src/HOL/Codatatype/Tools/bnf_wrap.ML
author blanchet
Mon Sep 10 21:44:43 2012 +0200 (2012-09-10)
changeset 49266 70ffce5b65a4
parent 49265 059aa3088ae3
child 49277 aee77001243f
permissions -rw-r--r--
generate "sel_coiters" and friends
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(*  Title:      HOL/Codatatype/Tools/bnf_wrap.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Wrapping existing datatypes.
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*)
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signature BNF_WRAP =
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sig
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  val no_binder: binding
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  val mk_half_pairss: 'a list -> ('a * 'a) list list
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  val mk_ctr: typ list -> term -> term
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  val wrap_datatype: ({prems: thm list, context: Proof.context} -> tactic) list list ->
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    (term list * term) * (binding list * binding list list) -> local_theory ->
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    (term list list * thm list * thm list list) * local_theory
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end;
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structure BNF_Wrap : BNF_WRAP =
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struct
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open BNF_Util
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open BNF_Wrap_Tactics
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val isN = "is_";
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val unN = "un_";
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fun mk_unN 1 1 suf = unN ^ suf
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  | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
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val case_congN = "case_cong";
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val case_eqN = "case_eq";
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val casesN = "cases";
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val collapseN = "collapse";
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val disc_excludeN = "disc_exclude";
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val disc_exhaustN = "disc_exhaust";
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val discsN = "discs";
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val distinctN = "distinct";
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val exhaustN = "exhaust";
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val injectN = "inject";
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val nchotomyN = "nchotomy";
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val selsN = "sels";
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val splitN = "split";
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val split_asmN = "split_asm";
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val weak_case_cong_thmsN = "weak_case_cong";
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val no_binder = @{binding ""};
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val fallback_binder = @{binding _};
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fun pad_list x n xs = xs @ replicate (n - length xs) x;
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fun unflat_lookup eq ys zs = map (map (fn x => nth zs (find_index (curry eq x) ys)));
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fun mk_half_pairss' _ [] = []
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  | mk_half_pairss' indent (y :: ys) =
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    indent @ fold_rev (cons o single o pair y) ys (mk_half_pairss' ([] :: indent) ys);
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fun mk_half_pairss ys = mk_half_pairss' [[]] ys;
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(* TODO: provide a way to have a different default value, e.g. "tl Nil = Nil" *)
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fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T);
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fun mk_ctr Ts ctr =
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  let val Type (_, Ts0) = body_type (fastype_of ctr) in
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    Term.subst_atomic_types (Ts0 ~~ Ts) ctr
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  end;
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fun eta_expand_case_arg xs f_xs = fold_rev Term.lambda xs f_xs;
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fun name_of_ctr c =
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  case head_of c of
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    Const (s, _) => s
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  | Free (s, _) => s
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  | _ => error "Cannot extract name of constructor";
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fun prepare_wrap_datatype prep_term ((raw_ctrs, raw_case), (raw_disc_binders, raw_sel_binderss))
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  no_defs_lthy =
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  let
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    (* TODO: sanity checks on arguments *)
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    (* TODO: attributes (simp, case_names, etc.) *)
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    (* TODO: case syntax *)
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    (* TODO: integration with function package ("size") *)
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    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
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    val case0 = prep_term no_defs_lthy raw_case;
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    val n = length ctrs0;
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    val ks = 1 upto n;
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    val _ = if n > 0 then () else error "No constructors specified";
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    val Type (fpT_name, As0) = body_type (fastype_of (hd ctrs0));
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    val b = Binding.qualified_name fpT_name;
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    val (As, B) =
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      no_defs_lthy
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      |> mk_TFrees (length As0)
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      ||> the_single o fst o mk_TFrees 1;
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    val fpT = Type (fpT_name, As);
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    val ctrs = map (mk_ctr As) ctrs0;
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    val ctr_Tss = map (binder_types o fastype_of) ctrs;
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    val ms = map length ctr_Tss;
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    val raw_disc_binders' = pad_list no_binder n raw_disc_binders;
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    fun can_really_rely_on_disc k =
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      not (Binding.eq_name (nth raw_disc_binders' (k - 1), no_binder)) orelse nth ms (k - 1) = 0;
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    fun can_rely_on_disc k =
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      can_really_rely_on_disc k orelse (k = 1 andalso not (can_really_rely_on_disc 2));
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    fun can_omit_disc_binder k m =
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      n = 1 orelse m = 0 orelse (n = 2 andalso can_rely_on_disc (3 - k));
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    val fallback_disc_binder = Binding.name o prefix isN o Long_Name.base_name o name_of_ctr;
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    val disc_binders =
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      raw_disc_binders'
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      |> map4 (fn k => fn m => fn ctr => fn disc =>
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        if Binding.eq_name (disc, no_binder) then
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          if can_omit_disc_binder k m then NONE else SOME (fallback_disc_binder ctr)
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        else if Binding.eq_name (disc, fallback_binder) then
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          SOME (fallback_disc_binder ctr)
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        else
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          SOME disc) ks ms ctrs0;
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    val no_discs = map is_none disc_binders;
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    val no_discs_at_all = forall I no_discs;
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    fun fallback_sel_binder m l = Binding.name o mk_unN m l o Long_Name.base_name o name_of_ctr;
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    val sel_binderss =
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      pad_list [] n raw_sel_binderss
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      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
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        if Binding.eq_name (sel, no_binder) orelse Binding.eq_name (sel, fallback_binder) then
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          fallback_sel_binder m l ctr
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        else
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          sel) (1 upto m) o pad_list no_binder m) ctrs0 ms;
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    fun mk_case Ts T =
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      let
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        val (binders, body) = strip_type (fastype_of case0)
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        val Type (_, Ts0) = List.last binders
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      in Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) case0 end;
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    val casex = mk_case As B;
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    val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
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    val (((((((xss, yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |>
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      mk_Freess "x" ctr_Tss
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      ||>> mk_Freess "y" ctr_Tss
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      ||>> mk_Frees "f" case_Ts
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      ||>> mk_Frees "g" case_Ts
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      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") fpT
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      ||>> yield_singleton (mk_Frees "w") fpT
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      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
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    val q = Free (fst p', B --> HOLogic.boolT);
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    fun ap_v t = t $ v;
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    fun mk_v_eq_v () = HOLogic.mk_eq (v, v);
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    val xctrs = map2 (curry Term.list_comb) ctrs xss;
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    val yctrs = map2 (curry Term.list_comb) ctrs yss;
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    val xfs = map2 (curry Term.list_comb) fs xss;
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    val xgs = map2 (curry Term.list_comb) gs xss;
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    val eta_fs = map2 eta_expand_case_arg xss xfs;
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    val eta_gs = map2 eta_expand_case_arg xss xgs;
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    val fcase = Term.list_comb (casex, eta_fs);
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    val gcase = Term.list_comb (casex, eta_gs);
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    val exist_xs_v_eq_ctrs =
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      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss;
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    fun disc_free b = Free (Binding.name_of b, fpT --> HOLogic.boolT);
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    fun disc_spec b exist_xs_v_eq_ctr = mk_Trueprop_eq (disc_free b $ v, exist_xs_v_eq_ctr);
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    fun alternate_disc_lhs k =
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      HOLogic.mk_not
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        (case nth disc_binders (k - 1) of
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          NONE => nth exist_xs_v_eq_ctrs (k - 1)
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        | SOME b => disc_free b $ v);
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    fun alternate_disc k =
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      if n = 2 then Term.lambda v (alternate_disc_lhs (3 - k)) else error "Cannot use \"*\" here"
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    fun mk_sel_case_args proto_sels T =
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      map2 (fn Ts => fn i =>
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        case AList.lookup (op =) proto_sels i of
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          NONE => mk_undef T Ts
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        | SOME (xs, x) => fold_rev Term.lambda xs x) ctr_Tss ks;
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    fun sel_spec b proto_sels =
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      let
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        val _ =
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          (case duplicates (op =) (map fst proto_sels) of
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             k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
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               " for constructor " ^ quote (Syntax.string_of_term no_defs_lthy (nth ctrs (k - 1))))
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           | [] => ())
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        val T =
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          (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
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            [T] => T
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          | T :: T' :: _ => error ("Inconsistent range type for selector " ^
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              quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^
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              " vs. " ^ quote (Syntax.string_of_typ no_defs_lthy T')));
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      in
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        mk_Trueprop_eq (Free (Binding.name_of b, fpT --> T) $ v,
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          Term.list_comb (mk_case As T, mk_sel_case_args proto_sels T) $ v)
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      end;
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    val missing_unique_disc_def = TrueI; (*arbitrary marker*)
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    val missing_alternate_disc_def = FalseE; (*arbitrary marker*)
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    val proto_selss = map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss;
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    val sel_bundles = AList.group Binding.eq_name (flat sel_binderss ~~ flat proto_selss);
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    val sel_binders = map fst sel_bundles;
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    fun unflat_selss xs = unflat_lookup Binding.eq_name sel_binders xs sel_binderss;
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    val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
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      no_defs_lthy
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      |> apfst split_list o fold_map4 (fn k => fn m => fn exist_xs_v_eq_ctr =>
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        fn NONE =>
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           if n = 1 then pair (Term.lambda v (mk_v_eq_v ()), missing_unique_disc_def)
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           else if m = 0 then pair (Term.lambda v exist_xs_v_eq_ctr, refl)
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           else pair (alternate_disc k, missing_alternate_disc_def)
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         | SOME b => Specification.definition (SOME (b, NONE, NoSyn),
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             ((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr)) #>> apsnd snd)
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        ks ms exist_xs_v_eq_ctrs disc_binders
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      ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
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        Specification.definition (SOME (b, NONE, NoSyn),
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          ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_bundles
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      ||> `Local_Theory.restore;
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    (*transforms defined frees into consts (and more)*)
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    val phi = Proof_Context.export_morphism lthy lthy';
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    val disc_defs = map (Morphism.thm phi) raw_disc_defs;
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    val sel_defss = unflat_selss (map (Morphism.thm phi) raw_sel_defs);
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    val discs0 = map (Morphism.term phi) raw_discs;
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    val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
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    fun mk_disc_or_sel Ts c =
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      Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of c))) ~~ Ts) c;
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    val discs = map (mk_disc_or_sel As) discs0;
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    val selss = map (map (mk_disc_or_sel As)) selss0;
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    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
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    val goal_exhaust =
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      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in
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        fold_rev Logic.all [p, v] (mk_imp_p (map2 mk_prem xctrs xss))
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      end;
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    val goal_injectss =
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      let
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        fun mk_goal _ _ [] [] = []
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          | mk_goal xctr yctr xs ys =
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            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
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              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
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      in
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        map4 mk_goal xctrs yctrs xss yss
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      end;
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    val goal_half_distinctss =
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      let
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        fun mk_goal ((xs, xc), (xs', xc')) =
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          fold_rev Logic.all (xs @ xs')
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            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
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      in
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        map (map mk_goal) (mk_half_pairss (xss ~~ xctrs))
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      end;
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    val goal_cases =
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      map3 (fn xs => fn xctr => fn xf =>
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        fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xss xctrs xfs;
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    val goalss = [goal_exhaust] :: goal_injectss @ goal_half_distinctss @ [goal_cases];
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    fun after_qed thmss lthy =
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      let
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        val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
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          (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
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        val exhaust_thm' =
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          let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in
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            Drule.instantiate' [] [SOME (certify lthy v)]
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              (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm))
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          end;
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        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
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        val (distinct_thmsss', distinct_thmsss) =
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          map2 (map2 append) (Library.chop_groups n half_distinct_thmss)
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            (transpose (Library.chop_groups n other_half_distinct_thmss))
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          |> `transpose;
blanchet@49048
   301
        val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss);
blanchet@49019
   302
blanchet@49020
   303
        val nchotomy_thm =
blanchet@49020
   304
          let
blanchet@49020
   305
            val goal =
blanchet@49022
   306
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',
blanchet@49029
   307
                Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));
blanchet@49020
   308
          in
blanchet@49020
   309
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
blanchet@49020
   310
          end;
blanchet@49020
   311
blanchet@49030
   312
        val sel_thmss =
blanchet@49258
   313
          map2 (fn case_thm => map (fn sel_def => case_thm RS (sel_def RS trans))) case_thms
blanchet@49258
   314
            sel_defss;
blanchet@49025
   315
blanchet@49157
   316
        fun mk_unique_disc_def () =
blanchet@49137
   317
          let
blanchet@49137
   318
            val m = the_single ms;
blanchet@49137
   319
            val goal = mk_Trueprop_eq (mk_v_eq_v (), the_single exist_xs_v_eq_ctrs);
blanchet@49137
   320
          in
blanchet@49137
   321
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_unique_disc_def_tac m exhaust_thm')
blanchet@49137
   322
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49137
   323
            |> Thm.close_derivation
blanchet@49137
   324
          end;
blanchet@49137
   325
blanchet@49137
   326
        fun mk_alternate_disc_def k =
blanchet@49116
   327
          let
blanchet@49116
   328
            val goal =
blanchet@49152
   329
              mk_Trueprop_eq (Morphism.term phi (alternate_disc_lhs (3 - k)),
blanchet@49116
   330
                nth exist_xs_v_eq_ctrs (k - 1));
blanchet@49116
   331
          in
blanchet@49116
   332
            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49148
   333
              mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k)) (nth distinct_thms (2 - k))
blanchet@49116
   334
                exhaust_thm')
blanchet@49116
   335
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49125
   336
            |> Thm.close_derivation
blanchet@49116
   337
          end;
blanchet@49116
   338
blanchet@49137
   339
        val has_alternate_disc_def =
blanchet@49137
   340
          exists (fn def => Thm.eq_thm_prop (def, missing_alternate_disc_def)) disc_defs;
blanchet@49116
   341
blanchet@49116
   342
        val disc_defs' =
blanchet@49116
   343
          map2 (fn k => fn def =>
blanchet@49157
   344
            if Thm.eq_thm_prop (def, missing_unique_disc_def) then mk_unique_disc_def ()
blanchet@49137
   345
            else if Thm.eq_thm_prop (def, missing_alternate_disc_def) then mk_alternate_disc_def k
blanchet@49137
   346
            else def)
blanchet@49116
   347
          ks disc_defs;
blanchet@49116
   348
blanchet@49116
   349
        val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49028
   350
        val discI_thms =
blanchet@49116
   351
          map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs';
blanchet@49137
   352
        val not_discI_thms =
blanchet@49030
   353
          map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49116
   354
            (Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49116
   355
          ms disc_defs';
blanchet@49028
   356
blanchet@49050
   357
        val (disc_thmss', disc_thmss) =
blanchet@49027
   358
          let
blanchet@49048
   359
            fun mk_thm discI _ [] = refl RS discI
blanchet@49137
   360
              | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49137
   361
            fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49027
   362
          in
blanchet@49137
   363
            map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49027
   364
          end;
blanchet@49025
   365
blanchet@49116
   366
        val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss);
blanchet@49116
   367
blanchet@49122
   368
        val disc_exclude_thms =
blanchet@49137
   369
          if has_alternate_disc_def then
blanchet@49116
   370
            []
blanchet@49116
   371
          else
blanchet@49116
   372
            let
blanchet@49116
   373
              fun mk_goal [] = []
blanchet@49116
   374
                | mk_goal [((_, true), (_, true))] = []
blanchet@49116
   375
                | mk_goal [(((_, disc), _), ((_, disc'), _))] =
blanchet@49116
   376
                  [Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (betapply (disc, v)),
blanchet@49116
   377
                     HOLogic.mk_Trueprop (HOLogic.mk_not (betapply (disc', v)))))];
blanchet@49116
   378
              fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
blanchet@49028
   379
blanchet@49116
   380
              val bundles = ms ~~ discD_thms ~~ discs ~~ no_discs;
blanchet@49116
   381
              val half_pairss = mk_half_pairss bundles;
blanchet@49028
   382
blanchet@49116
   383
              val goal_halvess = map mk_goal half_pairss;
blanchet@49116
   384
              val half_thmss =
blanchet@49116
   385
                map3 (fn [] => K (K []) | [goal] => fn [((((m, discD), _), _), _)] => fn disc_thm =>
blanchet@49122
   386
                  [prove (mk_half_disc_exclude_tac m discD disc_thm) goal])
blanchet@49116
   387
                goal_halvess half_pairss (flat disc_thmss');
blanchet@49028
   388
blanchet@49116
   389
              val goal_other_halvess = map (mk_goal o map swap) half_pairss;
blanchet@49116
   390
              val other_half_thmss =
blanchet@49122
   391
                map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss goal_other_halvess;
blanchet@49116
   392
            in
blanchet@49116
   393
              interleave (flat half_thmss) (flat other_half_thmss)
blanchet@49116
   394
            end;
blanchet@49025
   395
blanchet@49116
   396
        val disc_exhaust_thms =
blanchet@49137
   397
          if has_alternate_disc_def orelse no_discs_at_all then
blanchet@49116
   398
            []
blanchet@49116
   399
          else
blanchet@49116
   400
            let
blanchet@49116
   401
              fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (betapply (disc, v))];
blanchet@49121
   402
              val goal = fold_rev Logic.all [p, v] (mk_imp_p (map mk_prem discs));
blanchet@49116
   403
            in
blanchet@49116
   404
              [Skip_Proof.prove lthy [] [] goal (fn _ =>
blanchet@49116
   405
                 mk_disc_exhaust_tac n exhaust_thm discI_thms)]
blanchet@49116
   406
            end;
blanchet@49025
   407
blanchet@49118
   408
        val collapse_thms =
blanchet@49030
   409
          let
blanchet@49030
   410
            fun mk_goal ctr disc sels =
blanchet@49114
   411
              let
blanchet@49114
   412
                val prem = HOLogic.mk_Trueprop (betapply (disc, v));
blanchet@49114
   413
                val concl =
blanchet@49210
   414
                  mk_Trueprop_eq ((null sels ? swap) (Term.list_comb (ctr, map ap_v sels), v));
blanchet@49114
   415
              in
blanchet@49114
   416
                if prem aconv concl then NONE
blanchet@49114
   417
                else SOME (Logic.all v (Logic.mk_implies (prem, concl)))
blanchet@49114
   418
              end;
blanchet@49030
   419
            val goals = map3 mk_goal ctrs discs selss;
blanchet@49030
   420
          in
blanchet@49114
   421
            map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
blanchet@49030
   422
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49137
   423
                mk_collapse_tac ctxt m discD sel_thms)
blanchet@49137
   424
              |> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals
blanchet@49114
   425
            |> map_filter I
blanchet@49030
   426
          end;
blanchet@49025
   427
blanchet@49116
   428
        val case_eq_thm =
blanchet@49031
   429
          let
blanchet@49210
   430
            fun mk_body f sels = Term.list_comb (f, map ap_v sels);
blanchet@49210
   431
            val goal =
blanchet@49210
   432
              mk_Trueprop_eq (fcase $ v, mk_IfN B (map ap_v discs) (map2 mk_body fs selss));
blanchet@49031
   433
          in
blanchet@49031
   434
            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49153
   435
              mk_case_eq_tac ctxt n exhaust_thm' case_thms disc_thmss' sel_thmss)
blanchet@49031
   436
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49031
   437
          end;
blanchet@49025
   438
blanchet@49033
   439
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   440
          let
blanchet@49032
   441
            fun mk_prem xctr xs f g =
blanchet@49045
   442
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),
blanchet@49032
   443
                mk_Trueprop_eq (f, g)));
blanchet@49033
   444
blanchet@49033
   445
            val v_eq_w = mk_Trueprop_eq (v, w);
blanchet@49032
   446
blanchet@49032
   447
            val goal =
blanchet@49033
   448
              Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,
blanchet@49201
   449
                 mk_Trueprop_eq (fcase $ v, gcase $ w));
blanchet@49201
   450
            val goal_weak = Logic.mk_implies (v_eq_w, mk_Trueprop_eq (fcase $ v, fcase $ w));
blanchet@49032
   451
          in
blanchet@49049
   452
            (Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms),
blanchet@49033
   453
             Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))
blanchet@49033
   454
            |> pairself (singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   455
          end;
blanchet@49025
   456
blanchet@49044
   457
        val (split_thm, split_asm_thm) =
blanchet@49043
   458
          let
blanchet@49044
   459
            fun mk_conjunct xctr xs f_xs =
blanchet@49043
   460
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));
blanchet@49044
   461
            fun mk_disjunct xctr xs f_xs =
blanchet@49044
   462
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),
blanchet@49044
   463
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   464
blanchet@49201
   465
            val lhs = q $ (fcase $ v);
blanchet@49044
   466
blanchet@49043
   467
            val goal =
blanchet@49044
   468
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49044
   469
            val goal_asm =
blanchet@49044
   470
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   471
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   472
blanchet@49044
   473
            val split_thm =
blanchet@49049
   474
              Skip_Proof.prove lthy [] [] goal
blanchet@49052
   475
                (fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss)
blanchet@49044
   476
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49044
   477
            val split_asm_thm =
blanchet@49044
   478
              Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>
blanchet@49044
   479
                mk_split_asm_tac ctxt split_thm)
blanchet@49044
   480
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49043
   481
          in
blanchet@49044
   482
            (split_thm, split_asm_thm)
blanchet@49043
   483
          end;
blanchet@49025
   484
blanchet@49052
   485
        val notes =
blanchet@49052
   486
          [(case_congN, [case_cong_thm]),
blanchet@49116
   487
           (case_eqN, [case_eq_thm]),
blanchet@49052
   488
           (casesN, case_thms),
blanchet@49118
   489
           (collapseN, collapse_thms),
blanchet@49116
   490
           (discsN, disc_thms),
blanchet@49122
   491
           (disc_excludeN, disc_exclude_thms),
blanchet@49116
   492
           (disc_exhaustN, disc_exhaust_thms),
blanchet@49052
   493
           (distinctN, distinct_thms),
blanchet@49052
   494
           (exhaustN, [exhaust_thm]),
blanchet@49121
   495
           (injectN, flat inject_thmss),
blanchet@49052
   496
           (nchotomyN, [nchotomy_thm]),
blanchet@49121
   497
           (selsN, flat sel_thmss),
blanchet@49052
   498
           (splitN, [split_thm]),
blanchet@49052
   499
           (split_asmN, [split_asm_thm]),
blanchet@49052
   500
           (weak_case_cong_thmsN, [weak_case_cong_thm])]
blanchet@49116
   501
          |> filter_out (null o snd)
blanchet@49052
   502
          |> map (fn (thmN, thms) =>
blanchet@49052
   503
            ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
blanchet@49019
   504
      in
blanchet@49266
   505
        ((selss, discI_thms, sel_thmss), lthy |> Local_Theory.notes notes |> snd)
blanchet@49019
   506
      end;
blanchet@49017
   507
  in
blanchet@49121
   508
    (goalss, after_qed, lthy')
blanchet@49017
   509
  end;
blanchet@49017
   510
blanchet@49199
   511
fun wrap_datatype tacss = (fn (goalss, after_qed, lthy) =>
blanchet@49111
   512
  map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss
blanchet@49111
   513
  |> (fn thms => after_qed thms lthy)) oo
blanchet@49199
   514
  prepare_wrap_datatype (K I) (* FIXME? (singleton o Type_Infer_Context.infer_types) *)
blanchet@49111
   515
blanchet@49114
   516
val parse_bindings = Parse.$$$ "[" |-- Parse.list Parse.binding --| Parse.$$$ "]";
blanchet@49057
   517
val parse_bindingss = Parse.$$$ "[" |-- Parse.list parse_bindings --| Parse.$$$ "]";
blanchet@49017
   518
blanchet@49199
   519
val wrap_datatype_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49266
   520
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@49199
   521
  prepare_wrap_datatype Syntax.read_term;
blanchet@49017
   522
blanchet@49017
   523
val _ =
blanchet@49074
   524
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
blanchet@49023
   525
    (((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term --
blanchet@49057
   526
      Scan.optional (parse_bindings -- Scan.optional parse_bindingss []) ([], []))
blanchet@49199
   527
     >> wrap_datatype_cmd);
blanchet@49017
   528
blanchet@49017
   529
end;