src/HOL/Codatatype/Tools/bnf_fp_sugar.ML
author blanchet
Fri Sep 21 15:53:29 2012 +0200 (2012-09-21)
changeset 49504 df9b897fb254
parent 49502 92a7c1842c78
child 49505 a944eefb67e6
permissions -rw-r--r--
renamed "iter"/"coiter" to "fold"/"unfold" (cf. Wadler)
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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 u f = Term.lambda u (HOLogic.mk_prod (u, f $ u));
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fun tack z_name (c, u) f =
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  let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in
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    Term.lambda z (mk_sum_case (Term.lambda u u, 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_b_names = map Binding.name_of fp_bs;
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    val fp_common_name = mk_common_name fp_b_names;
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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_name => map (Binding.qualify false fp_b_name o ctr_of)) fp_b_names 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, ((dtors0, ctors0, fp_folds0, fp_recs0, fp_induct, dtor_ctors, ctor_dtors,
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           ctor_injects, fp_fold_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_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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    val ctors = map (mk_ctor As) ctors0;
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    val dtors = map (mk_dtor As) dtors0;
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    val fpTs = map (domain_type o fastype_of) dtors;
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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_rec_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_folds as fp_fold1 :: _ = map (mk_rec_like As Cs) fp_folds0;
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    val fp_recs as fp_rec1 :: _ = map (mk_rec_like As Cs) fp_recs0;
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    val fp_fold_fun_Ts = fst (split_last (binder_types (fastype_of fp_fold1)));
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    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
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    val (((fold_only as (gss, _, _), rec_only as (hss, _, _)),
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          (zs, cs, cpss, unfold_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))),
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         names_lthy) =
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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_fold_fun_Ts;
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          val g_Tss = map2 (map2 (curry (op --->))) 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 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, lthy) =
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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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            ([], [], [], (([], []), ([], [])), (([], []), ([], [])))), lthy)
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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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          val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_fold_fun_Ts;
blanchet@49211
   291
blanchet@49484
   292
          val ((((Free (z, _), cs), pss), gssss), lthy) =
blanchet@49210
   293
            lthy
blanchet@49233
   294
            |> yield_singleton (mk_Frees "z") dummyT
blanchet@49233
   295
            ||>> mk_Frees "a" Cs
blanchet@49211
   296
            ||>> mk_Freess "p" p_Tss
blanchet@49275
   297
            ||>> mk_Freessss "g" g_Tssss;
blanchet@49275
   298
          val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@49274
   299
blanchet@49274
   300
          fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
blanchet@49274
   301
              if member (op =) Cs U then Us else [T]
blanchet@49274
   302
            | dest_corec_sumT T = [T];
blanchet@49274
   303
blanchet@49275
   304
          val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
blanchet@49210
   305
blanchet@49298
   306
          val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@49484
   307
          val ((sssss, hssss_tl), lthy) =
blanchet@49275
   308
            lthy
blanchet@49275
   309
            |> mk_Freessss "q" s_Tssss
blanchet@49275
   310
            ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@49275
   311
          val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@49211
   312
blanchet@49212
   313
          val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
blanchet@49212
   314
blanchet@49276
   315
          fun mk_preds_getters_join [] [cf] = cf
blanchet@49276
   316
            | mk_preds_getters_join [cq] [cf, cf'] =
blanchet@49276
   317
              mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
blanchet@49276
   318
blanchet@49275
   319
          fun mk_terms qssss fssss =
blanchet@49212
   320
            let
blanchet@49276
   321
              val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
blanchet@49275
   322
              val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
blanchet@49274
   323
              val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
blanchet@49276
   324
              val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
blanchet@49276
   325
            in (pfss, cqfsss) end;
blanchet@49210
   326
        in
blanchet@49484
   327
          (((([], [], []), ([], [], [])),
blanchet@49484
   328
            ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
blanchet@49484
   329
             (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss)))), lthy)
blanchet@49210
   330
        end;
blanchet@49210
   331
blanchet@49504
   332
    fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), ctor), dtor), fp_fold), fp_rec),
blanchet@49501
   333
          ctor_dtor), dtor_ctor), ctor_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), ctr_Tss),
blanchet@49370
   334
        disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   335
      let
blanchet@49498
   336
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
   337
blanchet@49501
   338
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
   339
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   340
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   341
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   342
blanchet@49498
   343
        val ((((w, fs), xss), u'), _) =
blanchet@49204
   344
          no_defs_lthy
blanchet@49501
   345
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
   346
          ||>> mk_Frees "f" case_Ts
blanchet@49370
   347
          ||>> mk_Freess "x" ctr_Tss
blanchet@49498
   348
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
   349
blanchet@49498
   350
        val u = Free (u', fpT);
blanchet@49121
   351
blanchet@49129
   352
        val ctr_rhss =
blanchet@49501
   353
          map2 (fn k => fn xs => fold_rev Term.lambda xs (ctor $
blanchet@49256
   354
            mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
blanchet@49121
   355
blanchet@49336
   356
        val case_binding = Binding.suffix_name ("_" ^ caseN) fp_b;
blanchet@49129
   357
blanchet@49134
   358
        val case_rhs =
blanchet@49498
   359
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
   360
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
   361
blanchet@49201
   362
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   363
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
   364
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
   365
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   366
          ||> `Local_Theory.restore;
blanchet@49121
   367
blanchet@49121
   368
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   369
blanchet@49121
   370
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49130
   371
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   372
blanchet@49203
   373
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   374
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   375
blanchet@49203
   376
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   377
blanchet@49135
   378
        fun exhaust_tac {context = ctxt, ...} =
blanchet@49123
   379
          let
blanchet@49501
   380
            val ctor_iff_dtor_thm =
blanchet@49135
   381
              let
blanchet@49135
   382
                val goal =
blanchet@49498
   383
                  fold_rev Logic.all [w, u]
blanchet@49501
   384
                    (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49135
   385
              in
blanchet@49135
   386
                Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49501
   387
                  mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49501
   388
                    (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49135
   389
                |> Thm.close_derivation
blanchet@49135
   390
                |> Morphism.thm phi
blanchet@49135
   391
              end;
blanchet@49135
   392
blanchet@49135
   393
            val sumEN_thm' =
blanchet@49504
   394
              unfold_thms lthy @{thms all_unit_eq}
blanchet@49255
   395
                (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49255
   396
                   (mk_sumEN_balanced n))
blanchet@49135
   397
              |> Morphism.thm phi;
blanchet@49123
   398
          in
blanchet@49501
   399
            mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49123
   400
          end;
blanchet@49121
   401
blanchet@49126
   402
        val inject_tacss =
blanchet@49205
   403
          map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49501
   404
              mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49126
   405
blanchet@49127
   406
        val half_distinct_tacss =
blanchet@49127
   407
          map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49501
   408
            mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss ctr_defs);
blanchet@49127
   409
blanchet@49130
   410
        val case_tacs =
blanchet@49130
   411
          map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49501
   412
            mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49121
   413
blanchet@49121
   414
        val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49134
   415
blanchet@49504
   416
        fun define_fold_rec (wrap_res, no_defs_lthy) =
blanchet@49134
   417
          let
blanchet@49208
   418
            val fpT_to_C = fpT --> C;
blanchet@49199
   419
blanchet@49504
   420
            fun generate_rec_like (suf, fp_rec_like, (fss, f_Tss, xssss)) =
blanchet@49215
   421
              let
blanchet@49215
   422
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49336
   423
                val binding = Binding.suffix_name ("_" ^ suf) fp_b;
blanchet@49215
   424
                val spec =
blanchet@49336
   425
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   426
                    Term.list_comb (fp_rec_like,
blanchet@49255
   427
                      map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
blanchet@49336
   428
              in (binding, spec) end;
blanchet@49199
   429
blanchet@49504
   430
            val rec_like_infos =
blanchet@49504
   431
              [(foldN, fp_fold, fold_only),
blanchet@49215
   432
               (recN, fp_rec, rec_only)];
blanchet@49215
   433
blanchet@49504
   434
            val (bindings, specs) = map generate_rec_like rec_like_infos |> split_list;
blanchet@49215
   435
blanchet@49215
   436
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   437
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   438
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   439
                #>> apsnd snd) bindings specs
blanchet@49199
   440
              ||> `Local_Theory.restore;
blanchet@49201
   441
blanchet@49201
   442
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   443
blanchet@49504
   444
            val [fold_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   445
blanchet@49504
   446
            val [foldx, recx] = map (mk_rec_like As Cs o Morphism.term phi) csts;
blanchet@49134
   447
          in
blanchet@49504
   448
            ((wrap_res, ctrs, foldx, recx, xss, ctr_defs, fold_def, rec_def), lthy)
blanchet@49134
   449
          end;
blanchet@49134
   450
blanchet@49504
   451
        fun define_unfold_corec (wrap_res, no_defs_lthy) =
blanchet@49210
   452
          let
blanchet@49210
   453
            val B_to_fpT = C --> fpT;
blanchet@49211
   454
blanchet@49276
   455
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
   456
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
   457
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
   458
blanchet@49504
   459
            fun generate_corec_like (suf, fp_rec_like, ((pfss, cqfsss), (f_sum_prod_Ts,
blanchet@49274
   460
                pf_Tss))) =
blanchet@49211
   461
              let
blanchet@49211
   462
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49336
   463
                val binding = Binding.suffix_name ("_" ^ suf) fp_b;
blanchet@49211
   464
                val spec =
blanchet@49336
   465
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   466
                    Term.list_comb (fp_rec_like,
blanchet@49276
   467
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49336
   468
              in (binding, spec) end;
blanchet@49210
   469
blanchet@49504
   470
            val corec_like_infos =
blanchet@49504
   471
              [(unfoldN, fp_fold, unfold_only),
blanchet@49215
   472
               (corecN, fp_rec, corec_only)];
blanchet@49212
   473
blanchet@49504
   474
            val (bindings, specs) = map generate_corec_like corec_like_infos |> split_list;
blanchet@49211
   475
blanchet@49211
   476
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   477
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   478
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   479
                #>> apsnd snd) bindings specs
blanchet@49210
   480
              ||> `Local_Theory.restore;
blanchet@49210
   481
blanchet@49210
   482
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   483
blanchet@49504
   484
            val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   485
blanchet@49504
   486
            val [unfold, corec] = map (mk_rec_like As Cs o Morphism.term phi) csts;
blanchet@49210
   487
          in
blanchet@49504
   488
            ((wrap_res, ctrs, unfold, corec, xss, ctr_defs, unfold_def, corec_def), lthy)
blanchet@49210
   489
          end;
blanchet@49286
   490
blanchet@49287
   491
        fun wrap lthy =
blanchet@49287
   492
          let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
blanchet@49336
   493
            wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_bindings, (sel_bindingss,
blanchet@49287
   494
              sel_defaultss))) lthy
blanchet@49287
   495
          end;
blanchet@49287
   496
blanchet@49504
   497
        val define_rec_likes = if lfp then define_fold_rec else define_unfold_corec;
blanchet@49119
   498
      in
blanchet@49504
   499
        ((wrap, define_rec_likes), lthy')
blanchet@49119
   500
      end;
blanchet@49167
   501
blanchet@49226
   502
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49342
   503
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49368
   504
    val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs;
blanchet@49363
   505
    val nesting_map_ids = map map_id_of_bnf nesting_bnfs;
blanchet@49226
   506
blanchet@49393
   507
    fun mk_map live Ts Us t =
blanchet@49426
   508
      let
blanchet@49426
   509
        val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last
blanchet@49426
   510
      in
blanchet@49214
   511
        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49214
   512
      end;
blanchet@49214
   513
blanchet@49437
   514
    fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
blanchet@49234
   515
      let
blanchet@49392
   516
        val bnf = the (bnf_of lthy s);
blanchet@49393
   517
        val live = live_of_bnf bnf;
blanchet@49393
   518
        val mapx = mk_map live Ts Us (map_of_bnf bnf);
blanchet@49393
   519
        val TUs = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
blanchet@49234
   520
        val args = map build_arg TUs;
blanchet@49234
   521
      in Term.list_comb (mapx, args) end;
blanchet@49234
   522
blanchet@49479
   523
    val mk_simp_thmss =
blanchet@49504
   524
      map3 (fn (_, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn rec_likes =>
blanchet@49504
   525
        injects @ distincts @ cases @ rec_likes @ rec_likes);
blanchet@49479
   526
blanchet@49504
   527
    fun derive_induct_fold_rec_thms_for_types ((wrap_ress, ctrss, folds, recs, xsss, ctr_defss,
blanchet@49504
   528
        fold_defs, rec_defs), lthy) =
blanchet@49202
   529
      let
blanchet@49498
   530
        val (((phis, phis'), us'), names_lthy) =
blanchet@49370
   531
          lthy
blanchet@49463
   532
          |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@49498
   533
          ||>> Variable.variant_fixes fp_b_names;
blanchet@49370
   534
blanchet@49498
   535
        val us = map2 (curry Free) us' fpTs;
blanchet@49370
   536
blanchet@49362
   537
        fun mk_sets_nested bnf =
blanchet@49362
   538
          let
blanchet@49362
   539
            val Type (T_name, Us) = T_of_bnf bnf;
blanchet@49362
   540
            val lives = lives_of_bnf bnf;
blanchet@49362
   541
            val sets = sets_of_bnf bnf;
blanchet@49362
   542
            fun mk_set U =
blanchet@49362
   543
              (case find_index (curry (op =) U) lives of
blanchet@49362
   544
                ~1 => Term.dummy
blanchet@49362
   545
              | i => nth sets i);
blanchet@49362
   546
          in
blanchet@49362
   547
            (T_name, map mk_set Us)
blanchet@49362
   548
          end;
blanchet@49362
   549
blanchet@49362
   550
        val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@49362
   551
blanchet@49337
   552
        val (induct_thms, induct_thm) =
blanchet@49337
   553
          let
blanchet@49362
   554
            fun mk_set Ts t =
blanchet@49362
   555
              let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@49362
   556
                Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49362
   557
              end;
blanchet@49362
   558
blanchet@49375
   559
            fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
blanchet@49361
   560
                (case find_index (curry (op =) T) fpTs of
blanchet@49362
   561
                  ~1 =>
blanchet@49362
   562
                  (case AList.lookup (op =) setss_nested T_name of
blanchet@49362
   563
                    NONE => []
blanchet@49362
   564
                  | SOME raw_sets0 =>
blanchet@49362
   565
                    let
blanchet@49362
   566
                      val (Ts, raw_sets) =
blanchet@49362
   567
                        split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
blanchet@49362
   568
                      val sets = map (mk_set Ts0) raw_sets;
blanchet@49362
   569
                      val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@49375
   570
                      val xysets = map (pair x) (ys ~~ sets);
blanchet@49375
   571
                      val ppremss = map (mk_raw_prem_prems names_lthy') ys;
blanchet@49362
   572
                    in
blanchet@49375
   573
                      flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@49362
   574
                    end)
blanchet@49376
   575
                | i => [([], (i + 1, x))])
blanchet@49375
   576
              | mk_raw_prem_prems _ _ = [];
blanchet@49342
   577
blanchet@49378
   578
            fun close_prem_prem xs t =
blanchet@49378
   579
              fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@49378
   580
                (rev (Term.add_frees t (map dest_Free xs @ phis'))))) t;
blanchet@49362
   581
blanchet@49378
   582
            fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@49378
   583
              close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@49376
   584
                  HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@49376
   585
                HOLogic.mk_Trueprop (nth phis (j - 1) $ x)));
blanchet@49375
   586
blanchet@49372
   587
            fun mk_raw_prem phi ctr ctr_Ts =
blanchet@49362
   588
              let
blanchet@49362
   589
                val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@49376
   590
                val pprems = maps (mk_raw_prem_prems names_lthy') xs;
blanchet@49378
   591
              in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@49342
   592
blanchet@49376
   593
            fun mk_prem (xs, raw_pprems, concl) =
blanchet@49378
   594
              fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@49368
   595
blanchet@49389
   596
            val raw_premss = map3 (map2 o mk_raw_prem) phis ctrss ctr_Tsss;
blanchet@49389
   597
blanchet@49361
   598
            val goal =
blanchet@49372
   599
              Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@49498
   600
                HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) phis us)));
blanchet@49368
   601
blanchet@49429
   602
            val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@49368
   603
blanchet@49501
   604
            val ctor_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@49342
   605
blanchet@49342
   606
            val induct_thm =
blanchet@49361
   607
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49501
   608
                mk_induct_tac ctxt ns mss kksss (flat ctr_defss) ctor_induct'
blanchet@49389
   609
                  nested_set_natural's pre_set_defss)
blanchet@49368
   610
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49337
   611
          in
blanchet@49367
   612
            `(conj_dests nn) induct_thm
blanchet@49337
   613
          end;
blanchet@49201
   614
blanchet@49438
   615
        (* TODO: Generate nicer names in case of clashes *)
blanchet@49437
   616
        val induct_cases = Datatype_Prop.indexify_names (maps (map base_name_of_ctr) ctrss);
blanchet@49437
   617
blanchet@49504
   618
        val (fold_thmss, rec_thmss) =
blanchet@49207
   619
          let
blanchet@49337
   620
            val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49504
   621
            val gfolds = map (lists_bmoc gss) folds;
blanchet@49337
   622
            val hrecs = map (lists_bmoc hss) recs;
blanchet@49337
   623
blanchet@49504
   624
            fun mk_goal fss frec_like xctr f xs fxs =
blanchet@49207
   625
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49504
   626
                (mk_Trueprop_eq (frec_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   627
blanchet@49504
   628
            fun build_call frec_likes maybe_tick (T, U) =
blanchet@49234
   629
              if T = U then
blanchet@49368
   630
                id_const T
blanchet@49234
   631
              else
blanchet@49234
   632
                (case find_index (curry (op =) T) fpTs of
blanchet@49504
   633
                  ~1 => build_map (build_call frec_likes maybe_tick) T U
blanchet@49504
   634
                | j => maybe_tick (nth us j) (nth frec_likes j));
blanchet@49233
   635
blanchet@49274
   636
            fun mk_U maybe_mk_prodT =
blanchet@49274
   637
              typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
blanchet@49214
   638
blanchet@49504
   639
            fun intr_calls frec_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
blanchet@49214
   640
              if member (op =) fpTs T then
blanchet@49504
   641
                maybe_cons x [build_call frec_likes (K I) (T, mk_U (K I) T) $ x]
blanchet@49362
   642
              else if exists_fp_subtype T then
blanchet@49504
   643
                [build_call frec_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
blanchet@49214
   644
              else
blanchet@49214
   645
                [x];
blanchet@49214
   646
blanchet@49504
   647
            val gxsss = map (map (maps (intr_calls gfolds (K I) (K I) (K I)))) xsss;
blanchet@49342
   648
            val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
blanchet@49204
   649
blanchet@49504
   650
            val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
blanchet@49484
   651
            val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   652
blanchet@49504
   653
            val fold_tacss =
blanchet@49504
   654
              map2 (map o mk_rec_like_tac pre_map_defs nesting_map_ids fold_defs) fp_fold_thms
blanchet@49363
   655
                ctr_defss;
blanchet@49203
   656
            val rec_tacss =
blanchet@49504
   657
              map2 (map o mk_rec_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms
blanchet@49363
   658
                ctr_defss;
blanchet@49484
   659
blanchet@49484
   660
            fun prove goal tac = Skip_Proof.prove lthy [] [] goal (tac o #context);
blanchet@49202
   661
          in
blanchet@49504
   662
            (map2 (map2 prove) fold_goalss fold_tacss,
blanchet@49484
   663
             map2 (map2 prove) rec_goalss rec_tacss)
blanchet@49202
   664
          end;
blanchet@49201
   665
blanchet@49504
   666
        val simp_thmss = mk_simp_thmss wrap_ress rec_thmss fold_thmss;
blanchet@49438
   667
blanchet@49437
   668
        val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@49437
   669
        fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name));
blanchet@49437
   670
blanchet@49450
   671
        (* TODO: Also note "recs", "simps", and "splits" if "nn > 1" (for compatibility with the
blanchet@49479
   672
           old package)? And for codatatypes as well? *)
blanchet@49337
   673
        val common_notes =
blanchet@49437
   674
          (if nn > 1 then [(inductN, [induct_thm], [induct_case_names_attr])] else [])
blanchet@49337
   675
          |> map (fn (thmN, thms, attrs) =>
blanchet@49479
   676
            ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49337
   677
blanchet@49226
   678
        val notes =
blanchet@49437
   679
          [(inductN, map single induct_thms,
blanchet@49437
   680
            fn T_name => [induct_case_names_attr, induct_type_attr T_name]),
blanchet@49504
   681
           (foldsN, fold_thmss, K (Code.add_default_eqn_attrib :: simp_attrs)),
blanchet@49438
   682
           (recsN, rec_thmss, K (Code.add_default_eqn_attrib :: simp_attrs)),
blanchet@49438
   683
           (simpsN, simp_thmss, K [])]
blanchet@49300
   684
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@49437
   685
            map3 (fn b => fn Type (T_name, _) => fn thms =>
blanchet@49437
   686
              ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs T_name),
blanchet@49437
   687
                [(thms, [])])) fp_bs fpTs thmss);
blanchet@49202
   688
      in
blanchet@49337
   689
        lthy |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@49202
   690
      end;
blanchet@49202
   691
blanchet@49504
   692
    fun derive_coinduct_unfold_corec_thms_for_types ((wrap_ress, ctrss, unfolds, corecs, _,
blanchet@49504
   693
        ctr_defss, unfold_defs, corec_defs), lthy) =
blanchet@49212
   694
      let
blanchet@49484
   695
        val discss = map (map (mk_disc_or_sel As) o #1) wrap_ress;
blanchet@49484
   696
        val selsss = map #2 wrap_ress;
blanchet@49484
   697
        val disc_thmsss = map #6 wrap_ress;
blanchet@49484
   698
        val discIss = map #7 wrap_ress;
blanchet@49484
   699
        val sel_thmsss = map #8 wrap_ress;
blanchet@49438
   700
blanchet@49498
   701
        val (us', _) =
blanchet@49370
   702
          lthy
blanchet@49498
   703
          |> Variable.variant_fixes fp_b_names;
blanchet@49370
   704
blanchet@49498
   705
        val us = map2 (curry Free) us' fpTs;
blanchet@49370
   706
blanchet@49337
   707
        val (coinduct_thms, coinduct_thm) =
blanchet@49337
   708
          let
blanchet@49337
   709
            val coinduct_thm = fp_induct;
blanchet@49337
   710
          in
blanchet@49367
   711
            `(conj_dests nn) coinduct_thm
blanchet@49337
   712
          end;
blanchet@49212
   713
blanchet@49484
   714
        fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@49484
   715
blanchet@49484
   716
        val z = the_single zs;
blanchet@49504
   717
        val gunfolds = map (lists_bmoc pgss) unfolds;
blanchet@49484
   718
        val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49484
   719
blanchet@49504
   720
        val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@49212
   721
          let
blanchet@49504
   722
            fun mk_goal pfss c cps fcorec_like n k ctr m cfs' =
blanchet@49212
   723
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49484
   724
                (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@49504
   725
                   mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
   726
blanchet@49504
   727
            fun build_call frec_likes maybe_tack (T, U) =
blanchet@49234
   728
              if T = U then
blanchet@49368
   729
                id_const T
blanchet@49234
   730
              else
blanchet@49234
   731
                (case find_index (curry (op =) U) fpTs of
blanchet@49504
   732
                  ~1 => build_map (build_call frec_likes maybe_tack) T U
blanchet@49504
   733
                | j => maybe_tack (nth cs j, nth us j) (nth frec_likes j));
blanchet@49233
   734
blanchet@49274
   735
            fun mk_U maybe_mk_sumT =
blanchet@49274
   736
              typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@49212
   737
blanchet@49504
   738
            fun intr_calls frec_likes maybe_mk_sumT maybe_tack cqf =
blanchet@49276
   739
              let val T = fastype_of cqf in
blanchet@49276
   740
                if exists_subtype (member (op =) Cs) T then
blanchet@49504
   741
                  build_call frec_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
blanchet@49276
   742
                else
blanchet@49276
   743
                  cqf
blanchet@49276
   744
              end;
blanchet@49232
   745
blanchet@49504
   746
            val crgsss' = map (map (map (intr_calls gunfolds (K I) (K I)))) crgsss;
blanchet@49342
   747
            val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
blanchet@49212
   748
blanchet@49504
   749
            val unfold_goalss =
blanchet@49504
   750
              map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss';
blanchet@49484
   751
            val corec_goalss =
blanchet@49484
   752
              map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@49213
   753
blanchet@49504
   754
            val unfold_tacss =
blanchet@49504
   755
              map3 (map oo mk_corec_like_tac unfold_defs nesting_map_ids) fp_fold_thms pre_map_defs
blanchet@49226
   756
                ctr_defss;
blanchet@49233
   757
            val corec_tacss =
blanchet@49504
   758
              map3 (map oo mk_corec_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs
blanchet@49233
   759
                ctr_defss;
blanchet@49479
   760
blanchet@49484
   761
            fun prove goal tac =
blanchet@49484
   762
              Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation;
blanchet@49484
   763
blanchet@49504
   764
            val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@49479
   765
            val corec_thmss =
blanchet@49484
   766
              map2 (map2 prove) corec_goalss corec_tacss
blanchet@49504
   767
              |> map (map (unfold_thms lthy @{thms sum_case_if}));
blanchet@49479
   768
blanchet@49504
   769
            val unfold_safesss = map2 (map2 (map2 (curry (op =)))) crgsss' crgsss;
blanchet@49479
   770
            val corec_safesss = map2 (map2 (map2 (curry (op =)))) cshsss' cshsss;
blanchet@49479
   771
blanchet@49479
   772
            val filter_safesss =
blanchet@49479
   773
              map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@49479
   774
                curry (op ~~));
blanchet@49479
   775
blanchet@49504
   776
            val safe_unfold_thmss = filter_safesss unfold_safesss unfold_thmss;
blanchet@49479
   777
            val safe_corec_thmss = filter_safesss corec_safesss corec_thmss;
blanchet@49479
   778
          in
blanchet@49504
   779
            (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@49212
   780
          end;
blanchet@49212
   781
blanchet@49504
   782
        val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@49482
   783
          let
blanchet@49504
   784
            fun mk_goal c cps fcorec_like n k disc =
blanchet@49504
   785
              mk_Trueprop_eq (disc $ (fcorec_like $ c),
blanchet@49484
   786
                if n = 1 then @{const True}
blanchet@49484
   787
                else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@49484
   788
blanchet@49504
   789
            val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@49484
   790
            val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@49484
   791
blanchet@49484
   792
            fun mk_case_split' cp =
blanchet@49484
   793
              Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@49484
   794
blanchet@49484
   795
            val case_splitss' = map (map mk_case_split') cpss;
blanchet@49482
   796
blanchet@49504
   797
            val unfold_tacss =
blanchet@49504
   798
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@49484
   799
            val corec_tacss =
blanchet@49504
   800
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@49484
   801
blanchet@49484
   802
            fun prove goal tac =
blanchet@49484
   803
              Skip_Proof.prove lthy [] [] goal (tac o #context)
blanchet@49484
   804
              |> Thm.close_derivation
blanchet@49484
   805
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49484
   806
blanchet@49484
   807
            fun proves [_] [_] = []
blanchet@49484
   808
              | proves goals tacs = map2 prove goals tacs;
blanchet@49482
   809
          in
blanchet@49504
   810
            (map2 proves unfold_goalss unfold_tacss,
blanchet@49484
   811
             map2 proves corec_goalss corec_tacss)
blanchet@49482
   812
          end;
blanchet@49482
   813
blanchet@49504
   814
        fun mk_disc_corec_like_thms corec_likes discIs =
blanchet@49504
   815
          map (op RS) (filter_out (is_triv_implies o snd) (corec_likes ~~ discIs));
blanchet@49266
   816
blanchet@49504
   817
        val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss;
blanchet@49504
   818
        val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss;
blanchet@49266
   819
blanchet@49504
   820
        fun mk_sel_corec_like_thm corec_like_thm sel sel_thm =
blanchet@49266
   821
          let
blanchet@49479
   822
            val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@49266
   823
            val arg_cong' =
blanchet@49266
   824
              Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@49479
   825
                [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@49267
   826
              |> Thm.varifyT_global;
blanchet@49266
   827
            val sel_thm' = sel_thm RSN (2, trans);
blanchet@49266
   828
          in
blanchet@49504
   829
            corec_like_thm RS arg_cong' RS sel_thm'
blanchet@49266
   830
          end;
blanchet@49266
   831
blanchet@49504
   832
        fun mk_sel_corec_like_thms corec_likess =
blanchet@49504
   833
          map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss |> map flat;
blanchet@49479
   834
blanchet@49504
   835
        val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss;
blanchet@49504
   836
        val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss;
blanchet@49479
   837
blanchet@49504
   838
        fun zip_corec_like_thms corec_likes disc_corec_likes sel_corec_likes =
blanchet@49504
   839
          corec_likes @ disc_corec_likes @ sel_corec_likes;
blanchet@49479
   840
blanchet@49479
   841
        val simp_thmss =
blanchet@49479
   842
          mk_simp_thmss wrap_ress
blanchet@49504
   843
            (map3 zip_corec_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@49504
   844
            (map3 zip_corec_like_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss);
blanchet@49479
   845
blanchet@49479
   846
        val anonymous_notes =
blanchet@49504
   847
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
   848
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
   849
blanchet@49342
   850
        val common_notes =
blanchet@49367
   851
          (if nn > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else [])
blanchet@49342
   852
          |> map (fn (thmN, thms, attrs) =>
blanchet@49479
   853
            ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49342
   854
blanchet@49212
   855
        val notes =
blanchet@49342
   856
          [(coinductN, map single coinduct_thms, []), (* FIXME: attribs *)
blanchet@49504
   857
           (unfoldsN, unfold_thmss, []),
blanchet@49482
   858
           (corecsN, corec_thmss, []),
blanchet@49504
   859
           (disc_unfold_iffN, disc_unfold_iff_thmss, simp_attrs),
blanchet@49504
   860
           (disc_unfoldsN, disc_unfold_thmss, simp_attrs),
blanchet@49484
   861
           (disc_corec_iffN, disc_corec_iff_thmss, simp_attrs),
blanchet@49482
   862
           (disc_corecsN, disc_corec_thmss, simp_attrs),
blanchet@49504
   863
           (sel_unfoldsN, sel_unfold_thmss, simp_attrs),
blanchet@49479
   864
           (sel_corecsN, sel_corec_thmss, simp_attrs),
blanchet@49479
   865
           (simpsN, simp_thmss, [])]
blanchet@49300
   866
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@49266
   867
            map_filter (fn (_, []) => NONE | (b, thms) =>
blanchet@49300
   868
              SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
blanchet@49302
   869
                [(thms, [])])) (fp_bs ~~ thmss));
blanchet@49212
   870
      in
blanchet@49479
   871
        lthy |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@49212
   872
      end;
blanchet@49212
   873
blanchet@49504
   874
    fun wrap_types_and_define_rec_likes ((wraps, define_rec_likess), lthy) =
blanchet@49504
   875
      fold_map2 (curry (op o)) define_rec_likess wraps lthy |>> split_list8
blanchet@49287
   876
blanchet@49204
   877
    val lthy' = lthy
blanchet@49504
   878
      |> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~ fp_folds ~~
blanchet@49501
   879
        fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ ns ~~ kss ~~ mss ~~ ctr_bindingss ~~
blanchet@49370
   880
        ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
blanchet@49504
   881
      |>> split_list |> wrap_types_and_define_rec_likes
blanchet@49504
   882
      |> (if lfp then derive_induct_fold_rec_thms_for_types
blanchet@49504
   883
          else derive_coinduct_unfold_corec_thms_for_types);
blanchet@49167
   884
blanchet@49167
   885
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
   886
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
   887
  in
blanchet@49308
   888
    timer; lthy'
blanchet@49112
   889
  end;
blanchet@49112
   890
blanchet@49298
   891
val datatyp = define_datatype (K I) (K I) (K I);
blanchet@49297
   892
blanchet@49298
   893
val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
blanchet@49119
   894
blanchet@49112
   895
val parse_ctr_arg =
blanchet@49329
   896
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
   897
  (Parse.typ >> pair Binding.empty);
blanchet@49112
   898
blanchet@49286
   899
val parse_defaults =
blanchet@49286
   900
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
   901
blanchet@49112
   902
val parse_single_spec =
blanchet@49112
   903
  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
blanchet@49119
   904
  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
blanchet@49286
   905
    Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
blanchet@49112
   906
blanchet@49278
   907
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
blanchet@49278
   908
blanchet@49308
   909
fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;
blanchet@49112
   910
blanchet@49112
   911
end;