src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Fri Apr 26 12:09:51 2013 +0200 (2013-04-26)
changeset 51790 22517d04d20b
parent 51788 5fe72280a49f
child 51793 22f22172a361
permissions -rw-r--r--
more intuitive syntax for equality-style discriminators of nullary constructors
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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_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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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 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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    (* 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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    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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    (* 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_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;
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    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
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    val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_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;
blanchet@51766
   296
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51766
   297
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@49585
   298
blanchet@49585
   299
    val live = live_of_bnf any_fp_bnf;
blanchet@49585
   300
blanchet@49585
   301
    val Bs =
blanchet@49585
   302
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
   303
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
   304
blanchet@49585
   305
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
   306
blanchet@49501
   307
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
   308
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
   309
blanchet@49501
   310
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
   311
blanchet@51780
   312
    fun massage_simple_notes base =
blanchet@51780
   313
      filter_out (null o #2)
blanchet@51780
   314
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
   315
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
   316
blanchet@51780
   317
    val massage_multi_notes =
blanchet@51780
   318
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
   319
        if forall null thmss then
blanchet@51780
   320
          []
blanchet@51780
   321
        else
blanchet@51780
   322
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@51780
   323
            ((qualify true fp_b_name (Binding.name thmN), attrs T_name),
blanchet@51780
   324
             [(thms, [])])) fp_b_names fpTs thmss);
blanchet@51780
   325
blanchet@49362
   326
    val exists_fp_subtype = exists_subtype (member (op =) fpTs);
blanchet@49670
   327
    val exists_Cs_subtype = exists_subtype (member (op =) Cs);
blanchet@49362
   328
blanchet@49536
   329
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
blanchet@49203
   330
    val ns = map length ctr_Tsss;
blanchet@49212
   331
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
   332
    val mss = map (map length) ctr_Tsss;
blanchet@49203
   333
    val Css = map2 replicate ns Cs;
blanchet@49203
   334
blanchet@49585
   335
    val fp_folds as any_fp_fold :: _ = map (mk_rec_like lfp As Cs) fp_folds0;
blanchet@49585
   336
    val fp_recs as any_fp_rec :: _ = map (mk_rec_like lfp As Cs) fp_recs0;
blanchet@49210
   337
blanchet@49585
   338
    val fp_fold_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_fold)));
blanchet@49585
   339
    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_rec)));
blanchet@49204
   340
blanchet@49504
   341
    val (((fold_only as (gss, _, _), rec_only as (hss, _, _)),
blanchet@49683
   342
          (cs, cpss, unfold_only as ((pgss, crssss, cgssss), (_, g_Tsss, _)),
blanchet@49683
   343
           corec_only as ((phss, csssss, chssss), (_, h_Tsss, _)))), names_lthy0) =
blanchet@49208
   344
      if lfp then
blanchet@49208
   345
        let
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   346
          val y_Tsss =
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   347
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49504
   348
              ns mss fp_fold_fun_Ts;
blanchet@49208
   349
          val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
blanchet@49208
   350
blanchet@49484
   351
          val ((gss, ysss), lthy) =
blanchet@49208
   352
            lthy
blanchet@49208
   353
            |> mk_Freess "f" g_Tss
blanchet@49208
   354
            ||>> mk_Freesss "x" y_Tsss;
blanchet@49670
   355
blanchet@49670
   356
          fun proj_recT proj (Type (s as @{type_name prod}, Ts as [T, U])) =
blanchet@49670
   357
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_recT proj) Ts)
blanchet@49670
   358
            | proj_recT proj (Type (s, Ts)) = Type (s, map (proj_recT proj) Ts)
blanchet@49670
   359
            | proj_recT _ T = T;
blanchet@49274
   360
blanchet@49670
   361
          fun unzip_recT T =
blanchet@49670
   362
            if exists_fp_subtype T then [proj_recT fst T, proj_recT snd T] else [T];
blanchet@49204
   363
blanchet@49670
   364
          val z_Tsss =
blanchet@49670
   365
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49670
   366
              ns mss fp_rec_fun_Ts;
blanchet@49670
   367
          val z_Tssss = map (map (map unzip_recT)) z_Tsss;
blanchet@49208
   368
          val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
blanchet@49204
   369
blanchet@49298
   370
          val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@49670
   371
          val zsss = map2 (map2 (map2 retype_free)) z_Tsss ysss;
blanchet@49210
   372
        in
blanchet@49670
   373
          ((((gss, g_Tss, ysss), (hss, h_Tss, zsss)),
blanchet@49683
   374
            ([], [], (([], [], []), ([], [], [])), (([], [], []), ([], [], [])))), lthy)
blanchet@49210
   375
        end
blanchet@49208
   376
      else
blanchet@49210
   377
        let
blanchet@49221
   378
          (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@49221
   379
          val mss' =  map (fn [0] => [1] | ms => ms) mss;
blanchet@49221
   380
blanchet@49463
   381
          val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@49275
   382
blanchet@49587
   383
          fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss);
blanchet@49211
   384
blanchet@49587
   385
          fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss
blanchet@49587
   386
            | flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
blanchet@49587
   387
              p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss;
blanchet@49274
   388
blanchet@49681
   389
          fun mk_types maybe_unzipT fun_Ts =
blanchet@49212
   390
            let
blanchet@49212
   391
              val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@49255
   392
              val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@49681
   393
              val f_Tsss = map2 (map2 dest_tupleT) mss' f_prod_Tss;
blanchet@49275
   394
              val f_Tssss =
blanchet@49681
   395
                map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
blanchet@49275
   396
              val q_Tssss =
blanchet@49463
   397
                map (map (map (fn [_] => [] | [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss;
blanchet@49587
   398
              val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@49681
   399
            in (q_Tssss, f_sum_prod_Ts, f_Tsss, f_Tssss, pf_Tss) end;
blanchet@49176
   400
blanchet@49681
   401
          val (r_Tssss, g_sum_prod_Ts, g_Tsss, g_Tssss, pg_Tss) = mk_types single fp_fold_fun_Ts;
blanchet@49211
   402
blanchet@49683
   403
          val (((cs, pss), gssss), lthy) =
blanchet@49210
   404
            lthy
blanchet@49683
   405
            |> mk_Frees "a" Cs
blanchet@49211
   406
            ||>> mk_Freess "p" p_Tss
blanchet@49275
   407
            ||>> mk_Freessss "g" g_Tssss;
blanchet@49275
   408
          val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@49274
   409
blanchet@49681
   410
          fun proj_corecT proj (Type (s as @{type_name sum}, Ts as [T, U])) =
blanchet@49681
   411
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   412
            | proj_corecT proj (Type (s, Ts)) = Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   413
            | proj_corecT _ T = T;
blanchet@49274
   414
blanchet@49681
   415
          fun unzip_corecT T =
blanchet@49681
   416
            if exists_fp_subtype T then [proj_corecT fst T, proj_corecT snd T] else [T];
blanchet@49681
   417
blanchet@49681
   418
          val (s_Tssss, h_sum_prod_Ts, h_Tsss, h_Tssss, ph_Tss) =
blanchet@49681
   419
            mk_types unzip_corecT fp_rec_fun_Ts;
blanchet@49210
   420
blanchet@49298
   421
          val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@49484
   422
          val ((sssss, hssss_tl), lthy) =
blanchet@49275
   423
            lthy
blanchet@49275
   424
            |> mk_Freessss "q" s_Tssss
blanchet@49275
   425
            ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@49275
   426
          val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@49211
   427
blanchet@49681
   428
          val cpss = map2 (map o rapp) cs pss;
blanchet@49212
   429
blanchet@49683
   430
          fun mk_terms qssss fssss =
blanchet@49212
   431
            let
blanchet@49587
   432
              val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
blanchet@49681
   433
              val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@49681
   434
              val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@49683
   435
            in (pfss, cqssss, cfssss) end;
blanchet@49210
   436
        in
blanchet@49484
   437
          (((([], [], []), ([], [], [])),
blanchet@49683
   438
            (cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, g_Tsss, pg_Tss)),
blanchet@49683
   439
             (mk_terms sssss hssss, (h_sum_prod_Ts, h_Tsss, ph_Tss)))), lthy)
blanchet@49210
   440
        end;
blanchet@49210
   441
blanchet@49585
   442
    fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@49585
   443
            fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@49585
   444
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@49585
   445
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   446
      let
blanchet@49498
   447
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
   448
blanchet@49501
   449
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
   450
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   451
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   452
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   453
blanchet@49593
   454
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
   455
          no_defs_lthy
blanchet@49501
   456
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
   457
          ||>> mk_Frees "f" case_Ts
blanchet@49370
   458
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
   459
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
   460
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
   461
blanchet@49498
   462
        val u = Free (u', fpT);
blanchet@49121
   463
blanchet@49585
   464
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
   465
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
   466
blanchet@49129
   467
        val ctr_rhss =
blanchet@49585
   468
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
   469
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
   470
blanchet@49633
   471
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
   472
blanchet@49134
   473
        val case_rhs =
blanchet@49498
   474
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
   475
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
   476
blanchet@49201
   477
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   478
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
   479
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
   480
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   481
          ||> `Local_Theory.restore;
blanchet@49121
   482
blanchet@49121
   483
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   484
blanchet@49121
   485
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
   486
        val ctr_defs' =
blanchet@49585
   487
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
   488
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   489
blanchet@49203
   490
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   491
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   492
blanchet@49203
   493
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   494
blanchet@49585
   495
        fun wrap lthy =
blanchet@49123
   496
          let
traytel@50170
   497
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
   498
              let
blanchet@49585
   499
                val ctor_iff_dtor_thm =
blanchet@49585
   500
                  let
blanchet@49585
   501
                    val goal =
blanchet@49585
   502
                      fold_rev Logic.all [w, u]
blanchet@49585
   503
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
   504
                  in
wenzelm@51551
   505
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
   506
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
   507
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
   508
                    |> Thm.close_derivation
blanchet@49585
   509
                    |> Morphism.thm phi
blanchet@49585
   510
                  end;
blanchet@49585
   511
blanchet@49585
   512
                val sumEN_thm' =
blanchet@49585
   513
                  unfold_thms lthy @{thms all_unit_eq}
blanchet@49585
   514
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
   515
                       (mk_sumEN_balanced n))
blanchet@49585
   516
                  |> Morphism.thm phi;
blanchet@49135
   517
              in
blanchet@49585
   518
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
   519
              end;
blanchet@49135
   520
blanchet@49585
   521
            val inject_tacss =
blanchet@49585
   522
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
   523
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
   524
blanchet@49585
   525
            val half_distinct_tacss =
blanchet@49585
   526
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
   527
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
   528
blanchet@49585
   529
            val case_tacs =
blanchet@49585
   530
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
   531
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
   532
blanchet@49585
   533
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
   534
blanchet@49585
   535
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
   536
          in
blanchet@51781
   537
            wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
blanchet@51781
   538
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
   539
          end;
blanchet@49121
   540
blanchet@49585
   541
        fun derive_maps_sets_rels (wrap_res, lthy) =
blanchet@49585
   542
          let
blanchet@49585
   543
            val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@49585
   544
            val nones = replicate live NONE;
blanchet@49585
   545
blanchet@49585
   546
            val ctor_cong =
blanchet@51746
   547
              if lfp then
blanchet@51746
   548
                Drule.dummy_thm
blanchet@51746
   549
              else
blanchet@51746
   550
                let val ctor' = mk_ctor Bs ctor in
blanchet@51746
   551
                  cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51746
   552
                end;
blanchet@49585
   553
blanchet@49585
   554
            fun mk_cIn ify =
blanchet@49585
   555
              certify lthy o (not lfp ? curry (op $) (map_types ify ctor)) oo
blanchet@49585
   556
              mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
   557
blanchet@49585
   558
            val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@49585
   559
            val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
   560
blanchet@49682
   561
            fun mk_map_thm ctr_def' cxIn =
blanchet@49585
   562
              fold_thms lthy [ctr_def']
blanchet@49585
   563
                (unfold_thms lthy (pre_map_def ::
blanchet@49585
   564
                     (if lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@49585
   565
                   (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@49585
   566
                      (if lfp then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@49593
   567
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   568
blanchet@49682
   569
            fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@49585
   570
              fold_thms lthy [ctr_def']
blanchet@51766
   571
                (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@49585
   572
                     (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@49585
   573
                   (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@49593
   574
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   575
blanchet@49682
   576
            fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49585
   577
blanchet@49682
   578
            val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@49585
   579
            val set_thmss = map mk_set_thms fp_set_thms;
blanchet@49127
   580
blanchet@49682
   581
            val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
   582
blanchet@49682
   583
            fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@49585
   584
              fold_thms lthy ctr_defs'
blanchet@51745
   585
                 (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@51745
   586
                      (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@49585
   587
                    (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@49593
   588
              |> postproc
blanchet@49593
   589
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   590
blanchet@49682
   591
            fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@49682
   592
              mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
   593
blanchet@49592
   594
            val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
   595
blanchet@49682
   596
            fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@49585
   597
              mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@49682
   598
                cxIn cyIn;
blanchet@49121
   599
blanchet@49592
   600
            fun mk_other_half_rel_distinct_thm thm =
blanchet@49585
   601
              flip_rels lthy live thm RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
   602
blanchet@49592
   603
            val half_rel_distinct_thmss =
blanchet@49592
   604
              map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@49592
   605
            val other_half_rel_distinct_thmss =
blanchet@49592
   606
              map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@49592
   607
            val (rel_distinct_thms, _) =
blanchet@49592
   608
              join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
   609
blanchet@49585
   610
            val notes =
blanchet@49594
   611
              [(mapN, map_thms, code_simp_attrs),
blanchet@49592
   612
               (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@49592
   613
               (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@49585
   614
               (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51780
   615
              |> massage_simple_notes fp_b_name;
blanchet@49585
   616
          in
blanchet@49585
   617
            (wrap_res, lthy |> Local_Theory.notes notes |> snd)
blanchet@49585
   618
          end;
blanchet@49585
   619
blanchet@49585
   620
        fun define_fold_rec no_defs_lthy =
blanchet@49134
   621
          let
blanchet@49208
   622
            val fpT_to_C = fpT --> C;
blanchet@49199
   623
blanchet@49681
   624
            fun build_prod_proj mk_proj (T, U) =
blanchet@49670
   625
              if T = U then
blanchet@49670
   626
                id_const T
blanchet@49670
   627
              else
blanchet@49670
   628
                (case (T, U) of
blanchet@49670
   629
                  (Type (s, _), Type (s', _)) =>
blanchet@49681
   630
                  if s = s' then build_map (build_prod_proj mk_proj) T U else mk_proj T
blanchet@49670
   631
                | _ => mk_proj T);
blanchet@49670
   632
blanchet@49681
   633
            (* TODO: Avoid these complications; cf. corec case *)
blanchet@49672
   634
            fun mk_U proj (Type (s as @{type_name prod}, Ts as [T', U])) =
blanchet@49672
   635
                if member (op =) fpTs T' then proj (T', U) else Type (s, map (mk_U proj) Ts)
blanchet@49670
   636
              | mk_U proj (Type (s, Ts)) = Type (s, map (mk_U proj) Ts)
blanchet@49670
   637
              | mk_U _ T = T;
blanchet@49670
   638
blanchet@49670
   639
            fun unzip_rec (x as Free (_, T)) =
blanchet@49670
   640
              if exists_fp_subtype T then
blanchet@49681
   641
                [build_prod_proj fst_const (T, mk_U fst T) $ x,
blanchet@49681
   642
                 build_prod_proj snd_const (T, mk_U snd T) $ x]
blanchet@49670
   643
              else
blanchet@49670
   644
                [x];
blanchet@49670
   645
blanchet@49670
   646
            fun mk_rec_like_arg f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f (maps unzip_rec xs);
blanchet@49670
   647
blanchet@49670
   648
            fun generate_rec_like (suf, fp_rec_like, (fss, f_Tss, xsss)) =
blanchet@49215
   649
              let
blanchet@49215
   650
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49633
   651
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49215
   652
                val spec =
blanchet@49336
   653
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   654
                    Term.list_comb (fp_rec_like,
blanchet@49670
   655
                      map2 (mk_sum_caseN_balanced oo map2 mk_rec_like_arg) fss xsss));
blanchet@49336
   656
              in (binding, spec) end;
blanchet@49199
   657
blanchet@49504
   658
            val rec_like_infos =
blanchet@49504
   659
              [(foldN, fp_fold, fold_only),
blanchet@49215
   660
               (recN, fp_rec, rec_only)];
blanchet@49215
   661
blanchet@49504
   662
            val (bindings, specs) = map generate_rec_like rec_like_infos |> split_list;
blanchet@49215
   663
blanchet@49215
   664
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   665
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   666
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   667
                #>> apsnd snd) bindings specs
blanchet@49199
   668
              ||> `Local_Theory.restore;
blanchet@49201
   669
blanchet@49201
   670
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   671
blanchet@49504
   672
            val [fold_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   673
blanchet@49536
   674
            val [foldx, recx] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49134
   675
          in
blanchet@49693
   676
            ((foldx, recx, fold_def, rec_def), lthy')
blanchet@49134
   677
          end;
blanchet@49134
   678
blanchet@49585
   679
        fun define_unfold_corec no_defs_lthy =
blanchet@49210
   680
          let
blanchet@49210
   681
            val B_to_fpT = C --> fpT;
blanchet@49211
   682
blanchet@49683
   683
            fun build_sum_inj mk_inj (T, U) =
blanchet@49683
   684
              if T = U then
blanchet@49683
   685
                id_const T
blanchet@49683
   686
              else
blanchet@49683
   687
                (case (T, U) of
blanchet@49683
   688
                  (Type (s, _), Type (s', _)) =>
blanchet@49683
   689
                  if s = s' then build_map (build_sum_inj mk_inj) T U
blanchet@49683
   690
                  else uncurry mk_inj (dest_sumT U)
blanchet@49683
   691
                | _ => uncurry mk_inj (dest_sumT U));
blanchet@49683
   692
blanchet@49683
   693
            fun build_dtor_corec_like_arg _ [] [cf] = cf
blanchet@49683
   694
              | build_dtor_corec_like_arg T [cq] [cf, cf'] =
blanchet@49683
   695
                mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@49683
   696
                  (build_sum_inj Inr_const (fastype_of cf', T) $ cf')
blanchet@49683
   697
blanchet@49683
   698
            val crgsss = map3 (map3 (map3 build_dtor_corec_like_arg)) g_Tsss crssss cgssss;
blanchet@49683
   699
            val cshsss = map3 (map3 (map3 build_dtor_corec_like_arg)) h_Tsss csssss chssss;
blanchet@49683
   700
blanchet@49276
   701
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
   702
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
   703
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
   704
blanchet@49683
   705
            fun generate_corec_like (suf, fp_rec_like, (cqfsss, ((pfss, _, _), (f_sum_prod_Ts, _,
blanchet@49683
   706
                pf_Tss)))) =
blanchet@49211
   707
              let
blanchet@49211
   708
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49633
   709
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49211
   710
                val spec =
blanchet@49336
   711
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   712
                    Term.list_comb (fp_rec_like,
blanchet@49276
   713
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49336
   714
              in (binding, spec) end;
blanchet@49210
   715
blanchet@49504
   716
            val corec_like_infos =
blanchet@49683
   717
              [(unfoldN, fp_fold, (crgsss, unfold_only)),
blanchet@49683
   718
               (corecN, fp_rec, (cshsss, corec_only))];
blanchet@49212
   719
blanchet@49504
   720
            val (bindings, specs) = map generate_corec_like corec_like_infos |> split_list;
blanchet@49211
   721
blanchet@49211
   722
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   723
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   724
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   725
                #>> apsnd snd) bindings specs
blanchet@49210
   726
              ||> `Local_Theory.restore;
blanchet@49210
   727
blanchet@49210
   728
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   729
blanchet@49504
   730
            val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   731
blanchet@49536
   732
            val [unfold, corec] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49210
   733
          in
blanchet@49693
   734
            ((unfold, corec, unfold_def, corec_def), lthy')
blanchet@49287
   735
          end;
blanchet@49287
   736
blanchet@49504
   737
        val define_rec_likes = if lfp then define_fold_rec else define_unfold_corec;
blanchet@49585
   738
blanchet@49585
   739
        fun massage_res ((wrap_res, rec_like_res), lthy) =
blanchet@49585
   740
          (((ctrs, xss, ctr_defs, wrap_res), rec_like_res), lthy);
blanchet@49119
   741
      in
blanchet@49585
   742
        (wrap #> (live > 0 ? derive_maps_sets_rels) ##>> define_rec_likes #> massage_res, lthy')
blanchet@49119
   743
      end;
blanchet@49167
   744
blanchet@49585
   745
    fun wrap_types_and_more (wrap_types_and_mores, lthy) =
blanchet@49585
   746
      fold_map I wrap_types_and_mores lthy
blanchet@49585
   747
      |>> apsnd split_list4 o apfst split_list4 o split_list;
blanchet@49226
   748
blanchet@49585
   749
    (* TODO: Add map, sets, rel simps *)
blanchet@49479
   750
    val mk_simp_thmss =
blanchet@49591
   751
      map3 (fn (_, _, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn fold_likes =>
blanchet@49505
   752
        injects @ distincts @ cases @ rec_likes @ fold_likes);
blanchet@49479
   753
blanchet@49585
   754
    fun derive_induct_fold_rec_thms_for_types (((ctrss, xsss, ctr_defss, wrap_ress), (folds, recs,
blanchet@49585
   755
        fold_defs, rec_defs)), lthy) =
blanchet@49202
   756
      let
blanchet@49591
   757
        val (((ps, ps'), us'), names_lthy) =
blanchet@49370
   758
          lthy
blanchet@49463
   759
          |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@49498
   760
          ||>> Variable.variant_fixes fp_b_names;
blanchet@49370
   761
blanchet@49498
   762
        val us = map2 (curry Free) us' fpTs;
blanchet@49370
   763
blanchet@49362
   764
        fun mk_sets_nested bnf =
blanchet@49362
   765
          let
blanchet@49362
   766
            val Type (T_name, Us) = T_of_bnf bnf;
blanchet@49362
   767
            val lives = lives_of_bnf bnf;
blanchet@49362
   768
            val sets = sets_of_bnf bnf;
blanchet@49362
   769
            fun mk_set U =
blanchet@49362
   770
              (case find_index (curry (op =) U) lives of
blanchet@49362
   771
                ~1 => Term.dummy
blanchet@49362
   772
              | i => nth sets i);
blanchet@49362
   773
          in
blanchet@49362
   774
            (T_name, map mk_set Us)
blanchet@49362
   775
          end;
blanchet@49362
   776
blanchet@49362
   777
        val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@49362
   778
blanchet@49337
   779
        val (induct_thms, induct_thm) =
blanchet@49337
   780
          let
blanchet@49362
   781
            fun mk_set Ts t =
blanchet@49362
   782
              let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@49362
   783
                Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49362
   784
              end;
blanchet@49362
   785
blanchet@49375
   786
            fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
blanchet@49361
   787
                (case find_index (curry (op =) T) fpTs of
blanchet@49362
   788
                  ~1 =>
blanchet@49362
   789
                  (case AList.lookup (op =) setss_nested T_name of
blanchet@49362
   790
                    NONE => []
blanchet@49362
   791
                  | SOME raw_sets0 =>
blanchet@49362
   792
                    let
blanchet@49362
   793
                      val (Ts, raw_sets) =
blanchet@49362
   794
                        split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
blanchet@49362
   795
                      val sets = map (mk_set Ts0) raw_sets;
blanchet@49362
   796
                      val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@49375
   797
                      val xysets = map (pair x) (ys ~~ sets);
blanchet@49375
   798
                      val ppremss = map (mk_raw_prem_prems names_lthy') ys;
blanchet@49362
   799
                    in
blanchet@49375
   800
                      flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@49362
   801
                    end)
blanchet@49591
   802
                | kk => [([], (kk + 1, x))])
blanchet@49375
   803
              | mk_raw_prem_prems _ _ = [];
blanchet@49342
   804
blanchet@49378
   805
            fun close_prem_prem xs t =
blanchet@49378
   806
              fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@49591
   807
                (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@49362
   808
blanchet@49378
   809
            fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@49378
   810
              close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@49376
   811
                  HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@49591
   812
                HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@49375
   813
blanchet@49372
   814
            fun mk_raw_prem phi ctr ctr_Ts =
blanchet@49362
   815
              let
blanchet@49362
   816
                val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@49376
   817
                val pprems = maps (mk_raw_prem_prems names_lthy') xs;
blanchet@49378
   818
              in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@49342
   819
blanchet@49376
   820
            fun mk_prem (xs, raw_pprems, concl) =
blanchet@49378
   821
              fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@49368
   822
blanchet@49591
   823
            val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss;
blanchet@49389
   824
blanchet@49361
   825
            val goal =
blanchet@49372
   826
              Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@49591
   827
                HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@49368
   828
blanchet@49429
   829
            val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@49368
   830
blanchet@49501
   831
            val ctor_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@49342
   832
blanchet@49591
   833
            val thm =
wenzelm@51551
   834
              Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51766
   835
                mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
blanchet@51766
   836
                  pre_set_defss)
blanchet@49368
   837
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49591
   838
              |> Thm.close_derivation;
blanchet@49337
   839
          in
blanchet@49591
   840
            `(conj_dests nn) thm
blanchet@49337
   841
          end;
blanchet@49201
   842
blanchet@49622
   843
        val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@49437
   844
blanchet@49504
   845
        val (fold_thmss, rec_thmss) =
blanchet@49207
   846
          let
blanchet@49337
   847
            val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49504
   848
            val gfolds = map (lists_bmoc gss) folds;
blanchet@49337
   849
            val hrecs = map (lists_bmoc hss) recs;
blanchet@49337
   850
blanchet@49504
   851
            fun mk_goal fss frec_like xctr f xs fxs =
blanchet@49207
   852
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49504
   853
                (mk_Trueprop_eq (frec_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   854
blanchet@49682
   855
            fun build_rec_like frec_likes (T, U) =
blanchet@49234
   856
              if T = U then
blanchet@49368
   857
                id_const T
blanchet@49234
   858
              else
blanchet@49234
   859
                (case find_index (curry (op =) T) fpTs of
blanchet@49682
   860
                  ~1 => build_map (build_rec_like frec_likes) T U
blanchet@49682
   861
                | kk => nth frec_likes kk);
blanchet@49233
   862
blanchet@49682
   863
            val mk_U = typ_subst (map2 pair fpTs Cs);
blanchet@49214
   864
blanchet@49682
   865
            fun intr_rec_likes frec_likes maybe_cons (x as Free (_, T)) =
blanchet@49670
   866
              if exists_fp_subtype T then
blanchet@49682
   867
                maybe_cons x [build_rec_like frec_likes (T, mk_U T) $ x]
blanchet@49214
   868
              else
blanchet@49214
   869
                [x];
blanchet@49214
   870
blanchet@49682
   871
            val gxsss = map (map (maps (intr_rec_likes gfolds (K I)))) xsss;
blanchet@49682
   872
            val hxsss = map (map (maps (intr_rec_likes hrecs cons))) xsss;
blanchet@49204
   873
blanchet@49504
   874
            val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
blanchet@49484
   875
            val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   876
blanchet@49504
   877
            val fold_tacss =
blanchet@49670
   878
              map2 (map o mk_rec_like_tac pre_map_defs [] nesting_map_ids'' fold_defs) fp_fold_thms
blanchet@49363
   879
                ctr_defss;
blanchet@49203
   880
            val rec_tacss =
blanchet@49670
   881
              map2 (map o mk_rec_like_tac pre_map_defs nested_map_comp's
blanchet@49670
   882
                (nested_map_ids'' @ nesting_map_ids'') rec_defs) fp_rec_thms ctr_defss;
blanchet@49484
   883
blanchet@49591
   884
            fun prove goal tac =
wenzelm@51551
   885
              Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@49591
   886
              |> Thm.close_derivation;
blanchet@49202
   887
          in
blanchet@49595
   888
            (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
blanchet@49202
   889
          end;
blanchet@49201
   890
blanchet@49504
   891
        val simp_thmss = mk_simp_thmss wrap_ress rec_thmss fold_thmss;
blanchet@49438
   892
blanchet@49437
   893
        val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@49437
   894
        fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name));
blanchet@49437
   895
blanchet@49337
   896
        val common_notes =
blanchet@49437
   897
          (if nn > 1 then [(inductN, [induct_thm], [induct_case_names_attr])] else [])
blanchet@51780
   898
          |> massage_simple_notes fp_common_name;
blanchet@49337
   899
blanchet@49226
   900
        val notes =
blanchet@49633
   901
          [(foldN, fold_thmss, K code_simp_attrs),
blanchet@49633
   902
           (inductN, map single induct_thms,
blanchet@49437
   903
            fn T_name => [induct_case_names_attr, induct_type_attr T_name]),
blanchet@49622
   904
           (recN, rec_thmss, K code_simp_attrs),
blanchet@49585
   905
           (simpsN, simp_thmss, K [])]
blanchet@51780
   906
          |> massage_multi_notes;
blanchet@49202
   907
      in
blanchet@49337
   908
        lthy |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@49202
   909
      end;
blanchet@49202
   910
blanchet@49585
   911
    fun derive_coinduct_unfold_corec_thms_for_types (((ctrss, _, ctr_defss, wrap_ress), (unfolds,
blanchet@49585
   912
        corecs, unfold_defs, corec_defs)), lthy) =
blanchet@49212
   913
      let
blanchet@49591
   914
        val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@49591
   915
blanchet@49484
   916
        val discss = map (map (mk_disc_or_sel As) o #1) wrap_ress;
blanchet@49591
   917
        val selsss = map (map (map (mk_disc_or_sel As)) o #2) wrap_ress;
blanchet@49591
   918
        val exhaust_thms = map #3 wrap_ress;
blanchet@49591
   919
        val disc_thmsss = map #7 wrap_ress;
blanchet@49591
   920
        val discIss = map #8 wrap_ress;
blanchet@49591
   921
        val sel_thmsss = map #9 wrap_ress;
blanchet@49438
   922
blanchet@49591
   923
        val (((rs, us'), vs'), names_lthy) =
blanchet@49370
   924
          lthy
blanchet@49591
   925
          |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@49591
   926
          ||>> Variable.variant_fixes fp_b_names
blanchet@49591
   927
          ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@49370
   928
blanchet@49498
   929
        val us = map2 (curry Free) us' fpTs;
blanchet@49591
   930
        val udiscss = map2 (map o rapp) us discss;
blanchet@49591
   931
        val uselsss = map2 (map o map o rapp) us selsss;
blanchet@49370
   932
blanchet@49591
   933
        val vs = map2 (curry Free) vs' fpTs;
blanchet@49591
   934
        val vdiscss = map2 (map o rapp) vs discss;
blanchet@49591
   935
        val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@49591
   936
blanchet@49591
   937
        val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
blanchet@49337
   938
          let
blanchet@49591
   939
            val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@49591
   940
            val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@49591
   941
            val strong_rs =
blanchet@49591
   942
              map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@49591
   943
                fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@49591
   944
blanchet@49591
   945
            fun build_rel rs' T =
blanchet@49591
   946
              (case find_index (curry (op =) T) fpTs of
blanchet@49591
   947
                ~1 =>
blanchet@49683
   948
                if exists_fp_subtype T then build_rel_step (build_rel rs') T else HOLogic.eq_const T
blanchet@49591
   949
              | kk => nth rs' kk);
blanchet@49591
   950
blanchet@49591
   951
            fun build_rel_app rs' usel vsel =
blanchet@49591
   952
              fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@49591
   953
blanchet@49591
   954
            fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@49591
   955
              (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@49591
   956
              (if null usels then
blanchet@49591
   957
                 []
blanchet@49591
   958
               else
blanchet@49591
   959
                 [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@49591
   960
                    Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@49591
   961
blanchet@49591
   962
            fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@49591
   963
              Library.foldr1 HOLogic.mk_conj
blanchet@49591
   964
                (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@49591
   965
              handle List.Empty => @{term True};
blanchet@49591
   966
blanchet@49591
   967
            fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@49591
   968
              fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@49591
   969
                HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@49591
   970
blanchet@49591
   971
            val concl =
blanchet@49591
   972
              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49591
   973
                (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@49591
   974
                   uvrs us vs));
blanchet@49591
   975
blanchet@49591
   976
            fun mk_goal rs' =
blanchet@49591
   977
              Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@49591
   978
                concl);
blanchet@49591
   979
blanchet@49591
   980
            val goal = mk_goal rs;
blanchet@49591
   981
            val strong_goal = mk_goal strong_rs;
blanchet@49591
   982
blanchet@49591
   983
            fun prove dtor_coinduct' goal =
wenzelm@51551
   984
              Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49591
   985
                mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@49591
   986
                  exhaust_thms ctr_defss disc_thmsss sel_thmsss)
blanchet@49591
   987
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49591
   988
              |> Thm.close_derivation;
blanchet@49591
   989
blanchet@49590
   990
            fun postproc nn thm =
blanchet@49590
   991
              Thm.permute_prems 0 nn
blanchet@49591
   992
                (if nn = 1 then thm RS mp
blanchet@49591
   993
                 else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@49591
   994
              |> Drule.zero_var_indexes
blanchet@49591
   995
              |> `(conj_dests nn);
blanchet@49337
   996
          in
blanchet@49591
   997
            (postproc nn (prove fp_induct goal), postproc nn (prove fp_strong_induct strong_goal))
blanchet@49337
   998
          end;
blanchet@49212
   999
blanchet@51777
  1000
        fun mk_coinduct_concls ms discs ctrs =
blanchet@51777
  1001
          let
blanchet@51777
  1002
            fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51777
  1003
            fun mk_ctr_concl 0 _ = []
blanchet@51777
  1004
              | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51777
  1005
            val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51777
  1006
            val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51777
  1007
          in
blanchet@51777
  1008
            flat (map2 append disc_concls ctr_concls)
blanchet@51777
  1009
          end;
blanchet@51777
  1010
blanchet@51777
  1011
        val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51777
  1012
        val coinduct_conclss =
blanchet@51777
  1013
          map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51777
  1014
blanchet@49484
  1015
        fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@49484
  1016
blanchet@49504
  1017
        val gunfolds = map (lists_bmoc pgss) unfolds;
blanchet@49484
  1018
        val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49484
  1019
blanchet@49504
  1020
        val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@49212
  1021
          let
blanchet@49504
  1022
            fun mk_goal pfss c cps fcorec_like n k ctr m cfs' =
blanchet@49212
  1023
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49484
  1024
                (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@49504
  1025
                   mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
  1026
blanchet@49683
  1027
            fun build_corec_like fcorec_likes (T, U) =
blanchet@49234
  1028
              if T = U then
blanchet@49368
  1029
                id_const T
blanchet@49234
  1030
              else
blanchet@49234
  1031
                (case find_index (curry (op =) U) fpTs of
blanchet@49683
  1032
                  ~1 => build_map (build_corec_like fcorec_likes) T U
blanchet@49683
  1033
                | kk => nth fcorec_likes kk);
blanchet@49683
  1034
blanchet@49683
  1035
            val mk_U = typ_subst (map2 pair Cs fpTs);
blanchet@49233
  1036
blanchet@49683
  1037
            fun intr_corec_likes fcorec_likes [] [cf] =
blanchet@49683
  1038
                let val T = fastype_of cf in
blanchet@49683
  1039
                  if exists_Cs_subtype T then build_corec_like fcorec_likes (T, mk_U T) $ cf else cf
blanchet@49683
  1040
                end
blanchet@49683
  1041
              | intr_corec_likes fcorec_likes [cq] [cf, cf'] =
blanchet@49683
  1042
                mk_If cq (intr_corec_likes fcorec_likes [] [cf])
blanchet@49683
  1043
                  (intr_corec_likes fcorec_likes [] [cf']);
blanchet@49683
  1044
blanchet@49683
  1045
            val crgsss = map2 (map2 (map2 (intr_corec_likes gunfolds))) crssss cgssss;
blanchet@49683
  1046
            val cshsss = map2 (map2 (map2 (intr_corec_likes hcorecs))) csssss chssss;
blanchet@49212
  1047
blanchet@49683
  1048
            val unfold_goalss =
blanchet@49683
  1049
              map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
blanchet@49683
  1050
            val corec_goalss =
blanchet@49683
  1051
              map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
blanchet@49683
  1052
blanchet@49683
  1053
            fun mk_map_if_distrib bnf =
blanchet@49683
  1054
              let
blanchet@49683
  1055
                val mapx = map_of_bnf bnf;
blanchet@49683
  1056
                val live = live_of_bnf bnf;
blanchet@49683
  1057
                val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
blanchet@49683
  1058
                val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
blanchet@49683
  1059
                val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
blanchet@49683
  1060
              in
blanchet@49683
  1061
                Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
blanchet@49683
  1062
                  @{thm if_distrib}
blanchet@49276
  1063
              end;
blanchet@49232
  1064
blanchet@49683
  1065
            val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
blanchet@49213
  1066
blanchet@49504
  1067
            val unfold_tacss =
blanchet@49683
  1068
              map3 (map oo mk_corec_like_tac unfold_defs [] [] nesting_map_ids'' [])
blanchet@49683
  1069
                fp_fold_thms pre_map_defs ctr_defss;
blanchet@49233
  1070
            val corec_tacss =
blanchet@49683
  1071
              map3 (map oo mk_corec_like_tac corec_defs nested_map_comps'' nested_map_comp's
blanchet@49683
  1072
                  (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
blanchet@49683
  1073
                fp_rec_thms pre_map_defs ctr_defss;
blanchet@49479
  1074
blanchet@49484
  1075
            fun prove goal tac =
wenzelm@51551
  1076
              Goal.prove_sorry lthy [] [] goal (tac o #context) |> Thm.close_derivation;
blanchet@49484
  1077
blanchet@49504
  1078
            val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@49683
  1079
            val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
blanchet@49479
  1080
blanchet@49479
  1081
            val filter_safesss =
blanchet@49479
  1082
              map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@49683
  1083
                curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
blanchet@49479
  1084
blanchet@49683
  1085
            val safe_unfold_thmss = filter_safesss unfold_thmss;
blanchet@49683
  1086
            val safe_corec_thmss = filter_safesss corec_thmss;
blanchet@49479
  1087
          in
blanchet@49504
  1088
            (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@49212
  1089
          end;
blanchet@49212
  1090
blanchet@49504
  1091
        val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@49482
  1092
          let
blanchet@49504
  1093
            fun mk_goal c cps fcorec_like n k disc =
blanchet@49504
  1094
              mk_Trueprop_eq (disc $ (fcorec_like $ c),
blanchet@49484
  1095
                if n = 1 then @{const True}
blanchet@49484
  1096
                else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@49484
  1097
blanchet@49504
  1098
            val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@49484
  1099
            val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@49484
  1100
blanchet@49484
  1101
            fun mk_case_split' cp =
blanchet@49484
  1102
              Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@49484
  1103
blanchet@49484
  1104
            val case_splitss' = map (map mk_case_split') cpss;
blanchet@49482
  1105
blanchet@49504
  1106
            val unfold_tacss =
blanchet@49504
  1107
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@49484
  1108
            val corec_tacss =
blanchet@49504
  1109
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@49484
  1110
blanchet@49484
  1111
            fun prove goal tac =
wenzelm@51551
  1112
              Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@49591
  1113
              |> singleton (Proof_Context.export names_lthy0 no_defs_lthy)
blanchet@49591
  1114
              |> Thm.close_derivation;
blanchet@49484
  1115
blanchet@49484
  1116
            fun proves [_] [_] = []
blanchet@49484
  1117
              | proves goals tacs = map2 prove goals tacs;
blanchet@49482
  1118
          in
blanchet@49504
  1119
            (map2 proves unfold_goalss unfold_tacss,
blanchet@49484
  1120
             map2 proves corec_goalss corec_tacss)
blanchet@49482
  1121
          end;
blanchet@49482
  1122
blanchet@49605
  1123
        val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@49605
  1124
blanchet@49504
  1125
        fun mk_disc_corec_like_thms corec_likes discIs =
blanchet@49605
  1126
          map (op RS) (filter_out (is_triv_discI o snd) (corec_likes ~~ discIs));
blanchet@49266
  1127
blanchet@49504
  1128
        val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss;
blanchet@49504
  1129
        val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss;
blanchet@49266
  1130
blanchet@49504
  1131
        fun mk_sel_corec_like_thm corec_like_thm sel sel_thm =
blanchet@49266
  1132
          let
blanchet@49479
  1133
            val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@49266
  1134
            val arg_cong' =
blanchet@49266
  1135
              Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@49479
  1136
                [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@49267
  1137
              |> Thm.varifyT_global;
blanchet@49266
  1138
            val sel_thm' = sel_thm RSN (2, trans);
blanchet@49266
  1139
          in
blanchet@49504
  1140
            corec_like_thm RS arg_cong' RS sel_thm'
blanchet@49266
  1141
          end;
blanchet@49266
  1142
blanchet@49504
  1143
        fun mk_sel_corec_like_thms corec_likess =
blanchet@49504
  1144
          map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss |> map flat;
blanchet@49479
  1145
blanchet@49504
  1146
        val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss;
blanchet@49504
  1147
        val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss;
blanchet@49479
  1148
blanchet@49587
  1149
        fun flat_corec_like_thms corec_likes disc_corec_likes sel_corec_likes =
blanchet@49504
  1150
          corec_likes @ disc_corec_likes @ sel_corec_likes;
blanchet@49479
  1151
blanchet@49479
  1152
        val simp_thmss =
blanchet@49479
  1153
          mk_simp_thmss wrap_ress
blanchet@49587
  1154
            (map3 flat_corec_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@49587
  1155
            (map3 flat_corec_like_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss);
blanchet@49479
  1156
blanchet@49479
  1157
        val anonymous_notes =
blanchet@49504
  1158
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1159
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1160
blanchet@51777
  1161
        val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51777
  1162
        val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51777
  1163
        val coinduct_case_concl_attrs =
blanchet@51777
  1164
          map2 (fn casex => fn concls =>
blanchet@51777
  1165
              Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51777
  1166
            coinduct_cases coinduct_conclss;
blanchet@51777
  1167
        val coinduct_case_attrs =
blanchet@51777
  1168
          coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51780
  1169
        fun coinduct_type_attr T_name = Attrib.internal (K (Induct.coinduct_type T_name));
blanchet@51777
  1170
blanchet@49342
  1171
        val common_notes =
blanchet@49591
  1172
          (if nn > 1 then
blanchet@51777
  1173
             [(coinductN, [coinduct_thm], coinduct_case_attrs),
blanchet@51777
  1174
              (strong_coinductN, [strong_coinduct_thm], coinduct_case_attrs)]
blanchet@49591
  1175
           else
blanchet@49591
  1176
             [])
blanchet@51780
  1177
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1178
blanchet@49212
  1179
        val notes =
blanchet@51780
  1180
          [(coinductN, map single coinduct_thms,
blanchet@51780
  1181
            fn T_name => coinduct_case_attrs @ [coinduct_type_attr T_name]),
blanchet@51780
  1182
           (corecN, corec_thmss, K []),
blanchet@51780
  1183
           (disc_corecN, disc_corec_thmss, K simp_attrs),
blanchet@51780
  1184
           (disc_corec_iffN, disc_corec_iff_thmss, K simp_attrs),
blanchet@51780
  1185
           (disc_unfoldN, disc_unfold_thmss, K simp_attrs),
blanchet@51780
  1186
           (disc_unfold_iffN, disc_unfold_iff_thmss, K simp_attrs),
blanchet@51780
  1187
           (sel_corecN, sel_corec_thmss, K simp_attrs),
blanchet@51780
  1188
           (sel_unfoldN, sel_unfold_thmss, K simp_attrs),
blanchet@51780
  1189
           (simpsN, simp_thmss, K []),
blanchet@51780
  1190
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_case_attrs),
blanchet@51780
  1191
           (unfoldN, unfold_thmss, K [])]
blanchet@51780
  1192
          |> massage_multi_notes;
blanchet@49212
  1193
      in
blanchet@49479
  1194
        lthy |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@49212
  1195
      end;
blanchet@49212
  1196
blanchet@49204
  1197
    val lthy' = lthy
blanchet@49585
  1198
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@49585
  1199
        fp_folds ~~ fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@49585
  1200
        pre_set_defss ~~ pre_rel_defs ~~ fp_map_thms ~~ fp_set_thmss ~~ fp_rel_thms ~~ ns ~~ kss ~~
blanchet@49585
  1201
        mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
blanchet@49585
  1202
        raw_sel_defaultsss)
blanchet@49585
  1203
      |> wrap_types_and_more
blanchet@49585
  1204
      |> (if lfp then derive_induct_fold_rec_thms_for_types
blanchet@49585
  1205
          else derive_coinduct_unfold_corec_thms_for_types);
blanchet@49167
  1206
blanchet@49167
  1207
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
  1208
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
  1209
  in
blanchet@49308
  1210
    timer; lthy'
blanchet@49112
  1211
  end;
blanchet@49112
  1212
blanchet@49536
  1213
val datatypes = define_datatypes (K I) (K I) (K I);
blanchet@49297
  1214
blanchet@51380
  1215
val datatype_cmd = define_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1216
blanchet@49112
  1217
val parse_ctr_arg =
blanchet@49329
  1218
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1219
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1220
blanchet@49286
  1221
val parse_defaults =
blanchet@49286
  1222
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1223
blanchet@51758
  1224
val parse_type_arg_constrained =
blanchet@51790
  1225
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1226
blanchet@51790
  1227
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1228
blanchet@51758
  1229
val parse_type_args_named_constrained =
blanchet@51758
  1230
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1231
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1232
  Scan.succeed [];
blanchet@51756
  1233
blanchet@51790
  1234
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1235
blanchet@51767
  1236
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1237
blanchet@51767
  1238
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51767
  1239
   that we don't want them to be highlighted everywhere because of some obscure feature of the BNF
blanchet@51767
  1240
   package. *)
blanchet@51767
  1241
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1242
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1243
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1244
blanchet@51767
  1245
val parse_map_rel_bindings =
blanchet@51767
  1246
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1247
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1248
  Scan.succeed no_map_rel;
blanchet@51767
  1249
blanchet@51767
  1250
val parse_ctr_spec =
blanchet@51790
  1251
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1252
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1253
blanchet@51767
  1254
val parse_spec =
blanchet@51790
  1255
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1256
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1257
blanchet@51767
  1258
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1259
blanchet@49585
  1260
fun parse_datatype_cmd lfp construct_fp = parse_datatype >> datatype_cmd lfp construct_fp;
blanchet@49112
  1261
blanchet@49112
  1262
end;