src/HOL/Codatatype/Tools/bnf_fp_sugar.ML
author blanchet
Thu Sep 20 13:32:48 2012 +0200 (2012-09-20)
changeset 49479 504f0a38f608
parent 49478 416ad6e2343b
child 49482 e6d6869eed08
permissions -rw-r--r--
added "simp"s to coiter/corec theorems + export under "simps" name
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(*  Title:      HOL/Codatatype/Tools/bnf_fp_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_SUGAR =
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sig
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  val datatyp: bool ->
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    (mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list ->
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      BNF_Def.BNF list -> local_theory ->
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      (term list * term list * term list * term list * thm * thm list * thm list * thm list *
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         thm list * thm list) * local_theory) ->
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    bool * ((((typ * sort) list * binding) * mixfix) * ((((binding * binding) *
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      (binding * typ) list) * (binding * term) list) * 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 -> typ list * typ list list ->
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      BNF_Def.BNF list -> local_theory ->
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      (term list * term list * term list * term list * thm * thm list * thm list * thm list *
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         thm list * thm list) * local_theory) ->
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    (local_theory -> local_theory) parser
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end;
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structure BNF_FP_Sugar : BNF_FP_SUGAR =
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struct
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open BNF_Util
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open BNF_Wrap
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open BNF_Def
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open BNF_FP
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open BNF_FP_Sugar_Tactics
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val simp_attrs = @{attributes [simp]};
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fun split_list8 xs =
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  (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs);
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fun resort_tfree S (TFree (s, _)) = TFree (s, S);
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fun typ_subst 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 inst) Ts)
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    | SOME T' => T')
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  | typ_subst inst T = the_default T (AList.lookup (op =) inst T);
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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
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fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
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fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
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fun mk_uncurried2_fun f xss =
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  mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
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fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
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fun tack z_name (c, v) f =
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  let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
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    Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
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  end;
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fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
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fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
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fun merge_type_args (As, As') =
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  if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
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fun is_triv_implies thm =
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  op aconv (Logic.dest_implies (Thm.prop_of thm))
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  handle TERM _ => false;
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fun type_args_constrained_of (((cAs, _), _), _) = cAs;
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fun type_binding_of (((_, b), _), _) = b;
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fun mixfix_of ((_, mx), _) = mx;
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fun ctr_specs_of (_, ctr_specs) = ctr_specs;
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fun disc_of ((((disc, _), _), _), _) = disc;
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fun ctr_of ((((_, ctr), _), _), _) = ctr;
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fun args_of (((_, args), _), _) = args;
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fun defaults_of ((_, ds), _) = ds;
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fun ctr_mixfix_of (_, mx) = mx;
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fun define_datatype prepare_constraint prepare_typ prepare_term lfp construct (no_dests, specs)
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    no_defs_lthy0 =
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  let
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    (* TODO: sanity checks on arguments *)
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    (* TODO: integration with function package ("size") *)
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    val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
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      else ();
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    val nn = length specs;
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    val fp_bs = map type_binding_of specs;
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    val fp_common_name = mk_common_name fp_bs;
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    fun prepare_type_arg (ty, c) =
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      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
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        TFree (s, prepare_constraint no_defs_lthy0 c)
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      end;
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    val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs;
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    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
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    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
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    val ((Bs, Cs), no_defs_lthy) =
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      no_defs_lthy0
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      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
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      |> mk_TFrees nn
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      ||>> mk_TFrees nn;
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    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
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    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
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      locale and shadows an existing global type*)
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    val fake_thy =
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      Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy
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        (type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
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    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
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    fun mk_fake_T b =
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      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
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        unsorted_As);
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    val fake_Ts = map mk_fake_T fp_bs;
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    val mixfixes = map mixfix_of specs;
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    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
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      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
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    val ctr_specss = map ctr_specs_of specs;
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    val disc_bindingss = map (map disc_of) ctr_specss;
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    val ctr_bindingss =
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      map2 (fn fp_b => map (Binding.qualify false (Binding.name_of fp_b) o ctr_of))
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        fp_bs ctr_specss;
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    val ctr_argsss = map (map args_of) ctr_specss;
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    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
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    val sel_bindingsss = map (map (map fst)) ctr_argsss;
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    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
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    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
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    val (As :: _) :: fake_ctr_Tsss =
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      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
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    val _ = (case duplicates (op =) unsorted_As of [] => ()
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      | A :: _ => error ("Duplicate type parameter " ^
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          quote (Syntax.string_of_typ no_defs_lthy A)));
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    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
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    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
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        [] => ()
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      | A' :: _ => error ("Extra type variable on right-hand side: " ^
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          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
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    fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
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        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
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          quote (Syntax.string_of_typ fake_lthy T)))
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      | eq_fpT _ _ = false;
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    fun freeze_fp (T as Type (s, Us)) =
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        (case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
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      | freeze_fp T = T;
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    val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
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    val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
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    val fp_eqs =
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      map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
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    val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, fp_induct, unf_flds, fld_unfs, fld_injects,
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        fp_iter_thms, fp_rec_thms), lthy)) =
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      fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
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    fun add_nesty_bnf_names Us =
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      let
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        fun add (Type (s, Ts)) ss =
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            let val (needs, ss') = fold_map add Ts ss in
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              if exists I needs then (true, insert (op =) s ss') else (false, ss')
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            end
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          | add T ss = (member (op =) Us T, ss);
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      in snd oo add end;
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    fun nesty_bnfs Us =
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      map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssBs []);
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    val nesting_bnfs = nesty_bnfs As;
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    val nested_bnfs = nesty_bnfs Bs;
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    val timer = time (Timer.startRealTimer ());
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    fun mk_unf_or_fld 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_unf = mk_unf_or_fld domain_type;
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    val mk_fld = mk_unf_or_fld range_type;
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    val unfs = map (mk_unf As) unfs0;
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    val flds = map (mk_fld As) flds0;
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    val fpTs = map (domain_type o fastype_of) unfs;
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    val exists_fp_subtype = exists_subtype (member (op =) fpTs);
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    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
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    val ns = map length ctr_Tsss;
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    val kss = map (fn n => 1 upto n) ns;
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    val mss = map (map length) ctr_Tsss;
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    val Css = map2 replicate ns Cs;
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    fun mk_iter_like 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 fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
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    val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
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    val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
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    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
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    val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
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         (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
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      if lfp then
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        let
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          val y_Tsss =
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            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
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              ns mss fp_iter_fun_Ts;
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          val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
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          val ((gss, ysss), _) =
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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 yssss = map (map (map single)) ysss;
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          fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
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              if member (op =) Cs U then Us else [T]
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            | dest_rec_prodT T = [T];
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          val z_Tssss =
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            map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
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              dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
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          val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
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          val hss = map2 (map2 retype_free) h_Tss gss;
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          val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
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          val (zssss_tl, _) =
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            lthy
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            |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
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          val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
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        in
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          (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
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           ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
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        end
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      else
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        let
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          (*avoid "'a itself" arguments in coiterators and corecursors*)
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          val mss' =  map (fn [0] => [1] | ms => ms) mss;
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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 zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
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          fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
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            | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
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              p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
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          fun mk_types maybe_dest_sumT 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_Tssss =
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                map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
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                  Cs mss' f_prod_Tss;
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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 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
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            in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
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   289
          val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
blanchet@49211
   290
blanchet@49275
   291
          val ((((Free (z, _), cs), pss), gssss), _) =
blanchet@49210
   292
            lthy
blanchet@49233
   293
            |> yield_singleton (mk_Frees "z") dummyT
blanchet@49233
   294
            ||>> mk_Frees "a" Cs
blanchet@49211
   295
            ||>> mk_Freess "p" p_Tss
blanchet@49275
   296
            ||>> mk_Freessss "g" g_Tssss;
blanchet@49275
   297
          val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@49274
   298
blanchet@49274
   299
          fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
blanchet@49274
   300
              if member (op =) Cs U then Us else [T]
blanchet@49274
   301
            | dest_corec_sumT T = [T];
blanchet@49274
   302
blanchet@49275
   303
          val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
blanchet@49210
   304
blanchet@49298
   305
          val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@49275
   306
          val ((sssss, hssss_tl), _) =
blanchet@49275
   307
            lthy
blanchet@49275
   308
            |> mk_Freessss "q" s_Tssss
blanchet@49275
   309
            ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@49275
   310
          val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@49211
   311
blanchet@49212
   312
          val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
blanchet@49212
   313
blanchet@49276
   314
          fun mk_preds_getters_join [] [cf] = cf
blanchet@49276
   315
            | mk_preds_getters_join [cq] [cf, cf'] =
blanchet@49276
   316
              mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
blanchet@49276
   317
blanchet@49275
   318
          fun mk_terms qssss fssss =
blanchet@49212
   319
            let
blanchet@49276
   320
              val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
blanchet@49275
   321
              val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
blanchet@49274
   322
              val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
blanchet@49276
   323
              val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
blanchet@49276
   324
            in (pfss, cqfsss) end;
blanchet@49210
   325
        in
blanchet@49212
   326
          ((([], [], []), ([], [], [])),
blanchet@49275
   327
           ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
blanchet@49275
   328
            (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
blanchet@49210
   329
        end;
blanchet@49210
   330
blanchet@49370
   331
    fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), fld), unf), fp_iter), fp_rec),
blanchet@49370
   332
          fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), ctr_Tss),
blanchet@49370
   333
        disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   334
      let
blanchet@49201
   335
        val unfT = domain_type (fastype_of fld);
blanchet@49210
   336
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   337
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   338
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   339
blanchet@49370
   340
        val ((((u, fs), xss), v'), _) =
blanchet@49204
   341
          no_defs_lthy
blanchet@49201
   342
          |> yield_singleton (mk_Frees "u") unfT
blanchet@49176
   343
          ||>> mk_Frees "f" case_Ts
blanchet@49370
   344
          ||>> mk_Freess "x" ctr_Tss
blanchet@49370
   345
          ||>> yield_singleton (Variable.variant_fixes) (Binding.name_of fp_b);
blanchet@49370
   346
blanchet@49370
   347
        val v = Free (v', fpT);
blanchet@49121
   348
blanchet@49129
   349
        val ctr_rhss =
blanchet@49256
   350
          map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
blanchet@49256
   351
            mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
blanchet@49121
   352
blanchet@49336
   353
        val case_binding = Binding.suffix_name ("_" ^ caseN) fp_b;
blanchet@49129
   354
blanchet@49134
   355
        val case_rhs =
blanchet@49255
   356
          fold_rev Term.lambda (fs @ [v])
blanchet@49255
   357
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
blanchet@49129
   358
blanchet@49201
   359
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   360
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
   361
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
   362
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   363
          ||> `Local_Theory.restore;
blanchet@49121
   364
blanchet@49121
   365
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   366
blanchet@49121
   367
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49130
   368
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   369
blanchet@49203
   370
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   371
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   372
blanchet@49203
   373
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   374
blanchet@49135
   375
        fun exhaust_tac {context = ctxt, ...} =
blanchet@49123
   376
          let
blanchet@49135
   377
            val fld_iff_unf_thm =
blanchet@49135
   378
              let
blanchet@49135
   379
                val goal =
blanchet@49135
   380
                  fold_rev Logic.all [u, v]
blanchet@49135
   381
                    (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
blanchet@49135
   382
              in
blanchet@49135
   383
                Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49201
   384
                  mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
blanchet@49176
   385
                    (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
blanchet@49135
   386
                |> Thm.close_derivation
blanchet@49135
   387
                |> Morphism.thm phi
blanchet@49135
   388
              end;
blanchet@49135
   389
blanchet@49135
   390
            val sumEN_thm' =
blanchet@49463
   391
              unfold_defs lthy @{thms all_unit_eq}
blanchet@49255
   392
                (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49255
   393
                   (mk_sumEN_balanced n))
blanchet@49135
   394
              |> Morphism.thm phi;
blanchet@49123
   395
          in
blanchet@49161
   396
            mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
blanchet@49123
   397
          end;
blanchet@49121
   398
blanchet@49126
   399
        val inject_tacss =
blanchet@49205
   400
          map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49205
   401
              mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
blanchet@49126
   402
blanchet@49127
   403
        val half_distinct_tacss =
blanchet@49127
   404
          map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49127
   405
            mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
blanchet@49127
   406
blanchet@49130
   407
        val case_tacs =
blanchet@49130
   408
          map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49130
   409
            mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
blanchet@49121
   410
blanchet@49121
   411
        val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49134
   412
blanchet@49438
   413
        fun define_iter_rec (wrap_res, no_defs_lthy) =
blanchet@49134
   414
          let
blanchet@49208
   415
            val fpT_to_C = fpT --> C;
blanchet@49199
   416
blanchet@49215
   417
            fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
blanchet@49215
   418
              let
blanchet@49215
   419
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49336
   420
                val binding = Binding.suffix_name ("_" ^ suf) fp_b;
blanchet@49215
   421
                val spec =
blanchet@49336
   422
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@49215
   423
                    Term.list_comb (fp_iter_like,
blanchet@49255
   424
                      map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
blanchet@49336
   425
              in (binding, spec) end;
blanchet@49199
   426
blanchet@49300
   427
            val iter_like_infos =
blanchet@49215
   428
              [(iterN, fp_iter, iter_only),
blanchet@49215
   429
               (recN, fp_rec, rec_only)];
blanchet@49215
   430
blanchet@49336
   431
            val (bindings, specs) = map generate_iter_like iter_like_infos |> split_list;
blanchet@49215
   432
blanchet@49215
   433
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   434
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   435
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   436
                #>> apsnd snd) bindings specs
blanchet@49199
   437
              ||> `Local_Theory.restore;
blanchet@49201
   438
blanchet@49201
   439
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   440
blanchet@49215
   441
            val [iter_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   442
blanchet@49215
   443
            val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49134
   444
          in
blanchet@49438
   445
            ((wrap_res, ctrs, iter, recx, xss, ctr_defs, iter_def, rec_def), lthy)
blanchet@49134
   446
          end;
blanchet@49134
   447
blanchet@49438
   448
        fun define_coiter_corec (wrap_res, no_defs_lthy) =
blanchet@49210
   449
          let
blanchet@49210
   450
            val B_to_fpT = C --> fpT;
blanchet@49211
   451
blanchet@49276
   452
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
   453
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
   454
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
   455
blanchet@49276
   456
            fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
blanchet@49274
   457
                pf_Tss))) =
blanchet@49211
   458
              let
blanchet@49211
   459
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49336
   460
                val binding = Binding.suffix_name ("_" ^ suf) fp_b;
blanchet@49211
   461
                val spec =
blanchet@49336
   462
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@49211
   463
                    Term.list_comb (fp_iter_like,
blanchet@49276
   464
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49336
   465
              in (binding, spec) end;
blanchet@49210
   466
blanchet@49300
   467
            val coiter_like_infos =
blanchet@49215
   468
              [(coiterN, fp_iter, coiter_only),
blanchet@49215
   469
               (corecN, fp_rec, corec_only)];
blanchet@49212
   470
blanchet@49336
   471
            val (bindings, specs) = map generate_coiter_like coiter_like_infos |> split_list;
blanchet@49211
   472
blanchet@49211
   473
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   474
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   475
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   476
                #>> apsnd snd) bindings specs
blanchet@49210
   477
              ||> `Local_Theory.restore;
blanchet@49210
   478
blanchet@49210
   479
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   480
blanchet@49211
   481
            val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   482
blanchet@49211
   483
            val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49210
   484
          in
blanchet@49438
   485
            ((wrap_res, ctrs, coiter, corec, xss, ctr_defs, coiter_def, corec_def), lthy)
blanchet@49210
   486
          end;
blanchet@49286
   487
blanchet@49287
   488
        fun wrap lthy =
blanchet@49287
   489
          let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
blanchet@49336
   490
            wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_bindings, (sel_bindingss,
blanchet@49287
   491
              sel_defaultss))) lthy
blanchet@49287
   492
          end;
blanchet@49287
   493
blanchet@49287
   494
        val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
blanchet@49119
   495
      in
blanchet@49287
   496
        ((wrap, define_iter_likes), lthy')
blanchet@49119
   497
      end;
blanchet@49167
   498
blanchet@49226
   499
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49342
   500
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49368
   501
    val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs;
blanchet@49363
   502
    val nesting_map_ids = map map_id_of_bnf nesting_bnfs;
blanchet@49226
   503
blanchet@49393
   504
    fun mk_map live Ts Us t =
blanchet@49426
   505
      let
blanchet@49426
   506
        val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last
blanchet@49426
   507
      in
blanchet@49214
   508
        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49214
   509
      end;
blanchet@49214
   510
blanchet@49437
   511
    fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
blanchet@49234
   512
      let
blanchet@49392
   513
        val bnf = the (bnf_of lthy s);
blanchet@49393
   514
        val live = live_of_bnf bnf;
blanchet@49393
   515
        val mapx = mk_map live Ts Us (map_of_bnf bnf);
blanchet@49393
   516
        val TUs = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
blanchet@49234
   517
        val args = map build_arg TUs;
blanchet@49234
   518
      in Term.list_comb (mapx, args) end;
blanchet@49234
   519
blanchet@49479
   520
    val mk_simp_thmss =
blanchet@49479
   521
      map3 (fn (_, injects, distincts, cases, _, _) => fn rec_likes => fn iter_likes =>
blanchet@49479
   522
        injects @ distincts @ cases @ rec_likes @ iter_likes);
blanchet@49479
   523
blanchet@49438
   524
    fun derive_induct_iter_rec_thms_for_types ((wrap_ress, ctrss, iters, recs, xsss, ctr_defss,
blanchet@49337
   525
        iter_defs, rec_defs), lthy) =
blanchet@49202
   526
      let
blanchet@49370
   527
        val (((phis, phis'), vs'), names_lthy) =
blanchet@49370
   528
          lthy
blanchet@49463
   529
          |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@49370
   530
          ||>> Variable.variant_fixes (map Binding.name_of fp_bs);
blanchet@49370
   531
blanchet@49370
   532
        val vs = map2 (curry Free) vs' fpTs;
blanchet@49370
   533
blanchet@49362
   534
        fun mk_sets_nested bnf =
blanchet@49362
   535
          let
blanchet@49362
   536
            val Type (T_name, Us) = T_of_bnf bnf;
blanchet@49362
   537
            val lives = lives_of_bnf bnf;
blanchet@49362
   538
            val sets = sets_of_bnf bnf;
blanchet@49362
   539
            fun mk_set U =
blanchet@49362
   540
              (case find_index (curry (op =) U) lives of
blanchet@49362
   541
                ~1 => Term.dummy
blanchet@49362
   542
              | i => nth sets i);
blanchet@49362
   543
          in
blanchet@49362
   544
            (T_name, map mk_set Us)
blanchet@49362
   545
          end;
blanchet@49362
   546
blanchet@49362
   547
        val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@49362
   548
blanchet@49337
   549
        val (induct_thms, induct_thm) =
blanchet@49337
   550
          let
blanchet@49362
   551
            fun mk_set Ts t =
blanchet@49362
   552
              let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@49362
   553
                Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49362
   554
              end;
blanchet@49362
   555
blanchet@49375
   556
            fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
blanchet@49361
   557
                (case find_index (curry (op =) T) fpTs of
blanchet@49362
   558
                  ~1 =>
blanchet@49362
   559
                  (case AList.lookup (op =) setss_nested T_name of
blanchet@49362
   560
                    NONE => []
blanchet@49362
   561
                  | SOME raw_sets0 =>
blanchet@49362
   562
                    let
blanchet@49362
   563
                      val (Ts, raw_sets) =
blanchet@49362
   564
                        split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
blanchet@49362
   565
                      val sets = map (mk_set Ts0) raw_sets;
blanchet@49362
   566
                      val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@49375
   567
                      val xysets = map (pair x) (ys ~~ sets);
blanchet@49375
   568
                      val ppremss = map (mk_raw_prem_prems names_lthy') ys;
blanchet@49362
   569
                    in
blanchet@49375
   570
                      flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@49362
   571
                    end)
blanchet@49376
   572
                | i => [([], (i + 1, x))])
blanchet@49375
   573
              | mk_raw_prem_prems _ _ = [];
blanchet@49342
   574
blanchet@49378
   575
            fun close_prem_prem xs t =
blanchet@49378
   576
              fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@49378
   577
                (rev (Term.add_frees t (map dest_Free xs @ phis'))))) t;
blanchet@49362
   578
blanchet@49378
   579
            fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@49378
   580
              close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@49376
   581
                  HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@49376
   582
                HOLogic.mk_Trueprop (nth phis (j - 1) $ x)));
blanchet@49375
   583
blanchet@49372
   584
            fun mk_raw_prem phi ctr ctr_Ts =
blanchet@49362
   585
              let
blanchet@49362
   586
                val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@49376
   587
                val pprems = maps (mk_raw_prem_prems names_lthy') xs;
blanchet@49378
   588
              in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@49342
   589
blanchet@49376
   590
            fun mk_prem (xs, raw_pprems, concl) =
blanchet@49378
   591
              fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@49368
   592
blanchet@49389
   593
            val raw_premss = map3 (map2 o mk_raw_prem) phis ctrss ctr_Tsss;
blanchet@49389
   594
blanchet@49361
   595
            val goal =
blanchet@49372
   596
              Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@49368
   597
                HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49368
   598
                  (map2 (curry (op $)) phis vs)));
blanchet@49368
   599
blanchet@49429
   600
            val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@49368
   601
blanchet@49368
   602
            val fld_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@49342
   603
blanchet@49342
   604
            val induct_thm =
blanchet@49361
   605
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49429
   606
                mk_induct_tac ctxt ns mss kksss (flat ctr_defss) fld_induct'
blanchet@49389
   607
                  nested_set_natural's pre_set_defss)
blanchet@49368
   608
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49337
   609
          in
blanchet@49367
   610
            `(conj_dests nn) induct_thm
blanchet@49337
   611
          end;
blanchet@49201
   612
blanchet@49438
   613
        (* TODO: Generate nicer names in case of clashes *)
blanchet@49437
   614
        val induct_cases = Datatype_Prop.indexify_names (maps (map base_name_of_ctr) ctrss);
blanchet@49437
   615
blanchet@49202
   616
        val (iter_thmss, rec_thmss) =
blanchet@49207
   617
          let
blanchet@49337
   618
            val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49337
   619
            val giters = map (lists_bmoc gss) iters;
blanchet@49337
   620
            val hrecs = map (lists_bmoc hss) recs;
blanchet@49337
   621
blanchet@49458
   622
            fun mk_iter_like_goal fss fiter_like xctr f xs fxs =
blanchet@49207
   623
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49212
   624
                (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   625
blanchet@49234
   626
            fun build_call fiter_likes maybe_tick (T, U) =
blanchet@49234
   627
              if T = U then
blanchet@49368
   628
                id_const T
blanchet@49234
   629
              else
blanchet@49234
   630
                (case find_index (curry (op =) T) fpTs of
blanchet@49234
   631
                  ~1 => build_map (build_call fiter_likes maybe_tick) T U
blanchet@49234
   632
                | j => maybe_tick (nth vs j) (nth fiter_likes j));
blanchet@49233
   633
blanchet@49274
   634
            fun mk_U maybe_mk_prodT =
blanchet@49274
   635
              typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
blanchet@49214
   636
blanchet@49342
   637
            fun intr_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
blanchet@49214
   638
              if member (op =) fpTs T then
blanchet@49233
   639
                maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
blanchet@49362
   640
              else if exists_fp_subtype T then
blanchet@49274
   641
                [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
blanchet@49214
   642
              else
blanchet@49214
   643
                [x];
blanchet@49214
   644
blanchet@49342
   645
            val gxsss = map (map (maps (intr_calls giters (K I) (K I) (K I)))) xsss;
blanchet@49342
   646
            val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
blanchet@49204
   647
blanchet@49458
   648
            val iterss_goal = map5 (map4 o mk_iter_like_goal gss) giters xctrss gss xsss gxsss;
blanchet@49458
   649
            val recss_goal = map5 (map4 o mk_iter_like_goal hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   650
blanchet@49203
   651
            val iter_tacss =
blanchet@49363
   652
              map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids iter_defs) fp_iter_thms
blanchet@49363
   653
                ctr_defss;
blanchet@49203
   654
            val rec_tacss =
blanchet@49363
   655
              map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms
blanchet@49363
   656
                ctr_defss;
blanchet@49202
   657
          in
blanchet@49276
   658
            (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49458
   659
               iterss_goal iter_tacss,
blanchet@49276
   660
             map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49458
   661
               recss_goal rec_tacss)
blanchet@49202
   662
          end;
blanchet@49201
   663
blanchet@49479
   664
        val simp_thmss = mk_simp_thmss wrap_ress rec_thmss iter_thmss;
blanchet@49438
   665
blanchet@49437
   666
        val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@49437
   667
        fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name));
blanchet@49437
   668
blanchet@49450
   669
        (* TODO: Also note "recs", "simps", and "splits" if "nn > 1" (for compatibility with the
blanchet@49479
   670
           old package)? And for codatatypes as well? *)
blanchet@49337
   671
        val common_notes =
blanchet@49437
   672
          (if nn > 1 then [(inductN, [induct_thm], [induct_case_names_attr])] else [])
blanchet@49337
   673
          |> map (fn (thmN, thms, attrs) =>
blanchet@49479
   674
            ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49337
   675
blanchet@49226
   676
        val notes =
blanchet@49437
   677
          [(inductN, map single induct_thms,
blanchet@49437
   678
            fn T_name => [induct_case_names_attr, induct_type_attr T_name]),
blanchet@49479
   679
           (itersN, iter_thmss, K (Code.add_default_eqn_attrib :: simp_attrs)),
blanchet@49438
   680
           (recsN, rec_thmss, K (Code.add_default_eqn_attrib :: simp_attrs)),
blanchet@49438
   681
           (simpsN, simp_thmss, K [])]
blanchet@49300
   682
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@49437
   683
            map3 (fn b => fn Type (T_name, _) => fn thms =>
blanchet@49437
   684
              ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs T_name),
blanchet@49437
   685
                [(thms, [])])) fp_bs fpTs thmss);
blanchet@49202
   686
      in
blanchet@49337
   687
        lthy |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@49202
   688
      end;
blanchet@49202
   689
blanchet@49438
   690
    fun derive_coinduct_coiter_corec_thms_for_types ((wrap_ress, ctrss, coiters, corecs, _,
blanchet@49438
   691
        ctr_defss, coiter_defs, corec_defs), lthy) =
blanchet@49212
   692
      let
blanchet@49479
   693
        val selsss = map #1 wrap_ress;
blanchet@49438
   694
        val discIss = map #5 wrap_ress;
blanchet@49438
   695
        val sel_thmsss = map #6 wrap_ress;
blanchet@49438
   696
blanchet@49372
   697
        val (vs', _) =
blanchet@49370
   698
          lthy
blanchet@49370
   699
          |> Variable.variant_fixes (map Binding.name_of fp_bs);
blanchet@49370
   700
blanchet@49370
   701
        val vs = map2 (curry Free) vs' fpTs;
blanchet@49370
   702
blanchet@49337
   703
        val (coinduct_thms, coinduct_thm) =
blanchet@49337
   704
          let
blanchet@49337
   705
            val coinduct_thm = fp_induct;
blanchet@49337
   706
          in
blanchet@49367
   707
            `(conj_dests nn) coinduct_thm
blanchet@49337
   708
          end;
blanchet@49212
   709
blanchet@49479
   710
        val (coiter_thmss, corec_thmss, safe_coiter_thmss, safe_corec_thmss) =
blanchet@49212
   711
          let
blanchet@49337
   712
            val z = the_single zs;
blanchet@49337
   713
            val gcoiters = map (lists_bmoc pgss) coiters;
blanchet@49337
   714
            val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49337
   715
blanchet@49458
   716
            fun mk_cond_goal pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
blanchet@49212
   717
blanchet@49458
   718
            fun mk_coiter_like_goal pfss c cps fcoiter_like n k ctr m cfs' =
blanchet@49212
   719
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49458
   720
                (Logic.list_implies (seq_conds mk_cond_goal n k cps,
blanchet@49276
   721
                   mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
   722
blanchet@49234
   723
            fun build_call fiter_likes maybe_tack (T, U) =
blanchet@49234
   724
              if T = U then
blanchet@49368
   725
                id_const T
blanchet@49234
   726
              else
blanchet@49234
   727
                (case find_index (curry (op =) U) fpTs of
blanchet@49234
   728
                  ~1 => build_map (build_call fiter_likes maybe_tack) T U
blanchet@49234
   729
                | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
blanchet@49233
   730
blanchet@49274
   731
            fun mk_U maybe_mk_sumT =
blanchet@49274
   732
              typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@49212
   733
blanchet@49342
   734
            fun intr_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
blanchet@49276
   735
              let val T = fastype_of cqf in
blanchet@49276
   736
                if exists_subtype (member (op =) Cs) T then
blanchet@49276
   737
                  build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
blanchet@49276
   738
                else
blanchet@49276
   739
                  cqf
blanchet@49276
   740
              end;
blanchet@49232
   741
blanchet@49342
   742
            val crgsss' = map (map (map (intr_calls gcoiters (K I) (K I)))) crgsss;
blanchet@49342
   743
            val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
blanchet@49212
   744
blanchet@49458
   745
            val coiterss_goal =
blanchet@49458
   746
              map8 (map4 oooo mk_coiter_like_goal pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
blanchet@49458
   747
            val corecss_goal =
blanchet@49458
   748
              map8 (map4 oooo mk_coiter_like_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@49213
   749
blanchet@49213
   750
            val coiter_tacss =
blanchet@49363
   751
              map3 (map oo mk_coiter_like_tac coiter_defs nesting_map_ids) fp_iter_thms pre_map_defs
blanchet@49226
   752
                ctr_defss;
blanchet@49233
   753
            val corec_tacss =
blanchet@49363
   754
              map3 (map oo mk_coiter_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs
blanchet@49233
   755
                ctr_defss;
blanchet@49479
   756
blanchet@49479
   757
            val coiter_thmss =
blanchet@49479
   758
              map2 (map2 (fn goal => fn tac =>
blanchet@49276
   759
                 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
blanchet@49479
   760
               coiterss_goal coiter_tacss;
blanchet@49479
   761
            val corec_thmss =
blanchet@49479
   762
              map2 (map2 (fn goal => fn tac =>
blanchet@49276
   763
                 Skip_Proof.prove lthy [] [] goal (tac o #context)
blanchet@49463
   764
                 |> unfold_defs lthy @{thms sum_case_if} |> Thm.close_derivation))
blanchet@49479
   765
               corecss_goal corec_tacss;
blanchet@49479
   766
blanchet@49479
   767
            val coiter_safesss = map2 (map2 (map2 (curry (op =)))) crgsss' crgsss;
blanchet@49479
   768
            val corec_safesss = map2 (map2 (map2 (curry (op =)))) cshsss' cshsss;
blanchet@49479
   769
blanchet@49479
   770
            val filter_safesss =
blanchet@49479
   771
              map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@49479
   772
                curry (op ~~));
blanchet@49479
   773
blanchet@49479
   774
            val safe_coiter_thmss = filter_safesss coiter_safesss coiter_thmss;
blanchet@49479
   775
            val safe_corec_thmss = filter_safesss corec_safesss corec_thmss;
blanchet@49479
   776
          in
blanchet@49479
   777
            (coiter_thmss, corec_thmss, safe_coiter_thmss, safe_corec_thmss)
blanchet@49212
   778
          end;
blanchet@49212
   779
blanchet@49479
   780
        fun mk_disc_coiter_like_thms coiter_likes discIs =
blanchet@49479
   781
          map (op RS) (filter_out (is_triv_implies o snd) (coiter_likes ~~ discIs));
blanchet@49266
   782
blanchet@49266
   783
        val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
blanchet@49266
   784
        val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
blanchet@49266
   785
blanchet@49479
   786
        fun mk_sel_coiter_like_thm coiter_like_thm sel sel_thm =
blanchet@49266
   787
          let
blanchet@49479
   788
            val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@49266
   789
            val arg_cong' =
blanchet@49266
   790
              Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@49479
   791
                [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@49267
   792
              |> Thm.varifyT_global;
blanchet@49266
   793
            val sel_thm' = sel_thm RSN (2, trans);
blanchet@49266
   794
          in
blanchet@49267
   795
            coiter_like_thm RS arg_cong' RS sel_thm'
blanchet@49266
   796
          end;
blanchet@49266
   797
blanchet@49479
   798
        fun mk_sel_coiter_like_thms coiter_likess =
blanchet@49479
   799
          map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_likess selsss sel_thmsss |> map flat;
blanchet@49479
   800
blanchet@49479
   801
        val sel_coiter_thmss = mk_sel_coiter_like_thms coiter_thmss;
blanchet@49479
   802
        val sel_corec_thmss = mk_sel_coiter_like_thms corec_thmss;
blanchet@49479
   803
blanchet@49479
   804
        fun zip_coiter_like_thms coiter_likes disc_coiter_likes sel_coiter_likes =
blanchet@49479
   805
          coiter_likes @ disc_coiter_likes @ sel_coiter_likes;
blanchet@49479
   806
blanchet@49479
   807
        val simp_thmss =
blanchet@49479
   808
          mk_simp_thmss wrap_ress
blanchet@49479
   809
            (map3 zip_coiter_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@49479
   810
            (map3 zip_coiter_like_thms safe_coiter_thmss disc_coiter_thmss sel_coiter_thmss);
blanchet@49479
   811
blanchet@49479
   812
        val anonymous_notes =
blanchet@49479
   813
          [(flat safe_coiter_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
   814
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
   815
blanchet@49342
   816
        val common_notes =
blanchet@49367
   817
          (if nn > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else [])
blanchet@49342
   818
          |> map (fn (thmN, thms, attrs) =>
blanchet@49479
   819
            ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49342
   820
blanchet@49212
   821
        val notes =
blanchet@49342
   822
          [(coinductN, map single coinduct_thms, []), (* FIXME: attribs *)
blanchet@49342
   823
           (coitersN, coiter_thmss, []),
blanchet@49479
   824
           (disc_coitersN, disc_coiter_thmss, simp_attrs),
blanchet@49479
   825
           (sel_coitersN, sel_coiter_thmss, simp_attrs),
blanchet@49300
   826
           (corecsN, corec_thmss, []),
blanchet@49479
   827
           (disc_corecsN, disc_corec_thmss, simp_attrs),
blanchet@49479
   828
           (sel_corecsN, sel_corec_thmss, simp_attrs),
blanchet@49479
   829
           (simpsN, simp_thmss, [])]
blanchet@49300
   830
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@49266
   831
            map_filter (fn (_, []) => NONE | (b, thms) =>
blanchet@49300
   832
              SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
blanchet@49302
   833
                [(thms, [])])) (fp_bs ~~ thmss));
blanchet@49212
   834
      in
blanchet@49479
   835
        lthy |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@49212
   836
      end;
blanchet@49212
   837
blanchet@49287
   838
    fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
blanchet@49438
   839
      fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list8
blanchet@49287
   840
blanchet@49204
   841
    val lthy' = lthy
blanchet@49370
   842
      |> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
blanchet@49370
   843
        fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_bindingss ~~
blanchet@49370
   844
        ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
blanchet@49287
   845
      |>> split_list |> wrap_types_and_define_iter_likes
blanchet@49337
   846
      |> (if lfp then derive_induct_iter_rec_thms_for_types
blanchet@49337
   847
          else derive_coinduct_coiter_corec_thms_for_types);
blanchet@49167
   848
blanchet@49167
   849
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
   850
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
   851
  in
blanchet@49308
   852
    timer; lthy'
blanchet@49112
   853
  end;
blanchet@49112
   854
blanchet@49298
   855
val datatyp = define_datatype (K I) (K I) (K I);
blanchet@49297
   856
blanchet@49298
   857
val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
blanchet@49119
   858
blanchet@49112
   859
val parse_ctr_arg =
blanchet@49329
   860
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
   861
  (Parse.typ >> pair Binding.empty);
blanchet@49112
   862
blanchet@49286
   863
val parse_defaults =
blanchet@49286
   864
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
   865
blanchet@49112
   866
val parse_single_spec =
blanchet@49112
   867
  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
blanchet@49119
   868
  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
blanchet@49286
   869
    Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
blanchet@49112
   870
blanchet@49278
   871
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
blanchet@49278
   872
blanchet@49308
   873
fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;
blanchet@49112
   874
blanchet@49112
   875
end;