src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Mon May 27 13:30:08 2013 +0200 (2013-05-27)
changeset 52170 564be617ae84
parent 52169 418f5ad4c1c5
child 52171 012679d3a5af
permissions -rw-r--r--
generalized "mk_co_iter" to handle mutualized (co)iterators
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(*  Title:      HOL/BNF/Tools/bnf_fp_def_sugar.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Sugared datatype and codatatype constructions.
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*)
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signature BNF_FP_DEF_SUGAR =
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sig
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  type fp_sugar =
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    {T: typ,
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     lfp: bool,
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     index: int,
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     pre_bnfs: BNF_Def.bnf list,
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     fp_res: BNF_FP_Util.fp_result,
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     ctr_defss: thm list list,
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     ctr_sugars: BNF_Ctr_Sugar.ctr_sugar list,
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     un_folds: term list,
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     co_recs: term list,
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     co_induct: thm,
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     strong_co_induct: thm,
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     un_fold_thmss: thm list list,
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     co_rec_thmss: thm list list};
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  val morph_fp_sugar: morphism -> fp_sugar -> fp_sugar
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  val fp_sugar_of: Proof.context -> string -> fp_sugar option
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  val tvar_subst: theory -> typ list -> typ list -> ((string * int) * typ) list
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  val exists_subtype_in: typ list -> typ -> bool
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  val nesty_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
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  val indexify_fst: ''a list -> (int -> ''a * 'b -> 'c) -> ''a * 'b -> 'c
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  val mk_un_fold_co_rec_prelims: bool -> typ list -> typ list -> int list -> int list list ->
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    term list -> term list -> Proof.context ->
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    (term list * term list * ((term list list * typ list list * term list list list)
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       * (term list list * typ list list * term list list list)) option
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     * (term list * term list list
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        * ((term list list * term list list list list * term list list list list)
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           * (typ list * typ list list list * typ list list))
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        * ((term list list * term list list list list * term list list list list)
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           * (typ list * typ list list list * typ list list))) option)
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    * Proof.context
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  val build_map: local_theory -> (typ * typ -> term) -> typ * typ -> term
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  val mk_iter_fun_arg_types_pairsss: typ list -> int list -> int list list -> term ->
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    (typ list * typ list) list list list
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  val define_fold_rec: (term list list * typ list list * term list list list)
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      * (term list list * typ list list * term list list list) -> (string -> binding) -> typ list ->
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    typ list -> typ list -> term -> term -> Proof.context ->
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    (term * term * thm * thm) * Proof.context
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  val define_unfold_corec: term list * term list list
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      * ((term list list * term list list list list * term list list list list)
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         * (typ list * typ list list list * typ list list))
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      * ((term list list * term list list list list * term list list list list)
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         * (typ list * typ list list list * typ list list)) ->
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    (string -> binding) -> 'a list -> typ list -> typ list -> term -> term -> Proof.context ->
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    (term * term * thm * thm) * Proof.context
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  val derive_induct_fold_rec_thms_for_types: BNF_Def.bnf list -> term list -> term list -> thm ->
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    thm list -> thm list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list ->
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    term list list -> thm list list -> term list -> term list -> thm list -> thm list ->
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    local_theory ->
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    (thm * thm list * Args.src list) * (thm list list * Args.src list)
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    * (thm list list * Args.src list)
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  val derive_coinduct_unfold_corec_thms_for_types: BNF_Def.bnf list -> term list -> term list ->
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    thm -> thm -> thm list -> thm list -> thm list -> BNF_Def.bnf list -> BNF_Def.bnf list ->
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    typ list -> typ list -> typ list -> int list list -> int list list -> int list ->
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    thm list list -> BNF_Ctr_Sugar.ctr_sugar list -> term list -> term list -> thm list ->
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    thm list -> local_theory ->
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    (thm * thm list * thm * thm list * Args.src list)
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    * (thm list list * thm list list * Args.src list)
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    * (thm list list * thm list list) * (thm list list * thm list list * Args.src list)
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    * (thm list list * thm list list * Args.src list)
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    * (thm list list * thm list list * Args.src list)
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  val co_datatypes: bool -> (mixfix list -> binding list -> binding list -> binding list 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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    (bool * bool) * (((((binding * (typ * sort)) list * binding) * (binding * binding)) * mixfix) *
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      ((((binding * binding) * (binding * typ) list) * (binding * term) list) *
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        mixfix) list) list ->
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    local_theory -> local_theory
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  val parse_co_datatype_cmd: bool -> (mixfix list -> binding list -> binding list ->
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      binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
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      BNF_Def.bnf list -> local_theory -> BNF_FP_Util.fp_result * local_theory) ->
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    (local_theory -> local_theory) parser
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end;
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structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
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struct
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open BNF_Util
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open BNF_Ctr_Sugar
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open BNF_Def
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open BNF_FP_Util
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open BNF_FP_Def_Sugar_Tactics
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val EqN = "Eq_";
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type fp_sugar =
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  {T: typ,
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   lfp: bool,
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   index: int,
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   pre_bnfs: bnf list,
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   fp_res: fp_result,
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   ctr_defss: thm list list,
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   ctr_sugars: ctr_sugar list,
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   un_folds: term list,
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   co_recs: term list,
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   co_induct: thm,
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   strong_co_induct: thm,
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   un_fold_thmss: thm list list,
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   co_rec_thmss: thm list list};
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fun eq_fp_sugar ({T = T1, lfp = lfp1, index = index1, fp_res = fp_res1, ...} : fp_sugar,
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    {T = T2, lfp = lfp2, index = index2, fp_res = fp_res2, ...} : fp_sugar) =
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  T1 = T2 andalso lfp1 = lfp2 andalso index1 = index2 andalso eq_fp_result (fp_res1, fp_res2);
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fun morph_fp_sugar phi {T, lfp, index, pre_bnfs, fp_res, ctr_defss, ctr_sugars, un_folds, co_recs,
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    co_induct, strong_co_induct, un_fold_thmss, co_rec_thmss} =
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  {T = Morphism.typ phi T, lfp = lfp, index = index, pre_bnfs = map (morph_bnf phi) pre_bnfs,
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   fp_res = morph_fp_result phi fp_res, ctr_defss = map (map (Morphism.thm phi)) ctr_defss,
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   ctr_sugars = map (morph_ctr_sugar phi) ctr_sugars, un_folds = map (Morphism.term phi) un_folds,
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   co_recs = map (Morphism.term phi) co_recs, co_induct = Morphism.thm phi co_induct,
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   strong_co_induct = Morphism.thm phi strong_co_induct,
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   un_fold_thmss = map (map (Morphism.thm phi)) un_fold_thmss,
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   co_rec_thmss = map (map (Morphism.thm phi)) co_rec_thmss};
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structure Data = Generic_Data
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(
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  type T = fp_sugar Symtab.table;
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  val empty = Symtab.empty;
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  val extend = I;
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  val merge = Symtab.merge eq_fp_sugar;
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);
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val fp_sugar_of = Symtab.lookup o Data.get o Context.Proof;
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fun register_fp_sugar key fp_sugar =
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  Local_Theory.declaration {syntax = false, pervasive = true}
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    (fn phi => Data.map (Symtab.update_new (key, morph_fp_sugar phi fp_sugar)));
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fun register_fp_sugars lfp pre_bnfs (fp_res as {Ts, ...}) ctr_defss ctr_sugars un_folds co_recs
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    co_induct strong_co_induct un_fold_thmss co_rec_thmss lthy =
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  (0, lthy)
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  |> fold (fn T as Type (s, _) => fn (kk, lthy) => (kk + 1,
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    register_fp_sugar s {T = T, lfp = lfp, index = kk, pre_bnfs = pre_bnfs, fp_res = fp_res,
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      ctr_defss = ctr_defss, ctr_sugars = ctr_sugars, un_folds = un_folds, co_recs = co_recs,
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      co_induct = co_induct, strong_co_induct = strong_co_induct, un_fold_thmss = un_fold_thmss,
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      co_rec_thmss = co_rec_thmss} lthy)) Ts
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  |> snd;
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(* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A"). *)
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fun quasi_unambiguous_case_names names =
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  let
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    val ps = map (`Long_Name.base_name) names;
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    val dups = Library.duplicates (op =) (map fst ps);
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    fun underscore s =
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      let val ss = space_explode Long_Name.separator s in
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        space_implode "_" (drop (length ss - 2) ss)
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      end;
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  in
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    map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
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  end;
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val mp_conj = @{thm mp_conj};
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val simp_attrs = @{attributes [simp]};
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val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs;
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fun tvar_subst thy Ts Us =
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  Vartab.fold (cons o apsnd snd) (fold (Sign.typ_match thy) (Ts ~~ Us) Vartab.empty) [];
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val exists_subtype_in = Term.exists_subtype o member (op =);
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fun resort_tfree S (TFree (s, _)) = TFree (s, S);
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fun typ_subst_nonatomic inst (T as Type (s, Ts)) =
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    (case AList.lookup (op =) inst T of
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      NONE => Type (s, map (typ_subst_nonatomic inst) Ts)
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    | SOME T' => T')
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  | typ_subst_nonatomic inst T = the_default T (AList.lookup (op =) inst T);
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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
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fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
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fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
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fun flat_rec unzipf xs =
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  let val ps = map unzipf xs in
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    (* The first line below gives the preferred order. The second line is for compatibility with the
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       old datatype package: *)
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(*
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    maps (op @) ps
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*)
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    maps fst ps @ maps snd ps
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  end;
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fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss);
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fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss
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  | flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
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    p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss;
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fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
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  Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
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fun flip_rels lthy n thm =
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  let
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    val Rs = Term.add_vars (prop_of thm) [];
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    val Rs' = rev (drop (length Rs - n) Rs);
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    val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs';
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  in
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    Drule.cterm_instantiate cRs thm
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  end;
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fun mk_ctor_or_dtor get_T Ts t =
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  let val Type (_, Ts0) = get_T (fastype_of t) in
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    Term.subst_atomic_types (Ts0 ~~ Ts) t
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  end;
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val mk_ctor = mk_ctor_or_dtor range_type;
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val mk_dtor = mk_ctor_or_dtor domain_type;
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fun mk_co_iter thy lfp fpT Us t =
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  let
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    val (bindings, body) = strip_type (fastype_of t);
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    val (f_Us, prebody) = split_last bindings;
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    val fpT0 = if lfp then prebody else body;
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    val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
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    val rho = tvar_subst thy (fpT0 :: Us0) (fpT :: Us);
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  in
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    Term.subst_TVars rho t
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  end;
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fun mk_co_iters thy lfp fpTs Cs ts0 =
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  let
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    val nn = length fpTs;
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    val (fpTs0, Cs0) =
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      map ((not lfp ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0
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      |> split_list;
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    val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs);
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  in
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    map (Term.subst_TVars rho) ts0
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  end;
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val mk_fp_iter_fun_types = fst o split_last o binder_types o fastype_of;
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fun mk_fp_iters thy lfp fpTs Cs fp_iters0 =
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  mk_co_iters thy lfp fpTs Cs fp_iters0
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  |> (fn ts => (ts, mk_fp_iter_fun_types (hd ts)));
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fun unzip_recT fpTs T =
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  let
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    fun project_recT proj =
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      let
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        fun project (Type (s as @{type_name prod}, Ts as [T, U])) =
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            if member (op =) fpTs T then proj (T, U) else Type (s, map project Ts)
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          | project (Type (s, Ts)) = Type (s, map project Ts)
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          | project T = T;
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      in project end;
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  in
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    if exists_subtype_in fpTs T then ([project_recT fst T], [project_recT snd T]) else ([T], [])
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  end;
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fun mk_fold_fun_typess y_Tsss Cs = map2 (fn C => map (fn y_Ts => y_Ts ---> C)) Cs y_Tsss;
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val mk_rec_fun_typess = mk_fold_fun_typess oo map o map o flat_rec o unzip_recT;
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fun mk_fun_arg_typess n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type;
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fun mk_iter_fun_arg_types_pairsss fpTs ns mss =
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  mk_fp_iter_fun_types
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  #> map3 mk_fun_arg_typess ns mss
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  #> map (map (map (unzip_recT fpTs)));
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fun mk_fold_rec_args_types fpTs Cs ns mss ctor_fold_fun_Ts ctor_rec_fun_Ts lthy =
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  let
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    val y_Tsss = map3 mk_fun_arg_typess ns mss ctor_fold_fun_Ts;
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    val g_Tss = mk_fold_fun_typess y_Tsss Cs;
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    val ((gss, ysss), lthy) =
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      lthy
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      |> mk_Freess "f" g_Tss
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      ||>> mk_Freesss "x" y_Tsss;
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    val z_Tsss = map3 mk_fun_arg_typess ns mss ctor_rec_fun_Ts;
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   285
    val h_Tss = mk_rec_fun_typess fpTs z_Tsss Cs;
blanchet@51832
   286
blanchet@51832
   287
    val hss = map2 (map2 retype_free) h_Tss gss;
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   288
    val zsss = map2 (map2 (map2 retype_free)) z_Tsss ysss;
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   289
  in
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   290
    (((gss, g_Tss, ysss), (hss, h_Tss, zsss)), lthy)
blanchet@51832
   291
  end;
blanchet@51832
   292
blanchet@51888
   293
fun mk_unfold_corec_args_types fpTs Cs ns mss dtor_unfold_fun_Ts dtor_corec_fun_Ts lthy =
blanchet@51829
   294
  let
blanchet@51829
   295
    (*avoid "'a itself" arguments in coiterators and corecursors*)
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   296
    fun repair_arity [0] = [1]
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   297
      | repair_arity ms = ms;
blanchet@51829
   298
blanchet@51829
   299
    fun project_corecT proj =
blanchet@51829
   300
      let
blanchet@51829
   301
        fun project (Type (s as @{type_name sum}, Ts as [T, U])) =
blanchet@51829
   302
            if member (op =) fpTs T then proj (T, U) else Type (s, map project Ts)
blanchet@51829
   303
          | project (Type (s, Ts)) = Type (s, map project Ts)
blanchet@51829
   304
          | project T = T;
blanchet@51829
   305
      in project end;
blanchet@51829
   306
blanchet@51829
   307
    fun unzip_corecT T =
blanchet@51829
   308
      if exists_subtype_in fpTs T then [project_corecT fst T, project_corecT snd T] else [T];
blanchet@51829
   309
blanchet@51831
   310
    val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@51829
   311
blanchet@51829
   312
    fun mk_types maybe_unzipT fun_Ts =
blanchet@51829
   313
      let
blanchet@51829
   314
        val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@51829
   315
        val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@51829
   316
        val f_Tsss = map2 (map2 dest_tupleT o repair_arity) mss f_prod_Tss;
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   317
        val f_Tssss = map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
blanchet@51829
   318
        val q_Tssss =
blanchet@51829
   319
          map (map (map (fn [_] => [] | [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss;
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   320
        val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@51889
   321
      in (q_Tssss, f_Tssss, (f_sum_prod_Ts, f_Tsss, pf_Tss)) end;
blanchet@51829
   322
blanchet@51889
   323
    val (r_Tssss, g_Tssss, unfold_types) = mk_types single dtor_unfold_fun_Ts;
blanchet@51889
   324
    val (s_Tssss, h_Tssss, corec_types) = mk_types unzip_corecT dtor_corec_fun_Ts;
blanchet@51831
   325
blanchet@51829
   326
    val (((cs, pss), gssss), lthy) =
blanchet@51829
   327
      lthy
blanchet@51829
   328
      |> mk_Frees "a" Cs
blanchet@51829
   329
      ||>> mk_Freess "p" p_Tss
blanchet@51829
   330
      ||>> mk_Freessss "g" g_Tssss;
blanchet@51829
   331
    val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@51829
   332
blanchet@51829
   333
    val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@51829
   334
    val ((sssss, hssss_tl), lthy) =
blanchet@51829
   335
      lthy
blanchet@51829
   336
      |> mk_Freessss "q" s_Tssss
blanchet@51829
   337
      ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@51829
   338
    val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@51831
   339
blanchet@51831
   340
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   341
blanchet@51889
   342
    fun mk_args qssss fssss =
blanchet@51831
   343
      let
blanchet@51831
   344
        val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
blanchet@51831
   345
        val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@51831
   346
        val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@51831
   347
      in (pfss, cqssss, cfssss) end;
blanchet@51831
   348
blanchet@51889
   349
    val unfold_args = mk_args rssss gssss;
blanchet@51889
   350
    val corec_args = mk_args sssss hssss;
blanchet@51831
   351
  in
blanchet@51889
   352
    ((cs, cpss, (unfold_args, unfold_types), (corec_args, corec_types)), lthy)
blanchet@51831
   353
  end;
blanchet@51829
   354
blanchet@51912
   355
fun mk_un_fold_co_rec_prelims lfp fpTs Cs ns mss fp_folds0 fp_recs0 lthy =
blanchet@51903
   356
  let
blanchet@52169
   357
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   358
blanchet@52169
   359
    val (fp_folds, fp_fold_fun_Ts) = mk_fp_iters thy lfp fpTs Cs fp_folds0;
blanchet@52169
   360
    val (fp_recs, fp_rec_fun_Ts) = mk_fp_iters thy lfp fpTs Cs fp_recs0;
blanchet@51903
   361
blanchet@51903
   362
    val ((fold_rec_args_types, unfold_corec_args_types), lthy') =
blanchet@51903
   363
      if lfp then
blanchet@51903
   364
        mk_fold_rec_args_types fpTs Cs ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy
blanchet@51903
   365
        |>> (rpair NONE o SOME)
blanchet@51903
   366
      else
blanchet@51903
   367
        mk_unfold_corec_args_types fpTs Cs ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy
blanchet@51903
   368
        |>> (pair NONE o SOME)
blanchet@51903
   369
  in
blanchet@51903
   370
    ((fp_folds, fp_recs, fold_rec_args_types, unfold_corec_args_types), lthy')
blanchet@51903
   371
  end;
blanchet@51903
   372
blanchet@49536
   373
fun mk_map live Ts Us t =
blanchet@49536
   374
  let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in
blanchet@49536
   375
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49536
   376
  end;
blanchet@49536
   377
blanchet@49591
   378
fun mk_rel live Ts Us t =
blanchet@49591
   379
  let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in
blanchet@49591
   380
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49591
   381
  end;
blanchet@49591
   382
blanchet@49585
   383
fun liveness_of_fp_bnf n bnf =
blanchet@49585
   384
  (case T_of_bnf bnf of
blanchet@49585
   385
    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
blanchet@49585
   386
  | _ => replicate n false);
blanchet@49536
   387
blanchet@49124
   388
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
blanchet@49119
   389
blanchet@49298
   390
fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
blanchet@49119
   391
blanchet@49298
   392
fun merge_type_args (As, As') =
blanchet@49298
   393
  if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
blanchet@49119
   394
blanchet@49591
   395
fun reassoc_conjs thm =
blanchet@49591
   396
  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
blanchet@49591
   397
  handle THM _ => thm;
blanchet@49591
   398
blanchet@51767
   399
fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs;
blanchet@51767
   400
fun type_binding_of ((((_, b), _), _), _) = b;
blanchet@51767
   401
fun map_binding_of (((_, (b, _)), _), _) = b;
blanchet@51767
   402
fun rel_binding_of (((_, (_, b)), _), _) = b;
blanchet@49181
   403
fun mixfix_of ((_, mx), _) = mx;
blanchet@49121
   404
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
blanchet@49119
   405
blanchet@49286
   406
fun disc_of ((((disc, _), _), _), _) = disc;
blanchet@49286
   407
fun ctr_of ((((_, ctr), _), _), _) = ctr;
blanchet@49286
   408
fun args_of (((_, args), _), _) = args;
blanchet@49286
   409
fun defaults_of ((_, ds), _) = ds;
blanchet@49181
   410
fun ctr_mixfix_of (_, mx) = mx;
blanchet@49119
   411
blanchet@51907
   412
fun add_nesty_bnf_names Us =
blanchet@51907
   413
  let
blanchet@51907
   414
    fun add (Type (s, Ts)) ss =
blanchet@51907
   415
        let val (needs, ss') = fold_map add Ts ss in
blanchet@51907
   416
          if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@51907
   417
        end
blanchet@51907
   418
      | add T ss = (member (op =) Us T, ss);
blanchet@51907
   419
  in snd oo add end;
blanchet@51907
   420
blanchet@51907
   421
fun nesty_bnfs ctxt ctr_Tsss Us =
blanchet@51907
   422
  map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
blanchet@51907
   423
blanchet@51855
   424
fun indexify_fst xs f (x, y) = f (find_index (curry (op =) x) xs) (x, y);
blanchet@51855
   425
blanchet@51854
   426
fun build_map lthy build_simple =
blanchet@51853
   427
  let
blanchet@51853
   428
    fun build (TU as (T, U)) =
blanchet@51853
   429
      if T = U then
blanchet@51853
   430
        id_const T
blanchet@51853
   431
      else
blanchet@51853
   432
        (case TU of
blanchet@51854
   433
          (Type (s, Ts), Type (s', Us)) =>
blanchet@51854
   434
          if s = s' then
blanchet@51854
   435
            let
blanchet@51854
   436
              val bnf = the (bnf_of lthy s);
blanchet@51854
   437
              val live = live_of_bnf bnf;
blanchet@51854
   438
              val mapx = mk_map live Ts Us (map_of_bnf bnf);
blanchet@51854
   439
              val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
blanchet@51854
   440
            in Term.list_comb (mapx, map build TUs') end
blanchet@51854
   441
          else
blanchet@51854
   442
            build_simple TU
blanchet@51853
   443
        | _ => build_simple TU);
blanchet@51853
   444
  in build end;
blanchet@51853
   445
blanchet@51884
   446
fun mk_iter_body lthy fpTs ctor_iter fss xsss =
blanchet@51884
   447
  let
blanchet@51884
   448
    fun build_prod_proj mk_proj = build_map lthy (mk_proj o fst);
blanchet@51884
   449
blanchet@51884
   450
    (* TODO: Avoid these complications; cf. corec case *)
blanchet@51884
   451
    fun mk_U proj (Type (s as @{type_name prod}, Ts as [T', U])) =
blanchet@51884
   452
        if member (op =) fpTs T' then proj (T', U) else Type (s, map (mk_U proj) Ts)
blanchet@51884
   453
      | mk_U proj (Type (s, Ts)) = Type (s, map (mk_U proj) Ts)
blanchet@51884
   454
      | mk_U _ T = T;
blanchet@51884
   455
blanchet@51884
   456
    fun unzip_rec (x as Free (_, T)) =
blanchet@51884
   457
      if exists_subtype_in fpTs T then
blanchet@51884
   458
        ([build_prod_proj fst_const (T, mk_U fst T) $ x],
blanchet@51884
   459
         [build_prod_proj snd_const (T, mk_U snd T) $ x])
blanchet@51884
   460
      else
blanchet@51884
   461
        ([x], []);
blanchet@51884
   462
blanchet@51884
   463
    fun mk_iter_arg f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f (flat_rec unzip_rec xs);
blanchet@51884
   464
  in
blanchet@51884
   465
    Term.list_comb (ctor_iter, map2 (mk_sum_caseN_balanced oo map2 mk_iter_arg) fss xsss)
blanchet@51884
   466
  end;
blanchet@51884
   467
blanchet@51900
   468
fun mk_preds_getterss_join c cps sum_prod_T cqfss =
blanchet@51900
   469
  let val n = length cqfss in
blanchet@51900
   470
    Term.lambda c (mk_IfN sum_prod_T cps
blanchet@51900
   471
      (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)))
blanchet@51900
   472
  end;
blanchet@51886
   473
blanchet@51900
   474
fun mk_coiter_body lthy cs cpss f_sum_prod_Ts f_Tsss cqssss cfssss dtor_coiter =
blanchet@51888
   475
  let
blanchet@51888
   476
    fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@51888
   477
blanchet@51888
   478
    fun build_dtor_coiter_arg _ [] [cf] = cf
blanchet@51888
   479
      | build_dtor_coiter_arg T [cq] [cf, cf'] =
blanchet@51888
   480
        mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@51888
   481
          (build_sum_inj Inr_const (fastype_of cf', T) $ cf')
blanchet@51888
   482
blanchet@51888
   483
    val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
blanchet@51888
   484
  in
blanchet@51900
   485
    Term.list_comb (dtor_coiter, map4 mk_preds_getterss_join cs cpss f_sum_prod_Ts cqfsss)
blanchet@51888
   486
  end;
blanchet@51886
   487
blanchet@51907
   488
fun define_fold_rec (fold_only, rec_only) mk_binding fpTs As Cs ctor_fold ctor_rec lthy0 =
blanchet@51897
   489
  let
blanchet@52170
   490
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   491
blanchet@51899
   492
    val nn = length fpTs;
blanchet@51899
   493
blanchet@52170
   494
    val fpT_to_C as Type (_, [fpT, _]) = snd (strip_typeN nn (fastype_of ctor_fold));
blanchet@51897
   495
blanchet@51897
   496
    fun generate_iter (suf, ctor_iter, (fss, f_Tss, xsss)) =
blanchet@51897
   497
      let
blanchet@51899
   498
        val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@51897
   499
        val binding = mk_binding suf;
blanchet@51897
   500
        val spec =
blanchet@51897
   501
          mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@51907
   502
            mk_iter_body lthy0 fpTs ctor_iter fss xsss);
blanchet@51897
   503
      in (binding, spec) end;
blanchet@51897
   504
blanchet@51897
   505
    val binding_specs =
blanchet@51897
   506
      map generate_iter [(foldN, ctor_fold, fold_only), (recN, ctor_rec, rec_only)];
blanchet@51897
   507
blanchet@51907
   508
    val ((csts, defs), (lthy', lthy)) = lthy0
blanchet@51897
   509
      |> apfst split_list o fold_map (fn (b, spec) =>
blanchet@51897
   510
        Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@51897
   511
        #>> apsnd snd) binding_specs
blanchet@51897
   512
      ||> `Local_Theory.restore;
blanchet@51897
   513
blanchet@51897
   514
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@51897
   515
blanchet@51897
   516
    val [fold_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@51897
   517
blanchet@52170
   518
    val [foldx, recx] = map (mk_co_iter thy true fpT Cs o Morphism.term phi) csts;
blanchet@51897
   519
  in
blanchet@51897
   520
    ((foldx, recx, fold_def, rec_def), lthy')
blanchet@51897
   521
  end;
blanchet@51897
   522
blanchet@51902
   523
fun define_unfold_corec (cs, cpss, unfold_only, corec_only) mk_binding fpTs As Cs dtor_unfold
blanchet@51907
   524
    dtor_corec lthy0 =
blanchet@51897
   525
  let
blanchet@52170
   526
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   527
blanchet@51899
   528
    val nn = length fpTs;
blanchet@51899
   529
blanchet@52170
   530
    val C_to_fpT as Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of dtor_unfold));
blanchet@51897
   531
blanchet@51897
   532
    fun generate_coiter (suf, dtor_coiter, ((pfss, cqssss, cfssss),
blanchet@51897
   533
        (f_sum_prod_Ts, f_Tsss, pf_Tss))) =
blanchet@51897
   534
      let
blanchet@51899
   535
        val res_T = fold_rev (curry (op --->)) pf_Tss C_to_fpT;
blanchet@51897
   536
        val binding = mk_binding suf;
blanchet@51897
   537
        val spec =
blanchet@51897
   538
          mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@51907
   539
            mk_coiter_body lthy0 cs cpss f_sum_prod_Ts f_Tsss cqssss cfssss dtor_coiter);
blanchet@51897
   540
      in (binding, spec) end;
blanchet@51897
   541
blanchet@51897
   542
    val binding_specs =
blanchet@51897
   543
      map generate_coiter [(unfoldN, dtor_unfold, unfold_only), (corecN, dtor_corec, corec_only)];
blanchet@51897
   544
blanchet@51907
   545
    val ((csts, defs), (lthy', lthy)) = lthy0
blanchet@51897
   546
      |> apfst split_list o fold_map (fn (b, spec) =>
blanchet@51897
   547
        Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@51897
   548
        #>> apsnd snd) binding_specs
blanchet@51897
   549
      ||> `Local_Theory.restore;
blanchet@51897
   550
blanchet@51897
   551
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@51897
   552
blanchet@51897
   553
    val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@51897
   554
blanchet@52170
   555
    val [unfold, corec] = map (mk_co_iter thy false fpT Cs o Morphism.term phi) csts;
blanchet@51897
   556
  in
blanchet@51897
   557
    ((unfold, corec, unfold_def, corec_def), lthy')
blanchet@51897
   558
  end;
blanchet@51897
   559
blanchet@51827
   560
fun derive_induct_fold_rec_thms_for_types pre_bnfs ctor_folds0 ctor_recs0 ctor_induct ctor_fold_thms
blanchet@51912
   561
    ctor_rec_thms nesting_bnfs nested_bnfs fpTs Cs ctrss ctr_defss folds recs fold_defs rec_defs
blanchet@51827
   562
    lthy =
blanchet@51808
   563
  let
blanchet@52169
   564
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   565
blanchet@51827
   566
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   567
blanchet@51815
   568
    val nn = length pre_bnfs;
blanchet@51827
   569
    val ns = map length ctr_Tsss;
blanchet@51827
   570
    val mss = map (map length) ctr_Tsss;
blanchet@51815
   571
blanchet@51808
   572
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   573
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@51830
   574
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51808
   575
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
blanchet@51808
   576
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
blanchet@51810
   577
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51808
   578
blanchet@51816
   579
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   580
blanchet@52169
   581
    val (_, ctor_fold_fun_Ts) = mk_fp_iters thy true fpTs Cs ctor_folds0;
blanchet@52169
   582
    val (_, ctor_rec_fun_Ts) = mk_fp_iters thy true fpTs Cs ctor_recs0;
blanchet@51827
   583
blanchet@51835
   584
    val (((gss, _, _), (hss, _, _)), names_lthy0) =
blanchet@51889
   585
      mk_fold_rec_args_types fpTs Cs ns mss ctor_fold_fun_Ts ctor_rec_fun_Ts lthy;
blanchet@51827
   586
blanchet@51832
   587
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@51832
   588
      names_lthy0
blanchet@51808
   589
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   590
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   591
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   592
blanchet@51808
   593
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   594
blanchet@51808
   595
    fun mk_sets_nested bnf =
blanchet@51808
   596
      let
blanchet@51808
   597
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   598
        val lives = lives_of_bnf bnf;
blanchet@51808
   599
        val sets = sets_of_bnf bnf;
blanchet@51808
   600
        fun mk_set U =
blanchet@51808
   601
          (case find_index (curry (op =) U) lives of
blanchet@51808
   602
            ~1 => Term.dummy
blanchet@51808
   603
          | i => nth sets i);
blanchet@51808
   604
      in
blanchet@51808
   605
        (T_name, map mk_set Us)
blanchet@51808
   606
      end;
blanchet@51808
   607
blanchet@51808
   608
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   609
blanchet@51808
   610
    val (induct_thms, induct_thm) =
blanchet@51808
   611
      let
blanchet@51808
   612
        fun mk_set Ts t =
blanchet@51808
   613
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   614
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   615
          end;
blanchet@51808
   616
blanchet@51808
   617
        fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
blanchet@51808
   618
            (case find_index (curry (op =) T) fpTs of
blanchet@51808
   619
              ~1 =>
blanchet@51808
   620
              (case AList.lookup (op =) setss_nested T_name of
blanchet@51808
   621
                NONE => []
blanchet@51808
   622
              | SOME raw_sets0 =>
blanchet@51808
   623
                let
blanchet@51808
   624
                  val (Ts, raw_sets) =
blanchet@51808
   625
                    split_list (filter (exists_subtype_in fpTs o fst) (Ts0 ~~ raw_sets0));
blanchet@51808
   626
                  val sets = map (mk_set Ts0) raw_sets;
blanchet@51808
   627
                  val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@51808
   628
                  val xysets = map (pair x) (ys ~~ sets);
blanchet@51808
   629
                  val ppremss = map (mk_raw_prem_prems names_lthy') ys;
blanchet@51808
   630
                in
blanchet@51808
   631
                  flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@51808
   632
                end)
blanchet@51808
   633
            | kk => [([], (kk + 1, x))])
blanchet@51808
   634
          | mk_raw_prem_prems _ _ = [];
blanchet@51808
   635
blanchet@51808
   636
        fun close_prem_prem xs t =
blanchet@51808
   637
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   638
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   639
blanchet@51808
   640
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   641
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   642
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   643
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   644
blanchet@51808
   645
        fun mk_raw_prem phi ctr ctr_Ts =
blanchet@51808
   646
          let
blanchet@51808
   647
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@51808
   648
            val pprems = maps (mk_raw_prem_prems names_lthy') xs;
blanchet@51808
   649
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   650
blanchet@51808
   651
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   652
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   653
blanchet@51808
   654
        val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss;
blanchet@51808
   655
blanchet@51808
   656
        val goal =
blanchet@51808
   657
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@51808
   658
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@51808
   659
blanchet@51808
   660
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   661
blanchet@51814
   662
        val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@51808
   663
blanchet@51808
   664
        val thm =
blanchet@51808
   665
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51808
   666
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
blanchet@51808
   667
              pre_set_defss)
blanchet@51808
   668
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51808
   669
          |> Thm.close_derivation;
blanchet@51808
   670
      in
blanchet@51808
   671
        `(conj_dests nn) thm
blanchet@51808
   672
      end;
blanchet@51808
   673
blanchet@51808
   674
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@51808
   675
blanchet@51808
   676
    val (fold_thmss, rec_thmss) =
blanchet@51808
   677
      let
blanchet@51808
   678
        val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@51808
   679
        val gfolds = map (lists_bmoc gss) folds;
blanchet@51808
   680
        val hrecs = map (lists_bmoc hss) recs;
blanchet@51808
   681
blanchet@51843
   682
        fun mk_goal fss fiter xctr f xs fxs =
blanchet@51808
   683
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@51843
   684
            (mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   685
blanchet@51845
   686
        val mk_U = typ_subst_nonatomic (map2 pair fpTs Cs);
blanchet@51808
   687
blanchet@51843
   688
        fun unzip_iters fiters combine (x as Free (_, T)) =
blanchet@51808
   689
          if exists_subtype_in fpTs T then
blanchet@51855
   690
            combine (x, build_map lthy (indexify_fst fpTs (K o nth fiters)) (T, mk_U T) $ x)
blanchet@51808
   691
          else
blanchet@51808
   692
            ([x], []);
blanchet@51808
   693
blanchet@51843
   694
        val gxsss = map (map (flat_rec (unzip_iters gfolds (fn (_, t) => ([t], []))))) xsss;
blanchet@51843
   695
        val hxsss = map (map (flat_rec (unzip_iters hrecs (pairself single)))) xsss;
blanchet@51808
   696
blanchet@51808
   697
        val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
blanchet@51808
   698
        val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
blanchet@51808
   699
blanchet@51808
   700
        val fold_tacss =
blanchet@51843
   701
          map2 (map o mk_iter_tac pre_map_defs [] nesting_map_ids'' fold_defs) ctor_fold_thms
blanchet@51808
   702
            ctr_defss;
blanchet@51808
   703
        val rec_tacss =
blanchet@51843
   704
          map2 (map o mk_iter_tac pre_map_defs nested_map_comp's
blanchet@51814
   705
            (nested_map_ids'' @ nesting_map_ids'') rec_defs) ctor_rec_thms ctr_defss;
blanchet@51808
   706
blanchet@51808
   707
        fun prove goal tac =
blanchet@51808
   708
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   709
          |> Thm.close_derivation;
blanchet@51808
   710
      in
blanchet@51808
   711
        (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
blanchet@51808
   712
      end;
blanchet@51808
   713
blanchet@51808
   714
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   715
  in
blanchet@51810
   716
    ((induct_thm, induct_thms, [induct_case_names_attr]),
blanchet@51808
   717
     (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
blanchet@51808
   718
  end;
blanchet@51808
   719
blanchet@51829
   720
fun derive_coinduct_unfold_corec_thms_for_types pre_bnfs dtor_unfolds0 dtor_corecs0 dtor_coinduct
blanchet@51814
   721
    dtor_strong_induct dtor_ctors dtor_unfold_thms dtor_corec_thms nesting_bnfs nested_bnfs fpTs Cs
blanchet@51840
   722
    As kss mss ns ctr_defss ctr_sugars unfolds corecs unfold_defs corec_defs lthy =
blanchet@51810
   723
  let
blanchet@52169
   724
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   725
blanchet@51815
   726
    val nn = length pre_bnfs;
blanchet@51815
   727
blanchet@51810
   728
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   729
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
   730
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51830
   731
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   732
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
blanchet@51810
   733
    val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs;
blanchet@51810
   734
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
blanchet@51810
   735
blanchet@51816
   736
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   737
blanchet@52169
   738
    val (_, dtor_unfold_fun_Ts) = mk_fp_iters thy false fpTs Cs dtor_unfolds0;
blanchet@52169
   739
    val (_, dtor_corec_fun_Ts) = mk_fp_iters thy false fpTs Cs dtor_corecs0;
blanchet@51829
   740
blanchet@51840
   741
    val ctrss = map (map (mk_ctr As) o #ctrs) ctr_sugars;
blanchet@51840
   742
    val discss = map (map (mk_disc_or_sel As) o #discs) ctr_sugars;
blanchet@51840
   743
    val selsss = map (map (map (mk_disc_or_sel As)) o #selss) ctr_sugars;
blanchet@51840
   744
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   745
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   746
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   747
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   748
blanchet@51831
   749
    val ((cs, cpss, ((pgss, crssss, cgssss), _), ((phss, csssss, chssss), _)), names_lthy0) =
blanchet@51888
   750
      mk_unfold_corec_args_types fpTs Cs ns mss dtor_unfold_fun_Ts dtor_corec_fun_Ts lthy;
blanchet@51831
   751
blanchet@51810
   752
    val (((rs, us'), vs'), names_lthy) =
blanchet@51831
   753
      names_lthy0
blanchet@51810
   754
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   755
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   756
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   757
blanchet@51810
   758
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   759
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   760
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   761
blanchet@51810
   762
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   763
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   764
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   765
blanchet@51810
   766
    val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
blanchet@51810
   767
      let
blanchet@51810
   768
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   769
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   770
        val strong_rs =
blanchet@51810
   771
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   772
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   773
blanchet@51810
   774
        fun build_rel rs' T =
blanchet@51810
   775
          (case find_index (curry (op =) T) fpTs of
blanchet@51810
   776
            ~1 =>
blanchet@51856
   777
            if exists_subtype_in fpTs T then
blanchet@51856
   778
              let
blanchet@51856
   779
                val Type (s, Ts) = T
blanchet@51856
   780
                val bnf = the (bnf_of lthy s);
blanchet@51856
   781
                val live = live_of_bnf bnf;
blanchet@51856
   782
                val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
blanchet@51856
   783
                val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
blanchet@51856
   784
              in Term.list_comb (rel, map (build_rel rs') Ts') end
blanchet@51856
   785
            else
blanchet@51856
   786
              HOLogic.eq_const T
blanchet@51810
   787
          | kk => nth rs' kk);
blanchet@51810
   788
blanchet@51856
   789
        fun build_rel_app rs' usel vsel = fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@51810
   790
blanchet@51810
   791
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@51810
   792
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   793
          (if null usels then
blanchet@51810
   794
             []
blanchet@51810
   795
           else
blanchet@51810
   796
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@51810
   797
                Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@51810
   798
blanchet@51810
   799
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@51810
   800
          Library.foldr1 HOLogic.mk_conj
blanchet@51810
   801
            (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@51810
   802
          handle List.Empty => @{term True};
blanchet@51810
   803
blanchet@51810
   804
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@51810
   805
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@51810
   806
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@51810
   807
blanchet@51810
   808
        val concl =
blanchet@51810
   809
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   810
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   811
               uvrs us vs));
blanchet@51810
   812
blanchet@51810
   813
        fun mk_goal rs' =
blanchet@51810
   814
          Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@51810
   815
            concl);
blanchet@51810
   816
blanchet@51810
   817
        val goal = mk_goal rs;
blanchet@51810
   818
        val strong_goal = mk_goal strong_rs;
blanchet@51810
   819
blanchet@51810
   820
        fun prove dtor_coinduct' goal =
blanchet@51810
   821
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51810
   822
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@51819
   823
              exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   824
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   825
          |> Thm.close_derivation;
blanchet@51810
   826
blanchet@51810
   827
        fun postproc nn thm =
blanchet@51810
   828
          Thm.permute_prems 0 nn
blanchet@51828
   829
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   830
          |> Drule.zero_var_indexes
blanchet@51810
   831
          |> `(conj_dests nn);
blanchet@51810
   832
      in
blanchet@51814
   833
        (postproc nn (prove dtor_coinduct goal), postproc nn (prove dtor_strong_induct strong_goal))
blanchet@51810
   834
      end;
blanchet@51810
   835
blanchet@51810
   836
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   837
      let
blanchet@51810
   838
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   839
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   840
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   841
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   842
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   843
      in
blanchet@51810
   844
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   845
      end;
blanchet@51810
   846
blanchet@51816
   847
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   848
    val coinduct_conclss =
blanchet@51810
   849
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   850
blanchet@51810
   851
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   852
blanchet@51810
   853
    val gunfolds = map (lists_bmoc pgss) unfolds;
blanchet@51810
   854
    val hcorecs = map (lists_bmoc phss) corecs;
blanchet@51810
   855
blanchet@51810
   856
    val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@51810
   857
      let
blanchet@51843
   858
        fun mk_goal pfss c cps fcoiter n k ctr m cfs' =
blanchet@51810
   859
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   860
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@51843
   861
               mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   862
blanchet@51845
   863
        val mk_U = typ_subst_nonatomic (map2 pair Cs fpTs);
blanchet@51810
   864
blanchet@51843
   865
        fun intr_coiters fcoiters [] [cf] =
blanchet@51810
   866
            let val T = fastype_of cf in
blanchet@51855
   867
              if exists_subtype_in Cs T then
blanchet@51855
   868
                build_map lthy (indexify_fst Cs (K o nth fcoiters)) (T, mk_U T) $ cf
blanchet@51855
   869
              else
blanchet@51855
   870
                cf
blanchet@51810
   871
            end
blanchet@51843
   872
          | intr_coiters fcoiters [cq] [cf, cf'] =
blanchet@51843
   873
            mk_If cq (intr_coiters fcoiters [] [cf]) (intr_coiters fcoiters [] [cf']);
blanchet@51810
   874
blanchet@51843
   875
        val crgsss = map2 (map2 (map2 (intr_coiters gunfolds))) crssss cgssss;
blanchet@51843
   876
        val cshsss = map2 (map2 (map2 (intr_coiters hcorecs))) csssss chssss;
blanchet@51810
   877
blanchet@51828
   878
        val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
blanchet@51828
   879
        val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
blanchet@51810
   880
blanchet@51810
   881
        fun mk_map_if_distrib bnf =
blanchet@51810
   882
          let
blanchet@51810
   883
            val mapx = map_of_bnf bnf;
blanchet@51810
   884
            val live = live_of_bnf bnf;
blanchet@51810
   885
            val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
blanchet@51810
   886
            val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
blanchet@51810
   887
            val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
blanchet@51810
   888
          in
blanchet@51810
   889
            Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
blanchet@51810
   890
              @{thm if_distrib}
blanchet@51810
   891
          end;
blanchet@51810
   892
blanchet@51810
   893
        val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
blanchet@51810
   894
blanchet@51810
   895
        val unfold_tacss =
blanchet@51843
   896
          map3 (map oo mk_coiter_tac unfold_defs [] [] nesting_map_ids'' [])
blanchet@51814
   897
            dtor_unfold_thms pre_map_defs ctr_defss;
blanchet@51810
   898
        val corec_tacss =
blanchet@51843
   899
          map3 (map oo mk_coiter_tac corec_defs nested_map_comps'' nested_map_comp's
blanchet@51810
   900
              (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
blanchet@51814
   901
            dtor_corec_thms pre_map_defs ctr_defss;
blanchet@51810
   902
blanchet@51810
   903
        fun prove goal tac =
blanchet@51815
   904
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   905
          |> Thm.close_derivation;
blanchet@51810
   906
blanchet@51810
   907
        val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@51810
   908
        val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
blanchet@51810
   909
blanchet@51810
   910
        val filter_safesss =
blanchet@51810
   911
          map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@51810
   912
            curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
blanchet@51810
   913
blanchet@51810
   914
        val safe_unfold_thmss = filter_safesss unfold_thmss;
blanchet@51810
   915
        val safe_corec_thmss = filter_safesss corec_thmss;
blanchet@51810
   916
      in
blanchet@51810
   917
        (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@51810
   918
      end;
blanchet@51810
   919
blanchet@51810
   920
    val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@51810
   921
      let
blanchet@51843
   922
        fun mk_goal c cps fcoiter n k disc =
blanchet@51843
   923
          mk_Trueprop_eq (disc $ (fcoiter $ c),
blanchet@51810
   924
            if n = 1 then @{const True}
blanchet@51810
   925
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   926
blanchet@51810
   927
        val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@51810
   928
        val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   929
blanchet@51828
   930
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   931
blanchet@51810
   932
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   933
blanchet@51810
   934
        val unfold_tacss =
blanchet@51843
   935
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@51810
   936
        val corec_tacss =
blanchet@51843
   937
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   938
blanchet@51810
   939
        fun prove goal tac =
blanchet@51810
   940
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51829
   941
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   942
          |> Thm.close_derivation;
blanchet@51810
   943
blanchet@51810
   944
        fun proves [_] [_] = []
blanchet@51810
   945
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   946
      in
blanchet@51828
   947
        (map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss)
blanchet@51810
   948
      end;
blanchet@51810
   949
blanchet@51810
   950
    val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@51810
   951
blanchet@51843
   952
    fun mk_disc_coiter_thms coiters discIs =
blanchet@51843
   953
      map (op RS) (filter_out (is_triv_discI o snd) (coiters ~~ discIs));
blanchet@51810
   954
blanchet@51843
   955
    val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss;
blanchet@51843
   956
    val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
blanchet@51810
   957
blanchet@51843
   958
    fun mk_sel_coiter_thm coiter_thm sel sel_thm =
blanchet@51810
   959
      let
blanchet@51810
   960
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   961
        val arg_cong' =
blanchet@51810
   962
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   963
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   964
          |> Thm.varifyT_global;
blanchet@51810
   965
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   966
      in
blanchet@51843
   967
        coiter_thm RS arg_cong' RS sel_thm'
blanchet@51810
   968
      end;
blanchet@51810
   969
blanchet@51843
   970
    fun mk_sel_coiter_thms coiterss =
blanchet@51843
   971
      map3 (map3 (map2 o mk_sel_coiter_thm)) coiterss selsss sel_thmsss |> map flat;
blanchet@51810
   972
blanchet@51843
   973
    val sel_unfold_thmss = mk_sel_coiter_thms unfold_thmss;
blanchet@51843
   974
    val sel_corec_thmss = mk_sel_coiter_thms corec_thmss;
blanchet@51810
   975
blanchet@51810
   976
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   977
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   978
    val coinduct_case_concl_attrs =
blanchet@51810
   979
      map2 (fn casex => fn concls =>
blanchet@51810
   980
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   981
        coinduct_cases coinduct_conclss;
blanchet@51810
   982
    val coinduct_case_attrs =
blanchet@51810
   983
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   984
  in
blanchet@51810
   985
    ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms, coinduct_case_attrs),
blanchet@51810
   986
     (unfold_thmss, corec_thmss, []),
blanchet@51810
   987
     (safe_unfold_thmss, safe_corec_thmss),
blanchet@51810
   988
     (disc_unfold_thmss, disc_corec_thmss, simp_attrs),
blanchet@51810
   989
     (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
blanchet@51810
   990
     (sel_unfold_thmss, sel_corec_thmss, simp_attrs))
blanchet@51810
   991
  end;
blanchet@51810
   992
blanchet@51863
   993
fun define_co_datatypes prepare_constraint prepare_typ prepare_term lfp construct_fp
blanchet@49633
   994
    (wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
blanchet@49112
   995
  let
blanchet@49298
   996
    (* TODO: sanity checks on arguments *)
blanchet@49298
   997
blanchet@49286
   998
    val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
blanchet@49278
   999
      else ();
blanchet@49278
  1000
blanchet@49633
  1001
    fun qualify mandatory fp_b_name =
blanchet@49633
  1002
      Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
  1003
blanchet@49367
  1004
    val nn = length specs;
blanchet@49361
  1005
    val fp_bs = map type_binding_of specs;
blanchet@49498
  1006
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
  1007
    val fp_common_name = mk_common_name fp_b_names;
blanchet@51758
  1008
    val map_bs = map map_binding_of specs;
blanchet@51767
  1009
    val rel_bs = map rel_binding_of specs;
blanchet@49298
  1010
blanchet@51758
  1011
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
  1012
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
  1013
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
  1014
      end;
blanchet@49298
  1015
blanchet@51758
  1016
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs;
blanchet@49298
  1017
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@49298
  1018
    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
blanchet@51758
  1019
    val set_bss = map (map fst o type_args_named_constrained_of) specs;
blanchet@49119
  1020
blanchet@49585
  1021
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
  1022
      no_defs_lthy0
blanchet@49298
  1023
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@49585
  1024
      |> mk_TFrees (length unsorted_As)
blanchet@49585
  1025
      ||>> mk_TFrees nn
blanchet@51858
  1026
      ||>> variant_tfrees fp_b_names;
blanchet@49119
  1027
blanchet@49298
  1028
    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
blanchet@49298
  1029
    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
blanchet@49298
  1030
      locale and shadows an existing global type*)
blanchet@51768
  1031
blanchet@51769
  1032
    fun add_fake_type spec =
blanchet@51768
  1033
      Sign.add_type no_defs_lthy (type_binding_of spec,
blanchet@51769
  1034
        length (type_args_named_constrained_of spec), mixfix_of spec);
blanchet@51768
  1035
blanchet@51769
  1036
    val fake_thy = Theory.copy #> fold add_fake_type specs;
blanchet@49298
  1037
    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
blanchet@49119
  1038
blanchet@49182
  1039
    fun mk_fake_T b =
blanchet@49121
  1040
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49298
  1041
        unsorted_As);
blanchet@49121
  1042
blanchet@49302
  1043
    val fake_Ts = map mk_fake_T fp_bs;
blanchet@49121
  1044
blanchet@49181
  1045
    val mixfixes = map mixfix_of specs;
blanchet@49119
  1046
blanchet@49302
  1047
    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
  1048
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
  1049
blanchet@49121
  1050
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
  1051
blanchet@49336
  1052
    val disc_bindingss = map (map disc_of) ctr_specss;
blanchet@49336
  1053
    val ctr_bindingss =
blanchet@49633
  1054
      map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
blanchet@49121
  1055
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49181
  1056
    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
blanchet@49119
  1057
blanchet@49336
  1058
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
  1059
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49286
  1060
    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
blanchet@49286
  1061
blanchet@49308
  1062
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
  1063
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@49298
  1064
blanchet@49298
  1065
    val _ = (case duplicates (op =) unsorted_As of [] => ()
blanchet@49298
  1066
      | A :: _ => error ("Duplicate type parameter " ^
blanchet@49298
  1067
          quote (Syntax.string_of_typ no_defs_lthy A)));
blanchet@49298
  1068
blanchet@49183
  1069
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@49298
  1070
    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
blanchet@49165
  1071
        [] => ()
blanchet@49342
  1072
      | A' :: _ => error ("Extra type variable on right-hand side: " ^
blanchet@49204
  1073
          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
blanchet@49165
  1074
blanchet@49591
  1075
    fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
  1076
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
  1077
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49591
  1078
      | eq_fpT_check _ _ = false;
blanchet@49146
  1079
blanchet@49204
  1080
    fun freeze_fp (T as Type (s, Us)) =
blanchet@49591
  1081
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@49591
  1082
          ~1 => Type (s, map freeze_fp Us)
blanchet@49591
  1083
        | kk => nth Xs kk)
blanchet@49204
  1084
      | freeze_fp T = T;
blanchet@49121
  1085
blanchet@49536
  1086
    val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@49536
  1087
    val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
blanchet@49119
  1088
blanchet@49298
  1089
    val fp_eqs =
blanchet@49536
  1090
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsXs;
blanchet@49121
  1091
blanchet@51839
  1092
    val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0,
blanchet@51869
  1093
           un_folds = fp_folds0, co_recs = fp_recs0, co_induct = fp_induct,
blanchet@51869
  1094
           strong_co_induct = fp_strong_induct, dtor_ctors, ctor_dtors, ctor_injects,
blanchet@51869
  1095
           map_thms = fp_map_thms, set_thmss = fp_set_thmss, rel_thms = fp_rel_thms,
blanchet@51869
  1096
           un_fold_thms = fp_fold_thms, co_rec_thms = fp_rec_thms, ...}, lthy)) =
blanchet@51868
  1097
      fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As) fp_eqs
blanchet@51868
  1098
        no_defs_lthy0;
blanchet@49585
  1099
blanchet@49585
  1100
    val timer = time (Timer.startRealTimer ());
blanchet@49121
  1101
blanchet@51907
  1102
    val nesting_bnfs = nesty_bnfs lthy ctr_TsssXs As;
blanchet@51907
  1103
    val nested_bnfs = nesty_bnfs lthy ctr_TsssXs Xs;
blanchet@49226
  1104
blanchet@49585
  1105
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
  1106
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
  1107
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
  1108
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@51766
  1109
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@49585
  1110
blanchet@49585
  1111
    val live = live_of_bnf any_fp_bnf;
blanchet@49585
  1112
blanchet@49585
  1113
    val Bs =
blanchet@49585
  1114
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
  1115
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
  1116
blanchet@49585
  1117
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
  1118
blanchet@49501
  1119
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
  1120
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
  1121
blanchet@49501
  1122
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
  1123
blanchet@51780
  1124
    fun massage_simple_notes base =
blanchet@51780
  1125
      filter_out (null o #2)
blanchet@51780
  1126
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
  1127
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
  1128
blanchet@51780
  1129
    val massage_multi_notes =
blanchet@51780
  1130
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
  1131
        if forall null thmss then
blanchet@51780
  1132
          []
blanchet@51780
  1133
        else
blanchet@51780
  1134
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@51780
  1135
            ((qualify true fp_b_name (Binding.name thmN), attrs T_name),
blanchet@51780
  1136
             [(thms, [])])) fp_b_names fpTs thmss);
blanchet@51780
  1137
blanchet@49536
  1138
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
blanchet@49203
  1139
    val ns = map length ctr_Tsss;
blanchet@49212
  1140
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
  1141
    val mss = map (map length) ctr_Tsss;
blanchet@49203
  1142
blanchet@51903
  1143
    val ((fp_folds, fp_recs, fold_rec_args_types, unfold_corec_args_types), lthy) =
blanchet@51912
  1144
      mk_un_fold_co_rec_prelims lfp fpTs Cs ns mss fp_folds0 fp_recs0 lthy;
blanchet@49210
  1145
blanchet@49585
  1146
    fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@49585
  1147
            fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@49585
  1148
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@49585
  1149
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
  1150
      let
blanchet@49498
  1151
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1152
blanchet@49501
  1153
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
  1154
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
  1155
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
  1156
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
  1157
blanchet@49593
  1158
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
  1159
          no_defs_lthy
blanchet@49501
  1160
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
  1161
          ||>> mk_Frees "f" case_Ts
blanchet@49370
  1162
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1163
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1164
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1165
blanchet@49498
  1166
        val u = Free (u', fpT);
blanchet@49121
  1167
blanchet@49585
  1168
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
  1169
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
  1170
blanchet@49129
  1171
        val ctr_rhss =
blanchet@49585
  1172
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
  1173
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
  1174
blanchet@49633
  1175
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
  1176
blanchet@49134
  1177
        val case_rhs =
blanchet@49498
  1178
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
  1179
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
  1180
blanchet@49201
  1181
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1182
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
  1183
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
  1184
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
  1185
          ||> `Local_Theory.restore;
blanchet@49121
  1186
blanchet@49121
  1187
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1188
blanchet@49121
  1189
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1190
        val ctr_defs' =
blanchet@49585
  1191
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1192
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
  1193
blanchet@49203
  1194
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1195
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
  1196
blanchet@49203
  1197
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1198
blanchet@51897
  1199
        fun wrap_ctrs lthy =
blanchet@49123
  1200
          let
traytel@50170
  1201
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1202
              let
blanchet@49585
  1203
                val ctor_iff_dtor_thm =
blanchet@49585
  1204
                  let
blanchet@49585
  1205
                    val goal =
blanchet@49585
  1206
                      fold_rev Logic.all [w, u]
blanchet@49585
  1207
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1208
                  in
wenzelm@51551
  1209
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
  1210
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
  1211
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
  1212
                    |> Thm.close_derivation
blanchet@49585
  1213
                    |> Morphism.thm phi
blanchet@49585
  1214
                  end;
blanchet@49585
  1215
blanchet@49585
  1216
                val sumEN_thm' =
blanchet@49585
  1217
                  unfold_thms lthy @{thms all_unit_eq}
blanchet@49585
  1218
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
  1219
                       (mk_sumEN_balanced n))
blanchet@49585
  1220
                  |> Morphism.thm phi;
blanchet@49135
  1221
              in
blanchet@49585
  1222
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1223
              end;
blanchet@49135
  1224
blanchet@49585
  1225
            val inject_tacss =
blanchet@49585
  1226
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
  1227
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
  1228
blanchet@49585
  1229
            val half_distinct_tacss =
blanchet@49585
  1230
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
  1231
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1232
blanchet@49585
  1233
            val case_tacs =
blanchet@49585
  1234
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
  1235
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
  1236
blanchet@49585
  1237
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
  1238
blanchet@49585
  1239
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
  1240
          in
blanchet@51781
  1241
            wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
blanchet@51781
  1242
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
  1243
          end;
blanchet@49121
  1244
blanchet@51840
  1245
        fun derive_maps_sets_rels (ctr_sugar, lthy) =
blanchet@51835
  1246
          if live = 0 then
blanchet@51840
  1247
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1248
          else
blanchet@51835
  1249
            let
blanchet@51835
  1250
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1251
              val nones = replicate live NONE;
blanchet@49585
  1252
blanchet@51835
  1253
              val ctor_cong =
blanchet@51835
  1254
                if lfp then
blanchet@51835
  1255
                  Drule.dummy_thm
blanchet@51835
  1256
                else
blanchet@51835
  1257
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1258
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1259
                  end;
blanchet@49585
  1260
blanchet@51835
  1261
              fun mk_cIn ify =
blanchet@51835
  1262
                certify lthy o (not lfp ? curry (op $) (map_types ify ctor)) oo
blanchet@51835
  1263
                mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
  1264
blanchet@51835
  1265
              val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@51835
  1266
              val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
  1267
blanchet@51835
  1268
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1269
                fold_thms lthy [ctr_def']
blanchet@51835
  1270
                  (unfold_thms lthy (pre_map_def ::
blanchet@51835
  1271
                       (if lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@51835
  1272
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@51835
  1273
                        (if lfp then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1274
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1275
blanchet@51835
  1276
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1277
                fold_thms lthy [ctr_def']
blanchet@51835
  1278
                  (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@51835
  1279
                       (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@51835
  1280
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1281
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1282
blanchet@51835
  1283
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1284
blanchet@51835
  1285
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1286
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@51835
  1287
blanchet@51835
  1288
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1289
blanchet@51835
  1290
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1291
                fold_thms lthy ctr_defs'
blanchet@51835
  1292
                   (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@51835
  1293
                        (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@51835
  1294
                      (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1295
                |> postproc
blanchet@51835
  1296
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1297
blanchet@51835
  1298
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1299
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1300
blanchet@51835
  1301
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1302
blanchet@51835
  1303
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1304
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1305
                  cxIn cyIn;
blanchet@49121
  1306
blanchet@51835
  1307
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1308
                flip_rels lthy live thm
blanchet@51835
  1309
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1310
blanchet@51835
  1311
              val half_rel_distinct_thmss =
blanchet@51835
  1312
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1313
              val other_half_rel_distinct_thmss =
blanchet@51835
  1314
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1315
              val (rel_distinct_thms, _) =
blanchet@51835
  1316
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1317
blanchet@51835
  1318
              val notes =
blanchet@51835
  1319
                [(mapN, map_thms, code_simp_attrs),
blanchet@51835
  1320
                 (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@51835
  1321
                 (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@51835
  1322
                 (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51835
  1323
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1324
            in
blanchet@51840
  1325
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@51835
  1326
               lthy |> Local_Theory.notes notes |> snd)
blanchet@51835
  1327
            end;
blanchet@49585
  1328
blanchet@51897
  1329
        fun mk_binding suf = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49287
  1330
blanchet@51883
  1331
        fun massage_res (((maps_sets_rels, ctr_sugar), co_iter_res), lthy) =
blanchet@51883
  1332
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_iter_res), lthy);
blanchet@49119
  1333
      in
blanchet@51897
  1334
        (wrap_ctrs
blanchet@51835
  1335
         #> derive_maps_sets_rels
blanchet@51903
  1336
         ##>> (if lfp then define_fold_rec (the fold_rec_args_types)
blanchet@51903
  1337
           else define_unfold_corec (the unfold_corec_args_types))
blanchet@51897
  1338
             mk_binding fpTs As Cs fp_fold fp_rec
blanchet@51835
  1339
         #> massage_res, lthy')
blanchet@49119
  1340
      end;
blanchet@49167
  1341
blanchet@51835
  1342
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1343
      fold_map I wrap_types_etcs lthy
blanchet@51835
  1344
      |>> apsnd split_list4 o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@51835
  1345
        o split_list;
blanchet@49226
  1346
blanchet@49479
  1347
    val mk_simp_thmss =
blanchet@51857
  1348
      map7 (fn {injects, distincts, case_thms, ...} => fn un_folds => fn co_recs =>
blanchet@51835
  1349
        fn mapsx => fn rel_injects => fn rel_distincts => fn setss =>
blanchet@51857
  1350
          injects @ distincts @ case_thms @ co_recs @ un_folds @ mapsx @ rel_injects
blanchet@51835
  1351
          @ rel_distincts @ flat setss);
blanchet@49479
  1352
blanchet@51810
  1353
    fun derive_and_note_induct_fold_rec_thms_for_types
blanchet@51840
  1354
        ((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@51835
  1355
          (folds, recs, fold_defs, rec_defs)), lthy) =
blanchet@49202
  1356
      let
blanchet@51833
  1357
        val ((induct_thm, induct_thms, induct_attrs), (fold_thmss, fold_attrs),
blanchet@51808
  1358
             (rec_thmss, rec_attrs)) =
blanchet@51827
  1359
          derive_induct_fold_rec_thms_for_types pre_bnfs fp_folds0 fp_recs0 fp_induct fp_fold_thms
blanchet@51912
  1360
            fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs ctrss ctr_defss folds recs fold_defs
blanchet@51827
  1361
            rec_defs lthy;
blanchet@49201
  1362
blanchet@51830
  1363
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1364
blanchet@51835
  1365
        val simp_thmss =
blanchet@51843
  1366
          mk_simp_thmss ctr_sugars fold_thmss rec_thmss mapsx rel_injects rel_distincts setss;
blanchet@49438
  1367
blanchet@49337
  1368
        val common_notes =
blanchet@51808
  1369
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1370
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1371
blanchet@49226
  1372
        val notes =
blanchet@51808
  1373
          [(foldN, fold_thmss, K fold_attrs),
blanchet@51810
  1374
           (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@51808
  1375
           (recN, rec_thmss, K rec_attrs),
blanchet@49585
  1376
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1377
          |> massage_multi_notes;
blanchet@49202
  1378
      in
blanchet@51824
  1379
        lthy
blanchet@51824
  1380
        |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@51906
  1381
        |> register_fp_sugars true pre_bnfs fp_res ctr_defss ctr_sugars folds recs induct_thm
blanchet@51906
  1382
          induct_thm fold_thmss rec_thmss
blanchet@49202
  1383
      end;
blanchet@49202
  1384
blanchet@51810
  1385
    fun derive_and_note_coinduct_unfold_corec_thms_for_types
blanchet@51859
  1386
        ((((mapsx, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
blanchet@51835
  1387
          (unfolds, corecs, unfold_defs, corec_defs)), lthy) =
blanchet@49212
  1388
      let
blanchet@51810
  1389
        val ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms,
blanchet@51810
  1390
              coinduct_attrs),
blanchet@51843
  1391
             (unfold_thmss, corec_thmss, coiter_attrs),
blanchet@51810
  1392
             (safe_unfold_thmss, safe_corec_thmss),
blanchet@51843
  1393
             (disc_unfold_thmss, disc_corec_thmss, disc_coiter_attrs),
blanchet@51843
  1394
             (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_coiter_iff_attrs),
blanchet@51843
  1395
             (sel_unfold_thmss, sel_corec_thmss, sel_coiter_attrs)) =
blanchet@51829
  1396
          derive_coinduct_unfold_corec_thms_for_types pre_bnfs fp_folds0 fp_recs0 fp_induct
blanchet@51811
  1397
            fp_strong_induct dtor_ctors fp_fold_thms fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs As
blanchet@51840
  1398
            kss mss ns ctr_defss ctr_sugars unfolds corecs unfold_defs corec_defs lthy;
blanchet@49212
  1399
blanchet@51830
  1400
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1401
blanchet@51843
  1402
        fun flat_coiter_thms coiters disc_coiters sel_coiters =
blanchet@51843
  1403
          coiters @ disc_coiters @ sel_coiters;
blanchet@49479
  1404
blanchet@49479
  1405
        val simp_thmss =
blanchet@51840
  1406
          mk_simp_thmss ctr_sugars
blanchet@51843
  1407
            (map3 flat_coiter_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss)
blanchet@51843
  1408
            (map3 flat_coiter_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@51835
  1409
            mapsx rel_injects rel_distincts setss;
blanchet@49479
  1410
blanchet@49479
  1411
        val anonymous_notes =
blanchet@49504
  1412
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1413
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1414
blanchet@49342
  1415
        val common_notes =
blanchet@49591
  1416
          (if nn > 1 then
blanchet@51810
  1417
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1418
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1419
           else
blanchet@49591
  1420
             [])
blanchet@51780
  1421
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1422
blanchet@49212
  1423
        val notes =
blanchet@51780
  1424
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1425
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@51843
  1426
           (corecN, corec_thmss, K coiter_attrs),
blanchet@51843
  1427
           (disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
blanchet@51843
  1428
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1429
           (disc_unfoldN, disc_unfold_thmss, K disc_coiter_attrs),
blanchet@51843
  1430
           (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1431
           (sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
blanchet@51843
  1432
           (sel_unfoldN, sel_unfold_thmss, K sel_coiter_attrs),
blanchet@51780
  1433
           (simpsN, simp_thmss, K []),
blanchet@51810
  1434
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
blanchet@51843
  1435
           (unfoldN, unfold_thmss, K coiter_attrs)]
blanchet@51780
  1436
          |> massage_multi_notes;
blanchet@49212
  1437
      in
blanchet@51824
  1438
        lthy
blanchet@51824
  1439
        |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@51906
  1440
        |> register_fp_sugars false pre_bnfs fp_res ctr_defss ctr_sugars unfolds corecs coinduct_thm
blanchet@51864
  1441
          strong_coinduct_thm unfold_thmss corec_thmss
blanchet@49212
  1442
      end;
blanchet@49212
  1443
blanchet@49204
  1444
    val lthy' = lthy
blanchet@49585
  1445
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@49585
  1446
        fp_folds ~~ fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@49585
  1447
        pre_set_defss ~~ pre_rel_defs ~~ fp_map_thms ~~ fp_set_thmss ~~ fp_rel_thms ~~ ns ~~ kss ~~
blanchet@49585
  1448
        mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
blanchet@49585
  1449
        raw_sel_defaultsss)
blanchet@51835
  1450
      |> wrap_types_etc
blanchet@51808
  1451
      |> (if lfp then derive_and_note_induct_fold_rec_thms_for_types
blanchet@51808
  1452
          else derive_and_note_coinduct_unfold_corec_thms_for_types);
blanchet@49167
  1453
blanchet@49167
  1454
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@51863
  1455
      datatype_word lfp));
blanchet@49112
  1456
  in
blanchet@49308
  1457
    timer; lthy'
blanchet@49112
  1458
  end;
blanchet@49112
  1459
blanchet@51863
  1460
val co_datatypes = define_co_datatypes (K I) (K I) (K I);
blanchet@49297
  1461
blanchet@51863
  1462
val co_datatype_cmd =
blanchet@51863
  1463
  define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1464
blanchet@49112
  1465
val parse_ctr_arg =
blanchet@49329
  1466
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1467
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1468
blanchet@49286
  1469
val parse_defaults =
blanchet@49286
  1470
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1471
blanchet@51758
  1472
val parse_type_arg_constrained =
blanchet@51790
  1473
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1474
blanchet@51790
  1475
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1476
blanchet@51758
  1477
val parse_type_args_named_constrained =
blanchet@51758
  1478
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1479
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1480
  Scan.succeed [];
blanchet@51756
  1481
blanchet@51790
  1482
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1483
blanchet@51767
  1484
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1485
blanchet@51767
  1486
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51833
  1487
   that we don't want them to be highlighted everywhere. *)
blanchet@51767
  1488
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1489
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1490
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1491
blanchet@51767
  1492
val parse_map_rel_bindings =
blanchet@51767
  1493
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1494
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1495
  Scan.succeed no_map_rel;
blanchet@51767
  1496
blanchet@51767
  1497
val parse_ctr_spec =
blanchet@51790
  1498
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1499
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1500
blanchet@51767
  1501
val parse_spec =
blanchet@51790
  1502
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1503
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1504
blanchet@51863
  1505
val parse_co_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1506
blanchet@51863
  1507
fun parse_co_datatype_cmd lfp construct_fp = parse_co_datatype >> co_datatype_cmd lfp construct_fp;
blanchet@49112
  1508
blanchet@49112
  1509
end;