src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Mon Apr 29 14:06:37 2013 +0200 (2013-04-29)
changeset 51816 5f1dec4297da
parent 51815 efacb9b99865
child 51819 9df935196be9
permissions -rw-r--r--
use base names, not full names
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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 derive_induct_fold_rec_thms_for_types: BNF_Def.BNF list -> thm -> thm list -> thm list ->
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    BNF_Def.BNF list -> BNF_Def.BNF list -> typ list -> typ list -> typ list list list ->
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    int list list -> int list -> term list list -> term list list -> term list list -> term list
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    list list -> thm list list -> term list -> term list -> thm list -> thm list -> Proof.context ->
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    (thm * thm list * Args.src list) * (thm list list * Args.src list)
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      * (thm list list * Args.src list)
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  val derive_coinduct_unfold_corec_thms_for_types: Proof.context -> Proof.context ->
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    BNF_Def.BNF list -> thm -> thm -> thm list -> thm list -> thm list -> BNF_Def.BNF list ->
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    BNF_Def.BNF list -> typ list -> typ list -> typ list -> int list list -> int list list ->
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    int list -> term list -> term list list -> term list list -> term list list list list ->
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    term list list list list -> term list list -> term list list list list ->
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    term list list list list -> term list list -> thm list list ->
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    BNF_Ctr_Sugar.ctr_wrap_result list -> term list -> term list -> thm list -> thm list ->
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    Proof.context ->
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    (thm * thm list * thm * thm list * Args.src list) * (thm list list * thm list list * 'e list)
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    * (thm list list * thm list list) * (thm list list * thm list list * Args.src list)
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    * (thm list list * thm list list * Args.src list) *
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    (thm list list * thm list list * Args.src list)
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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 add_components_of_typ (Type (s, Ts)) =
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    fold add_components_of_typ Ts #> cons (Long_Name.base_name s)
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  | add_components_of_typ _ = I;
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fun base_name_of_typ T = space_implode "_" (add_components_of_typ T []);
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fun exists_subtype_in Ts = exists_subtype (member (op =) Ts);
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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 build_map lthy 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 lthy 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 derive_induct_fold_rec_thms_for_types pre_bnfs ctor_induct ctor_fold_thms ctor_rec_thms
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    nesting_bnfs nested_bnfs fpTs Cs ctr_Tsss mss ns gss hss ctrss xsss ctr_defss folds recs
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    fold_defs rec_defs lthy =
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  let
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    val nn = length pre_bnfs;
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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 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 nested_set_map's = maps set_map'_of_bnf nested_bnfs;
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    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
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    val fp_b_names = map base_name_of_typ fpTs;
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    val (((ps, ps'), us'), names_lthy) =
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      lthy
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      |> mk_Frees' "P" (map mk_pred1T fpTs)
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      ||>> Variable.variant_fixes fp_b_names;
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    val us = map2 (curry Free) us' fpTs;
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    fun mk_sets_nested bnf =
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      let
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        val Type (T_name, Us) = T_of_bnf bnf;
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        val lives = lives_of_bnf bnf;
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        val sets = sets_of_bnf bnf;
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        fun mk_set U =
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          (case find_index (curry (op =) U) lives of
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            ~1 => Term.dummy
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          | i => nth sets i);
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      in
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        (T_name, map mk_set Us)
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      end;
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    val setss_nested = map mk_sets_nested nested_bnfs;
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    val (induct_thms, induct_thm) =
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      let
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        fun mk_set Ts t =
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          let val Type (_, Ts0) = domain_type (fastype_of t) in
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            Term.subst_atomic_types (Ts0 ~~ Ts) t
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          end;
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        fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
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            (case find_index (curry (op =) T) fpTs of
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              ~1 =>
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              (case AList.lookup (op =) setss_nested T_name of
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                NONE => []
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              | SOME raw_sets0 =>
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                let
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                  val (Ts, raw_sets) =
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                    split_list (filter (exists_subtype_in fpTs o fst) (Ts0 ~~ raw_sets0));
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                  val sets = map (mk_set Ts0) raw_sets;
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                  val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
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                  val xysets = map (pair x) (ys ~~ sets);
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                  val ppremss = map (mk_raw_prem_prems names_lthy') ys;
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                in
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                  flat (map2 (map o apfst o cons) xysets ppremss)
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                end)
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            | kk => [([], (kk + 1, x))])
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          | mk_raw_prem_prems _ _ = [];
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        fun close_prem_prem xs t =
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          fold_rev Logic.all (map Free (drop (nn + length xs)
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            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
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        fun mk_prem_prem xs (xysets, (j, x)) =
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          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
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              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
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            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
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        fun mk_raw_prem phi ctr ctr_Ts =
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          let
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            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
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            val pprems = maps (mk_raw_prem_prems names_lthy') xs;
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          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
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        fun mk_prem (xs, raw_pprems, concl) =
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          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
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        val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss;
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        val goal =
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          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
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            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
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        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
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        val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
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        val thm =
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          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
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            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
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              pre_set_defss)
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   295
          |> singleton (Proof_Context.export names_lthy lthy)
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   296
          |> Thm.close_derivation;
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      in
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   298
        `(conj_dests nn) thm
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   299
      end;
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   301
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
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   303
    val (fold_thmss, rec_thmss) =
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   304
      let
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        val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
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        val gfolds = map (lists_bmoc gss) folds;
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   307
        val hrecs = map (lists_bmoc hss) recs;
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   308
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        fun mk_goal fss frec_like xctr f xs fxs =
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   310
          fold_rev (fold_rev Logic.all) (xs :: fss)
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            (mk_Trueprop_eq (frec_like $ xctr, Term.list_comb (f, fxs)));
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   312
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   313
        fun build_rec_like frec_likes (T, U) =
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   314
          if T = U then
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   315
            id_const T
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   316
          else
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   317
            (case find_index (curry (op =) T) fpTs of
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   318
              ~1 => build_map lthy (build_rec_like frec_likes) T U
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   319
            | kk => nth frec_likes kk);
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   320
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   321
        val mk_U = typ_subst (map2 pair fpTs Cs);
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   322
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   323
        fun unzip_rec_likes frec_likes combine (x as Free (_, T)) =
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   324
          if exists_subtype_in fpTs T then
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   325
            combine (x, build_rec_like frec_likes (T, mk_U T) $ x)
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   326
          else
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   327
            ([x], []);
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   328
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   329
        val gxsss = map (map (flat_rec (unzip_rec_likes gfolds (fn (_, t) => ([t], []))))) xsss;
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   330
        val hxsss = map (map (flat_rec (unzip_rec_likes hrecs (pairself single)))) xsss;
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   331
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   332
        val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
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   333
        val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
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   334
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   335
        val fold_tacss =
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   336
          map2 (map o mk_rec_like_tac pre_map_defs [] nesting_map_ids'' fold_defs) ctor_fold_thms
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   337
            ctr_defss;
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   338
        val rec_tacss =
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   339
          map2 (map o mk_rec_like_tac pre_map_defs nested_map_comp's
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   340
            (nested_map_ids'' @ nesting_map_ids'') rec_defs) ctor_rec_thms ctr_defss;
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   341
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   342
        fun prove goal tac =
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   343
          Goal.prove_sorry lthy [] [] goal (tac o #context)
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   344
          |> Thm.close_derivation;
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   345
      in
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   346
        (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
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   347
      end;
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   348
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   349
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
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   350
  in
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    ((induct_thm, induct_thms, [induct_case_names_attr]),
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   352
     (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
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   353
  end;
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   354
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   355
fun derive_coinduct_unfold_corec_thms_for_types names_lthy0 no_defs_lthy pre_bnfs dtor_coinduct
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   356
    dtor_strong_induct dtor_ctors dtor_unfold_thms dtor_corec_thms nesting_bnfs nested_bnfs fpTs Cs
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   357
    As kss mss ns cs cpss pgss crssss cgssss phss csssss chssss ctrss ctr_defss ctr_wrap_ress
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   358
    unfolds corecs unfold_defs corec_defs lthy =
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   359
  let
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   360
    val nn = length pre_bnfs;
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   361
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   362
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
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   363
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
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   364
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
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   365
    val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs;
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   366
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
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   367
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
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   368
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
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   369
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   370
    val fp_b_names = map base_name_of_typ fpTs;
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   371
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   372
    val discss = map (map (mk_disc_or_sel As) o #1) ctr_wrap_ress;
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   373
    val selsss = map (map (map (mk_disc_or_sel As)) o #2) ctr_wrap_ress;
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   374
    val exhaust_thms = map #3 ctr_wrap_ress;
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   375
    val disc_thmsss = map #7 ctr_wrap_ress;
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   376
    val discIss = map #8 ctr_wrap_ress;
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   377
    val sel_thmsss = map #9 ctr_wrap_ress;
blanchet@51810
   378
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   379
    val (((rs, us'), vs'), names_lthy) =
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   380
      lthy
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   381
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
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   382
      ||>> Variable.variant_fixes fp_b_names
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   383
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   384
blanchet@51810
   385
    val us = map2 (curry Free) us' fpTs;
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   386
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   387
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   388
blanchet@51810
   389
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   390
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   391
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   392
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   393
    val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
blanchet@51810
   394
      let
blanchet@51810
   395
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   396
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   397
        val strong_rs =
blanchet@51810
   398
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   399
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   400
blanchet@51810
   401
        fun build_rel rs' T =
blanchet@51810
   402
          (case find_index (curry (op =) T) fpTs of
blanchet@51810
   403
            ~1 =>
blanchet@51810
   404
            if exists_subtype_in fpTs T then build_rel_step lthy (build_rel rs') T
blanchet@51810
   405
            else HOLogic.eq_const T
blanchet@51810
   406
          | kk => nth rs' kk);
blanchet@51810
   407
blanchet@51810
   408
        fun build_rel_app rs' usel vsel =
blanchet@51810
   409
          fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@51810
   410
blanchet@51810
   411
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@51810
   412
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   413
          (if null usels then
blanchet@51810
   414
             []
blanchet@51810
   415
           else
blanchet@51810
   416
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@51810
   417
                Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@51810
   418
blanchet@51810
   419
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@51810
   420
          Library.foldr1 HOLogic.mk_conj
blanchet@51810
   421
            (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@51810
   422
          handle List.Empty => @{term True};
blanchet@51810
   423
blanchet@51810
   424
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@51810
   425
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@51810
   426
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@51810
   427
blanchet@51810
   428
        val concl =
blanchet@51810
   429
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   430
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   431
               uvrs us vs));
blanchet@51810
   432
blanchet@51810
   433
        fun mk_goal rs' =
blanchet@51810
   434
          Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@51810
   435
            concl);
blanchet@51810
   436
blanchet@51810
   437
        val goal = mk_goal rs;
blanchet@51810
   438
        val strong_goal = mk_goal strong_rs;
blanchet@51810
   439
blanchet@51810
   440
        fun prove dtor_coinduct' goal =
blanchet@51810
   441
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51810
   442
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@51810
   443
              exhaust_thms ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   444
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   445
          |> Thm.close_derivation;
blanchet@51810
   446
blanchet@51810
   447
        fun postproc nn thm =
blanchet@51810
   448
          Thm.permute_prems 0 nn
blanchet@51810
   449
            (if nn = 1 then thm RS mp
blanchet@51810
   450
             else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   451
          |> Drule.zero_var_indexes
blanchet@51810
   452
          |> `(conj_dests nn);
blanchet@51810
   453
      in
blanchet@51814
   454
        (postproc nn (prove dtor_coinduct goal), postproc nn (prove dtor_strong_induct strong_goal))
blanchet@51810
   455
      end;
blanchet@51810
   456
blanchet@51810
   457
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   458
      let
blanchet@51810
   459
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   460
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   461
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   462
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   463
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   464
      in
blanchet@51810
   465
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   466
      end;
blanchet@51810
   467
blanchet@51816
   468
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   469
    val coinduct_conclss =
blanchet@51810
   470
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   471
blanchet@51810
   472
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   473
blanchet@51810
   474
    val gunfolds = map (lists_bmoc pgss) unfolds;
blanchet@51810
   475
    val hcorecs = map (lists_bmoc phss) corecs;
blanchet@51810
   476
blanchet@51810
   477
    val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@51810
   478
      let
blanchet@51810
   479
        fun mk_goal pfss c cps fcorec_like n k ctr m cfs' =
blanchet@51810
   480
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   481
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@51810
   482
               mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   483
blanchet@51810
   484
        fun build_corec_like fcorec_likes (T, U) =
blanchet@51810
   485
          if T = U then
blanchet@51810
   486
            id_const T
blanchet@51810
   487
          else
blanchet@51810
   488
            (case find_index (curry (op =) U) fpTs of
blanchet@51810
   489
              ~1 => build_map lthy (build_corec_like fcorec_likes) T U
blanchet@51810
   490
            | kk => nth fcorec_likes kk);
blanchet@51810
   491
blanchet@51810
   492
        val mk_U = typ_subst (map2 pair Cs fpTs);
blanchet@51810
   493
blanchet@51810
   494
        fun intr_corec_likes fcorec_likes [] [cf] =
blanchet@51810
   495
            let val T = fastype_of cf in
blanchet@51810
   496
              if exists_subtype_in Cs T then build_corec_like fcorec_likes (T, mk_U T) $ cf
blanchet@51810
   497
              else cf
blanchet@51810
   498
            end
blanchet@51810
   499
          | intr_corec_likes fcorec_likes [cq] [cf, cf'] =
blanchet@51810
   500
            mk_If cq (intr_corec_likes fcorec_likes [] [cf])
blanchet@51810
   501
              (intr_corec_likes fcorec_likes [] [cf']);
blanchet@51810
   502
blanchet@51810
   503
        val crgsss = map2 (map2 (map2 (intr_corec_likes gunfolds))) crssss cgssss;
blanchet@51810
   504
        val cshsss = map2 (map2 (map2 (intr_corec_likes hcorecs))) csssss chssss;
blanchet@51810
   505
blanchet@51810
   506
        val unfold_goalss =
blanchet@51810
   507
          map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
blanchet@51810
   508
        val corec_goalss =
blanchet@51810
   509
          map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
blanchet@51810
   510
blanchet@51810
   511
        fun mk_map_if_distrib bnf =
blanchet@51810
   512
          let
blanchet@51810
   513
            val mapx = map_of_bnf bnf;
blanchet@51810
   514
            val live = live_of_bnf bnf;
blanchet@51810
   515
            val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
blanchet@51810
   516
            val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
blanchet@51810
   517
            val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
blanchet@51810
   518
          in
blanchet@51810
   519
            Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
blanchet@51810
   520
              @{thm if_distrib}
blanchet@51810
   521
          end;
blanchet@51810
   522
blanchet@51810
   523
        val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
blanchet@51810
   524
blanchet@51810
   525
        val unfold_tacss =
blanchet@51810
   526
          map3 (map oo mk_corec_like_tac unfold_defs [] [] nesting_map_ids'' [])
blanchet@51814
   527
            dtor_unfold_thms pre_map_defs ctr_defss;
blanchet@51810
   528
        val corec_tacss =
blanchet@51810
   529
          map3 (map oo mk_corec_like_tac corec_defs nested_map_comps'' nested_map_comp's
blanchet@51810
   530
              (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
blanchet@51814
   531
            dtor_corec_thms pre_map_defs ctr_defss;
blanchet@51810
   532
blanchet@51810
   533
        fun prove goal tac =
blanchet@51815
   534
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   535
          |> Thm.close_derivation;
blanchet@51810
   536
blanchet@51810
   537
        val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@51810
   538
        val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
blanchet@51810
   539
blanchet@51810
   540
        val filter_safesss =
blanchet@51810
   541
          map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@51810
   542
            curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
blanchet@51810
   543
blanchet@51810
   544
        val safe_unfold_thmss = filter_safesss unfold_thmss;
blanchet@51810
   545
        val safe_corec_thmss = filter_safesss corec_thmss;
blanchet@51810
   546
      in
blanchet@51810
   547
        (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@51810
   548
      end;
blanchet@51810
   549
blanchet@51810
   550
    val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@51810
   551
      let
blanchet@51810
   552
        fun mk_goal c cps fcorec_like n k disc =
blanchet@51810
   553
          mk_Trueprop_eq (disc $ (fcorec_like $ c),
blanchet@51810
   554
            if n = 1 then @{const True}
blanchet@51810
   555
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   556
blanchet@51810
   557
        val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@51810
   558
        val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   559
blanchet@51810
   560
        fun mk_case_split' cp =
blanchet@51810
   561
          Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   562
blanchet@51810
   563
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   564
blanchet@51810
   565
        val unfold_tacss =
blanchet@51810
   566
          map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@51810
   567
        val corec_tacss =
blanchet@51810
   568
          map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   569
blanchet@51810
   570
        fun prove goal tac =
blanchet@51810
   571
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51810
   572
          |> singleton (Proof_Context.export names_lthy0 no_defs_lthy)
blanchet@51810
   573
          |> Thm.close_derivation;
blanchet@51810
   574
blanchet@51810
   575
        fun proves [_] [_] = []
blanchet@51810
   576
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   577
      in
blanchet@51810
   578
        (map2 proves unfold_goalss unfold_tacss,
blanchet@51810
   579
         map2 proves corec_goalss corec_tacss)
blanchet@51810
   580
      end;
blanchet@51810
   581
blanchet@51810
   582
    val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@51810
   583
blanchet@51810
   584
    fun mk_disc_corec_like_thms corec_likes discIs =
blanchet@51810
   585
      map (op RS) (filter_out (is_triv_discI o snd) (corec_likes ~~ discIs));
blanchet@51810
   586
blanchet@51810
   587
    val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss;
blanchet@51810
   588
    val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss;
blanchet@51810
   589
blanchet@51810
   590
    fun mk_sel_corec_like_thm corec_like_thm sel sel_thm =
blanchet@51810
   591
      let
blanchet@51810
   592
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   593
        val arg_cong' =
blanchet@51810
   594
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   595
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   596
          |> Thm.varifyT_global;
blanchet@51810
   597
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   598
      in
blanchet@51810
   599
        corec_like_thm RS arg_cong' RS sel_thm'
blanchet@51810
   600
      end;
blanchet@51810
   601
blanchet@51810
   602
    fun mk_sel_corec_like_thms corec_likess =
blanchet@51810
   603
      map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss |> map flat;
blanchet@51810
   604
blanchet@51810
   605
    val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss;
blanchet@51810
   606
    val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss;
blanchet@51810
   607
blanchet@51810
   608
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   609
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   610
    val coinduct_case_concl_attrs =
blanchet@51810
   611
      map2 (fn casex => fn concls =>
blanchet@51810
   612
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   613
        coinduct_cases coinduct_conclss;
blanchet@51810
   614
    val coinduct_case_attrs =
blanchet@51810
   615
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   616
  in
blanchet@51810
   617
    ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms, coinduct_case_attrs),
blanchet@51810
   618
     (unfold_thmss, corec_thmss, []),
blanchet@51810
   619
     (safe_unfold_thmss, safe_corec_thmss),
blanchet@51810
   620
     (disc_unfold_thmss, disc_corec_thmss, simp_attrs),
blanchet@51810
   621
     (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
blanchet@51810
   622
     (sel_unfold_thmss, sel_corec_thmss, simp_attrs))
blanchet@51810
   623
  end;
blanchet@51810
   624
blanchet@49633
   625
fun define_datatypes prepare_constraint prepare_typ prepare_term lfp construct_fp
blanchet@49633
   626
    (wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
blanchet@49112
   627
  let
blanchet@49298
   628
    (* TODO: sanity checks on arguments *)
blanchet@49298
   629
blanchet@49286
   630
    val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
blanchet@49278
   631
      else ();
blanchet@49278
   632
blanchet@49633
   633
    fun qualify mandatory fp_b_name =
blanchet@49633
   634
      Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
   635
blanchet@49367
   636
    val nn = length specs;
blanchet@49361
   637
    val fp_bs = map type_binding_of specs;
blanchet@49498
   638
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
   639
    val fp_common_name = mk_common_name fp_b_names;
blanchet@51758
   640
    val map_bs = map map_binding_of specs;
blanchet@51767
   641
    val rel_bs = map rel_binding_of specs;
blanchet@49298
   642
blanchet@51758
   643
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
   644
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
   645
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   646
      end;
blanchet@49298
   647
blanchet@51758
   648
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs;
blanchet@49298
   649
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@49298
   650
    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
blanchet@51758
   651
    val set_bss = map (map fst o type_args_named_constrained_of) specs;
blanchet@49119
   652
blanchet@49585
   653
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
   654
      no_defs_lthy0
blanchet@49298
   655
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@49585
   656
      |> mk_TFrees (length unsorted_As)
blanchet@49585
   657
      ||>> mk_TFrees nn
blanchet@49585
   658
      ||>> apfst (map TFree) o
blanchet@49585
   659
        variant_types (map (prefix "'") fp_b_names) (replicate nn HOLogic.typeS);
blanchet@49119
   660
blanchet@49298
   661
    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
blanchet@49298
   662
    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
blanchet@49298
   663
      locale and shadows an existing global type*)
blanchet@51768
   664
blanchet@51769
   665
    fun add_fake_type spec =
blanchet@51768
   666
      Sign.add_type no_defs_lthy (type_binding_of spec,
blanchet@51769
   667
        length (type_args_named_constrained_of spec), mixfix_of spec);
blanchet@51768
   668
blanchet@51769
   669
    val fake_thy = Theory.copy #> fold add_fake_type specs;
blanchet@49298
   670
    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
blanchet@49119
   671
blanchet@49182
   672
    fun mk_fake_T b =
blanchet@49121
   673
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49298
   674
        unsorted_As);
blanchet@49121
   675
blanchet@49302
   676
    val fake_Ts = map mk_fake_T fp_bs;
blanchet@49121
   677
blanchet@49181
   678
    val mixfixes = map mixfix_of specs;
blanchet@49119
   679
blanchet@49302
   680
    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
   681
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
   682
blanchet@49121
   683
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
   684
blanchet@49336
   685
    val disc_bindingss = map (map disc_of) ctr_specss;
blanchet@49336
   686
    val ctr_bindingss =
blanchet@49633
   687
      map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
blanchet@49121
   688
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49181
   689
    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
blanchet@49119
   690
blanchet@49336
   691
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
   692
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49286
   693
    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
blanchet@49286
   694
blanchet@49308
   695
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
   696
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@49298
   697
blanchet@49298
   698
    val _ = (case duplicates (op =) unsorted_As of [] => ()
blanchet@49298
   699
      | A :: _ => error ("Duplicate type parameter " ^
blanchet@49298
   700
          quote (Syntax.string_of_typ no_defs_lthy A)));
blanchet@49298
   701
blanchet@49183
   702
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@49298
   703
    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
blanchet@49165
   704
        [] => ()
blanchet@49342
   705
      | A' :: _ => error ("Extra type variable on right-hand side: " ^
blanchet@49204
   706
          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
blanchet@49165
   707
blanchet@49591
   708
    fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
   709
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
   710
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49591
   711
      | eq_fpT_check _ _ = false;
blanchet@49146
   712
blanchet@49204
   713
    fun freeze_fp (T as Type (s, Us)) =
blanchet@49591
   714
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@49591
   715
          ~1 => Type (s, map freeze_fp Us)
blanchet@49591
   716
        | kk => nth Xs kk)
blanchet@49204
   717
      | freeze_fp T = T;
blanchet@49121
   718
blanchet@49536
   719
    val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@49536
   720
    val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
blanchet@49119
   721
blanchet@49298
   722
    val fp_eqs =
blanchet@49536
   723
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsXs;
blanchet@49121
   724
blanchet@51805
   725
    val (pre_bnfs, ({bnfs = fp_bnfs as any_fp_bnf :: _, dtors = dtors0, ctors = ctors0,
blanchet@51805
   726
           folds = fp_folds0, recs = fp_recs0, induct = fp_induct, strong_induct = fp_strong_induct,
blanchet@51805
   727
           dtor_ctors, ctor_dtors, ctor_injects, map_thms = fp_map_thms, set_thmss = fp_set_thmss,
blanchet@51805
   728
           rel_thms = fp_rel_thms, fold_thms = fp_fold_thms, rec_thms = fp_rec_thms}, lthy)) =
blanchet@51767
   729
      fp_bnf construct_fp fp_bs mixfixes map_bs rel_bs set_bss (map dest_TFree unsorted_As) fp_eqs
blanchet@51758
   730
        no_defs_lthy0;
blanchet@49585
   731
blanchet@49585
   732
    val timer = time (Timer.startRealTimer ());
blanchet@49121
   733
blanchet@49363
   734
    fun add_nesty_bnf_names Us =
blanchet@49226
   735
      let
blanchet@49226
   736
        fun add (Type (s, Ts)) ss =
blanchet@49226
   737
            let val (needs, ss') = fold_map add Ts ss in
blanchet@49226
   738
              if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@49226
   739
            end
blanchet@49363
   740
          | add T ss = (member (op =) Us T, ss);
blanchet@49226
   741
      in snd oo add end;
blanchet@49226
   742
blanchet@49363
   743
    fun nesty_bnfs Us =
blanchet@49536
   744
      map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssXs []);
blanchet@49363
   745
blanchet@49363
   746
    val nesting_bnfs = nesty_bnfs As;
blanchet@49536
   747
    val nested_bnfs = nesty_bnfs Xs;
blanchet@49226
   748
blanchet@49585
   749
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
   750
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
   751
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51766
   752
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51766
   753
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@49585
   754
blanchet@49585
   755
    val live = live_of_bnf any_fp_bnf;
blanchet@49585
   756
blanchet@49585
   757
    val Bs =
blanchet@49585
   758
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
   759
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
   760
blanchet@49585
   761
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
   762
blanchet@49501
   763
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
   764
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
   765
blanchet@49501
   766
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
   767
blanchet@51780
   768
    fun massage_simple_notes base =
blanchet@51780
   769
      filter_out (null o #2)
blanchet@51780
   770
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
   771
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
   772
blanchet@51780
   773
    val massage_multi_notes =
blanchet@51780
   774
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
   775
        if forall null thmss then
blanchet@51780
   776
          []
blanchet@51780
   777
        else
blanchet@51780
   778
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@51780
   779
            ((qualify true fp_b_name (Binding.name thmN), attrs T_name),
blanchet@51780
   780
             [(thms, [])])) fp_b_names fpTs thmss);
blanchet@51780
   781
blanchet@49536
   782
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
blanchet@49203
   783
    val ns = map length ctr_Tsss;
blanchet@49212
   784
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
   785
    val mss = map (map length) ctr_Tsss;
blanchet@49203
   786
    val Css = map2 replicate ns Cs;
blanchet@49203
   787
blanchet@49585
   788
    val fp_folds as any_fp_fold :: _ = map (mk_rec_like lfp As Cs) fp_folds0;
blanchet@49585
   789
    val fp_recs as any_fp_rec :: _ = map (mk_rec_like lfp As Cs) fp_recs0;
blanchet@49210
   790
blanchet@49585
   791
    val fp_fold_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_fold)));
blanchet@49585
   792
    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_rec)));
blanchet@49204
   793
blanchet@49504
   794
    val (((fold_only as (gss, _, _), rec_only as (hss, _, _)),
blanchet@49683
   795
          (cs, cpss, unfold_only as ((pgss, crssss, cgssss), (_, g_Tsss, _)),
blanchet@49683
   796
           corec_only as ((phss, csssss, chssss), (_, h_Tsss, _)))), names_lthy0) =
blanchet@49208
   797
      if lfp then
blanchet@49208
   798
        let
blanchet@49208
   799
          val y_Tsss =
blanchet@49255
   800
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49504
   801
              ns mss fp_fold_fun_Ts;
blanchet@49208
   802
          val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
blanchet@49208
   803
blanchet@49484
   804
          val ((gss, ysss), lthy) =
blanchet@49208
   805
            lthy
blanchet@49208
   806
            |> mk_Freess "f" g_Tss
blanchet@49208
   807
            ||>> mk_Freesss "x" y_Tsss;
blanchet@49670
   808
blanchet@49670
   809
          fun proj_recT proj (Type (s as @{type_name prod}, Ts as [T, U])) =
blanchet@49670
   810
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_recT proj) Ts)
blanchet@49670
   811
            | proj_recT proj (Type (s, Ts)) = Type (s, map (proj_recT proj) Ts)
blanchet@49670
   812
            | proj_recT _ T = T;
blanchet@49274
   813
blanchet@51794
   814
          fun unzip_recT T =
blanchet@51808
   815
            if exists_subtype_in fpTs T then ([proj_recT fst T], [proj_recT snd T]) else ([T], []);
blanchet@49204
   816
blanchet@49670
   817
          val z_Tsss =
blanchet@49670
   818
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49670
   819
              ns mss fp_rec_fun_Ts;
blanchet@51794
   820
          val z_Tsss' = map (map (flat_rec unzip_recT)) z_Tsss;
blanchet@51794
   821
          val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' Css;
blanchet@49204
   822
blanchet@49298
   823
          val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@49670
   824
          val zsss = map2 (map2 (map2 retype_free)) z_Tsss ysss;
blanchet@49210
   825
        in
blanchet@49670
   826
          ((((gss, g_Tss, ysss), (hss, h_Tss, zsss)),
blanchet@49683
   827
            ([], [], (([], [], []), ([], [], [])), (([], [], []), ([], [], [])))), lthy)
blanchet@49210
   828
        end
blanchet@49208
   829
      else
blanchet@49210
   830
        let
blanchet@49221
   831
          (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@49221
   832
          val mss' =  map (fn [0] => [1] | ms => ms) mss;
blanchet@49221
   833
blanchet@49463
   834
          val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@49275
   835
blanchet@49587
   836
          fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss);
blanchet@49211
   837
blanchet@49587
   838
          fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss
blanchet@49587
   839
            | flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
blanchet@49587
   840
              p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss;
blanchet@49274
   841
blanchet@49681
   842
          fun mk_types maybe_unzipT fun_Ts =
blanchet@49212
   843
            let
blanchet@49212
   844
              val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@49255
   845
              val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@49681
   846
              val f_Tsss = map2 (map2 dest_tupleT) mss' f_prod_Tss;
blanchet@49275
   847
              val f_Tssss =
blanchet@49681
   848
                map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
blanchet@49275
   849
              val q_Tssss =
blanchet@49463
   850
                map (map (map (fn [_] => [] | [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss;
blanchet@49587
   851
              val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@49681
   852
            in (q_Tssss, f_sum_prod_Ts, f_Tsss, f_Tssss, pf_Tss) end;
blanchet@49176
   853
blanchet@49681
   854
          val (r_Tssss, g_sum_prod_Ts, g_Tsss, g_Tssss, pg_Tss) = mk_types single fp_fold_fun_Ts;
blanchet@49211
   855
blanchet@49683
   856
          val (((cs, pss), gssss), lthy) =
blanchet@49210
   857
            lthy
blanchet@49683
   858
            |> mk_Frees "a" Cs
blanchet@49211
   859
            ||>> mk_Freess "p" p_Tss
blanchet@49275
   860
            ||>> mk_Freessss "g" g_Tssss;
blanchet@49275
   861
          val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@49274
   862
blanchet@49681
   863
          fun proj_corecT proj (Type (s as @{type_name sum}, Ts as [T, U])) =
blanchet@49681
   864
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   865
            | proj_corecT proj (Type (s, Ts)) = Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   866
            | proj_corecT _ T = T;
blanchet@49274
   867
blanchet@49681
   868
          fun unzip_corecT T =
blanchet@51808
   869
            if exists_subtype_in fpTs T then [proj_corecT fst T, proj_corecT snd T] else [T];
blanchet@49681
   870
blanchet@49681
   871
          val (s_Tssss, h_sum_prod_Ts, h_Tsss, h_Tssss, ph_Tss) =
blanchet@49681
   872
            mk_types unzip_corecT fp_rec_fun_Ts;
blanchet@49210
   873
blanchet@49298
   874
          val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@49484
   875
          val ((sssss, hssss_tl), lthy) =
blanchet@49275
   876
            lthy
blanchet@49275
   877
            |> mk_Freessss "q" s_Tssss
blanchet@49275
   878
            ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@49275
   879
          val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@49211
   880
blanchet@49681
   881
          val cpss = map2 (map o rapp) cs pss;
blanchet@49212
   882
blanchet@49683
   883
          fun mk_terms qssss fssss =
blanchet@49212
   884
            let
blanchet@49587
   885
              val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
blanchet@49681
   886
              val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@49681
   887
              val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@49683
   888
            in (pfss, cqssss, cfssss) end;
blanchet@49210
   889
        in
blanchet@49484
   890
          (((([], [], []), ([], [], [])),
blanchet@49683
   891
            (cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, g_Tsss, pg_Tss)),
blanchet@49683
   892
             (mk_terms sssss hssss, (h_sum_prod_Ts, h_Tsss, ph_Tss)))), lthy)
blanchet@49210
   893
        end;
blanchet@49210
   894
blanchet@49585
   895
    fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@49585
   896
            fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@49585
   897
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@49585
   898
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   899
      let
blanchet@49498
   900
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
   901
blanchet@49501
   902
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
   903
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   904
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   905
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   906
blanchet@49593
   907
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
   908
          no_defs_lthy
blanchet@49501
   909
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
   910
          ||>> mk_Frees "f" case_Ts
blanchet@49370
   911
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
   912
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
   913
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
   914
blanchet@49498
   915
        val u = Free (u', fpT);
blanchet@49121
   916
blanchet@49585
   917
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
   918
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
   919
blanchet@49129
   920
        val ctr_rhss =
blanchet@49585
   921
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
   922
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
   923
blanchet@49633
   924
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
   925
blanchet@49134
   926
        val case_rhs =
blanchet@49498
   927
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
   928
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
   929
blanchet@49201
   930
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   931
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
   932
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
   933
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   934
          ||> `Local_Theory.restore;
blanchet@49121
   935
blanchet@49121
   936
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   937
blanchet@49121
   938
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
   939
        val ctr_defs' =
blanchet@49585
   940
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
   941
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   942
blanchet@49203
   943
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   944
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   945
blanchet@49203
   946
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   947
blanchet@49585
   948
        fun wrap lthy =
blanchet@49123
   949
          let
traytel@50170
   950
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
   951
              let
blanchet@49585
   952
                val ctor_iff_dtor_thm =
blanchet@49585
   953
                  let
blanchet@49585
   954
                    val goal =
blanchet@49585
   955
                      fold_rev Logic.all [w, u]
blanchet@49585
   956
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
   957
                  in
wenzelm@51551
   958
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
   959
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
   960
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
   961
                    |> Thm.close_derivation
blanchet@49585
   962
                    |> Morphism.thm phi
blanchet@49585
   963
                  end;
blanchet@49585
   964
blanchet@49585
   965
                val sumEN_thm' =
blanchet@49585
   966
                  unfold_thms lthy @{thms all_unit_eq}
blanchet@49585
   967
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
   968
                       (mk_sumEN_balanced n))
blanchet@49585
   969
                  |> Morphism.thm phi;
blanchet@49135
   970
              in
blanchet@49585
   971
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
   972
              end;
blanchet@49135
   973
blanchet@49585
   974
            val inject_tacss =
blanchet@49585
   975
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
   976
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
   977
blanchet@49585
   978
            val half_distinct_tacss =
blanchet@49585
   979
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
   980
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
   981
blanchet@49585
   982
            val case_tacs =
blanchet@49585
   983
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
   984
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
   985
blanchet@49585
   986
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
   987
blanchet@49585
   988
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
   989
          in
blanchet@51781
   990
            wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
blanchet@51781
   991
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
   992
          end;
blanchet@49121
   993
blanchet@51810
   994
        fun derive_maps_sets_rels (ctr_wrap_res, lthy) =
blanchet@49585
   995
          let
blanchet@49585
   996
            val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@49585
   997
            val nones = replicate live NONE;
blanchet@49585
   998
blanchet@49585
   999
            val ctor_cong =
blanchet@51746
  1000
              if lfp then
blanchet@51746
  1001
                Drule.dummy_thm
blanchet@51746
  1002
              else
blanchet@51746
  1003
                let val ctor' = mk_ctor Bs ctor in
blanchet@51746
  1004
                  cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51746
  1005
                end;
blanchet@49585
  1006
blanchet@49585
  1007
            fun mk_cIn ify =
blanchet@49585
  1008
              certify lthy o (not lfp ? curry (op $) (map_types ify ctor)) oo
blanchet@49585
  1009
              mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
  1010
blanchet@49585
  1011
            val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@49585
  1012
            val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
  1013
blanchet@49682
  1014
            fun mk_map_thm ctr_def' cxIn =
blanchet@49585
  1015
              fold_thms lthy [ctr_def']
blanchet@49585
  1016
                (unfold_thms lthy (pre_map_def ::
blanchet@49585
  1017
                     (if lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@49585
  1018
                   (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@49585
  1019
                      (if lfp then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@49593
  1020
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1021
blanchet@49682
  1022
            fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@49585
  1023
              fold_thms lthy [ctr_def']
blanchet@51766
  1024
                (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@49585
  1025
                     (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@49585
  1026
                   (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@49593
  1027
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1028
blanchet@49682
  1029
            fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49585
  1030
blanchet@49682
  1031
            val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@49585
  1032
            val set_thmss = map mk_set_thms fp_set_thms;
blanchet@49127
  1033
blanchet@49682
  1034
            val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1035
blanchet@49682
  1036
            fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@49585
  1037
              fold_thms lthy ctr_defs'
blanchet@51745
  1038
                 (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@51745
  1039
                      (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@49585
  1040
                    (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@49593
  1041
              |> postproc
blanchet@49593
  1042
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1043
blanchet@49682
  1044
            fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@49682
  1045
              mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1046
blanchet@49592
  1047
            val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1048
blanchet@49682
  1049
            fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@49585
  1050
              mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@49682
  1051
                cxIn cyIn;
blanchet@49121
  1052
blanchet@49592
  1053
            fun mk_other_half_rel_distinct_thm thm =
blanchet@49585
  1054
              flip_rels lthy live thm RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1055
blanchet@49592
  1056
            val half_rel_distinct_thmss =
blanchet@49592
  1057
              map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@49592
  1058
            val other_half_rel_distinct_thmss =
blanchet@49592
  1059
              map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@49592
  1060
            val (rel_distinct_thms, _) =
blanchet@49592
  1061
              join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1062
blanchet@49585
  1063
            val notes =
blanchet@49594
  1064
              [(mapN, map_thms, code_simp_attrs),
blanchet@49592
  1065
               (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@49592
  1066
               (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@49585
  1067
               (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51780
  1068
              |> massage_simple_notes fp_b_name;
blanchet@49585
  1069
          in
blanchet@51810
  1070
            (ctr_wrap_res, lthy |> Local_Theory.notes notes |> snd)
blanchet@49585
  1071
          end;
blanchet@49585
  1072
blanchet@49585
  1073
        fun define_fold_rec no_defs_lthy =
blanchet@49134
  1074
          let
blanchet@49208
  1075
            val fpT_to_C = fpT --> C;
blanchet@49199
  1076
blanchet@49681
  1077
            fun build_prod_proj mk_proj (T, U) =
blanchet@49670
  1078
              if T = U then
blanchet@49670
  1079
                id_const T
blanchet@49670
  1080
              else
blanchet@49670
  1081
                (case (T, U) of
blanchet@49670
  1082
                  (Type (s, _), Type (s', _)) =>
blanchet@51808
  1083
                  if s = s' then build_map lthy (build_prod_proj mk_proj) T U else mk_proj T
blanchet@49670
  1084
                | _ => mk_proj T);
blanchet@49670
  1085
blanchet@49681
  1086
            (* TODO: Avoid these complications; cf. corec case *)
blanchet@49672
  1087
            fun mk_U proj (Type (s as @{type_name prod}, Ts as [T', U])) =
blanchet@49672
  1088
                if member (op =) fpTs T' then proj (T', U) else Type (s, map (mk_U proj) Ts)
blanchet@49670
  1089
              | mk_U proj (Type (s, Ts)) = Type (s, map (mk_U proj) Ts)
blanchet@49670
  1090
              | mk_U _ T = T;
blanchet@49670
  1091
blanchet@51794
  1092
            fun unzip_rec (x as Free (_, T)) =
blanchet@51808
  1093
              if exists_subtype_in fpTs T then
blanchet@51794
  1094
                ([build_prod_proj fst_const (T, mk_U fst T) $ x],
blanchet@51794
  1095
                 [build_prod_proj snd_const (T, mk_U snd T) $ x])
blanchet@49670
  1096
              else
blanchet@51794
  1097
                ([x], []);
blanchet@49670
  1098
blanchet@51793
  1099
            fun mk_rec_like_arg f xs =
blanchet@51794
  1100
              mk_tupled_fun (HOLogic.mk_tuple xs) f (flat_rec unzip_rec xs);
blanchet@49670
  1101
blanchet@49670
  1102
            fun generate_rec_like (suf, fp_rec_like, (fss, f_Tss, xsss)) =
blanchet@49215
  1103
              let
blanchet@49215
  1104
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49633
  1105
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49215
  1106
                val spec =
blanchet@49336
  1107
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@49504
  1108
                    Term.list_comb (fp_rec_like,
blanchet@49670
  1109
                      map2 (mk_sum_caseN_balanced oo map2 mk_rec_like_arg) fss xsss));
blanchet@49336
  1110
              in (binding, spec) end;
blanchet@49199
  1111
blanchet@49504
  1112
            val rec_like_infos =
blanchet@49504
  1113
              [(foldN, fp_fold, fold_only),
blanchet@49215
  1114
               (recN, fp_rec, rec_only)];
blanchet@49215
  1115
blanchet@49504
  1116
            val (bindings, specs) = map generate_rec_like rec_like_infos |> split_list;
blanchet@49215
  1117
blanchet@49215
  1118
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
  1119
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
  1120
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
  1121
                #>> apsnd snd) bindings specs
blanchet@49199
  1122
              ||> `Local_Theory.restore;
blanchet@49201
  1123
blanchet@49201
  1124
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
  1125
blanchet@49504
  1126
            val [fold_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
  1127
blanchet@49536
  1128
            val [foldx, recx] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49134
  1129
          in
blanchet@49693
  1130
            ((foldx, recx, fold_def, rec_def), lthy')
blanchet@49134
  1131
          end;
blanchet@49134
  1132
blanchet@49585
  1133
        fun define_unfold_corec no_defs_lthy =
blanchet@49210
  1134
          let
blanchet@49210
  1135
            val B_to_fpT = C --> fpT;
blanchet@49211
  1136
blanchet@49683
  1137
            fun build_sum_inj mk_inj (T, U) =
blanchet@49683
  1138
              if T = U then
blanchet@49683
  1139
                id_const T
blanchet@49683
  1140
              else
blanchet@49683
  1141
                (case (T, U) of
blanchet@49683
  1142
                  (Type (s, _), Type (s', _)) =>
blanchet@51808
  1143
                  if s = s' then build_map lthy (build_sum_inj mk_inj) T U
blanchet@49683
  1144
                  else uncurry mk_inj (dest_sumT U)
blanchet@49683
  1145
                | _ => uncurry mk_inj (dest_sumT U));
blanchet@49683
  1146
blanchet@49683
  1147
            fun build_dtor_corec_like_arg _ [] [cf] = cf
blanchet@49683
  1148
              | build_dtor_corec_like_arg T [cq] [cf, cf'] =
blanchet@49683
  1149
                mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@49683
  1150
                  (build_sum_inj Inr_const (fastype_of cf', T) $ cf')
blanchet@49683
  1151
blanchet@49683
  1152
            val crgsss = map3 (map3 (map3 build_dtor_corec_like_arg)) g_Tsss crssss cgssss;
blanchet@49683
  1153
            val cshsss = map3 (map3 (map3 build_dtor_corec_like_arg)) h_Tsss csssss chssss;
blanchet@49683
  1154
blanchet@49276
  1155
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
  1156
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
  1157
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
  1158
blanchet@49683
  1159
            fun generate_corec_like (suf, fp_rec_like, (cqfsss, ((pfss, _, _), (f_sum_prod_Ts, _,
blanchet@49683
  1160
                pf_Tss)))) =
blanchet@49211
  1161
              let
blanchet@49211
  1162
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49633
  1163
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49211
  1164
                val spec =
blanchet@49336
  1165
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@49504
  1166
                    Term.list_comb (fp_rec_like,
blanchet@49276
  1167
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49336
  1168
              in (binding, spec) end;
blanchet@49210
  1169
blanchet@49504
  1170
            val corec_like_infos =
blanchet@49683
  1171
              [(unfoldN, fp_fold, (crgsss, unfold_only)),
blanchet@49683
  1172
               (corecN, fp_rec, (cshsss, corec_only))];
blanchet@49212
  1173
blanchet@49504
  1174
            val (bindings, specs) = map generate_corec_like corec_like_infos |> split_list;
blanchet@49211
  1175
blanchet@49211
  1176
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
  1177
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
  1178
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
  1179
                #>> apsnd snd) bindings specs
blanchet@49210
  1180
              ||> `Local_Theory.restore;
blanchet@49210
  1181
blanchet@49210
  1182
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
  1183
blanchet@49504
  1184
            val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
  1185
blanchet@49536
  1186
            val [unfold, corec] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49210
  1187
          in
blanchet@49693
  1188
            ((unfold, corec, unfold_def, corec_def), lthy')
blanchet@49287
  1189
          end;
blanchet@49287
  1190
blanchet@49504
  1191
        val define_rec_likes = if lfp then define_fold_rec else define_unfold_corec;
blanchet@49585
  1192
blanchet@51810
  1193
        fun massage_res ((ctr_wrap_res, rec_like_res), lthy) =
blanchet@51810
  1194
          (((ctrs, xss, ctr_defs, ctr_wrap_res), rec_like_res), lthy);
blanchet@49119
  1195
      in
blanchet@49585
  1196
        (wrap #> (live > 0 ? derive_maps_sets_rels) ##>> define_rec_likes #> massage_res, lthy')
blanchet@49119
  1197
      end;
blanchet@49167
  1198
blanchet@49585
  1199
    fun wrap_types_and_more (wrap_types_and_mores, lthy) =
blanchet@49585
  1200
      fold_map I wrap_types_and_mores lthy
blanchet@49585
  1201
      |>> apsnd split_list4 o apfst split_list4 o split_list;
blanchet@49226
  1202
blanchet@49585
  1203
    (* TODO: Add map, sets, rel simps *)
blanchet@49479
  1204
    val mk_simp_thmss =
blanchet@49591
  1205
      map3 (fn (_, _, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn fold_likes =>
blanchet@49505
  1206
        injects @ distincts @ cases @ rec_likes @ fold_likes);
blanchet@49479
  1207
blanchet@51810
  1208
    fun derive_and_note_induct_fold_rec_thms_for_types
blanchet@51811
  1209
        (((ctrss, xsss, ctr_defss, ctr_wrap_ress), (folds, recs, fold_defs, rec_defs)), lthy) =
blanchet@49202
  1210
      let
blanchet@51810
  1211
        val ((induct_thm, induct_thms, induct_attrs),
blanchet@51810
  1212
             (fold_thmss, fold_attrs),
blanchet@51808
  1213
             (rec_thmss, rec_attrs)) =
blanchet@51815
  1214
          derive_induct_fold_rec_thms_for_types pre_bnfs fp_induct fp_fold_thms fp_rec_thms
blanchet@51811
  1215
            nesting_bnfs nested_bnfs fpTs Cs ctr_Tsss mss ns gss hss ctrss xsss ctr_defss folds recs
blanchet@51811
  1216
            fold_defs rec_defs lthy;
blanchet@49201
  1217
blanchet@51810
  1218
        fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name));
blanchet@51810
  1219
blanchet@51810
  1220
        val simp_thmss = mk_simp_thmss ctr_wrap_ress rec_thmss fold_thmss;
blanchet@49438
  1221
blanchet@49337
  1222
        val common_notes =
blanchet@51808
  1223
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1224
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1225
blanchet@49226
  1226
        val notes =
blanchet@51808
  1227
          [(foldN, fold_thmss, K fold_attrs),
blanchet@51810
  1228
           (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@51808
  1229
           (recN, rec_thmss, K rec_attrs),
blanchet@49585
  1230
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1231
          |> massage_multi_notes;
blanchet@49202
  1232
      in
blanchet@49337
  1233
        lthy |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@49202
  1234
      end;
blanchet@49202
  1235
blanchet@51810
  1236
    fun derive_and_note_coinduct_unfold_corec_thms_for_types
blanchet@51811
  1237
        (((ctrss, _, ctr_defss, ctr_wrap_ress), (unfolds, corecs, unfold_defs, corec_defs)), lthy) =
blanchet@49212
  1238
      let
blanchet@51810
  1239
        val ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms,
blanchet@51810
  1240
              coinduct_attrs),
blanchet@51810
  1241
             (unfold_thmss, corec_thmss, corec_like_attrs),
blanchet@51810
  1242
             (safe_unfold_thmss, safe_corec_thmss),
blanchet@51810
  1243
             (disc_unfold_thmss, disc_corec_thmss, disc_corec_like_attrs),
blanchet@51810
  1244
             (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_corec_like_iff_attrs),
blanchet@51810
  1245
             (sel_unfold_thmss, sel_corec_thmss, sel_corec_like_attrs)) =
blanchet@51815
  1246
          derive_coinduct_unfold_corec_thms_for_types names_lthy0 no_defs_lthy pre_bnfs fp_induct
blanchet@51811
  1247
            fp_strong_induct dtor_ctors fp_fold_thms fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs As
blanchet@51811
  1248
            kss mss ns cs cpss pgss crssss cgssss phss csssss chssss ctrss ctr_defss ctr_wrap_ress
blanchet@51811
  1249
            unfolds corecs unfold_defs corec_defs lthy;
blanchet@49212
  1250
blanchet@51810
  1251
        fun coinduct_type_attr T_name = Attrib.internal (K (Induct.coinduct_type T_name));
blanchet@49479
  1252
blanchet@49587
  1253
        fun flat_corec_like_thms corec_likes disc_corec_likes sel_corec_likes =
blanchet@49504
  1254
          corec_likes @ disc_corec_likes @ sel_corec_likes;
blanchet@49479
  1255
blanchet@49479
  1256
        val simp_thmss =
blanchet@51810
  1257
          mk_simp_thmss ctr_wrap_ress
blanchet@49587
  1258
            (map3 flat_corec_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@49587
  1259
            (map3 flat_corec_like_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss);
blanchet@49479
  1260
blanchet@49479
  1261
        val anonymous_notes =
blanchet@49504
  1262
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1263
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1264
blanchet@49342
  1265
        val common_notes =
blanchet@49591
  1266
          (if nn > 1 then
blanchet@51810
  1267
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1268
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1269
           else
blanchet@49591
  1270
             [])
blanchet@51780
  1271
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1272
blanchet@49212
  1273
        val notes =
blanchet@51780
  1274
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1275
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@51810
  1276
           (corecN, corec_thmss, K corec_like_attrs),
blanchet@51810
  1277
           (disc_corecN, disc_corec_thmss, K disc_corec_like_attrs),
blanchet@51810
  1278
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_corec_like_iff_attrs),
blanchet@51810
  1279
           (disc_unfoldN, disc_unfold_thmss, K disc_corec_like_attrs),
blanchet@51810
  1280
           (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_corec_like_iff_attrs),
blanchet@51810
  1281
           (sel_corecN, sel_corec_thmss, K sel_corec_like_attrs),
blanchet@51810
  1282
           (sel_unfoldN, sel_unfold_thmss, K sel_corec_like_attrs),
blanchet@51780
  1283
           (simpsN, simp_thmss, K []),
blanchet@51810
  1284
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
blanchet@51810
  1285
           (unfoldN, unfold_thmss, K corec_like_attrs)]
blanchet@51780
  1286
          |> massage_multi_notes;
blanchet@49212
  1287
      in
blanchet@49479
  1288
        lthy |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@49212
  1289
      end;
blanchet@49212
  1290
blanchet@49204
  1291
    val lthy' = lthy
blanchet@49585
  1292
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@49585
  1293
        fp_folds ~~ fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@49585
  1294
        pre_set_defss ~~ pre_rel_defs ~~ fp_map_thms ~~ fp_set_thmss ~~ fp_rel_thms ~~ ns ~~ kss ~~
blanchet@49585
  1295
        mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
blanchet@49585
  1296
        raw_sel_defaultsss)
blanchet@49585
  1297
      |> wrap_types_and_more
blanchet@51808
  1298
      |> (if lfp then derive_and_note_induct_fold_rec_thms_for_types
blanchet@51808
  1299
          else derive_and_note_coinduct_unfold_corec_thms_for_types);
blanchet@49167
  1300
blanchet@49167
  1301
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
  1302
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
  1303
  in
blanchet@49308
  1304
    timer; lthy'
blanchet@49112
  1305
  end;
blanchet@49112
  1306
blanchet@49536
  1307
val datatypes = define_datatypes (K I) (K I) (K I);
blanchet@49297
  1308
blanchet@51380
  1309
val datatype_cmd = define_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1310
blanchet@49112
  1311
val parse_ctr_arg =
blanchet@49329
  1312
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1313
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1314
blanchet@49286
  1315
val parse_defaults =
blanchet@49286
  1316
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1317
blanchet@51758
  1318
val parse_type_arg_constrained =
blanchet@51790
  1319
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1320
blanchet@51790
  1321
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1322
blanchet@51758
  1323
val parse_type_args_named_constrained =
blanchet@51758
  1324
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1325
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1326
  Scan.succeed [];
blanchet@51756
  1327
blanchet@51790
  1328
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1329
blanchet@51767
  1330
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1331
blanchet@51767
  1332
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51767
  1333
   that we don't want them to be highlighted everywhere because of some obscure feature of the BNF
blanchet@51767
  1334
   package. *)
blanchet@51767
  1335
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1336
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1337
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1338
blanchet@51767
  1339
val parse_map_rel_bindings =
blanchet@51767
  1340
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1341
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1342
  Scan.succeed no_map_rel;
blanchet@51767
  1343
blanchet@51767
  1344
val parse_ctr_spec =
blanchet@51790
  1345
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1346
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1347
blanchet@51767
  1348
val parse_spec =
blanchet@51790
  1349
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1350
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1351
blanchet@51767
  1352
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1353
blanchet@49585
  1354
fun parse_datatype_cmd lfp construct_fp = parse_datatype >> datatype_cmd lfp construct_fp;
blanchet@49112
  1355
blanchet@49112
  1356
end;