src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Mon Apr 29 09:45:14 2013 +0200 (2013-04-29)
changeset 51805 67757f1d5e71
parent 51804 be6e703908f4
child 51808 355dcd6a9b3c
permissions -rw-r--r--
use record instead of huge tuple
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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 -> binding list -> binding list ->
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      binding list list -> typ list * typ list list -> BNF_Def.BNF list -> local_theory ->
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      BNF_FP.fp_result * local_theory) ->
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    (bool * bool) * (((((binding * (typ * sort)) list * binding) * (binding * binding)) * mixfix) *
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      ((((binding * binding) * (binding * typ) list) * (binding * term) list) *
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        mixfix) list) list ->
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    local_theory -> local_theory
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  val parse_datatype_cmd: bool ->
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    (mixfix list -> (string * sort) list option -> binding list -> binding list -> binding list ->
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      binding list list -> typ list * typ list list -> BNF_Def.BNF list -> local_theory ->
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      BNF_FP.fp_result * local_theory) ->
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    (local_theory -> local_theory) parser
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end;
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structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
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struct
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open BNF_Util
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open BNF_Ctr_Sugar
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open BNF_Def
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open BNF_FP
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open BNF_FP_Def_Sugar_Tactics
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val EqN = "Eq_";
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(* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A"). *)
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fun quasi_unambiguous_case_names names =
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  let
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    val ps = map (`Long_Name.base_name) names;
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    val dups = Library.duplicates (op =) (map fst ps);
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    fun underscore s =
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      let val ss = space_explode Long_Name.separator s in
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        space_implode "_" (drop (length ss - 2) ss)
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      end;
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  in
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    map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
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  end;
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val mp_conj = @{thm mp_conj};
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val simp_attrs = @{attributes [simp]};
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val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs;
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fun split_list4 [] = ([], [], [], [])
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  | split_list4 ((x1, x2, x3, x4) :: xs) =
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    let val (xs1, xs2, xs3, xs4) = split_list4 xs;
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    in (x1 :: xs1, x2 :: xs2, x3 :: xs3, x4 :: xs4) end;
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fun 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 flat_rec unzipf xs =
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  let val ps = map unzipf xs in
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    (* The first line below gives the preferred order. The second line is for compatibility with the
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       old datatype package: *)
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(*
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    maps (op @) ps
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*)
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    maps fst ps @ maps snd ps
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  end;
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fun 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 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_named_constrained_of ((((ncAs, _), _), _), _) = ncAs;
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fun type_binding_of ((((_, b), _), _), _) = b;
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fun map_binding_of (((_, (b, _)), _), _) = b;
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fun rel_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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    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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    val map_bs = map map_binding_of specs;
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    val rel_bs = map rel_binding_of specs;
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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_named_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 set_bss = map (map fst o type_args_named_constrained_of) specs;
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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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    fun add_fake_type spec =
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      Sign.add_type no_defs_lthy (type_binding_of spec,
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        length (type_args_named_constrained_of spec), mixfix_of spec);
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    val fake_thy = Theory.copy #> fold add_fake_type 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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    val (pre_bnfs, ({bnfs = fp_bnfs as any_fp_bnf :: _, dtors = dtors0, ctors = ctors0,
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           folds = fp_folds0, recs = fp_recs0, induct = fp_induct, strong_induct = fp_strong_induct,
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           dtor_ctors, ctor_dtors, ctor_injects, map_thms = fp_map_thms, set_thmss = fp_set_thmss,
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           rel_thms = fp_rel_thms, fold_thms = fp_fold_thms, rec_thms = fp_rec_thms}, lthy)) =
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      fp_bnf construct_fp fp_bs mixfixes map_bs rel_bs set_bss (map dest_TFree unsorted_As) fp_eqs
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        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;
blanchet@49585
   300
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@49683
   301
    val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs;
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   302
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
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   303
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
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   304
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51766
   305
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51766
   306
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@49585
   307
blanchet@49585
   308
    val live = live_of_bnf any_fp_bnf;
blanchet@49585
   309
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   310
    val Bs =
blanchet@49585
   311
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
   312
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
   313
blanchet@49585
   314
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
   315
blanchet@49501
   316
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
   317
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
   318
blanchet@49501
   319
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
   320
blanchet@51780
   321
    fun massage_simple_notes base =
blanchet@51780
   322
      filter_out (null o #2)
blanchet@51780
   323
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
   324
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
   325
blanchet@51780
   326
    val massage_multi_notes =
blanchet@51780
   327
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
   328
        if forall null thmss then
blanchet@51780
   329
          []
blanchet@51780
   330
        else
blanchet@51780
   331
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@51780
   332
            ((qualify true fp_b_name (Binding.name thmN), attrs T_name),
blanchet@51780
   333
             [(thms, [])])) fp_b_names fpTs thmss);
blanchet@51780
   334
blanchet@49362
   335
    val exists_fp_subtype = exists_subtype (member (op =) fpTs);
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   336
    val exists_Cs_subtype = exists_subtype (member (op =) Cs);
blanchet@49362
   337
blanchet@49536
   338
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
blanchet@49203
   339
    val ns = map length ctr_Tsss;
blanchet@49212
   340
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
   341
    val mss = map (map length) ctr_Tsss;
blanchet@49203
   342
    val Css = map2 replicate ns Cs;
blanchet@49203
   343
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   344
    val fp_folds as any_fp_fold :: _ = map (mk_rec_like lfp As Cs) fp_folds0;
blanchet@49585
   345
    val fp_recs as any_fp_rec :: _ = map (mk_rec_like lfp As Cs) fp_recs0;
blanchet@49210
   346
blanchet@49585
   347
    val fp_fold_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_fold)));
blanchet@49585
   348
    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_rec)));
blanchet@49204
   349
blanchet@49504
   350
    val (((fold_only as (gss, _, _), rec_only as (hss, _, _)),
blanchet@49683
   351
          (cs, cpss, unfold_only as ((pgss, crssss, cgssss), (_, g_Tsss, _)),
blanchet@49683
   352
           corec_only as ((phss, csssss, chssss), (_, h_Tsss, _)))), names_lthy0) =
blanchet@49208
   353
      if lfp then
blanchet@49208
   354
        let
blanchet@49208
   355
          val y_Tsss =
blanchet@49255
   356
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49504
   357
              ns mss fp_fold_fun_Ts;
blanchet@49208
   358
          val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
blanchet@49208
   359
blanchet@49484
   360
          val ((gss, ysss), lthy) =
blanchet@49208
   361
            lthy
blanchet@49208
   362
            |> mk_Freess "f" g_Tss
blanchet@49208
   363
            ||>> mk_Freesss "x" y_Tsss;
blanchet@49670
   364
blanchet@49670
   365
          fun proj_recT proj (Type (s as @{type_name prod}, Ts as [T, U])) =
blanchet@49670
   366
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_recT proj) Ts)
blanchet@49670
   367
            | proj_recT proj (Type (s, Ts)) = Type (s, map (proj_recT proj) Ts)
blanchet@49670
   368
            | proj_recT _ T = T;
blanchet@49274
   369
blanchet@51794
   370
          fun unzip_recT T =
blanchet@51794
   371
            if exists_fp_subtype T then ([proj_recT fst T], [proj_recT snd T]) else ([T], []);
blanchet@49204
   372
blanchet@49670
   373
          val z_Tsss =
blanchet@49670
   374
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49670
   375
              ns mss fp_rec_fun_Ts;
blanchet@51794
   376
          val z_Tsss' = map (map (flat_rec unzip_recT)) z_Tsss;
blanchet@51794
   377
          val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' Css;
blanchet@49204
   378
blanchet@49298
   379
          val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@49670
   380
          val zsss = map2 (map2 (map2 retype_free)) z_Tsss ysss;
blanchet@49210
   381
        in
blanchet@49670
   382
          ((((gss, g_Tss, ysss), (hss, h_Tss, zsss)),
blanchet@49683
   383
            ([], [], (([], [], []), ([], [], [])), (([], [], []), ([], [], [])))), lthy)
blanchet@49210
   384
        end
blanchet@49208
   385
      else
blanchet@49210
   386
        let
blanchet@49221
   387
          (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@49221
   388
          val mss' =  map (fn [0] => [1] | ms => ms) mss;
blanchet@49221
   389
blanchet@49463
   390
          val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@49275
   391
blanchet@49587
   392
          fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss);
blanchet@49211
   393
blanchet@49587
   394
          fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss
blanchet@49587
   395
            | flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
blanchet@49587
   396
              p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss;
blanchet@49274
   397
blanchet@49681
   398
          fun mk_types maybe_unzipT fun_Ts =
blanchet@49212
   399
            let
blanchet@49212
   400
              val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@49255
   401
              val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@49681
   402
              val f_Tsss = map2 (map2 dest_tupleT) mss' f_prod_Tss;
blanchet@49275
   403
              val f_Tssss =
blanchet@49681
   404
                map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
blanchet@49275
   405
              val q_Tssss =
blanchet@49463
   406
                map (map (map (fn [_] => [] | [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss;
blanchet@49587
   407
              val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@49681
   408
            in (q_Tssss, f_sum_prod_Ts, f_Tsss, f_Tssss, pf_Tss) end;
blanchet@49176
   409
blanchet@49681
   410
          val (r_Tssss, g_sum_prod_Ts, g_Tsss, g_Tssss, pg_Tss) = mk_types single fp_fold_fun_Ts;
blanchet@49211
   411
blanchet@49683
   412
          val (((cs, pss), gssss), lthy) =
blanchet@49210
   413
            lthy
blanchet@49683
   414
            |> mk_Frees "a" Cs
blanchet@49211
   415
            ||>> mk_Freess "p" p_Tss
blanchet@49275
   416
            ||>> mk_Freessss "g" g_Tssss;
blanchet@49275
   417
          val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@49274
   418
blanchet@49681
   419
          fun proj_corecT proj (Type (s as @{type_name sum}, Ts as [T, U])) =
blanchet@49681
   420
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   421
            | proj_corecT proj (Type (s, Ts)) = Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   422
            | proj_corecT _ T = T;
blanchet@49274
   423
blanchet@49681
   424
          fun unzip_corecT T =
blanchet@49681
   425
            if exists_fp_subtype T then [proj_corecT fst T, proj_corecT snd T] else [T];
blanchet@49681
   426
blanchet@49681
   427
          val (s_Tssss, h_sum_prod_Ts, h_Tsss, h_Tssss, ph_Tss) =
blanchet@49681
   428
            mk_types unzip_corecT fp_rec_fun_Ts;
blanchet@49210
   429
blanchet@49298
   430
          val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@49484
   431
          val ((sssss, hssss_tl), lthy) =
blanchet@49275
   432
            lthy
blanchet@49275
   433
            |> mk_Freessss "q" s_Tssss
blanchet@49275
   434
            ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@49275
   435
          val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@49211
   436
blanchet@49681
   437
          val cpss = map2 (map o rapp) cs pss;
blanchet@49212
   438
blanchet@49683
   439
          fun mk_terms qssss fssss =
blanchet@49212
   440
            let
blanchet@49587
   441
              val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
blanchet@49681
   442
              val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@49681
   443
              val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@49683
   444
            in (pfss, cqssss, cfssss) end;
blanchet@49210
   445
        in
blanchet@49484
   446
          (((([], [], []), ([], [], [])),
blanchet@49683
   447
            (cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, g_Tsss, pg_Tss)),
blanchet@49683
   448
             (mk_terms sssss hssss, (h_sum_prod_Ts, h_Tsss, ph_Tss)))), lthy)
blanchet@49210
   449
        end;
blanchet@49210
   450
blanchet@49585
   451
    fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@49585
   452
            fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@49585
   453
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@49585
   454
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   455
      let
blanchet@49498
   456
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
   457
blanchet@49501
   458
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
   459
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   460
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   461
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   462
blanchet@49593
   463
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
   464
          no_defs_lthy
blanchet@49501
   465
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
   466
          ||>> mk_Frees "f" case_Ts
blanchet@49370
   467
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
   468
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
   469
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
   470
blanchet@49498
   471
        val u = Free (u', fpT);
blanchet@49121
   472
blanchet@49585
   473
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
   474
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
   475
blanchet@49129
   476
        val ctr_rhss =
blanchet@49585
   477
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
   478
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
   479
blanchet@49633
   480
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
   481
blanchet@49134
   482
        val case_rhs =
blanchet@49498
   483
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
   484
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
   485
blanchet@49201
   486
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   487
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
   488
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
   489
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   490
          ||> `Local_Theory.restore;
blanchet@49121
   491
blanchet@49121
   492
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   493
blanchet@49121
   494
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
   495
        val ctr_defs' =
blanchet@49585
   496
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
   497
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   498
blanchet@49203
   499
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   500
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   501
blanchet@49203
   502
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   503
blanchet@49585
   504
        fun wrap lthy =
blanchet@49123
   505
          let
traytel@50170
   506
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
   507
              let
blanchet@49585
   508
                val ctor_iff_dtor_thm =
blanchet@49585
   509
                  let
blanchet@49585
   510
                    val goal =
blanchet@49585
   511
                      fold_rev Logic.all [w, u]
blanchet@49585
   512
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
   513
                  in
wenzelm@51551
   514
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
   515
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
   516
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
   517
                    |> Thm.close_derivation
blanchet@49585
   518
                    |> Morphism.thm phi
blanchet@49585
   519
                  end;
blanchet@49585
   520
blanchet@49585
   521
                val sumEN_thm' =
blanchet@49585
   522
                  unfold_thms lthy @{thms all_unit_eq}
blanchet@49585
   523
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
   524
                       (mk_sumEN_balanced n))
blanchet@49585
   525
                  |> Morphism.thm phi;
blanchet@49135
   526
              in
blanchet@49585
   527
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
   528
              end;
blanchet@49135
   529
blanchet@49585
   530
            val inject_tacss =
blanchet@49585
   531
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
   532
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
   533
blanchet@49585
   534
            val half_distinct_tacss =
blanchet@49585
   535
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
   536
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
   537
blanchet@49585
   538
            val case_tacs =
blanchet@49585
   539
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
   540
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
   541
blanchet@49585
   542
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
   543
blanchet@49585
   544
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
   545
          in
blanchet@51781
   546
            wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
blanchet@51781
   547
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
   548
          end;
blanchet@49121
   549
blanchet@49585
   550
        fun derive_maps_sets_rels (wrap_res, lthy) =
blanchet@49585
   551
          let
blanchet@49585
   552
            val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@49585
   553
            val nones = replicate live NONE;
blanchet@49585
   554
blanchet@49585
   555
            val ctor_cong =
blanchet@51746
   556
              if lfp then
blanchet@51746
   557
                Drule.dummy_thm
blanchet@51746
   558
              else
blanchet@51746
   559
                let val ctor' = mk_ctor Bs ctor in
blanchet@51746
   560
                  cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51746
   561
                end;
blanchet@49585
   562
blanchet@49585
   563
            fun mk_cIn ify =
blanchet@49585
   564
              certify lthy o (not lfp ? curry (op $) (map_types ify ctor)) oo
blanchet@49585
   565
              mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
   566
blanchet@49585
   567
            val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@49585
   568
            val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
   569
blanchet@49682
   570
            fun mk_map_thm ctr_def' cxIn =
blanchet@49585
   571
              fold_thms lthy [ctr_def']
blanchet@49585
   572
                (unfold_thms lthy (pre_map_def ::
blanchet@49585
   573
                     (if lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@49585
   574
                   (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@49585
   575
                      (if lfp then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@49593
   576
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   577
blanchet@49682
   578
            fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@49585
   579
              fold_thms lthy [ctr_def']
blanchet@51766
   580
                (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@49585
   581
                     (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@49585
   582
                   (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@49593
   583
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   584
blanchet@49682
   585
            fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49585
   586
blanchet@49682
   587
            val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@49585
   588
            val set_thmss = map mk_set_thms fp_set_thms;
blanchet@49127
   589
blanchet@49682
   590
            val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
   591
blanchet@49682
   592
            fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@49585
   593
              fold_thms lthy ctr_defs'
blanchet@51745
   594
                 (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@51745
   595
                      (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@49585
   596
                    (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@49593
   597
              |> postproc
blanchet@49593
   598
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   599
blanchet@49682
   600
            fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@49682
   601
              mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
   602
blanchet@49592
   603
            val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
   604
blanchet@49682
   605
            fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@49585
   606
              mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@49682
   607
                cxIn cyIn;
blanchet@49121
   608
blanchet@49592
   609
            fun mk_other_half_rel_distinct_thm thm =
blanchet@49585
   610
              flip_rels lthy live thm RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
   611
blanchet@49592
   612
            val half_rel_distinct_thmss =
blanchet@49592
   613
              map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@49592
   614
            val other_half_rel_distinct_thmss =
blanchet@49592
   615
              map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@49592
   616
            val (rel_distinct_thms, _) =
blanchet@49592
   617
              join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
   618
blanchet@49585
   619
            val notes =
blanchet@49594
   620
              [(mapN, map_thms, code_simp_attrs),
blanchet@49592
   621
               (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@49592
   622
               (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@49585
   623
               (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51780
   624
              |> massage_simple_notes fp_b_name;
blanchet@49585
   625
          in
blanchet@49585
   626
            (wrap_res, lthy |> Local_Theory.notes notes |> snd)
blanchet@49585
   627
          end;
blanchet@49585
   628
blanchet@49585
   629
        fun define_fold_rec no_defs_lthy =
blanchet@49134
   630
          let
blanchet@49208
   631
            val fpT_to_C = fpT --> C;
blanchet@49199
   632
blanchet@49681
   633
            fun build_prod_proj mk_proj (T, U) =
blanchet@49670
   634
              if T = U then
blanchet@49670
   635
                id_const T
blanchet@49670
   636
              else
blanchet@49670
   637
                (case (T, U) of
blanchet@49670
   638
                  (Type (s, _), Type (s', _)) =>
blanchet@49681
   639
                  if s = s' then build_map (build_prod_proj mk_proj) T U else mk_proj T
blanchet@49670
   640
                | _ => mk_proj T);
blanchet@49670
   641
blanchet@49681
   642
            (* TODO: Avoid these complications; cf. corec case *)
blanchet@49672
   643
            fun mk_U proj (Type (s as @{type_name prod}, Ts as [T', U])) =
blanchet@49672
   644
                if member (op =) fpTs T' then proj (T', U) else Type (s, map (mk_U proj) Ts)
blanchet@49670
   645
              | mk_U proj (Type (s, Ts)) = Type (s, map (mk_U proj) Ts)
blanchet@49670
   646
              | mk_U _ T = T;
blanchet@49670
   647
blanchet@51794
   648
            fun unzip_rec (x as Free (_, T)) =
blanchet@49670
   649
              if exists_fp_subtype T then
blanchet@51794
   650
                ([build_prod_proj fst_const (T, mk_U fst T) $ x],
blanchet@51794
   651
                 [build_prod_proj snd_const (T, mk_U snd T) $ x])
blanchet@49670
   652
              else
blanchet@51794
   653
                ([x], []);
blanchet@49670
   654
blanchet@51793
   655
            fun mk_rec_like_arg f xs =
blanchet@51794
   656
              mk_tupled_fun (HOLogic.mk_tuple xs) f (flat_rec unzip_rec xs);
blanchet@49670
   657
blanchet@49670
   658
            fun generate_rec_like (suf, fp_rec_like, (fss, f_Tss, xsss)) =
blanchet@49215
   659
              let
blanchet@49215
   660
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49633
   661
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49215
   662
                val spec =
blanchet@49336
   663
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   664
                    Term.list_comb (fp_rec_like,
blanchet@49670
   665
                      map2 (mk_sum_caseN_balanced oo map2 mk_rec_like_arg) fss xsss));
blanchet@49336
   666
              in (binding, spec) end;
blanchet@49199
   667
blanchet@49504
   668
            val rec_like_infos =
blanchet@49504
   669
              [(foldN, fp_fold, fold_only),
blanchet@49215
   670
               (recN, fp_rec, rec_only)];
blanchet@49215
   671
blanchet@49504
   672
            val (bindings, specs) = map generate_rec_like rec_like_infos |> split_list;
blanchet@49215
   673
blanchet@49215
   674
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   675
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   676
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   677
                #>> apsnd snd) bindings specs
blanchet@49199
   678
              ||> `Local_Theory.restore;
blanchet@49201
   679
blanchet@49201
   680
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   681
blanchet@49504
   682
            val [fold_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   683
blanchet@49536
   684
            val [foldx, recx] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49134
   685
          in
blanchet@49693
   686
            ((foldx, recx, fold_def, rec_def), lthy')
blanchet@49134
   687
          end;
blanchet@49134
   688
blanchet@49585
   689
        fun define_unfold_corec no_defs_lthy =
blanchet@49210
   690
          let
blanchet@49210
   691
            val B_to_fpT = C --> fpT;
blanchet@49211
   692
blanchet@49683
   693
            fun build_sum_inj mk_inj (T, U) =
blanchet@49683
   694
              if T = U then
blanchet@49683
   695
                id_const T
blanchet@49683
   696
              else
blanchet@49683
   697
                (case (T, U) of
blanchet@49683
   698
                  (Type (s, _), Type (s', _)) =>
blanchet@49683
   699
                  if s = s' then build_map (build_sum_inj mk_inj) T U
blanchet@49683
   700
                  else uncurry mk_inj (dest_sumT U)
blanchet@49683
   701
                | _ => uncurry mk_inj (dest_sumT U));
blanchet@49683
   702
blanchet@49683
   703
            fun build_dtor_corec_like_arg _ [] [cf] = cf
blanchet@49683
   704
              | build_dtor_corec_like_arg T [cq] [cf, cf'] =
blanchet@49683
   705
                mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@49683
   706
                  (build_sum_inj Inr_const (fastype_of cf', T) $ cf')
blanchet@49683
   707
blanchet@49683
   708
            val crgsss = map3 (map3 (map3 build_dtor_corec_like_arg)) g_Tsss crssss cgssss;
blanchet@49683
   709
            val cshsss = map3 (map3 (map3 build_dtor_corec_like_arg)) h_Tsss csssss chssss;
blanchet@49683
   710
blanchet@49276
   711
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
   712
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
   713
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
   714
blanchet@49683
   715
            fun generate_corec_like (suf, fp_rec_like, (cqfsss, ((pfss, _, _), (f_sum_prod_Ts, _,
blanchet@49683
   716
                pf_Tss)))) =
blanchet@49211
   717
              let
blanchet@49211
   718
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49633
   719
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49211
   720
                val spec =
blanchet@49336
   721
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   722
                    Term.list_comb (fp_rec_like,
blanchet@49276
   723
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49336
   724
              in (binding, spec) end;
blanchet@49210
   725
blanchet@49504
   726
            val corec_like_infos =
blanchet@49683
   727
              [(unfoldN, fp_fold, (crgsss, unfold_only)),
blanchet@49683
   728
               (corecN, fp_rec, (cshsss, corec_only))];
blanchet@49212
   729
blanchet@49504
   730
            val (bindings, specs) = map generate_corec_like corec_like_infos |> split_list;
blanchet@49211
   731
blanchet@49211
   732
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   733
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   734
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   735
                #>> apsnd snd) bindings specs
blanchet@49210
   736
              ||> `Local_Theory.restore;
blanchet@49210
   737
blanchet@49210
   738
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   739
blanchet@49504
   740
            val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   741
blanchet@49536
   742
            val [unfold, corec] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49210
   743
          in
blanchet@49693
   744
            ((unfold, corec, unfold_def, corec_def), lthy')
blanchet@49287
   745
          end;
blanchet@49287
   746
blanchet@49504
   747
        val define_rec_likes = if lfp then define_fold_rec else define_unfold_corec;
blanchet@49585
   748
blanchet@49585
   749
        fun massage_res ((wrap_res, rec_like_res), lthy) =
blanchet@49585
   750
          (((ctrs, xss, ctr_defs, wrap_res), rec_like_res), lthy);
blanchet@49119
   751
      in
blanchet@49585
   752
        (wrap #> (live > 0 ? derive_maps_sets_rels) ##>> define_rec_likes #> massage_res, lthy')
blanchet@49119
   753
      end;
blanchet@49167
   754
blanchet@49585
   755
    fun wrap_types_and_more (wrap_types_and_mores, lthy) =
blanchet@49585
   756
      fold_map I wrap_types_and_mores lthy
blanchet@49585
   757
      |>> apsnd split_list4 o apfst split_list4 o split_list;
blanchet@49226
   758
blanchet@49585
   759
    (* TODO: Add map, sets, rel simps *)
blanchet@49479
   760
    val mk_simp_thmss =
blanchet@49591
   761
      map3 (fn (_, _, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn fold_likes =>
blanchet@49505
   762
        injects @ distincts @ cases @ rec_likes @ fold_likes);
blanchet@49479
   763
blanchet@49585
   764
    fun derive_induct_fold_rec_thms_for_types (((ctrss, xsss, ctr_defss, wrap_ress), (folds, recs,
blanchet@49585
   765
        fold_defs, rec_defs)), lthy) =
blanchet@49202
   766
      let
blanchet@49591
   767
        val (((ps, ps'), us'), names_lthy) =
blanchet@49370
   768
          lthy
blanchet@49463
   769
          |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@49498
   770
          ||>> Variable.variant_fixes fp_b_names;
blanchet@49370
   771
blanchet@49498
   772
        val us = map2 (curry Free) us' fpTs;
blanchet@49370
   773
blanchet@49362
   774
        fun mk_sets_nested bnf =
blanchet@49362
   775
          let
blanchet@49362
   776
            val Type (T_name, Us) = T_of_bnf bnf;
blanchet@49362
   777
            val lives = lives_of_bnf bnf;
blanchet@49362
   778
            val sets = sets_of_bnf bnf;
blanchet@49362
   779
            fun mk_set U =
blanchet@49362
   780
              (case find_index (curry (op =) U) lives of
blanchet@49362
   781
                ~1 => Term.dummy
blanchet@49362
   782
              | i => nth sets i);
blanchet@49362
   783
          in
blanchet@49362
   784
            (T_name, map mk_set Us)
blanchet@49362
   785
          end;
blanchet@49362
   786
blanchet@49362
   787
        val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@49362
   788
blanchet@49337
   789
        val (induct_thms, induct_thm) =
blanchet@49337
   790
          let
blanchet@49362
   791
            fun mk_set Ts t =
blanchet@49362
   792
              let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@49362
   793
                Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49362
   794
              end;
blanchet@49362
   795
blanchet@49375
   796
            fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
blanchet@49361
   797
                (case find_index (curry (op =) T) fpTs of
blanchet@49362
   798
                  ~1 =>
blanchet@49362
   799
                  (case AList.lookup (op =) setss_nested T_name of
blanchet@49362
   800
                    NONE => []
blanchet@49362
   801
                  | SOME raw_sets0 =>
blanchet@49362
   802
                    let
blanchet@49362
   803
                      val (Ts, raw_sets) =
blanchet@49362
   804
                        split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
blanchet@49362
   805
                      val sets = map (mk_set Ts0) raw_sets;
blanchet@49362
   806
                      val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@49375
   807
                      val xysets = map (pair x) (ys ~~ sets);
blanchet@49375
   808
                      val ppremss = map (mk_raw_prem_prems names_lthy') ys;
blanchet@49362
   809
                    in
blanchet@49375
   810
                      flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@49362
   811
                    end)
blanchet@49591
   812
                | kk => [([], (kk + 1, x))])
blanchet@49375
   813
              | mk_raw_prem_prems _ _ = [];
blanchet@49342
   814
blanchet@49378
   815
            fun close_prem_prem xs t =
blanchet@49378
   816
              fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@49591
   817
                (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@49362
   818
blanchet@49378
   819
            fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@49378
   820
              close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@49376
   821
                  HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@49591
   822
                HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@49375
   823
blanchet@49372
   824
            fun mk_raw_prem phi ctr ctr_Ts =
blanchet@49362
   825
              let
blanchet@49362
   826
                val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@49376
   827
                val pprems = maps (mk_raw_prem_prems names_lthy') xs;
blanchet@49378
   828
              in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@49342
   829
blanchet@49376
   830
            fun mk_prem (xs, raw_pprems, concl) =
blanchet@49378
   831
              fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@49368
   832
blanchet@49591
   833
            val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss;
blanchet@49389
   834
blanchet@49361
   835
            val goal =
blanchet@49372
   836
              Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@49591
   837
                HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@49368
   838
blanchet@49429
   839
            val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@49368
   840
blanchet@49501
   841
            val ctor_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@49342
   842
blanchet@49591
   843
            val thm =
wenzelm@51551
   844
              Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51766
   845
                mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
blanchet@51766
   846
                  pre_set_defss)
blanchet@49368
   847
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49591
   848
              |> Thm.close_derivation;
blanchet@49337
   849
          in
blanchet@49591
   850
            `(conj_dests nn) thm
blanchet@49337
   851
          end;
blanchet@49201
   852
blanchet@49622
   853
        val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@49437
   854
blanchet@49504
   855
        val (fold_thmss, rec_thmss) =
blanchet@49207
   856
          let
blanchet@49337
   857
            val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49504
   858
            val gfolds = map (lists_bmoc gss) folds;
blanchet@49337
   859
            val hrecs = map (lists_bmoc hss) recs;
blanchet@49337
   860
blanchet@49504
   861
            fun mk_goal fss frec_like xctr f xs fxs =
blanchet@49207
   862
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49504
   863
                (mk_Trueprop_eq (frec_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   864
blanchet@49682
   865
            fun build_rec_like frec_likes (T, U) =
blanchet@49234
   866
              if T = U then
blanchet@49368
   867
                id_const T
blanchet@49234
   868
              else
blanchet@49234
   869
                (case find_index (curry (op =) T) fpTs of
blanchet@49682
   870
                  ~1 => build_map (build_rec_like frec_likes) T U
blanchet@49682
   871
                | kk => nth frec_likes kk);
blanchet@49233
   872
blanchet@49682
   873
            val mk_U = typ_subst (map2 pair fpTs Cs);
blanchet@49214
   874
blanchet@51794
   875
            fun unzip_rec_likes frec_likes combine (x as Free (_, T)) =
blanchet@49670
   876
              if exists_fp_subtype T then
blanchet@51794
   877
                combine (x, build_rec_like frec_likes (T, mk_U T) $ x)
blanchet@49214
   878
              else
blanchet@51794
   879
                ([x], []);
blanchet@49214
   880
blanchet@51794
   881
            val gxsss = map (map (flat_rec (unzip_rec_likes gfolds (fn (_, t) => ([t], []))))) xsss;
blanchet@51794
   882
            val hxsss = map (map (flat_rec (unzip_rec_likes hrecs (pairself single)))) xsss;
blanchet@49204
   883
blanchet@49504
   884
            val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
blanchet@49484
   885
            val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   886
blanchet@49504
   887
            val fold_tacss =
blanchet@49670
   888
              map2 (map o mk_rec_like_tac pre_map_defs [] nesting_map_ids'' fold_defs) fp_fold_thms
blanchet@49363
   889
                ctr_defss;
blanchet@49203
   890
            val rec_tacss =
blanchet@49670
   891
              map2 (map o mk_rec_like_tac pre_map_defs nested_map_comp's
blanchet@49670
   892
                (nested_map_ids'' @ nesting_map_ids'') rec_defs) fp_rec_thms ctr_defss;
blanchet@49484
   893
blanchet@49591
   894
            fun prove goal tac =
wenzelm@51551
   895
              Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@49591
   896
              |> Thm.close_derivation;
blanchet@49202
   897
          in
blanchet@49595
   898
            (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
blanchet@49202
   899
          end;
blanchet@49201
   900
blanchet@49504
   901
        val simp_thmss = mk_simp_thmss wrap_ress rec_thmss fold_thmss;
blanchet@49438
   902
blanchet@49437
   903
        val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@49437
   904
        fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name));
blanchet@49437
   905
blanchet@49337
   906
        val common_notes =
blanchet@49437
   907
          (if nn > 1 then [(inductN, [induct_thm], [induct_case_names_attr])] else [])
blanchet@51780
   908
          |> massage_simple_notes fp_common_name;
blanchet@49337
   909
blanchet@49226
   910
        val notes =
blanchet@49633
   911
          [(foldN, fold_thmss, K code_simp_attrs),
blanchet@49633
   912
           (inductN, map single induct_thms,
blanchet@49437
   913
            fn T_name => [induct_case_names_attr, induct_type_attr T_name]),
blanchet@49622
   914
           (recN, rec_thmss, K code_simp_attrs),
blanchet@49585
   915
           (simpsN, simp_thmss, K [])]
blanchet@51780
   916
          |> massage_multi_notes;
blanchet@49202
   917
      in
blanchet@49337
   918
        lthy |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@49202
   919
      end;
blanchet@49202
   920
blanchet@49585
   921
    fun derive_coinduct_unfold_corec_thms_for_types (((ctrss, _, ctr_defss, wrap_ress), (unfolds,
blanchet@49585
   922
        corecs, unfold_defs, corec_defs)), lthy) =
blanchet@49212
   923
      let
blanchet@49591
   924
        val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@49591
   925
blanchet@49484
   926
        val discss = map (map (mk_disc_or_sel As) o #1) wrap_ress;
blanchet@49591
   927
        val selsss = map (map (map (mk_disc_or_sel As)) o #2) wrap_ress;
blanchet@49591
   928
        val exhaust_thms = map #3 wrap_ress;
blanchet@49591
   929
        val disc_thmsss = map #7 wrap_ress;
blanchet@49591
   930
        val discIss = map #8 wrap_ress;
blanchet@49591
   931
        val sel_thmsss = map #9 wrap_ress;
blanchet@49438
   932
blanchet@49591
   933
        val (((rs, us'), vs'), names_lthy) =
blanchet@49370
   934
          lthy
blanchet@49591
   935
          |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@49591
   936
          ||>> Variable.variant_fixes fp_b_names
blanchet@49591
   937
          ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@49370
   938
blanchet@49498
   939
        val us = map2 (curry Free) us' fpTs;
blanchet@49591
   940
        val udiscss = map2 (map o rapp) us discss;
blanchet@49591
   941
        val uselsss = map2 (map o map o rapp) us selsss;
blanchet@49370
   942
blanchet@49591
   943
        val vs = map2 (curry Free) vs' fpTs;
blanchet@49591
   944
        val vdiscss = map2 (map o rapp) vs discss;
blanchet@49591
   945
        val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@49591
   946
blanchet@49591
   947
        val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
blanchet@49337
   948
          let
blanchet@49591
   949
            val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@49591
   950
            val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@49591
   951
            val strong_rs =
blanchet@49591
   952
              map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@49591
   953
                fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@49591
   954
blanchet@49591
   955
            fun build_rel rs' T =
blanchet@49591
   956
              (case find_index (curry (op =) T) fpTs of
blanchet@49591
   957
                ~1 =>
blanchet@49683
   958
                if exists_fp_subtype T then build_rel_step (build_rel rs') T else HOLogic.eq_const T
blanchet@49591
   959
              | kk => nth rs' kk);
blanchet@49591
   960
blanchet@49591
   961
            fun build_rel_app rs' usel vsel =
blanchet@49591
   962
              fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@49591
   963
blanchet@49591
   964
            fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@49591
   965
              (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@49591
   966
              (if null usels then
blanchet@49591
   967
                 []
blanchet@49591
   968
               else
blanchet@49591
   969
                 [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@49591
   970
                    Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@49591
   971
blanchet@49591
   972
            fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@49591
   973
              Library.foldr1 HOLogic.mk_conj
blanchet@49591
   974
                (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@49591
   975
              handle List.Empty => @{term True};
blanchet@49591
   976
blanchet@49591
   977
            fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@49591
   978
              fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@49591
   979
                HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@49591
   980
blanchet@49591
   981
            val concl =
blanchet@49591
   982
              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49591
   983
                (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@49591
   984
                   uvrs us vs));
blanchet@49591
   985
blanchet@49591
   986
            fun mk_goal rs' =
blanchet@49591
   987
              Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@49591
   988
                concl);
blanchet@49591
   989
blanchet@49591
   990
            val goal = mk_goal rs;
blanchet@49591
   991
            val strong_goal = mk_goal strong_rs;
blanchet@49591
   992
blanchet@49591
   993
            fun prove dtor_coinduct' goal =
wenzelm@51551
   994
              Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49591
   995
                mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@49591
   996
                  exhaust_thms ctr_defss disc_thmsss sel_thmsss)
blanchet@49591
   997
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49591
   998
              |> Thm.close_derivation;
blanchet@49591
   999
blanchet@49590
  1000
            fun postproc nn thm =
blanchet@49590
  1001
              Thm.permute_prems 0 nn
blanchet@49591
  1002
                (if nn = 1 then thm RS mp
blanchet@49591
  1003
                 else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@49591
  1004
              |> Drule.zero_var_indexes
blanchet@49591
  1005
              |> `(conj_dests nn);
blanchet@49337
  1006
          in
blanchet@49591
  1007
            (postproc nn (prove fp_induct goal), postproc nn (prove fp_strong_induct strong_goal))
blanchet@49337
  1008
          end;
blanchet@49212
  1009
blanchet@51777
  1010
        fun mk_coinduct_concls ms discs ctrs =
blanchet@51777
  1011
          let
blanchet@51777
  1012
            fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51777
  1013
            fun mk_ctr_concl 0 _ = []
blanchet@51777
  1014
              | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51777
  1015
            val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51777
  1016
            val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51777
  1017
          in
blanchet@51777
  1018
            flat (map2 append disc_concls ctr_concls)
blanchet@51777
  1019
          end;
blanchet@51777
  1020
blanchet@51777
  1021
        val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51777
  1022
        val coinduct_conclss =
blanchet@51777
  1023
          map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51777
  1024
blanchet@49484
  1025
        fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@49484
  1026
blanchet@49504
  1027
        val gunfolds = map (lists_bmoc pgss) unfolds;
blanchet@49484
  1028
        val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49484
  1029
blanchet@49504
  1030
        val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@49212
  1031
          let
blanchet@49504
  1032
            fun mk_goal pfss c cps fcorec_like n k ctr m cfs' =
blanchet@49212
  1033
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49484
  1034
                (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@49504
  1035
                   mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
  1036
blanchet@49683
  1037
            fun build_corec_like fcorec_likes (T, U) =
blanchet@49234
  1038
              if T = U then
blanchet@49368
  1039
                id_const T
blanchet@49234
  1040
              else
blanchet@49234
  1041
                (case find_index (curry (op =) U) fpTs of
blanchet@49683
  1042
                  ~1 => build_map (build_corec_like fcorec_likes) T U
blanchet@49683
  1043
                | kk => nth fcorec_likes kk);
blanchet@49683
  1044
blanchet@49683
  1045
            val mk_U = typ_subst (map2 pair Cs fpTs);
blanchet@49233
  1046
blanchet@49683
  1047
            fun intr_corec_likes fcorec_likes [] [cf] =
blanchet@49683
  1048
                let val T = fastype_of cf in
blanchet@49683
  1049
                  if exists_Cs_subtype T then build_corec_like fcorec_likes (T, mk_U T) $ cf else cf
blanchet@49683
  1050
                end
blanchet@49683
  1051
              | intr_corec_likes fcorec_likes [cq] [cf, cf'] =
blanchet@49683
  1052
                mk_If cq (intr_corec_likes fcorec_likes [] [cf])
blanchet@49683
  1053
                  (intr_corec_likes fcorec_likes [] [cf']);
blanchet@49683
  1054
blanchet@49683
  1055
            val crgsss = map2 (map2 (map2 (intr_corec_likes gunfolds))) crssss cgssss;
blanchet@49683
  1056
            val cshsss = map2 (map2 (map2 (intr_corec_likes hcorecs))) csssss chssss;
blanchet@49212
  1057
blanchet@49683
  1058
            val unfold_goalss =
blanchet@49683
  1059
              map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
blanchet@49683
  1060
            val corec_goalss =
blanchet@49683
  1061
              map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
blanchet@49683
  1062
blanchet@49683
  1063
            fun mk_map_if_distrib bnf =
blanchet@49683
  1064
              let
blanchet@49683
  1065
                val mapx = map_of_bnf bnf;
blanchet@49683
  1066
                val live = live_of_bnf bnf;
blanchet@49683
  1067
                val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
blanchet@49683
  1068
                val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
blanchet@49683
  1069
                val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
blanchet@49683
  1070
              in
blanchet@49683
  1071
                Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
blanchet@49683
  1072
                  @{thm if_distrib}
blanchet@49276
  1073
              end;
blanchet@49232
  1074
blanchet@49683
  1075
            val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
blanchet@49213
  1076
blanchet@49504
  1077
            val unfold_tacss =
blanchet@49683
  1078
              map3 (map oo mk_corec_like_tac unfold_defs [] [] nesting_map_ids'' [])
blanchet@49683
  1079
                fp_fold_thms pre_map_defs ctr_defss;
blanchet@49233
  1080
            val corec_tacss =
blanchet@49683
  1081
              map3 (map oo mk_corec_like_tac corec_defs nested_map_comps'' nested_map_comp's
blanchet@49683
  1082
                  (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
blanchet@49683
  1083
                fp_rec_thms pre_map_defs ctr_defss;
blanchet@49479
  1084
blanchet@49484
  1085
            fun prove goal tac =
wenzelm@51551
  1086
              Goal.prove_sorry lthy [] [] goal (tac o #context) |> Thm.close_derivation;
blanchet@49484
  1087
blanchet@49504
  1088
            val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@49683
  1089
            val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
blanchet@49479
  1090
blanchet@49479
  1091
            val filter_safesss =
blanchet@49479
  1092
              map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@49683
  1093
                curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
blanchet@49479
  1094
blanchet@49683
  1095
            val safe_unfold_thmss = filter_safesss unfold_thmss;
blanchet@49683
  1096
            val safe_corec_thmss = filter_safesss corec_thmss;
blanchet@49479
  1097
          in
blanchet@49504
  1098
            (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@49212
  1099
          end;
blanchet@49212
  1100
blanchet@49504
  1101
        val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@49482
  1102
          let
blanchet@49504
  1103
            fun mk_goal c cps fcorec_like n k disc =
blanchet@49504
  1104
              mk_Trueprop_eq (disc $ (fcorec_like $ c),
blanchet@49484
  1105
                if n = 1 then @{const True}
blanchet@49484
  1106
                else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@49484
  1107
blanchet@49504
  1108
            val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@49484
  1109
            val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@49484
  1110
blanchet@49484
  1111
            fun mk_case_split' cp =
blanchet@49484
  1112
              Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@49484
  1113
blanchet@49484
  1114
            val case_splitss' = map (map mk_case_split') cpss;
blanchet@49482
  1115
blanchet@49504
  1116
            val unfold_tacss =
blanchet@49504
  1117
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@49484
  1118
            val corec_tacss =
blanchet@49504
  1119
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@49484
  1120
blanchet@49484
  1121
            fun prove goal tac =
wenzelm@51551
  1122
              Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@49591
  1123
              |> singleton (Proof_Context.export names_lthy0 no_defs_lthy)
blanchet@49591
  1124
              |> Thm.close_derivation;
blanchet@49484
  1125
blanchet@49484
  1126
            fun proves [_] [_] = []
blanchet@49484
  1127
              | proves goals tacs = map2 prove goals tacs;
blanchet@49482
  1128
          in
blanchet@49504
  1129
            (map2 proves unfold_goalss unfold_tacss,
blanchet@49484
  1130
             map2 proves corec_goalss corec_tacss)
blanchet@49482
  1131
          end;
blanchet@49482
  1132
blanchet@49605
  1133
        val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@49605
  1134
blanchet@49504
  1135
        fun mk_disc_corec_like_thms corec_likes discIs =
blanchet@49605
  1136
          map (op RS) (filter_out (is_triv_discI o snd) (corec_likes ~~ discIs));
blanchet@49266
  1137
blanchet@49504
  1138
        val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss;
blanchet@49504
  1139
        val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss;
blanchet@49266
  1140
blanchet@49504
  1141
        fun mk_sel_corec_like_thm corec_like_thm sel sel_thm =
blanchet@49266
  1142
          let
blanchet@49479
  1143
            val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@49266
  1144
            val arg_cong' =
blanchet@49266
  1145
              Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@49479
  1146
                [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@49267
  1147
              |> Thm.varifyT_global;
blanchet@49266
  1148
            val sel_thm' = sel_thm RSN (2, trans);
blanchet@49266
  1149
          in
blanchet@49504
  1150
            corec_like_thm RS arg_cong' RS sel_thm'
blanchet@49266
  1151
          end;
blanchet@49266
  1152
blanchet@49504
  1153
        fun mk_sel_corec_like_thms corec_likess =
blanchet@49504
  1154
          map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss |> map flat;
blanchet@49479
  1155
blanchet@49504
  1156
        val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss;
blanchet@49504
  1157
        val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss;
blanchet@49479
  1158
blanchet@49587
  1159
        fun flat_corec_like_thms corec_likes disc_corec_likes sel_corec_likes =
blanchet@49504
  1160
          corec_likes @ disc_corec_likes @ sel_corec_likes;
blanchet@49479
  1161
blanchet@49479
  1162
        val simp_thmss =
blanchet@49479
  1163
          mk_simp_thmss wrap_ress
blanchet@49587
  1164
            (map3 flat_corec_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@49587
  1165
            (map3 flat_corec_like_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss);
blanchet@49479
  1166
blanchet@49479
  1167
        val anonymous_notes =
blanchet@49504
  1168
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1169
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1170
blanchet@51777
  1171
        val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51777
  1172
        val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51777
  1173
        val coinduct_case_concl_attrs =
blanchet@51777
  1174
          map2 (fn casex => fn concls =>
blanchet@51777
  1175
              Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51777
  1176
            coinduct_cases coinduct_conclss;
blanchet@51777
  1177
        val coinduct_case_attrs =
blanchet@51777
  1178
          coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51780
  1179
        fun coinduct_type_attr T_name = Attrib.internal (K (Induct.coinduct_type T_name));
blanchet@51777
  1180
blanchet@49342
  1181
        val common_notes =
blanchet@49591
  1182
          (if nn > 1 then
blanchet@51777
  1183
             [(coinductN, [coinduct_thm], coinduct_case_attrs),
blanchet@51777
  1184
              (strong_coinductN, [strong_coinduct_thm], coinduct_case_attrs)]
blanchet@49591
  1185
           else
blanchet@49591
  1186
             [])
blanchet@51780
  1187
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1188
blanchet@49212
  1189
        val notes =
blanchet@51780
  1190
          [(coinductN, map single coinduct_thms,
blanchet@51780
  1191
            fn T_name => coinduct_case_attrs @ [coinduct_type_attr T_name]),
blanchet@51780
  1192
           (corecN, corec_thmss, K []),
blanchet@51780
  1193
           (disc_corecN, disc_corec_thmss, K simp_attrs),
blanchet@51780
  1194
           (disc_corec_iffN, disc_corec_iff_thmss, K simp_attrs),
blanchet@51780
  1195
           (disc_unfoldN, disc_unfold_thmss, K simp_attrs),
blanchet@51780
  1196
           (disc_unfold_iffN, disc_unfold_iff_thmss, K simp_attrs),
blanchet@51780
  1197
           (sel_corecN, sel_corec_thmss, K simp_attrs),
blanchet@51780
  1198
           (sel_unfoldN, sel_unfold_thmss, K simp_attrs),
blanchet@51780
  1199
           (simpsN, simp_thmss, K []),
blanchet@51780
  1200
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_case_attrs),
blanchet@51780
  1201
           (unfoldN, unfold_thmss, K [])]
blanchet@51780
  1202
          |> massage_multi_notes;
blanchet@49212
  1203
      in
blanchet@49479
  1204
        lthy |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@49212
  1205
      end;
blanchet@49212
  1206
blanchet@49204
  1207
    val lthy' = lthy
blanchet@49585
  1208
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@49585
  1209
        fp_folds ~~ fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@49585
  1210
        pre_set_defss ~~ pre_rel_defs ~~ fp_map_thms ~~ fp_set_thmss ~~ fp_rel_thms ~~ ns ~~ kss ~~
blanchet@49585
  1211
        mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
blanchet@49585
  1212
        raw_sel_defaultsss)
blanchet@49585
  1213
      |> wrap_types_and_more
blanchet@49585
  1214
      |> (if lfp then derive_induct_fold_rec_thms_for_types
blanchet@49585
  1215
          else derive_coinduct_unfold_corec_thms_for_types);
blanchet@49167
  1216
blanchet@49167
  1217
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
  1218
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
  1219
  in
blanchet@49308
  1220
    timer; lthy'
blanchet@49112
  1221
  end;
blanchet@49112
  1222
blanchet@49536
  1223
val datatypes = define_datatypes (K I) (K I) (K I);
blanchet@49297
  1224
blanchet@51380
  1225
val datatype_cmd = define_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1226
blanchet@49112
  1227
val parse_ctr_arg =
blanchet@49329
  1228
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1229
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1230
blanchet@49286
  1231
val parse_defaults =
blanchet@49286
  1232
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1233
blanchet@51758
  1234
val parse_type_arg_constrained =
blanchet@51790
  1235
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1236
blanchet@51790
  1237
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1238
blanchet@51758
  1239
val parse_type_args_named_constrained =
blanchet@51758
  1240
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1241
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1242
  Scan.succeed [];
blanchet@51756
  1243
blanchet@51790
  1244
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1245
blanchet@51767
  1246
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1247
blanchet@51767
  1248
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51767
  1249
   that we don't want them to be highlighted everywhere because of some obscure feature of the BNF
blanchet@51767
  1250
   package. *)
blanchet@51767
  1251
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1252
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1253
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1254
blanchet@51767
  1255
val parse_map_rel_bindings =
blanchet@51767
  1256
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1257
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1258
  Scan.succeed no_map_rel;
blanchet@51767
  1259
blanchet@51767
  1260
val parse_ctr_spec =
blanchet@51790
  1261
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1262
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1263
blanchet@51767
  1264
val parse_spec =
blanchet@51790
  1265
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1266
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1267
blanchet@51767
  1268
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1269
blanchet@49585
  1270
fun parse_datatype_cmd lfp construct_fp = parse_datatype >> datatype_cmd lfp construct_fp;
blanchet@49112
  1271
blanchet@49112
  1272
end;