src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Thu Jun 06 12:16:35 2013 +0200 (2013-06-06)
changeset 52315 fafab8eac3ee
parent 52314 9606cf677021
child 52317 7132de305921
permissions -rw-r--r--
avoid duplicate call to "mk_fold_rec_args_types" function
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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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     fp: BNF_FP_Util.fp_kind,
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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 of_fp_sugar: (fp_sugar -> 'a list) -> fp_sugar -> 'a
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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 flat_rec: 'a list list -> 'a list
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  val mk_co_iter: theory -> BNF_FP_Util.fp_kind -> typ -> typ list -> term -> term
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  val nesty_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
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  val mk_un_fold_co_rec_prelims: BNF_FP_Util.fp_kind -> typ list -> typ list -> int list ->
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    int list list -> term list list -> Proof.context ->
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    (term list list
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     * (typ list list * typ list list list list * term list list
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        * term list list 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 mk_map: int -> typ list -> typ list -> term -> term
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  val build_map: local_theory -> (typ * typ -> term) -> typ * typ -> term
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  val mk_iter_fun_arg_typessss: typ list -> int list -> int list list -> term ->
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    typ list list list list
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  val define_fold_rec:
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    (typ list list * typ list list list list * term list list * term list list list list) list ->
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    (string -> binding) -> 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) -> 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 list ->
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    (typ list list * typ list list list list * term list list * term list list list list) list ->
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    thm -> thm list list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list ->
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    typ list -> typ list list list -> term list list -> thm list list -> term list list ->
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    thm list list -> 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: BNF_FP_Util.fp_kind -> (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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    (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: BNF_FP_Util.fp_kind -> (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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   fp: fp_kind,
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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 of_fp_sugar f (fp_sugar as {index, ...}) = nth (f fp_sugar) index;
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fun eq_fp_sugar ({T = T1, fp = fp1, index = index1, fp_res = fp_res1, ...} : fp_sugar,
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    {T = T2, fp = fp2, index = index2, fp_res = fp_res2, ...} : fp_sugar) =
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  T1 = T2 andalso fp1 = fp2 andalso index1 = index2 andalso eq_fp_result (fp_res1, fp_res2);
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fun morph_fp_sugar phi {T, fp, index, pre_bnfs, fp_res, ctr_defss, ctr_sugars, un_folds,
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    co_recs, co_induct, strong_co_induct, un_fold_thmss, co_rec_thmss} =
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  {T = Morphism.typ phi T, fp = fp, index = index, pre_bnfs = map (morph_bnf phi)
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   pre_bnfs, fp_res = morph_fp_result phi fp_res,
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   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 fp 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, fp = fp, 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 flat_rec xss =
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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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  flat xss
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*)
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  map hd xss @ maps tl xss;
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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_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 mk_uncurried2_fun f xss =
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  mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat_rec xss);
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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 fp fpT Cs t =
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  let
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    val (binders, body) = strip_type (fastype_of t);
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    val (f_Cs, prebody) = split_last binders;
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    val fpT0 = if fp = Least_FP then prebody else body;
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    val Cs0 = distinct (op =) (map (if fp = Least_FP then body_type else domain_type) f_Cs);
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    val rho = tvar_subst thy (fpT0 :: Cs0) (fpT :: Cs);
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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 fp 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 ((fp = Greatest_FP ? 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 project_co_recT special_Tname Cs proj =
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  let
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    fun project (Type (s, Ts as [T, U])) =
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        if s = special_Tname andalso member (op =) Cs U then proj (T, U)
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        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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val project_corecT = project_co_recT @{type_name sum};
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fun unzip_recT Cs (T as Type (@{type_name prod}, Ts as [_, U])) =
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    if member (op =) Cs U then Ts else [T]
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  | unzip_recT _ T = [T];
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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_typessss Cs 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 Cs)));
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fun mk_fold_rec_args_types Cs ns mss [ctor_fold_fun_Ts, ctor_rec_fun_Ts] lthy =
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  let
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    val Css = map2 replicate ns Cs;
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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 = map2 (fn C => map (fn y_Ts => y_Ts ---> C)) Cs y_Tsss;
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    val ((gss, ysss), lthy) =
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      lthy
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      |> mk_Freess "f" g_Tss
blanchet@51832
   286
      ||>> mk_Freesss "x" y_Tsss;
blanchet@52301
   287
blanchet@52301
   288
    val y_Tssss = map (map (map single)) y_Tsss;
blanchet@52214
   289
    val yssss = map (map (map single)) ysss;
blanchet@52214
   290
blanchet@52214
   291
    val z_Tssss =
blanchet@52296
   292
      map3 (fn n => fn ms => map2 (map (unzip_recT Cs) oo dest_tupleT) ms o
blanchet@52214
   293
        dest_sumTN_balanced n o domain_type) ns mss ctor_rec_fun_Ts;
blanchet@51832
   294
blanchet@52301
   295
    val z_Tsss' = map (map flat_rec) z_Tssss;
blanchet@52215
   296
    val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' Css;
blanchet@51832
   297
blanchet@51832
   298
    val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@52214
   299
    val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
blanchet@52214
   300
    val (zssss_tl, lthy) =
blanchet@52214
   301
      lthy
blanchet@52214
   302
      |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
blanchet@52214
   303
    val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
blanchet@51832
   304
  in
blanchet@52315
   305
    ([(g_Tss, y_Tssss, gss, yssss), (h_Tss, z_Tssss, hss, zssss)], lthy)
blanchet@51832
   306
  end;
blanchet@51832
   307
blanchet@52315
   308
fun mk_unfold_corec_args_types Cs ns mss [dtor_unfold_fun_Ts, dtor_corec_fun_Ts] lthy =
blanchet@51829
   309
  let
blanchet@51829
   310
    (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@51829
   311
    fun repair_arity [0] = [1]
blanchet@51829
   312
      | repair_arity ms = ms;
blanchet@51829
   313
blanchet@51829
   314
    fun unzip_corecT T =
blanchet@52297
   315
      if exists_subtype_in Cs T then [project_corecT Cs fst T, project_corecT Cs snd T]
blanchet@52209
   316
      else [T];
blanchet@51829
   317
blanchet@51831
   318
    val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@51829
   319
blanchet@51829
   320
    fun mk_types maybe_unzipT fun_Ts =
blanchet@51829
   321
      let
blanchet@51829
   322
        val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@51829
   323
        val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@51829
   324
        val f_Tsss = map2 (map2 dest_tupleT o repair_arity) mss f_prod_Tss;
blanchet@51889
   325
        val f_Tssss = map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
blanchet@51829
   326
        val q_Tssss =
blanchet@52213
   327
          map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
blanchet@51829
   328
        val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@51889
   329
      in (q_Tssss, f_Tssss, (f_sum_prod_Ts, f_Tsss, pf_Tss)) end;
blanchet@51829
   330
blanchet@51889
   331
    val (r_Tssss, g_Tssss, unfold_types) = mk_types single dtor_unfold_fun_Ts;
blanchet@51889
   332
    val (s_Tssss, h_Tssss, corec_types) = mk_types unzip_corecT dtor_corec_fun_Ts;
blanchet@51831
   333
blanchet@51829
   334
    val (((cs, pss), gssss), lthy) =
blanchet@51829
   335
      lthy
blanchet@51829
   336
      |> mk_Frees "a" Cs
blanchet@51829
   337
      ||>> mk_Freess "p" p_Tss
blanchet@51829
   338
      ||>> mk_Freessss "g" g_Tssss;
blanchet@51829
   339
    val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@51829
   340
blanchet@51829
   341
    val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@51829
   342
    val ((sssss, hssss_tl), lthy) =
blanchet@51829
   343
      lthy
blanchet@51829
   344
      |> mk_Freessss "q" s_Tssss
blanchet@51829
   345
      ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@51829
   346
    val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@51831
   347
blanchet@51831
   348
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   349
blanchet@51889
   350
    fun mk_args qssss fssss =
blanchet@51831
   351
      let
blanchet@51831
   352
        val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
blanchet@51831
   353
        val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@51831
   354
        val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@51831
   355
      in (pfss, cqssss, cfssss) end;
blanchet@51831
   356
blanchet@51889
   357
    val unfold_args = mk_args rssss gssss;
blanchet@51889
   358
    val corec_args = mk_args sssss hssss;
blanchet@51831
   359
  in
blanchet@51889
   360
    ((cs, cpss, (unfold_args, unfold_types), (corec_args, corec_types)), lthy)
blanchet@51831
   361
  end;
blanchet@51829
   362
blanchet@52315
   363
fun mk_un_fold_co_rec_prelims fp fpTs Cs ns mss [xtor_un_folds0, xtor_co_recs0] lthy =
blanchet@51903
   364
  let
blanchet@52169
   365
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   366
blanchet@52313
   367
    val (xtor_un_fold_fun_Ts, xtor_un_folds) = mk_co_iters thy fp fpTs Cs xtor_un_folds0
blanchet@52173
   368
      |> `(mk_fp_iter_fun_types o hd);
blanchet@52313
   369
    val (xtor_co_rec_fun_Ts, xtor_co_recs) = mk_co_iters thy fp fpTs Cs xtor_co_recs0
blanchet@52173
   370
      |> `(mk_fp_iter_fun_types o hd);
blanchet@51903
   371
blanchet@51903
   372
    val ((fold_rec_args_types, unfold_corec_args_types), lthy') =
blanchet@52207
   373
      if fp = Least_FP then
blanchet@52315
   374
        mk_fold_rec_args_types Cs ns mss [xtor_un_fold_fun_Ts, xtor_co_rec_fun_Ts] lthy
blanchet@51903
   375
        |>> (rpair NONE o SOME)
blanchet@51903
   376
      else
blanchet@52315
   377
        mk_unfold_corec_args_types Cs ns mss [xtor_un_fold_fun_Ts, xtor_co_rec_fun_Ts] lthy
blanchet@51903
   378
        |>> (pair NONE o SOME)
blanchet@51903
   379
  in
blanchet@52315
   380
    (([xtor_un_folds, xtor_co_recs], fold_rec_args_types, unfold_corec_args_types), lthy')
blanchet@51903
   381
  end;
blanchet@51903
   382
blanchet@49536
   383
fun mk_map live Ts Us t =
blanchet@49536
   384
  let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in
blanchet@49536
   385
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49536
   386
  end;
blanchet@49536
   387
blanchet@49591
   388
fun mk_rel live Ts Us t =
blanchet@49591
   389
  let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in
blanchet@49591
   390
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49591
   391
  end;
blanchet@49591
   392
blanchet@49585
   393
fun liveness_of_fp_bnf n bnf =
blanchet@49585
   394
  (case T_of_bnf bnf of
blanchet@49585
   395
    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
blanchet@49585
   396
  | _ => replicate n false);
blanchet@49536
   397
blanchet@49124
   398
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
blanchet@49119
   399
blanchet@49298
   400
fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
blanchet@49119
   401
blanchet@49298
   402
fun merge_type_args (As, As') =
blanchet@49298
   403
  if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
blanchet@49119
   404
blanchet@49591
   405
fun reassoc_conjs thm =
blanchet@49591
   406
  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
blanchet@49591
   407
  handle THM _ => thm;
blanchet@49591
   408
blanchet@51767
   409
fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs;
blanchet@51767
   410
fun type_binding_of ((((_, b), _), _), _) = b;
blanchet@51767
   411
fun map_binding_of (((_, (b, _)), _), _) = b;
blanchet@51767
   412
fun rel_binding_of (((_, (_, b)), _), _) = b;
blanchet@49181
   413
fun mixfix_of ((_, mx), _) = mx;
blanchet@49121
   414
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
blanchet@49119
   415
blanchet@49286
   416
fun disc_of ((((disc, _), _), _), _) = disc;
blanchet@49286
   417
fun ctr_of ((((_, ctr), _), _), _) = ctr;
blanchet@49286
   418
fun args_of (((_, args), _), _) = args;
blanchet@49286
   419
fun defaults_of ((_, ds), _) = ds;
blanchet@49181
   420
fun ctr_mixfix_of (_, mx) = mx;
blanchet@49119
   421
blanchet@51907
   422
fun add_nesty_bnf_names Us =
blanchet@51907
   423
  let
blanchet@51907
   424
    fun add (Type (s, Ts)) ss =
blanchet@51907
   425
        let val (needs, ss') = fold_map add Ts ss in
blanchet@51907
   426
          if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@51907
   427
        end
blanchet@51907
   428
      | add T ss = (member (op =) Us T, ss);
blanchet@51907
   429
  in snd oo add end;
blanchet@51907
   430
blanchet@51907
   431
fun nesty_bnfs ctxt ctr_Tsss Us =
blanchet@51907
   432
  map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
blanchet@51907
   433
blanchet@52302
   434
fun indexify proj xs f p = f (find_index (curry (op =) (proj p)) xs) p;
blanchet@51855
   435
blanchet@51854
   436
fun build_map lthy build_simple =
blanchet@51853
   437
  let
blanchet@51853
   438
    fun build (TU as (T, U)) =
blanchet@51853
   439
      if T = U then
blanchet@51853
   440
        id_const T
blanchet@51853
   441
      else
blanchet@51853
   442
        (case TU of
blanchet@51854
   443
          (Type (s, Ts), Type (s', Us)) =>
blanchet@51854
   444
          if s = s' then
blanchet@51854
   445
            let
blanchet@51854
   446
              val bnf = the (bnf_of lthy s);
blanchet@51854
   447
              val live = live_of_bnf bnf;
blanchet@51854
   448
              val mapx = mk_map live Ts Us (map_of_bnf bnf);
blanchet@51854
   449
              val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
blanchet@51854
   450
            in Term.list_comb (mapx, map build TUs') end
blanchet@51854
   451
          else
blanchet@51854
   452
            build_simple TU
blanchet@51853
   453
        | _ => build_simple TU);
blanchet@51853
   454
  in build end;
blanchet@51853
   455
blanchet@52298
   456
fun mk_iter_body ctor_iter fss xssss =
blanchet@52298
   457
  Term.list_comb (ctor_iter, map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss);
blanchet@51884
   458
blanchet@51900
   459
fun mk_preds_getterss_join c cps sum_prod_T cqfss =
blanchet@51900
   460
  let val n = length cqfss in
blanchet@51900
   461
    Term.lambda c (mk_IfN sum_prod_T cps
blanchet@51900
   462
      (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)))
blanchet@51900
   463
  end;
blanchet@51886
   464
blanchet@51900
   465
fun mk_coiter_body lthy cs cpss f_sum_prod_Ts f_Tsss cqssss cfssss dtor_coiter =
blanchet@51888
   466
  let
blanchet@51888
   467
    fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@51888
   468
blanchet@51888
   469
    fun build_dtor_coiter_arg _ [] [cf] = cf
blanchet@51888
   470
      | build_dtor_coiter_arg T [cq] [cf, cf'] =
blanchet@51888
   471
        mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@51888
   472
          (build_sum_inj Inr_const (fastype_of cf', T) $ cf')
blanchet@51888
   473
blanchet@51888
   474
    val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
blanchet@51888
   475
  in
blanchet@51900
   476
    Term.list_comb (dtor_coiter, map4 mk_preds_getterss_join cs cpss f_sum_prod_Ts cqfsss)
blanchet@51888
   477
  end;
blanchet@51886
   478
blanchet@52315
   479
fun define_fold_rec [fold_args_types, rec_args_types] mk_binding fpTs Cs ctor_fold ctor_rec lthy0 =
blanchet@51897
   480
  let
blanchet@52170
   481
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   482
blanchet@51899
   483
    val nn = length fpTs;
blanchet@51899
   484
blanchet@52170
   485
    val fpT_to_C as Type (_, [fpT, _]) = snd (strip_typeN nn (fastype_of ctor_fold));
blanchet@51897
   486
blanchet@52301
   487
    fun generate_iter (suf, ctor_iter, (f_Tss, _, fss, xssss)) =
blanchet@51897
   488
      let
blanchet@51899
   489
        val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@52309
   490
        val b = mk_binding suf;
blanchet@51897
   491
        val spec =
blanchet@52309
   492
          mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of b, res_T)),
blanchet@52298
   493
            mk_iter_body ctor_iter fss xssss);
blanchet@52309
   494
      in (b, spec) end;
blanchet@51897
   495
blanchet@51897
   496
    val binding_specs =
blanchet@52315
   497
      map generate_iter [(foldN, ctor_fold, fold_args_types), (recN, ctor_rec, rec_args_types)];
blanchet@51897
   498
blanchet@51907
   499
    val ((csts, defs), (lthy', lthy)) = lthy0
blanchet@51897
   500
      |> apfst split_list o fold_map (fn (b, spec) =>
blanchet@51897
   501
        Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@51897
   502
        #>> apsnd snd) binding_specs
blanchet@51897
   503
      ||> `Local_Theory.restore;
blanchet@51897
   504
blanchet@51897
   505
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@51897
   506
blanchet@51897
   507
    val [fold_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@51897
   508
blanchet@52207
   509
    val [foldx, recx] = map (mk_co_iter thy Least_FP fpT Cs o Morphism.term phi) csts;
blanchet@51897
   510
  in
blanchet@51897
   511
    ((foldx, recx, fold_def, rec_def), lthy')
blanchet@51897
   512
  end;
blanchet@51897
   513
blanchet@52207
   514
(* TODO: merge with above function? *)
blanchet@52315
   515
fun define_unfold_corec (cs, cpss, unfold_args_types, corec_args_types) mk_binding fpTs Cs
blanchet@52315
   516
    dtor_unfold dtor_corec lthy0 =
blanchet@51897
   517
  let
blanchet@52170
   518
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   519
blanchet@51899
   520
    val nn = length fpTs;
blanchet@51899
   521
blanchet@52170
   522
    val C_to_fpT as Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of dtor_unfold));
blanchet@51897
   523
blanchet@51897
   524
    fun generate_coiter (suf, dtor_coiter, ((pfss, cqssss, cfssss),
blanchet@51897
   525
        (f_sum_prod_Ts, f_Tsss, pf_Tss))) =
blanchet@51897
   526
      let
blanchet@51899
   527
        val res_T = fold_rev (curry (op --->)) pf_Tss C_to_fpT;
blanchet@52309
   528
        val b = mk_binding suf;
blanchet@51897
   529
        val spec =
blanchet@52309
   530
          mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of b, res_T)),
blanchet@51907
   531
            mk_coiter_body lthy0 cs cpss f_sum_prod_Ts f_Tsss cqssss cfssss dtor_coiter);
blanchet@52309
   532
      in (b, spec) end;
blanchet@51897
   533
blanchet@51897
   534
    val binding_specs =
blanchet@52315
   535
      map generate_coiter [(unfoldN, dtor_unfold, unfold_args_types),
blanchet@52315
   536
        (corecN, dtor_corec, corec_args_types)];
blanchet@51897
   537
blanchet@51907
   538
    val ((csts, defs), (lthy', lthy)) = lthy0
blanchet@51897
   539
      |> apfst split_list o fold_map (fn (b, spec) =>
blanchet@51897
   540
        Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@51897
   541
        #>> apsnd snd) binding_specs
blanchet@51897
   542
      ||> `Local_Theory.restore;
blanchet@51897
   543
blanchet@51897
   544
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@51897
   545
blanchet@51897
   546
    val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@51897
   547
blanchet@52207
   548
    val [unfold, corec] = map (mk_co_iter thy Greatest_FP fpT Cs o Morphism.term phi) csts;
blanchet@51897
   549
  in
blanchet@51897
   550
    ((unfold, corec, unfold_def, corec_def), lthy')
blanchet@52172
   551
  end ;
blanchet@51897
   552
blanchet@52315
   553
fun derive_induct_fold_rec_thms_for_types pre_bnfs [ctor_folds, ctor_recs]
blanchet@52315
   554
    [fold_args_types, rec_args_types] ctor_induct [ctor_fold_thms, ctor_rec_thms] nesting_bnfs
blanchet@52315
   555
    nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss [folds, recs] [fold_defs, rec_defs] lthy =
blanchet@51808
   556
  let
blanchet@51827
   557
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   558
blanchet@51815
   559
    val nn = length pre_bnfs;
blanchet@51827
   560
    val ns = map length ctr_Tsss;
blanchet@51827
   561
    val mss = map (map length) ctr_Tsss;
blanchet@51815
   562
blanchet@51808
   563
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   564
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@51830
   565
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51808
   566
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
blanchet@51810
   567
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51808
   568
blanchet@51816
   569
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   570
blanchet@52171
   571
    val ctor_fold_fun_Ts = mk_fp_iter_fun_types (hd ctor_folds);
blanchet@52171
   572
    val ctor_rec_fun_Ts = mk_fp_iter_fun_types (hd ctor_recs);
blanchet@51827
   573
blanchet@51832
   574
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@52315
   575
      lthy
blanchet@51808
   576
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   577
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   578
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   579
blanchet@51808
   580
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   581
blanchet@51808
   582
    fun mk_sets_nested bnf =
blanchet@51808
   583
      let
blanchet@51808
   584
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   585
        val lives = lives_of_bnf bnf;
blanchet@51808
   586
        val sets = sets_of_bnf bnf;
blanchet@51808
   587
        fun mk_set U =
blanchet@51808
   588
          (case find_index (curry (op =) U) lives of
blanchet@51808
   589
            ~1 => Term.dummy
blanchet@51808
   590
          | i => nth sets i);
blanchet@51808
   591
      in
blanchet@51808
   592
        (T_name, map mk_set Us)
blanchet@51808
   593
      end;
blanchet@51808
   594
blanchet@51808
   595
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   596
blanchet@51808
   597
    val (induct_thms, induct_thm) =
blanchet@51808
   598
      let
blanchet@51808
   599
        fun mk_set Ts t =
blanchet@51808
   600
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   601
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   602
          end;
blanchet@51808
   603
blanchet@52310
   604
        fun mk_raw_prem_prems _ (x as Free (_, Type _)) (X as TFree _) =
blanchet@52310
   605
            [([], (find_index (curry (op =) X) Xs + 1, x))]
blanchet@52310
   606
          | mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
blanchet@52310
   607
            (case AList.lookup (op =) setss_nested T_name of
blanchet@52310
   608
              NONE => []
blanchet@52310
   609
            | SOME raw_sets0 =>
blanchet@52310
   610
              let
blanchet@52310
   611
                val (Xs_Ts, (Ts, raw_sets)) =
blanchet@52310
   612
                  filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
blanchet@52310
   613
                  |> split_list ||> split_list;
blanchet@52310
   614
                val sets = map (mk_set Ts0) raw_sets;
blanchet@52310
   615
                val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@52310
   616
                val xysets = map (pair x) (ys ~~ sets);
blanchet@52310
   617
                val ppremss = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
blanchet@52310
   618
              in
blanchet@52310
   619
                flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@52310
   620
              end)
blanchet@52310
   621
          | mk_raw_prem_prems _ _ _ = [];
blanchet@51808
   622
blanchet@51808
   623
        fun close_prem_prem xs t =
blanchet@51808
   624
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   625
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   626
blanchet@51808
   627
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   628
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   629
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   630
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   631
blanchet@52310
   632
        fun mk_raw_prem phi ctr ctr_Ts ctrXs_Ts =
blanchet@51808
   633
          let
blanchet@51808
   634
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@52310
   635
            val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
blanchet@51808
   636
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   637
blanchet@51808
   638
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   639
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   640
blanchet@52310
   641
        val raw_premss = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_Tsss;
blanchet@51808
   642
blanchet@51808
   643
        val goal =
blanchet@51808
   644
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@51808
   645
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@51808
   646
blanchet@51808
   647
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   648
blanchet@51814
   649
        val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@51808
   650
blanchet@51808
   651
        val thm =
blanchet@51808
   652
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51808
   653
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
blanchet@51808
   654
              pre_set_defss)
blanchet@51808
   655
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51808
   656
          |> Thm.close_derivation;
blanchet@51808
   657
      in
blanchet@51808
   658
        `(conj_dests nn) thm
blanchet@51808
   659
      end;
blanchet@51808
   660
blanchet@51808
   661
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@52305
   662
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   663
blanchet@52305
   664
    val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@52305
   665
blanchet@52306
   666
    fun mk_iter_thmss (_, x_Tssss, fss, _) iters iter_defs ctor_iter_thms =
blanchet@51808
   667
      let
blanchet@52305
   668
        val fiters = map (lists_bmoc fss) iters;
blanchet@51808
   669
blanchet@51843
   670
        fun mk_goal fss fiter xctr f xs fxs =
blanchet@51808
   671
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@51843
   672
            (mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   673
blanchet@52302
   674
        fun maybe_tick (T, U) u f =
blanchet@52302
   675
          if try (fst o HOLogic.dest_prodT) U = SOME T then
blanchet@52302
   676
            Term.lambda u (HOLogic.mk_prod (u, f $ u))
blanchet@52302
   677
          else
blanchet@52302
   678
            f;
blanchet@51808
   679
blanchet@52305
   680
        fun unzip_iters (x as Free (_, T)) =
blanchet@52301
   681
          map (fn U => if U = T then x else
blanchet@52303
   682
            build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
blanchet@52305
   683
              (fn kk => fn TU => maybe_tick TU (nth us kk) (nth fiters kk))) (T, U) $ x);
blanchet@52301
   684
blanchet@52305
   685
        val fxsss = map2 (map2 (flat_rec oo map2 unzip_iters)) xsss x_Tssss;
blanchet@51808
   686
blanchet@52306
   687
        val goalss = map5 (map4 o mk_goal fss) fiters xctrss fss xsss fxsss;
blanchet@51808
   688
blanchet@52305
   689
        val tacss =
blanchet@52305
   690
          map2 (map o mk_iter_tac pre_map_defs (nested_map_ids'' @ nesting_map_ids'') iter_defs)
blanchet@52305
   691
            ctor_iter_thms ctr_defss;
blanchet@51808
   692
blanchet@51808
   693
        fun prove goal tac =
blanchet@51808
   694
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   695
          |> Thm.close_derivation;
blanchet@51808
   696
      in
blanchet@52305
   697
        map2 (map2 prove) goalss tacss
blanchet@51808
   698
      end;
blanchet@51808
   699
blanchet@52315
   700
    val fold_thmss = mk_iter_thmss fold_args_types folds fold_defs ctor_fold_thms;
blanchet@52315
   701
    val rec_thmss = mk_iter_thmss rec_args_types recs rec_defs ctor_rec_thms;
blanchet@51808
   702
  in
blanchet@51810
   703
    ((induct_thm, induct_thms, [induct_case_names_attr]),
blanchet@51808
   704
     (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
blanchet@51808
   705
  end;
blanchet@51808
   706
blanchet@52171
   707
fun derive_coinduct_unfold_corec_thms_for_types pre_bnfs dtor_unfolds dtor_corecs dtor_coinduct
blanchet@51814
   708
    dtor_strong_induct dtor_ctors dtor_unfold_thms dtor_corec_thms nesting_bnfs nested_bnfs fpTs Cs
blanchet@51840
   709
    As kss mss ns ctr_defss ctr_sugars unfolds corecs unfold_defs corec_defs lthy =
blanchet@51810
   710
  let
blanchet@51815
   711
    val nn = length pre_bnfs;
blanchet@51815
   712
blanchet@51810
   713
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   714
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
   715
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51830
   716
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   717
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
blanchet@51810
   718
    val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs;
blanchet@51810
   719
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
blanchet@51810
   720
blanchet@51816
   721
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   722
blanchet@52171
   723
    val dtor_unfold_fun_Ts = mk_fp_iter_fun_types (hd dtor_unfolds);
blanchet@52171
   724
    val dtor_corec_fun_Ts = mk_fp_iter_fun_types (hd dtor_corecs);
blanchet@51829
   725
blanchet@51840
   726
    val ctrss = map (map (mk_ctr As) o #ctrs) ctr_sugars;
blanchet@51840
   727
    val discss = map (map (mk_disc_or_sel As) o #discs) ctr_sugars;
blanchet@51840
   728
    val selsss = map (map (map (mk_disc_or_sel As)) o #selss) ctr_sugars;
blanchet@51840
   729
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   730
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   731
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   732
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   733
blanchet@51831
   734
    val ((cs, cpss, ((pgss, crssss, cgssss), _), ((phss, csssss, chssss), _)), names_lthy0) =
blanchet@52315
   735
      mk_unfold_corec_args_types Cs ns mss [dtor_unfold_fun_Ts, dtor_corec_fun_Ts] lthy;
blanchet@51831
   736
blanchet@51810
   737
    val (((rs, us'), vs'), names_lthy) =
blanchet@51831
   738
      names_lthy0
blanchet@51810
   739
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   740
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   741
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   742
blanchet@51810
   743
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   744
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   745
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   746
blanchet@51810
   747
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   748
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   749
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   750
blanchet@51810
   751
    val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
blanchet@51810
   752
      let
blanchet@51810
   753
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   754
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   755
        val strong_rs =
blanchet@51810
   756
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   757
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   758
blanchet@51810
   759
        fun build_rel rs' T =
blanchet@51810
   760
          (case find_index (curry (op =) T) fpTs of
blanchet@51810
   761
            ~1 =>
blanchet@51856
   762
            if exists_subtype_in fpTs T then
blanchet@51856
   763
              let
blanchet@51856
   764
                val Type (s, Ts) = T
blanchet@51856
   765
                val bnf = the (bnf_of lthy s);
blanchet@51856
   766
                val live = live_of_bnf bnf;
blanchet@51856
   767
                val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
blanchet@51856
   768
                val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
blanchet@51856
   769
              in Term.list_comb (rel, map (build_rel rs') Ts') end
blanchet@51856
   770
            else
blanchet@51856
   771
              HOLogic.eq_const T
blanchet@51810
   772
          | kk => nth rs' kk);
blanchet@51810
   773
blanchet@51856
   774
        fun build_rel_app rs' usel vsel = fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@51810
   775
blanchet@51810
   776
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@51810
   777
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   778
          (if null usels then
blanchet@51810
   779
             []
blanchet@51810
   780
           else
blanchet@51810
   781
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@51810
   782
                Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@51810
   783
blanchet@51810
   784
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@51810
   785
          Library.foldr1 HOLogic.mk_conj
blanchet@51810
   786
            (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@51810
   787
          handle List.Empty => @{term True};
blanchet@51810
   788
blanchet@51810
   789
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@51810
   790
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@51810
   791
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@51810
   792
blanchet@51810
   793
        val concl =
blanchet@51810
   794
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   795
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   796
               uvrs us vs));
blanchet@51810
   797
blanchet@51810
   798
        fun mk_goal rs' =
blanchet@51810
   799
          Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@51810
   800
            concl);
blanchet@51810
   801
blanchet@51810
   802
        val goal = mk_goal rs;
blanchet@51810
   803
        val strong_goal = mk_goal strong_rs;
blanchet@51810
   804
blanchet@51810
   805
        fun prove dtor_coinduct' goal =
blanchet@51810
   806
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51810
   807
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@51819
   808
              exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   809
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   810
          |> Thm.close_derivation;
blanchet@51810
   811
blanchet@51810
   812
        fun postproc nn thm =
blanchet@51810
   813
          Thm.permute_prems 0 nn
blanchet@51828
   814
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   815
          |> Drule.zero_var_indexes
blanchet@51810
   816
          |> `(conj_dests nn);
blanchet@51810
   817
      in
blanchet@51814
   818
        (postproc nn (prove dtor_coinduct goal), postproc nn (prove dtor_strong_induct strong_goal))
blanchet@51810
   819
      end;
blanchet@51810
   820
blanchet@51810
   821
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   822
      let
blanchet@51810
   823
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   824
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   825
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   826
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   827
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   828
      in
blanchet@51810
   829
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   830
      end;
blanchet@51810
   831
blanchet@51816
   832
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   833
    val coinduct_conclss =
blanchet@51810
   834
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   835
blanchet@51810
   836
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   837
blanchet@51810
   838
    val gunfolds = map (lists_bmoc pgss) unfolds;
blanchet@51810
   839
    val hcorecs = map (lists_bmoc phss) corecs;
blanchet@51810
   840
blanchet@51810
   841
    val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@51810
   842
      let
blanchet@51843
   843
        fun mk_goal pfss c cps fcoiter n k ctr m cfs' =
blanchet@51810
   844
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   845
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@51843
   846
               mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   847
blanchet@51845
   848
        val mk_U = typ_subst_nonatomic (map2 pair Cs fpTs);
blanchet@51810
   849
blanchet@51843
   850
        fun intr_coiters fcoiters [] [cf] =
blanchet@51810
   851
            let val T = fastype_of cf in
blanchet@51855
   852
              if exists_subtype_in Cs T then
blanchet@52302
   853
                build_map lthy (indexify fst Cs (K o nth fcoiters)) (T, mk_U T) $ cf
blanchet@51855
   854
              else
blanchet@51855
   855
                cf
blanchet@51810
   856
            end
blanchet@51843
   857
          | intr_coiters fcoiters [cq] [cf, cf'] =
blanchet@51843
   858
            mk_If cq (intr_coiters fcoiters [] [cf]) (intr_coiters fcoiters [] [cf']);
blanchet@51810
   859
blanchet@51843
   860
        val crgsss = map2 (map2 (map2 (intr_coiters gunfolds))) crssss cgssss;
blanchet@51843
   861
        val cshsss = map2 (map2 (map2 (intr_coiters hcorecs))) csssss chssss;
blanchet@51810
   862
blanchet@51828
   863
        val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
blanchet@51828
   864
        val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
blanchet@51810
   865
blanchet@51810
   866
        fun mk_map_if_distrib bnf =
blanchet@51810
   867
          let
blanchet@51810
   868
            val mapx = map_of_bnf bnf;
blanchet@51810
   869
            val live = live_of_bnf bnf;
blanchet@51810
   870
            val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
blanchet@51810
   871
            val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
blanchet@51810
   872
            val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
blanchet@51810
   873
          in
blanchet@51810
   874
            Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
blanchet@51810
   875
              @{thm if_distrib}
blanchet@51810
   876
          end;
blanchet@51810
   877
blanchet@51810
   878
        val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
blanchet@51810
   879
blanchet@51810
   880
        val unfold_tacss =
blanchet@51843
   881
          map3 (map oo mk_coiter_tac unfold_defs [] [] nesting_map_ids'' [])
blanchet@51814
   882
            dtor_unfold_thms pre_map_defs ctr_defss;
blanchet@51810
   883
        val corec_tacss =
blanchet@51843
   884
          map3 (map oo mk_coiter_tac corec_defs nested_map_comps'' nested_map_comp's
blanchet@51810
   885
              (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
blanchet@51814
   886
            dtor_corec_thms pre_map_defs ctr_defss;
blanchet@51810
   887
blanchet@51810
   888
        fun prove goal tac =
blanchet@51815
   889
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   890
          |> Thm.close_derivation;
blanchet@51810
   891
blanchet@51810
   892
        val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@51810
   893
        val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
blanchet@51810
   894
blanchet@51810
   895
        val filter_safesss =
blanchet@51810
   896
          map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@51810
   897
            curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
blanchet@51810
   898
blanchet@51810
   899
        val safe_unfold_thmss = filter_safesss unfold_thmss;
blanchet@51810
   900
        val safe_corec_thmss = filter_safesss corec_thmss;
blanchet@51810
   901
      in
blanchet@51810
   902
        (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@51810
   903
      end;
blanchet@51810
   904
blanchet@51810
   905
    val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@51810
   906
      let
blanchet@51843
   907
        fun mk_goal c cps fcoiter n k disc =
blanchet@51843
   908
          mk_Trueprop_eq (disc $ (fcoiter $ c),
blanchet@51810
   909
            if n = 1 then @{const True}
blanchet@51810
   910
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   911
blanchet@51810
   912
        val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@51810
   913
        val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   914
blanchet@51828
   915
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   916
blanchet@51810
   917
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   918
blanchet@51810
   919
        val unfold_tacss =
blanchet@51843
   920
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@51810
   921
        val corec_tacss =
blanchet@51843
   922
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   923
blanchet@51810
   924
        fun prove goal tac =
blanchet@51810
   925
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51829
   926
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   927
          |> Thm.close_derivation;
blanchet@51810
   928
blanchet@51810
   929
        fun proves [_] [_] = []
blanchet@51810
   930
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   931
      in
blanchet@51828
   932
        (map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss)
blanchet@51810
   933
      end;
blanchet@51810
   934
blanchet@51810
   935
    val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@51810
   936
blanchet@51843
   937
    fun mk_disc_coiter_thms coiters discIs =
blanchet@51843
   938
      map (op RS) (filter_out (is_triv_discI o snd) (coiters ~~ discIs));
blanchet@51810
   939
blanchet@51843
   940
    val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss;
blanchet@51843
   941
    val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
blanchet@51810
   942
blanchet@51843
   943
    fun mk_sel_coiter_thm coiter_thm sel sel_thm =
blanchet@51810
   944
      let
blanchet@51810
   945
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   946
        val arg_cong' =
blanchet@51810
   947
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   948
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   949
          |> Thm.varifyT_global;
blanchet@51810
   950
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   951
      in
blanchet@51843
   952
        coiter_thm RS arg_cong' RS sel_thm'
blanchet@51810
   953
      end;
blanchet@51810
   954
blanchet@51843
   955
    fun mk_sel_coiter_thms coiterss =
blanchet@51843
   956
      map3 (map3 (map2 o mk_sel_coiter_thm)) coiterss selsss sel_thmsss |> map flat;
blanchet@51810
   957
blanchet@51843
   958
    val sel_unfold_thmss = mk_sel_coiter_thms unfold_thmss;
blanchet@51843
   959
    val sel_corec_thmss = mk_sel_coiter_thms corec_thmss;
blanchet@51810
   960
blanchet@51810
   961
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   962
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   963
    val coinduct_case_concl_attrs =
blanchet@51810
   964
      map2 (fn casex => fn concls =>
blanchet@51810
   965
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   966
        coinduct_cases coinduct_conclss;
blanchet@51810
   967
    val coinduct_case_attrs =
blanchet@51810
   968
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   969
  in
blanchet@51810
   970
    ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms, coinduct_case_attrs),
blanchet@51810
   971
     (unfold_thmss, corec_thmss, []),
blanchet@51810
   972
     (safe_unfold_thmss, safe_corec_thmss),
blanchet@51810
   973
     (disc_unfold_thmss, disc_corec_thmss, simp_attrs),
blanchet@51810
   974
     (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
blanchet@51810
   975
     (sel_unfold_thmss, sel_corec_thmss, simp_attrs))
blanchet@51810
   976
  end;
blanchet@51810
   977
blanchet@52207
   978
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
blanchet@49633
   979
    (wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
blanchet@49112
   980
  let
blanchet@49298
   981
    (* TODO: sanity checks on arguments *)
blanchet@49298
   982
blanchet@52207
   983
    val _ = if fp = Greatest_FP andalso no_dests then
blanchet@52207
   984
        error "Cannot define destructor-less codatatypes"
blanchet@52207
   985
      else
blanchet@52207
   986
        ();
blanchet@49278
   987
blanchet@49633
   988
    fun qualify mandatory fp_b_name =
blanchet@49633
   989
      Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
   990
blanchet@49367
   991
    val nn = length specs;
blanchet@49361
   992
    val fp_bs = map type_binding_of specs;
blanchet@49498
   993
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
   994
    val fp_common_name = mk_common_name fp_b_names;
blanchet@51758
   995
    val map_bs = map map_binding_of specs;
blanchet@51767
   996
    val rel_bs = map rel_binding_of specs;
blanchet@49298
   997
blanchet@51758
   998
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
   999
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
  1000
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
  1001
      end;
blanchet@49298
  1002
blanchet@51758
  1003
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs;
blanchet@49298
  1004
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@49298
  1005
    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
blanchet@51758
  1006
    val set_bss = map (map fst o type_args_named_constrained_of) specs;
blanchet@49119
  1007
blanchet@49585
  1008
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
  1009
      no_defs_lthy0
blanchet@49298
  1010
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@49585
  1011
      |> mk_TFrees (length unsorted_As)
blanchet@49585
  1012
      ||>> mk_TFrees nn
blanchet@51858
  1013
      ||>> variant_tfrees fp_b_names;
blanchet@49119
  1014
blanchet@52195
  1015
    (* TODO: Cleaner handling of fake contexts, without "background_theory". The case where the new
blanchet@52195
  1016
       type is defined in a locale and shadows an existing global type is currently not handled. *)
blanchet@51768
  1017
blanchet@51769
  1018
    fun add_fake_type spec =
blanchet@51768
  1019
      Sign.add_type no_defs_lthy (type_binding_of spec,
blanchet@51769
  1020
        length (type_args_named_constrained_of spec), mixfix_of spec);
blanchet@51768
  1021
blanchet@51769
  1022
    val fake_thy = Theory.copy #> fold add_fake_type specs;
blanchet@49298
  1023
    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
blanchet@49119
  1024
blanchet@49182
  1025
    fun mk_fake_T b =
blanchet@49121
  1026
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49298
  1027
        unsorted_As);
blanchet@49121
  1028
blanchet@49302
  1029
    val fake_Ts = map mk_fake_T fp_bs;
blanchet@49121
  1030
blanchet@49181
  1031
    val mixfixes = map mixfix_of specs;
blanchet@49119
  1032
blanchet@49302
  1033
    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
  1034
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
  1035
blanchet@49121
  1036
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
  1037
blanchet@49336
  1038
    val disc_bindingss = map (map disc_of) ctr_specss;
blanchet@49336
  1039
    val ctr_bindingss =
blanchet@49633
  1040
      map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
blanchet@49121
  1041
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49181
  1042
    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
blanchet@49119
  1043
blanchet@49336
  1044
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
  1045
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49286
  1046
    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
blanchet@49286
  1047
blanchet@49308
  1048
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
  1049
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@49298
  1050
blanchet@49298
  1051
    val _ = (case duplicates (op =) unsorted_As of [] => ()
blanchet@49298
  1052
      | A :: _ => error ("Duplicate type parameter " ^
blanchet@49298
  1053
          quote (Syntax.string_of_typ no_defs_lthy A)));
blanchet@49298
  1054
blanchet@49183
  1055
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@49298
  1056
    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
blanchet@49165
  1057
        [] => ()
blanchet@49342
  1058
      | A' :: _ => error ("Extra type variable on right-hand side: " ^
blanchet@49204
  1059
          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
blanchet@49165
  1060
blanchet@49591
  1061
    fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
  1062
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
  1063
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49591
  1064
      | eq_fpT_check _ _ = false;
blanchet@49146
  1065
blanchet@49204
  1066
    fun freeze_fp (T as Type (s, Us)) =
blanchet@49591
  1067
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@49591
  1068
          ~1 => Type (s, map freeze_fp Us)
blanchet@49591
  1069
        | kk => nth Xs kk)
blanchet@49204
  1070
      | freeze_fp T = T;
blanchet@49121
  1071
blanchet@52310
  1072
    val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@52310
  1073
    val ctrXs_sum_prod_Ts = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
blanchet@49119
  1074
blanchet@49298
  1075
    val fp_eqs =
blanchet@52310
  1076
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_sum_prod_Ts;
blanchet@49121
  1077
blanchet@51839
  1078
    val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0,
blanchet@52313
  1079
           xtor_un_folds = xtor_un_folds0, xtor_co_recs = xtor_co_recs0, xtor_co_induct,
blanchet@52314
  1080
           xtor_strong_co_induct, dtor_ctors, ctor_dtors, ctor_injects, xtor_map_thms,
blanchet@52314
  1081
           xtor_set_thmss, xtor_rel_thms, xtor_un_fold_thms, xtor_co_rec_thms, ...}, lthy)) =
blanchet@51868
  1082
      fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As) fp_eqs
blanchet@51868
  1083
        no_defs_lthy0;
blanchet@49585
  1084
blanchet@49585
  1085
    val timer = time (Timer.startRealTimer ());
blanchet@49121
  1086
blanchet@52310
  1087
    val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
blanchet@52310
  1088
    val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
blanchet@49226
  1089
blanchet@49585
  1090
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
  1091
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
  1092
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
  1093
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@51766
  1094
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@49585
  1095
blanchet@49585
  1096
    val live = live_of_bnf any_fp_bnf;
blanchet@49585
  1097
blanchet@49585
  1098
    val Bs =
blanchet@49585
  1099
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
  1100
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
  1101
blanchet@49585
  1102
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
  1103
blanchet@49501
  1104
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
  1105
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
  1106
blanchet@49501
  1107
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
  1108
blanchet@51780
  1109
    fun massage_simple_notes base =
blanchet@51780
  1110
      filter_out (null o #2)
blanchet@51780
  1111
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
  1112
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
  1113
blanchet@51780
  1114
    val massage_multi_notes =
blanchet@51780
  1115
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
  1116
        if forall null thmss then
blanchet@51780
  1117
          []
blanchet@51780
  1118
        else
blanchet@51780
  1119
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@52311
  1120
              ((qualify true fp_b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
blanchet@52311
  1121
            fp_b_names fpTs thmss);
blanchet@51780
  1122
blanchet@52310
  1123
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctrXs_Tsss;
blanchet@49203
  1124
    val ns = map length ctr_Tsss;
blanchet@49212
  1125
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
  1126
    val mss = map (map length) ctr_Tsss;
blanchet@49203
  1127
blanchet@52315
  1128
    val (([xtor_un_folds, xtor_co_recs], fold_rec_args_types, unfold_corec_args_types), lthy) =
blanchet@52315
  1129
      mk_un_fold_co_rec_prelims fp fpTs Cs ns mss [xtor_un_folds0, xtor_co_recs0] lthy;
blanchet@49210
  1130
blanchet@49585
  1131
    fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@52313
  1132
              xtor_un_fold), xtor_co_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def),
blanchet@52313
  1133
            pre_set_defs), pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms),
blanchet@52313
  1134
          ctr_bindings), ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss)
blanchet@52313
  1135
        no_defs_lthy =
blanchet@49176
  1136
      let
blanchet@49498
  1137
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1138
blanchet@49501
  1139
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
  1140
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
  1141
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
  1142
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
  1143
blanchet@49593
  1144
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
  1145
          no_defs_lthy
blanchet@49501
  1146
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
  1147
          ||>> mk_Frees "f" case_Ts
blanchet@49370
  1148
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1149
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1150
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1151
blanchet@49498
  1152
        val u = Free (u', fpT);
blanchet@49121
  1153
blanchet@49585
  1154
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
  1155
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
  1156
blanchet@49129
  1157
        val ctr_rhss =
blanchet@49585
  1158
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
  1159
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
  1160
blanchet@49633
  1161
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
  1162
blanchet@49134
  1163
        val case_rhs =
blanchet@49498
  1164
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
  1165
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
  1166
blanchet@49201
  1167
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1168
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
  1169
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
  1170
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
  1171
          ||> `Local_Theory.restore;
blanchet@49121
  1172
blanchet@49121
  1173
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1174
blanchet@49121
  1175
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1176
        val ctr_defs' =
blanchet@49585
  1177
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1178
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
  1179
blanchet@49203
  1180
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1181
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
  1182
blanchet@49203
  1183
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1184
blanchet@51897
  1185
        fun wrap_ctrs lthy =
blanchet@49123
  1186
          let
traytel@50170
  1187
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1188
              let
blanchet@49585
  1189
                val ctor_iff_dtor_thm =
blanchet@49585
  1190
                  let
blanchet@49585
  1191
                    val goal =
blanchet@49585
  1192
                      fold_rev Logic.all [w, u]
blanchet@49585
  1193
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1194
                  in
wenzelm@51551
  1195
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
  1196
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
  1197
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
  1198
                    |> Thm.close_derivation
blanchet@49585
  1199
                    |> Morphism.thm phi
blanchet@49585
  1200
                  end;
blanchet@49585
  1201
blanchet@49585
  1202
                val sumEN_thm' =
blanchet@49585
  1203
                  unfold_thms lthy @{thms all_unit_eq}
blanchet@49585
  1204
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
  1205
                       (mk_sumEN_balanced n))
blanchet@49585
  1206
                  |> Morphism.thm phi;
blanchet@49135
  1207
              in
blanchet@49585
  1208
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1209
              end;
blanchet@49135
  1210
blanchet@49585
  1211
            val inject_tacss =
blanchet@49585
  1212
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
  1213
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
  1214
blanchet@49585
  1215
            val half_distinct_tacss =
blanchet@49585
  1216
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
  1217
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1218
blanchet@49585
  1219
            val case_tacs =
blanchet@49585
  1220
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
  1221
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
  1222
blanchet@49585
  1223
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
  1224
blanchet@49585
  1225
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
  1226
          in
blanchet@51781
  1227
            wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
blanchet@51781
  1228
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
  1229
          end;
blanchet@49121
  1230
blanchet@51840
  1231
        fun derive_maps_sets_rels (ctr_sugar, lthy) =
blanchet@51835
  1232
          if live = 0 then
blanchet@51840
  1233
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1234
          else
blanchet@51835
  1235
            let
blanchet@51835
  1236
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1237
              val nones = replicate live NONE;
blanchet@49585
  1238
blanchet@51835
  1239
              val ctor_cong =
blanchet@52207
  1240
                if fp = Least_FP then
blanchet@51835
  1241
                  Drule.dummy_thm
blanchet@51835
  1242
                else
blanchet@51835
  1243
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1244
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1245
                  end;
blanchet@49585
  1246
blanchet@51835
  1247
              fun mk_cIn ify =
blanchet@52207
  1248
                certify lthy o (fp = Greatest_FP ? curry (op $) (map_types ify ctor)) oo
blanchet@51835
  1249
                mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
  1250
blanchet@51835
  1251
              val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@51835
  1252
              val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
  1253
blanchet@51835
  1254
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1255
                fold_thms lthy [ctr_def']
blanchet@51835
  1256
                  (unfold_thms lthy (pre_map_def ::
blanchet@52207
  1257
                       (if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@51835
  1258
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@52207
  1259
                        (if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1260
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1261
blanchet@51835
  1262
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1263
                fold_thms lthy [ctr_def']
blanchet@51835
  1264
                  (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@52207
  1265
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@51835
  1266
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1267
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1268
blanchet@51835
  1269
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1270
blanchet@51835
  1271
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1272
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@51835
  1273
blanchet@51835
  1274
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1275
blanchet@51835
  1276
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1277
                fold_thms lthy ctr_defs'
blanchet@51835
  1278
                   (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@52207
  1279
                        (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@51835
  1280
                      (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1281
                |> postproc
blanchet@51835
  1282
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1283
blanchet@51835
  1284
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1285
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1286
blanchet@51835
  1287
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1288
blanchet@51835
  1289
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1290
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1291
                  cxIn cyIn;
blanchet@49121
  1292
blanchet@51835
  1293
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1294
                flip_rels lthy live thm
blanchet@51835
  1295
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1296
blanchet@51835
  1297
              val half_rel_distinct_thmss =
blanchet@51835
  1298
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1299
              val other_half_rel_distinct_thmss =
blanchet@51835
  1300
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1301
              val (rel_distinct_thms, _) =
blanchet@51835
  1302
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1303
blanchet@51835
  1304
              val notes =
blanchet@51835
  1305
                [(mapN, map_thms, code_simp_attrs),
blanchet@51835
  1306
                 (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@51835
  1307
                 (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@51835
  1308
                 (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51835
  1309
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1310
            in
blanchet@51840
  1311
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@51835
  1312
               lthy |> Local_Theory.notes notes |> snd)
blanchet@51835
  1313
            end;
blanchet@49585
  1314
blanchet@51897
  1315
        fun mk_binding suf = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49287
  1316
blanchet@51883
  1317
        fun massage_res (((maps_sets_rels, ctr_sugar), co_iter_res), lthy) =
blanchet@51883
  1318
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_iter_res), lthy);
blanchet@49119
  1319
      in
blanchet@51897
  1320
        (wrap_ctrs
blanchet@51835
  1321
         #> derive_maps_sets_rels
blanchet@52313
  1322
         ##>>
blanchet@52313
  1323
           (if fp = Least_FP then define_fold_rec (the fold_rec_args_types)
blanchet@52313
  1324
            else define_unfold_corec (the unfold_corec_args_types))
blanchet@52313
  1325
             mk_binding fpTs Cs xtor_un_fold xtor_co_rec
blanchet@51835
  1326
         #> massage_res, lthy')
blanchet@49119
  1327
      end;
blanchet@49167
  1328
blanchet@51835
  1329
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1330
      fold_map I wrap_types_etcs lthy
blanchet@51835
  1331
      |>> apsnd split_list4 o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@51835
  1332
        o split_list;
blanchet@49226
  1333
blanchet@49479
  1334
    val mk_simp_thmss =
blanchet@51857
  1335
      map7 (fn {injects, distincts, case_thms, ...} => fn un_folds => fn co_recs =>
blanchet@51835
  1336
        fn mapsx => fn rel_injects => fn rel_distincts => fn setss =>
blanchet@51857
  1337
          injects @ distincts @ case_thms @ co_recs @ un_folds @ mapsx @ rel_injects
blanchet@51835
  1338
          @ rel_distincts @ flat setss);
blanchet@49479
  1339
blanchet@51810
  1340
    fun derive_and_note_induct_fold_rec_thms_for_types
blanchet@51840
  1341
        ((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@51835
  1342
          (folds, recs, fold_defs, rec_defs)), lthy) =
blanchet@49202
  1343
      let
blanchet@51833
  1344
        val ((induct_thm, induct_thms, induct_attrs), (fold_thmss, fold_attrs),
blanchet@51808
  1345
             (rec_thmss, rec_attrs)) =
blanchet@52313
  1346
          derive_induct_fold_rec_thms_for_types pre_bnfs [xtor_un_folds, xtor_co_recs]
blanchet@52315
  1347
            (the fold_rec_args_types) xtor_co_induct [xtor_un_fold_thms, xtor_co_rec_thms]
blanchet@52315
  1348
            nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss [folds, recs]
blanchet@52315
  1349
            [fold_defs, rec_defs] lthy;
blanchet@49201
  1350
blanchet@51830
  1351
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1352
blanchet@51835
  1353
        val simp_thmss =
blanchet@51843
  1354
          mk_simp_thmss ctr_sugars fold_thmss rec_thmss mapsx rel_injects rel_distincts setss;
blanchet@49438
  1355
blanchet@49337
  1356
        val common_notes =
blanchet@51808
  1357
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1358
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1359
blanchet@49226
  1360
        val notes =
blanchet@51808
  1361
          [(foldN, fold_thmss, K fold_attrs),
blanchet@51810
  1362
           (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@51808
  1363
           (recN, rec_thmss, K rec_attrs),
blanchet@49585
  1364
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1365
          |> massage_multi_notes;
blanchet@49202
  1366
      in
blanchet@51824
  1367
        lthy
blanchet@51824
  1368
        |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@52299
  1369
        |> register_fp_sugars Least_FP pre_bnfs fp_res ctr_defss ctr_sugars folds recs induct_thm
blanchet@52299
  1370
          induct_thm fold_thmss rec_thmss
blanchet@49202
  1371
      end;
blanchet@49202
  1372
blanchet@51810
  1373
    fun derive_and_note_coinduct_unfold_corec_thms_for_types
blanchet@51859
  1374
        ((((mapsx, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
blanchet@51835
  1375
          (unfolds, corecs, unfold_defs, corec_defs)), lthy) =
blanchet@49212
  1376
      let
blanchet@51810
  1377
        val ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms,
blanchet@51810
  1378
              coinduct_attrs),
blanchet@51843
  1379
             (unfold_thmss, corec_thmss, coiter_attrs),
blanchet@51810
  1380
             (safe_unfold_thmss, safe_corec_thmss),
blanchet@51843
  1381
             (disc_unfold_thmss, disc_corec_thmss, disc_coiter_attrs),
blanchet@51843
  1382
             (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_coiter_iff_attrs),
blanchet@51843
  1383
             (sel_unfold_thmss, sel_corec_thmss, sel_coiter_attrs)) =
blanchet@52313
  1384
          derive_coinduct_unfold_corec_thms_for_types pre_bnfs xtor_un_folds xtor_co_recs
blanchet@52313
  1385
            xtor_co_induct xtor_strong_co_induct dtor_ctors xtor_un_fold_thms xtor_co_rec_thms
blanchet@52313
  1386
            nesting_bnfs nested_bnfs fpTs Cs As kss mss ns ctr_defss ctr_sugars unfolds corecs
blanchet@52313
  1387
            unfold_defs corec_defs lthy;
blanchet@49212
  1388
blanchet@51830
  1389
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1390
blanchet@51843
  1391
        fun flat_coiter_thms coiters disc_coiters sel_coiters =
blanchet@51843
  1392
          coiters @ disc_coiters @ sel_coiters;
blanchet@49479
  1393
blanchet@49479
  1394
        val simp_thmss =
blanchet@51840
  1395
          mk_simp_thmss ctr_sugars
blanchet@51843
  1396
            (map3 flat_coiter_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss)
blanchet@51843
  1397
            (map3 flat_coiter_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@51835
  1398
            mapsx rel_injects rel_distincts setss;
blanchet@49479
  1399
blanchet@49479
  1400
        val anonymous_notes =
blanchet@49504
  1401
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1402
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1403
blanchet@49342
  1404
        val common_notes =
blanchet@49591
  1405
          (if nn > 1 then
blanchet@51810
  1406
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1407
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1408
           else
blanchet@49591
  1409
             [])
blanchet@51780
  1410
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1411
blanchet@49212
  1412
        val notes =
blanchet@51780
  1413
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1414
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@51843
  1415
           (corecN, corec_thmss, K coiter_attrs),
blanchet@51843
  1416
           (disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
blanchet@51843
  1417
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1418
           (disc_unfoldN, disc_unfold_thmss, K disc_coiter_attrs),
blanchet@51843
  1419
           (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1420
           (sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
blanchet@51843
  1421
           (sel_unfoldN, sel_unfold_thmss, K sel_coiter_attrs),
blanchet@51780
  1422
           (simpsN, simp_thmss, K []),
blanchet@51810
  1423
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
blanchet@51843
  1424
           (unfoldN, unfold_thmss, K coiter_attrs)]
blanchet@51780
  1425
          |> massage_multi_notes;
blanchet@49212
  1426
      in
blanchet@51824
  1427
        lthy
blanchet@51824
  1428
        |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@52299
  1429
        |> register_fp_sugars Greatest_FP pre_bnfs fp_res ctr_defss ctr_sugars unfolds corecs
blanchet@52299
  1430
          coinduct_thm strong_coinduct_thm unfold_thmss corec_thmss
blanchet@49212
  1431
      end;
blanchet@49212
  1432
blanchet@49204
  1433
    val lthy' = lthy
blanchet@49585
  1434
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@52313
  1435
        xtor_un_folds ~~ xtor_co_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@52314
  1436
        pre_set_defss ~~ pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~
blanchet@52314
  1437
        kss ~~ mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~
blanchet@52314
  1438
        sel_bindingsss ~~ raw_sel_defaultsss)
blanchet@51835
  1439
      |> wrap_types_etc
blanchet@52207
  1440
      |> (if fp = Least_FP then derive_and_note_induct_fold_rec_thms_for_types
blanchet@51808
  1441
          else derive_and_note_coinduct_unfold_corec_thms_for_types);
blanchet@49167
  1442
blanchet@49167
  1443
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@52207
  1444
      datatype_word fp));
blanchet@49112
  1445
  in
blanchet@49308
  1446
    timer; lthy'
blanchet@49112
  1447
  end;
blanchet@49112
  1448
blanchet@51863
  1449
val co_datatypes = define_co_datatypes (K I) (K I) (K I);
blanchet@49297
  1450
blanchet@51863
  1451
val co_datatype_cmd =
blanchet@51863
  1452
  define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1453
blanchet@49112
  1454
val parse_ctr_arg =
blanchet@49329
  1455
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1456
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1457
blanchet@49286
  1458
val parse_defaults =
blanchet@49286
  1459
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1460
blanchet@51758
  1461
val parse_type_arg_constrained =
blanchet@51790
  1462
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1463
blanchet@51790
  1464
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1465
blanchet@51758
  1466
val parse_type_args_named_constrained =
blanchet@51758
  1467
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1468
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1469
  Scan.succeed [];
blanchet@51756
  1470
blanchet@51790
  1471
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1472
blanchet@51767
  1473
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1474
blanchet@51767
  1475
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51833
  1476
   that we don't want them to be highlighted everywhere. *)
blanchet@51767
  1477
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1478
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1479
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1480
blanchet@51767
  1481
val parse_map_rel_bindings =
blanchet@51767
  1482
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1483
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1484
  Scan.succeed no_map_rel;
blanchet@51767
  1485
blanchet@51767
  1486
val parse_ctr_spec =
blanchet@51790
  1487
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1488
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1489
blanchet@51767
  1490
val parse_spec =
blanchet@51790
  1491
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1492
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1493
blanchet@51863
  1494
val parse_co_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1495
blanchet@52207
  1496
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
blanchet@49112
  1497
blanchet@49112
  1498
end;