src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Mon Apr 29 10:37:23 2013 +0200 (2013-04-29)
changeset 51808 355dcd6a9b3c
parent 51805 67757f1d5e71
child 51810 7b75fab5ebf5
permissions -rw-r--r--
factored out derivation of induction principles, folds and recs, in preparation for reduction of nested to mutual
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(*  Title:      HOL/BNF/Tools/bnf_fp_def_sugar.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Sugared datatype and codatatype constructions.
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*)
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signature BNF_FP_DEF_SUGAR =
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sig
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  val datatypes: bool ->
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    (mixfix list -> (string * sort) list option -> binding list -> binding list -> binding list ->
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      binding list list -> typ list * typ list list -> BNF_Def.BNF list -> local_theory ->
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      BNF_FP.fp_result * local_theory) ->
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    (bool * bool) * (((((binding * (typ * sort)) list * binding) * (binding * binding)) * mixfix) *
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      ((((binding * binding) * (binding * typ) list) * (binding * term) list) *
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        mixfix) list) list ->
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    local_theory -> local_theory
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  val parse_datatype_cmd: bool ->
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    (mixfix list -> (string * sort) list option -> binding list -> binding list -> binding list ->
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      binding list list -> typ list * typ list list -> BNF_Def.BNF list -> local_theory ->
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      BNF_FP.fp_result * local_theory) ->
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    (local_theory -> local_theory) parser
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end;
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structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
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struct
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open BNF_Util
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open BNF_Ctr_Sugar
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open BNF_Def
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open BNF_FP
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open BNF_FP_Def_Sugar_Tactics
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val EqN = "Eq_";
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(* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A"). *)
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fun quasi_unambiguous_case_names names =
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  let
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    val ps = map (`Long_Name.base_name) names;
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    val dups = Library.duplicates (op =) (map fst ps);
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    fun underscore s =
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      let val ss = space_explode Long_Name.separator s in
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        space_implode "_" (drop (length ss - 2) ss)
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      end;
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  in
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    map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
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  end;
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val mp_conj = @{thm mp_conj};
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val simp_attrs = @{attributes [simp]};
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val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs;
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fun split_list4 [] = ([], [], [], [])
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  | split_list4 ((x1, x2, x3, x4) :: xs) =
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    let val (xs1, xs2, xs3, xs4) = split_list4 xs;
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    in (x1 :: xs1, x2 :: xs2, x3 :: xs3, x4 :: xs4) end;
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fun 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
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    nn fp_b_names pre_bnfs fp_induct fp_fold_thms fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs
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    ctr_Tsss mss ns gss hss ((ctrss, xsss, ctr_defss, _), (folds, recs, fold_defs, rec_defs)) lthy =
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  let
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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 nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
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    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
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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' = fp_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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          |> singleton (Proof_Context.export names_lthy lthy)
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          |> Thm.close_derivation;
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      in
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        `(conj_dests nn) thm
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      end;
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    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
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    val (fold_thmss, rec_thmss) =
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      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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        val hrecs = map (lists_bmoc hss) recs;
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        fun mk_goal fss frec_like xctr f xs fxs =
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          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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        fun build_rec_like frec_likes (T, U) =
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          if T = U then
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            id_const T
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          else
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            (case find_index (curry (op =) T) fpTs of
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              ~1 => build_map lthy (build_rec_like frec_likes) T U
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            | kk => nth frec_likes kk);
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        val mk_U = typ_subst (map2 pair fpTs Cs);
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        fun unzip_rec_likes frec_likes combine (x as Free (_, T)) =
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          if exists_subtype_in fpTs T then
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            combine (x, build_rec_like frec_likes (T, mk_U T) $ x)
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          else
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            ([x], []);
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        val gxsss = map (map (flat_rec (unzip_rec_likes gfolds (fn (_, t) => ([t], []))))) xsss;
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   302
        val hxsss = map (map (flat_rec (unzip_rec_likes hrecs (pairself single)))) xsss;
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   303
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   304
        val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
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   305
        val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
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   306
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   307
        val fold_tacss =
blanchet@51808
   308
          map2 (map o mk_rec_like_tac pre_map_defs [] nesting_map_ids'' fold_defs) fp_fold_thms
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   309
            ctr_defss;
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   310
        val rec_tacss =
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   311
          map2 (map o mk_rec_like_tac pre_map_defs nested_map_comp's
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   312
            (nested_map_ids'' @ nesting_map_ids'') rec_defs) fp_rec_thms ctr_defss;
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   313
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   314
        fun prove goal tac =
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   315
          Goal.prove_sorry lthy [] [] goal (tac o #context)
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   316
          |> Thm.close_derivation;
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   317
      in
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   318
        (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
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   319
      end;
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   320
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   321
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
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   322
    fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name));
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   323
  in
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   324
    ((induct_thm, [induct_case_names_attr]),
blanchet@51808
   325
     (induct_thms, fn T_name => [induct_case_names_attr, induct_type_attr T_name]),
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   326
     (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
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   327
  end;
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   328
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   329
fun define_datatypes prepare_constraint prepare_typ prepare_term lfp construct_fp
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   330
    (wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
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   331
  let
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   332
    (* TODO: sanity checks on arguments *)
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   333
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   334
    val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
blanchet@49278
   335
      else ();
blanchet@49278
   336
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   337
    fun qualify mandatory fp_b_name =
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   338
      Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
   339
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   340
    val nn = length specs;
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   341
    val fp_bs = map type_binding_of specs;
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   342
    val fp_b_names = map Binding.name_of fp_bs;
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   343
    val fp_common_name = mk_common_name fp_b_names;
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   344
    val map_bs = map map_binding_of specs;
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   345
    val rel_bs = map rel_binding_of specs;
blanchet@49298
   346
blanchet@51758
   347
    fun prepare_type_arg (_, (ty, c)) =
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   348
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
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   349
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   350
      end;
blanchet@49298
   351
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   352
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs;
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   353
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@49298
   354
    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
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   355
    val set_bss = map (map fst o type_args_named_constrained_of) specs;
blanchet@49119
   356
blanchet@49585
   357
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
   358
      no_defs_lthy0
blanchet@49298
   359
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@49585
   360
      |> mk_TFrees (length unsorted_As)
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   361
      ||>> mk_TFrees nn
blanchet@49585
   362
      ||>> apfst (map TFree) o
blanchet@49585
   363
        variant_types (map (prefix "'") fp_b_names) (replicate nn HOLogic.typeS);
blanchet@49119
   364
blanchet@49298
   365
    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
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   366
    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
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   367
      locale and shadows an existing global type*)
blanchet@51768
   368
blanchet@51769
   369
    fun add_fake_type spec =
blanchet@51768
   370
      Sign.add_type no_defs_lthy (type_binding_of spec,
blanchet@51769
   371
        length (type_args_named_constrained_of spec), mixfix_of spec);
blanchet@51768
   372
blanchet@51769
   373
    val fake_thy = Theory.copy #> fold add_fake_type specs;
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   374
    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
blanchet@49119
   375
blanchet@49182
   376
    fun mk_fake_T b =
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   377
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49298
   378
        unsorted_As);
blanchet@49121
   379
blanchet@49302
   380
    val fake_Ts = map mk_fake_T fp_bs;
blanchet@49121
   381
blanchet@49181
   382
    val mixfixes = map mixfix_of specs;
blanchet@49119
   383
blanchet@49302
   384
    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
   385
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
   386
blanchet@49121
   387
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
   388
blanchet@49336
   389
    val disc_bindingss = map (map disc_of) ctr_specss;
blanchet@49336
   390
    val ctr_bindingss =
blanchet@49633
   391
      map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
blanchet@49121
   392
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49181
   393
    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
blanchet@49119
   394
blanchet@49336
   395
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
   396
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49286
   397
    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
blanchet@49286
   398
blanchet@49308
   399
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
   400
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@49298
   401
blanchet@49298
   402
    val _ = (case duplicates (op =) unsorted_As of [] => ()
blanchet@49298
   403
      | A :: _ => error ("Duplicate type parameter " ^
blanchet@49298
   404
          quote (Syntax.string_of_typ no_defs_lthy A)));
blanchet@49298
   405
blanchet@49183
   406
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@49298
   407
    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
blanchet@49165
   408
        [] => ()
blanchet@49342
   409
      | A' :: _ => error ("Extra type variable on right-hand side: " ^
blanchet@49204
   410
          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
blanchet@49165
   411
blanchet@49591
   412
    fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
   413
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
   414
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49591
   415
      | eq_fpT_check _ _ = false;
blanchet@49146
   416
blanchet@49204
   417
    fun freeze_fp (T as Type (s, Us)) =
blanchet@49591
   418
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@49591
   419
          ~1 => Type (s, map freeze_fp Us)
blanchet@49591
   420
        | kk => nth Xs kk)
blanchet@49204
   421
      | freeze_fp T = T;
blanchet@49121
   422
blanchet@49536
   423
    val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@49536
   424
    val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs;
blanchet@49119
   425
blanchet@49298
   426
    val fp_eqs =
blanchet@49536
   427
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsXs;
blanchet@49121
   428
blanchet@51805
   429
    val (pre_bnfs, ({bnfs = fp_bnfs as any_fp_bnf :: _, dtors = dtors0, ctors = ctors0,
blanchet@51805
   430
           folds = fp_folds0, recs = fp_recs0, induct = fp_induct, strong_induct = fp_strong_induct,
blanchet@51805
   431
           dtor_ctors, ctor_dtors, ctor_injects, map_thms = fp_map_thms, set_thmss = fp_set_thmss,
blanchet@51805
   432
           rel_thms = fp_rel_thms, fold_thms = fp_fold_thms, rec_thms = fp_rec_thms}, lthy)) =
blanchet@51767
   433
      fp_bnf construct_fp fp_bs mixfixes map_bs rel_bs set_bss (map dest_TFree unsorted_As) fp_eqs
blanchet@51758
   434
        no_defs_lthy0;
blanchet@49585
   435
blanchet@49585
   436
    val timer = time (Timer.startRealTimer ());
blanchet@49121
   437
blanchet@49363
   438
    fun add_nesty_bnf_names Us =
blanchet@49226
   439
      let
blanchet@49226
   440
        fun add (Type (s, Ts)) ss =
blanchet@49226
   441
            let val (needs, ss') = fold_map add Ts ss in
blanchet@49226
   442
              if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@49226
   443
            end
blanchet@49363
   444
          | add T ss = (member (op =) Us T, ss);
blanchet@49226
   445
      in snd oo add end;
blanchet@49226
   446
blanchet@49363
   447
    fun nesty_bnfs Us =
blanchet@49536
   448
      map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssXs []);
blanchet@49363
   449
blanchet@49363
   450
    val nesting_bnfs = nesty_bnfs As;
blanchet@49536
   451
    val nested_bnfs = nesty_bnfs Xs;
blanchet@49226
   452
blanchet@49585
   453
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
   454
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
   455
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@49683
   456
    val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs;
blanchet@49670
   457
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
blanchet@49670
   458
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
blanchet@49671
   459
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51766
   460
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51766
   461
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@49585
   462
blanchet@49585
   463
    val live = live_of_bnf any_fp_bnf;
blanchet@49585
   464
blanchet@49585
   465
    val Bs =
blanchet@49585
   466
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
   467
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
   468
blanchet@49585
   469
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
   470
blanchet@49501
   471
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
   472
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
   473
blanchet@49501
   474
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
   475
blanchet@51780
   476
    fun massage_simple_notes base =
blanchet@51780
   477
      filter_out (null o #2)
blanchet@51780
   478
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
   479
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
   480
blanchet@51780
   481
    val massage_multi_notes =
blanchet@51780
   482
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
   483
        if forall null thmss then
blanchet@51780
   484
          []
blanchet@51780
   485
        else
blanchet@51780
   486
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@51780
   487
            ((qualify true fp_b_name (Binding.name thmN), attrs T_name),
blanchet@51780
   488
             [(thms, [])])) fp_b_names fpTs thmss);
blanchet@51780
   489
blanchet@49536
   490
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
blanchet@49203
   491
    val ns = map length ctr_Tsss;
blanchet@49212
   492
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
   493
    val mss = map (map length) ctr_Tsss;
blanchet@49203
   494
    val Css = map2 replicate ns Cs;
blanchet@49203
   495
blanchet@49585
   496
    val fp_folds as any_fp_fold :: _ = map (mk_rec_like lfp As Cs) fp_folds0;
blanchet@49585
   497
    val fp_recs as any_fp_rec :: _ = map (mk_rec_like lfp As Cs) fp_recs0;
blanchet@49210
   498
blanchet@49585
   499
    val fp_fold_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_fold)));
blanchet@49585
   500
    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of any_fp_rec)));
blanchet@49204
   501
blanchet@49504
   502
    val (((fold_only as (gss, _, _), rec_only as (hss, _, _)),
blanchet@49683
   503
          (cs, cpss, unfold_only as ((pgss, crssss, cgssss), (_, g_Tsss, _)),
blanchet@49683
   504
           corec_only as ((phss, csssss, chssss), (_, h_Tsss, _)))), names_lthy0) =
blanchet@49208
   505
      if lfp then
blanchet@49208
   506
        let
blanchet@49208
   507
          val y_Tsss =
blanchet@49255
   508
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49504
   509
              ns mss fp_fold_fun_Ts;
blanchet@49208
   510
          val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
blanchet@49208
   511
blanchet@49484
   512
          val ((gss, ysss), lthy) =
blanchet@49208
   513
            lthy
blanchet@49208
   514
            |> mk_Freess "f" g_Tss
blanchet@49208
   515
            ||>> mk_Freesss "x" y_Tsss;
blanchet@49670
   516
blanchet@49670
   517
          fun proj_recT proj (Type (s as @{type_name prod}, Ts as [T, U])) =
blanchet@49670
   518
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_recT proj) Ts)
blanchet@49670
   519
            | proj_recT proj (Type (s, Ts)) = Type (s, map (proj_recT proj) Ts)
blanchet@49670
   520
            | proj_recT _ T = T;
blanchet@49274
   521
blanchet@51794
   522
          fun unzip_recT T =
blanchet@51808
   523
            if exists_subtype_in fpTs T then ([proj_recT fst T], [proj_recT snd T]) else ([T], []);
blanchet@49204
   524
blanchet@49670
   525
          val z_Tsss =
blanchet@49670
   526
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49670
   527
              ns mss fp_rec_fun_Ts;
blanchet@51794
   528
          val z_Tsss' = map (map (flat_rec unzip_recT)) z_Tsss;
blanchet@51794
   529
          val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' Css;
blanchet@49204
   530
blanchet@49298
   531
          val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@49670
   532
          val zsss = map2 (map2 (map2 retype_free)) z_Tsss ysss;
blanchet@49210
   533
        in
blanchet@49670
   534
          ((((gss, g_Tss, ysss), (hss, h_Tss, zsss)),
blanchet@49683
   535
            ([], [], (([], [], []), ([], [], [])), (([], [], []), ([], [], [])))), lthy)
blanchet@49210
   536
        end
blanchet@49208
   537
      else
blanchet@49210
   538
        let
blanchet@49221
   539
          (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@49221
   540
          val mss' =  map (fn [0] => [1] | ms => ms) mss;
blanchet@49221
   541
blanchet@49463
   542
          val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@49275
   543
blanchet@49587
   544
          fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss);
blanchet@49211
   545
blanchet@49587
   546
          fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss
blanchet@49587
   547
            | flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
blanchet@49587
   548
              p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss;
blanchet@49274
   549
blanchet@49681
   550
          fun mk_types maybe_unzipT fun_Ts =
blanchet@49212
   551
            let
blanchet@49212
   552
              val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@49255
   553
              val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@49681
   554
              val f_Tsss = map2 (map2 dest_tupleT) mss' f_prod_Tss;
blanchet@49275
   555
              val f_Tssss =
blanchet@49681
   556
                map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
blanchet@49275
   557
              val q_Tssss =
blanchet@49463
   558
                map (map (map (fn [_] => [] | [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss;
blanchet@49587
   559
              val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@49681
   560
            in (q_Tssss, f_sum_prod_Ts, f_Tsss, f_Tssss, pf_Tss) end;
blanchet@49176
   561
blanchet@49681
   562
          val (r_Tssss, g_sum_prod_Ts, g_Tsss, g_Tssss, pg_Tss) = mk_types single fp_fold_fun_Ts;
blanchet@49211
   563
blanchet@49683
   564
          val (((cs, pss), gssss), lthy) =
blanchet@49210
   565
            lthy
blanchet@49683
   566
            |> mk_Frees "a" Cs
blanchet@49211
   567
            ||>> mk_Freess "p" p_Tss
blanchet@49275
   568
            ||>> mk_Freessss "g" g_Tssss;
blanchet@49275
   569
          val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@49274
   570
blanchet@49681
   571
          fun proj_corecT proj (Type (s as @{type_name sum}, Ts as [T, U])) =
blanchet@49681
   572
              if member (op =) fpTs T then proj (T, U) else Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   573
            | proj_corecT proj (Type (s, Ts)) = Type (s, map (proj_corecT proj) Ts)
blanchet@49681
   574
            | proj_corecT _ T = T;
blanchet@49274
   575
blanchet@49681
   576
          fun unzip_corecT T =
blanchet@51808
   577
            if exists_subtype_in fpTs T then [proj_corecT fst T, proj_corecT snd T] else [T];
blanchet@49681
   578
blanchet@49681
   579
          val (s_Tssss, h_sum_prod_Ts, h_Tsss, h_Tssss, ph_Tss) =
blanchet@49681
   580
            mk_types unzip_corecT fp_rec_fun_Ts;
blanchet@49210
   581
blanchet@49298
   582
          val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@49484
   583
          val ((sssss, hssss_tl), lthy) =
blanchet@49275
   584
            lthy
blanchet@49275
   585
            |> mk_Freessss "q" s_Tssss
blanchet@49275
   586
            ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@49275
   587
          val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@49211
   588
blanchet@49681
   589
          val cpss = map2 (map o rapp) cs pss;
blanchet@49212
   590
blanchet@49683
   591
          fun mk_terms qssss fssss =
blanchet@49212
   592
            let
blanchet@49587
   593
              val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
blanchet@49681
   594
              val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@49681
   595
              val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@49683
   596
            in (pfss, cqssss, cfssss) end;
blanchet@49210
   597
        in
blanchet@49484
   598
          (((([], [], []), ([], [], [])),
blanchet@49683
   599
            (cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, g_Tsss, pg_Tss)),
blanchet@49683
   600
             (mk_terms sssss hssss, (h_sum_prod_Ts, h_Tsss, ph_Tss)))), lthy)
blanchet@49210
   601
        end;
blanchet@49210
   602
blanchet@49585
   603
    fun define_ctrs_case_for_type (((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@49585
   604
            fp_fold), fp_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@49585
   605
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@49585
   606
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   607
      let
blanchet@49498
   608
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
   609
blanchet@49501
   610
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
   611
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   612
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   613
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   614
blanchet@49593
   615
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
   616
          no_defs_lthy
blanchet@49501
   617
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
   618
          ||>> mk_Frees "f" case_Ts
blanchet@49370
   619
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
   620
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
   621
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
   622
blanchet@49498
   623
        val u = Free (u', fpT);
blanchet@49121
   624
blanchet@49585
   625
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
   626
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
   627
blanchet@49129
   628
        val ctr_rhss =
blanchet@49585
   629
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
   630
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
   631
blanchet@49633
   632
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
   633
blanchet@49134
   634
        val case_rhs =
blanchet@49498
   635
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
   636
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
   637
blanchet@49201
   638
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   639
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
   640
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
   641
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   642
          ||> `Local_Theory.restore;
blanchet@49121
   643
blanchet@49121
   644
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   645
blanchet@49121
   646
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
   647
        val ctr_defs' =
blanchet@49585
   648
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
   649
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   650
blanchet@49203
   651
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   652
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   653
blanchet@49203
   654
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   655
blanchet@49585
   656
        fun wrap lthy =
blanchet@49123
   657
          let
traytel@50170
   658
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
   659
              let
blanchet@49585
   660
                val ctor_iff_dtor_thm =
blanchet@49585
   661
                  let
blanchet@49585
   662
                    val goal =
blanchet@49585
   663
                      fold_rev Logic.all [w, u]
blanchet@49585
   664
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
   665
                  in
wenzelm@51551
   666
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
   667
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
   668
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
   669
                    |> Thm.close_derivation
blanchet@49585
   670
                    |> Morphism.thm phi
blanchet@49585
   671
                  end;
blanchet@49585
   672
blanchet@49585
   673
                val sumEN_thm' =
blanchet@49585
   674
                  unfold_thms lthy @{thms all_unit_eq}
blanchet@49585
   675
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
   676
                       (mk_sumEN_balanced n))
blanchet@49585
   677
                  |> Morphism.thm phi;
blanchet@49135
   678
              in
blanchet@49585
   679
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
   680
              end;
blanchet@49135
   681
blanchet@49585
   682
            val inject_tacss =
blanchet@49585
   683
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
   684
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
   685
blanchet@49585
   686
            val half_distinct_tacss =
blanchet@49585
   687
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
   688
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
   689
blanchet@49585
   690
            val case_tacs =
blanchet@49585
   691
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
   692
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
   693
blanchet@49585
   694
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
   695
blanchet@49585
   696
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
   697
          in
blanchet@51781
   698
            wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
blanchet@51781
   699
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
   700
          end;
blanchet@49121
   701
blanchet@49585
   702
        fun derive_maps_sets_rels (wrap_res, lthy) =
blanchet@49585
   703
          let
blanchet@49585
   704
            val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@49585
   705
            val nones = replicate live NONE;
blanchet@49585
   706
blanchet@49585
   707
            val ctor_cong =
blanchet@51746
   708
              if lfp then
blanchet@51746
   709
                Drule.dummy_thm
blanchet@51746
   710
              else
blanchet@51746
   711
                let val ctor' = mk_ctor Bs ctor in
blanchet@51746
   712
                  cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51746
   713
                end;
blanchet@49585
   714
blanchet@49585
   715
            fun mk_cIn ify =
blanchet@49585
   716
              certify lthy o (not lfp ? curry (op $) (map_types ify ctor)) oo
blanchet@49585
   717
              mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
   718
blanchet@49585
   719
            val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@49585
   720
            val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
   721
blanchet@49682
   722
            fun mk_map_thm ctr_def' cxIn =
blanchet@49585
   723
              fold_thms lthy [ctr_def']
blanchet@49585
   724
                (unfold_thms lthy (pre_map_def ::
blanchet@49585
   725
                     (if lfp then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@49585
   726
                   (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@49585
   727
                      (if lfp then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@49593
   728
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   729
blanchet@49682
   730
            fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@49585
   731
              fold_thms lthy [ctr_def']
blanchet@51766
   732
                (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@49585
   733
                     (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@49585
   734
                   (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@49593
   735
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   736
blanchet@49682
   737
            fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49585
   738
blanchet@49682
   739
            val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@49585
   740
            val set_thmss = map mk_set_thms fp_set_thms;
blanchet@49127
   741
blanchet@49682
   742
            val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
   743
blanchet@49682
   744
            fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@49585
   745
              fold_thms lthy ctr_defs'
blanchet@51745
   746
                 (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@51745
   747
                      (if lfp then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@49585
   748
                    (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@49593
   749
              |> postproc
blanchet@49593
   750
              |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
   751
blanchet@49682
   752
            fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@49682
   753
              mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
   754
blanchet@49592
   755
            val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
   756
blanchet@49682
   757
            fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@49585
   758
              mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@49682
   759
                cxIn cyIn;
blanchet@49121
   760
blanchet@49592
   761
            fun mk_other_half_rel_distinct_thm thm =
blanchet@49585
   762
              flip_rels lthy live thm RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
   763
blanchet@49592
   764
            val half_rel_distinct_thmss =
blanchet@49592
   765
              map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@49592
   766
            val other_half_rel_distinct_thmss =
blanchet@49592
   767
              map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@49592
   768
            val (rel_distinct_thms, _) =
blanchet@49592
   769
              join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
   770
blanchet@49585
   771
            val notes =
blanchet@49594
   772
              [(mapN, map_thms, code_simp_attrs),
blanchet@49592
   773
               (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@49592
   774
               (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@49585
   775
               (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51780
   776
              |> massage_simple_notes fp_b_name;
blanchet@49585
   777
          in
blanchet@49585
   778
            (wrap_res, lthy |> Local_Theory.notes notes |> snd)
blanchet@49585
   779
          end;
blanchet@49585
   780
blanchet@49585
   781
        fun define_fold_rec no_defs_lthy =
blanchet@49134
   782
          let
blanchet@49208
   783
            val fpT_to_C = fpT --> C;
blanchet@49199
   784
blanchet@49681
   785
            fun build_prod_proj mk_proj (T, U) =
blanchet@49670
   786
              if T = U then
blanchet@49670
   787
                id_const T
blanchet@49670
   788
              else
blanchet@49670
   789
                (case (T, U) of
blanchet@49670
   790
                  (Type (s, _), Type (s', _)) =>
blanchet@51808
   791
                  if s = s' then build_map lthy (build_prod_proj mk_proj) T U else mk_proj T
blanchet@49670
   792
                | _ => mk_proj T);
blanchet@49670
   793
blanchet@49681
   794
            (* TODO: Avoid these complications; cf. corec case *)
blanchet@49672
   795
            fun mk_U proj (Type (s as @{type_name prod}, Ts as [T', U])) =
blanchet@49672
   796
                if member (op =) fpTs T' then proj (T', U) else Type (s, map (mk_U proj) Ts)
blanchet@49670
   797
              | mk_U proj (Type (s, Ts)) = Type (s, map (mk_U proj) Ts)
blanchet@49670
   798
              | mk_U _ T = T;
blanchet@49670
   799
blanchet@51794
   800
            fun unzip_rec (x as Free (_, T)) =
blanchet@51808
   801
              if exists_subtype_in fpTs T then
blanchet@51794
   802
                ([build_prod_proj fst_const (T, mk_U fst T) $ x],
blanchet@51794
   803
                 [build_prod_proj snd_const (T, mk_U snd T) $ x])
blanchet@49670
   804
              else
blanchet@51794
   805
                ([x], []);
blanchet@49670
   806
blanchet@51793
   807
            fun mk_rec_like_arg f xs =
blanchet@51794
   808
              mk_tupled_fun (HOLogic.mk_tuple xs) f (flat_rec unzip_rec xs);
blanchet@49670
   809
blanchet@49670
   810
            fun generate_rec_like (suf, fp_rec_like, (fss, f_Tss, xsss)) =
blanchet@49215
   811
              let
blanchet@49215
   812
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49633
   813
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49215
   814
                val spec =
blanchet@49336
   815
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   816
                    Term.list_comb (fp_rec_like,
blanchet@49670
   817
                      map2 (mk_sum_caseN_balanced oo map2 mk_rec_like_arg) fss xsss));
blanchet@49336
   818
              in (binding, spec) end;
blanchet@49199
   819
blanchet@49504
   820
            val rec_like_infos =
blanchet@49504
   821
              [(foldN, fp_fold, fold_only),
blanchet@49215
   822
               (recN, fp_rec, rec_only)];
blanchet@49215
   823
blanchet@49504
   824
            val (bindings, specs) = map generate_rec_like rec_like_infos |> split_list;
blanchet@49215
   825
blanchet@49215
   826
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   827
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   828
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   829
                #>> apsnd snd) bindings specs
blanchet@49199
   830
              ||> `Local_Theory.restore;
blanchet@49201
   831
blanchet@49201
   832
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   833
blanchet@49504
   834
            val [fold_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   835
blanchet@49536
   836
            val [foldx, recx] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49134
   837
          in
blanchet@49693
   838
            ((foldx, recx, fold_def, rec_def), lthy')
blanchet@49134
   839
          end;
blanchet@49134
   840
blanchet@49585
   841
        fun define_unfold_corec no_defs_lthy =
blanchet@49210
   842
          let
blanchet@49210
   843
            val B_to_fpT = C --> fpT;
blanchet@49211
   844
blanchet@49683
   845
            fun build_sum_inj mk_inj (T, U) =
blanchet@49683
   846
              if T = U then
blanchet@49683
   847
                id_const T
blanchet@49683
   848
              else
blanchet@49683
   849
                (case (T, U) of
blanchet@49683
   850
                  (Type (s, _), Type (s', _)) =>
blanchet@51808
   851
                  if s = s' then build_map lthy (build_sum_inj mk_inj) T U
blanchet@49683
   852
                  else uncurry mk_inj (dest_sumT U)
blanchet@49683
   853
                | _ => uncurry mk_inj (dest_sumT U));
blanchet@49683
   854
blanchet@49683
   855
            fun build_dtor_corec_like_arg _ [] [cf] = cf
blanchet@49683
   856
              | build_dtor_corec_like_arg T [cq] [cf, cf'] =
blanchet@49683
   857
                mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@49683
   858
                  (build_sum_inj Inr_const (fastype_of cf', T) $ cf')
blanchet@49683
   859
blanchet@49683
   860
            val crgsss = map3 (map3 (map3 build_dtor_corec_like_arg)) g_Tsss crssss cgssss;
blanchet@49683
   861
            val cshsss = map3 (map3 (map3 build_dtor_corec_like_arg)) h_Tsss csssss chssss;
blanchet@49683
   862
blanchet@49276
   863
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
   864
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
   865
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
   866
blanchet@49683
   867
            fun generate_corec_like (suf, fp_rec_like, (cqfsss, ((pfss, _, _), (f_sum_prod_Ts, _,
blanchet@49683
   868
                pf_Tss)))) =
blanchet@49211
   869
              let
blanchet@49211
   870
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49633
   871
                val binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49211
   872
                val spec =
blanchet@49336
   873
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@49504
   874
                    Term.list_comb (fp_rec_like,
blanchet@49276
   875
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49336
   876
              in (binding, spec) end;
blanchet@49210
   877
blanchet@49504
   878
            val corec_like_infos =
blanchet@49683
   879
              [(unfoldN, fp_fold, (crgsss, unfold_only)),
blanchet@49683
   880
               (corecN, fp_rec, (cshsss, corec_only))];
blanchet@49212
   881
blanchet@49504
   882
            val (bindings, specs) = map generate_corec_like corec_like_infos |> split_list;
blanchet@49211
   883
blanchet@49211
   884
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   885
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   886
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   887
                #>> apsnd snd) bindings specs
blanchet@49210
   888
              ||> `Local_Theory.restore;
blanchet@49210
   889
blanchet@49210
   890
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   891
blanchet@49504
   892
            val [unfold_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   893
blanchet@49536
   894
            val [unfold, corec] = map (mk_rec_like lfp As Cs o Morphism.term phi) csts;
blanchet@49210
   895
          in
blanchet@49693
   896
            ((unfold, corec, unfold_def, corec_def), lthy')
blanchet@49287
   897
          end;
blanchet@49287
   898
blanchet@49504
   899
        val define_rec_likes = if lfp then define_fold_rec else define_unfold_corec;
blanchet@49585
   900
blanchet@49585
   901
        fun massage_res ((wrap_res, rec_like_res), lthy) =
blanchet@49585
   902
          (((ctrs, xss, ctr_defs, wrap_res), rec_like_res), lthy);
blanchet@49119
   903
      in
blanchet@49585
   904
        (wrap #> (live > 0 ? derive_maps_sets_rels) ##>> define_rec_likes #> massage_res, lthy')
blanchet@49119
   905
      end;
blanchet@49167
   906
blanchet@49585
   907
    fun wrap_types_and_more (wrap_types_and_mores, lthy) =
blanchet@49585
   908
      fold_map I wrap_types_and_mores lthy
blanchet@49585
   909
      |>> apsnd split_list4 o apfst split_list4 o split_list;
blanchet@49226
   910
blanchet@49585
   911
    (* TODO: Add map, sets, rel simps *)
blanchet@49479
   912
    val mk_simp_thmss =
blanchet@49591
   913
      map3 (fn (_, _, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn fold_likes =>
blanchet@49505
   914
        injects @ distincts @ cases @ rec_likes @ fold_likes);
blanchet@49479
   915
blanchet@51808
   916
    fun derive_and_note_induct_fold_rec_thms_for_types (info as ((_, _, _, wrap_ress), _), lthy) =
blanchet@49202
   917
      let
blanchet@51808
   918
        val ((induct_thm, induct_attrs), (induct_thms, inducts_attrs), (fold_thmss, fold_attrs),
blanchet@51808
   919
             (rec_thmss, rec_attrs)) =
blanchet@51808
   920
          derive_induct_fold_rec_thms_for_types nn fp_b_names pre_bnfs fp_induct fp_fold_thms
blanchet@51808
   921
            fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs ctr_Tsss mss ns gss hss info lthy;
blanchet@49201
   922
blanchet@49504
   923
        val simp_thmss = mk_simp_thmss wrap_ress rec_thmss fold_thmss;
blanchet@49438
   924
blanchet@49337
   925
        val common_notes =
blanchet@51808
   926
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
   927
          |> massage_simple_notes fp_common_name;
blanchet@49337
   928
blanchet@49226
   929
        val notes =
blanchet@51808
   930
          [(foldN, fold_thmss, K fold_attrs),
blanchet@51808
   931
           (inductN, map single induct_thms, inducts_attrs),
blanchet@51808
   932
           (recN, rec_thmss, K rec_attrs),
blanchet@49585
   933
           (simpsN, simp_thmss, K [])]
blanchet@51780
   934
          |> massage_multi_notes;
blanchet@49202
   935
      in
blanchet@49337
   936
        lthy |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@49202
   937
      end;
blanchet@49202
   938
blanchet@51808
   939
    fun derive_and_note_coinduct_unfold_corec_thms_for_types (((ctrss, _, ctr_defss, wrap_ress),
blanchet@51808
   940
        (unfolds, corecs, unfold_defs, corec_defs)), lthy) =
blanchet@49212
   941
      let
blanchet@49591
   942
        val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@49591
   943
blanchet@49484
   944
        val discss = map (map (mk_disc_or_sel As) o #1) wrap_ress;
blanchet@49591
   945
        val selsss = map (map (map (mk_disc_or_sel As)) o #2) wrap_ress;
blanchet@49591
   946
        val exhaust_thms = map #3 wrap_ress;
blanchet@49591
   947
        val disc_thmsss = map #7 wrap_ress;
blanchet@49591
   948
        val discIss = map #8 wrap_ress;
blanchet@49591
   949
        val sel_thmsss = map #9 wrap_ress;
blanchet@49438
   950
blanchet@49591
   951
        val (((rs, us'), vs'), names_lthy) =
blanchet@49370
   952
          lthy
blanchet@49591
   953
          |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@49591
   954
          ||>> Variable.variant_fixes fp_b_names
blanchet@49591
   955
          ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@49370
   956
blanchet@49498
   957
        val us = map2 (curry Free) us' fpTs;
blanchet@49591
   958
        val udiscss = map2 (map o rapp) us discss;
blanchet@49591
   959
        val uselsss = map2 (map o map o rapp) us selsss;
blanchet@49370
   960
blanchet@49591
   961
        val vs = map2 (curry Free) vs' fpTs;
blanchet@49591
   962
        val vdiscss = map2 (map o rapp) vs discss;
blanchet@49591
   963
        val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@49591
   964
blanchet@49591
   965
        val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
blanchet@49337
   966
          let
blanchet@49591
   967
            val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@49591
   968
            val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@49591
   969
            val strong_rs =
blanchet@49591
   970
              map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@49591
   971
                fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@49591
   972
blanchet@49591
   973
            fun build_rel rs' T =
blanchet@49591
   974
              (case find_index (curry (op =) T) fpTs of
blanchet@49591
   975
                ~1 =>
blanchet@51808
   976
                if exists_subtype_in fpTs T then build_rel_step lthy (build_rel rs') T
blanchet@51808
   977
                else HOLogic.eq_const T
blanchet@49591
   978
              | kk => nth rs' kk);
blanchet@49591
   979
blanchet@49591
   980
            fun build_rel_app rs' usel vsel =
blanchet@49591
   981
              fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@49591
   982
blanchet@49591
   983
            fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@49591
   984
              (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@49591
   985
              (if null usels then
blanchet@49591
   986
                 []
blanchet@49591
   987
               else
blanchet@49591
   988
                 [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@49591
   989
                    Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@49591
   990
blanchet@49591
   991
            fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@49591
   992
              Library.foldr1 HOLogic.mk_conj
blanchet@49591
   993
                (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@49591
   994
              handle List.Empty => @{term True};
blanchet@49591
   995
blanchet@49591
   996
            fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@49591
   997
              fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@49591
   998
                HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@49591
   999
blanchet@49591
  1000
            val concl =
blanchet@49591
  1001
              HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49591
  1002
                (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@49591
  1003
                   uvrs us vs));
blanchet@49591
  1004
blanchet@49591
  1005
            fun mk_goal rs' =
blanchet@49591
  1006
              Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@49591
  1007
                concl);
blanchet@49591
  1008
blanchet@49591
  1009
            val goal = mk_goal rs;
blanchet@49591
  1010
            val strong_goal = mk_goal strong_rs;
blanchet@49591
  1011
blanchet@49591
  1012
            fun prove dtor_coinduct' goal =
wenzelm@51551
  1013
              Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49591
  1014
                mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@49591
  1015
                  exhaust_thms ctr_defss disc_thmsss sel_thmsss)
blanchet@49591
  1016
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49591
  1017
              |> Thm.close_derivation;
blanchet@49591
  1018
blanchet@49590
  1019
            fun postproc nn thm =
blanchet@49590
  1020
              Thm.permute_prems 0 nn
blanchet@49591
  1021
                (if nn = 1 then thm RS mp
blanchet@49591
  1022
                 else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@49591
  1023
              |> Drule.zero_var_indexes
blanchet@49591
  1024
              |> `(conj_dests nn);
blanchet@49337
  1025
          in
blanchet@49591
  1026
            (postproc nn (prove fp_induct goal), postproc nn (prove fp_strong_induct strong_goal))
blanchet@49337
  1027
          end;
blanchet@49212
  1028
blanchet@51777
  1029
        fun mk_coinduct_concls ms discs ctrs =
blanchet@51777
  1030
          let
blanchet@51777
  1031
            fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51777
  1032
            fun mk_ctr_concl 0 _ = []
blanchet@51777
  1033
              | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51777
  1034
            val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51777
  1035
            val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51777
  1036
          in
blanchet@51777
  1037
            flat (map2 append disc_concls ctr_concls)
blanchet@51777
  1038
          end;
blanchet@51777
  1039
blanchet@51777
  1040
        val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51777
  1041
        val coinduct_conclss =
blanchet@51777
  1042
          map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51777
  1043
blanchet@49484
  1044
        fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@49484
  1045
blanchet@49504
  1046
        val gunfolds = map (lists_bmoc pgss) unfolds;
blanchet@49484
  1047
        val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49484
  1048
blanchet@49504
  1049
        val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@49212
  1050
          let
blanchet@49504
  1051
            fun mk_goal pfss c cps fcorec_like n k ctr m cfs' =
blanchet@49212
  1052
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49484
  1053
                (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@49504
  1054
                   mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
  1055
blanchet@49683
  1056
            fun build_corec_like fcorec_likes (T, U) =
blanchet@49234
  1057
              if T = U then
blanchet@49368
  1058
                id_const T
blanchet@49234
  1059
              else
blanchet@49234
  1060
                (case find_index (curry (op =) U) fpTs of
blanchet@51808
  1061
                  ~1 => build_map lthy (build_corec_like fcorec_likes) T U
blanchet@49683
  1062
                | kk => nth fcorec_likes kk);
blanchet@49683
  1063
blanchet@49683
  1064
            val mk_U = typ_subst (map2 pair Cs fpTs);
blanchet@49233
  1065
blanchet@49683
  1066
            fun intr_corec_likes fcorec_likes [] [cf] =
blanchet@49683
  1067
                let val T = fastype_of cf in
blanchet@51808
  1068
                  if exists_subtype_in Cs T then build_corec_like fcorec_likes (T, mk_U T) $ cf
blanchet@51808
  1069
                  else cf
blanchet@49683
  1070
                end
blanchet@49683
  1071
              | intr_corec_likes fcorec_likes [cq] [cf, cf'] =
blanchet@49683
  1072
                mk_If cq (intr_corec_likes fcorec_likes [] [cf])
blanchet@49683
  1073
                  (intr_corec_likes fcorec_likes [] [cf']);
blanchet@49683
  1074
blanchet@49683
  1075
            val crgsss = map2 (map2 (map2 (intr_corec_likes gunfolds))) crssss cgssss;
blanchet@49683
  1076
            val cshsss = map2 (map2 (map2 (intr_corec_likes hcorecs))) csssss chssss;
blanchet@49212
  1077
blanchet@49683
  1078
            val unfold_goalss =
blanchet@49683
  1079
              map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
blanchet@49683
  1080
            val corec_goalss =
blanchet@49683
  1081
              map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
blanchet@49683
  1082
blanchet@49683
  1083
            fun mk_map_if_distrib bnf =
blanchet@49683
  1084
              let
blanchet@49683
  1085
                val mapx = map_of_bnf bnf;
blanchet@49683
  1086
                val live = live_of_bnf bnf;
blanchet@49683
  1087
                val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
blanchet@49683
  1088
                val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
blanchet@49683
  1089
                val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
blanchet@49683
  1090
              in
blanchet@49683
  1091
                Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
blanchet@49683
  1092
                  @{thm if_distrib}
blanchet@49276
  1093
              end;
blanchet@49232
  1094
blanchet@49683
  1095
            val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
blanchet@49213
  1096
blanchet@49504
  1097
            val unfold_tacss =
blanchet@49683
  1098
              map3 (map oo mk_corec_like_tac unfold_defs [] [] nesting_map_ids'' [])
blanchet@49683
  1099
                fp_fold_thms pre_map_defs ctr_defss;
blanchet@49233
  1100
            val corec_tacss =
blanchet@49683
  1101
              map3 (map oo mk_corec_like_tac corec_defs nested_map_comps'' nested_map_comp's
blanchet@49683
  1102
                  (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
blanchet@49683
  1103
                fp_rec_thms pre_map_defs ctr_defss;
blanchet@49479
  1104
blanchet@49484
  1105
            fun prove goal tac =
wenzelm@51551
  1106
              Goal.prove_sorry lthy [] [] goal (tac o #context) |> Thm.close_derivation;
blanchet@49484
  1107
blanchet@49504
  1108
            val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@49683
  1109
            val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
blanchet@49479
  1110
blanchet@49479
  1111
            val filter_safesss =
blanchet@49479
  1112
              map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@49683
  1113
                curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
blanchet@49479
  1114
blanchet@49683
  1115
            val safe_unfold_thmss = filter_safesss unfold_thmss;
blanchet@49683
  1116
            val safe_corec_thmss = filter_safesss corec_thmss;
blanchet@49479
  1117
          in
blanchet@49504
  1118
            (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@49212
  1119
          end;
blanchet@49212
  1120
blanchet@49504
  1121
        val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@49482
  1122
          let
blanchet@49504
  1123
            fun mk_goal c cps fcorec_like n k disc =
blanchet@49504
  1124
              mk_Trueprop_eq (disc $ (fcorec_like $ c),
blanchet@49484
  1125
                if n = 1 then @{const True}
blanchet@49484
  1126
                else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@49484
  1127
blanchet@49504
  1128
            val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@49484
  1129
            val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@49484
  1130
blanchet@49484
  1131
            fun mk_case_split' cp =
blanchet@49484
  1132
              Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@49484
  1133
blanchet@49484
  1134
            val case_splitss' = map (map mk_case_split') cpss;
blanchet@49482
  1135
blanchet@49504
  1136
            val unfold_tacss =
blanchet@49504
  1137
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@49484
  1138
            val corec_tacss =
blanchet@49504
  1139
              map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@49484
  1140
blanchet@49484
  1141
            fun prove goal tac =
wenzelm@51551
  1142
              Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@49591
  1143
              |> singleton (Proof_Context.export names_lthy0 no_defs_lthy)
blanchet@49591
  1144
              |> Thm.close_derivation;
blanchet@49484
  1145
blanchet@49484
  1146
            fun proves [_] [_] = []
blanchet@49484
  1147
              | proves goals tacs = map2 prove goals tacs;
blanchet@49482
  1148
          in
blanchet@49504
  1149
            (map2 proves unfold_goalss unfold_tacss,
blanchet@49484
  1150
             map2 proves corec_goalss corec_tacss)
blanchet@49482
  1151
          end;
blanchet@49482
  1152
blanchet@49605
  1153
        val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@49605
  1154
blanchet@49504
  1155
        fun mk_disc_corec_like_thms corec_likes discIs =
blanchet@49605
  1156
          map (op RS) (filter_out (is_triv_discI o snd) (corec_likes ~~ discIs));
blanchet@49266
  1157
blanchet@49504
  1158
        val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss;
blanchet@49504
  1159
        val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss;
blanchet@49266
  1160
blanchet@49504
  1161
        fun mk_sel_corec_like_thm corec_like_thm sel sel_thm =
blanchet@49266
  1162
          let
blanchet@49479
  1163
            val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@49266
  1164
            val arg_cong' =
blanchet@49266
  1165
              Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@49479
  1166
                [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@49267
  1167
              |> Thm.varifyT_global;
blanchet@49266
  1168
            val sel_thm' = sel_thm RSN (2, trans);
blanchet@49266
  1169
          in
blanchet@49504
  1170
            corec_like_thm RS arg_cong' RS sel_thm'
blanchet@49266
  1171
          end;
blanchet@49266
  1172
blanchet@49504
  1173
        fun mk_sel_corec_like_thms corec_likess =
blanchet@49504
  1174
          map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss |> map flat;
blanchet@49479
  1175
blanchet@49504
  1176
        val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss;
blanchet@49504
  1177
        val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss;
blanchet@49479
  1178
blanchet@49587
  1179
        fun flat_corec_like_thms corec_likes disc_corec_likes sel_corec_likes =
blanchet@49504
  1180
          corec_likes @ disc_corec_likes @ sel_corec_likes;
blanchet@49479
  1181
blanchet@49479
  1182
        val simp_thmss =
blanchet@49479
  1183
          mk_simp_thmss wrap_ress
blanchet@49587
  1184
            (map3 flat_corec_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@49587
  1185
            (map3 flat_corec_like_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss);
blanchet@49479
  1186
blanchet@49479
  1187
        val anonymous_notes =
blanchet@49504
  1188
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1189
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1190
blanchet@51777
  1191
        val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51777
  1192
        val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51777
  1193
        val coinduct_case_concl_attrs =
blanchet@51777
  1194
          map2 (fn casex => fn concls =>
blanchet@51777
  1195
              Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51777
  1196
            coinduct_cases coinduct_conclss;
blanchet@51777
  1197
        val coinduct_case_attrs =
blanchet@51777
  1198
          coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51780
  1199
        fun coinduct_type_attr T_name = Attrib.internal (K (Induct.coinduct_type T_name));
blanchet@51777
  1200
blanchet@49342
  1201
        val common_notes =
blanchet@49591
  1202
          (if nn > 1 then
blanchet@51777
  1203
             [(coinductN, [coinduct_thm], coinduct_case_attrs),
blanchet@51777
  1204
              (strong_coinductN, [strong_coinduct_thm], coinduct_case_attrs)]
blanchet@49591
  1205
           else
blanchet@49591
  1206
             [])
blanchet@51780
  1207
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1208
blanchet@49212
  1209
        val notes =
blanchet@51780
  1210
          [(coinductN, map single coinduct_thms,
blanchet@51780
  1211
            fn T_name => coinduct_case_attrs @ [coinduct_type_attr T_name]),
blanchet@51780
  1212
           (corecN, corec_thmss, K []),
blanchet@51780
  1213
           (disc_corecN, disc_corec_thmss, K simp_attrs),
blanchet@51780
  1214
           (disc_corec_iffN, disc_corec_iff_thmss, K simp_attrs),
blanchet@51780
  1215
           (disc_unfoldN, disc_unfold_thmss, K simp_attrs),
blanchet@51780
  1216
           (disc_unfold_iffN, disc_unfold_iff_thmss, K simp_attrs),
blanchet@51780
  1217
           (sel_corecN, sel_corec_thmss, K simp_attrs),
blanchet@51780
  1218
           (sel_unfoldN, sel_unfold_thmss, K simp_attrs),
blanchet@51780
  1219
           (simpsN, simp_thmss, K []),
blanchet@51780
  1220
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_case_attrs),
blanchet@51780
  1221
           (unfoldN, unfold_thmss, K [])]
blanchet@51780
  1222
          |> massage_multi_notes;
blanchet@49212
  1223
      in
blanchet@49479
  1224
        lthy |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@49212
  1225
      end;
blanchet@49212
  1226
blanchet@49204
  1227
    val lthy' = lthy
blanchet@49585
  1228
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@49585
  1229
        fp_folds ~~ fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@49585
  1230
        pre_set_defss ~~ pre_rel_defs ~~ fp_map_thms ~~ fp_set_thmss ~~ fp_rel_thms ~~ ns ~~ kss ~~
blanchet@49585
  1231
        mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
blanchet@49585
  1232
        raw_sel_defaultsss)
blanchet@49585
  1233
      |> wrap_types_and_more
blanchet@51808
  1234
      |> (if lfp then derive_and_note_induct_fold_rec_thms_for_types
blanchet@51808
  1235
          else derive_and_note_coinduct_unfold_corec_thms_for_types);
blanchet@49167
  1236
blanchet@49167
  1237
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
  1238
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
  1239
  in
blanchet@49308
  1240
    timer; lthy'
blanchet@49112
  1241
  end;
blanchet@49112
  1242
blanchet@49536
  1243
val datatypes = define_datatypes (K I) (K I) (K I);
blanchet@49297
  1244
blanchet@51380
  1245
val datatype_cmd = define_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1246
blanchet@49112
  1247
val parse_ctr_arg =
blanchet@49329
  1248
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1249
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1250
blanchet@49286
  1251
val parse_defaults =
blanchet@49286
  1252
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1253
blanchet@51758
  1254
val parse_type_arg_constrained =
blanchet@51790
  1255
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1256
blanchet@51790
  1257
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1258
blanchet@51758
  1259
val parse_type_args_named_constrained =
blanchet@51758
  1260
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1261
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1262
  Scan.succeed [];
blanchet@51756
  1263
blanchet@51790
  1264
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1265
blanchet@51767
  1266
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1267
blanchet@51767
  1268
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51767
  1269
   that we don't want them to be highlighted everywhere because of some obscure feature of the BNF
blanchet@51767
  1270
   package. *)
blanchet@51767
  1271
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1272
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1273
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1274
blanchet@51767
  1275
val parse_map_rel_bindings =
blanchet@51767
  1276
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1277
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1278
  Scan.succeed no_map_rel;
blanchet@51767
  1279
blanchet@51767
  1280
val parse_ctr_spec =
blanchet@51790
  1281
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1282
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1283
blanchet@51767
  1284
val parse_spec =
blanchet@51790
  1285
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1286
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1287
blanchet@51767
  1288
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1289
blanchet@49585
  1290
fun parse_datatype_cmd lfp construct_fp = parse_datatype >> datatype_cmd lfp construct_fp;
blanchet@49112
  1291
blanchet@49112
  1292
end;