src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Tue Oct 02 01:00:18 2012 +0200 (2012-10-02)
changeset 49681 aa66ea552357
parent 49672 902b24e0ffb4
child 49682 f57af1c46f99
permissions -rw-r--r--
changed type of corecursor for the nested recursion case
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(*  Title:      HOL/BNF/Tools/bnf_fp_def_sugar.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Sugared datatype and codatatype constructions.
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*)
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signature BNF_FP_DEF_SUGAR =
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sig
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  val datatypes: 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 -> BNF_FP.fp_result * local_theory) ->
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    (bool * 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 -> BNF_FP.fp_result * local_theory) ->
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    (local_theory -> local_theory) parser
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end;
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structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
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struct
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open BNF_Util
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open BNF_Wrap
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open BNF_Def
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open BNF_FP
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open BNF_FP_Def_Sugar_Tactics
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(* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A") *)
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fun quasi_unambiguous_case_names names =
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  let
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    val ps = map (`Long_Name.base_name) names;
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    val dups = Library.duplicates (op =) (map fst ps);
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    fun underscore s =
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      let val ss = space_explode Long_Name.separator s in
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        space_implode "_" (drop (length ss - 2) ss)
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      end;
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  in
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    map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
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  end;
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val mp_conj = @{thm mp_conj};
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val simp_attrs = @{attributes [simp]};
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val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs;
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fun split_list4 xs = (map #1 xs, map #2 xs, map #3 xs, map #4 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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fun variant_types ss Ss ctxt =
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  let
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    val (tfrees, _) =
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      fold_map2 (fn s => fn S => Name.variant s #> apfst (rpair S)) ss Ss (Variable.names_of ctxt);
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    val ctxt' = fold (Variable.declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
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  in (tfrees, ctxt') end;
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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
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fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
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fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
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fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
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  Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
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fun flip_rels lthy n thm =
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  let
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    val Rs = Term.add_vars (prop_of thm) [];
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    val Rs' = rev (drop (length Rs - n) Rs);
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    val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs';
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  in
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    Drule.cterm_instantiate cRs thm
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  end;
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fun mk_ctor_or_dtor get_T Ts t =
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  let val Type (_, Ts0) = get_T (fastype_of t) in
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    Term.subst_atomic_types (Ts0 ~~ Ts) t
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  end;
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val mk_ctor = mk_ctor_or_dtor range_type;
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val mk_dtor = mk_ctor_or_dtor domain_type;
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fun mk_rec_like lfp Ts Us t =
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  let
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    val (bindings, body) = strip_type (fastype_of t);
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    val (f_Us, prebody) = split_last bindings;
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    val Type (_, Ts0) = if lfp then prebody else body;
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    val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
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  in
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    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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  end;
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fun mk_map live Ts Us t =
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  let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in
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    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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  end;
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fun mk_rel live Ts Us t =
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  let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in
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    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
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  end;
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fun liveness_of_fp_bnf n bnf =
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  (case T_of_bnf bnf of
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    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
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  | _ => replicate n false);
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fun 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 reassoc_conjs thm =
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  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
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  handle THM _ => thm;
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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_datatypes prepare_constraint prepare_typ prepare_term lfp construct_fp
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    (wrap_opts as (no_dests, rep_compat), specs) 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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    fun qualify mandatory fp_b_name =
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      Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
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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 (((Bs0, Cs), Xs), 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 (length unsorted_As)
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      ||>> mk_TFrees nn
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      ||>> apfst (map TFree) o
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        variant_types (map (prefix "'") fp_b_names) (replicate nn HOLogic.typeS);
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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 (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_check (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_check _ _ = false;
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    fun freeze_fp (T as Type (s, Us)) =
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        (case find_index (eq_fpT_check T) fake_Ts of
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          ~1 => Type (s, map freeze_fp Us)
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        | kk => nth Xs kk)
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      | freeze_fp T = T;
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    val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
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    val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
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    val fp_eqs =
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      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsXs;
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    (* TODO: clean up list *)
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    val (pre_bnfs, ((fp_bnfs as any_fp_bnf :: _, dtors0, ctors0, fp_folds0, fp_recs0, fp_induct,
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           fp_strong_induct, dtor_ctors, ctor_dtors, ctor_injects, fp_map_thms, fp_set_thmss,
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           fp_rel_thms, fp_fold_thms, fp_rec_thms), lthy)) =
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      fp_bnf construct_fp fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
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    val timer = time (Timer.startRealTimer ());
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    fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
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      let
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        val bnf = the (bnf_of lthy s);
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        val live = live_of_bnf bnf;
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        val mapx = mk_map live Ts Us (map_of_bnf bnf);
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        val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
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      in Term.list_comb (mapx, map build_arg TUs') end;
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    fun build_rel_step build_arg (Type (s, Ts)) =
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      let
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        val bnf = the (bnf_of lthy s);
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        val live = live_of_bnf bnf;
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        val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
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        val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
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      in Term.list_comb (rel, map build_arg Ts') end;
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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_TsssXs []);
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    val nesting_bnfs = nesty_bnfs As;
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    val nested_bnfs = nesty_bnfs Xs;
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    val pre_map_defs = map map_def_of_bnf pre_bnfs;
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    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
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    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
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    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
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    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
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    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
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    val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs;
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    val nesting_set_natural's = maps set_natural'_of_bnf nesting_bnfs;
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    val live = live_of_bnf any_fp_bnf;
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    val Bs =
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      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
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        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
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    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
   295
blanchet@49501
   296
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
   297
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
   298
blanchet@49501
   299
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
   300
blanchet@49362
   301
    val exists_fp_subtype = exists_subtype (member (op =) fpTs);
blanchet@49670
   302
    val exists_Cs_subtype = exists_subtype (member (op =) Cs);
blanchet@49362
   303
blanchet@49536
   304
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
blanchet@49203
   305
    val ns = map length ctr_Tsss;
blanchet@49212
   306
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
   307
    val mss = map (map length) ctr_Tsss;
blanchet@49203
   308
    val Css = map2 replicate ns Cs;
blanchet@49203
   309
blanchet@49585
   310
    val fp_folds as any_fp_fold :: _ = map (mk_rec_like lfp As Cs) fp_folds0;
blanchet@49585
   311
    val fp_recs as any_fp_rec :: _ = map (mk_rec_like lfp As Cs) fp_recs0;
blanchet@49210
   312
blanchet@49585
   313
    val fp_fold_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_fold)));
blanchet@49585
   314
    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_rec)));
blanchet@49204
   315
blanchet@49504
   316
    val (((fold_only as (gss, _, _), rec_only as (hss, _, _)),
blanchet@49504
   317
          (zs, cs, cpss, unfold_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))),
blanchet@49591
   318
         names_lthy0) =
blanchet@49208
   319
      if lfp then
blanchet@49208
   320
        let
blanchet@49208
   321
          val y_Tsss =
blanchet@49255
   322
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49504
   323
              ns mss fp_fold_fun_Ts;
blanchet@49208
   324
          val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
blanchet@49208
   325
blanchet@49484
   326
          val ((gss, ysss), lthy) =
blanchet@49208
   327
            lthy
blanchet@49208
   328
            |> mk_Freess "f" g_Tss
blanchet@49208
   329
            ||>> mk_Freesss "x" y_Tsss;
blanchet@49670
   330
blanchet@49670
   331
          fun proj_recT proj (Type (s as @{type_name prod}, Ts as [T, U])) =
blanchet@49670
   332
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_recT proj) Ts)
blanchet@49670
   333
            | proj_recT proj (Type (s, Ts)) = Type (s, map (proj_recT proj) Ts)
blanchet@49670
   334
            | proj_recT _ T = T;
blanchet@49274
   335
blanchet@49670
   336
          fun unzip_recT T =
blanchet@49670
   337
            if exists_fp_subtype T then [proj_recT fst T, proj_recT snd T] else [T];
blanchet@49204
   338
blanchet@49670
   339
          val z_Tsss =
blanchet@49670
   340
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49670
   341
              ns mss fp_rec_fun_Ts;
blanchet@49670
   342
          val z_Tssss = map (map (map unzip_recT)) z_Tsss;
blanchet@49208
   343
          val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
blanchet@49204
   344
blanchet@49298
   345
          val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@49670
   346
          val zsss = map2 (map2 (map2 retype_free)) z_Tsss ysss;
blanchet@49210
   347
        in
blanchet@49670
   348
          ((((gss, g_Tss, ysss), (hss, h_Tss, zsss)),
blanchet@49484
   349
            ([], [], [], (([], []), ([], [])), (([], []), ([], [])))), lthy)
blanchet@49210
   350
        end
blanchet@49208
   351
      else
blanchet@49210
   352
        let
blanchet@49221
   353
          (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@49221
   354
          val mss' =  map (fn [0] => [1] | ms => ms) mss;
blanchet@49221
   355
blanchet@49463
   356
          val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@49275
   357
blanchet@49587
   358
          fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss);
blanchet@49211
   359
blanchet@49587
   360
          fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss
blanchet@49587
   361
            | flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
blanchet@49587
   362
              p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss;
blanchet@49274
   363
blanchet@49681
   364
          fun mk_types maybe_unzipT fun_Ts =
blanchet@49212
   365
            let
blanchet@49212
   366
              val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@49255
   367
              val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@49681
   368
              val f_Tsss = map2 (map2 dest_tupleT) mss' f_prod_Tss;
blanchet@49275
   369
              val f_Tssss =
blanchet@49681
   370
                map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
blanchet@49275
   371
              val q_Tssss =
blanchet@49463
   372
                map (map (map (fn [_] => [] | [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss;
blanchet@49587
   373
              val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@49681
   374
            in (q_Tssss, f_sum_prod_Ts, f_Tsss, f_Tssss, pf_Tss) end;
blanchet@49176
   375
blanchet@49681
   376
          val (r_Tssss, g_sum_prod_Ts, g_Tsss, g_Tssss, pg_Tss) = mk_types single fp_fold_fun_Ts;
blanchet@49211
   377
blanchet@49484
   378
          val ((((Free (z, _), cs), pss), gssss), lthy) =
blanchet@49210
   379
            lthy
blanchet@49233
   380
            |> yield_singleton (mk_Frees "z") dummyT
blanchet@49233
   381
            ||>> mk_Frees "a" Cs
blanchet@49211
   382
            ||>> mk_Freess "p" p_Tss
blanchet@49275
   383
            ||>> mk_Freessss "g" g_Tssss;
blanchet@49275
   384
          val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@49274
   385
blanchet@49681
   386
          fun proj_corecT proj (Type (s as @{type_name sum}, Ts as [T, U])) =
blanchet@49681
   387
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   388
            | proj_corecT proj (Type (s, Ts)) = Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   389
            | proj_corecT _ T = T;
blanchet@49274
   390
blanchet@49681
   391
          fun unzip_corecT T =
blanchet@49681
   392
            if exists_fp_subtype T then [proj_corecT fst T, proj_corecT snd T] else [T];
blanchet@49681
   393
blanchet@49681
   394
          val (s_Tssss, h_sum_prod_Ts, h_Tsss, h_Tssss, ph_Tss) =
blanchet@49681
   395
            mk_types unzip_corecT fp_rec_fun_Ts;
blanchet@49210
   396
blanchet@49298
   397
          val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@49484
   398
          val ((sssss, hssss_tl), lthy) =
blanchet@49275
   399
            lthy
blanchet@49275
   400
            |> mk_Freessss "q" s_Tssss
blanchet@49275
   401
            ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@49275
   402
          val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@49211
   403
blanchet@49681
   404
          val cpss = map2 (map o rapp) cs pss;
blanchet@49212
   405
blanchet@49681
   406
          fun build_sum_inj mk_inj (T, U) =
blanchet@49681
   407
            if T = U then
blanchet@49681
   408
              id_const T
blanchet@49681
   409
            else
blanchet@49681
   410
              (case (T, U) of
blanchet@49681
   411
                (Type (s, _), Type (s', _)) =>
blanchet@49681
   412
                if s = s' then build_map (build_sum_inj mk_inj) T U
blanchet@49681
   413
                else uncurry mk_inj (dest_sumT U)
blanchet@49681
   414
              | _ => uncurry mk_inj (dest_sumT U));
blanchet@49276
   415
blanchet@49681
   416
          fun build_dtor_corec_arg _ [] [cf] = cf
blanchet@49681
   417
            | build_dtor_corec_arg T [cq] [cf, cf'] =
blanchet@49681
   418
              mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@49681
   419
                (build_sum_inj Inr_const (fastype_of cf', T) $ cf')
blanchet@49681
   420
blanchet@49681
   421
          fun mk_terms f_Tsss qssss fssss =
blanchet@49212
   422
            let
blanchet@49587
   423
              val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
blanchet@49681
   424
              val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@49681
   425
              val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@49681
   426
              val cqfsss = map3 (map3 (map3 build_dtor_corec_arg)) f_Tsss cqssss cfssss;
blanchet@49276
   427
            in (pfss, cqfsss) end;
blanchet@49210
   428
        in
blanchet@49484
   429
          (((([], [], []), ([], [], [])),
blanchet@49681
   430
            ([z], cs, cpss, (mk_terms g_Tsss rssss gssss, (g_sum_prod_Ts, pg_Tss)),
blanchet@49681
   431
             (mk_terms h_Tsss sssss hssss, (h_sum_prod_Ts, ph_Tss)))), lthy)
blanchet@49210
   432
        end;
blanchet@49210
   433
blanchet@49585
   434
    fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@49585
   435
            fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@49585
   436
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@49585
   437
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   438
      let
blanchet@49498
   439
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
   440
blanchet@49501
   441
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
   442
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   443
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   444
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   445
blanchet@49593
   446
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
   447
          no_defs_lthy
blanchet@49501
   448
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
   449
          ||>> mk_Frees "f" case_Ts
blanchet@49370
   450
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
   451
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
   452
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
   453
blanchet@49498
   454
        val u = Free (u', fpT);
blanchet@49121
   455
blanchet@49585
   456
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
   457
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
   458
blanchet@49129
   459
        val ctr_rhss =
blanchet@49585
   460
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
   461
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
   462
blanchet@49633
   463
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
   464
blanchet@49134
   465
        val case_rhs =
blanchet@49498
   466
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
   467
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
   468
blanchet@49201
   469
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   470
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
   471
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
   472
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   473
          ||> `Local_Theory.restore;
blanchet@49121
   474
blanchet@49121
   475
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   476
blanchet@49121
   477
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
   478
        val ctr_defs' =
blanchet@49585
   479
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
   480
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   481
blanchet@49203
   482
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   483
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   484
blanchet@49203
   485
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   486
blanchet@49585
   487
        fun wrap lthy =
blanchet@49123
   488
          let
blanchet@49585
   489
            fun exhaust_tac {context = ctxt, ...} =
blanchet@49135
   490
              let
blanchet@49585
   491
                val ctor_iff_dtor_thm =
blanchet@49585
   492
                  let
blanchet@49585
   493
                    val goal =
blanchet@49585
   494
                      fold_rev Logic.all [w, u]
blanchet@49585
   495
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
   496
                  in
blanchet@49585
   497
                    Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
   498
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
   499
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
   500
                    |> Thm.close_derivation
blanchet@49585
   501
                    |> Morphism.thm phi
blanchet@49585
   502
                  end;
blanchet@49585
   503
blanchet@49585
   504
                val sumEN_thm' =
blanchet@49585
   505
                  unfold_thms lthy @{thms all_unit_eq}
blanchet@49585
   506
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
   507
                       (mk_sumEN_balanced n))
blanchet@49585
   508
                  |> Morphism.thm phi;
blanchet@49135
   509
              in
blanchet@49585
   510
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
   511
              end;
blanchet@49135
   512
blanchet@49585
   513
            val inject_tacss =
blanchet@49585
   514
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
   515
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
   516
blanchet@49585
   517
            val half_distinct_tacss =
blanchet@49585
   518
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
   519
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
   520
blanchet@49585
   521
            val case_tacs =
blanchet@49585
   522
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
   523
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
   524
blanchet@49585
   525
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
   526
blanchet@49585
   527
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
   528
          in
blanchet@49633
   529
            wrap_datatype tacss (((wrap_opts, ctrs0), casex0), (disc_bindings, (sel_bindingss,
blanchet@49585
   530
              sel_defaultss))) lthy
blanchet@49123
   531
          end;
blanchet@49121
   532
blanchet@49585
   533
        fun derive_maps_sets_rels (wrap_res, lthy) =
blanchet@49585
   534
          let
blanchet@49585
   535
            val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@49585
   536
            val nones = replicate live NONE;
blanchet@49585
   537
blanchet@49585
   538
            val ctor_cong =
blanchet@49585
   539
              if lfp then Drule.dummy_thm
blanchet@49585
   540
              else cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor)] arg_cong;
blanchet@49585
   541
blanchet@49585
   542
            fun mk_cIn ify =
blanchet@49585
   543
              certify lthy o (not lfp ? curry (op $) (map_types ify ctor)) oo
blanchet@49585
   544
              mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
   545
blanchet@49585
   546
            val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@49585
   547
            val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
   548
blanchet@49585
   549
            fun mk_map_thm ctr_def' xs cxIn =
blanchet@49585
   550
              fold_thms lthy [ctr_def']
blanchet@49585
   551
                (unfold_thms lthy (pre_map_def ::
blanchet@49585
   552
                     (if lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@49585
   553
                   (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@49585
   554
                      (if lfp then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@49593
   555
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   556
blanchet@49585
   557
            fun mk_set_thm fp_set_thm ctr_def' xs cxIn =
blanchet@49585
   558
              fold_thms lthy [ctr_def']
blanchet@49585
   559
                (unfold_thms lthy (pre_set_defs @ nested_set_natural's @ nesting_set_natural's @
blanchet@49585
   560
                     (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@49585
   561
                   (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@49593
   562
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   563
blanchet@49585
   564
            fun mk_set_thms fp_set_thm = map3 (mk_set_thm fp_set_thm) ctr_defs' xss cxIns;
blanchet@49585
   565
blanchet@49585
   566
            val map_thms = map3 mk_map_thm ctr_defs' xss cxIns;
blanchet@49585
   567
            val set_thmss = map mk_set_thms fp_set_thms;
blanchet@49127
   568
blanchet@49585
   569
            val rel_infos = (ctr_defs' ~~ xss ~~ cxIns, ctr_defs' ~~ yss ~~ cyIns);
blanchet@49585
   570
blanchet@49590
   571
            fun mk_rel_thm postproc ctr_defs' xs cxIn ys cyIn =
blanchet@49585
   572
              fold_thms lthy ctr_defs'
blanchet@49591
   573
                 (unfold_thms lthy (pre_rel_def :: (if lfp then [] else [dtor_ctor]) @
blanchet@49591
   574
                      sum_prod_thms_rel)
blanchet@49585
   575
                    (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@49593
   576
              |> postproc
blanchet@49593
   577
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   578
blanchet@49592
   579
            fun mk_rel_inject_thm (((ctr_def', xs), cxIn), ((_, ys), cyIn)) =
blanchet@49591
   580
              mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] xs cxIn ys cyIn;
blanchet@49585
   581
blanchet@49592
   582
            val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
   583
blanchet@49592
   584
            fun mk_half_rel_distinct_thm (((xctr_def', xs), cxIn), ((yctr_def', ys), cyIn)) =
blanchet@49585
   585
              mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@49585
   586
                xs cxIn ys cyIn;
blanchet@49121
   587
blanchet@49592
   588
            fun mk_other_half_rel_distinct_thm thm =
blanchet@49585
   589
              flip_rels lthy live thm RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
   590
blanchet@49592
   591
            val half_rel_distinct_thmss =
blanchet@49592
   592
              map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@49592
   593
            val other_half_rel_distinct_thmss =
blanchet@49592
   594
              map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@49592
   595
            val (rel_distinct_thms, _) =
blanchet@49592
   596
              join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
   597
blanchet@49585
   598
            val notes =
blanchet@49594
   599
              [(mapN, map_thms, code_simp_attrs),
blanchet@49592
   600
               (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@49592
   601
               (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@49585
   602
               (setsN, flat set_thmss, code_simp_attrs)]
blanchet@49585
   603
              |> filter_out (null o #2)
blanchet@49585
   604
              |> map (fn (thmN, thms, attrs) =>
blanchet@49633
   605
                ((qualify true fp_b_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49585
   606
          in
blanchet@49585
   607
            (wrap_res, lthy |> Local_Theory.notes notes |> snd)
blanchet@49585
   608
          end;
blanchet@49585
   609
blanchet@49585
   610
        fun define_fold_rec no_defs_lthy =
blanchet@49134
   611
          let
blanchet@49208
   612
            val fpT_to_C = fpT --> C;
blanchet@49199
   613
blanchet@49681
   614
            fun build_prod_proj mk_proj (T, U) =
blanchet@49670
   615
              if T = U then
blanchet@49670
   616
                id_const T
blanchet@49670
   617
              else
blanchet@49670
   618
                (case (T, U) of
blanchet@49670
   619
                  (Type (s, _), Type (s', _)) =>
blanchet@49681
   620
                  if s = s' then build_map (build_prod_proj mk_proj) T U else mk_proj T
blanchet@49670
   621
                | _ => mk_proj T);
blanchet@49670
   622
blanchet@49681
   623
            (* TODO: Avoid these complications; cf. corec case *)
blanchet@49672
   624
            fun mk_U proj (Type (s as @{type_name prod}, Ts as [T', U])) =
blanchet@49672
   625
                if member (op =) fpTs T' then proj (T', U) else Type (s, map (mk_U proj) Ts)
blanchet@49670
   626
              | mk_U proj (Type (s, Ts)) = Type (s, map (mk_U proj) Ts)
blanchet@49670
   627
              | mk_U _ T = T;
blanchet@49670
   628
blanchet@49670
   629
            fun unzip_rec (x as Free (_, T)) =
blanchet@49670
   630
              if exists_fp_subtype T then
blanchet@49681
   631
                [build_prod_proj fst_const (T, mk_U fst T) $ x,
blanchet@49681
   632
                 build_prod_proj snd_const (T, mk_U snd T) $ x]
blanchet@49670
   633
              else
blanchet@49670
   634
                [x];
blanchet@49670
   635
blanchet@49670
   636
            fun mk_rec_like_arg f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f (maps unzip_rec xs);
blanchet@49670
   637
blanchet@49670
   638
            fun generate_rec_like (suf, fp_rec_like, (fss, f_Tss, xsss)) =
blanchet@49215
   639
              let
blanchet@49215
   640
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49633
   641
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49215
   642
                val spec =
blanchet@49336
   643
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   644
                    Term.list_comb (fp_rec_like,
blanchet@49670
   645
                      map2 (mk_sum_caseN_balanced oo map2 mk_rec_like_arg) fss xsss));
blanchet@49336
   646
              in (binding, spec) end;
blanchet@49199
   647
blanchet@49504
   648
            val rec_like_infos =
blanchet@49504
   649
              [(foldN, fp_fold, fold_only),
blanchet@49215
   650
               (recN, fp_rec, rec_only)];
blanchet@49215
   651
blanchet@49504
   652
            val (bindings, specs) = map generate_rec_like rec_like_infos |> split_list;
blanchet@49215
   653
blanchet@49215
   654
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   655
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   656
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   657
                #>> apsnd snd) bindings specs
blanchet@49199
   658
              ||> `Local_Theory.restore;
blanchet@49201
   659
blanchet@49201
   660
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   661
blanchet@49504
   662
            val [fold_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   663
blanchet@49536
   664
            val [foldx, recx] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49134
   665
          in
blanchet@49585
   666
            ((foldx, recx, fold_def, rec_def), lthy)
blanchet@49134
   667
          end;
blanchet@49134
   668
blanchet@49585
   669
        fun define_unfold_corec no_defs_lthy =
blanchet@49210
   670
          let
blanchet@49210
   671
            val B_to_fpT = C --> fpT;
blanchet@49211
   672
blanchet@49276
   673
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
   674
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
   675
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
   676
blanchet@49504
   677
            fun generate_corec_like (suf, fp_rec_like, ((pfss, cqfsss), (f_sum_prod_Ts,
blanchet@49274
   678
                pf_Tss))) =
blanchet@49211
   679
              let
blanchet@49211
   680
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49633
   681
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49211
   682
                val spec =
blanchet@49336
   683
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   684
                    Term.list_comb (fp_rec_like,
blanchet@49276
   685
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49336
   686
              in (binding, spec) end;
blanchet@49210
   687
blanchet@49504
   688
            val corec_like_infos =
blanchet@49504
   689
              [(unfoldN, fp_fold, unfold_only),
blanchet@49215
   690
               (corecN, fp_rec, corec_only)];
blanchet@49212
   691
blanchet@49504
   692
            val (bindings, specs) = map generate_corec_like corec_like_infos |> split_list;
blanchet@49211
   693
blanchet@49211
   694
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   695
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   696
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   697
                #>> apsnd snd) bindings specs
blanchet@49210
   698
              ||> `Local_Theory.restore;
blanchet@49210
   699
blanchet@49210
   700
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   701
blanchet@49504
   702
            val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   703
blanchet@49536
   704
            val [unfold, corec] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49210
   705
          in
blanchet@49585
   706
            ((unfold, corec, unfold_def, corec_def), lthy)
blanchet@49287
   707
          end;
blanchet@49287
   708
blanchet@49504
   709
        val define_rec_likes = if lfp then define_fold_rec else define_unfold_corec;
blanchet@49585
   710
blanchet@49585
   711
        fun massage_res ((wrap_res, rec_like_res), lthy) =
blanchet@49585
   712
          (((ctrs, xss, ctr_defs, wrap_res), rec_like_res), lthy);
blanchet@49119
   713
      in
blanchet@49585
   714
        (wrap #> (live > 0 ? derive_maps_sets_rels) ##>> define_rec_likes #> massage_res, lthy')
blanchet@49119
   715
      end;
blanchet@49167
   716
blanchet@49585
   717
    fun wrap_types_and_more (wrap_types_and_mores, lthy) =
blanchet@49585
   718
      fold_map I wrap_types_and_mores lthy
blanchet@49585
   719
      |>> apsnd split_list4 o apfst split_list4 o split_list;
blanchet@49226
   720
blanchet@49585
   721
    (* TODO: Add map, sets, rel simps *)
blanchet@49479
   722
    val mk_simp_thmss =
blanchet@49591
   723
      map3 (fn (_, _, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn fold_likes =>
blanchet@49505
   724
        injects @ distincts @ cases @ rec_likes @ fold_likes);
blanchet@49479
   725
blanchet@49585
   726
    fun derive_induct_fold_rec_thms_for_types (((ctrss, xsss, ctr_defss, wrap_ress), (folds, recs,
blanchet@49585
   727
        fold_defs, rec_defs)), lthy) =
blanchet@49202
   728
      let
blanchet@49591
   729
        val (((ps, ps'), us'), names_lthy) =
blanchet@49370
   730
          lthy
blanchet@49463
   731
          |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@49498
   732
          ||>> Variable.variant_fixes fp_b_names;
blanchet@49370
   733
blanchet@49498
   734
        val us = map2 (curry Free) us' fpTs;
blanchet@49370
   735
blanchet@49362
   736
        fun mk_sets_nested bnf =
blanchet@49362
   737
          let
blanchet@49362
   738
            val Type (T_name, Us) = T_of_bnf bnf;
blanchet@49362
   739
            val lives = lives_of_bnf bnf;
blanchet@49362
   740
            val sets = sets_of_bnf bnf;
blanchet@49362
   741
            fun mk_set U =
blanchet@49362
   742
              (case find_index (curry (op =) U) lives of
blanchet@49362
   743
                ~1 => Term.dummy
blanchet@49362
   744
              | i => nth sets i);
blanchet@49362
   745
          in
blanchet@49362
   746
            (T_name, map mk_set Us)
blanchet@49362
   747
          end;
blanchet@49362
   748
blanchet@49362
   749
        val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@49362
   750
blanchet@49337
   751
        val (induct_thms, induct_thm) =
blanchet@49337
   752
          let
blanchet@49362
   753
            fun mk_set Ts t =
blanchet@49362
   754
              let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@49362
   755
                Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49362
   756
              end;
blanchet@49362
   757
blanchet@49375
   758
            fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
blanchet@49361
   759
                (case find_index (curry (op =) T) fpTs of
blanchet@49362
   760
                  ~1 =>
blanchet@49362
   761
                  (case AList.lookup (op =) setss_nested T_name of
blanchet@49362
   762
                    NONE => []
blanchet@49362
   763
                  | SOME raw_sets0 =>
blanchet@49362
   764
                    let
blanchet@49362
   765
                      val (Ts, raw_sets) =
blanchet@49362
   766
                        split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
blanchet@49362
   767
                      val sets = map (mk_set Ts0) raw_sets;
blanchet@49362
   768
                      val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@49375
   769
                      val xysets = map (pair x) (ys ~~ sets);
blanchet@49375
   770
                      val ppremss = map (mk_raw_prem_prems names_lthy') ys;
blanchet@49362
   771
                    in
blanchet@49375
   772
                      flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@49362
   773
                    end)
blanchet@49591
   774
                | kk => [([], (kk + 1, x))])
blanchet@49375
   775
              | mk_raw_prem_prems _ _ = [];
blanchet@49342
   776
blanchet@49378
   777
            fun close_prem_prem xs t =
blanchet@49378
   778
              fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@49591
   779
                (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@49362
   780
blanchet@49378
   781
            fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@49378
   782
              close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@49376
   783
                  HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@49591
   784
                HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@49375
   785
blanchet@49372
   786
            fun mk_raw_prem phi ctr ctr_Ts =
blanchet@49362
   787
              let
blanchet@49362
   788
                val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@49376
   789
                val pprems = maps (mk_raw_prem_prems names_lthy') xs;
blanchet@49378
   790
              in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@49342
   791
blanchet@49376
   792
            fun mk_prem (xs, raw_pprems, concl) =
blanchet@49378
   793
              fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@49368
   794
blanchet@49591
   795
            val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss;
blanchet@49389
   796
blanchet@49361
   797
            val goal =
blanchet@49372
   798
              Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@49591
   799
                HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@49368
   800
blanchet@49429
   801
            val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@49368
   802
blanchet@49501
   803
            val ctor_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@49342
   804
blanchet@49591
   805
            val thm =
blanchet@49361
   806
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49590
   807
                mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct'
blanchet@49389
   808
                  nested_set_natural's pre_set_defss)
blanchet@49368
   809
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49591
   810
              |> Thm.close_derivation;
blanchet@49337
   811
          in
blanchet@49591
   812
            `(conj_dests nn) thm
blanchet@49337
   813
          end;
blanchet@49201
   814
blanchet@49622
   815
        val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@49437
   816
blanchet@49504
   817
        val (fold_thmss, rec_thmss) =
blanchet@49207
   818
          let
blanchet@49337
   819
            val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49504
   820
            val gfolds = map (lists_bmoc gss) folds;
blanchet@49337
   821
            val hrecs = map (lists_bmoc hss) recs;
blanchet@49337
   822
blanchet@49504
   823
            fun mk_goal fss frec_like xctr f xs fxs =
blanchet@49207
   824
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49504
   825
                (mk_Trueprop_eq (frec_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   826
blanchet@49591
   827
            fun build_rec_like frec_likes maybe_tick (T, U) =
blanchet@49234
   828
              if T = U then
blanchet@49368
   829
                id_const T
blanchet@49234
   830
              else
blanchet@49234
   831
                (case find_index (curry (op =) T) fpTs of
blanchet@49591
   832
                  ~1 => build_map (build_rec_like frec_likes maybe_tick) T U
blanchet@49591
   833
                | kk => maybe_tick (nth us kk) (nth frec_likes kk));
blanchet@49233
   834
blanchet@49274
   835
            fun mk_U maybe_mk_prodT =
blanchet@49274
   836
              typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
blanchet@49214
   837
blanchet@49591
   838
            fun intr_rec_likes frec_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
blanchet@49670
   839
              if exists_fp_subtype T then
blanchet@49591
   840
                maybe_cons x [build_rec_like frec_likes (K I) (T, mk_U (K I) T) $ x]
blanchet@49214
   841
              else
blanchet@49214
   842
                [x];
blanchet@49214
   843
blanchet@49591
   844
            val gxsss = map (map (maps (intr_rec_likes gfolds (K I) (K I) (K I)))) xsss;
blanchet@49591
   845
            val hxsss =
blanchet@49591
   846
              map (map (maps (intr_rec_likes hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
blanchet@49204
   847
blanchet@49504
   848
            val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
blanchet@49484
   849
            val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   850
blanchet@49504
   851
            val fold_tacss =
blanchet@49670
   852
              map2 (map o mk_rec_like_tac pre_map_defs [] nesting_map_ids'' fold_defs) fp_fold_thms
blanchet@49363
   853
                ctr_defss;
blanchet@49203
   854
            val rec_tacss =
blanchet@49670
   855
              map2 (map o mk_rec_like_tac pre_map_defs nested_map_comp's
blanchet@49670
   856
                (nested_map_ids'' @ nesting_map_ids'') rec_defs) fp_rec_thms ctr_defss;
blanchet@49484
   857
blanchet@49591
   858
            fun prove goal tac =
blanchet@49591
   859
              Skip_Proof.prove lthy [] [] goal (tac o #context)
blanchet@49591
   860
              |> Thm.close_derivation;
blanchet@49202
   861
          in
blanchet@49595
   862
            (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
blanchet@49202
   863
          end;
blanchet@49201
   864
blanchet@49504
   865
        val simp_thmss = mk_simp_thmss wrap_ress rec_thmss fold_thmss;
blanchet@49438
   866
blanchet@49437
   867
        val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@49437
   868
        fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name));
blanchet@49437
   869
blanchet@49337
   870
        val common_notes =
blanchet@49437
   871
          (if nn > 1 then [(inductN, [induct_thm], [induct_case_names_attr])] else [])
blanchet@49337
   872
          |> map (fn (thmN, thms, attrs) =>
blanchet@49633
   873
            ((qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49337
   874
blanchet@49226
   875
        val notes =
blanchet@49633
   876
          [(foldN, fold_thmss, K code_simp_attrs),
blanchet@49633
   877
           (inductN, map single induct_thms,
blanchet@49437
   878
            fn T_name => [induct_case_names_attr, induct_type_attr T_name]),
blanchet@49622
   879
           (recN, rec_thmss, K code_simp_attrs),
blanchet@49585
   880
           (simpsN, simp_thmss, K [])]
blanchet@49300
   881
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@49633
   882
            map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@49633
   883
              ((qualify true fp_b_name (Binding.name thmN), attrs T_name),
blanchet@49633
   884
               [(thms, [])])) fp_b_names fpTs thmss);
blanchet@49202
   885
      in
blanchet@49337
   886
        lthy |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@49202
   887
      end;
blanchet@49202
   888
blanchet@49585
   889
    fun derive_coinduct_unfold_corec_thms_for_types (((ctrss, _, ctr_defss, wrap_ress), (unfolds,
blanchet@49585
   890
        corecs, unfold_defs, corec_defs)), lthy) =
blanchet@49212
   891
      let
blanchet@49591
   892
        val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@49591
   893
blanchet@49484
   894
        val discss = map (map (mk_disc_or_sel As) o #1) wrap_ress;
blanchet@49591
   895
        val selsss = map (map (map (mk_disc_or_sel As)) o #2) wrap_ress;
blanchet@49591
   896
        val exhaust_thms = map #3 wrap_ress;
blanchet@49591
   897
        val disc_thmsss = map #7 wrap_ress;
blanchet@49591
   898
        val discIss = map #8 wrap_ress;
blanchet@49591
   899
        val sel_thmsss = map #9 wrap_ress;
blanchet@49438
   900
blanchet@49591
   901
        val (((rs, us'), vs'), names_lthy) =
blanchet@49370
   902
          lthy
blanchet@49591
   903
          |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@49591
   904
          ||>> Variable.variant_fixes fp_b_names
blanchet@49591
   905
          ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@49370
   906
blanchet@49498
   907
        val us = map2 (curry Free) us' fpTs;
blanchet@49591
   908
        val udiscss = map2 (map o rapp) us discss;
blanchet@49591
   909
        val uselsss = map2 (map o map o rapp) us selsss;
blanchet@49370
   910
blanchet@49591
   911
        val vs = map2 (curry Free) vs' fpTs;
blanchet@49591
   912
        val vdiscss = map2 (map o rapp) vs discss;
blanchet@49591
   913
        val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@49591
   914
blanchet@49591
   915
        val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
blanchet@49337
   916
          let
blanchet@49591
   917
            val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@49591
   918
            val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@49591
   919
            val strong_rs =
blanchet@49591
   920
              map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@49591
   921
                fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@49591
   922
blanchet@49591
   923
            fun build_rel rs' T =
blanchet@49591
   924
              (case find_index (curry (op =) T) fpTs of
blanchet@49591
   925
                ~1 =>
blanchet@49591
   926
                if exists_fp_subtype T then build_rel_step (build_rel rs') T
blanchet@49591
   927
                else HOLogic.eq_const T
blanchet@49591
   928
              | kk => nth rs' kk);
blanchet@49591
   929
blanchet@49591
   930
            fun build_rel_app rs' usel vsel =
blanchet@49591
   931
              fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@49591
   932
blanchet@49591
   933
            fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@49591
   934
              (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@49591
   935
              (if null usels then
blanchet@49591
   936
                 []
blanchet@49591
   937
               else
blanchet@49591
   938
                 [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@49591
   939
                    Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@49591
   940
blanchet@49591
   941
            fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@49591
   942
              Library.foldr1 HOLogic.mk_conj
blanchet@49591
   943
                (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@49591
   944
              handle List.Empty => @{term True};
blanchet@49591
   945
blanchet@49591
   946
            fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@49591
   947
              fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@49591
   948
                HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@49591
   949
blanchet@49591
   950
            val concl =
blanchet@49591
   951
              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49591
   952
                (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@49591
   953
                   uvrs us vs));
blanchet@49591
   954
blanchet@49591
   955
            fun mk_goal rs' =
blanchet@49591
   956
              Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@49591
   957
                concl);
blanchet@49591
   958
blanchet@49591
   959
            val goal = mk_goal rs;
blanchet@49591
   960
            val strong_goal = mk_goal strong_rs;
blanchet@49591
   961
blanchet@49591
   962
            fun prove dtor_coinduct' goal =
blanchet@49591
   963
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49591
   964
                mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@49591
   965
                  exhaust_thms ctr_defss disc_thmsss sel_thmsss)
blanchet@49591
   966
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49591
   967
              |> Thm.close_derivation;
blanchet@49591
   968
blanchet@49590
   969
            fun postproc nn thm =
blanchet@49590
   970
              Thm.permute_prems 0 nn
blanchet@49591
   971
                (if nn = 1 then thm RS mp
blanchet@49591
   972
                 else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@49591
   973
              |> Drule.zero_var_indexes
blanchet@49591
   974
              |> `(conj_dests nn);
blanchet@49337
   975
          in
blanchet@49591
   976
            (postproc nn (prove fp_induct goal), postproc nn (prove fp_strong_induct strong_goal))
blanchet@49337
   977
          end;
blanchet@49212
   978
blanchet@49484
   979
        fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@49484
   980
blanchet@49484
   981
        val z = the_single zs;
blanchet@49504
   982
        val gunfolds = map (lists_bmoc pgss) unfolds;
blanchet@49484
   983
        val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49484
   984
blanchet@49504
   985
        val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@49212
   986
          let
blanchet@49504
   987
            fun mk_goal pfss c cps fcorec_like n k ctr m cfs' =
blanchet@49212
   988
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49484
   989
                (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@49504
   990
                   mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
   991
blanchet@49591
   992
            fun build_corec_like fcorec_likes maybe_tack (T, U) =
blanchet@49234
   993
              if T = U then
blanchet@49368
   994
                id_const T
blanchet@49234
   995
              else
blanchet@49234
   996
                (case find_index (curry (op =) U) fpTs of
blanchet@49591
   997
                  ~1 => build_map (build_corec_like fcorec_likes maybe_tack) T U
blanchet@49591
   998
                | kk => maybe_tack (nth cs kk, nth us kk) (nth fcorec_likes kk));
blanchet@49233
   999
blanchet@49274
  1000
            fun mk_U maybe_mk_sumT =
blanchet@49274
  1001
              typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@49212
  1002
blanchet@49591
  1003
            fun intr_corec_likes fcorec_likes maybe_mk_sumT maybe_tack cqf =
blanchet@49276
  1004
              let val T = fastype_of cqf in
blanchet@49670
  1005
                if exists_Cs_subtype T then
blanchet@49591
  1006
                  build_corec_like fcorec_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
blanchet@49276
  1007
                else
blanchet@49276
  1008
                  cqf
blanchet@49276
  1009
              end;
blanchet@49232
  1010
blanchet@49591
  1011
            val crgsss' = map (map (map (intr_corec_likes gunfolds (K I) (K I)))) crgsss;
blanchet@49591
  1012
            val cshsss' =
blanchet@49591
  1013
              map (map (map (intr_corec_likes hcorecs (curry mk_sumT) (tack z)))) cshsss;
blanchet@49212
  1014
blanchet@49504
  1015
            val unfold_goalss =
blanchet@49504
  1016
              map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss';
blanchet@49484
  1017
            val corec_goalss =
blanchet@49484
  1018
              map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@49213
  1019
blanchet@49504
  1020
            val unfold_tacss =
blanchet@49671
  1021
              map3 (map oo mk_corec_like_tac unfold_defs nesting_map_ids'') fp_fold_thms
blanchet@49671
  1022
                pre_map_defs ctr_defss;
blanchet@49233
  1023
            val corec_tacss =
blanchet@49671
  1024
              map3 (map oo mk_corec_like_tac corec_defs nesting_map_ids'') fp_rec_thms pre_map_defs
blanchet@49233
  1025
                ctr_defss;
blanchet@49479
  1026
blanchet@49484
  1027
            fun prove goal tac =
blanchet@49484
  1028
              Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation;
blanchet@49484
  1029
blanchet@49504
  1030
            val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@49479
  1031
            val corec_thmss =
blanchet@49484
  1032
              map2 (map2 prove) corec_goalss corec_tacss
blanchet@49504
  1033
              |> map (map (unfold_thms lthy @{thms sum_case_if}));
blanchet@49479
  1034
blanchet@49504
  1035
            val unfold_safesss = map2 (map2 (map2 (curry (op =)))) crgsss' crgsss;
blanchet@49479
  1036
            val corec_safesss = map2 (map2 (map2 (curry (op =)))) cshsss' cshsss;
blanchet@49479
  1037
blanchet@49479
  1038
            val filter_safesss =
blanchet@49479
  1039
              map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@49479
  1040
                curry (op ~~));
blanchet@49479
  1041
blanchet@49504
  1042
            val safe_unfold_thmss = filter_safesss unfold_safesss unfold_thmss;
blanchet@49479
  1043
            val safe_corec_thmss = filter_safesss corec_safesss corec_thmss;
blanchet@49479
  1044
          in
blanchet@49504
  1045
            (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@49212
  1046
          end;
blanchet@49212
  1047
blanchet@49504
  1048
        val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@49482
  1049
          let
blanchet@49504
  1050
            fun mk_goal c cps fcorec_like n k disc =
blanchet@49504
  1051
              mk_Trueprop_eq (disc $ (fcorec_like $ c),
blanchet@49484
  1052
                if n = 1 then @{const True}
blanchet@49484
  1053
                else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@49484
  1054
blanchet@49504
  1055
            val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@49484
  1056
            val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@49484
  1057
blanchet@49484
  1058
            fun mk_case_split' cp =
blanchet@49484
  1059
              Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@49484
  1060
blanchet@49484
  1061
            val case_splitss' = map (map mk_case_split') cpss;
blanchet@49482
  1062
blanchet@49504
  1063
            val unfold_tacss =
blanchet@49504
  1064
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@49484
  1065
            val corec_tacss =
blanchet@49504
  1066
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@49484
  1067
blanchet@49484
  1068
            fun prove goal tac =
blanchet@49484
  1069
              Skip_Proof.prove lthy [] [] goal (tac o #context)
blanchet@49591
  1070
              |> singleton (Proof_Context.export names_lthy0 no_defs_lthy)
blanchet@49591
  1071
              |> Thm.close_derivation;
blanchet@49484
  1072
blanchet@49484
  1073
            fun proves [_] [_] = []
blanchet@49484
  1074
              | proves goals tacs = map2 prove goals tacs;
blanchet@49482
  1075
          in
blanchet@49504
  1076
            (map2 proves unfold_goalss unfold_tacss,
blanchet@49484
  1077
             map2 proves corec_goalss corec_tacss)
blanchet@49482
  1078
          end;
blanchet@49482
  1079
blanchet@49605
  1080
        val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@49605
  1081
blanchet@49504
  1082
        fun mk_disc_corec_like_thms corec_likes discIs =
blanchet@49605
  1083
          map (op RS) (filter_out (is_triv_discI o snd) (corec_likes ~~ discIs));
blanchet@49266
  1084
blanchet@49504
  1085
        val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss;
blanchet@49504
  1086
        val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss;
blanchet@49266
  1087
blanchet@49504
  1088
        fun mk_sel_corec_like_thm corec_like_thm sel sel_thm =
blanchet@49266
  1089
          let
blanchet@49479
  1090
            val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@49266
  1091
            val arg_cong' =
blanchet@49266
  1092
              Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@49479
  1093
                [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@49267
  1094
              |> Thm.varifyT_global;
blanchet@49266
  1095
            val sel_thm' = sel_thm RSN (2, trans);
blanchet@49266
  1096
          in
blanchet@49504
  1097
            corec_like_thm RS arg_cong' RS sel_thm'
blanchet@49266
  1098
          end;
blanchet@49266
  1099
blanchet@49504
  1100
        fun mk_sel_corec_like_thms corec_likess =
blanchet@49504
  1101
          map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss |> map flat;
blanchet@49479
  1102
blanchet@49504
  1103
        val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss;
blanchet@49504
  1104
        val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss;
blanchet@49479
  1105
blanchet@49587
  1106
        fun flat_corec_like_thms corec_likes disc_corec_likes sel_corec_likes =
blanchet@49504
  1107
          corec_likes @ disc_corec_likes @ sel_corec_likes;
blanchet@49479
  1108
blanchet@49479
  1109
        val simp_thmss =
blanchet@49479
  1110
          mk_simp_thmss wrap_ress
blanchet@49587
  1111
            (map3 flat_corec_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@49587
  1112
            (map3 flat_corec_like_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss);
blanchet@49479
  1113
blanchet@49479
  1114
        val anonymous_notes =
blanchet@49504
  1115
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1116
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1117
blanchet@49342
  1118
        val common_notes =
blanchet@49591
  1119
          (if nn > 1 then
blanchet@49591
  1120
             (* FIXME: attribs *)
blanchet@49591
  1121
             [(coinductN, [coinduct_thm], []),
blanchet@49591
  1122
              (strong_coinductN, [strong_coinduct_thm], [])]
blanchet@49591
  1123
           else
blanchet@49591
  1124
             [])
blanchet@49342
  1125
          |> map (fn (thmN, thms, attrs) =>
blanchet@49633
  1126
            ((qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49342
  1127
blanchet@49212
  1128
        val notes =
blanchet@49342
  1129
          [(coinductN, map single coinduct_thms, []), (* FIXME: attribs *)
blanchet@49594
  1130
           (corecN, corec_thmss, []),
blanchet@49594
  1131
           (disc_corecN, disc_corec_thmss, simp_attrs),
blanchet@49594
  1132
           (disc_corec_iffN, disc_corec_iff_thmss, simp_attrs),
blanchet@49594
  1133
           (disc_unfoldN, disc_unfold_thmss, simp_attrs),
blanchet@49594
  1134
           (disc_unfold_iffN, disc_unfold_iff_thmss, simp_attrs),
blanchet@49594
  1135
           (sel_corecN, sel_corec_thmss, simp_attrs),
blanchet@49594
  1136
           (sel_unfoldN, sel_unfold_thmss, simp_attrs),
blanchet@49585
  1137
           (simpsN, simp_thmss, []),
blanchet@49591
  1138
           (strong_coinductN, map single strong_coinduct_thms, []), (* FIXME: attribs *)
blanchet@49594
  1139
           (unfoldN, unfold_thmss, [])]
blanchet@49300
  1140
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@49633
  1141
            map_filter (fn (_, []) => NONE | (fp_b_name, thms) =>
blanchet@49633
  1142
              SOME ((qualify true fp_b_name (Binding.name thmN), attrs),
blanchet@49633
  1143
                [(thms, [])])) (fp_b_names ~~ thmss));
blanchet@49212
  1144
      in
blanchet@49479
  1145
        lthy |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@49212
  1146
      end;
blanchet@49212
  1147
blanchet@49204
  1148
    val lthy' = lthy
blanchet@49585
  1149
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@49585
  1150
        fp_folds ~~ fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@49585
  1151
        pre_set_defss ~~ pre_rel_defs ~~ fp_map_thms ~~ fp_set_thmss ~~ fp_rel_thms ~~ ns ~~ kss ~~
blanchet@49585
  1152
        mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
blanchet@49585
  1153
        raw_sel_defaultsss)
blanchet@49585
  1154
      |> wrap_types_and_more
blanchet@49585
  1155
      |> (if lfp then derive_induct_fold_rec_thms_for_types
blanchet@49585
  1156
          else derive_coinduct_unfold_corec_thms_for_types);
blanchet@49167
  1157
blanchet@49167
  1158
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
  1159
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
  1160
  in
blanchet@49308
  1161
    timer; lthy'
blanchet@49112
  1162
  end;
blanchet@49112
  1163
blanchet@49536
  1164
val datatypes = define_datatypes (K I) (K I) (K I);
blanchet@49297
  1165
blanchet@49536
  1166
val datatype_cmd = define_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
blanchet@49119
  1167
blanchet@49112
  1168
val parse_ctr_arg =
blanchet@49329
  1169
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1170
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1171
blanchet@49286
  1172
val parse_defaults =
blanchet@49286
  1173
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1174
blanchet@49112
  1175
val parse_single_spec =
blanchet@49112
  1176
  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
blanchet@49119
  1177
  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
blanchet@49286
  1178
    Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
blanchet@49112
  1179
blanchet@49278
  1180
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
blanchet@49278
  1181
blanchet@49585
  1182
fun parse_datatype_cmd lfp construct_fp = parse_datatype >> datatype_cmd lfp construct_fp;
blanchet@49112
  1183
blanchet@49112
  1184
end;