src/HOL/Codatatype/Tools/bnf_wrap.ML
author blanchet
Tue Sep 11 17:06:27 2012 +0200 (2012-09-11)
changeset 49281 3d87f4fd0d50
parent 49280 52413dc96326
child 49285 036b833b99aa
permissions -rw-r--r--
generate all sel theorems
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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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    ((bool * term list) * term) *
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      (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
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    (term list list * thm list * thm list list) * local_theory
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  val parse_wrap_options: bool parser
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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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fun mk_undefined T = Const (@{const_name undefined}, 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 (((no_dests, raw_ctrs), raw_case),
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    (raw_disc_binders, (raw_sel_binderss, raw_sel_defaultss))) 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 n = length raw_ctrs;
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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 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 sel_defaultss =
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      pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
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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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    val unique_disc_no_def = TrueI; (*arbitrary marker*)
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    val alternate_disc_no_def = FalseE; (*arbitrary marker*)
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    fun alternate_disc_lhs get_disc 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 => get_disc b (k - 1) $ v);
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    val (discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
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      if no_dests then
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        ([], [], [], [], [], no_defs_lthy)
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      else
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        let
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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 k = Term.lambda v (alternate_disc_lhs (K o disc_free) (3 - k));
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          fun mk_sel_case_args b proto_sels T =
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            map2 (fn Ts => fn k =>
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              (case AList.lookup (op =) proto_sels k of
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                NONE =>
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                let val def_T = Ts ---> T in
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                  (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
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                    NONE => mk_undefined def_T
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                  | SOME t => fold_rev (fn T => Term.lambda (Free (Name.uu, T))) Ts
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                      (Term.subst_atomic_types [(fastype_of t, T)] t))
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                end
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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 " ^
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                     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 b proto_sels T) $ v)
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            end;
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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 ()), unique_disc_no_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, alternate_disc_no_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_defs = map (Morphism.thm phi) raw_sel_defs;
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          val sel_defss = unflat_selss 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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        in
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          (discs, selss, disc_defs, sel_defs, sel_defss, lthy')
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        end;
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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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blanchet@49019
   302
    fun after_qed thmss lthy =
blanchet@49019
   303
      let
blanchet@49048
   304
        val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
blanchet@49048
   305
          (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
blanchet@49019
   306
blanchet@49032
   307
        val exhaust_thm' =
blanchet@49032
   308
          let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in
blanchet@49032
   309
            Drule.instantiate' [] [SOME (certify lthy v)]
blanchet@49032
   310
              (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm))
blanchet@49032
   311
          end;
blanchet@49032
   312
blanchet@49048
   313
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   314
blanchet@49052
   315
        val (distinct_thmsss', distinct_thmsss) =
blanchet@49048
   316
          map2 (map2 append) (Library.chop_groups n half_distinct_thmss)
blanchet@49052
   317
            (transpose (Library.chop_groups n other_half_distinct_thmss))
blanchet@49052
   318
          |> `transpose;
blanchet@49048
   319
        val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss);
blanchet@49019
   320
blanchet@49020
   321
        val nchotomy_thm =
blanchet@49020
   322
          let
blanchet@49020
   323
            val goal =
blanchet@49022
   324
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',
blanchet@49029
   325
                Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));
blanchet@49020
   326
          in
blanchet@49020
   327
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
blanchet@49020
   328
          end;
blanchet@49020
   329
blanchet@49281
   330
        val (all_sel_thms, sel_thmss, disc_thms, discI_thms, disc_exclude_thms, disc_exhaust_thms,
blanchet@49281
   331
             collapse_thms, case_eq_thms) =
blanchet@49278
   332
          if no_dests then
blanchet@49281
   333
            ([], [], [], [], [], [], [], [])
blanchet@49116
   334
          else
blanchet@49116
   335
            let
blanchet@49281
   336
              fun make_sel_thm case_thm sel_def = case_thm RS (sel_def RS trans);
blanchet@49281
   337
blanchet@49281
   338
              fun has_undefined_rhs thm =
blanchet@49281
   339
                (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
blanchet@49281
   340
                  Const (@{const_name undefined}, _) => true
blanchet@49281
   341
                | _ => false);
blanchet@49281
   342
blanchet@49281
   343
              val sel_thmss = map2 (map o make_sel_thm) case_thms sel_defss;
blanchet@49281
   344
blanchet@49281
   345
              val all_sel_thms =
blanchet@49281
   346
                if forall null sel_defaultss then
blanchet@49281
   347
                  flat (transpose sel_thmss)
blanchet@49281
   348
                else
blanchet@49281
   349
                  map_product (fn s => fn c => make_sel_thm c s) sel_defs case_thms
blanchet@49281
   350
                  |> filter_out has_undefined_rhs;
blanchet@49278
   351
blanchet@49278
   352
              fun mk_unique_disc_def () =
blanchet@49278
   353
                let
blanchet@49278
   354
                  val m = the_single ms;
blanchet@49278
   355
                  val goal = mk_Trueprop_eq (mk_v_eq_v (), the_single exist_xs_v_eq_ctrs);
blanchet@49278
   356
                in
blanchet@49278
   357
                  Skip_Proof.prove lthy [] [] goal (fn _ => mk_unique_disc_def_tac m exhaust_thm')
blanchet@49278
   358
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   359
                  |> Thm.close_derivation
blanchet@49278
   360
                end;
blanchet@49278
   361
blanchet@49278
   362
              fun mk_alternate_disc_def k =
blanchet@49278
   363
                let
blanchet@49278
   364
                  val goal =
blanchet@49278
   365
                    mk_Trueprop_eq (alternate_disc_lhs (K (nth discs)) (3 - k),
blanchet@49278
   366
                      nth exist_xs_v_eq_ctrs (k - 1));
blanchet@49278
   367
                in
blanchet@49278
   368
                  Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   369
                    mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
blanchet@49278
   370
                      (nth distinct_thms (2 - k)) exhaust_thm')
blanchet@49278
   371
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   372
                  |> Thm.close_derivation
blanchet@49278
   373
                end;
blanchet@49028
   374
blanchet@49278
   375
              val has_alternate_disc_def =
blanchet@49278
   376
                exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
blanchet@49278
   377
blanchet@49278
   378
              val disc_defs' =
blanchet@49278
   379
                map2 (fn k => fn def =>
blanchet@49278
   380
                  if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
blanchet@49278
   381
                  else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
blanchet@49278
   382
                  else def) ks disc_defs;
blanchet@49278
   383
blanchet@49278
   384
              val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49278
   385
              val discI_thms =
blanchet@49278
   386
                map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
blanchet@49278
   387
                  disc_defs';
blanchet@49278
   388
              val not_discI_thms =
blanchet@49278
   389
                map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49278
   390
                    (Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49278
   391
                  ms disc_defs';
blanchet@49278
   392
blanchet@49278
   393
              val (disc_thmss', disc_thmss) =
blanchet@49278
   394
                let
blanchet@49278
   395
                  fun mk_thm discI _ [] = refl RS discI
blanchet@49278
   396
                    | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49278
   397
                  fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49278
   398
                in
blanchet@49278
   399
                  map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49278
   400
                end;
blanchet@49278
   401
blanchet@49278
   402
              val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss);
blanchet@49028
   403
blanchet@49278
   404
              val disc_exclude_thms =
blanchet@49278
   405
                if has_alternate_disc_def then
blanchet@49278
   406
                  []
blanchet@49278
   407
                else
blanchet@49278
   408
                  let
blanchet@49278
   409
                    fun mk_goal [] = []
blanchet@49278
   410
                      | mk_goal [((_, true), (_, true))] = []
blanchet@49278
   411
                      | mk_goal [(((_, disc), _), ((_, disc'), _))] =
blanchet@49278
   412
                        [Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (betapply (disc, v)),
blanchet@49278
   413
                           HOLogic.mk_Trueprop (HOLogic.mk_not (betapply (disc', v)))))];
blanchet@49278
   414
                    fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
blanchet@49278
   415
blanchet@49278
   416
                    val bundles = ms ~~ discD_thms ~~ discs ~~ no_discs;
blanchet@49278
   417
                    val half_pairss = mk_half_pairss bundles;
blanchet@49278
   418
blanchet@49278
   419
                    val goal_halvess = map mk_goal half_pairss;
blanchet@49278
   420
                    val half_thmss =
blanchet@49278
   421
                      map3 (fn [] => K (K []) | [goal] => fn [((((m, discD), _), _), _)] =>
blanchet@49278
   422
                          fn disc_thm => [prove (mk_half_disc_exclude_tac m discD disc_thm) goal])
blanchet@49278
   423
                        goal_halvess half_pairss (flat disc_thmss');
blanchet@49278
   424
blanchet@49278
   425
                    val goal_other_halvess = map (mk_goal o map swap) half_pairss;
blanchet@49278
   426
                    val other_half_thmss =
blanchet@49278
   427
                      map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
blanchet@49278
   428
                        goal_other_halvess;
blanchet@49278
   429
                  in
blanchet@49278
   430
                    interleave (flat half_thmss) (flat other_half_thmss)
blanchet@49278
   431
                  end;
blanchet@49028
   432
blanchet@49278
   433
              val disc_exhaust_thms =
blanchet@49278
   434
                if has_alternate_disc_def orelse no_discs_at_all then
blanchet@49278
   435
                  []
blanchet@49278
   436
                else
blanchet@49278
   437
                  let
blanchet@49278
   438
                    fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (betapply (disc, v))];
blanchet@49278
   439
                    val goal = fold_rev Logic.all [p, v] (mk_imp_p (map mk_prem discs));
blanchet@49278
   440
                  in
blanchet@49278
   441
                    [Skip_Proof.prove lthy [] [] goal (fn _ =>
blanchet@49278
   442
                       mk_disc_exhaust_tac n exhaust_thm discI_thms)]
blanchet@49278
   443
                  end;
blanchet@49025
   444
blanchet@49278
   445
              val collapse_thms =
blanchet@49278
   446
                if no_dests then
blanchet@49278
   447
                  []
blanchet@49278
   448
                else
blanchet@49278
   449
                  let
blanchet@49278
   450
                    fun mk_goal ctr disc sels =
blanchet@49278
   451
                      let
blanchet@49278
   452
                        val prem = HOLogic.mk_Trueprop (betapply (disc, v));
blanchet@49278
   453
                        val concl =
blanchet@49278
   454
                          mk_Trueprop_eq ((null sels ? swap)
blanchet@49278
   455
                            (Term.list_comb (ctr, map ap_v sels), v));
blanchet@49278
   456
                      in
blanchet@49278
   457
                        if prem aconv concl then NONE
blanchet@49278
   458
                        else SOME (Logic.all v (Logic.mk_implies (prem, concl)))
blanchet@49278
   459
                      end;
blanchet@49278
   460
                    val goals = map3 mk_goal ctrs discs selss;
blanchet@49278
   461
                  in
blanchet@49278
   462
                    map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
blanchet@49278
   463
                      Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   464
                        mk_collapse_tac ctxt m discD sel_thms)
blanchet@49278
   465
                      |> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals
blanchet@49278
   466
                    |> map_filter I
blanchet@49278
   467
                  end;
blanchet@49278
   468
blanchet@49278
   469
              val case_eq_thms =
blanchet@49278
   470
                if no_dests then
blanchet@49278
   471
                  []
blanchet@49278
   472
                else
blanchet@49278
   473
                  let
blanchet@49278
   474
                    fun mk_body f sels = Term.list_comb (f, map ap_v sels);
blanchet@49278
   475
                    val goal =
blanchet@49278
   476
                      mk_Trueprop_eq (fcase $ v, mk_IfN B (map ap_v discs) (map2 mk_body fs selss));
blanchet@49278
   477
                  in
blanchet@49278
   478
                    [Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   479
                      mk_case_eq_tac ctxt n exhaust_thm' case_thms disc_thmss' sel_thmss)]
blanchet@49278
   480
                    |> Proof_Context.export names_lthy lthy
blanchet@49278
   481
                  end;
blanchet@49116
   482
            in
blanchet@49281
   483
              (all_sel_thms, sel_thmss, disc_thms, discI_thms, disc_exclude_thms, disc_exhaust_thms,
blanchet@49278
   484
               collapse_thms, case_eq_thms)
blanchet@49116
   485
            end;
blanchet@49025
   486
blanchet@49033
   487
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   488
          let
blanchet@49032
   489
            fun mk_prem xctr xs f g =
blanchet@49045
   490
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),
blanchet@49032
   491
                mk_Trueprop_eq (f, g)));
blanchet@49033
   492
blanchet@49033
   493
            val v_eq_w = mk_Trueprop_eq (v, w);
blanchet@49032
   494
blanchet@49032
   495
            val goal =
blanchet@49033
   496
              Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,
blanchet@49201
   497
                 mk_Trueprop_eq (fcase $ v, gcase $ w));
blanchet@49201
   498
            val goal_weak = Logic.mk_implies (v_eq_w, mk_Trueprop_eq (fcase $ v, fcase $ w));
blanchet@49032
   499
          in
blanchet@49049
   500
            (Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms),
blanchet@49033
   501
             Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))
blanchet@49033
   502
            |> pairself (singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   503
          end;
blanchet@49025
   504
blanchet@49044
   505
        val (split_thm, split_asm_thm) =
blanchet@49043
   506
          let
blanchet@49044
   507
            fun mk_conjunct xctr xs f_xs =
blanchet@49043
   508
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));
blanchet@49044
   509
            fun mk_disjunct xctr xs f_xs =
blanchet@49044
   510
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),
blanchet@49044
   511
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   512
blanchet@49201
   513
            val lhs = q $ (fcase $ v);
blanchet@49044
   514
blanchet@49043
   515
            val goal =
blanchet@49044
   516
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49044
   517
            val goal_asm =
blanchet@49044
   518
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   519
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   520
blanchet@49044
   521
            val split_thm =
blanchet@49049
   522
              Skip_Proof.prove lthy [] [] goal
blanchet@49052
   523
                (fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss)
blanchet@49044
   524
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49044
   525
            val split_asm_thm =
blanchet@49044
   526
              Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>
blanchet@49044
   527
                mk_split_asm_tac ctxt split_thm)
blanchet@49044
   528
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49043
   529
          in
blanchet@49044
   530
            (split_thm, split_asm_thm)
blanchet@49043
   531
          end;
blanchet@49025
   532
blanchet@49052
   533
        val notes =
blanchet@49052
   534
          [(case_congN, [case_cong_thm]),
blanchet@49278
   535
           (case_eqN, case_eq_thms),
blanchet@49052
   536
           (casesN, case_thms),
blanchet@49118
   537
           (collapseN, collapse_thms),
blanchet@49116
   538
           (discsN, disc_thms),
blanchet@49122
   539
           (disc_excludeN, disc_exclude_thms),
blanchet@49116
   540
           (disc_exhaustN, disc_exhaust_thms),
blanchet@49052
   541
           (distinctN, distinct_thms),
blanchet@49052
   542
           (exhaustN, [exhaust_thm]),
blanchet@49121
   543
           (injectN, flat inject_thmss),
blanchet@49052
   544
           (nchotomyN, [nchotomy_thm]),
blanchet@49281
   545
           (selsN, all_sel_thms),
blanchet@49052
   546
           (splitN, [split_thm]),
blanchet@49052
   547
           (split_asmN, [split_asm_thm]),
blanchet@49052
   548
           (weak_case_cong_thmsN, [weak_case_cong_thm])]
blanchet@49116
   549
          |> filter_out (null o snd)
blanchet@49052
   550
          |> map (fn (thmN, thms) =>
blanchet@49052
   551
            ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
blanchet@49019
   552
      in
blanchet@49266
   553
        ((selss, discI_thms, sel_thmss), lthy |> Local_Theory.notes notes |> snd)
blanchet@49019
   554
      end;
blanchet@49017
   555
  in
blanchet@49121
   556
    (goalss, after_qed, lthy')
blanchet@49017
   557
  end;
blanchet@49017
   558
blanchet@49199
   559
fun wrap_datatype tacss = (fn (goalss, after_qed, lthy) =>
blanchet@49111
   560
  map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss
blanchet@49280
   561
  |> (fn thms => after_qed thms lthy)) oo prepare_wrap_datatype (K I);
blanchet@49280
   562
blanchet@49280
   563
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
blanchet@49111
   564
blanchet@49280
   565
val parse_bindings = parse_bracket_list Parse.binding;
blanchet@49280
   566
val parse_bindingss = parse_bracket_list parse_bindings;
blanchet@49280
   567
blanchet@49280
   568
val parse_bound_term = (Parse.binding --| @{keyword ":"}) -- Parse.term;
blanchet@49280
   569
val parse_bound_terms = parse_bracket_list parse_bound_term;
blanchet@49280
   570
val parse_bound_termss = parse_bracket_list parse_bound_terms;
blanchet@49017
   571
blanchet@49199
   572
val wrap_datatype_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49266
   573
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@49199
   574
  prepare_wrap_datatype Syntax.read_term;
blanchet@49017
   575
blanchet@49278
   576
val parse_wrap_options =
blanchet@49278
   577
  Scan.optional (@{keyword "("} |-- (@{keyword "no_dests"} >> K true) --| @{keyword ")"}) false;
blanchet@49278
   578
blanchet@49017
   579
val _ =
blanchet@49074
   580
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
blanchet@49278
   581
    ((parse_wrap_options -- (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) --
blanchet@49280
   582
      Parse.term -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
blanchet@49280
   583
        Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
blanchet@49199
   584
     >> wrap_datatype_cmd);
blanchet@49017
   585
blanchet@49017
   586
end;