfold_safesss = map2 (map2 (map2 (curry (op =)))) crgsss' crgsss; |
|
997 val corec_safesss = map2 (map2 (map2 (curry (op =)))) cshsss' cshsss; |
|
998 |
|
999 val filter_safesss = |
|
1000 map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo |
|
1001 curry (op ~~)); |
|
1002 |
|
1003 val safe_unfold_thmss = filter_safesss unfold_safesss unfold_thmss; |
|
1004 val safe_corec_thmss = filter_safesss corec_safesss corec_thmss; |
|
1005 in |
|
1006 (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) |
|
1007 end; |
|
1008 |
|
1009 val (disc_unfold_iff_thmss, disc_corec_iff_thmss) = |
|
1010 let |
|
1011 fun mk_goal c cps fcorec_like n k disc = |
|
1012 mk_Trueprop_eq (disc $ (fcorec_like $ c), |
|
1013 if n = 1 then @{const True} |
|
1014 else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps)); |
|
1015 |
|
1016 val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss; |
|
1017 val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss; |
|
1018 |
|
1019 fun mk_case_split' cp = |
|
1020 Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split}; |
|
1021 |
|
1022 val case_splitss' = map (map mk_case_split') cpss; |
|
1023 |
|
1024 val unfold_tacss = |
|
1025 map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss; |
|
1026 val corec_tacss = |
|
1027 map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss; |
|
1028 |
|
1029 fun prove goal tac = |
|
1030 Skip_Proof.prove lthy [] [] goal (tac o #context) |
|
1031 |> singleton (Proof_Context.export names_lthy0 no_defs_lthy) |
|
1032 |> Thm.close_derivation; |
|
1033 |
|
1034 fun proves [_] [_] = [] |
|
1035 | proves goals tacs = map2 prove goals tacs; |
|
1036 in |
|
1037 (map2 proves unfold_goalss unfold_tacss, |
|
1038 map2 proves corec_goalss corec_tacss) |
|
1039 end; |
|
1040 |
|
1041 val is_triv_discI = is_triv_implies orf is_concl_refl; |
|
1042 |
|
1043 fun mk_disc_corec_like_thms corec_likes discIs = |
|
1044 map (op RS) (filter_out (is_triv_discI o snd) (corec_likes ~~ discIs)); |
|
1045 |
|
1046 val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss; |
|
1047 val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss; |
|
1048 |
|
1049 fun mk_sel_corec_like_thm corec_like_thm sel sel_thm = |
|
1050 let |
|
1051 val (domT, ranT) = dest_funT (fastype_of sel); |
|
1052 val arg_cong' = |
|
1053 Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT]) |
|
1054 [NONE, NONE, SOME (certify lthy sel)] arg_cong |
|
1055 |> Thm.varifyT_global; |
|
1056 val sel_thm' = sel_thm RSN (2, trans); |
|
1057 in |
|
1058 corec_like_thm RS arg_cong' RS sel_thm' |
|
1059 end; |
|
1060 |
|
1061 fun mk_sel_corec_like_thms corec_likess = |
|
1062 map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss |> map flat; |
|
1063 |
|
1064 val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss; |
|
1065 val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss; |
|
1066 |
|
1067 fun flat_corec_like_thms corec_likes disc_corec_likes sel_corec_likes = |
|
1068 corec_likes @ disc_corec_likes @ sel_corec_likes; |
|
1069 |
|
1070 val simp_thmss = |
|
1071 mk_simp_thmss wrap_ress |
|
1072 (map3 flat_corec_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss) |
|
1073 (map3 flat_corec_like_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss); |
|
1074 |
|
1075 val anonymous_notes = |
|
1076 [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)] |
|
1077 |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])])); |
|
1078 |
|
1079 val common_notes = |
|
1080 (if nn > 1 then |
|
1081 (* FIXME: attribs *) |
|
1082 [(coinductN, [coinduct_thm], []), |
|
1083 (strong_coinductN, [strong_coinduct_thm], [])] |
|
1084 else |
|
1085 []) |
|
1086 |> map (fn (thmN, thms, attrs) => |
|
1087 ((qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])])); |
|
1088 |
|
1089 val notes = |
|
1090 [(coinductN, map single coinduct_thms, []), (* FIXME: attribs *) |
|
1091 (corecN, corec_thmss, []), |
|
1092 (disc_corecN, disc_corec_thmss, simp_attrs), |
|
1093 (disc_corec_iffN, disc_corec_iff_thmss, simp_attrs), |
|
1094 (disc_unfoldN, disc_unfold_thmss, simp_attrs), |
|
1095 (disc_unfold_iffN, disc_unfold_iff_thmss, simp_attrs), |
|
1096 (sel_corecN, sel_corec_thmss, simp_attrs), |
|
1097 (sel_unfoldN, sel_unfold_thmss, simp_attrs), |
|
1098 (simpsN, simp_thmss, []), |
|
1099 (strong_coinductN, map single strong_coinduct_thms, []), (* FIXME: attribs *) |
|
1100 (unfoldN, unfold_thmss, [])] |
|
1101 |> maps (fn (thmN, thmss, attrs) => |
|
1102 map_filter (fn (_, []) => NONE | (fp_b_name, thms) => |
|
1103 SOME ((qualify true fp_b_name (Binding.name thmN), attrs), |
|
1104 [(thms, [])])) (fp_b_names ~~ thmss)); |
|
1105 in |
|
1106 lthy |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd |
|
1107 end; |
|
1108 |
|
1109 val lthy' = lthy |
|
1110 |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~ |
|
1111 fp_folds ~~ fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~ |
|
1112 pre_set_defss ~~ pre_rel_defs ~~ fp_map_thms ~~ fp_set_thmss ~~ fp_rel_thms ~~ ns ~~ kss ~~ |
|
1113 mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ |
|
1114 raw_sel_defaultsss) |
|
1115 |> wrap_types_and_more |
|
1116 |> (if lfp then derive_induct_fold_rec_thms_for_types |
|
1117 else derive_coinduct_unfold_corec_thms_for_types); |
|
1118 |
|
1119 val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ |
|
1120 (if lfp then "" else "co") ^ "datatype")); |
|
1121 in |
|
1122 timer; lthy' |
|
1123 end; |
|
1124 |
|
1125 val datatypes = define_datatypes (K I) (K I) (K I); |
|
1126 |
|
1127 val datatype_cmd = define_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.read_term; |
|
1128 |
|
1129 val parse_ctr_arg = |
|
1130 @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} || |
|
1131 (Parse.typ >> pair Binding.empty); |
|
1132 |
|
1133 val parse_defaults = |
|
1134 @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"}; |
|
1135 |
|
1136 val parse_single_spec = |
|
1137 Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix -- |
|
1138 (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding -- |
|
1139 Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix)); |
|
1140 |
|
1141 val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec; |
|
1142 |
|
1143 fun parse_datatype_cmd lfp construct_fp = parse_datatype >> datatype_cmd lfp construct_fp; |
|
1144 |
|
1145 end; |