src/HOL/Tools/BNF/bnf_fp_def_sugar.ML
author blanchet
Wed Apr 23 10:23:27 2014 +0200 (2014-04-23)
changeset 56650 1f9ab71d43a5
parent 56648 2ffa440b3074
child 56651 fc105315822a
permissions -rw-r--r--
no need to make 'size' generation an interpretation -- overkill
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(*  Title:      HOL/Tools/BNF/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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  val fp_sugar_of: Proof.context -> string -> BNF_FP_Util.fp_sugar option
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  val fp_sugars_of: Proof.context -> BNF_FP_Util.fp_sugar list
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  val fp_sugar_interpretation: (BNF_FP_Util.fp_sugar list -> theory -> theory) -> theory -> theory
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  val register_fp_sugars: BNF_FP_Util.fp_sugar list -> local_theory -> local_theory
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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 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 nesty_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
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  type lfp_sugar_thms =
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    (thm list * thm * Args.src list) * (thm list list * Args.src list)
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  val morph_lfp_sugar_thms: morphism -> lfp_sugar_thms -> lfp_sugar_thms
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  val transfer_lfp_sugar_thms: Proof.context -> lfp_sugar_thms -> lfp_sugar_thms
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  type gfp_sugar_thms =
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    ((thm list * thm) list * Args.src list)
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    * (thm list list * Args.src list)
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    * (thm list list * Args.src list)
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    * (thm list list * Args.src list)
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    * (thm list list list * Args.src list)
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  val morph_gfp_sugar_thms: morphism -> gfp_sugar_thms -> gfp_sugar_thms
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  val transfer_gfp_sugar_thms: Proof.context -> gfp_sugar_thms -> gfp_sugar_thms
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  val mk_co_recs_prelims: BNF_Util.fp_kind -> typ list list list -> typ list -> typ list ->
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     typ list -> typ list -> int list -> int list list -> term list -> Proof.context ->
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     (term list
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      * (typ list list * typ list list list list * term list list * term 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)) option)
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     * Proof.context
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  val repair_nullary_single_ctr: typ list list -> typ list list
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  val mk_corec_p_pred_types: typ list -> int list -> typ list list
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  val mk_corec_fun_arg_types: typ list list list -> typ list -> typ list -> typ list -> int list ->
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    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_rec:
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    typ list list * typ list list list list * term list list * term list list list list ->
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    (string -> binding) -> typ list -> typ list -> term list -> term -> Proof.context ->
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    (term * thm) * Proof.context
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  val define_corec: 'a * term list * term list list
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      * ((term list list * term list list list) * typ list) -> (string -> binding) -> 'b list ->
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    typ list -> term list -> term -> local_theory -> (term * thm) * local_theory
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  val derive_induct_recs_thms_for_types: BNF_Def.bnf list ->
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     ('a * typ list list list list * term list list * 'b) option -> thm -> thm list ->
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     BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list -> typ list ->
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     typ list list list -> thm list -> thm list -> thm list -> term list list -> thm list list ->
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     term list -> thm list -> Proof.context -> lfp_sugar_thms
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  val derive_coinduct_corecs_thms_for_types: BNF_Def.bnf list ->
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    string * term list * term list list * ((term list list * term list list list) * typ list) ->
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    thm -> thm list -> thm list -> thm list -> BNF_Def.bnf list -> typ list -> typ list ->
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    typ list -> typ list list list -> int list list -> int list list -> int list -> thm list ->
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    thm list -> (thm -> thm) -> thm list list -> Ctr_Sugar.ctr_sugar list -> term list ->
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    thm list -> (thm list -> thm list) -> Proof.context -> gfp_sugar_thms
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  type co_datatype_spec =
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    ((((binding option * (typ * sort)) list * binding) * (binding * binding)) * mixfix)
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    * ((binding, binding * typ, term) Ctr_Sugar.ctr_spec * mixfix) list
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  val co_datatypes: BNF_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 -> BNF_Comp.absT_info list -> local_theory ->
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      BNF_FP_Util.fp_result * local_theory) ->
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    (bool * bool) * co_datatype_spec list ->
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    local_theory -> local_theory
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  val parse_co_datatype_cmd: BNF_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 -> BNF_Comp.absT_info list -> local_theory ->
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      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 Ctr_Sugar
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open BNF_FP_Rec_Sugar_Util
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open BNF_Util
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open BNF_Comp
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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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open BNF_LFP_Size
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val EqN = "Eq_";
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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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  fun merge data : T = Symtab.merge (K true) data;
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);
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fun fp_sugar_of ctxt =
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  Symtab.lookup (Data.get (Context.Proof ctxt))
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  #> Option.map (transfer_fp_sugar ctxt);
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fun fp_sugars_of ctxt =
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  Symtab.fold (cons o transfer_fp_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
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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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structure FP_Sugar_Interpretation = Interpretation
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(
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  type T = fp_sugar list;
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  val eq: T * T -> bool = op = o pairself (map #T);
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);
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fun with_repaired_path f (fp_sugars as ({T = Type (s, _), ...} : fp_sugar) :: _) thy =
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  thy
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  |> Sign.root_path (* FIXME *)
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  |> Sign.add_path (Long_Name.qualifier s)
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  |> f fp_sugars
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  |> Sign.restore_naming thy;
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val fp_sugar_interpretation = FP_Sugar_Interpretation.interpretation o with_repaired_path;
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fun register_fp_sugars (fp_sugars as {fp, ...} :: _) =
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  fold (fn fp_sugar as {T = Type (s, _), ...} =>
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      Local_Theory.declaration {syntax = false, pervasive = true}
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        (fn phi => Data.map (Symtab.update (s, morph_fp_sugar phi fp_sugar))))
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    fp_sugars
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  #> Local_Theory.background_theory (generate_lfp_size fp_sugars)
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  #> Local_Theory.background_theory (FP_Sugar_Interpretation.data fp_sugars);
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fun register_as_fp_sugars Ts BTs Xs fp pre_bnfs absT_infos nested_bnfs nesting_bnfs fp_res
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    ctrXs_Tsss ctr_defss ctr_sugars co_recs co_rec_defs mapss common_co_inducts co_inductss
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    co_rec_thmss disc_co_recss sel_co_recsss rel_injectss rel_distinctss =
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  let
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    val fp_sugars =
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      map_index (fn (kk, T) =>
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        {T = T, BT = nth BTs kk, X = nth Xs kk, fp = fp, fp_res = fp_res, fp_res_index = kk,
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         pre_bnf = nth pre_bnfs kk, absT_info = nth absT_infos kk, nested_bnfs = nested_bnfs,
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         nesting_bnfs = nesting_bnfs, ctrXs_Tss = nth ctrXs_Tsss kk, ctr_defs = nth ctr_defss kk,
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         ctr_sugar = nth ctr_sugars kk, co_rec = nth co_recs kk, co_rec_def = nth co_rec_defs kk,
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         maps = nth mapss kk, common_co_inducts = common_co_inducts,
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         co_inducts = nth co_inductss kk, co_rec_thms = nth co_rec_thmss kk,
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         disc_co_recs = nth disc_co_recss kk, sel_co_recss = nth sel_co_recsss kk,
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         rel_injects = nth rel_injectss kk, rel_distincts = nth rel_distinctss kk}) Ts
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  in
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    register_fp_sugars fp_sugars
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  end;
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(* This function could produce (fairly harmless) clashes in contrived examples (e.g., "x.A",
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   "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 fundefcong_attrs = @{attributes [fundef_cong]};
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val nitpicksimp_attrs = @{attributes [nitpick_simp]};
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val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
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val simp_attrs = @{attributes [simp]};
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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
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fun flat_corec_predss_getterss qss gss = maps (op @) (qss ~~ gss);
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fun flat_corec_preds_predsss_gettersss [] [qss] [gss] = flat_corec_predss_getterss qss gss
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  | flat_corec_preds_predsss_gettersss (p :: ps) (qss :: qsss) (gss :: gsss) =
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    p :: flat_corec_predss_getterss qss gss @ flat_corec_preds_predsss_gettersss ps qsss gsss;
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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_xtor_co_recs 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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fun unzip_recT (Type (@{type_name prod}, _)) T = [T]
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  | unzip_recT _ (Type (@{type_name prod}, Ts)) = Ts
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  | unzip_recT _ T = [T];
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fun unzip_corecT (Type (@{type_name sum}, _)) T = [T]
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  | unzip_corecT _ (Type (@{type_name sum}, Ts)) = Ts
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  | unzip_corecT _ T = [T];
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fun liveness_of_fp_bnf n bnf =
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  (case T_of_bnf bnf of
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    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
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  | _ => replicate n false);
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fun cannot_merge_types fp =
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  error ("Mutually " ^ co_prefix fp ^ "recursive types must have the same type parameters");
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fun merge_type_arg fp T T' = if T = T' then T else cannot_merge_types fp;
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fun merge_type_args fp (As, As') =
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  if length As = length As' then map2 (merge_type_arg fp) As As' else cannot_merge_types fp;
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fun reassoc_conjs thm =
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  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
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  handle THM _ => thm;
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type co_datatype_spec =
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  ((((binding option * (typ * sort)) list * binding) * (binding * binding)) * mixfix)
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  * ((binding, binding * typ, term) ctr_spec * mixfix) list;
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fun type_args_named_constrained_of_spec ((((ncAs, _), _), _), _) = ncAs;
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fun type_binding_of_spec ((((_, b), _), _), _) = b;
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fun map_binding_of_spec (((_, (b, _)), _), _) = b;
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fun rel_binding_of_spec (((_, (_, b)), _), _) = b;
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fun mixfix_of_spec ((_, mx), _) = mx;
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fun mixfixed_ctr_specs_of_spec (_, mx_ctr_specs) = mx_ctr_specs;
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fun add_nesty_bnf_names Us =
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  let
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    fun add (Type (s, Ts)) ss =
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        let val (needs, ss') = fold_map add Ts ss in
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          if exists I needs then (true, insert (op =) s ss') else (false, ss')
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        end
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      | add T ss = (member (op =) Us T, ss);
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  in snd oo add end;
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fun nesty_bnfs ctxt ctr_Tsss Us =
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  map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
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fun indexify proj xs f p = f (find_index (curry (op =) (proj p)) xs) p;
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type lfp_sugar_thms =
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  (thm list * thm * Args.src list) * (thm list list * Args.src list);
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fun morph_lfp_sugar_thms phi ((inducts, induct, induct_attrs), (recss, rec_attrs)) =
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  ((map (Morphism.thm phi) inducts, Morphism.thm phi induct, induct_attrs),
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   (map (map (Morphism.thm phi)) recss, rec_attrs))
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  : lfp_sugar_thms;
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val transfer_lfp_sugar_thms =
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  morph_lfp_sugar_thms o Morphism.transfer_morphism o Proof_Context.theory_of;
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type gfp_sugar_thms =
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  ((thm list * thm) list * Args.src list)
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   284
  * (thm list list * Args.src list)
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   285
  * (thm list list * Args.src list)
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   286
  * (thm list list * Args.src list)
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   287
  * (thm list list list * Args.src list);
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   288
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   289
fun morph_gfp_sugar_thms phi ((coinducts_pairs, coinduct_attrs),
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   290
    (corecss, corec_attrs), (disc_corecss, disc_corec_attrs),
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   291
    (disc_corec_iffss, disc_corec_iff_attrs), (sel_corecsss, sel_corec_attrs)) =
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   292
  ((map (apfst (map (Morphism.thm phi)) o apsnd (Morphism.thm phi)) coinducts_pairs,
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   293
    coinduct_attrs),
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   294
   (map (map (Morphism.thm phi)) corecss, corec_attrs),
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   295
   (map (map (Morphism.thm phi)) disc_corecss, disc_corec_attrs),
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   296
   (map (map (Morphism.thm phi)) disc_corec_iffss, disc_corec_iff_attrs),
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   297
   (map (map (map (Morphism.thm phi))) sel_corecsss, sel_corec_attrs)) : gfp_sugar_thms;
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   298
blanchet@54256
   299
val transfer_gfp_sugar_thms =
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   300
  morph_gfp_sugar_thms o Morphism.transfer_morphism o Proof_Context.theory_of;
blanchet@54256
   301
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   302
fun mk_recs_args_types ctr_Tsss Cs absTs repTs ns mss ctor_rec_fun_Ts lthy =
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   303
  let
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   304
    val Css = map2 replicate ns Cs;
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   305
    val x_Tssss =
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   306
      map6 (fn absT => fn repT => fn n => fn ms => fn ctr_Tss => fn ctor_rec_fun_T =>
traytel@55803
   307
          map2 (map2 unzip_recT)
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   308
            ctr_Tss (dest_absumprodT absT repT n ms (domain_type ctor_rec_fun_T)))
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   309
        absTs repTs ns mss ctr_Tsss ctor_rec_fun_Ts;
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   310
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   311
    val x_Tsss' = map (map flat_rec_arg_args) x_Tssss;
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   312
    val f_Tss = map2 (map2 (curry (op --->))) x_Tsss' Css;
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   313
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   314
    val ((fss, xssss), lthy) =
blanchet@52214
   315
      lthy
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   316
      |> mk_Freess "f" f_Tss
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   317
      ||>> mk_Freessss "x" x_Tssss;
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   318
  in
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   319
    ((f_Tss, x_Tssss, fss, xssss), lthy)
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   320
  end;
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   321
blanchet@55867
   322
(*avoid "'a itself" arguments in corecursors*)
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   323
fun repair_nullary_single_ctr [[]] = [[HOLogic.unitT]]
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   324
  | repair_nullary_single_ctr Tss = Tss;
blanchet@55772
   325
blanchet@55867
   326
fun mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss fun_Ts =
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   327
  let
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   328
    val ctr_Tsss' = map repair_nullary_single_ctr ctr_Tsss;
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   329
    val g_absTs = map range_type fun_Ts;
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   330
    val g_Tsss = map repair_nullary_single_ctr (map5 dest_absumprodT absTs repTs ns mss g_absTs);
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   331
    val g_Tssss = map3 (fn C => map2 (map2 (map (curry (op -->) C) oo unzip_corecT)))
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   332
      Cs ctr_Tsss' g_Tsss;
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   333
    val q_Tssss = map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) g_Tssss;
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   334
  in
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   335
    (q_Tssss, g_Tsss, g_Tssss, g_absTs)
blanchet@52870
   336
  end;
blanchet@51829
   337
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   338
fun mk_corec_p_pred_types Cs ns = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@52898
   339
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   340
fun mk_corec_fun_arg_types ctr_Tsss Cs absTs repTs ns mss dtor_corec =
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   341
  (mk_corec_p_pred_types Cs ns,
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   342
   mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss
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   343
     (binder_fun_types (fastype_of dtor_corec)));
blanchet@51829
   344
blanchet@55867
   345
fun mk_corecs_args_types ctr_Tsss Cs absTs repTs ns mss dtor_corec_fun_Ts lthy =
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   346
  let
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   347
    val p_Tss = mk_corec_p_pred_types Cs ns;
blanchet@51829
   348
blanchet@55869
   349
    val (q_Tssss, g_Tsss, g_Tssss, corec_types) =
blanchet@55867
   350
      mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss dtor_corec_fun_Ts;
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   351
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   352
    val (((((Free (x, _), cs), pss), qssss), gssss), lthy) =
blanchet@51829
   353
      lthy
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   354
      |> yield_singleton (mk_Frees "x") dummyT
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   355
      ||>> mk_Frees "a" Cs
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   356
      ||>> mk_Freess "p" p_Tss
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   357
      ||>> mk_Freessss "q" q_Tssss
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   358
      ||>> mk_Freessss "g" g_Tssss;
blanchet@51831
   359
blanchet@51831
   360
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   361
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   362
    fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@52347
   363
blanchet@55871
   364
    fun build_dtor_corec_arg _ [] [cg] = cg
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   365
      | build_dtor_corec_arg T [cq] [cg, cg'] =
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   366
        mk_If cq (build_sum_inj Inl_const (fastype_of cg, T) $ cg)
blanchet@55871
   367
          (build_sum_inj Inr_const (fastype_of cg', T) $ cg');
blanchet@52347
   368
blanchet@55869
   369
    val pgss = map3 flat_corec_preds_predsss_gettersss pss qssss gssss;
blanchet@55869
   370
    val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@55869
   371
    val cgssss = map2 (map o map o map o rapp) cs gssss;
blanchet@55869
   372
    val cqgsss = map3 (map3 (map3 build_dtor_corec_arg)) g_Tsss cqssss cgssss;
blanchet@51831
   373
  in
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   374
    ((x, cs, cpss, ((pgss, cqgsss), corec_types)), lthy)
blanchet@51831
   375
  end;
blanchet@51829
   376
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   377
fun mk_co_recs_prelims fp ctr_Tsss fpTs Cs absTs repTs ns mss xtor_co_recs0 lthy =
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   378
  let
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   379
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   380
blanchet@55867
   381
    val (xtor_co_rec_fun_Ts, xtor_co_recs) =
blanchet@55867
   382
      mk_xtor_co_recs thy fp fpTs Cs xtor_co_recs0 |> `(binder_fun_types o fastype_of o hd);
blanchet@51903
   383
blanchet@55867
   384
    val ((recs_args_types, corecs_args_types), lthy') =
blanchet@52207
   385
      if fp = Least_FP then
blanchet@56641
   386
        mk_recs_args_types ctr_Tsss Cs absTs repTs ns mss xtor_co_rec_fun_Ts lthy
blanchet@56641
   387
        |>> (rpair NONE o SOME)
blanchet@51903
   388
      else
blanchet@55867
   389
        mk_corecs_args_types ctr_Tsss Cs absTs repTs ns mss xtor_co_rec_fun_Ts lthy
traytel@55803
   390
        |>> (pair NONE o SOME);
blanchet@51903
   391
  in
blanchet@55867
   392
    ((xtor_co_recs, recs_args_types, corecs_args_types), lthy')
blanchet@51903
   393
  end;
blanchet@51903
   394
blanchet@55869
   395
fun mk_preds_getterss_join c cps absT abs cqgss =
traytel@55803
   396
  let
blanchet@55869
   397
    val n = length cqgss;
blanchet@55869
   398
    val ts = map2 (mk_absumprod absT abs n) (1 upto n) cqgss;
traytel@55803
   399
  in
traytel@55803
   400
    Term.lambda c (mk_IfN absT cps ts)
blanchet@51900
   401
  end;
blanchet@51886
   402
blanchet@55867
   403
fun define_co_rec fp fpT Cs b rhs lthy0 =
blanchet@51897
   404
  let
blanchet@52170
   405
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   406
traytel@53569
   407
    val maybe_conceal_def_binding = Thm.def_binding
traytel@53569
   408
      #> Config.get lthy0 bnf_note_all = false ? Binding.conceal;
traytel@53569
   409
blanchet@55864
   410
    val ((cst, (_, def)), (lthy', lthy)) = lthy0
blanchet@55864
   411
      |> Local_Theory.define ((b, NoSyn), ((maybe_conceal_def_binding b, []), rhs))
blanchet@52327
   412
      ||> `Local_Theory.restore;
blanchet@52327
   413
blanchet@52327
   414
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52327
   415
blanchet@55869
   416
    val cst' = mk_co_rec thy fp fpT Cs (Morphism.term phi cst);
blanchet@55864
   417
    val def' = Morphism.thm phi def;
blanchet@52327
   418
  in
blanchet@55864
   419
    ((cst', def'), lthy')
blanchet@52327
   420
  end;
blanchet@52327
   421
blanchet@56641
   422
fun define_rec (_, _, fss, xssss) mk_binding fpTs Cs reps ctor_rec =
blanchet@56641
   423
  let
blanchet@56641
   424
    val nn = length fpTs;
blanchet@56641
   425
    val (ctor_rec_absTs, fpT) = strip_typeN nn (fastype_of ctor_rec)
blanchet@56641
   426
      |>> map domain_type ||> domain_type;
blanchet@56641
   427
  in
blanchet@56641
   428
    define_co_rec Least_FP fpT Cs (mk_binding recN)
blanchet@56641
   429
      (fold_rev (fold_rev Term.lambda) fss (Term.list_comb (ctor_rec,
blanchet@56641
   430
         map4 (fn ctor_rec_absT => fn rep => fn fs => fn xsss =>
blanchet@56641
   431
             mk_case_absumprod ctor_rec_absT rep fs (map (map HOLogic.mk_tuple) xsss)
blanchet@56641
   432
               (map flat_rec_arg_args xsss))
blanchet@56641
   433
           ctor_rec_absTs reps fss xssss)))
blanchet@56641
   434
  end;
blanchet@51897
   435
blanchet@55869
   436
fun define_corec (_, cs, cpss, ((pgss, cqgsss), f_absTs)) mk_binding fpTs Cs abss dtor_corec =
blanchet@51897
   437
  let
blanchet@51899
   438
    val nn = length fpTs;
blanchet@55867
   439
    val fpT = range_type (snd (strip_typeN nn (fastype_of dtor_corec)));
blanchet@51897
   440
  in
blanchet@55867
   441
    define_co_rec Greatest_FP fpT Cs (mk_binding corecN)
blanchet@55869
   442
      (fold_rev (fold_rev Term.lambda) pgss (Term.list_comb (dtor_corec,
blanchet@55869
   443
         map5 mk_preds_getterss_join cs cpss f_absTs abss cqgsss)))
blanchet@52320
   444
  end;
blanchet@51897
   445
blanchet@55867
   446
fun derive_induct_recs_thms_for_types pre_bnfs rec_args_typess ctor_induct ctor_rec_thms
blanchet@55856
   447
    nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss fp_abs_inverses fp_type_definitions abs_inverses
blanchet@55864
   448
    ctrss ctr_defss recs rec_defs lthy =
blanchet@51808
   449
  let
blanchet@51827
   450
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   451
blanchet@51815
   452
    val nn = length pre_bnfs;
blanchet@51827
   453
    val ns = map length ctr_Tsss;
blanchet@51827
   454
    val mss = map (map length) ctr_Tsss;
blanchet@51815
   455
blanchet@51808
   456
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   457
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@53329
   458
    val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
blanchet@53329
   459
    val nested_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nested_bnfs;
blanchet@53290
   460
    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
blanchet@51808
   461
blanchet@51816
   462
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   463
blanchet@51832
   464
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@52315
   465
      lthy
blanchet@51808
   466
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   467
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   468
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   469
blanchet@51808
   470
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   471
blanchet@51808
   472
    fun mk_sets_nested bnf =
blanchet@51808
   473
      let
blanchet@51808
   474
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   475
        val lives = lives_of_bnf bnf;
blanchet@51808
   476
        val sets = sets_of_bnf bnf;
blanchet@51808
   477
        fun mk_set U =
blanchet@54237
   478
          (case find_index (curry (op =) U) lives of
blanchet@51808
   479
            ~1 => Term.dummy
blanchet@51808
   480
          | i => nth sets i);
blanchet@51808
   481
      in
blanchet@51808
   482
        (T_name, map mk_set Us)
blanchet@51808
   483
      end;
blanchet@51808
   484
blanchet@51808
   485
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   486
blanchet@51808
   487
    val (induct_thms, induct_thm) =
blanchet@51808
   488
      let
blanchet@51808
   489
        fun mk_set Ts t =
blanchet@51808
   490
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   491
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   492
          end;
blanchet@51808
   493
blanchet@52310
   494
        fun mk_raw_prem_prems _ (x as Free (_, Type _)) (X as TFree _) =
blanchet@54237
   495
            [([], (find_index (curry (op =) X) Xs + 1, x))]
blanchet@52310
   496
          | mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
blanchet@52310
   497
            (case AList.lookup (op =) setss_nested T_name of
blanchet@52310
   498
              NONE => []
blanchet@52310
   499
            | SOME raw_sets0 =>
blanchet@52310
   500
              let
blanchet@52310
   501
                val (Xs_Ts, (Ts, raw_sets)) =
blanchet@52310
   502
                  filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
blanchet@52310
   503
                  |> split_list ||> split_list;
blanchet@52310
   504
                val sets = map (mk_set Ts0) raw_sets;
blanchet@52310
   505
                val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@52310
   506
                val xysets = map (pair x) (ys ~~ sets);
blanchet@52310
   507
                val ppremss = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
blanchet@52310
   508
              in
blanchet@52310
   509
                flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@52310
   510
              end)
blanchet@52310
   511
          | mk_raw_prem_prems _ _ _ = [];
blanchet@51808
   512
blanchet@51808
   513
        fun close_prem_prem xs t =
blanchet@51808
   514
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   515
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   516
blanchet@51808
   517
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   518
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   519
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   520
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   521
blanchet@52310
   522
        fun mk_raw_prem phi ctr ctr_Ts ctrXs_Ts =
blanchet@51808
   523
          let
blanchet@51808
   524
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@52310
   525
            val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
blanchet@51808
   526
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   527
blanchet@51808
   528
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   529
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   530
blanchet@52310
   531
        val raw_premss = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_Tsss;
blanchet@51808
   532
blanchet@51808
   533
        val goal =
blanchet@51808
   534
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@54237
   535
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@51808
   536
blanchet@51808
   537
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   538
traytel@55803
   539
        val ctor_induct' = ctor_induct OF (map2 mk_absumprodE fp_type_definitions mss);
blanchet@51808
   540
blanchet@51808
   541
        val thm =
blanchet@51808
   542
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
   543
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' fp_abs_inverses
traytel@55803
   544
              abs_inverses nested_set_maps pre_set_defss)
blanchet@51808
   545
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@55409
   546
          (* for "datatype_realizer.ML": *)
blanchet@55409
   547
          |> Thm.name_derivation (fst (dest_Type (hd fpTs)) ^ Long_Name.separator ^
blanchet@55409
   548
            (if nn > 1 then space_implode "_" (tl fp_b_names) ^ Long_Name.separator else "") ^
blanchet@55409
   549
            inductN);
blanchet@51808
   550
      in
blanchet@51808
   551
        `(conj_dests nn) thm
blanchet@51808
   552
      end;
blanchet@51808
   553
blanchet@51808
   554
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@52305
   555
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   556
blanchet@52305
   557
    val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@52305
   558
blanchet@55867
   559
    fun mk_rec_thmss (_, x_Tssss, fss, _) recs rec_defs ctor_rec_thms =
blanchet@51808
   560
      let
blanchet@55867
   561
        val frecs = map (lists_bmoc fss) recs;
blanchet@51808
   562
blanchet@55871
   563
        fun mk_goal frec xctr f xs fxs =
blanchet@51808
   564
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@55867
   565
            (mk_Trueprop_eq (frec $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   566
blanchet@52302
   567
        fun maybe_tick (T, U) u f =
blanchet@52302
   568
          if try (fst o HOLogic.dest_prodT) U = SOME T then
blanchet@52302
   569
            Term.lambda u (HOLogic.mk_prod (u, f $ u))
blanchet@52302
   570
          else
blanchet@52302
   571
            f;
blanchet@51808
   572
blanchet@55867
   573
        fun build_rec (x as Free (_, T)) U =
blanchet@52368
   574
          if T = U then
blanchet@52368
   575
            x
blanchet@52368
   576
          else
blanchet@52303
   577
            build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
blanchet@55867
   578
              (fn kk => fn TU => maybe_tick TU (nth us kk) (nth frecs kk))) (T, U) $ x;
blanchet@52301
   579
blanchet@55867
   580
        val fxsss = map2 (map2 (flat_rec_arg_args oo map2 (map o build_rec))) xsss x_Tssss;
blanchet@55871
   581
        val goalss = map5 (map4 o mk_goal) frecs xctrss fss xsss fxsss;
blanchet@51808
   582
blanchet@52305
   583
        val tacss =
blanchet@55867
   584
          map4 (map ooo mk_rec_tac pre_map_defs (nested_map_idents @ nesting_map_idents) rec_defs)
blanchet@55867
   585
            ctor_rec_thms fp_abs_inverses abs_inverses ctr_defss;
blanchet@51808
   586
blanchet@51808
   587
        fun prove goal tac =
blanchet@51808
   588
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   589
          |> Thm.close_derivation;
blanchet@51808
   590
      in
blanchet@52305
   591
        map2 (map2 prove) goalss tacss
blanchet@51808
   592
      end;
blanchet@51808
   593
blanchet@56641
   594
    val rec_thmss = mk_rec_thmss (the rec_args_typess) recs rec_defs ctor_rec_thms;
blanchet@51808
   595
  in
blanchet@52345
   596
    ((induct_thms, induct_thm, [induct_case_names_attr]),
blanchet@55856
   597
     (rec_thmss, code_nitpicksimp_attrs @ simp_attrs))
blanchet@51808
   598
  end;
blanchet@51808
   599
blanchet@55871
   600
fun derive_coinduct_corecs_thms_for_types pre_bnfs (x, cs, cpss, ((pgss, cqgsss), _))
blanchet@55867
   601
    dtor_coinduct dtor_injects dtor_ctors dtor_corec_thms nesting_bnfs fpTs Cs Xs ctrXs_Tsss kss
traytel@55803
   602
    mss ns fp_abs_inverses abs_inverses mk_vimage2p ctr_defss (ctr_sugars : ctr_sugar list)
blanchet@55864
   603
    corecs corec_defs export_args lthy =
blanchet@51810
   604
  let
blanchet@55867
   605
    fun mk_ctor_dtor_corec_thm dtor_inject dtor_ctor corec =
blanchet@55867
   606
      iffD1 OF [dtor_inject, trans OF [corec, dtor_ctor RS sym]];
traytel@53203
   607
blanchet@55867
   608
    val ctor_dtor_corec_thms = map3 mk_ctor_dtor_corec_thm dtor_injects dtor_ctors dtor_corec_thms;
traytel@53203
   609
blanchet@51815
   610
    val nn = length pre_bnfs;
blanchet@51815
   611
blanchet@51810
   612
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   613
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@53329
   614
    val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
blanchet@51830
   615
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   616
blanchet@51816
   617
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   618
blanchet@53210
   619
    val ctrss = map #ctrs ctr_sugars;
blanchet@53210
   620
    val discss = map #discs ctr_sugars;
blanchet@53210
   621
    val selsss = map #selss ctr_sugars;
blanchet@51840
   622
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   623
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   624
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   625
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   626
blanchet@51810
   627
    val (((rs, us'), vs'), names_lthy) =
blanchet@52341
   628
      lthy
blanchet@51810
   629
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   630
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   631
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   632
blanchet@51810
   633
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   634
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   635
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   636
blanchet@51810
   637
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   638
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   639
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   640
blanchet@52345
   641
    val coinduct_thms_pairs =
blanchet@51810
   642
      let
blanchet@51810
   643
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   644
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   645
        val strong_rs =
blanchet@51810
   646
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   647
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   648
blanchet@54237
   649
        fun build_the_rel rs' T Xs_T =
blanchet@54237
   650
          build_rel lthy (fn (_, X) => nth rs' (find_index (curry (op =) X) Xs)) (T, Xs_T)
blanchet@54237
   651
          |> Term.subst_atomic_types (Xs ~~ fpTs);
blanchet@51810
   652
blanchet@54237
   653
        fun build_rel_app rs' usel vsel Xs_T =
blanchet@54237
   654
          fold rapp [usel, vsel] (build_the_rel rs' (fastype_of usel) Xs_T);
blanchet@51810
   655
blanchet@54237
   656
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels ctrXs_Ts =
blanchet@51810
   657
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   658
          (if null usels then
blanchet@51810
   659
             []
blanchet@51810
   660
           else
blanchet@51810
   661
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@54237
   662
                Library.foldr1 HOLogic.mk_conj (map3 (build_rel_app rs') usels vsels ctrXs_Ts))]);
blanchet@51810
   663
blanchet@54237
   664
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss ctrXs_Tss =
blanchet@54237
   665
          Library.foldr1 HOLogic.mk_conj (flat (map6 (mk_prem_ctr_concls rs' n)
blanchet@54237
   666
            (1 upto n) udiscs uselss vdiscs vselss ctrXs_Tss))
blanchet@51810
   667
          handle List.Empty => @{term True};
blanchet@51810
   668
blanchet@54237
   669
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss ctrXs_Tss =
blanchet@51810
   670
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@54237
   671
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss ctrXs_Tss)));
blanchet@51810
   672
blanchet@51810
   673
        val concl =
blanchet@51810
   674
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   675
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   676
               uvrs us vs));
blanchet@51810
   677
blanchet@51810
   678
        fun mk_goal rs' =
blanchet@54237
   679
          Logic.list_implies (map9 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss
blanchet@54237
   680
            ctrXs_Tsss, concl);
blanchet@51810
   681
blanchet@52345
   682
        val goals = map mk_goal [rs, strong_rs];
blanchet@51810
   683
blanchet@51810
   684
        fun prove dtor_coinduct' goal =
blanchet@51810
   685
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
   686
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses
traytel@55803
   687
              abs_inverses dtor_ctors exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   688
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   689
          |> Thm.close_derivation;
blanchet@51810
   690
blanchet@51810
   691
        fun postproc nn thm =
blanchet@51810
   692
          Thm.permute_prems 0 nn
blanchet@51828
   693
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   694
          |> Drule.zero_var_indexes
blanchet@51810
   695
          |> `(conj_dests nn);
traytel@53106
   696
traytel@53106
   697
        val rel_eqs = map rel_eq_of_bnf pre_bnfs;
traytel@53106
   698
        val rel_monos = map rel_mono_of_bnf pre_bnfs;
traytel@53106
   699
        val dtor_coinducts =
traytel@55803
   700
          [dtor_coinduct, mk_strong_coinduct_thm dtor_coinduct rel_eqs rel_monos mk_vimage2p lthy]
blanchet@51810
   701
      in
blanchet@52345
   702
        map2 (postproc nn oo prove) dtor_coinducts goals
blanchet@51810
   703
      end;
blanchet@51810
   704
blanchet@51810
   705
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   706
      let
blanchet@51810
   707
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   708
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   709
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   710
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   711
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   712
      in
blanchet@51810
   713
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   714
      end;
blanchet@51810
   715
blanchet@51816
   716
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   717
    val coinduct_conclss =
blanchet@51810
   718
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   719
blanchet@51810
   720
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   721
blanchet@55869
   722
    val gcorecs = map (lists_bmoc pgss) corecs;
blanchet@51810
   723
blanchet@55856
   724
    val corec_thmss =
blanchet@51810
   725
      let
blanchet@55869
   726
        fun mk_goal c cps gcorec n k ctr m cfs' =
blanchet@55869
   727
          fold_rev (fold_rev Logic.all) ([c] :: pgss)
blanchet@51810
   728
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@55869
   729
               mk_Trueprop_eq (gcorec $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   730
blanchet@55869
   731
        val mk_U = typ_subst_nonatomic (map2 (fn C => fn fpT => (mk_sumT (fpT, C), fpT)) Cs fpTs);
blanchet@52347
   732
blanchet@55869
   733
        fun tack (c, u) f =
blanchet@55869
   734
          let val x' = Free (x, mk_sumT (fastype_of u, fastype_of c)) in
blanchet@55869
   735
            Term.lambda x' (mk_case_sum (Term.lambda u u, Term.lambda c (f $ c)) $ x')
blanchet@52347
   736
          end;
blanchet@51810
   737
blanchet@55869
   738
        fun build_corec cqg =
blanchet@55869
   739
          let val T = fastype_of cqg in
blanchet@52347
   740
            if exists_subtype_in Cs T then
blanchet@55869
   741
              let val U = mk_U T in
blanchet@55869
   742
                build_map lthy (indexify fst (map2 (curry mk_sumT) fpTs Cs) (fn kk => fn _ =>
blanchet@55869
   743
                  tack (nth cs kk, nth us kk) (nth gcorecs kk))) (T, U) $ cqg
blanchet@52368
   744
              end
blanchet@52347
   745
            else
blanchet@55869
   746
              cqg
blanchet@52347
   747
          end;
blanchet@51810
   748
blanchet@55869
   749
        val cqgsss' = map (map (map build_corec)) cqgsss;
blanchet@55869
   750
        val goalss = map8 (map4 oooo mk_goal) cs cpss gcorecs ns kss ctrss mss cqgsss';
blanchet@51810
   751
blanchet@55856
   752
        val tacss =
blanchet@55867
   753
          map4 (map ooo mk_corec_tac corec_defs nesting_map_idents)
blanchet@55867
   754
            ctor_dtor_corec_thms pre_map_defs abs_inverses ctr_defss;
blanchet@51810
   755
blanchet@51810
   756
        fun prove goal tac =
blanchet@51815
   757
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   758
          |> Thm.close_derivation;
blanchet@51810
   759
      in
blanchet@55856
   760
        map2 (map2 prove) goalss tacss
blanchet@55856
   761
        |> map (map (unfold_thms lthy @{thms case_sum_if}))
blanchet@51810
   762
      end;
blanchet@51810
   763
blanchet@55856
   764
    val disc_corec_iff_thmss =
blanchet@51810
   765
      let
blanchet@55869
   766
        fun mk_goal c cps gcorec n k disc =
blanchet@55869
   767
          mk_Trueprop_eq (disc $ (gcorec $ c),
blanchet@51810
   768
            if n = 1 then @{const True}
blanchet@51810
   769
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   770
blanchet@55869
   771
        val goalss = map6 (map2 oooo mk_goal) cs cpss gcorecs ns kss discss;
blanchet@51810
   772
blanchet@51828
   773
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   774
blanchet@51810
   775
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   776
blanchet@55867
   777
        val tacss = map3 (map oo mk_disc_corec_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   778
blanchet@51810
   779
        fun prove goal tac =
blanchet@51810
   780
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@52357
   781
          |> singleton export_args
blanchet@51829
   782
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   783
          |> Thm.close_derivation;
blanchet@51810
   784
blanchet@51810
   785
        fun proves [_] [_] = []
blanchet@51810
   786
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   787
      in
blanchet@55856
   788
        map2 proves goalss tacss
blanchet@51810
   789
      end;
blanchet@51810
   790
blanchet@55867
   791
    fun mk_disc_corec_thms corecs discIs = map (op RS) (corecs ~~ discIs);
blanchet@51810
   792
blanchet@55867
   793
    val disc_corec_thmss = map2 mk_disc_corec_thms corec_thmss discIss;
blanchet@51810
   794
blanchet@55867
   795
    fun mk_sel_corec_thm corec_thm sel sel_thm =
blanchet@51810
   796
      let
blanchet@51810
   797
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   798
        val arg_cong' =
blanchet@51810
   799
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   800
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   801
          |> Thm.varifyT_global;
blanchet@51810
   802
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   803
      in
blanchet@55867
   804
        corec_thm RS arg_cong' RS sel_thm'
blanchet@51810
   805
      end;
blanchet@51810
   806
blanchet@55867
   807
    fun mk_sel_corec_thms corec_thmss =
blanchet@55867
   808
      map3 (map3 (map2 o mk_sel_corec_thm)) corec_thmss selsss sel_thmsss;
blanchet@51810
   809
blanchet@55867
   810
    val sel_corec_thmsss = mk_sel_corec_thms corec_thmss;
blanchet@51810
   811
blanchet@51810
   812
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   813
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   814
    val coinduct_case_concl_attrs =
blanchet@51810
   815
      map2 (fn casex => fn concls =>
blanchet@51810
   816
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   817
        coinduct_cases coinduct_conclss;
blanchet@51810
   818
    val coinduct_case_attrs =
blanchet@51810
   819
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   820
  in
blanchet@52345
   821
    ((coinduct_thms_pairs, coinduct_case_attrs),
blanchet@55856
   822
     (corec_thmss, code_nitpicksimp_attrs),
blanchet@55856
   823
     (disc_corec_thmss, []),
blanchet@55856
   824
     (disc_corec_iff_thmss, simp_attrs),
blanchet@55856
   825
     (sel_corec_thmsss, simp_attrs))
blanchet@51810
   826
  end;
blanchet@51810
   827
blanchet@52207
   828
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
blanchet@55410
   829
    (wrap_opts as (no_discs_sels, _), specs) no_defs_lthy0 =
blanchet@49112
   830
  let
blanchet@49298
   831
    (* TODO: sanity checks on arguments *)
blanchet@49298
   832
blanchet@52969
   833
    val _ = if fp = Greatest_FP andalso no_discs_sels then
blanchet@52969
   834
        error "Cannot define codatatypes without discriminators and selectors"
blanchet@52207
   835
      else
blanchet@52207
   836
        ();
blanchet@49278
   837
blanchet@49367
   838
    val nn = length specs;
blanchet@55469
   839
    val fp_bs = map type_binding_of_spec specs;
blanchet@49498
   840
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
   841
    val fp_common_name = mk_common_name fp_b_names;
blanchet@55469
   842
    val map_bs = map map_binding_of_spec specs;
blanchet@55469
   843
    val rel_bs = map rel_binding_of_spec specs;
blanchet@49298
   844
blanchet@51758
   845
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
   846
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
   847
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   848
      end;
blanchet@49298
   849
blanchet@55469
   850
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of_spec) specs;
wenzelm@56254
   851
    val unsorted_Ass0 = map (map (resort_tfree @{sort type})) Ass0;
blanchet@55700
   852
    val unsorted_As = Library.foldr1 (merge_type_args fp) unsorted_Ass0;
blanchet@53266
   853
    val num_As = length unsorted_As;
blanchet@55699
   854
blanchet@55699
   855
    val set_boss = map (map fst o type_args_named_constrained_of_spec) specs;
blanchet@55699
   856
    val set_bss = map (map (the_default Binding.empty)) set_boss;
blanchet@49119
   857
blanchet@49585
   858
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
   859
      no_defs_lthy0
blanchet@49298
   860
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@53266
   861
      |> mk_TFrees num_As
blanchet@49585
   862
      ||>> mk_TFrees nn
blanchet@51858
   863
      ||>> variant_tfrees fp_b_names;
blanchet@49119
   864
blanchet@55469
   865
    fun add_fake_type spec =
blanchet@55469
   866
      Typedecl.basic_typedecl (type_binding_of_spec spec, num_As, mixfix_of_spec spec);
blanchet@51768
   867
blanchet@53268
   868
    val (fake_T_names, fake_lthy) = fold_map add_fake_type specs no_defs_lthy0;
blanchet@49119
   869
blanchet@53262
   870
    val qsoty = quote o Syntax.string_of_typ fake_lthy;
blanchet@53262
   871
blanchet@54253
   872
    val _ = (case Library.duplicates (op =) unsorted_As of [] => ()
blanchet@53262
   873
      | A :: _ => error ("Duplicate type parameter " ^ qsoty A ^ " in " ^ co_prefix fp ^
blanchet@53262
   874
          "datatype specification"));
blanchet@53262
   875
blanchet@53262
   876
    val bad_args =
blanchet@53262
   877
      map (Logic.type_map (singleton (Variable.polymorphic no_defs_lthy0))) unsorted_As
blanchet@53262
   878
      |> filter_out Term.is_TVar;
blanchet@53262
   879
    val _ = null bad_args orelse
blanchet@53262
   880
      error ("Locally fixed type argument " ^ qsoty (hd bad_args) ^ " in " ^ co_prefix fp ^
blanchet@53262
   881
        "datatype specification");
blanchet@53262
   882
blanchet@55469
   883
    val mixfixes = map mixfix_of_spec specs;
blanchet@49119
   884
blanchet@54253
   885
    val _ = (case Library.duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
   886
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
   887
blanchet@55469
   888
    val mx_ctr_specss = map mixfixed_ctr_specs_of_spec specs;
blanchet@55469
   889
    val ctr_specss = map (map fst) mx_ctr_specss;
blanchet@55469
   890
    val ctr_mixfixess = map (map snd) mx_ctr_specss;
blanchet@49119
   891
blanchet@55469
   892
    val disc_bindingss = map (map disc_of_ctr_spec) ctr_specss;
blanchet@49336
   893
    val ctr_bindingss =
blanchet@55469
   894
      map2 (fn fp_b_name => map (Binding.qualify false fp_b_name o ctr_of_ctr_spec)) fp_b_names
blanchet@55469
   895
        ctr_specss;
blanchet@55469
   896
    val ctr_argsss = map (map args_of_ctr_spec) ctr_specss;
blanchet@49119
   897
blanchet@49336
   898
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
   899
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@55469
   900
    val raw_sel_defaultsss = map (map sel_defaults_of_ctr_spec) ctr_specss;
blanchet@49286
   901
blanchet@49308
   902
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
   903
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@53262
   904
    val As' = map dest_TFree As;
blanchet@49298
   905
blanchet@49183
   906
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@53262
   907
    val _ = (case subtract (op =) As' rhs_As' of [] => ()
blanchet@53262
   908
      | extras => error ("Extra type variables on right-hand side: " ^
blanchet@53262
   909
          commas (map (qsoty o TFree) extras)));
blanchet@49165
   910
blanchet@53268
   911
    val fake_Ts = map (fn s => Type (s, As)) fake_T_names;
blanchet@53268
   912
blanchet@53262
   913
    fun eq_fpT_check (T as Type (s, Ts)) (T' as Type (s', Ts')) =
blanchet@53262
   914
        s = s' andalso (Ts = Ts' orelse
blanchet@53262
   915
          error ("Wrong type arguments in " ^ co_prefix fp ^ "recursive type " ^ qsoty T ^
blanchet@53262
   916
            " (expected " ^ qsoty T' ^ ")"))
blanchet@49591
   917
      | eq_fpT_check _ _ = false;
blanchet@49146
   918
blanchet@53222
   919
    fun freeze_fp (T as Type (s, Ts)) =
blanchet@49591
   920
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@53222
   921
          ~1 => Type (s, map freeze_fp Ts)
blanchet@49591
   922
        | kk => nth Xs kk)
blanchet@49204
   923
      | freeze_fp T = T;
blanchet@49121
   924
blanchet@53222
   925
    val unfreeze_fp = Term.typ_subst_atomic (Xs ~~ fake_Ts);
blanchet@53222
   926
blanchet@52310
   927
    val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@55966
   928
    val ctrXs_repTs = map mk_sumprodT_balanced ctrXs_Tsss;
blanchet@49119
   929
blanchet@49298
   930
    val fp_eqs =
traytel@55803
   931
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_repTs;
blanchet@49121
   932
blanchet@53262
   933
    val rhsXs_As' = fold (fold (fold Term.add_tfreesT)) ctrXs_Tsss [];
blanchet@53262
   934
    val _ = (case subtract (op =) rhsXs_As' As' of [] => ()
blanchet@53266
   935
      | extras => List.app (fn extra => warning ("Unused type variable on right-hand side of " ^
blanchet@53266
   936
          co_prefix fp ^ "datatype definition: " ^ qsoty (TFree extra))) extras);
blanchet@53262
   937
blanchet@55701
   938
    val killed_As =
blanchet@55701
   939
      map_filter (fn (A, set_bos) => if exists is_none set_bos then SOME A else NONE)
blanchet@55701
   940
        (unsorted_As ~~ transpose set_boss);
blanchet@55701
   941
traytel@55803
   942
    val ((pre_bnfs, absT_infos), (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0,
blanchet@55868
   943
             dtors = dtors0, xtor_co_recs = xtor_co_recs0, xtor_co_induct, dtor_ctors,
traytel@55803
   944
             ctor_dtors, ctor_injects, dtor_injects, xtor_map_thms, xtor_set_thmss, xtor_rel_thms,
blanchet@55868
   945
             xtor_co_rec_thms, ...},
traytel@53203
   946
           lthy)) =
blanchet@55701
   947
      fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As)
blanchet@55701
   948
        (map dest_TFree killed_As) fp_eqs no_defs_lthy0
blanchet@53222
   949
      handle BAD_DEAD (X, X_backdrop) =>
blanchet@53222
   950
        (case X_backdrop of
blanchet@53222
   951
          Type (bad_tc, _) =>
blanchet@53222
   952
          let
blanchet@53222
   953
            val fake_T = qsoty (unfreeze_fp X);
blanchet@53222
   954
            val fake_T_backdrop = qsoty (unfreeze_fp X_backdrop);
blanchet@53222
   955
            fun register_hint () =
blanchet@53222
   956
              "\nUse the " ^ quote (fst (fst @{command_spec "bnf"})) ^ " command to register " ^
blanchet@53222
   957
              quote bad_tc ^ " as a bounded natural functor to allow nested (co)recursion through \
blanchet@53222
   958
              \it";
blanchet@53222
   959
          in
blanchet@53222
   960
            if is_some (bnf_of no_defs_lthy bad_tc) orelse
blanchet@53222
   961
               is_some (fp_sugar_of no_defs_lthy bad_tc) then
blanchet@53256
   962
              error ("Inadmissible " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53256
   963
                " in type expression " ^ fake_T_backdrop)
blanchet@53222
   964
            else if is_some (Datatype_Data.get_info (Proof_Context.theory_of no_defs_lthy)
blanchet@53222
   965
                bad_tc) then
blanchet@53222
   966
              error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53222
   967
                " via the old-style datatype " ^ quote bad_tc ^ " in type expression " ^
blanchet@53222
   968
                fake_T_backdrop ^ register_hint ())
blanchet@53222
   969
            else
blanchet@53222
   970
              error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53222
   971
                " via type constructor " ^ quote bad_tc ^ " in type expression " ^ fake_T_backdrop ^
blanchet@53222
   972
                register_hint ())
blanchet@53222
   973
          end);
blanchet@49585
   974
traytel@55803
   975
    val abss = map #abs absT_infos;
traytel@55803
   976
    val reps = map #rep absT_infos;
traytel@55803
   977
    val absTs = map #absT absT_infos;
traytel@55803
   978
    val repTs = map #repT absT_infos;
traytel@55803
   979
    val abs_injects = map #abs_inject absT_infos;
traytel@55803
   980
    val abs_inverses = map #abs_inverse absT_infos;
traytel@55803
   981
    val type_definitions = map #type_definition absT_infos;
traytel@55803
   982
traytel@53143
   983
    val time = time lthy;
blanchet@49585
   984
    val timer = time (Timer.startRealTimer ());
blanchet@49121
   985
blanchet@52310
   986
    val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
blanchet@52310
   987
    val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
blanchet@49226
   988
blanchet@49585
   989
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
   990
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
   991
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@53290
   992
    val nesting_set_maps = maps set_map_of_bnf nesting_bnfs;
blanchet@53290
   993
    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
blanchet@49585
   994
blanchet@49585
   995
    val live = live_of_bnf any_fp_bnf;
blanchet@52961
   996
    val _ =
blanchet@52961
   997
      if live = 0 andalso exists (not o Binding.is_empty) (map_bs @ rel_bs) then
blanchet@53266
   998
        warning "Map function and relator names ignored"
blanchet@52961
   999
      else
blanchet@52961
  1000
        ();
blanchet@49585
  1001
blanchet@49585
  1002
    val Bs =
blanchet@49585
  1003
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@53266
  1004
        (liveness_of_fp_bnf num_As any_fp_bnf) As Bs0;
blanchet@49585
  1005
blanchet@49585
  1006
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
  1007
blanchet@49501
  1008
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
  1009
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
  1010
blanchet@49501
  1011
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@56638
  1012
    val fpBTs = map B_ify fpTs;
blanchet@49362
  1013
blanchet@51780
  1014
    fun massage_simple_notes base =
blanchet@51780
  1015
      filter_out (null o #2)
blanchet@51780
  1016
      #> map (fn (thmN, thms, attrs) =>
blanchet@55410
  1017
        ((Binding.qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
  1018
blanchet@51780
  1019
    val massage_multi_notes =
blanchet@51780
  1020
      maps (fn (thmN, thmss, attrs) =>
blanchet@53792
  1021
        map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@55410
  1022
            ((Binding.qualify true fp_b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
blanchet@53792
  1023
          fp_b_names fpTs thmss)
blanchet@53792
  1024
      #> filter_out (null o fst o hd o snd);
blanchet@51780
  1025
blanchet@52310
  1026
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctrXs_Tsss;
blanchet@49203
  1027
    val ns = map length ctr_Tsss;
blanchet@49212
  1028
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
  1029
    val mss = map (map length) ctr_Tsss;
blanchet@49203
  1030
blanchet@55867
  1031
    val ((xtor_co_recs, recs_args_types, corecs_args_types), lthy') =
blanchet@55868
  1032
      mk_co_recs_prelims fp ctr_Tsss fpTs Cs absTs repTs ns mss xtor_co_recs0 lthy;
blanchet@49210
  1033
traytel@55803
  1034
    fun define_ctrs_dtrs_for_type (((((((((((((((((((((((((((fp_bnf, fp_b), fpT), ctor), dtor),
blanchet@55867
  1035
              xtor_co_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
traytel@55803
  1036
            pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), abs),
traytel@55803
  1037
          abs_inject), abs_inverse), type_definition), ctr_bindings), ctr_mixfixes), ctr_Tss),
traytel@55803
  1038
        disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
  1039
      let
blanchet@49498
  1040
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1041
traytel@55803
  1042
        val ctr_absT = domain_type (fastype_of ctor);
blanchet@49119
  1043
blanchet@52968
  1044
        val ((((w, xss), yss), u'), names_lthy) =
blanchet@49204
  1045
          no_defs_lthy
traytel@55803
  1046
          |> yield_singleton (mk_Frees "w") ctr_absT
blanchet@49370
  1047
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1048
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1049
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1050
blanchet@49498
  1051
        val u = Free (u', fpT);
blanchet@49121
  1052
blanchet@49129
  1053
        val ctr_rhss =
traytel@55803
  1054
          map2 (fn k => fn xs => fold_rev Term.lambda xs (ctor $ mk_absumprod ctr_absT abs n k xs))
traytel@55803
  1055
            ks xss;
blanchet@49121
  1056
traytel@53569
  1057
        val maybe_conceal_def_binding = Thm.def_binding
traytel@53569
  1058
          #> Config.get no_defs_lthy bnf_note_all = false ? Binding.conceal;
traytel@53569
  1059
blanchet@52968
  1060
        val ((raw_ctrs, raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1061
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
traytel@53569
  1062
              Local_Theory.define ((b, mx), ((maybe_conceal_def_binding b, []), rhs)) #>> apsnd snd)
blanchet@52968
  1063
            ctr_bindings ctr_mixfixes ctr_rhss
blanchet@49121
  1064
          ||> `Local_Theory.restore;
blanchet@49121
  1065
blanchet@49121
  1066
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1067
blanchet@49121
  1068
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1069
        val ctr_defs' =
blanchet@49585
  1070
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1071
blanchet@49203
  1072
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1073
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1074
blanchet@51897
  1075
        fun wrap_ctrs lthy =
blanchet@49123
  1076
          let
traytel@50170
  1077
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1078
              let
blanchet@49585
  1079
                val ctor_iff_dtor_thm =
blanchet@49585
  1080
                  let
blanchet@49585
  1081
                    val goal =
blanchet@49585
  1082
                      fold_rev Logic.all [w, u]
blanchet@49585
  1083
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1084
                  in
wenzelm@51551
  1085
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
  1086
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [ctr_absT, fpT])
blanchet@49585
  1087
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@55409
  1088
                    |> Morphism.thm phi
blanchet@49585
  1089
                    |> Thm.close_derivation
blanchet@49585
  1090
                  end;
blanchet@49585
  1091
blanchet@49585
  1092
                val sumEN_thm' =
traytel@55803
  1093
                  unfold_thms lthy @{thms unit_all_eq1} (mk_absumprodE type_definition ms)
blanchet@49585
  1094
                  |> Morphism.thm phi;
blanchet@49135
  1095
              in
blanchet@49585
  1096
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1097
              end;
blanchet@49135
  1098
blanchet@49585
  1099
            val inject_tacss =
traytel@55803
  1100
              map2 (fn ctr_def => fn 0 => [] | _ => [fn {context = ctxt, ...} =>
traytel@55803
  1101
                mk_inject_tac ctxt ctr_def ctor_inject abs_inject]) ctr_defs ms;
blanchet@49585
  1102
blanchet@49585
  1103
            val half_distinct_tacss =
blanchet@49585
  1104
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
traytel@55803
  1105
                  mk_half_distinct_tac ctxt ctor_inject abs_inject [def, def']))
traytel@55803
  1106
                (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1107
blanchet@52968
  1108
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss;
blanchet@49585
  1109
blanchet@49585
  1110
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@55469
  1111
blanchet@55469
  1112
            fun ctr_spec_of disc_b ctr0 sel_bs sel_defs = (((disc_b, ctr0), sel_bs), sel_defs);
blanchet@55469
  1113
            val ctr_specs = map4 ctr_spec_of disc_bindings ctrs0 sel_bindingss sel_defaultss;
blanchet@49123
  1114
          in
blanchet@55469
  1115
            free_constructors tacss ((wrap_opts, standard_binding), ctr_specs) lthy
blanchet@49123
  1116
          end;
blanchet@49121
  1117
blanchet@55397
  1118
        fun derive_maps_sets_rels (ctr_sugar as {case_cong, ...} : ctr_sugar, lthy) =
blanchet@51835
  1119
          if live = 0 then
blanchet@51840
  1120
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1121
          else
blanchet@51835
  1122
            let
blanchet@51835
  1123
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1124
              val nones = replicate live NONE;
blanchet@49585
  1125
blanchet@51835
  1126
              val ctor_cong =
blanchet@52207
  1127
                if fp = Least_FP then
blanchet@51835
  1128
                  Drule.dummy_thm
blanchet@51835
  1129
                else
blanchet@51835
  1130
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1131
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1132
                  end;
blanchet@49585
  1133
traytel@55803
  1134
              fun mk_cIn ctor k xs =
traytel@55803
  1135
                let val absT = domain_type (fastype_of ctor) in
traytel@55803
  1136
                  mk_absumprod absT abs n k xs
traytel@55803
  1137
                  |> fp = Greatest_FP ? curry (op $) ctor
traytel@55803
  1138
                  |> certify lthy
traytel@55803
  1139
                end;
blanchet@49585
  1140
traytel@55803
  1141
              val cxIns = map2 (mk_cIn ctor) ks xss;
blanchet@56638
  1142
              val cyIns = map2 (mk_cIn (Term.map_types B_ify ctor)) ks yss;
blanchet@49585
  1143
blanchet@51835
  1144
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1145
                fold_thms lthy [ctr_def']
traytel@55803
  1146
                  (unfold_thms lthy (o_apply :: pre_map_def ::
blanchet@55966
  1147
                       (if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sumprod_thms_map @
traytel@55803
  1148
                       abs_inverses)
blanchet@51835
  1149
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@52207
  1150
                        (if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1151
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1152
blanchet@51835
  1153
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1154
                fold_thms lthy [ctr_def']
blanchet@53290
  1155
                  (unfold_thms lthy (pre_set_defs @ nested_set_maps @ nesting_set_maps @
blanchet@55966
  1156
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sumprod_thms_set @
traytel@55803
  1157
                       abs_inverses)
blanchet@51835
  1158
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1159
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1160
blanchet@51835
  1161
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1162
blanchet@51835
  1163
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1164
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@55463
  1165
              val set_thms = flat set_thmss;
blanchet@51835
  1166
blanchet@51835
  1167
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1168
blanchet@51835
  1169
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1170
                fold_thms lthy ctr_defs'
traytel@55803
  1171
                  (unfold_thms lthy (pre_rel_def :: abs_inverse ::
blanchet@55966
  1172
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sumprod_thms_rel @
blanchet@56049
  1173
                       @{thms vimage2p_def sum.inject Inl_Inr_False})
blanchet@53266
  1174
                     (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1175
                |> postproc
blanchet@51835
  1176
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1177
blanchet@51835
  1178
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1179
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1180
blanchet@51835
  1181
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1182
blanchet@51835
  1183
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1184
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1185
                  cxIn cyIn;
blanchet@49121
  1186
blanchet@51835
  1187
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1188
                flip_rels lthy live thm
blanchet@51835
  1189
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1190
blanchet@51835
  1191
              val half_rel_distinct_thmss =
blanchet@51835
  1192
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1193
              val other_half_rel_distinct_thmss =
blanchet@51835
  1194
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1195
              val (rel_distinct_thms, _) =
blanchet@51835
  1196
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1197
blanchet@55463
  1198
              val rel_eq_thms =
blanchet@55463
  1199
                map (fn th => th RS @{thm eq_False[THEN iffD2]}) rel_distinct_thms @
blanchet@55463
  1200
                map2 (fn th => fn 0 => th RS @{thm eq_True[THEN iffD2]} | _ => th)
blanchet@55463
  1201
                  rel_inject_thms ms;
blanchet@55463
  1202
blanchet@54145
  1203
              val anonymous_notes =
blanchet@55397
  1204
                [([case_cong], fundefcong_attrs),
blanchet@55463
  1205
                 (rel_eq_thms, code_nitpicksimp_attrs)]
blanchet@54145
  1206
                |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@54145
  1207
blanchet@51835
  1208
              val notes =
blanchet@54145
  1209
                [(mapN, map_thms, code_nitpicksimp_attrs @ simp_attrs),
blanchet@54145
  1210
                 (rel_distinctN, rel_distinct_thms, simp_attrs),
blanchet@54145
  1211
                 (rel_injectN, rel_inject_thms, simp_attrs),
blanchet@55463
  1212
                 (setN, set_thms, code_nitpicksimp_attrs @ simp_attrs)]
blanchet@51835
  1213
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1214
            in
blanchet@51840
  1215
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@55463
  1216
               lthy
blanchet@55535
  1217
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) map_thms)
blanchet@55903
  1218
               |> fp = Least_FP
blanchet@55903
  1219
                 ? Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) rel_eq_thms)
blanchet@55535
  1220
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) set_thms)
blanchet@55463
  1221
               |> Local_Theory.notes (anonymous_notes @ notes)
blanchet@55463
  1222
               |> snd)
blanchet@51835
  1223
            end;
blanchet@49585
  1224
blanchet@55410
  1225
        fun mk_binding pre = Binding.qualify false fp_b_name (Binding.prefix_name (pre ^ "_") fp_b);
blanchet@49287
  1226
blanchet@55867
  1227
        fun massage_res (((maps_sets_rels, ctr_sugar), co_rec_res), lthy) =
blanchet@55867
  1228
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_rec_res), lthy);
blanchet@49119
  1229
      in
blanchet@51897
  1230
        (wrap_ctrs
blanchet@51835
  1231
         #> derive_maps_sets_rels
blanchet@52313
  1232
         ##>>
blanchet@56641
  1233
           (if fp = Least_FP then define_rec (the recs_args_types) mk_binding fpTs Cs reps
blanchet@55867
  1234
           else define_corec (the corecs_args_types) mk_binding fpTs Cs abss) xtor_co_rec
blanchet@51835
  1235
         #> massage_res, lthy')
blanchet@49119
  1236
      end;
blanchet@49167
  1237
blanchet@51835
  1238
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1239
      fold_map I wrap_types_etcs lthy
blanchet@52342
  1240
      |>> apsnd split_list o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@52342
  1241
        o split_list;
blanchet@49226
  1242
blanchet@55856
  1243
    fun mk_simp_thms ({injects, distincts, case_thms, ...} : ctr_sugar) co_recs mapsx rel_injects
blanchet@55856
  1244
        rel_distincts setss =
blanchet@55856
  1245
      injects @ distincts @ case_thms @ co_recs @ mapsx @ rel_injects @ rel_distincts @ flat setss;
blanchet@49479
  1246
blanchet@55867
  1247
    fun derive_note_induct_recs_thms_for_types
blanchet@56648
  1248
        ((((mapss, rel_injectss, rel_distinctss, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@55864
  1249
          (recs, rec_defs)), lthy) =
blanchet@49202
  1250
      let
blanchet@55869
  1251
        val ((induct_thms, induct_thm, induct_attrs), (rec_thmss, rec_attrs)) =
blanchet@55868
  1252
          derive_induct_recs_thms_for_types pre_bnfs recs_args_types xtor_co_induct xtor_co_rec_thms
blanchet@55868
  1253
            nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss abs_inverses type_definitions
blanchet@55868
  1254
            abs_inverses ctrss ctr_defss recs rec_defs lthy;
blanchet@49201
  1255
blanchet@51830
  1256
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1257
blanchet@51835
  1258
        val simp_thmss =
blanchet@56648
  1259
          map6 mk_simp_thms ctr_sugars rec_thmss mapss rel_injectss rel_distinctss setss;
blanchet@49438
  1260
blanchet@49337
  1261
        val common_notes =
blanchet@51808
  1262
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1263
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1264
blanchet@49226
  1265
        val notes =
blanchet@55856
  1266
          [(inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@55869
  1267
           (recN, rec_thmss, K rec_attrs),
blanchet@49585
  1268
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1269
          |> massage_multi_notes;
blanchet@49202
  1270
      in
blanchet@51824
  1271
        lthy
blanchet@56641
  1272
        |> Spec_Rules.add Spec_Rules.Equational (recs, flat rec_thmss)
blanchet@51824
  1273
        |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@56648
  1274
        |> register_as_fp_sugars fpTs fpBTs Xs Least_FP pre_bnfs absT_infos nested_bnfs nesting_bnfs
blanchet@56648
  1275
          fp_res ctrXs_Tsss ctr_defss ctr_sugars recs rec_defs mapss [induct_thm]
blanchet@56648
  1276
          (map single induct_thms) rec_thmss (replicate nn []) (replicate nn []) rel_injectss
blanchet@56648
  1277
          rel_distinctss
blanchet@49202
  1278
      end;
blanchet@49202
  1279
blanchet@55867
  1280
    fun derive_note_coinduct_corecs_thms_for_types
blanchet@56648
  1281
        ((((mapss, rel_injectss, rel_distinctss, setss), (_, _, ctr_defss, ctr_sugars)),
blanchet@55867
  1282
          (corecs, corec_defs)), lthy) =
blanchet@49212
  1283
      let
blanchet@52345
  1284
        val (([(coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)],
blanchet@51810
  1285
              coinduct_attrs),
blanchet@55871
  1286
             (corec_thmss, corec_attrs), (disc_corec_thmss, disc_corec_attrs),
blanchet@55871
  1287
             (disc_corec_iff_thmss, disc_corec_iff_attrs), (sel_corec_thmsss, sel_corec_attrs)) =
blanchet@55867
  1288
          derive_coinduct_corecs_thms_for_types pre_bnfs (the corecs_args_types) xtor_co_induct
blanchet@55868
  1289
            dtor_injects dtor_ctors xtor_co_rec_thms nesting_bnfs fpTs Cs Xs ctrXs_Tsss kss mss ns
blanchet@55868
  1290
            abs_inverses abs_inverses I ctr_defss ctr_sugars corecs corec_defs
traytel@55803
  1291
            (Proof_Context.export lthy' no_defs_lthy) lthy;
blanchet@49212
  1292
blanchet@53475
  1293
        val sel_corec_thmss = map flat sel_corec_thmsss;
blanchet@53475
  1294
blanchet@51830
  1295
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1296
blanchet@55867
  1297
        val flat_corec_thms = append oo append;
blanchet@49479
  1298
blanchet@49479
  1299
        val simp_thmss =
blanchet@55856
  1300
          map6 mk_simp_thms ctr_sugars
blanchet@55867
  1301
            (map3 flat_corec_thms disc_corec_thmss disc_corec_iff_thmss sel_corec_thmss)
blanchet@56648
  1302
            mapss rel_injectss rel_distinctss setss;
blanchet@49479
  1303
blanchet@49342
  1304
        val common_notes =
blanchet@49591
  1305
          (if nn > 1 then
blanchet@51810
  1306
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1307
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1308
           else
blanchet@49591
  1309
             [])
blanchet@51780
  1310
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1311
blanchet@49212
  1312
        val notes =
blanchet@51780
  1313
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1314
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@55867
  1315
           (corecN, corec_thmss, K corec_attrs),
blanchet@55867
  1316
           (disc_corecN, disc_corec_thmss, K disc_corec_attrs),
blanchet@55867
  1317
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_corec_iff_attrs),
blanchet@55867
  1318
           (sel_corecN, sel_corec_thmss, K sel_corec_attrs),
blanchet@51780
  1319
           (simpsN, simp_thmss, K []),
blanchet@55856
  1320
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs)]
blanchet@51780
  1321
          |> massage_multi_notes;
blanchet@49212
  1322
      in
blanchet@51824
  1323
        lthy
blanchet@55864
  1324
        (* TODO: code theorems *)
blanchet@55867
  1325
        |> fold (curry (Spec_Rules.add Spec_Rules.Equational) corecs)
blanchet@55864
  1326
          [flat sel_corec_thmss, flat corec_thmss]
blanchet@54030
  1327
        |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@56648
  1328
        |> register_as_fp_sugars fpTs fpBTs Xs Greatest_FP pre_bnfs absT_infos nested_bnfs
blanchet@56648
  1329
          nesting_bnfs fp_res ctrXs_Tsss ctr_defss ctr_sugars corecs corec_defs mapss
blanchet@56648
  1330
          [coinduct_thm, strong_coinduct_thm] (transpose [coinduct_thms, strong_coinduct_thms])
blanchet@56648
  1331
          corec_thmss disc_corec_thmss sel_corec_thmsss rel_injectss rel_distinctss
blanchet@49212
  1332
      end;
blanchet@49212
  1333
blanchet@52367
  1334
    val lthy'' = lthy'
blanchet@52968
  1335
      |> fold_map define_ctrs_dtrs_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ ctors ~~ dtors ~~
blanchet@55867
  1336
        xtor_co_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~ pre_set_defss ~~
blanchet@55867
  1337
        pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~ kss ~~ mss ~~
blanchet@55867
  1338
        abss ~~ abs_injects ~~ abs_inverses ~~ type_definitions ~~ ctr_bindingss ~~ ctr_mixfixess ~~
blanchet@55867
  1339
        ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
blanchet@51835
  1340
      |> wrap_types_etc
blanchet@55966
  1341
      |> case_fp fp derive_note_induct_recs_thms_for_types
blanchet@55867
  1342
           derive_note_coinduct_corecs_thms_for_types;
blanchet@49167
  1343
blanchet@49167
  1344
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@52899
  1345
      co_prefix fp ^ "datatype"));
blanchet@49112
  1346
  in
blanchet@52367
  1347
    timer; lthy''
blanchet@49112
  1348
  end;
blanchet@49112
  1349
wenzelm@53974
  1350
fun co_datatypes x = define_co_datatypes (K I) (K I) (K I) x;
blanchet@49297
  1351
wenzelm@53974
  1352
fun co_datatype_cmd x =
wenzelm@53974
  1353
  define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term x;
blanchet@49119
  1354
blanchet@55469
  1355
val parse_ctr_arg =
blanchet@55469
  1356
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
blanchet@55469
  1357
  (Parse.typ >> pair Binding.empty);
blanchet@55469
  1358
blanchet@55469
  1359
val parse_ctr_specs =
blanchet@55469
  1360
  Parse.enum1 "|" (parse_ctr_spec parse_binding parse_ctr_arg -- Parse.opt_mixfix);
blanchet@51767
  1361
blanchet@51767
  1362
val parse_spec =
blanchet@51790
  1363
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@55469
  1364
  Parse.opt_mixfix -- (@{keyword "="} |-- parse_ctr_specs);
blanchet@51767
  1365
blanchet@55469
  1366
val parse_co_datatype = parse_ctr_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1367
blanchet@52207
  1368
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
blanchet@49112
  1369
kuncar@56522
  1370
val _ = Context.>> (Context.map_theory FP_Sugar_Interpretation.init);
kuncar@56522
  1371
blanchet@49112
  1372
end;