src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author traytel
Tue Aug 20 17:39:08 2013 +0200 (2013-08-20)
changeset 53106 d81211f61a1b
parent 53037 e5fa456890b4
child 53126 f4d2c64c7aa8
permissions -rw-r--r--
moved derivation of strong coinduction to sugar
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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, 2013
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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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     nested_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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     co_iterss: term list list,
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     co_inducts: thm list,
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     co_iter_thmsss: thm list 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 co_induct_of: 'a list -> 'a
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  val strong_co_induct_of: 'a list -> 'a
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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_arg_args: 'a list list -> 'a list
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  val flat_corec_preds_predsss_gettersss: 'a list -> 'a list list list -> 'a list list list ->
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    '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_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 dest_map: Proof.context -> string -> term -> term * term list
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  val dest_ctr: Proof.context -> string -> term -> term * term list
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  val mk_co_iters_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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     * (string * term list * term list list
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        * ((term list list * term list list list) * (typ list * typ list list)) list) option)
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    * Proof.context
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  val mk_iter_fun_arg_types: typ list -> int list -> int list list -> term ->
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    typ list list list list
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  val mk_coiter_fun_arg_types: typ list -> int list -> int list list -> term ->
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    typ list list
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    * (typ list list list list * typ list list list * typ list list list list * typ list)
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  val define_iters: string 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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    (string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
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    (term list * thm list) * Proof.context
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  val define_coiters: string list -> string * term list * term list list
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    * ((term list list * term list list list) * (typ list * typ list list)) list ->
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    (string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
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    (term list * thm list) * Proof.context
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  val derive_induct_iters_thms_for_types: BNF_Def.bnf 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 list * thm * 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_coiters_thms_for_types: BNF_Def.bnf list ->
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    string * term list * term list list * ((term list list * term list list list)
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      * (typ list * typ list list)) list ->
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    thm -> thm list -> thm list list -> BNF_Def.bnf list -> typ list -> typ list -> typ list ->
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    int list list -> int list list -> int list -> thm list list -> BNF_Ctr_Sugar.ctr_sugar list ->
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    term list list -> thm list list -> (thm list -> thm list) -> local_theory ->
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    ((thm list * 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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   nested_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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   co_iterss: term list list,
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   co_inducts: thm list,
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   co_iter_thmsss: thm list 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, nested_bnfs, fp_res, ctr_defss, ctr_sugars,
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    co_iterss, co_inducts, co_iter_thmsss} =
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  {T = Morphism.typ phi T, fp = fp, index = index, pre_bnfs = map (morph_bnf phi) pre_bnfs,
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    nested_bnfs = map (morph_bnf phi) nested_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,
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   co_iterss = map (map (Morphism.term phi)) co_iterss,
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   co_inducts = map (Morphism.thm phi) co_inducts,
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   co_iter_thmsss = map (map (map (Morphism.thm phi))) co_iter_thmsss};
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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 co_induct_of (i :: _) = i;
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fun strong_co_induct_of [_, s] = s;
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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.default (key, morph_fp_sugar phi fp_sugar)));
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fun register_fp_sugars fp pre_bnfs nested_bnfs (fp_res as {Ts, ...}) ctr_defss ctr_sugars co_iterss
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    co_inducts co_iter_thmsss 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,
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        nested_bnfs = nested_bnfs, fp_res = fp_res, ctr_defss = ctr_defss, ctr_sugars = ctr_sugars,
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        co_iterss = co_iterss, co_inducts = co_inducts, co_iter_thmsss = co_iter_thmsss}
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      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 id_def = @{thm id_def};
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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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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
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fun flat_rec_arg_args xss =
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  (* FIXME (once the old datatype package is phased out): The first line below gives the preferred
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     order. The second line is for compatibility with the 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_corec_predss_getterss qss fss = maps (op @) (qss ~~ fss);
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fun flat_corec_preds_predsss_gettersss [] [qss] [fss] = flat_corec_predss_getterss qss fss
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  | flat_corec_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
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    p :: flat_corec_predss_getterss qss fss @ flat_corec_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_uncurried2_fun f xss =
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  mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat_rec_arg_args 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 (f_Cs, Type (_, [prebody, body])) = strip_fun_type (fastype_of t);
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    val fpT0 = fp_case fp prebody body;
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    val Cs0 = distinct (op =) (map (fp_case fp body_type 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 = binder_fun_types o fastype_of;
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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 unzip_corecT Cs (T as Type (@{type_name sum}, Ts as [_, U])) =
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    if member (op =) Cs U then Ts else [T]
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  | unzip_corecT _ T = [T];
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fun mk_map live Ts Us t =
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  let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in
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    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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  end;
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fun mk_rel live Ts Us t =
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  let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in
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    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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  end;
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fun build_map lthy build_simple =
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  let
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    fun build (TU as (T, U)) =
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      if T = U then
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        HOLogic.id_const T
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      else
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        (case TU of
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          (Type (s, Ts), Type (s', Us)) =>
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          if s = s' then
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            let
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              val bnf = the (bnf_of lthy s);
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              val live = live_of_bnf bnf;
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              val mapx = mk_map live Ts Us (map_of_bnf bnf);
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              val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
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            in Term.list_comb (mapx, map build TUs') end
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          else
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            build_simple TU
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        | _ => build_simple TU);
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  in build end;
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fun fo_match ctxt t pat =
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  let val thy = Proof_Context.theory_of ctxt in
blanchet@53033
   289
    Pattern.first_order_match thy (pat, t) (Vartab.empty, Vartab.empty)
blanchet@53033
   290
  end;
blanchet@53033
   291
blanchet@53031
   292
val dummy_var_name = "?f"
blanchet@53031
   293
blanchet@53031
   294
fun mk_map_pattern ctxt s =
blanchet@53031
   295
  let
blanchet@53031
   296
    val bnf = the (bnf_of ctxt s);
blanchet@53031
   297
    val mapx = map_of_bnf bnf;
blanchet@53031
   298
    val live = live_of_bnf bnf;
blanchet@53031
   299
    val (f_Ts, _) = strip_typeN live (fastype_of mapx);
blanchet@53031
   300
    val fs = map_index (fn (i, T) => Var ((dummy_var_name, i), T)) f_Ts;
blanchet@53031
   301
  in
blanchet@53031
   302
    (mapx, betapplys (mapx, fs))
blanchet@53031
   303
  end;
blanchet@53031
   304
blanchet@53031
   305
fun dest_map ctxt s call =
blanchet@53031
   306
  let
blanchet@53031
   307
    val (map0, pat) = mk_map_pattern ctxt s;
blanchet@53033
   308
    val (_, tenv) = fo_match ctxt call pat;
blanchet@53031
   309
  in
blanchet@53031
   310
    (map0, Vartab.fold_rev (fn (_, (_, f)) => cons f) tenv [])
blanchet@53031
   311
  end;
blanchet@53031
   312
blanchet@53033
   313
fun dest_ctr ctxt s t =
blanchet@53033
   314
  let
blanchet@53033
   315
    val (f, args) = Term.strip_comb t;
blanchet@53033
   316
  in
blanchet@53033
   317
    (case fp_sugar_of ctxt s of
blanchet@53033
   318
      SOME fp_sugar =>
blanchet@53033
   319
      (case find_first (can (fo_match ctxt f)) (#ctrs (of_fp_sugar #ctr_sugars fp_sugar)) of
blanchet@53033
   320
        SOME f' => (f', args)
blanchet@53033
   321
      | NONE => raise Fail "dest_ctr")
blanchet@53033
   322
    | NONE => raise Fail "dest_ctr")
blanchet@53033
   323
  end;
blanchet@53033
   324
blanchet@52347
   325
fun liveness_of_fp_bnf n bnf =
blanchet@52347
   326
  (case T_of_bnf bnf of
blanchet@52347
   327
    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
blanchet@52347
   328
  | _ => replicate n false);
blanchet@52347
   329
blanchet@52347
   330
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
blanchet@52347
   331
blanchet@52347
   332
fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
blanchet@52347
   333
blanchet@52347
   334
fun merge_type_args (As, As') =
blanchet@52347
   335
  if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
blanchet@52347
   336
blanchet@52347
   337
fun reassoc_conjs thm =
blanchet@52347
   338
  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
blanchet@52347
   339
  handle THM _ => thm;
blanchet@52347
   340
blanchet@52347
   341
fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs;
blanchet@52347
   342
fun type_binding_of ((((_, b), _), _), _) = b;
blanchet@52347
   343
fun map_binding_of (((_, (b, _)), _), _) = b;
blanchet@52347
   344
fun rel_binding_of (((_, (_, b)), _), _) = b;
blanchet@52347
   345
fun mixfix_of ((_, mx), _) = mx;
blanchet@52347
   346
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
blanchet@52347
   347
blanchet@52347
   348
fun disc_of ((((disc, _), _), _), _) = disc;
blanchet@52347
   349
fun ctr_of ((((_, ctr), _), _), _) = ctr;
blanchet@52347
   350
fun args_of (((_, args), _), _) = args;
blanchet@52347
   351
fun defaults_of ((_, ds), _) = ds;
blanchet@52347
   352
fun ctr_mixfix_of (_, mx) = mx;
blanchet@52347
   353
blanchet@52347
   354
fun add_nesty_bnf_names Us =
blanchet@52347
   355
  let
blanchet@52347
   356
    fun add (Type (s, Ts)) ss =
blanchet@52347
   357
        let val (needs, ss') = fold_map add Ts ss in
blanchet@52347
   358
          if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@52347
   359
        end
blanchet@52347
   360
      | add T ss = (member (op =) Us T, ss);
blanchet@52347
   361
  in snd oo add end;
blanchet@52347
   362
blanchet@52347
   363
fun nesty_bnfs ctxt ctr_Tsss Us =
blanchet@52347
   364
  map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
blanchet@52347
   365
traytel@52923
   366
fun indexify proj xs f p = f (find_index (curry op = (proj p)) xs) p;
blanchet@52347
   367
blanchet@52872
   368
fun mk_iter_fun_arg_types0 n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type;
blanchet@51846
   369
blanchet@52872
   370
fun mk_iter_fun_arg_types Cs ns mss =
blanchet@51885
   371
  mk_fp_iter_fun_types
blanchet@52872
   372
  #> map3 mk_iter_fun_arg_types0 ns mss
blanchet@52296
   373
  #> map (map (map (unzip_recT Cs)));
blanchet@51885
   374
blanchet@52335
   375
fun mk_iters_args_types Cs ns mss ctor_iter_fun_Tss lthy =
blanchet@51832
   376
  let
blanchet@52214
   377
    val Css = map2 replicate ns Cs;
blanchet@52872
   378
    val y_Tsss = map3 mk_iter_fun_arg_types0 ns mss (map un_fold_of ctor_iter_fun_Tss);
blanchet@52214
   379
    val g_Tss = map2 (fn C => map (fn y_Ts => y_Ts ---> C)) Cs y_Tsss;
blanchet@51832
   380
blanchet@51832
   381
    val ((gss, ysss), lthy) =
blanchet@51832
   382
      lthy
blanchet@51832
   383
      |> mk_Freess "f" g_Tss
blanchet@51832
   384
      ||>> mk_Freesss "x" y_Tsss;
blanchet@52301
   385
blanchet@52301
   386
    val y_Tssss = map (map (map single)) y_Tsss;
blanchet@52214
   387
    val yssss = map (map (map single)) ysss;
blanchet@52214
   388
blanchet@52214
   389
    val z_Tssss =
blanchet@52296
   390
      map3 (fn n => fn ms => map2 (map (unzip_recT Cs) oo dest_tupleT) ms o
blanchet@52335
   391
        dest_sumTN_balanced n o domain_type o co_rec_of) ns mss ctor_iter_fun_Tss;
blanchet@51832
   392
blanchet@52868
   393
    val z_Tsss' = map (map flat_rec_arg_args) z_Tssss;
traytel@52923
   394
    val h_Tss = map2 (map2 (curry op --->)) z_Tsss' Css;
blanchet@51832
   395
blanchet@51832
   396
    val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@52214
   397
    val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
blanchet@52214
   398
    val (zssss_tl, lthy) =
blanchet@52214
   399
      lthy
blanchet@52214
   400
      |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
blanchet@52214
   401
    val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
blanchet@51832
   402
  in
blanchet@52315
   403
    ([(g_Tss, y_Tssss, gss, yssss), (h_Tss, z_Tssss, hss, zssss)], lthy)
blanchet@51832
   404
  end;
blanchet@51832
   405
blanchet@52872
   406
fun mk_coiter_fun_arg_types0 Cs ns mss fun_Ts =
blanchet@51829
   407
  let
blanchet@51829
   408
    (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@51829
   409
    fun repair_arity [0] = [1]
blanchet@51829
   410
      | repair_arity ms = ms;
blanchet@51829
   411
blanchet@52870
   412
    val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@52870
   413
    val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@52870
   414
    val f_Tsss = map2 (map2 dest_tupleT o repair_arity) mss f_prod_Tss;
traytel@52923
   415
    val f_Tssss = map2 (fn C => map (map (map (curry op --> C) o unzip_corecT Cs))) Cs f_Tsss;
blanchet@52871
   416
    val q_Tssss = map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
blanchet@52870
   417
  in
blanchet@52870
   418
    (q_Tssss, f_Tsss, f_Tssss, f_sum_prod_Ts)
blanchet@52870
   419
  end;
blanchet@51829
   420
blanchet@52898
   421
fun mk_coiter_p_pred_types Cs ns = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@52898
   422
blanchet@52898
   423
fun mk_coiter_fun_arg_types Cs ns mss dtor_coiter =
blanchet@52898
   424
  (mk_coiter_p_pred_types Cs ns,
blanchet@52898
   425
   mk_fp_iter_fun_types dtor_coiter |> mk_coiter_fun_arg_types0 Cs ns mss);
blanchet@52872
   426
blanchet@52870
   427
fun mk_coiters_args_types Cs ns mss dtor_coiter_fun_Tss lthy =
blanchet@52870
   428
  let
blanchet@52898
   429
    val p_Tss = mk_coiter_p_pred_types Cs ns;
blanchet@51829
   430
blanchet@52871
   431
    fun mk_types get_Ts =
blanchet@51829
   432
      let
blanchet@52335
   433
        val fun_Ts = map get_Ts dtor_coiter_fun_Tss;
blanchet@52872
   434
        val (q_Tssss, f_Tsss, f_Tssss, f_sum_prod_Ts) = mk_coiter_fun_arg_types0 Cs ns mss fun_Ts;
blanchet@52868
   435
        val pf_Tss = map3 flat_corec_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@52870
   436
      in
blanchet@52870
   437
        (q_Tssss, f_Tsss, f_Tssss, (f_sum_prod_Ts, pf_Tss))
blanchet@52870
   438
      end;
blanchet@51829
   439
blanchet@52871
   440
    val (r_Tssss, g_Tsss, g_Tssss, unfold_types) = mk_types un_fold_of;
blanchet@52871
   441
    val (s_Tssss, h_Tsss, h_Tssss, corec_types) = mk_types co_rec_of;
blanchet@51831
   442
blanchet@52347
   443
    val ((((Free (z, _), cs), pss), gssss), lthy) =
blanchet@51829
   444
      lthy
blanchet@52347
   445
      |> yield_singleton (mk_Frees "z") dummyT
blanchet@52347
   446
      ||>> mk_Frees "a" Cs
blanchet@51829
   447
      ||>> mk_Freess "p" p_Tss
blanchet@51829
   448
      ||>> mk_Freessss "g" g_Tssss;
blanchet@51829
   449
    val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@51829
   450
blanchet@51829
   451
    val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@51829
   452
    val ((sssss, hssss_tl), lthy) =
blanchet@51829
   453
      lthy
blanchet@51829
   454
      |> mk_Freessss "q" s_Tssss
blanchet@51829
   455
      ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@51829
   456
    val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@51831
   457
blanchet@51831
   458
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   459
blanchet@52347
   460
    fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@52347
   461
blanchet@52347
   462
    fun build_dtor_coiter_arg _ [] [cf] = cf
blanchet@52347
   463
      | build_dtor_coiter_arg T [cq] [cf, cf'] =
blanchet@52347
   464
        mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@52347
   465
          (build_sum_inj Inr_const (fastype_of cf', T) $ cf');
blanchet@52347
   466
blanchet@52349
   467
    fun mk_args qssss fssss f_Tsss =
blanchet@51831
   468
      let
blanchet@52868
   469
        val pfss = map3 flat_corec_preds_predsss_gettersss pss qssss fssss;
blanchet@51831
   470
        val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@51831
   471
        val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@52347
   472
        val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
blanchet@52347
   473
      in (pfss, cqfsss) end;
blanchet@51831
   474
blanchet@52349
   475
    val unfold_args = mk_args rssss gssss g_Tsss;
blanchet@52349
   476
    val corec_args = mk_args sssss hssss h_Tsss;
blanchet@51831
   477
  in
blanchet@52347
   478
    ((z, cs, cpss, [(unfold_args, unfold_types), (corec_args, corec_types)]), lthy)
blanchet@51831
   479
  end;
blanchet@51829
   480
blanchet@52334
   481
fun mk_co_iters_prelims fp fpTs Cs ns mss xtor_co_iterss0 lthy =
blanchet@51903
   482
  let
blanchet@52169
   483
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   484
blanchet@52335
   485
    val (xtor_co_iter_fun_Tss, xtor_co_iterss) =
blanchet@52329
   486
      map (mk_co_iters thy fp fpTs Cs #> `(mk_fp_iter_fun_types o hd)) (transpose xtor_co_iterss0)
blanchet@52335
   487
      |> apsnd transpose o apfst transpose o split_list;
blanchet@51903
   488
blanchet@52329
   489
    val ((iters_args_types, coiters_args_types), lthy') =
blanchet@52207
   490
      if fp = Least_FP then
blanchet@52335
   491
        mk_iters_args_types Cs ns mss xtor_co_iter_fun_Tss lthy |>> (rpair NONE o SOME)
blanchet@51903
   492
      else
blanchet@52335
   493
        mk_coiters_args_types Cs ns mss xtor_co_iter_fun_Tss lthy |>> (pair NONE o SOME)
blanchet@51903
   494
  in
blanchet@52335
   495
    ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy')
blanchet@51903
   496
  end;
blanchet@51903
   497
blanchet@52298
   498
fun mk_iter_body ctor_iter fss xssss =
blanchet@52298
   499
  Term.list_comb (ctor_iter, map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss);
blanchet@51884
   500
blanchet@51900
   501
fun mk_preds_getterss_join c cps sum_prod_T cqfss =
blanchet@51900
   502
  let val n = length cqfss in
blanchet@51900
   503
    Term.lambda c (mk_IfN sum_prod_T cps
blanchet@51900
   504
      (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)))
blanchet@51900
   505
  end;
blanchet@51886
   506
blanchet@52348
   507
fun mk_coiter_body cs cpss f_sum_prod_Ts cqfsss dtor_coiter =
blanchet@52347
   508
  Term.list_comb (dtor_coiter, map4 mk_preds_getterss_join cs cpss f_sum_prod_Ts cqfsss);
blanchet@51886
   509
blanchet@52327
   510
fun define_co_iters fp fpT Cs binding_specs lthy0 =
blanchet@51897
   511
  let
blanchet@52170
   512
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   513
blanchet@52327
   514
    val ((csts, defs), (lthy', lthy)) = lthy0
blanchet@52327
   515
      |> apfst split_list o fold_map (fn (b, spec) =>
blanchet@52327
   516
        Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@52327
   517
        #>> apsnd snd) binding_specs
blanchet@52327
   518
      ||> `Local_Theory.restore;
blanchet@52327
   519
blanchet@52327
   520
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52327
   521
blanchet@52327
   522
    val csts' = map (mk_co_iter thy fp fpT Cs o Morphism.term phi) csts;
blanchet@52327
   523
    val defs' = map (Morphism.thm phi) defs;
blanchet@52327
   524
  in
blanchet@52327
   525
    ((csts', defs'), lthy')
blanchet@52327
   526
  end;
blanchet@52327
   527
blanchet@52327
   528
fun define_iters iterNs iter_args_typess' mk_binding fpTs Cs ctor_iters lthy =
blanchet@52327
   529
  let
blanchet@51899
   530
    val nn = length fpTs;
blanchet@51899
   531
blanchet@52320
   532
    val fpT_to_C as Type (_, [fpT, _]) = snd (strip_typeN nn (fastype_of (hd ctor_iters)));
blanchet@51897
   533
blanchet@52320
   534
    fun generate_iter suf (f_Tss, _, fss, xssss) ctor_iter =
blanchet@51897
   535
      let
traytel@52923
   536
        val res_T = fold_rev (curry op --->) f_Tss fpT_to_C;
blanchet@52309
   537
        val b = mk_binding suf;
blanchet@51897
   538
        val spec =
blanchet@52309
   539
          mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of b, res_T)),
blanchet@52298
   540
            mk_iter_body ctor_iter fss xssss);
blanchet@52309
   541
      in (b, spec) end;
blanchet@51897
   542
  in
blanchet@52327
   543
    define_co_iters Least_FP fpT Cs (map3 generate_iter iterNs iter_args_typess' ctor_iters) lthy
blanchet@51897
   544
  end;
blanchet@51897
   545
blanchet@52347
   546
fun define_coiters coiterNs (_, cs, cpss, coiter_args_typess') mk_binding fpTs Cs dtor_coiters
blanchet@52347
   547
    lthy =
blanchet@51897
   548
  let
blanchet@51899
   549
    val nn = length fpTs;
blanchet@51899
   550
blanchet@52326
   551
    val C_to_fpT as Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of (hd dtor_coiters)));
blanchet@51897
   552
blanchet@52349
   553
    fun generate_coiter suf ((pfss, cqfsss), (f_sum_prod_Ts, pf_Tss)) dtor_coiter =
blanchet@51897
   554
      let
traytel@52923
   555
        val res_T = fold_rev (curry op --->) pf_Tss C_to_fpT;
blanchet@52309
   556
        val b = mk_binding suf;
blanchet@51897
   557
        val spec =
blanchet@52309
   558
          mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of b, res_T)),
blanchet@52348
   559
            mk_coiter_body cs cpss f_sum_prod_Ts cqfsss dtor_coiter);
blanchet@52309
   560
      in (b, spec) end;
blanchet@51897
   561
  in
blanchet@52327
   562
    define_co_iters Greatest_FP fpT Cs
blanchet@52327
   563
      (map3 generate_coiter coiterNs coiter_args_typess' dtor_coiters) lthy
blanchet@52320
   564
  end;
blanchet@51897
   565
traytel@53106
   566
fun derive_induct_iters_thms_for_types pre_bnfs [fold_args_types, rec_args_types] ctor_induct
blanchet@52346
   567
    ctor_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss iter_defss
blanchet@52346
   568
    lthy =
blanchet@51808
   569
  let
blanchet@52340
   570
    val iterss' = transpose iterss;
blanchet@52340
   571
    val iter_defss' = transpose iter_defss;
blanchet@52340
   572
blanchet@52340
   573
    val [folds, recs] = iterss';
blanchet@52340
   574
    val [fold_defs, rec_defs] = iter_defss';
blanchet@52340
   575
blanchet@51827
   576
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   577
blanchet@51815
   578
    val nn = length pre_bnfs;
blanchet@51827
   579
    val ns = map length ctr_Tsss;
blanchet@51827
   580
    val mss = map (map length) ctr_Tsss;
blanchet@51815
   581
blanchet@51808
   582
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   583
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@52355
   584
    val nesting_map_ids'' = map (unfold_thms lthy [id_def] o map_id_of_bnf) nesting_bnfs;
blanchet@52355
   585
    val nested_map_ids'' = map (unfold_thms lthy [id_def] o map_id_of_bnf) nested_bnfs;
blanchet@51810
   586
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51808
   587
blanchet@51816
   588
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   589
blanchet@51832
   590
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@52315
   591
      lthy
blanchet@51808
   592
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   593
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   594
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   595
blanchet@51808
   596
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   597
blanchet@51808
   598
    fun mk_sets_nested bnf =
blanchet@51808
   599
      let
blanchet@51808
   600
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   601
        val lives = lives_of_bnf bnf;
blanchet@51808
   602
        val sets = sets_of_bnf bnf;
blanchet@51808
   603
        fun mk_set U =
traytel@52923
   604
          (case find_index (curry op = U) lives of
blanchet@51808
   605
            ~1 => Term.dummy
blanchet@51808
   606
          | i => nth sets i);
blanchet@51808
   607
      in
blanchet@51808
   608
        (T_name, map mk_set Us)
blanchet@51808
   609
      end;
blanchet@51808
   610
blanchet@51808
   611
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   612
blanchet@51808
   613
    val (induct_thms, induct_thm) =
blanchet@51808
   614
      let
blanchet@51808
   615
        fun mk_set Ts t =
blanchet@51808
   616
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   617
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   618
          end;
blanchet@51808
   619
blanchet@52310
   620
        fun mk_raw_prem_prems _ (x as Free (_, Type _)) (X as TFree _) =
traytel@52923
   621
            [([], (find_index (curry op = X) Xs + 1, x))]
blanchet@52310
   622
          | mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
blanchet@52310
   623
            (case AList.lookup (op =) setss_nested T_name of
blanchet@52310
   624
              NONE => []
blanchet@52310
   625
            | SOME raw_sets0 =>
blanchet@52310
   626
              let
blanchet@52310
   627
                val (Xs_Ts, (Ts, raw_sets)) =
blanchet@52310
   628
                  filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
blanchet@52310
   629
                  |> split_list ||> split_list;
blanchet@52310
   630
                val sets = map (mk_set Ts0) raw_sets;
blanchet@52310
   631
                val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@52310
   632
                val xysets = map (pair x) (ys ~~ sets);
blanchet@52310
   633
                val ppremss = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
blanchet@52310
   634
              in
blanchet@52310
   635
                flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@52310
   636
              end)
blanchet@52310
   637
          | mk_raw_prem_prems _ _ _ = [];
blanchet@51808
   638
blanchet@51808
   639
        fun close_prem_prem xs t =
blanchet@51808
   640
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   641
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   642
blanchet@51808
   643
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   644
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   645
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   646
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   647
blanchet@52310
   648
        fun mk_raw_prem phi ctr ctr_Ts ctrXs_Ts =
blanchet@51808
   649
          let
blanchet@51808
   650
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@52310
   651
            val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
blanchet@51808
   652
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   653
blanchet@51808
   654
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   655
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   656
blanchet@52310
   657
        val raw_premss = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_Tsss;
blanchet@51808
   658
blanchet@51808
   659
        val goal =
blanchet@51808
   660
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
traytel@52923
   661
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry op $) ps us)));
blanchet@51808
   662
blanchet@51808
   663
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   664
blanchet@51814
   665
        val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@51808
   666
blanchet@51808
   667
        val thm =
blanchet@51808
   668
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51808
   669
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
blanchet@51808
   670
              pre_set_defss)
blanchet@51808
   671
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51808
   672
          |> Thm.close_derivation;
blanchet@51808
   673
      in
blanchet@51808
   674
        `(conj_dests nn) thm
blanchet@51808
   675
      end;
blanchet@51808
   676
blanchet@51808
   677
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@52305
   678
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   679
blanchet@52305
   680
    val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@52305
   681
blanchet@52306
   682
    fun mk_iter_thmss (_, x_Tssss, fss, _) iters iter_defs ctor_iter_thms =
blanchet@51808
   683
      let
blanchet@52305
   684
        val fiters = map (lists_bmoc fss) iters;
blanchet@51808
   685
blanchet@51843
   686
        fun mk_goal fss fiter xctr f xs fxs =
blanchet@51808
   687
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@51843
   688
            (mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   689
blanchet@52302
   690
        fun maybe_tick (T, U) u f =
blanchet@52302
   691
          if try (fst o HOLogic.dest_prodT) U = SOME T then
blanchet@52302
   692
            Term.lambda u (HOLogic.mk_prod (u, f $ u))
blanchet@52302
   693
          else
blanchet@52302
   694
            f;
blanchet@51808
   695
blanchet@52368
   696
        fun build_iter (x as Free (_, T)) U =
blanchet@52368
   697
          if T = U then
blanchet@52368
   698
            x
blanchet@52368
   699
          else
blanchet@52303
   700
            build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
blanchet@52368
   701
              (fn kk => fn TU => maybe_tick TU (nth us kk) (nth fiters kk))) (T, U) $ x;
blanchet@52301
   702
blanchet@52868
   703
        val fxsss = map2 (map2 (flat_rec_arg_args oo map2 (map o build_iter))) xsss x_Tssss;
blanchet@51808
   704
blanchet@52306
   705
        val goalss = map5 (map4 o mk_goal fss) fiters xctrss fss xsss fxsss;
blanchet@51808
   706
blanchet@52305
   707
        val tacss =
blanchet@52305
   708
          map2 (map o mk_iter_tac pre_map_defs (nested_map_ids'' @ nesting_map_ids'') iter_defs)
blanchet@52305
   709
            ctor_iter_thms ctr_defss;
blanchet@51808
   710
blanchet@51808
   711
        fun prove goal tac =
blanchet@51808
   712
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   713
          |> Thm.close_derivation;
blanchet@51808
   714
      in
blanchet@52305
   715
        map2 (map2 prove) goalss tacss
blanchet@51808
   716
      end;
blanchet@51808
   717
blanchet@52340
   718
    val fold_thmss = mk_iter_thmss fold_args_types folds fold_defs (map un_fold_of ctor_iter_thmss);
blanchet@52340
   719
    val rec_thmss = mk_iter_thmss rec_args_types recs rec_defs (map co_rec_of ctor_iter_thmss);
blanchet@51808
   720
  in
blanchet@52345
   721
    ((induct_thms, induct_thm, [induct_case_names_attr]),
blanchet@51808
   722
     (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
blanchet@51808
   723
  end;
blanchet@51808
   724
blanchet@52347
   725
fun derive_coinduct_coiters_thms_for_types pre_bnfs (z, cs, cpss,
blanchet@52869
   726
      coiters_args_types as [((pgss, crgsss), _), ((phss, cshsss), _)])
traytel@53106
   727
    dtor_coinduct dtor_ctors dtor_coiter_thmss nesting_bnfs fpTs Cs As kss mss ns ctr_defss
blanchet@52968
   728
    ctr_sugars coiterss coiter_defss export_args lthy =
blanchet@51810
   729
  let
blanchet@52339
   730
    val coiterss' = transpose coiterss;
blanchet@52339
   731
    val coiter_defss' = transpose coiter_defss;
blanchet@52339
   732
blanchet@52339
   733
    val [unfold_defs, corec_defs] = coiter_defss';
blanchet@52338
   734
blanchet@51815
   735
    val nn = length pre_bnfs;
blanchet@51815
   736
blanchet@51810
   737
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   738
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@52355
   739
    val nesting_map_ids'' = map (unfold_thms lthy [id_def] o map_id_of_bnf) nesting_bnfs;
blanchet@51830
   740
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   741
blanchet@51816
   742
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   743
blanchet@51840
   744
    val ctrss = map (map (mk_ctr As) o #ctrs) ctr_sugars;
blanchet@51840
   745
    val discss = map (map (mk_disc_or_sel As) o #discs) ctr_sugars;
blanchet@51840
   746
    val selsss = map (map (map (mk_disc_or_sel As)) o #selss) ctr_sugars;
blanchet@51840
   747
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   748
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   749
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   750
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   751
blanchet@51810
   752
    val (((rs, us'), vs'), names_lthy) =
blanchet@52341
   753
      lthy
blanchet@51810
   754
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   755
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   756
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   757
blanchet@51810
   758
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   759
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   760
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   761
blanchet@51810
   762
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   763
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   764
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   765
blanchet@52345
   766
    val coinduct_thms_pairs =
blanchet@51810
   767
      let
blanchet@51810
   768
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   769
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   770
        val strong_rs =
blanchet@51810
   771
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   772
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   773
blanchet@52347
   774
        (* TODO: generalize (cf. "build_map") *)
blanchet@51810
   775
        fun build_rel rs' T =
traytel@52923
   776
          (case find_index (curry op = T) fpTs of
blanchet@51810
   777
            ~1 =>
blanchet@51856
   778
            if exists_subtype_in fpTs T then
blanchet@51856
   779
              let
blanchet@51856
   780
                val Type (s, Ts) = T
blanchet@51856
   781
                val bnf = the (bnf_of lthy s);
blanchet@51856
   782
                val live = live_of_bnf bnf;
blanchet@51856
   783
                val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
blanchet@51856
   784
                val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
blanchet@51856
   785
              in Term.list_comb (rel, map (build_rel rs') Ts') end
blanchet@51856
   786
            else
blanchet@51856
   787
              HOLogic.eq_const T
blanchet@51810
   788
          | kk => nth rs' kk);
blanchet@51810
   789
blanchet@51856
   790
        fun build_rel_app rs' usel vsel = fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@51810
   791
blanchet@51810
   792
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@51810
   793
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   794
          (if null usels then
blanchet@51810
   795
             []
blanchet@51810
   796
           else
blanchet@51810
   797
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@51810
   798
                Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@51810
   799
blanchet@51810
   800
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@51810
   801
          Library.foldr1 HOLogic.mk_conj
blanchet@51810
   802
            (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@51810
   803
          handle List.Empty => @{term True};
blanchet@51810
   804
blanchet@51810
   805
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@51810
   806
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@51810
   807
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@51810
   808
blanchet@51810
   809
        val concl =
blanchet@51810
   810
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   811
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   812
               uvrs us vs));
blanchet@51810
   813
blanchet@51810
   814
        fun mk_goal rs' =
blanchet@51810
   815
          Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@51810
   816
            concl);
blanchet@51810
   817
blanchet@52345
   818
        val goals = map mk_goal [rs, strong_rs];
blanchet@51810
   819
blanchet@51810
   820
        fun prove dtor_coinduct' goal =
blanchet@51810
   821
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51810
   822
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@51819
   823
              exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   824
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   825
          |> Thm.close_derivation;
blanchet@51810
   826
blanchet@51810
   827
        fun postproc nn thm =
blanchet@51810
   828
          Thm.permute_prems 0 nn
blanchet@51828
   829
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   830
          |> Drule.zero_var_indexes
blanchet@51810
   831
          |> `(conj_dests nn);
traytel@53106
   832
traytel@53106
   833
        val rel_eqs = map rel_eq_of_bnf pre_bnfs;
traytel@53106
   834
        val rel_monos = map rel_mono_of_bnf pre_bnfs;
traytel@53106
   835
        val dtor_coinducts =
traytel@53106
   836
          [dtor_coinduct, mk_strong_coinduct_thm dtor_coinduct rel_eqs rel_monos lthy];
blanchet@51810
   837
      in
blanchet@52345
   838
        map2 (postproc nn oo prove) dtor_coinducts goals
blanchet@51810
   839
      end;
blanchet@51810
   840
blanchet@51810
   841
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   842
      let
blanchet@51810
   843
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   844
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   845
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   846
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   847
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   848
      in
blanchet@51810
   849
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   850
      end;
blanchet@51810
   851
blanchet@51816
   852
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   853
    val coinduct_conclss =
blanchet@51810
   854
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   855
blanchet@51810
   856
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   857
blanchet@52339
   858
    val fcoiterss' as [gunfolds, hcorecs] =
blanchet@52869
   859
      map2 (fn (pfss, _) => map (lists_bmoc pfss)) (map fst coiters_args_types) coiterss';
blanchet@51810
   860
blanchet@51810
   861
    val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@51810
   862
      let
blanchet@51843
   863
        fun mk_goal pfss c cps fcoiter n k ctr m cfs' =
blanchet@51810
   864
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   865
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@51843
   866
               mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   867
blanchet@52347
   868
        fun mk_U maybe_mk_sumT =
blanchet@52347
   869
          typ_subst_nonatomic (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@52347
   870
blanchet@52347
   871
        fun tack z_name (c, u) f =
blanchet@52347
   872
          let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in
blanchet@52347
   873
            Term.lambda z (mk_sum_case (Term.lambda u u, Term.lambda c (f $ c)) $ z)
blanchet@52347
   874
          end;
blanchet@51810
   875
blanchet@52368
   876
        fun build_coiter fcoiters maybe_mk_sumT maybe_tack cqf =
blanchet@52347
   877
          let val T = fastype_of cqf in
blanchet@52347
   878
            if exists_subtype_in Cs T then
blanchet@52368
   879
              let val U = mk_U maybe_mk_sumT T in
blanchet@52968
   880
                build_map lthy (indexify snd fpTs (fn kk => fn _ =>
blanchet@52368
   881
                  maybe_tack (nth cs kk, nth us kk) (nth fcoiters kk))) (T, U) $ cqf
blanchet@52368
   882
              end
blanchet@52347
   883
            else
blanchet@52347
   884
              cqf
blanchet@52347
   885
          end;
blanchet@51810
   886
blanchet@52368
   887
        val crgsss' = map (map (map (build_coiter (un_fold_of fcoiterss') (K I) (K I)))) crgsss;
blanchet@52368
   888
        val cshsss' = map (map (map (build_coiter (co_rec_of fcoiterss') (curry mk_sumT) (tack z))))
blanchet@52351
   889
          cshsss;
blanchet@51810
   890
blanchet@52347
   891
        val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss';
blanchet@52347
   892
        val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@51810
   893
blanchet@51810
   894
        val unfold_tacss =
blanchet@52349
   895
          map3 (map oo mk_coiter_tac unfold_defs nesting_map_ids'')
blanchet@52340
   896
            (map un_fold_of dtor_coiter_thmss) pre_map_defs ctr_defss;
blanchet@51810
   897
        val corec_tacss =
blanchet@52349
   898
          map3 (map oo mk_coiter_tac corec_defs nesting_map_ids'')
blanchet@52340
   899
            (map co_rec_of dtor_coiter_thmss) pre_map_defs ctr_defss;
blanchet@51810
   900
blanchet@51810
   901
        fun prove goal tac =
blanchet@51815
   902
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   903
          |> Thm.close_derivation;
blanchet@51810
   904
blanchet@51810
   905
        val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@52347
   906
        val corec_thmss =
blanchet@52347
   907
          map2 (map2 prove) corec_goalss corec_tacss
blanchet@52347
   908
          |> map (map (unfold_thms lthy @{thms sum_case_if}));
blanchet@52347
   909
traytel@52923
   910
        val unfold_safesss = map2 (map2 (map2 (curry op =))) crgsss' crgsss;
traytel@52923
   911
        val corec_safesss = map2 (map2 (map2 (curry op =))) cshsss' cshsss;
blanchet@52347
   912
blanchet@51810
   913
        val filter_safesss =
blanchet@51810
   914
          map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@52347
   915
            curry (op ~~));
blanchet@51810
   916
blanchet@52347
   917
        val safe_unfold_thmss = filter_safesss unfold_safesss unfold_thmss;
blanchet@52347
   918
        val safe_corec_thmss = filter_safesss corec_safesss corec_thmss;
blanchet@51810
   919
      in
blanchet@51810
   920
        (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@51810
   921
      end;
blanchet@51810
   922
blanchet@51810
   923
    val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@51810
   924
      let
blanchet@51843
   925
        fun mk_goal c cps fcoiter n k disc =
blanchet@51843
   926
          mk_Trueprop_eq (disc $ (fcoiter $ c),
blanchet@51810
   927
            if n = 1 then @{const True}
blanchet@51810
   928
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   929
blanchet@51810
   930
        val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@51810
   931
        val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   932
blanchet@51828
   933
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   934
blanchet@51810
   935
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   936
blanchet@51810
   937
        val unfold_tacss =
blanchet@51843
   938
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@51810
   939
        val corec_tacss =
blanchet@51843
   940
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   941
blanchet@51810
   942
        fun prove goal tac =
blanchet@51810
   943
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@52357
   944
          |> singleton export_args
blanchet@51829
   945
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   946
          |> Thm.close_derivation;
blanchet@51810
   947
blanchet@51810
   948
        fun proves [_] [_] = []
blanchet@51810
   949
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   950
      in
blanchet@51828
   951
        (map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss)
blanchet@51810
   952
      end;
blanchet@51810
   953
blanchet@51810
   954
    val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@51810
   955
blanchet@51843
   956
    fun mk_disc_coiter_thms coiters discIs =
blanchet@51843
   957
      map (op RS) (filter_out (is_triv_discI o snd) (coiters ~~ discIs));
blanchet@51810
   958
blanchet@51843
   959
    val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss;
blanchet@51843
   960
    val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
blanchet@51810
   961
blanchet@51843
   962
    fun mk_sel_coiter_thm coiter_thm sel sel_thm =
blanchet@51810
   963
      let
blanchet@51810
   964
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   965
        val arg_cong' =
blanchet@51810
   966
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   967
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   968
          |> Thm.varifyT_global;
blanchet@51810
   969
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   970
      in
blanchet@51843
   971
        coiter_thm RS arg_cong' RS sel_thm'
blanchet@51810
   972
      end;
blanchet@51810
   973
blanchet@52321
   974
    fun mk_sel_coiter_thms coiter_thmss =
blanchet@52321
   975
      map3 (map3 (map2 o mk_sel_coiter_thm)) coiter_thmss selsss sel_thmsss |> map flat;
blanchet@51810
   976
blanchet@51843
   977
    val sel_unfold_thmss = mk_sel_coiter_thms unfold_thmss;
blanchet@51843
   978
    val sel_corec_thmss = mk_sel_coiter_thms corec_thmss;
blanchet@51810
   979
blanchet@51810
   980
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   981
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   982
    val coinduct_case_concl_attrs =
blanchet@51810
   983
      map2 (fn casex => fn concls =>
blanchet@51810
   984
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   985
        coinduct_cases coinduct_conclss;
blanchet@51810
   986
    val coinduct_case_attrs =
blanchet@51810
   987
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   988
  in
blanchet@52345
   989
    ((coinduct_thms_pairs, coinduct_case_attrs),
blanchet@51810
   990
     (unfold_thmss, corec_thmss, []),
blanchet@51810
   991
     (safe_unfold_thmss, safe_corec_thmss),
blanchet@51810
   992
     (disc_unfold_thmss, disc_corec_thmss, simp_attrs),
blanchet@51810
   993
     (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
blanchet@51810
   994
     (sel_unfold_thmss, sel_corec_thmss, simp_attrs))
blanchet@51810
   995
  end;
blanchet@51810
   996
blanchet@52207
   997
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
blanchet@52969
   998
    (wrap_opts as (no_discs_sels, rep_compat), specs) no_defs_lthy0 =
blanchet@49112
   999
  let
blanchet@49298
  1000
    (* TODO: sanity checks on arguments *)
blanchet@49298
  1001
blanchet@52969
  1002
    val _ = if fp = Greatest_FP andalso no_discs_sels then
blanchet@52969
  1003
        error "Cannot define codatatypes without discriminators and selectors"
blanchet@52207
  1004
      else
blanchet@52207
  1005
        ();
blanchet@49278
  1006
blanchet@49633
  1007
    fun qualify mandatory fp_b_name =
blanchet@49633
  1008
      Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
  1009
blanchet@49367
  1010
    val nn = length specs;
blanchet@49361
  1011
    val fp_bs = map type_binding_of specs;
blanchet@49498
  1012
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
  1013
    val fp_common_name = mk_common_name fp_b_names;
blanchet@52964
  1014
    val map_bs = map2 (fn fp_b_name => qualify false fp_b_name o map_binding_of) fp_b_names specs;
blanchet@52964
  1015
    val rel_bs = map2 (fn fp_b_name => qualify false fp_b_name o rel_binding_of) fp_b_names specs;
blanchet@49298
  1016
blanchet@51758
  1017
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
  1018
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
  1019
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
  1020
      end;
blanchet@49298
  1021
blanchet@51758
  1022
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs;
blanchet@49298
  1023
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@49298
  1024
    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
blanchet@51758
  1025
    val set_bss = map (map fst o type_args_named_constrained_of) specs;
blanchet@49119
  1026
blanchet@52960
  1027
    val _ = has_duplicates (op =) unsorted_As andalso
blanchet@52960
  1028
      error ("Duplicate parameters in " ^ co_prefix fp ^ "datatype specification");
blanchet@52960
  1029
blanchet@52959
  1030
    val bad_args =
blanchet@52959
  1031
      map (Logic.type_map (singleton (Variable.polymorphic no_defs_lthy0))) unsorted_As
blanchet@52959
  1032
      |> filter_out Term.is_TVar;
blanchet@52959
  1033
    val _ = null bad_args orelse
blanchet@52959
  1034
      error ("Locally fixed type argument " ^
blanchet@52959
  1035
        quote (Syntax.string_of_typ no_defs_lthy0 (hd bad_args)) ^ " in " ^ co_prefix fp ^
blanchet@52959
  1036
        "datatype specification");
blanchet@52959
  1037
blanchet@49585
  1038
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
  1039
      no_defs_lthy0
blanchet@49298
  1040
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@49585
  1041
      |> mk_TFrees (length unsorted_As)
blanchet@49585
  1042
      ||>> mk_TFrees nn
blanchet@51858
  1043
      ||>> variant_tfrees fp_b_names;
blanchet@49119
  1044
blanchet@52962
  1045
    (* TODO: Cleaner handling of fake contexts, without "background_theory". *)
blanchet@51768
  1046
blanchet@51769
  1047
    fun add_fake_type spec =
blanchet@52962
  1048
      (*The "qualify" hack below is for the case where the new type shadows an existing global type
blanchet@52962
  1049
        defined in the same theory.*)
blanchet@52962
  1050
      Sign.add_type no_defs_lthy (qualify false "" (type_binding_of spec),
blanchet@51769
  1051
        length (type_args_named_constrained_of spec), mixfix_of spec);
blanchet@51768
  1052
wenzelm@52788
  1053
    val fake_thy = fold add_fake_type specs;
blanchet@49298
  1054
    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
blanchet@49119
  1055
blanchet@49182
  1056
    fun mk_fake_T b =
blanchet@49121
  1057
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49298
  1058
        unsorted_As);
blanchet@49121
  1059
blanchet@49302
  1060
    val fake_Ts = map mk_fake_T fp_bs;
blanchet@49121
  1061
blanchet@49181
  1062
    val mixfixes = map mixfix_of specs;
blanchet@49119
  1063
blanchet@49302
  1064
    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
  1065
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
  1066
blanchet@49121
  1067
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
  1068
blanchet@49336
  1069
    val disc_bindingss = map (map disc_of) ctr_specss;
blanchet@49336
  1070
    val ctr_bindingss =
blanchet@49633
  1071
      map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
blanchet@49121
  1072
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49181
  1073
    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
blanchet@49119
  1074
blanchet@49336
  1075
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
  1076
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49286
  1077
    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
blanchet@49286
  1078
blanchet@49308
  1079
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
  1080
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@49298
  1081
blanchet@49298
  1082
    val _ = (case duplicates (op =) unsorted_As of [] => ()
blanchet@49298
  1083
      | A :: _ => error ("Duplicate type parameter " ^
blanchet@49298
  1084
          quote (Syntax.string_of_typ no_defs_lthy A)));
blanchet@49298
  1085
blanchet@49183
  1086
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@49298
  1087
    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
blanchet@49165
  1088
        [] => ()
blanchet@49342
  1089
      | A' :: _ => error ("Extra type variable on right-hand side: " ^
blanchet@49204
  1090
          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
blanchet@49165
  1091
blanchet@49591
  1092
    fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
  1093
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
  1094
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49591
  1095
      | eq_fpT_check _ _ = false;
blanchet@49146
  1096
blanchet@49204
  1097
    fun freeze_fp (T as Type (s, Us)) =
blanchet@49591
  1098
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@49591
  1099
          ~1 => Type (s, map freeze_fp Us)
blanchet@49591
  1100
        | kk => nth Xs kk)
blanchet@49204
  1101
      | freeze_fp T = T;
blanchet@49121
  1102
blanchet@52310
  1103
    val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@52310
  1104
    val ctrXs_sum_prod_Ts = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
blanchet@49119
  1105
blanchet@49298
  1106
    val fp_eqs =
blanchet@52310
  1107
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_sum_prod_Ts;
blanchet@49121
  1108
blanchet@51839
  1109
    val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0,
traytel@53106
  1110
           xtor_co_iterss = xtor_co_iterss0, xtor_co_induct, dtor_ctors, ctor_dtors, ctor_injects,
blanchet@52344
  1111
           xtor_map_thms, xtor_set_thmss, xtor_rel_thms, xtor_co_iter_thmss, ...}, lthy)) =
blanchet@51868
  1112
      fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As) fp_eqs
blanchet@51868
  1113
        no_defs_lthy0;
blanchet@49585
  1114
blanchet@49585
  1115
    val timer = time (Timer.startRealTimer ());
blanchet@49121
  1116
blanchet@52310
  1117
    val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
blanchet@52310
  1118
    val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
blanchet@49226
  1119
blanchet@49585
  1120
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
  1121
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
  1122
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
  1123
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@51766
  1124
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@49585
  1125
blanchet@49585
  1126
    val live = live_of_bnf any_fp_bnf;
blanchet@52961
  1127
    val _ =
blanchet@52961
  1128
      if live = 0 andalso exists (not o Binding.is_empty) (map_bs @ rel_bs) then
blanchet@52961
  1129
        warning ("Map function and relator names ignored")
blanchet@52961
  1130
      else
blanchet@52961
  1131
        ();
blanchet@49585
  1132
blanchet@49585
  1133
    val Bs =
blanchet@49585
  1134
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
  1135
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
  1136
blanchet@49585
  1137
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
  1138
blanchet@49501
  1139
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
  1140
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
  1141
blanchet@49501
  1142
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
  1143
blanchet@51780
  1144
    fun massage_simple_notes base =
blanchet@51780
  1145
      filter_out (null o #2)
blanchet@51780
  1146
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
  1147
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
  1148
blanchet@51780
  1149
    val massage_multi_notes =
blanchet@51780
  1150
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
  1151
        if forall null thmss then
blanchet@51780
  1152
          []
blanchet@51780
  1153
        else
blanchet@51780
  1154
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@52311
  1155
              ((qualify true fp_b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
blanchet@52311
  1156
            fp_b_names fpTs thmss);
blanchet@51780
  1157
blanchet@52310
  1158
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctrXs_Tsss;
blanchet@49203
  1159
    val ns = map length ctr_Tsss;
blanchet@49212
  1160
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
  1161
    val mss = map (map length) ctr_Tsss;
blanchet@49203
  1162
blanchet@52367
  1163
    val ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy') =
blanchet@52334
  1164
      mk_co_iters_prelims fp fpTs Cs ns mss xtor_co_iterss0 lthy;
blanchet@49210
  1165
blanchet@52968
  1166
    fun define_ctrs_dtrs_for_type (((((((((((((((((((((((fp_bnf, fp_b), fpT), ctor), dtor),
blanchet@52345
  1167
            xtor_co_iters), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@52345
  1168
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@52345
  1169
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
  1170
      let
blanchet@49498
  1171
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1172
blanchet@49501
  1173
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
  1174
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
  1175
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49119
  1176
blanchet@52968
  1177
        val ((((w, xss), yss), u'), names_lthy) =
blanchet@49204
  1178
          no_defs_lthy
blanchet@49501
  1179
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49370
  1180
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1181
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1182
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1183
blanchet@49498
  1184
        val u = Free (u', fpT);
blanchet@49121
  1185
blanchet@49585
  1186
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
  1187
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
  1188
blanchet@49129
  1189
        val ctr_rhss =
blanchet@49585
  1190
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
  1191
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
  1192
blanchet@52968
  1193
        val ((raw_ctrs, raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1194
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
  1195
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@52968
  1196
            ctr_bindings ctr_mixfixes ctr_rhss
blanchet@49121
  1197
          ||> `Local_Theory.restore;
blanchet@49121
  1198
blanchet@49121
  1199
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1200
blanchet@49121
  1201
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1202
        val ctr_defs' =
blanchet@49585
  1203
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1204
blanchet@49203
  1205
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1206
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1207
blanchet@51897
  1208
        fun wrap_ctrs lthy =
blanchet@49123
  1209
          let
traytel@50170
  1210
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1211
              let
blanchet@49585
  1212
                val ctor_iff_dtor_thm =
blanchet@49585
  1213
                  let
blanchet@49585
  1214
                    val goal =
blanchet@49585
  1215
                      fold_rev Logic.all [w, u]
blanchet@49585
  1216
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1217
                  in
wenzelm@51551
  1218
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
  1219
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
  1220
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
  1221
                    |> Thm.close_derivation
blanchet@49585
  1222
                    |> Morphism.thm phi
blanchet@49585
  1223
                  end;
blanchet@49585
  1224
blanchet@49585
  1225
                val sumEN_thm' =
traytel@52659
  1226
                  unfold_thms lthy @{thms unit_all_eq1}
blanchet@49585
  1227
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
  1228
                       (mk_sumEN_balanced n))
blanchet@49585
  1229
                  |> Morphism.thm phi;
blanchet@49135
  1230
              in
blanchet@49585
  1231
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1232
              end;
blanchet@49135
  1233
blanchet@49585
  1234
            val inject_tacss =
blanchet@49585
  1235
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
  1236
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
  1237
blanchet@49585
  1238
            val half_distinct_tacss =
blanchet@49585
  1239
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
  1240
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1241
blanchet@52968
  1242
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss;
blanchet@49585
  1243
blanchet@49585
  1244
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
  1245
          in
blanchet@52968
  1246
            wrap_free_constructors tacss (((wrap_opts, ctrs0), standard_binding), (disc_bindings,
blanchet@51781
  1247
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
  1248
          end;
blanchet@49121
  1249
blanchet@51840
  1250
        fun derive_maps_sets_rels (ctr_sugar, lthy) =
blanchet@51835
  1251
          if live = 0 then
blanchet@51840
  1252
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1253
          else
blanchet@51835
  1254
            let
blanchet@51835
  1255
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1256
              val nones = replicate live NONE;
blanchet@49585
  1257
blanchet@51835
  1258
              val ctor_cong =
blanchet@52207
  1259
                if fp = Least_FP then
blanchet@51835
  1260
                  Drule.dummy_thm
blanchet@51835
  1261
                else
blanchet@51835
  1262
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1263
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1264
                  end;
blanchet@49585
  1265
blanchet@51835
  1266
              fun mk_cIn ify =
blanchet@52207
  1267
                certify lthy o (fp = Greatest_FP ? curry (op $) (map_types ify ctor)) oo
blanchet@51835
  1268
                mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
  1269
blanchet@51835
  1270
              val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@51835
  1271
              val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
  1272
blanchet@51835
  1273
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1274
                fold_thms lthy [ctr_def']
blanchet@51835
  1275
                  (unfold_thms lthy (pre_map_def ::
blanchet@52207
  1276
                       (if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@51835
  1277
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@52207
  1278
                        (if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1279
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1280
blanchet@51835
  1281
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1282
                fold_thms lthy [ctr_def']
blanchet@51835
  1283
                  (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@52207
  1284
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@51835
  1285
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1286
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1287
blanchet@51835
  1288
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1289
blanchet@51835
  1290
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1291
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@51835
  1292
blanchet@51835
  1293
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1294
blanchet@51835
  1295
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1296
                fold_thms lthy ctr_defs'
blanchet@51835
  1297
                   (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@52207
  1298
                        (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@51835
  1299
                      (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1300
                |> postproc
blanchet@51835
  1301
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1302
blanchet@51835
  1303
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1304
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1305
blanchet@51835
  1306
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1307
blanchet@51835
  1308
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1309
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1310
                  cxIn cyIn;
blanchet@49121
  1311
blanchet@51835
  1312
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1313
                flip_rels lthy live thm
blanchet@51835
  1314
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1315
blanchet@51835
  1316
              val half_rel_distinct_thmss =
blanchet@51835
  1317
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1318
              val other_half_rel_distinct_thmss =
blanchet@51835
  1319
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1320
              val (rel_distinct_thms, _) =
blanchet@51835
  1321
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1322
blanchet@51835
  1323
              val notes =
blanchet@51835
  1324
                [(mapN, map_thms, code_simp_attrs),
blanchet@51835
  1325
                 (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@51835
  1326
                 (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@51835
  1327
                 (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51835
  1328
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1329
            in
blanchet@51840
  1330
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@51835
  1331
               lthy |> Local_Theory.notes notes |> snd)
blanchet@51835
  1332
            end;
blanchet@49585
  1333
blanchet@51897
  1334
        fun mk_binding suf = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49287
  1335
blanchet@51883
  1336
        fun massage_res (((maps_sets_rels, ctr_sugar), co_iter_res), lthy) =
blanchet@51883
  1337
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_iter_res), lthy);
blanchet@49119
  1338
      in
blanchet@51897
  1339
        (wrap_ctrs
blanchet@51835
  1340
         #> derive_maps_sets_rels
blanchet@52313
  1341
         ##>>
blanchet@52329
  1342
           (if fp = Least_FP then define_iters [foldN, recN] (the iters_args_types)
blanchet@52329
  1343
            else define_coiters [unfoldN, corecN] (the coiters_args_types))
blanchet@52328
  1344
             mk_binding fpTs Cs xtor_co_iters
blanchet@51835
  1345
         #> massage_res, lthy')
blanchet@49119
  1346
      end;
blanchet@49167
  1347
blanchet@51835
  1348
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1349
      fold_map I wrap_types_etcs lthy
blanchet@52342
  1350
      |>> apsnd split_list o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@52342
  1351
        o split_list;
blanchet@49226
  1352
blanchet@49479
  1353
    val mk_simp_thmss =
blanchet@51857
  1354
      map7 (fn {injects, distincts, case_thms, ...} => fn un_folds => fn co_recs =>
blanchet@51835
  1355
        fn mapsx => fn rel_injects => fn rel_distincts => fn setss =>
blanchet@51857
  1356
          injects @ distincts @ case_thms @ co_recs @ un_folds @ mapsx @ rel_injects
blanchet@51835
  1357
          @ rel_distincts @ flat setss);
blanchet@49479
  1358
blanchet@52329
  1359
    fun derive_and_note_induct_iters_thms_for_types
blanchet@51840
  1360
        ((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1361
          (iterss, iter_defss)), lthy) =
blanchet@49202
  1362
      let
blanchet@52345
  1363
        val ((induct_thms, induct_thm, induct_attrs), (fold_thmss, fold_attrs),
blanchet@51808
  1364
             (rec_thmss, rec_attrs)) =
traytel@53106
  1365
          derive_induct_iters_thms_for_types pre_bnfs (the iters_args_types) xtor_co_induct
blanchet@52346
  1366
            xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss
blanchet@52346
  1367
            iter_defss lthy;
blanchet@49201
  1368
blanchet@51830
  1369
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1370
blanchet@51835
  1371
        val simp_thmss =
blanchet@51843
  1372
          mk_simp_thmss ctr_sugars fold_thmss rec_thmss mapsx rel_injects rel_distincts setss;
blanchet@49438
  1373
blanchet@49337
  1374
        val common_notes =
blanchet@51808
  1375
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1376
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1377
blanchet@49226
  1378
        val notes =
blanchet@51808
  1379
          [(foldN, fold_thmss, K fold_attrs),
blanchet@51810
  1380
           (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@51808
  1381
           (recN, rec_thmss, K rec_attrs),
blanchet@49585
  1382
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1383
          |> massage_multi_notes;
blanchet@49202
  1384
      in
blanchet@51824
  1385
        lthy
blanchet@51824
  1386
        |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@52356
  1387
        |> register_fp_sugars Least_FP pre_bnfs nested_bnfs fp_res ctr_defss ctr_sugars iterss
blanchet@52356
  1388
          [induct_thm] (transpose [fold_thmss, rec_thmss])
blanchet@49202
  1389
      end;
blanchet@49202
  1390
blanchet@52329
  1391
    fun derive_and_note_coinduct_coiters_thms_for_types
blanchet@51859
  1392
        ((((mapsx, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1393
          (coiterss, coiter_defss)), lthy) =
blanchet@49212
  1394
      let
blanchet@52345
  1395
        val (([(coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)],
blanchet@51810
  1396
              coinduct_attrs),
blanchet@51843
  1397
             (unfold_thmss, corec_thmss, coiter_attrs),
blanchet@51810
  1398
             (safe_unfold_thmss, safe_corec_thmss),
blanchet@51843
  1399
             (disc_unfold_thmss, disc_corec_thmss, disc_coiter_attrs),
blanchet@51843
  1400
             (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_coiter_iff_attrs),
blanchet@51843
  1401
             (sel_unfold_thmss, sel_corec_thmss, sel_coiter_attrs)) =
traytel@53106
  1402
          derive_coinduct_coiters_thms_for_types pre_bnfs (the coiters_args_types) xtor_co_induct
blanchet@52968
  1403
            dtor_ctors xtor_co_iter_thmss nesting_bnfs fpTs Cs As kss mss ns ctr_defss ctr_sugars
blanchet@52968
  1404
            coiterss coiter_defss (Proof_Context.export lthy' no_defs_lthy) lthy;
blanchet@49212
  1405
blanchet@51830
  1406
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1407
blanchet@51843
  1408
        fun flat_coiter_thms coiters disc_coiters sel_coiters =
blanchet@51843
  1409
          coiters @ disc_coiters @ sel_coiters;
blanchet@49479
  1410
blanchet@49479
  1411
        val simp_thmss =
blanchet@51840
  1412
          mk_simp_thmss ctr_sugars
blanchet@51843
  1413
            (map3 flat_coiter_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss)
blanchet@51843
  1414
            (map3 flat_coiter_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@51835
  1415
            mapsx rel_injects rel_distincts setss;
blanchet@49479
  1416
blanchet@49479
  1417
        val anonymous_notes =
blanchet@49504
  1418
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1419
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1420
blanchet@49342
  1421
        val common_notes =
blanchet@49591
  1422
          (if nn > 1 then
blanchet@51810
  1423
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1424
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1425
           else
blanchet@49591
  1426
             [])
blanchet@51780
  1427
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1428
blanchet@49212
  1429
        val notes =
blanchet@51780
  1430
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1431
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@51843
  1432
           (corecN, corec_thmss, K coiter_attrs),
blanchet@51843
  1433
           (disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
blanchet@51843
  1434
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1435
           (disc_unfoldN, disc_unfold_thmss, K disc_coiter_attrs),
blanchet@51843
  1436
           (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1437
           (sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
blanchet@51843
  1438
           (sel_unfoldN, sel_unfold_thmss, K sel_coiter_attrs),
blanchet@51780
  1439
           (simpsN, simp_thmss, K []),
blanchet@51810
  1440
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
blanchet@51843
  1441
           (unfoldN, unfold_thmss, K coiter_attrs)]
blanchet@51780
  1442
          |> massage_multi_notes;
blanchet@49212
  1443
      in
blanchet@51824
  1444
        lthy
blanchet@51824
  1445
        |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@52356
  1446
        |> register_fp_sugars Greatest_FP pre_bnfs nested_bnfs fp_res ctr_defss ctr_sugars coiterss
blanchet@52343
  1447
          [coinduct_thm, strong_coinduct_thm] (transpose [unfold_thmss, corec_thmss])
blanchet@49212
  1448
      end;
blanchet@49212
  1449
blanchet@52367
  1450
    val lthy'' = lthy'
blanchet@52968
  1451
      |> fold_map define_ctrs_dtrs_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ ctors ~~ dtors ~~
blanchet@52330
  1452
        xtor_co_iterss ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@52314
  1453
        pre_set_defss ~~ pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~
blanchet@52314
  1454
        kss ~~ mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~
blanchet@52314
  1455
        sel_bindingsss ~~ raw_sel_defaultsss)
blanchet@51835
  1456
      |> wrap_types_etc
blanchet@53037
  1457
      |> fp_case fp derive_and_note_induct_iters_thms_for_types
blanchet@53037
  1458
           derive_and_note_coinduct_coiters_thms_for_types;
blanchet@49167
  1459
blanchet@49167
  1460
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@52899
  1461
      co_prefix fp ^ "datatype"));
blanchet@49112
  1462
  in
blanchet@52367
  1463
    timer; lthy''
blanchet@49112
  1464
  end;
blanchet@49112
  1465
blanchet@51863
  1466
val co_datatypes = define_co_datatypes (K I) (K I) (K I);
blanchet@49297
  1467
blanchet@51863
  1468
val co_datatype_cmd =
blanchet@51863
  1469
  define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1470
blanchet@49112
  1471
val parse_ctr_arg =
blanchet@49329
  1472
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1473
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1474
blanchet@49286
  1475
val parse_defaults =
blanchet@49286
  1476
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1477
blanchet@51758
  1478
val parse_type_arg_constrained =
blanchet@51790
  1479
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1480
blanchet@51790
  1481
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1482
blanchet@51758
  1483
val parse_type_args_named_constrained =
blanchet@51758
  1484
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1485
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1486
  Scan.succeed [];
blanchet@51756
  1487
blanchet@51790
  1488
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1489
blanchet@51767
  1490
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1491
blanchet@51767
  1492
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51833
  1493
   that we don't want them to be highlighted everywhere. *)
blanchet@51767
  1494
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1495
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1496
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1497
blanchet@51767
  1498
val parse_map_rel_bindings =
blanchet@51767
  1499
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1500
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1501
  Scan.succeed no_map_rel;
blanchet@51767
  1502
blanchet@51767
  1503
val parse_ctr_spec =
blanchet@51790
  1504
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1505
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1506
blanchet@51767
  1507
val parse_spec =
blanchet@51790
  1508
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1509
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1510
blanchet@52823
  1511
val parse_co_datatype = parse_wrap_free_constructors_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1512
blanchet@52207
  1513
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
blanchet@49112
  1514
blanchet@49112
  1515
end;