author | blanchet |
Mon, 17 Feb 2014 13:31:42 +0100 | |
changeset 55531 | 601ca8efa000 |
parent 55530 | 3dfb724db099 |
child 55539 | 0819931d652d |
permissions | -rw-r--r-- |
55061 | 1 |
(* Title: HOL/Tools/BNF/bnf_fp_n2m.ML |
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Author: Dmitriy Traytel, TU Muenchen |
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Copyright 2013 |
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Flattening of nested to mutual (co)recursion. |
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*) |
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signature BNF_FP_N2M = |
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sig |
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val construct_mutualized_fp: BNF_FP_Util.fp_kind -> typ list -> BNF_FP_Def_Sugar.fp_sugar list -> |
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binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list -> |
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local_theory -> BNF_FP_Util.fp_result * local_theory |
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end; |
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structure BNF_FP_N2M : BNF_FP_N2M = |
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struct |
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open BNF_Def |
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open BNF_Util |
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open BNF_FP_Util |
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open BNF_FP_Def_Sugar |
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open BNF_Tactics |
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open BNF_FP_N2M_Tactics |
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fun force_typ ctxt T = |
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map_types Type_Infer.paramify_vars |
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#> Type.constraint T |
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#> Syntax.check_term ctxt |
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#> singleton (Variable.polymorphic ctxt); |
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fun mk_prod_map f g = |
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let |
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val ((fAT, fBT), fT) = `dest_funT (fastype_of f); |
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val ((gAT, gBT), gT) = `dest_funT (fastype_of g); |
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in |
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Const (@{const_name map_pair}, |
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fT --> gT --> HOLogic.mk_prodT (fAT, gAT) --> HOLogic.mk_prodT (fBT, gBT)) $ f $ g |
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end; |
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fun mk_sum_map f g = |
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let |
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val ((fAT, fBT), fT) = `dest_funT (fastype_of f); |
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val ((gAT, gBT), gT) = `dest_funT (fastype_of g); |
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in |
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Const (@{const_name sum_map}, fT --> gT --> mk_sumT (fAT, gAT) --> mk_sumT (fBT, gBT)) $ f $ g |
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end; |
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fun construct_mutualized_fp fp fpTs fp_sugars bs resBs (resDs, Dss) bnfs lthy = |
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let |
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fun steal get = map (of_fp_sugar (get o #fp_res)) fp_sugars; |
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val n = length bnfs; |
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val deads = fold (union (op =)) Dss resDs; |
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val As = subtract (op =) deads (map TFree resBs); |
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val names_lthy = fold Variable.declare_typ (As @ deads) lthy; |
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val m = length As; |
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val live = m + n; |
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val ((Xs, Bs), names_lthy) = names_lthy |
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|> mk_TFrees n |
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||>> mk_TFrees m; |
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val allAs = As @ Xs; |
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val phiTs = map2 mk_pred2T As Bs; |
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val theta = As ~~ Bs; |
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val fpTs' = map (Term.typ_subst_atomic theta) fpTs; |
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val pre_phiTs = map2 mk_pred2T fpTs fpTs'; |
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fun mk_co_algT T U = fp_case fp (T --> U) (U --> T); |
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fun co_swap pair = fp_case fp I swap pair; |
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val dest_co_algT = co_swap o dest_funT; |
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val co_alg_argT = fp_case fp range_type domain_type; |
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val co_alg_funT = fp_case fp domain_type range_type; |
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val mk_co_product = curry (fp_case fp mk_convol mk_case_sum); |
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val mk_map_co_product = fp_case fp mk_prod_map mk_sum_map; |
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val co_proj1_const = fp_case fp (fst_const o fst) (uncurry Inl_const o dest_sumT o snd); |
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val mk_co_productT = curry (fp_case fp HOLogic.mk_prodT mk_sumT); |
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val dest_co_productT = fp_case fp HOLogic.dest_prodT dest_sumT; |
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val ((ctors, dtors), (xtor's, xtors)) = |
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let |
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val ctors = map2 (force_typ names_lthy o (fn T => dummyT --> T)) fpTs (steal #ctors); |
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val dtors = map2 (force_typ names_lthy o (fn T => T --> dummyT)) fpTs (steal #dtors); |
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in |
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((ctors, dtors), `(map (Term.subst_atomic_types theta)) (fp_case fp ctors dtors)) |
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end; |
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val xTs = map (domain_type o fastype_of) xtors; |
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val yTs = map (domain_type o fastype_of) xtor's; |
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val (((((phis, phis'), pre_phis), xs), ys), names_lthy) = names_lthy |
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|> mk_Frees' "R" phiTs |
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||>> mk_Frees "S" pre_phiTs |
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||>> mk_Frees "x" xTs |
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||>> mk_Frees "y" yTs; |
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val fp_bnfs = steal #bnfs; |
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val pre_bnfs = map (of_fp_sugar #pre_bnfs) fp_sugars; |
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val pre_bnfss = map #pre_bnfs fp_sugars; |
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val nesty_bnfss = map (fn sugar => #nested_bnfs sugar @ #nesting_bnfs sugar) fp_sugars; |
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val fp_nesty_bnfss = fp_bnfs :: nesty_bnfss; |
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val fp_nesty_bnfs = distinct (op = o pairself T_of_bnf) (flat fp_nesty_bnfss); |
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val rels = |
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103 |
let |
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104 |
fun find_rel T As Bs = fp_nesty_bnfss |
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105 |
|> map (filter_out (curry (op = o pairself name_of_bnf) BNF_Comp.DEADID_bnf)) |
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106 |
|> get_first (find_first (fn bnf => Type.could_unify (T_of_bnf bnf, T))) |
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107 |
|> Option.map (fn bnf => |
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108 |
let val live = live_of_bnf bnf; |
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109 |
in (mk_rel live As Bs (rel_of_bnf bnf), live) end) |
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110 |
|> the_default (HOLogic.eq_const T, 0); |
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|
111 |
|
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112 |
fun mk_rel (T as Type (_, Ts)) (Type (_, Us)) = |
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113 |
let |
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|
114 |
val (rel, live) = find_rel T Ts Us; |
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115 |
val (Ts', Us') = fastype_of rel |> strip_typeN live |> fst |> map_split dest_pred2T; |
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116 |
val rels = map2 mk_rel Ts' Us'; |
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117 |
in |
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118 |
Term.list_comb (rel, rels) |
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119 |
end |
54244 | 120 |
| mk_rel (T as TFree _) _ = (nth phis (find_index (curry op = T) As) |
121 |
handle General.Subscript => HOLogic.eq_const T) |
|
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122 |
| mk_rel _ _ = raise Fail "fpTs contains schematic type variables"; |
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123 |
in |
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124 |
map2 (fold_rev Term.absfree phis' oo mk_rel) fpTs fpTs' |
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125 |
end; |
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126 |
|
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127 |
val pre_rels = map2 (fn Ds => mk_rel_of_bnf Ds (As @ fpTs) (Bs @ fpTs')) Dss bnfs; |
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|
128 |
|
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129 |
val rel_unfoldss = map (maps (fn bnf => no_refl [rel_def_of_bnf bnf])) pre_bnfss; |
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130 |
val rel_xtor_co_inducts = steal (split_conj_thm o #rel_xtor_co_induct_thm) |
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131 |
|> map2 (fn unfs => unfold_thms lthy (id_apply :: unfs)) rel_unfoldss; |
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|
132 |
|
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133 |
val rel_defs = map rel_def_of_bnf bnfs; |
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134 |
val rel_monos = map rel_mono_of_bnf bnfs; |
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|
135 |
|
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136 |
val rel_xtor_co_induct_thm = |
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137 |
mk_rel_xtor_co_induct_thm fp pre_rels pre_phis rels phis xs ys xtors xtor's |
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138 |
(mk_rel_xtor_co_induct_tactic fp rel_xtor_co_inducts rel_defs rel_monos) lthy; |
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|
139 |
|
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140 |
val rel_eqs = no_refl (map rel_eq_of_bnf fp_nesty_bnfs); |
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141 |
val map_id0s = no_refl (map map_id0_of_bnf bnfs); |
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|
142 |
|
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143 |
val xtor_co_induct_thm = |
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144 |
(case fp of |
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145 |
Least_FP => |
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146 |
let |
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147 |
val (Ps, names_lthy) = names_lthy |
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148 |
|> mk_Frees "P" (map (fn T => T --> HOLogic.boolT) fpTs); |
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149 |
fun mk_Grp_id P = |
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150 |
let val T = domain_type (fastype_of P); |
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151 |
in mk_Grp (HOLogic.Collect_const T $ P) (HOLogic.id_const T) end; |
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152 |
val cts = map (SOME o certify lthy) (map HOLogic.eq_const As @ map mk_Grp_id Ps); |
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153 |
in |
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154 |
cterm_instantiate_pos cts rel_xtor_co_induct_thm |
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155 |
|> singleton (Proof_Context.export names_lthy lthy) |
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156 |
|> unfold_thms lthy (@{thms eq_le_Grp_id_iff all_simps(1,2)[symmetric]} @ rel_eqs) |
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157 |
|> funpow n (fn thm => thm RS spec) |
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|
158 |
|> unfold_thms lthy (@{thm eq_alt} :: map rel_Grp_of_bnf bnfs @ map_id0s) |
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159 |
|> unfold_thms lthy @{thms Grp_id_mono_subst eqTrueI[OF subset_UNIV] simp_thms(22)} |
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160 |
|> unfold_thms lthy @{thms subset_iff mem_Collect_eq |
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161 |
atomize_conjL[symmetric] atomize_all[symmetric] atomize_imp[symmetric]} |
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162 |
|> unfold_thms lthy (maps set_defs_of_bnf bnfs) |
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|
163 |
end |
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164 |
| Greatest_FP => |
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165 |
let |
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|
166 |
val cts = NONE :: map (SOME o certify lthy) (map HOLogic.eq_const As); |
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|
167 |
in |
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168 |
cterm_instantiate_pos cts rel_xtor_co_induct_thm |
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169 |
|> unfold_thms lthy (@{thms le_fun_def le_bool_def all_simps(1,2)[symmetric]} @ rel_eqs) |
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170 |
|> funpow (2 * n) (fn thm => thm RS spec) |
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|
171 |
|> Conv.fconv_rule (Object_Logic.atomize lthy) |
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172 |
|> funpow n (fn thm => thm RS mp) |
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|
173 |
end); |
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|
174 |
|
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175 |
val fold_preTs = map2 (fn Ds => mk_T_of_bnf Ds allAs) Dss bnfs; |
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176 |
val fold_pre_deads_only_Ts = map2 (fn Ds => mk_T_of_bnf Ds (replicate live dummyT)) Dss bnfs; |
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177 |
val rec_theta = Xs ~~ map2 mk_co_productT fpTs Xs; |
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178 |
val rec_preTs = map (Term.typ_subst_atomic rec_theta) fold_preTs; |
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|
179 |
|
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180 |
val fold_strTs = map2 mk_co_algT fold_preTs Xs; |
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181 |
val rec_strTs = map2 mk_co_algT rec_preTs Xs; |
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|
182 |
val resTs = map2 mk_co_algT fpTs Xs; |
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183 |
|
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184 |
val (((fold_strs, fold_strs'), (rec_strs, rec_strs')), names_lthy) = names_lthy |
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185 |
|> mk_Frees' "s" fold_strTs |
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186 |
||>> mk_Frees' "s" rec_strTs; |
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187 |
|
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188 |
val co_iters = steal #xtor_co_iterss; |
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189 |
val ns = map (length o #pre_bnfs) fp_sugars; |
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190 |
fun substT rho (Type (@{type_name "fun"}, [T, U])) = substT rho T --> substT rho U |
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191 |
| substT rho (Type (s, Ts)) = Type (s, map (typ_subst_nonatomic rho) Ts) |
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192 |
| substT _ T = T; |
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193 |
fun force_iter is_rec i TU TU_rec raw_iters = |
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194 |
let |
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195 |
val approx_fold = un_fold_of raw_iters |
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196 |
|> force_typ names_lthy |
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197 |
(replicate (nth ns i) dummyT ---> (if is_rec then TU_rec else TU)); |
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198 |
val subst = Term.typ_subst_atomic (Xs ~~ fpTs); |
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|
199 |
val TUs = map_split dest_co_algT (binder_fun_types (fastype_of approx_fold)) |
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200 |
|>> map subst |
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|
201 |
|> uncurry (map2 mk_co_algT); |
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|
202 |
val js = find_indices Type.could_unify TUs |
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203 |
(map2 (fn T => fn U => mk_co_algT (subst T) U) fold_preTs Xs); |
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204 |
val Tpats = map (fn j => mk_co_algT (nth fold_pre_deads_only_Ts j) (nth Xs j)) js; |
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|
205 |
val iter = raw_iters |> (if is_rec then co_rec_of else un_fold_of); |
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|
206 |
in |
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|
207 |
force_typ names_lthy (Tpats ---> TU) iter |
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|
208 |
end; |
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|
209 |
|
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|
210 |
fun mk_iter b_opt is_rec iters lthy TU = |
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|
211 |
let |
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|
212 |
val x = co_alg_argT TU; |
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|
213 |
val i = find_index (fn T => x = T) Xs; |
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|
214 |
val TUiter = |
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|
215 |
(case find_first (fn f => body_fun_type (fastype_of f) = TU) iters of |
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|
216 |
NONE => nth co_iters i |
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|
217 |
|> force_iter is_rec i |
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|
218 |
(TU |> (is_none b_opt andalso not is_rec) ? substT (fpTs ~~ Xs)) |
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|
219 |
(TU |> (is_none b_opt) ? substT (map2 mk_co_productT fpTs Xs ~~ Xs)) |
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|
220 |
| SOME f => f); |
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|
221 |
val TUs = binder_fun_types (fastype_of TUiter); |
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|
222 |
val iter_preTs = if is_rec then rec_preTs else fold_preTs; |
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|
223 |
val iter_strs = if is_rec then rec_strs else fold_strs; |
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|
224 |
fun mk_s TU' = |
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|
225 |
let |
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|
226 |
val i = find_index (fn T => co_alg_argT TU' = T) Xs; |
54233 | 227 |
val sF = co_alg_funT TU'; |
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|
228 |
val F = nth iter_preTs i; |
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|
229 |
val s = nth iter_strs i; |
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|
230 |
in |
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|
231 |
(if sF = F then s |
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|
232 |
else |
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|
233 |
let |
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|
234 |
val smapT = replicate live dummyT ---> mk_co_algT sF F; |
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|
235 |
fun hidden_to_unit t = |
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|
236 |
Term.subst_TVars (map (rpair HOLogic.unitT) (Term.add_tvar_names t [])) t; |
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|
237 |
val smap = map_of_bnf (nth bnfs i) |
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|
238 |
|> force_typ names_lthy smapT |
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|
239 |
|> hidden_to_unit; |
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|
240 |
val smap_argTs = strip_typeN live (fastype_of smap) |> fst; |
54233 | 241 |
fun mk_smap_arg TU = |
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242 |
(if domain_type TU = range_type TU then |
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243 |
HOLogic.id_const (domain_type TU) |
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244 |
else if is_rec then |
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|
245 |
let |
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|
246 |
val (TY, (U, X)) = TU |> dest_co_algT ||> dest_co_productT; |
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|
247 |
val T = mk_co_algT TY U; |
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|
248 |
in |
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|
249 |
(case try (force_typ lthy T o build_map lthy co_proj1_const o dest_funT) T of |
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|
250 |
SOME f => mk_co_product f |
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|
251 |
(fst (fst (mk_iter NONE is_rec iters lthy (mk_co_algT TY X)))) |
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|
252 |
| NONE => mk_map_co_product |
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|
253 |
(build_map lthy co_proj1_const |
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|
254 |
(dest_funT (mk_co_algT (dest_co_productT TY |> fst) U))) |
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|
255 |
(HOLogic.id_const X)) |
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|
256 |
end |
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|
257 |
else |
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|
258 |
fst (fst (mk_iter NONE is_rec iters lthy TU))) |
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|
259 |
val smap_args = map mk_smap_arg smap_argTs; |
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|
260 |
in |
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|
261 |
HOLogic.mk_comp (co_swap (s, Term.list_comb (smap, smap_args))) |
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|
262 |
end) |
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|
263 |
end; |
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|
264 |
val t = Term.list_comb (TUiter, map mk_s TUs); |
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|
265 |
in |
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|
266 |
(case b_opt of |
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|
267 |
NONE => ((t, Drule.dummy_thm), lthy) |
54233 | 268 |
| SOME b => Local_Theory.define ((b, NoSyn), ((Binding.conceal (Thm.def_binding b), []), |
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|
269 |
fold_rev Term.absfree (if is_rec then rec_strs' else fold_strs') t)) lthy |>> apsnd snd) |
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|
270 |
end; |
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|
271 |
|
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|
272 |
fun mk_iters is_rec name lthy = |
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|
273 |
fold2 (fn TU => fn b => fn ((iters, defs), lthy) => |
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|
274 |
mk_iter (SOME b) is_rec iters lthy TU |>> (fn (f, d) => (f :: iters, d :: defs))) |
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|
275 |
resTs (map (Binding.suffix_name ("_" ^ name)) bs) (([], []), lthy) |
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|
276 |
|>> apfst rev o apsnd rev; |
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|
277 |
val foldN = fp_case fp ctor_foldN dtor_unfoldN; |
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|
278 |
val recN = fp_case fp ctor_recN dtor_corecN; |
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|
279 |
val (((raw_un_folds, raw_un_fold_defs), (raw_co_recs, raw_co_rec_defs)), (lthy, raw_lthy)) = |
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|
280 |
lthy |
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|
281 |
|> mk_iters false foldN |
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|
282 |
||>> mk_iters true recN |
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|
283 |
||> `Local_Theory.restore; |
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|
284 |
|
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|
285 |
val phi = Proof_Context.export_morphism raw_lthy lthy; |
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|
286 |
|
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|
287 |
val un_folds = map (Morphism.term phi) raw_un_folds; |
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|
288 |
val co_recs = map (Morphism.term phi) raw_co_recs; |
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|
289 |
|
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|
290 |
val (xtor_un_fold_thms, xtor_co_rec_thms) = |
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|
291 |
let |
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|
292 |
val folds = map (fn f => Term.list_comb (f, fold_strs)) raw_un_folds; |
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|
293 |
val recs = map (fn r => Term.list_comb (r, rec_strs)) raw_co_recs; |
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|
294 |
val fold_mapTs = co_swap (As @ fpTs, As @ Xs); |
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|
295 |
val rec_mapTs = co_swap (As @ fpTs, As @ map2 mk_co_productT fpTs Xs); |
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|
296 |
val pre_fold_maps = |
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|
297 |
map2 (fn Ds => fn bnf => |
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|
298 |
Term.list_comb (uncurry (mk_map_of_bnf Ds) fold_mapTs bnf, |
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|
299 |
map HOLogic.id_const As @ folds)) |
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|
300 |
Dss bnfs; |
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|
301 |
val pre_rec_maps = |
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|
302 |
map2 (fn Ds => fn bnf => |
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|
303 |
Term.list_comb (uncurry (mk_map_of_bnf Ds) rec_mapTs bnf, |
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|
304 |
map HOLogic.id_const As @ map2 (mk_co_product o HOLogic.id_const) fpTs recs)) |
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305 |
Dss bnfs; |
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306 |
|
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307 |
fun mk_goals f xtor s smap = |
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308 |
((f, xtor), (s, smap)) |
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309 |
|> pairself (HOLogic.mk_comp o co_swap) |
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310 |
|> HOLogic.mk_eq; |
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311 |
|
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312 |
val fold_goals = map4 mk_goals folds xtors fold_strs pre_fold_maps |
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313 |
val rec_goals = map4 mk_goals recs xtors rec_strs pre_rec_maps; |
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314 |
|
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315 |
fun mk_thms ss goals tac = |
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316 |
Library.foldr1 HOLogic.mk_conj goals |
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317 |
|> HOLogic.mk_Trueprop |
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318 |
|> fold_rev Logic.all ss |
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|> (fn goal => Goal.prove_sorry raw_lthy [] [] goal tac) |
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320 |
|> Thm.close_derivation |
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321 |
|> Morphism.thm phi |
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322 |
|> split_conj_thm |
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|> map (fn thm => thm RS @{thm comp_eq_dest}); |
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324 |
|
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325 |
val pre_map_defs = no_refl (map map_def_of_bnf bnfs); |
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326 |
val fp_pre_map_defs = no_refl (map map_def_of_bnf pre_bnfs); |
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327 |
|
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328 |
val map_unfoldss = map (maps (fn bnf => no_refl [map_def_of_bnf bnf])) pre_bnfss; |
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329 |
val unfold_map = map2 (fn unfs => unfold_thms lthy (id_apply :: unfs)) map_unfoldss; |
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330 |
|
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331 |
val fp_xtor_co_iterss = steal #xtor_co_iter_thmss; |
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332 |
val fp_xtor_un_folds = map (mk_pointfree lthy o un_fold_of) fp_xtor_co_iterss |> unfold_map; |
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333 |
val fp_xtor_co_recs = map (mk_pointfree lthy o co_rec_of) fp_xtor_co_iterss |> unfold_map; |
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|
334 |
|
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335 |
val fp_co_iter_o_mapss = steal #xtor_co_iter_o_map_thmss; |
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336 |
val fp_fold_o_maps = map un_fold_of fp_co_iter_o_mapss |> unfold_map; |
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337 |
val fp_rec_o_maps = map co_rec_of fp_co_iter_o_mapss |> unfold_map; |
55067 | 338 |
val fold_thms = fp_case fp @{thm comp_assoc} @{thm comp_assoc[symmetric]} :: @{thms id_apply |
339 |
o_apply comp_id id_comp map_pair.comp map_pair.id sum_map.comp sum_map.id}; |
|
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340 |
val rec_thms = fold_thms @ fp_case fp |
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341 |
@{thms fst_convol map_pair_o_convol convol_o} |
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342 |
@{thms case_sum_o_inj(1) case_sum_o_sum_map o_case_sum}; |
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343 |
val map_thms = no_refl (maps (fn bnf => |
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344 |
[map_comp0_of_bnf bnf RS sym, map_id0_of_bnf bnf]) fp_nesty_bnfs); |
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345 |
|
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346 |
fun mk_tac defs o_map_thms xtor_thms thms {context = ctxt, prems = _} = |
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347 |
unfold_thms_tac ctxt |
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348 |
(flat [thms, defs, pre_map_defs, fp_pre_map_defs, xtor_thms, o_map_thms, map_thms]) THEN |
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349 |
CONJ_WRAP (K (HEADGOAL (rtac refl))) bnfs; |
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350 |
|
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351 |
val fold_tac = mk_tac raw_un_fold_defs fp_fold_o_maps fp_xtor_un_folds fold_thms; |
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352 |
val rec_tac = mk_tac raw_co_rec_defs fp_rec_o_maps fp_xtor_co_recs rec_thms; |
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353 |
in |
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354 |
(mk_thms fold_strs fold_goals fold_tac, mk_thms rec_strs rec_goals rec_tac) |
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355 |
end; |
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356 |
|
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357 |
(* These results are half broken. This is deliberate. We care only about those fields that are |
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358 |
used by "primrec", "primcorecursive", and "datatype_compat". *) |
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359 |
val fp_res = |
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360 |
({Ts = fpTs, |
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361 |
bnfs = steal #bnfs, |
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362 |
dtors = dtors, |
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363 |
ctors = ctors, |
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364 |
xtor_co_iterss = transpose [un_folds, co_recs], |
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365 |
xtor_co_induct = xtor_co_induct_thm, |
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366 |
dtor_ctors = steal #dtor_ctors (*too general types*), |
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367 |
ctor_dtors = steal #ctor_dtors (*too general types*), |
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ctor_injects = steal #ctor_injects (*too general types*), |
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dtor_injects = steal #dtor_injects (*too general types*), |
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370 |
xtor_map_thms = steal #xtor_map_thms (*too general types and terms*), |
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371 |
xtor_set_thmss = steal #xtor_set_thmss (*too general types and terms*), |
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372 |
xtor_rel_thms = steal #xtor_rel_thms (*too general types and terms*), |
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373 |
xtor_co_iter_thmss = transpose [xtor_un_fold_thms, xtor_co_rec_thms], |
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374 |
xtor_co_iter_o_map_thmss = steal #xtor_co_iter_o_map_thmss (*theorem about old constant*), |
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375 |
rel_xtor_co_induct_thm = rel_xtor_co_induct_thm} |
54740 | 376 |
|> morph_fp_result (Morphism.term_morphism "BNF" (singleton (Variable.polymorphic lthy)))); |
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377 |
in |
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378 |
(fp_res, lthy) |
54242 | 379 |
end; |
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380 |
|
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381 |
end; |