src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Thu May 02 10:11:14 2013 +0200 (2013-05-02)
changeset 51855 fcdf213d332c
parent 51854 af63d7f52c02
child 51856 b3368771c3cc
permissions -rw-r--r--
more code rationalization
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(*  Title:      HOL/BNF/Tools/bnf_fp_def_sugar.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Sugared datatype and codatatype constructions.
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*)
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signature BNF_FP_DEF_SUGAR =
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sig
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  type fp_sugar =
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    {lfp: bool,
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     index: int,
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     pre_bnfs: BNF_Def.bnf list,
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     fp_res: BNF_FP_Util.fp_result,
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     ctr_sugars: BNF_Ctr_Sugar.ctr_sugar list,
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     xxfolds: term list,
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     xxrecs: term list,
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     xxfold_thmss: thm list list,
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     xxrec_thmss: thm list list};
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  val fp_sugar_of: local_theory -> string -> fp_sugar option
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  val indexify_fst: ''a list -> (int -> ''a * 'b -> 'c) -> ''a * 'b -> 'c
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  val build_map: local_theory -> (typ * typ -> term) -> typ * typ -> term
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  val mk_fp_iter_fun_types: term -> typ list
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  val mk_fun_arg_typess: int -> int list -> typ -> typ list list
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  val unzip_recT: typ list -> typ -> typ list * typ list
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  val mk_fold_fun_typess: typ list list list -> typ list list -> typ list list
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  val mk_rec_fun_typess: typ list -> typ list list list -> typ list list -> typ list list
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  val derive_induct_fold_rec_thms_for_types: BNF_Def.bnf list -> term list -> term list -> thm ->
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    thm list -> thm list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list ->
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    typ list -> term list list -> thm list list -> term list -> term list -> thm list -> thm list ->
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    local_theory ->
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    (thm * thm list * Args.src list) * (thm list list * Args.src list)
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    * (thm list list * Args.src list)
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  val derive_coinduct_unfold_corec_thms_for_types: BNF_Def.bnf list -> term list -> term list ->
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    thm -> thm -> thm list -> thm list -> thm list -> BNF_Def.bnf list -> BNF_Def.bnf list ->
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    typ list -> typ list -> typ list -> int list list -> int list list -> int list ->
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    thm list list -> BNF_Ctr_Sugar.ctr_sugar list -> term list -> term list -> thm list ->
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    thm list -> local_theory ->
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    (thm * thm list * thm * thm list * Args.src list)
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    * (thm list list * thm list list * Args.src list)
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    * (thm list list * thm list list) * (thm list list * thm list list * Args.src list)
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    * (thm list list * thm list list * Args.src list)
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    * (thm list list * thm list list * Args.src list)
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  val datatypes: bool ->
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    (mixfix list -> (string * sort) list option -> binding list -> binding list -> binding list ->
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      binding list list -> typ list * typ list list -> BNF_Def.bnf list -> local_theory ->
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      BNF_FP_Util.fp_result * local_theory) ->
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    (bool * bool) * (((((binding * (typ * sort)) list * binding) * (binding * binding)) * mixfix) *
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      ((((binding * binding) * (binding * typ) list) * (binding * term) list) *
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        mixfix) list) list ->
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    local_theory -> local_theory
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  val parse_datatype_cmd: bool ->
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    (mixfix list -> (string * sort) list option -> binding list -> binding list -> binding list ->
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      binding list list -> typ list * typ list list -> BNF_Def.bnf 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 BNF_Util
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open BNF_Ctr_Sugar
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open BNF_Def
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open BNF_FP_Util
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open BNF_FP_Def_Sugar_Tactics
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val EqN = "Eq_";
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type fp_sugar =
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  {lfp: bool,
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   index: int,
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   pre_bnfs: bnf list,
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   fp_res: fp_result,
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   ctr_sugars: ctr_sugar list,
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   xxfolds: term list,
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   xxrecs: term list,
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   xxfold_thmss: thm list list,
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   xxrec_thmss: thm list list};
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fun eq_fp_sugar ({lfp = lfp1, index = index1, fp_res = fp_res1, ...} : fp_sugar,
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    {lfp = lfp2, index = index2, fp_res = fp_res2, ...} : fp_sugar) =
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  lfp1 = lfp2 andalso index1 = index2 andalso eq_fp_result (fp_res1, fp_res2);
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fun morph_fp_sugar phi {lfp, index, pre_bnfs, fp_res, ctr_sugars, xxfolds, xxrecs, xxfold_thmss,
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    xxrec_thmss} =
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  {lfp = lfp, index = index, pre_bnfs = map (morph_bnf phi) pre_bnfs,
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   fp_res = morph_fp_result phi fp_res, ctr_sugars = map (morph_ctr_sugar phi) ctr_sugars,
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   xxfolds = map (Morphism.term phi) xxfolds, xxrecs = map (Morphism.term phi) xxrecs,
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   xxfold_thmss = map (map (Morphism.thm phi)) xxfold_thmss,
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   xxrec_thmss = map (map (Morphism.thm phi)) xxrec_thmss};
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structure Data = Generic_Data
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(
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  type T = fp_sugar Symtab.table;
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  val empty = Symtab.empty;
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  val extend = I;
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  val merge = Symtab.merge eq_fp_sugar;
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);
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val fp_sugar_of = Symtab.lookup o Data.get o Context.Proof;
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fun register_fp_sugar key fp_sugar =
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  Local_Theory.declaration {syntax = false, pervasive = true}
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    (fn phi => Data.map (Symtab.update_new (key, morph_fp_sugar phi fp_sugar)));
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fun register_fp_sugars lfp pre_bnfs (fp_res as {ctors, ...}) ctr_sugars xxfolds xxrecs xxfold_thmss
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    xxrec_thmss lthy =
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  (0, lthy)
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  |> fold (fn ctor => fn (kk, lthy) => (kk + 1,
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    register_fp_sugar (fp_name_of_ctor ctor) {lfp = lfp, index = kk,
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      pre_bnfs = pre_bnfs, fp_res = fp_res, ctr_sugars = ctr_sugars, xxfolds = xxfolds,
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      xxrecs = xxrecs, xxfold_thmss = xxfold_thmss, xxrec_thmss = xxrec_thmss} lthy)) ctors
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  |> snd;
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(* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A"). *)
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fun quasi_unambiguous_case_names names =
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  let
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    val ps = map (`Long_Name.base_name) names;
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    val dups = Library.duplicates (op =) (map fst ps);
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    fun underscore s =
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      let val ss = space_explode Long_Name.separator s in
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        space_implode "_" (drop (length ss - 2) ss)
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      end;
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  in
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    map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
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  end;
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val mp_conj = @{thm mp_conj};
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val simp_attrs = @{attributes [simp]};
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val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs;
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fun split_list4 [] = ([], [], [], [])
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  | split_list4 ((x1, x2, x3, x4) :: xs) =
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    let val (xs1, xs2, xs3, xs4) = split_list4 xs;
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    in (x1 :: xs1, x2 :: xs2, x3 :: xs3, x4 :: xs4) end;
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fun add_components_of_typ (Type (s, Ts)) =
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    fold add_components_of_typ Ts #> cons (Long_Name.base_name s)
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  | add_components_of_typ _ = I;
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fun base_name_of_typ T = space_implode "_" (add_components_of_typ T []);
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fun exists_subtype_in Ts = exists_subtype (member (op =) Ts);
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fun resort_tfree S (TFree (s, _)) = TFree (s, S);
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fun typ_subst_nonatomic inst (T as Type (s, Ts)) =
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    (case AList.lookup (op =) inst T of
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      NONE => Type (s, map (typ_subst_nonatomic inst) Ts)
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    | SOME T' => T')
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  | typ_subst_nonatomic inst T = the_default T (AList.lookup (op =) inst T);
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fun variant_types ss Ss ctxt =
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  let
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    val (tfrees, _) =
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      fold_map2 (fn s => fn S => Name.variant s #> apfst (rpair S)) ss Ss (Variable.names_of ctxt);
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    val ctxt' = fold (Variable.declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
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  in (tfrees, ctxt') end;
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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
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fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
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fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
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fun flat_rec unzipf xs =
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  let val ps = map unzipf xs in
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    (* The first line below gives the preferred order. The second line is for compatibility with the
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       old datatype package: *)
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(*
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    maps (op @) ps
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*)
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    maps fst ps @ maps snd ps
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  end;
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fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss);
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fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss
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  | flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
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    p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss;
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fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
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  Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
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fun flip_rels lthy n thm =
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  let
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    val Rs = Term.add_vars (prop_of thm) [];
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    val Rs' = rev (drop (length Rs - n) Rs);
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    val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs';
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  in
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    Drule.cterm_instantiate cRs thm
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  end;
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fun mk_ctor_or_dtor get_T Ts t =
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  let val Type (_, Ts0) = get_T (fastype_of t) in
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    Term.subst_atomic_types (Ts0 ~~ Ts) t
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  end;
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val mk_ctor = mk_ctor_or_dtor range_type;
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val mk_dtor = mk_ctor_or_dtor domain_type;
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fun mk_xxiter lfp Ts Us t =
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  let
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    val (bindings, body) = strip_type (fastype_of t);
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    val (f_Us, prebody) = split_last bindings;
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    val Type (_, Ts0) = if lfp then prebody else body;
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    val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
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  in
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    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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  end;
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val mk_fp_iter_fun_types = fst o split_last o binder_types o fastype_of;
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fun mk_fp_iter lfp As Cs fp_iters0 =
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  map (mk_xxiter lfp As Cs) fp_iters0
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  |> (fn ts => (ts, mk_fp_iter_fun_types (hd ts)));
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fun unzip_recT fpTs T =
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  let
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    fun project_recT proj =
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      let
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        fun project (Type (s as @{type_name prod}, Ts as [T, U])) =
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            if member (op =) fpTs T then proj (T, U) else Type (s, map project Ts)
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          | project (Type (s, Ts)) = Type (s, map project Ts)
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          | project T = T;
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      in project end;
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  in
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    if exists_subtype_in fpTs T then ([project_recT fst T], [project_recT snd T]) else ([T], [])
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  end;
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val massage_rec_fun_arg_typesss = map o map o flat_rec o unzip_recT;
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val mk_fold_fun_typess = map2 (map2 (curry (op --->)));
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val mk_rec_fun_typess = mk_fold_fun_typess oo massage_rec_fun_arg_typesss;
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fun mk_fun_arg_typess n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type;
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fun mk_fold_rec_terms_types fpTs Css ns mss ctor_fold_fun_Ts ctor_rec_fun_Ts lthy =
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  let
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    val y_Tsss = map3 mk_fun_arg_typess ns mss ctor_fold_fun_Ts;
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    val g_Tss = mk_fold_fun_typess y_Tsss Css;
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    val ((gss, ysss), lthy) =
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      lthy
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      |> mk_Freess "f" g_Tss
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      ||>> mk_Freesss "x" y_Tsss;
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    val z_Tsss = map3 mk_fun_arg_typess ns mss ctor_rec_fun_Ts;
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    val h_Tss = mk_rec_fun_typess fpTs z_Tsss Css;
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    val hss = map2 (map2 retype_free) h_Tss gss;
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    val zsss = map2 (map2 (map2 retype_free)) z_Tsss ysss;
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  in
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    (((gss, g_Tss, ysss), (hss, h_Tss, zsss)), lthy)
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  end;
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fun mk_unfold_corec_terms_types fpTs Cs ns mss dtor_unfold_fun_Ts dtor_corec_fun_Ts lthy =
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  let
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    (*avoid "'a itself" arguments in coiterators and corecursors*)
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    fun repair_arity [0] = [1]
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      | repair_arity ms = ms;
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    fun project_corecT proj =
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      let
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        fun project (Type (s as @{type_name sum}, Ts as [T, U])) =
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            if member (op =) fpTs T then proj (T, U) else Type (s, map project Ts)
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          | project (Type (s, Ts)) = Type (s, map project Ts)
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          | project T = T;
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      in project end;
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    fun unzip_corecT T =
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      if exists_subtype_in fpTs T then [project_corecT fst T, project_corecT snd T] else [T];
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    val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
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    fun mk_types maybe_unzipT fun_Ts =
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      let
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        val f_sum_prod_Ts = map range_type fun_Ts;
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        val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
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        val f_Tsss = map2 (map2 dest_tupleT o repair_arity) mss f_prod_Tss;
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        val f_Tssss =
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          map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
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        val q_Tssss =
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          map (map (map (fn [_] => [] | [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss;
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        val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
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   292
      in (q_Tssss, f_sum_prod_Ts, f_Tsss, f_Tssss, pf_Tss) end;
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   293
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   294
    val (r_Tssss, g_sum_prod_Ts, g_Tsss, g_Tssss, pg_Tss) = mk_types single dtor_unfold_fun_Ts;
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   295
    val (s_Tssss, h_sum_prod_Ts, h_Tsss, h_Tssss, ph_Tss) = mk_types unzip_corecT dtor_corec_fun_Ts;
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   296
blanchet@51829
   297
    val (((cs, pss), gssss), lthy) =
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   298
      lthy
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   299
      |> mk_Frees "a" Cs
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   300
      ||>> mk_Freess "p" p_Tss
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   301
      ||>> mk_Freessss "g" g_Tssss;
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   302
    val rssss = map (map (map (fn [] => []))) r_Tssss;
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   303
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   304
    val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
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   305
    val ((sssss, hssss_tl), lthy) =
blanchet@51829
   306
      lthy
blanchet@51829
   307
      |> mk_Freessss "q" s_Tssss
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   308
      ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
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   309
    val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
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   310
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   311
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   312
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   313
    fun mk_terms qssss fssss =
blanchet@51831
   314
      let
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   315
        val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
blanchet@51831
   316
        val cqssss = map2 (map o map o map o rapp) cs qssss;
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   317
        val cfssss = map2 (map o map o map o rapp) cs fssss;
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   318
      in (pfss, cqssss, cfssss) end;
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   319
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   320
    val unfold_terms = mk_terms rssss gssss;
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   321
    val corec_terms = mk_terms sssss hssss;
blanchet@51831
   322
  in
blanchet@51831
   323
    ((cs, cpss, (unfold_terms, (g_sum_prod_Ts, g_Tsss, pg_Tss)),
blanchet@51831
   324
      (corec_terms, (h_sum_prod_Ts, h_Tsss, ph_Tss))), lthy)
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   325
  end;
blanchet@51829
   326
blanchet@49536
   327
fun mk_map live Ts Us t =
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   328
  let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in
blanchet@49536
   329
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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   330
  end;
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   331
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   332
fun mk_rel live Ts Us t =
blanchet@49591
   333
  let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in
blanchet@49591
   334
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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   335
  end;
blanchet@49591
   336
blanchet@49585
   337
fun liveness_of_fp_bnf n bnf =
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   338
  (case T_of_bnf bnf of
blanchet@49585
   339
    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
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   340
  | _ => replicate n false);
blanchet@49536
   341
blanchet@49124
   342
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
blanchet@49119
   343
blanchet@49298
   344
fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
blanchet@49119
   345
blanchet@49298
   346
fun merge_type_args (As, As') =
blanchet@49298
   347
  if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
blanchet@49119
   348
blanchet@49591
   349
fun reassoc_conjs thm =
blanchet@49591
   350
  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
blanchet@49591
   351
  handle THM _ => thm;
blanchet@49591
   352
blanchet@51767
   353
fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs;
blanchet@51767
   354
fun type_binding_of ((((_, b), _), _), _) = b;
blanchet@51767
   355
fun map_binding_of (((_, (b, _)), _), _) = b;
blanchet@51767
   356
fun rel_binding_of (((_, (_, b)), _), _) = b;
blanchet@49181
   357
fun mixfix_of ((_, mx), _) = mx;
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   358
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
blanchet@49119
   359
blanchet@49286
   360
fun disc_of ((((disc, _), _), _), _) = disc;
blanchet@49286
   361
fun ctr_of ((((_, ctr), _), _), _) = ctr;
blanchet@49286
   362
fun args_of (((_, args), _), _) = args;
blanchet@49286
   363
fun defaults_of ((_, ds), _) = ds;
blanchet@49181
   364
fun ctr_mixfix_of (_, mx) = mx;
blanchet@49119
   365
blanchet@51855
   366
fun indexify_fst xs f (x, y) = f (find_index (curry (op =) x) xs) (x, y);
blanchet@51855
   367
blanchet@51854
   368
fun build_map lthy build_simple =
blanchet@51853
   369
  let
blanchet@51853
   370
    fun build (TU as (T, U)) =
blanchet@51853
   371
      if T = U then
blanchet@51853
   372
        id_const T
blanchet@51853
   373
      else
blanchet@51853
   374
        (case TU of
blanchet@51854
   375
          (Type (s, Ts), Type (s', Us)) =>
blanchet@51854
   376
          if s = s' then
blanchet@51854
   377
            let
blanchet@51854
   378
              val bnf = the (bnf_of lthy s);
blanchet@51854
   379
              val live = live_of_bnf bnf;
blanchet@51854
   380
              val mapx = mk_map live Ts Us (map_of_bnf bnf);
blanchet@51854
   381
              val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
blanchet@51854
   382
            in Term.list_comb (mapx, map build TUs') end
blanchet@51854
   383
          else
blanchet@51854
   384
            build_simple TU
blanchet@51853
   385
        | _ => build_simple TU);
blanchet@51853
   386
  in build end;
blanchet@51853
   387
blanchet@51808
   388
fun build_rel_step lthy build_arg (Type (s, Ts)) =
blanchet@51808
   389
  let
blanchet@51808
   390
    val bnf = the (bnf_of lthy s);
blanchet@51808
   391
    val live = live_of_bnf bnf;
blanchet@51808
   392
    val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
blanchet@51808
   393
    val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
blanchet@51808
   394
  in Term.list_comb (rel, map build_arg Ts') end;
blanchet@51808
   395
blanchet@51827
   396
fun derive_induct_fold_rec_thms_for_types pre_bnfs ctor_folds0 ctor_recs0 ctor_induct ctor_fold_thms
blanchet@51827
   397
    ctor_rec_thms nesting_bnfs nested_bnfs fpTs Cs As ctrss ctr_defss folds recs fold_defs rec_defs
blanchet@51827
   398
    lthy =
blanchet@51808
   399
  let
blanchet@51827
   400
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   401
blanchet@51815
   402
    val nn = length pre_bnfs;
blanchet@51827
   403
    val ns = map length ctr_Tsss;
blanchet@51827
   404
    val mss = map (map length) ctr_Tsss;
blanchet@51827
   405
    val Css = map2 replicate ns Cs;
blanchet@51815
   406
blanchet@51808
   407
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   408
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@51830
   409
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51808
   410
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
blanchet@51808
   411
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
blanchet@51810
   412
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51808
   413
blanchet@51816
   414
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   415
blanchet@51843
   416
    val (_, ctor_fold_fun_Ts) = mk_fp_iter true As Cs ctor_folds0;
blanchet@51843
   417
    val (_, ctor_rec_fun_Ts) = mk_fp_iter true As Cs ctor_recs0;
blanchet@51827
   418
blanchet@51835
   419
    val (((gss, _, _), (hss, _, _)), names_lthy0) =
blanchet@51835
   420
      mk_fold_rec_terms_types fpTs Css ns mss ctor_fold_fun_Ts ctor_rec_fun_Ts lthy;
blanchet@51827
   421
blanchet@51832
   422
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@51832
   423
      names_lthy0
blanchet@51808
   424
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   425
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   426
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   427
blanchet@51808
   428
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   429
blanchet@51808
   430
    fun mk_sets_nested bnf =
blanchet@51808
   431
      let
blanchet@51808
   432
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   433
        val lives = lives_of_bnf bnf;
blanchet@51808
   434
        val sets = sets_of_bnf bnf;
blanchet@51808
   435
        fun mk_set U =
blanchet@51808
   436
          (case find_index (curry (op =) U) lives of
blanchet@51808
   437
            ~1 => Term.dummy
blanchet@51808
   438
          | i => nth sets i);
blanchet@51808
   439
      in
blanchet@51808
   440
        (T_name, map mk_set Us)
blanchet@51808
   441
      end;
blanchet@51808
   442
blanchet@51808
   443
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   444
blanchet@51808
   445
    val (induct_thms, induct_thm) =
blanchet@51808
   446
      let
blanchet@51808
   447
        fun mk_set Ts t =
blanchet@51808
   448
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   449
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   450
          end;
blanchet@51808
   451
blanchet@51808
   452
        fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
blanchet@51808
   453
            (case find_index (curry (op =) T) fpTs of
blanchet@51808
   454
              ~1 =>
blanchet@51808
   455
              (case AList.lookup (op =) setss_nested T_name of
blanchet@51808
   456
                NONE => []
blanchet@51808
   457
              | SOME raw_sets0 =>
blanchet@51808
   458
                let
blanchet@51808
   459
                  val (Ts, raw_sets) =
blanchet@51808
   460
                    split_list (filter (exists_subtype_in fpTs o fst) (Ts0 ~~ raw_sets0));
blanchet@51808
   461
                  val sets = map (mk_set Ts0) raw_sets;
blanchet@51808
   462
                  val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@51808
   463
                  val xysets = map (pair x) (ys ~~ sets);
blanchet@51808
   464
                  val ppremss = map (mk_raw_prem_prems names_lthy') ys;
blanchet@51808
   465
                in
blanchet@51808
   466
                  flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@51808
   467
                end)
blanchet@51808
   468
            | kk => [([], (kk + 1, x))])
blanchet@51808
   469
          | mk_raw_prem_prems _ _ = [];
blanchet@51808
   470
blanchet@51808
   471
        fun close_prem_prem xs t =
blanchet@51808
   472
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   473
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   474
blanchet@51808
   475
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   476
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   477
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   478
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   479
blanchet@51808
   480
        fun mk_raw_prem phi ctr ctr_Ts =
blanchet@51808
   481
          let
blanchet@51808
   482
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@51808
   483
            val pprems = maps (mk_raw_prem_prems names_lthy') xs;
blanchet@51808
   484
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   485
blanchet@51808
   486
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   487
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   488
blanchet@51808
   489
        val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss;
blanchet@51808
   490
blanchet@51808
   491
        val goal =
blanchet@51808
   492
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@51808
   493
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@51808
   494
blanchet@51808
   495
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   496
blanchet@51814
   497
        val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@51808
   498
blanchet@51808
   499
        val thm =
blanchet@51808
   500
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51808
   501
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
blanchet@51808
   502
              pre_set_defss)
blanchet@51808
   503
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51808
   504
          |> Thm.close_derivation;
blanchet@51808
   505
      in
blanchet@51808
   506
        `(conj_dests nn) thm
blanchet@51808
   507
      end;
blanchet@51808
   508
blanchet@51808
   509
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@51808
   510
blanchet@51808
   511
    val (fold_thmss, rec_thmss) =
blanchet@51808
   512
      let
blanchet@51808
   513
        val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@51808
   514
        val gfolds = map (lists_bmoc gss) folds;
blanchet@51808
   515
        val hrecs = map (lists_bmoc hss) recs;
blanchet@51808
   516
blanchet@51843
   517
        fun mk_goal fss fiter xctr f xs fxs =
blanchet@51808
   518
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@51843
   519
            (mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   520
blanchet@51845
   521
        val mk_U = typ_subst_nonatomic (map2 pair fpTs Cs);
blanchet@51808
   522
blanchet@51843
   523
        fun unzip_iters fiters combine (x as Free (_, T)) =
blanchet@51808
   524
          if exists_subtype_in fpTs T then
blanchet@51855
   525
            combine (x, build_map lthy (indexify_fst fpTs (K o nth fiters)) (T, mk_U T) $ x)
blanchet@51808
   526
          else
blanchet@51808
   527
            ([x], []);
blanchet@51808
   528
blanchet@51843
   529
        val gxsss = map (map (flat_rec (unzip_iters gfolds (fn (_, t) => ([t], []))))) xsss;
blanchet@51843
   530
        val hxsss = map (map (flat_rec (unzip_iters hrecs (pairself single)))) xsss;
blanchet@51808
   531
blanchet@51808
   532
        val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
blanchet@51808
   533
        val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
blanchet@51808
   534
blanchet@51808
   535
        val fold_tacss =
blanchet@51843
   536
          map2 (map o mk_iter_tac pre_map_defs [] nesting_map_ids'' fold_defs) ctor_fold_thms
blanchet@51808
   537
            ctr_defss;
blanchet@51808
   538
        val rec_tacss =
blanchet@51843
   539
          map2 (map o mk_iter_tac pre_map_defs nested_map_comp's
blanchet@51814
   540
            (nested_map_ids'' @ nesting_map_ids'') rec_defs) ctor_rec_thms ctr_defss;
blanchet@51808
   541
blanchet@51808
   542
        fun prove goal tac =
blanchet@51808
   543
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   544
          |> Thm.close_derivation;
blanchet@51808
   545
      in
blanchet@51808
   546
        (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
blanchet@51808
   547
      end;
blanchet@51808
   548
blanchet@51808
   549
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   550
  in
blanchet@51810
   551
    ((induct_thm, induct_thms, [induct_case_names_attr]),
blanchet@51808
   552
     (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
blanchet@51808
   553
  end;
blanchet@51808
   554
blanchet@51829
   555
fun derive_coinduct_unfold_corec_thms_for_types pre_bnfs dtor_unfolds0 dtor_corecs0 dtor_coinduct
blanchet@51814
   556
    dtor_strong_induct dtor_ctors dtor_unfold_thms dtor_corec_thms nesting_bnfs nested_bnfs fpTs Cs
blanchet@51840
   557
    As kss mss ns ctr_defss ctr_sugars unfolds corecs unfold_defs corec_defs lthy =
blanchet@51810
   558
  let
blanchet@51815
   559
    val nn = length pre_bnfs;
blanchet@51815
   560
blanchet@51810
   561
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   562
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
   563
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51830
   564
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   565
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
blanchet@51810
   566
    val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs;
blanchet@51810
   567
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
blanchet@51810
   568
blanchet@51816
   569
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   570
blanchet@51843
   571
    val (_, dtor_unfold_fun_Ts) = mk_fp_iter false As Cs dtor_unfolds0;
blanchet@51843
   572
    val (_, dtor_corec_fun_Ts) = mk_fp_iter false As Cs dtor_corecs0;
blanchet@51829
   573
blanchet@51840
   574
    val ctrss = map (map (mk_ctr As) o #ctrs) ctr_sugars;
blanchet@51840
   575
    val discss = map (map (mk_disc_or_sel As) o #discs) ctr_sugars;
blanchet@51840
   576
    val selsss = map (map (map (mk_disc_or_sel As)) o #selss) ctr_sugars;
blanchet@51840
   577
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   578
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   579
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   580
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   581
blanchet@51831
   582
    val ((cs, cpss, ((pgss, crssss, cgssss), _), ((phss, csssss, chssss), _)), names_lthy0) =
blanchet@51835
   583
      mk_unfold_corec_terms_types fpTs Cs ns mss dtor_unfold_fun_Ts dtor_corec_fun_Ts lthy;
blanchet@51831
   584
blanchet@51810
   585
    val (((rs, us'), vs'), names_lthy) =
blanchet@51831
   586
      names_lthy0
blanchet@51810
   587
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   588
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   589
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   590
blanchet@51810
   591
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   592
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   593
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   594
blanchet@51810
   595
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   596
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   597
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   598
blanchet@51810
   599
    val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
blanchet@51810
   600
      let
blanchet@51810
   601
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   602
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   603
        val strong_rs =
blanchet@51810
   604
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   605
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   606
blanchet@51810
   607
        fun build_rel rs' T =
blanchet@51810
   608
          (case find_index (curry (op =) T) fpTs of
blanchet@51810
   609
            ~1 =>
blanchet@51810
   610
            if exists_subtype_in fpTs T then build_rel_step lthy (build_rel rs') T
blanchet@51810
   611
            else HOLogic.eq_const T
blanchet@51810
   612
          | kk => nth rs' kk);
blanchet@51810
   613
blanchet@51810
   614
        fun build_rel_app rs' usel vsel =
blanchet@51810
   615
          fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@51810
   616
blanchet@51810
   617
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@51810
   618
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   619
          (if null usels then
blanchet@51810
   620
             []
blanchet@51810
   621
           else
blanchet@51810
   622
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@51810
   623
                Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@51810
   624
blanchet@51810
   625
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@51810
   626
          Library.foldr1 HOLogic.mk_conj
blanchet@51810
   627
            (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@51810
   628
          handle List.Empty => @{term True};
blanchet@51810
   629
blanchet@51810
   630
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@51810
   631
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@51810
   632
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@51810
   633
blanchet@51810
   634
        val concl =
blanchet@51810
   635
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   636
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   637
               uvrs us vs));
blanchet@51810
   638
blanchet@51810
   639
        fun mk_goal rs' =
blanchet@51810
   640
          Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@51810
   641
            concl);
blanchet@51810
   642
blanchet@51810
   643
        val goal = mk_goal rs;
blanchet@51810
   644
        val strong_goal = mk_goal strong_rs;
blanchet@51810
   645
blanchet@51810
   646
        fun prove dtor_coinduct' goal =
blanchet@51810
   647
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51810
   648
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@51819
   649
              exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   650
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   651
          |> Thm.close_derivation;
blanchet@51810
   652
blanchet@51810
   653
        fun postproc nn thm =
blanchet@51810
   654
          Thm.permute_prems 0 nn
blanchet@51828
   655
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   656
          |> Drule.zero_var_indexes
blanchet@51810
   657
          |> `(conj_dests nn);
blanchet@51810
   658
      in
blanchet@51814
   659
        (postproc nn (prove dtor_coinduct goal), postproc nn (prove dtor_strong_induct strong_goal))
blanchet@51810
   660
      end;
blanchet@51810
   661
blanchet@51810
   662
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   663
      let
blanchet@51810
   664
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   665
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   666
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   667
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   668
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   669
      in
blanchet@51810
   670
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   671
      end;
blanchet@51810
   672
blanchet@51816
   673
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   674
    val coinduct_conclss =
blanchet@51810
   675
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   676
blanchet@51810
   677
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   678
blanchet@51810
   679
    val gunfolds = map (lists_bmoc pgss) unfolds;
blanchet@51810
   680
    val hcorecs = map (lists_bmoc phss) corecs;
blanchet@51810
   681
blanchet@51810
   682
    val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@51810
   683
      let
blanchet@51843
   684
        fun mk_goal pfss c cps fcoiter n k ctr m cfs' =
blanchet@51810
   685
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   686
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@51843
   687
               mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   688
blanchet@51845
   689
        val mk_U = typ_subst_nonatomic (map2 pair Cs fpTs);
blanchet@51810
   690
blanchet@51843
   691
        fun intr_coiters fcoiters [] [cf] =
blanchet@51810
   692
            let val T = fastype_of cf in
blanchet@51855
   693
              if exists_subtype_in Cs T then
blanchet@51855
   694
                build_map lthy (indexify_fst Cs (K o nth fcoiters)) (T, mk_U T) $ cf
blanchet@51855
   695
              else
blanchet@51855
   696
                cf
blanchet@51810
   697
            end
blanchet@51843
   698
          | intr_coiters fcoiters [cq] [cf, cf'] =
blanchet@51843
   699
            mk_If cq (intr_coiters fcoiters [] [cf]) (intr_coiters fcoiters [] [cf']);
blanchet@51810
   700
blanchet@51843
   701
        val crgsss = map2 (map2 (map2 (intr_coiters gunfolds))) crssss cgssss;
blanchet@51843
   702
        val cshsss = map2 (map2 (map2 (intr_coiters hcorecs))) csssss chssss;
blanchet@51810
   703
blanchet@51828
   704
        val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
blanchet@51828
   705
        val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
blanchet@51810
   706
blanchet@51810
   707
        fun mk_map_if_distrib bnf =
blanchet@51810
   708
          let
blanchet@51810
   709
            val mapx = map_of_bnf bnf;
blanchet@51810
   710
            val live = live_of_bnf bnf;
blanchet@51810
   711
            val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
blanchet@51810
   712
            val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
blanchet@51810
   713
            val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
blanchet@51810
   714
          in
blanchet@51810
   715
            Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
blanchet@51810
   716
              @{thm if_distrib}
blanchet@51810
   717
          end;
blanchet@51810
   718
blanchet@51810
   719
        val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
blanchet@51810
   720
blanchet@51810
   721
        val unfold_tacss =
blanchet@51843
   722
          map3 (map oo mk_coiter_tac unfold_defs [] [] nesting_map_ids'' [])
blanchet@51814
   723
            dtor_unfold_thms pre_map_defs ctr_defss;
blanchet@51810
   724
        val corec_tacss =
blanchet@51843
   725
          map3 (map oo mk_coiter_tac corec_defs nested_map_comps'' nested_map_comp's
blanchet@51810
   726
              (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
blanchet@51814
   727
            dtor_corec_thms pre_map_defs ctr_defss;
blanchet@51810
   728
blanchet@51810
   729
        fun prove goal tac =
blanchet@51815
   730
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   731
          |> Thm.close_derivation;
blanchet@51810
   732
blanchet@51810
   733
        val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@51810
   734
        val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
blanchet@51810
   735
blanchet@51810
   736
        val filter_safesss =
blanchet@51810
   737
          map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@51810
   738
            curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
blanchet@51810
   739
blanchet@51810
   740
        val safe_unfold_thmss = filter_safesss unfold_thmss;
blanchet@51810
   741
        val safe_corec_thmss = filter_safesss corec_thmss;
blanchet@51810
   742
      in
blanchet@51810
   743
        (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@51810
   744
      end;
blanchet@51810
   745
blanchet@51810
   746
    val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@51810
   747
      let
blanchet@51843
   748
        fun mk_goal c cps fcoiter n k disc =
blanchet@51843
   749
          mk_Trueprop_eq (disc $ (fcoiter $ c),
blanchet@51810
   750
            if n = 1 then @{const True}
blanchet@51810
   751
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   752
blanchet@51810
   753
        val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@51810
   754
        val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   755
blanchet@51828
   756
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   757
blanchet@51810
   758
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   759
blanchet@51810
   760
        val unfold_tacss =
blanchet@51843
   761
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@51810
   762
        val corec_tacss =
blanchet@51843
   763
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   764
blanchet@51810
   765
        fun prove goal tac =
blanchet@51810
   766
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51829
   767
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   768
          |> Thm.close_derivation;
blanchet@51810
   769
blanchet@51810
   770
        fun proves [_] [_] = []
blanchet@51810
   771
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   772
      in
blanchet@51828
   773
        (map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss)
blanchet@51810
   774
      end;
blanchet@51810
   775
blanchet@51810
   776
    val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@51810
   777
blanchet@51843
   778
    fun mk_disc_coiter_thms coiters discIs =
blanchet@51843
   779
      map (op RS) (filter_out (is_triv_discI o snd) (coiters ~~ discIs));
blanchet@51810
   780
blanchet@51843
   781
    val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss;
blanchet@51843
   782
    val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
blanchet@51810
   783
blanchet@51843
   784
    fun mk_sel_coiter_thm coiter_thm sel sel_thm =
blanchet@51810
   785
      let
blanchet@51810
   786
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   787
        val arg_cong' =
blanchet@51810
   788
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   789
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   790
          |> Thm.varifyT_global;
blanchet@51810
   791
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   792
      in
blanchet@51843
   793
        coiter_thm RS arg_cong' RS sel_thm'
blanchet@51810
   794
      end;
blanchet@51810
   795
blanchet@51843
   796
    fun mk_sel_coiter_thms coiterss =
blanchet@51843
   797
      map3 (map3 (map2 o mk_sel_coiter_thm)) coiterss selsss sel_thmsss |> map flat;
blanchet@51810
   798
blanchet@51843
   799
    val sel_unfold_thmss = mk_sel_coiter_thms unfold_thmss;
blanchet@51843
   800
    val sel_corec_thmss = mk_sel_coiter_thms corec_thmss;
blanchet@51810
   801
blanchet@51810
   802
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   803
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   804
    val coinduct_case_concl_attrs =
blanchet@51810
   805
      map2 (fn casex => fn concls =>
blanchet@51810
   806
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   807
        coinduct_cases coinduct_conclss;
blanchet@51810
   808
    val coinduct_case_attrs =
blanchet@51810
   809
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   810
  in
blanchet@51810
   811
    ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms, coinduct_case_attrs),
blanchet@51810
   812
     (unfold_thmss, corec_thmss, []),
blanchet@51810
   813
     (safe_unfold_thmss, safe_corec_thmss),
blanchet@51810
   814
     (disc_unfold_thmss, disc_corec_thmss, simp_attrs),
blanchet@51810
   815
     (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
blanchet@51810
   816
     (sel_unfold_thmss, sel_corec_thmss, simp_attrs))
blanchet@51810
   817
  end;
blanchet@51810
   818
blanchet@49633
   819
fun define_datatypes prepare_constraint prepare_typ prepare_term lfp construct_fp
blanchet@49633
   820
    (wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
blanchet@49112
   821
  let
blanchet@49298
   822
    (* TODO: sanity checks on arguments *)
blanchet@49298
   823
blanchet@49286
   824
    val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
blanchet@49278
   825
      else ();
blanchet@49278
   826
blanchet@49633
   827
    fun qualify mandatory fp_b_name =
blanchet@49633
   828
      Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
   829
blanchet@49367
   830
    val nn = length specs;
blanchet@49361
   831
    val fp_bs = map type_binding_of specs;
blanchet@49498
   832
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
   833
    val fp_common_name = mk_common_name fp_b_names;
blanchet@51758
   834
    val map_bs = map map_binding_of specs;
blanchet@51767
   835
    val rel_bs = map rel_binding_of specs;
blanchet@49298
   836
blanchet@51758
   837
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
   838
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
   839
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   840
      end;
blanchet@49298
   841
blanchet@51758
   842
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs;
blanchet@49298
   843
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@49298
   844
    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
blanchet@51758
   845
    val set_bss = map (map fst o type_args_named_constrained_of) specs;
blanchet@49119
   846
blanchet@49585
   847
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
   848
      no_defs_lthy0
blanchet@49298
   849
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@49585
   850
      |> mk_TFrees (length unsorted_As)
blanchet@49585
   851
      ||>> mk_TFrees nn
blanchet@49585
   852
      ||>> apfst (map TFree) o
blanchet@49585
   853
        variant_types (map (prefix "'") fp_b_names) (replicate nn HOLogic.typeS);
blanchet@49119
   854
blanchet@49298
   855
    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
blanchet@49298
   856
    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
blanchet@49298
   857
      locale and shadows an existing global type*)
blanchet@51768
   858
blanchet@51769
   859
    fun add_fake_type spec =
blanchet@51768
   860
      Sign.add_type no_defs_lthy (type_binding_of spec,
blanchet@51769
   861
        length (type_args_named_constrained_of spec), mixfix_of spec);
blanchet@51768
   862
blanchet@51769
   863
    val fake_thy = Theory.copy #> fold add_fake_type specs;
blanchet@49298
   864
    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
blanchet@49119
   865
blanchet@49182
   866
    fun mk_fake_T b =
blanchet@49121
   867
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49298
   868
        unsorted_As);
blanchet@49121
   869
blanchet@49302
   870
    val fake_Ts = map mk_fake_T fp_bs;
blanchet@49121
   871
blanchet@49181
   872
    val mixfixes = map mixfix_of specs;
blanchet@49119
   873
blanchet@49302
   874
    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
   875
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
   876
blanchet@49121
   877
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
   878
blanchet@49336
   879
    val disc_bindingss = map (map disc_of) ctr_specss;
blanchet@49336
   880
    val ctr_bindingss =
blanchet@49633
   881
      map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
blanchet@49121
   882
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49181
   883
    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
blanchet@49119
   884
blanchet@49336
   885
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
   886
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49286
   887
    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
blanchet@49286
   888
blanchet@49308
   889
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
   890
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@49298
   891
blanchet@49298
   892
    val _ = (case duplicates (op =) unsorted_As of [] => ()
blanchet@49298
   893
      | A :: _ => error ("Duplicate type parameter " ^
blanchet@49298
   894
          quote (Syntax.string_of_typ no_defs_lthy A)));
blanchet@49298
   895
blanchet@49183
   896
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@49298
   897
    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
blanchet@49165
   898
        [] => ()
blanchet@49342
   899
      | A' :: _ => error ("Extra type variable on right-hand side: " ^
blanchet@49204
   900
          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
blanchet@49165
   901
blanchet@49591
   902
    fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
   903
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
   904
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49591
   905
      | eq_fpT_check _ _ = false;
blanchet@49146
   906
blanchet@49204
   907
    fun freeze_fp (T as Type (s, Us)) =
blanchet@49591
   908
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@49591
   909
          ~1 => Type (s, map freeze_fp Us)
blanchet@49591
   910
        | kk => nth Xs kk)
blanchet@49204
   911
      | freeze_fp T = T;
blanchet@49121
   912
blanchet@49536
   913
    val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@49536
   914
    val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
blanchet@49119
   915
blanchet@49298
   916
    val fp_eqs =
blanchet@49536
   917
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsXs;
blanchet@49121
   918
blanchet@51839
   919
    val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0,
blanchet@51805
   920
           folds = fp_folds0, recs = fp_recs0, induct = fp_induct, strong_induct = fp_strong_induct,
blanchet@51805
   921
           dtor_ctors, ctor_dtors, ctor_injects, map_thms = fp_map_thms, set_thmss = fp_set_thmss,
blanchet@51805
   922
           rel_thms = fp_rel_thms, fold_thms = fp_fold_thms, rec_thms = fp_rec_thms}, lthy)) =
blanchet@51767
   923
      fp_bnf construct_fp fp_bs mixfixes map_bs rel_bs set_bss (map dest_TFree unsorted_As) fp_eqs
blanchet@51758
   924
        no_defs_lthy0;
blanchet@49585
   925
blanchet@49585
   926
    val timer = time (Timer.startRealTimer ());
blanchet@49121
   927
blanchet@49363
   928
    fun add_nesty_bnf_names Us =
blanchet@49226
   929
      let
blanchet@49226
   930
        fun add (Type (s, Ts)) ss =
blanchet@49226
   931
            let val (needs, ss') = fold_map add Ts ss in
blanchet@49226
   932
              if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@49226
   933
            end
blanchet@49363
   934
          | add T ss = (member (op =) Us T, ss);
blanchet@49226
   935
      in snd oo add end;
blanchet@49226
   936
blanchet@49363
   937
    fun nesty_bnfs Us =
blanchet@49536
   938
      map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssXs []);
blanchet@49363
   939
blanchet@49363
   940
    val nesting_bnfs = nesty_bnfs As;
blanchet@49536
   941
    val nested_bnfs = nesty_bnfs Xs;
blanchet@49226
   942
blanchet@49585
   943
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
   944
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
   945
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
   946
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@51766
   947
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@49585
   948
blanchet@49585
   949
    val live = live_of_bnf any_fp_bnf;
blanchet@49585
   950
blanchet@49585
   951
    val Bs =
blanchet@49585
   952
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
   953
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
   954
blanchet@49585
   955
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
   956
blanchet@49501
   957
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
   958
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
   959
blanchet@49501
   960
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
   961
blanchet@51780
   962
    fun massage_simple_notes base =
blanchet@51780
   963
      filter_out (null o #2)
blanchet@51780
   964
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
   965
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
   966
blanchet@51780
   967
    val massage_multi_notes =
blanchet@51780
   968
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
   969
        if forall null thmss then
blanchet@51780
   970
          []
blanchet@51780
   971
        else
blanchet@51780
   972
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@51780
   973
            ((qualify true fp_b_name (Binding.name thmN), attrs T_name),
blanchet@51780
   974
             [(thms, [])])) fp_b_names fpTs thmss);
blanchet@51780
   975
blanchet@49536
   976
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
blanchet@49203
   977
    val ns = map length ctr_Tsss;
blanchet@49212
   978
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
   979
    val mss = map (map length) ctr_Tsss;
blanchet@49203
   980
    val Css = map2 replicate ns Cs;
blanchet@49203
   981
blanchet@51843
   982
    val (fp_folds, fp_fold_fun_Ts) = mk_fp_iter lfp As Cs fp_folds0;
blanchet@51843
   983
    val (fp_recs, fp_rec_fun_Ts) = mk_fp_iter lfp As Cs fp_recs0;
blanchet@49210
   984
blanchet@51827
   985
    val (((fold_only, rec_only),
blanchet@51830
   986
          (cs, cpss, unfold_only as ((_, crssss, cgssss), (_, g_Tsss, _)),
blanchet@51830
   987
           corec_only as ((_, csssss, chssss), (_, h_Tsss, _)))), _) =
blanchet@49208
   988
      if lfp then
blanchet@51835
   989
        mk_fold_rec_terms_types fpTs Css ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy
blanchet@51832
   990
        |>> rpair ([], [], (([], [], []), ([], [], [])), (([], [], []), ([], [], [])))
blanchet@49208
   991
      else
blanchet@51835
   992
        mk_unfold_corec_terms_types fpTs Cs ns mss fp_fold_fun_Ts fp_rec_fun_Ts lthy
blanchet@51831
   993
        |>> pair (([], [], []), ([], [], []));
blanchet@49210
   994
blanchet@49585
   995
    fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@49585
   996
            fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@49585
   997
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@49585
   998
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   999
      let
blanchet@49498
  1000
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1001
blanchet@49501
  1002
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
  1003
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
  1004
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
  1005
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
  1006
blanchet@49593
  1007
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
  1008
          no_defs_lthy
blanchet@49501
  1009
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
  1010
          ||>> mk_Frees "f" case_Ts
blanchet@49370
  1011
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1012
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1013
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1014
blanchet@49498
  1015
        val u = Free (u', fpT);
blanchet@49121
  1016
blanchet@49585
  1017
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
  1018
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
  1019
blanchet@49129
  1020
        val ctr_rhss =
blanchet@49585
  1021
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
  1022
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
  1023
blanchet@49633
  1024
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
  1025
blanchet@49134
  1026
        val case_rhs =
blanchet@49498
  1027
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
  1028
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
  1029
blanchet@49201
  1030
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1031
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
  1032
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
  1033
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
  1034
          ||> `Local_Theory.restore;
blanchet@49121
  1035
blanchet@49121
  1036
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1037
blanchet@49121
  1038
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1039
        val ctr_defs' =
blanchet@49585
  1040
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1041
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
  1042
blanchet@49203
  1043
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1044
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
  1045
blanchet@49203
  1046
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1047
blanchet@49585
  1048
        fun wrap lthy =
blanchet@49123
  1049
          let
traytel@50170
  1050
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1051
              let
blanchet@49585
  1052
                val ctor_iff_dtor_thm =
blanchet@49585
  1053
                  let
blanchet@49585
  1054
                    val goal =
blanchet@49585
  1055
                      fold_rev Logic.all [w, u]
blanchet@49585
  1056
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1057
                  in
wenzelm@51551
  1058
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
  1059
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
  1060
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
  1061
                    |> Thm.close_derivation
blanchet@49585
  1062
                    |> Morphism.thm phi
blanchet@49585
  1063
                  end;
blanchet@49585
  1064
blanchet@49585
  1065
                val sumEN_thm' =
blanchet@49585
  1066
                  unfold_thms lthy @{thms all_unit_eq}
blanchet@49585
  1067
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
  1068
                       (mk_sumEN_balanced n))
blanchet@49585
  1069
                  |> Morphism.thm phi;
blanchet@49135
  1070
              in
blanchet@49585
  1071
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1072
              end;
blanchet@49135
  1073
blanchet@49585
  1074
            val inject_tacss =
blanchet@49585
  1075
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
  1076
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
  1077
blanchet@49585
  1078
            val half_distinct_tacss =
blanchet@49585
  1079
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
  1080
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1081
blanchet@49585
  1082
            val case_tacs =
blanchet@49585
  1083
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
  1084
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
  1085
blanchet@49585
  1086
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
  1087
blanchet@49585
  1088
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
  1089
          in
blanchet@51781
  1090
            wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
blanchet@51781
  1091
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
  1092
          end;
blanchet@49121
  1093
blanchet@51840
  1094
        fun derive_maps_sets_rels (ctr_sugar, lthy) =
blanchet@51835
  1095
          if live = 0 then
blanchet@51840
  1096
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1097
          else
blanchet@51835
  1098
            let
blanchet@51835
  1099
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1100
              val nones = replicate live NONE;
blanchet@49585
  1101
blanchet@51835
  1102
              val ctor_cong =
blanchet@51835
  1103
                if lfp then
blanchet@51835
  1104
                  Drule.dummy_thm
blanchet@51835
  1105
                else
blanchet@51835
  1106
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1107
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1108
                  end;
blanchet@49585
  1109
blanchet@51835
  1110
              fun mk_cIn ify =
blanchet@51835
  1111
                certify lthy o (not lfp ? curry (op $) (map_types ify ctor)) oo
blanchet@51835
  1112
                mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
  1113
blanchet@51835
  1114
              val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@51835
  1115
              val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
  1116
blanchet@51835
  1117
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1118
                fold_thms lthy [ctr_def']
blanchet@51835
  1119
                  (unfold_thms lthy (pre_map_def ::
blanchet@51835
  1120
                       (if lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@51835
  1121
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@51835
  1122
                        (if lfp then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1123
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1124
blanchet@51835
  1125
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1126
                fold_thms lthy [ctr_def']
blanchet@51835
  1127
                  (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@51835
  1128
                       (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@51835
  1129
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1130
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1131
blanchet@51835
  1132
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1133
blanchet@51835
  1134
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1135
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@51835
  1136
blanchet@51835
  1137
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1138
blanchet@51835
  1139
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1140
                fold_thms lthy ctr_defs'
blanchet@51835
  1141
                   (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@51835
  1142
                        (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@51835
  1143
                      (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1144
                |> postproc
blanchet@51835
  1145
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1146
blanchet@51835
  1147
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1148
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1149
blanchet@51835
  1150
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1151
blanchet@51835
  1152
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1153
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1154
                  cxIn cyIn;
blanchet@49121
  1155
blanchet@51835
  1156
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1157
                flip_rels lthy live thm
blanchet@51835
  1158
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1159
blanchet@51835
  1160
              val half_rel_distinct_thmss =
blanchet@51835
  1161
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1162
              val other_half_rel_distinct_thmss =
blanchet@51835
  1163
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1164
              val (rel_distinct_thms, _) =
blanchet@51835
  1165
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1166
blanchet@51835
  1167
              val notes =
blanchet@51835
  1168
                [(mapN, map_thms, code_simp_attrs),
blanchet@51835
  1169
                 (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@51835
  1170
                 (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@51835
  1171
                 (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51835
  1172
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1173
            in
blanchet@51840
  1174
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@51835
  1175
               lthy |> Local_Theory.notes notes |> snd)
blanchet@51835
  1176
            end;
blanchet@49585
  1177
blanchet@49585
  1178
        fun define_fold_rec no_defs_lthy =
blanchet@49134
  1179
          let
blanchet@49208
  1180
            val fpT_to_C = fpT --> C;
blanchet@49199
  1181
blanchet@51854
  1182
            fun build_prod_proj mk_proj = build_map lthy (mk_proj o fst);
blanchet@49670
  1183
blanchet@49681
  1184
            (* TODO: Avoid these complications; cf. corec case *)
blanchet@49672
  1185
            fun mk_U proj (Type (s as @{type_name prod}, Ts as [T', U])) =
blanchet@49672
  1186
                if member (op =) fpTs T' then proj (T', U) else Type (s, map (mk_U proj) Ts)
blanchet@49670
  1187
              | mk_U proj (Type (s, Ts)) = Type (s, map (mk_U proj) Ts)
blanchet@49670
  1188
              | mk_U _ T = T;
blanchet@49670
  1189
blanchet@51794
  1190
            fun unzip_rec (x as Free (_, T)) =
blanchet@51808
  1191
              if exists_subtype_in fpTs T then
blanchet@51794
  1192
                ([build_prod_proj fst_const (T, mk_U fst T) $ x],
blanchet@51794
  1193
                 [build_prod_proj snd_const (T, mk_U snd T) $ x])
blanchet@49670
  1194
              else
blanchet@51794
  1195
                ([x], []);
blanchet@49670
  1196
blanchet@51843
  1197
            fun mk_iter_arg f xs =
blanchet@51794
  1198
              mk_tupled_fun (HOLogic.mk_tuple xs) f (flat_rec unzip_rec xs);
blanchet@49670
  1199
blanchet@51843
  1200
            fun generate_iter (suf, ctor_iter, (fss, f_Tss, xsss)) =
blanchet@49215
  1201
              let
blanchet@49215
  1202
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49633
  1203
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49215
  1204
                val spec =
blanchet@49336
  1205
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@51843
  1206
                    Term.list_comb (ctor_iter,
blanchet@51843
  1207
                      map2 (mk_sum_caseN_balanced oo map2 mk_iter_arg) fss xsss));
blanchet@49336
  1208
              in (binding, spec) end;
blanchet@49199
  1209
blanchet@51843
  1210
            val iter_infos =
blanchet@49504
  1211
              [(foldN, fp_fold, fold_only),
blanchet@49215
  1212
               (recN, fp_rec, rec_only)];
blanchet@49215
  1213
blanchet@51843
  1214
            val (bindings, specs) = map generate_iter iter_infos |> split_list;
blanchet@49215
  1215
blanchet@49215
  1216
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
  1217
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
  1218
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
  1219
                #>> apsnd snd) bindings specs
blanchet@49199
  1220
              ||> `Local_Theory.restore;
blanchet@49201
  1221
blanchet@49201
  1222
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
  1223
blanchet@49504
  1224
            val [fold_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
  1225
blanchet@51843
  1226
            val [foldx, recx] = map (mk_xxiter lfp As Cs o Morphism.term phi) csts;
blanchet@49134
  1227
          in
blanchet@49693
  1228
            ((foldx, recx, fold_def, rec_def), lthy')
blanchet@49134
  1229
          end;
blanchet@49134
  1230
blanchet@49585
  1231
        fun define_unfold_corec no_defs_lthy =
blanchet@49210
  1232
          let
blanchet@49210
  1233
            val B_to_fpT = C --> fpT;
blanchet@49211
  1234
blanchet@51854
  1235
            fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@49683
  1236
blanchet@51843
  1237
            fun build_dtor_coiter_arg _ [] [cf] = cf
blanchet@51843
  1238
              | build_dtor_coiter_arg T [cq] [cf, cf'] =
blanchet@49683
  1239
                mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@49683
  1240
                  (build_sum_inj Inr_const (fastype_of cf', T) $ cf')
blanchet@49683
  1241
blanchet@51843
  1242
            val crgsss = map3 (map3 (map3 build_dtor_coiter_arg)) g_Tsss crssss cgssss;
blanchet@51843
  1243
            val cshsss = map3 (map3 (map3 build_dtor_coiter_arg)) h_Tsss csssss chssss;
blanchet@49683
  1244
blanchet@49276
  1245
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
  1246
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
  1247
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
  1248
blanchet@51843
  1249
            fun generate_coiter (suf, dtor_coiter, (cqfsss, ((pfss, _, _),
blanchet@51843
  1250
                (f_sum_prod_Ts, _, pf_Tss)))) =
blanchet@49211
  1251
              let
blanchet@49211
  1252
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49633
  1253
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49211
  1254
                val spec =
blanchet@49336
  1255
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@51843
  1256
                    Term.list_comb (dtor_coiter,
blanchet@49276
  1257
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49336
  1258
              in (binding, spec) end;
blanchet@49210
  1259
blanchet@51843
  1260
            val coiter_infos =
blanchet@49683
  1261
              [(unfoldN, fp_fold, (crgsss, unfold_only)),
blanchet@49683
  1262
               (corecN, fp_rec, (cshsss, corec_only))];
blanchet@49212
  1263
blanchet@51843
  1264
            val (bindings, specs) = map generate_coiter coiter_infos |> split_list;
blanchet@49211
  1265
blanchet@49211
  1266
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
  1267
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
  1268
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
  1269
                #>> apsnd snd) bindings specs
blanchet@49210
  1270
              ||> `Local_Theory.restore;
blanchet@49210
  1271
blanchet@49210
  1272
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
  1273
blanchet@49504
  1274
            val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
  1275
blanchet@51843
  1276
            val [unfold, corec] = map (mk_xxiter lfp As Cs o Morphism.term phi) csts;
blanchet@49210
  1277
          in
blanchet@49693
  1278
            ((unfold, corec, unfold_def, corec_def), lthy')
blanchet@49287
  1279
          end;
blanchet@49287
  1280
blanchet@51843
  1281
        fun massage_res (((maps_sets_rels, ctr_sugar), xxiter_res), lthy) =
blanchet@51843
  1282
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), xxiter_res), lthy);
blanchet@49119
  1283
      in
blanchet@51835
  1284
        (wrap
blanchet@51835
  1285
         #> derive_maps_sets_rels
blanchet@51835
  1286
         ##>> (if lfp then define_fold_rec else define_unfold_corec)
blanchet@51835
  1287
         #> massage_res, lthy')
blanchet@49119
  1288
      end;
blanchet@49167
  1289
blanchet@51835
  1290
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1291
      fold_map I wrap_types_etcs lthy
blanchet@51835
  1292
      |>> apsnd split_list4 o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@51835
  1293
        o split_list;
blanchet@49226
  1294
blanchet@49479
  1295
    val mk_simp_thmss =
blanchet@51843
  1296
      map7 (fn {injects, distincts, case_thms, ...} => fn xxfolds => fn xxrecs =>
blanchet@51835
  1297
        fn mapsx => fn rel_injects => fn rel_distincts => fn setss =>
blanchet@51843
  1298
          injects @ distincts @ case_thms @ xxrecs @ xxfolds @ mapsx @ rel_injects
blanchet@51835
  1299
          @ rel_distincts @ flat setss);
blanchet@49479
  1300
blanchet@51810
  1301
    fun derive_and_note_induct_fold_rec_thms_for_types
blanchet@51840
  1302
        ((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@51835
  1303
          (folds, recs, fold_defs, rec_defs)), lthy) =
blanchet@49202
  1304
      let
blanchet@51833
  1305
        val ((induct_thm, induct_thms, induct_attrs), (fold_thmss, fold_attrs),
blanchet@51808
  1306
             (rec_thmss, rec_attrs)) =
blanchet@51827
  1307
          derive_induct_fold_rec_thms_for_types pre_bnfs fp_folds0 fp_recs0 fp_induct fp_fold_thms
blanchet@51827
  1308
            fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs As ctrss ctr_defss folds recs fold_defs
blanchet@51827
  1309
            rec_defs lthy;
blanchet@49201
  1310
blanchet@51830
  1311
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1312
blanchet@51835
  1313
        val simp_thmss =
blanchet@51843
  1314
          mk_simp_thmss ctr_sugars fold_thmss rec_thmss mapsx rel_injects rel_distincts setss;
blanchet@49438
  1315
blanchet@49337
  1316
        val common_notes =
blanchet@51808
  1317
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1318
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1319
blanchet@49226
  1320
        val notes =
blanchet@51808
  1321
          [(foldN, fold_thmss, K fold_attrs),
blanchet@51810
  1322
           (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@51808
  1323
           (recN, rec_thmss, K rec_attrs),
blanchet@49585
  1324
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1325
          |> massage_multi_notes;
blanchet@49202
  1326
      in
blanchet@51824
  1327
        lthy
blanchet@51824
  1328
        |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@51845
  1329
        |> register_fp_sugars true pre_bnfs fp_res ctr_sugars folds recs fold_thmss rec_thmss
blanchet@49202
  1330
      end;
blanchet@49202
  1331
blanchet@51810
  1332
    fun derive_and_note_coinduct_unfold_corec_thms_for_types
blanchet@51840
  1333
        ((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@51835
  1334
          (unfolds, corecs, unfold_defs, corec_defs)), lthy) =
blanchet@49212
  1335
      let
blanchet@51810
  1336
        val ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms,
blanchet@51810
  1337
              coinduct_attrs),
blanchet@51843
  1338
             (unfold_thmss, corec_thmss, coiter_attrs),
blanchet@51810
  1339
             (safe_unfold_thmss, safe_corec_thmss),
blanchet@51843
  1340
             (disc_unfold_thmss, disc_corec_thmss, disc_coiter_attrs),
blanchet@51843
  1341
             (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_coiter_iff_attrs),
blanchet@51843
  1342
             (sel_unfold_thmss, sel_corec_thmss, sel_coiter_attrs)) =
blanchet@51829
  1343
          derive_coinduct_unfold_corec_thms_for_types pre_bnfs fp_folds0 fp_recs0 fp_induct
blanchet@51811
  1344
            fp_strong_induct dtor_ctors fp_fold_thms fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs As
blanchet@51840
  1345
            kss mss ns ctr_defss ctr_sugars unfolds corecs unfold_defs corec_defs lthy;
blanchet@49212
  1346
blanchet@51830
  1347
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1348
blanchet@51843
  1349
        fun flat_coiter_thms coiters disc_coiters sel_coiters =
blanchet@51843
  1350
          coiters @ disc_coiters @ sel_coiters;
blanchet@49479
  1351
blanchet@49479
  1352
        val simp_thmss =
blanchet@51840
  1353
          mk_simp_thmss ctr_sugars
blanchet@51843
  1354
            (map3 flat_coiter_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss)
blanchet@51843
  1355
            (map3 flat_coiter_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@51835
  1356
            mapsx rel_injects rel_distincts setss;
blanchet@49479
  1357
blanchet@49479
  1358
        val anonymous_notes =
blanchet@49504
  1359
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1360
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1361
blanchet@49342
  1362
        val common_notes =
blanchet@49591
  1363
          (if nn > 1 then
blanchet@51810
  1364
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1365
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1366
           else
blanchet@49591
  1367
             [])
blanchet@51780
  1368
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1369
blanchet@49212
  1370
        val notes =
blanchet@51780
  1371
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1372
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@51843
  1373
           (corecN, corec_thmss, K coiter_attrs),
blanchet@51843
  1374
           (disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
blanchet@51843
  1375
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1376
           (disc_unfoldN, disc_unfold_thmss, K disc_coiter_attrs),
blanchet@51843
  1377
           (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1378
           (sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
blanchet@51843
  1379
           (sel_unfoldN, sel_unfold_thmss, K sel_coiter_attrs),
blanchet@51780
  1380
           (simpsN, simp_thmss, K []),
blanchet@51810
  1381
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
blanchet@51843
  1382
           (unfoldN, unfold_thmss, K coiter_attrs)]
blanchet@51780
  1383
          |> massage_multi_notes;
blanchet@49212
  1384
      in
blanchet@51824
  1385
        lthy
blanchet@51824
  1386
        |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@51845
  1387
        |> register_fp_sugars false pre_bnfs fp_res ctr_sugars unfolds corecs unfold_thmss
blanchet@51845
  1388
          corec_thmss
blanchet@49212
  1389
      end;
blanchet@49212
  1390
blanchet@49204
  1391
    val lthy' = lthy
blanchet@49585
  1392
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@49585
  1393
        fp_folds ~~ fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@49585
  1394
        pre_set_defss ~~ pre_rel_defs ~~ fp_map_thms ~~ fp_set_thmss ~~ fp_rel_thms ~~ ns ~~ kss ~~
blanchet@49585
  1395
        mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
blanchet@49585
  1396
        raw_sel_defaultsss)
blanchet@51835
  1397
      |> wrap_types_etc
blanchet@51808
  1398
      |> (if lfp then derive_and_note_induct_fold_rec_thms_for_types
blanchet@51808
  1399
          else derive_and_note_coinduct_unfold_corec_thms_for_types);
blanchet@49167
  1400
blanchet@49167
  1401
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
  1402
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
  1403
  in
blanchet@49308
  1404
    timer; lthy'
blanchet@49112
  1405
  end;
blanchet@49112
  1406
blanchet@49536
  1407
val datatypes = define_datatypes (K I) (K I) (K I);
blanchet@49297
  1408
blanchet@51380
  1409
val datatype_cmd = define_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1410
blanchet@49112
  1411
val parse_ctr_arg =
blanchet@49329
  1412
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1413
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1414
blanchet@49286
  1415
val parse_defaults =
blanchet@49286
  1416
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1417
blanchet@51758
  1418
val parse_type_arg_constrained =
blanchet@51790
  1419
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1420
blanchet@51790
  1421
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1422
blanchet@51758
  1423
val parse_type_args_named_constrained =
blanchet@51758
  1424
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1425
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1426
  Scan.succeed [];
blanchet@51756
  1427
blanchet@51790
  1428
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1429
blanchet@51767
  1430
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1431
blanchet@51767
  1432
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51833
  1433
   that we don't want them to be highlighted everywhere. *)
blanchet@51767
  1434
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1435
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1436
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1437
blanchet@51767
  1438
val parse_map_rel_bindings =
blanchet@51767
  1439
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1440
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1441
  Scan.succeed no_map_rel;
blanchet@51767
  1442
blanchet@51767
  1443
val parse_ctr_spec =
blanchet@51790
  1444
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1445
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1446
blanchet@51767
  1447
val parse_spec =
blanchet@51790
  1448
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1449
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1450
blanchet@51767
  1451
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1452
blanchet@49585
  1453
fun parse_datatype_cmd lfp construct_fp = parse_datatype >> datatype_cmd lfp construct_fp;
blanchet@49112
  1454
blanchet@49112
  1455
end;