src/HOL/Codatatype/Tools/bnf_wrap.ML
author blanchet
Tue Sep 04 13:02:32 2012 +0200 (2012-09-04)
changeset 49120 7f8e69fc6ac9
parent 49119 1f605c36869c
child 49121 9e0acaa470ab
permissions -rw-r--r--
smarter "*" syntax -- fallback on "_" if "*" is impossible
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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_name: binding
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  val wrap: ({prems: thm list, context: Proof.context} -> tactic) list list ->
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    (term list * term) * (binding list * binding list list) -> local_theory -> 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 is_N = "is_";
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val un_N = "un_";
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fun mk_un_N 1 1 suf = un_N ^ suf
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  | mk_un_N _ l suf = un_N ^ 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_exclusN = "disc_exclus";
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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_name = @{binding "*"};
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val fallback_name = @{binding _};
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fun pad_list x n xs = xs @ replicate (n - length xs) x;
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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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val mk_Trueprop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq;
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fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T);
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fun eta_expand_caseof_arg xs f_xs = fold_rev Term.lambda xs f_xs;
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fun name_of_ctr t =
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  case head_of t 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 prep_term ((raw_ctrs, raw_caseof), (raw_disc_names, raw_sel_namess))
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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 caseof0 = prep_term no_defs_lthy raw_caseof;
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    val n = length ctrs0;
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    val ks = 1 upto n;
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    val (T_name, As0) = dest_Type (body_type (fastype_of (hd ctrs0)));
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    val b = Binding.qualified_name T_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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    fun mk_ctr Ts ctr =
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      let val Ts0 = snd (dest_Type (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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    val T = Type (T_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_names' = pad_list no_name n raw_disc_names;
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    fun can_rely_on_disc i =
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      not (Binding.eq_name (nth raw_disc_names' i, no_name)) orelse nth ms i = 0;
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    fun can_omit_disc_name k m =
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      n = 1 orelse m = 0 orelse (n = 2 andalso can_rely_on_disc (2 - k))
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    val fallback_disc_name = Binding.name o prefix is_N o Long_Name.base_name o name_of_ctr;
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    val disc_names =
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      raw_disc_names'
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      |> map4 (fn k => fn m => fn ctr => fn disc =>
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        if Binding.eq_name (disc, no_name) then
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          if can_omit_disc_name k m then NONE else SOME (fallback_disc_name ctr)
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        else if Binding.eq_name (disc, fallback_name) then
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          SOME (fallback_disc_name 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_names;
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    fun fallback_sel_name m l = Binding.name o mk_un_N m l o Long_Name.base_name o name_of_ctr;
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    val sel_namess =
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      pad_list [] n raw_sel_namess
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      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
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        if Binding.eq_name (sel, no_name) orelse Binding.eq_name (sel, fallback_name) then
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          fallback_sel_name m l ctr
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        else
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          sel) (1 upto m) o pad_list no_name m) ctrs0 ms;
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    fun mk_caseof Ts T =
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      let val (binders, body) = strip_type (fastype_of caseof0) in
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        Term.subst_atomic_types ((body, T) :: (snd (dest_Type (List.last binders)) ~~ Ts)) caseof0
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      end;
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    val caseofB = mk_caseof As B;
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    val caseofB_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
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    fun mk_caseofB_term eta_fs = Term.list_comb (caseofB, eta_fs);
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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" caseofB_Ts
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      ||>> mk_Frees "g" caseofB_Ts
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      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T
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      ||>> yield_singleton (mk_Frees "w") T
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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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    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_caseof_arg xss xfs;
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    val eta_gs = map2 eta_expand_caseof_arg xss xgs;
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    val caseofB_fs = Term.list_comb (caseofB, eta_fs);
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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 mk_sel_caseof_args k xs x T =
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      map2 (fn Ts => fn i => if i = k then fold_rev Term.lambda xs x else mk_undef T Ts) ctr_Tss ks;
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    fun disc_free b = Free (Binding.name_of b, T --> 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 not_other_disc_lhs i =
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      HOLogic.mk_not
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        (case nth disc_names i of NONE => nth exist_xs_v_eq_ctrs i | SOME b => disc_free b $ v);
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    fun not_other_disc k =
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      if n = 2 then Term.lambda v (not_other_disc_lhs (2 - k)) else error "Cannot use \"*\" here"
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    fun sel_spec b x xs k =
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      let val T' = fastype_of x in
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        mk_Trueprop_eq (Free (Binding.name_of b, T --> T') $ v,
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          Term.list_comb (mk_caseof As T', mk_sel_caseof_args k xs x T') $ v)
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      end;
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    val missing_disc_def = TrueI; (* marker *)
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    val (((raw_discs, raw_disc_defs), (raw_selss, raw_sel_defss)), (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 m = 0 then pair (Term.lambda v exist_xs_v_eq_ctr, refl)
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           else pair (not_other_disc k, missing_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_names
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      ||>> apfst split_list o fold_map3 (fn bs => fn xs => fn k => apfst split_list o
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          fold_map2 (fn b => fn x => Specification.definition (SOME (b, NONE, NoSyn),
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            ((Thm.def_binding b, []), sel_spec b x xs k)) #>> apsnd snd) bs xs) sel_namess xss ks
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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 = map (map (Morphism.thm phi)) raw_sel_defss;
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    val discs0 = map (Morphism.term phi) raw_discs;
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    val selss0 = map (map (Morphism.term phi)) raw_selss;
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    fun mk_disc_or_sel Ts t =
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      Term.subst_atomic_types (snd (dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
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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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        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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            [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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      map (map (HOLogic.mk_Trueprop o HOLogic.mk_not o HOLogic.mk_eq)) (mk_half_pairss xctrs);
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    val goal_cases = map2 (fn xctr => fn xf => mk_Trueprop_eq (caseofB_fs $ xctr, xf)) xctrs xfs;
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    val goals = [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;
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        val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss);
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        val nchotomy_thm =
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          let
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            val goal =
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              HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',
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                Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));
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          in
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            Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
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          end;
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        val sel_thmss =
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          let
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            fun mk_thm k xs goal_case case_thm x sel_def =
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              let
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                val T = fastype_of x;
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                val cTs =
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                  map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree)
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                    (rev (Term.add_tfrees goal_case []));
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                val cxs = map (certify lthy) (mk_sel_caseof_args k xs x T);
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              in
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                Local_Defs.fold lthy [sel_def]
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                  (Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm)
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              end;
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            fun mk_thms k xs goal_case case_thm sel_defs =
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              map2 (mk_thm k xs goal_case case_thm) xs sel_defs;
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          in
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            map5 mk_thms ks xss goal_cases case_thms sel_defss
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          end;
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        fun not_other_disc_def k =
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          let
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            val goal =
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              mk_Trueprop_eq (Morphism.term phi (not_other_disc_lhs (2 - k)),
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                nth exist_xs_v_eq_ctrs (k - 1));
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          in
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            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
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              mk_not_other_disc_def_tac ctxt (nth disc_defs (2 - k)) (nth distinct_thms (2 - k))
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                exhaust_thm')
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            |> singleton (Proof_Context.export names_lthy lthy)
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          end;
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        val has_not_other_disc_def =
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          exists (fn def => Thm.eq_thm_prop (def, missing_disc_def)) disc_defs;
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        val disc_defs' =
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          map2 (fn k => fn def =>
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            if Thm.eq_thm_prop (def, missing_disc_def) then not_other_disc_def k else def)
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          ks disc_defs;
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   305
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   306
        val discD_thms = map (fn def => def RS iffD1) disc_defs';
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   307
        val discI_thms =
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   308
          map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs';
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   309
        val not_disc_thms =
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   310
          map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
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   311
            (Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
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   312
          ms disc_defs';
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   313
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   314
        val (disc_thmss', disc_thmss) =
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   315
          let
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   316
            fun mk_thm discI _ [] = refl RS discI
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   317
              | mk_thm _ not_disc [distinct] = distinct RS not_disc;
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   318
            fun mk_thms discI not_disc distinctss = map (mk_thm discI not_disc) distinctss;
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   319
          in
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   320
            map3 mk_thms discI_thms not_disc_thms distinct_thmsss' |> `transpose
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   321
          end;
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   322
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   323
        val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss);
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   324
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   325
        val disc_exclus_thms =
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   326
          if has_not_other_disc_def then
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   327
            []
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   328
          else
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   329
            let
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   330
              fun mk_goal [] = []
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   331
                | mk_goal [((_, true), (_, true))] = []
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   332
                | mk_goal [(((_, disc), _), ((_, disc'), _))] =
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   333
                  [Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (betapply (disc, v)),
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   334
                     HOLogic.mk_Trueprop (HOLogic.mk_not (betapply (disc', v)))))];
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   335
              fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
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   336
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   337
              val bundles = ms ~~ discD_thms ~~ discs ~~ no_discs;
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   338
              val half_pairss = mk_half_pairss bundles;
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   339
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   340
              val goal_halvess = map mk_goal half_pairss;
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   341
              val half_thmss =
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   342
                map3 (fn [] => K (K []) | [goal] => fn [((((m, discD), _), _), _)] => fn disc_thm =>
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   343
                  [prove (mk_half_disc_exclus_tac m discD disc_thm) goal])
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   344
                goal_halvess half_pairss (flat disc_thmss');
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   345
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   346
              val goal_other_halvess = map (mk_goal o map swap) half_pairss;
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   347
              val other_half_thmss =
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   348
                map2 (map2 (prove o mk_other_half_disc_exclus_tac)) half_thmss goal_other_halvess;
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   349
            in
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   350
              interleave (flat half_thmss) (flat other_half_thmss)
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   351
            end;
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   352
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   353
        val disc_exhaust_thms =
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   354
          if has_not_other_disc_def orelse forall I no_discs then
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   355
            []
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   356
          else
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   357
            let
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   358
              fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (betapply (disc, v))];
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   359
              val goal = fold Logic.all [p, v] (mk_imp_p (map mk_prem discs));
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   360
            in
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   361
              [Skip_Proof.prove lthy [] [] goal (fn _ =>
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   362
                 mk_disc_exhaust_tac n exhaust_thm discI_thms)]
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   363
            end;
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   364
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   365
        val collapse_thms =
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   366
          let
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   367
            fun mk_goal ctr disc sels =
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   368
              let
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   369
                val prem = HOLogic.mk_Trueprop (betapply (disc, v));
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   370
                val concl =
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   371
                  mk_Trueprop_eq ((null sels ? swap)
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   372
                    (Term.list_comb (ctr, map (fn sel => sel $ v) sels), v));
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   373
              in
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   374
                if prem aconv concl then NONE
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   375
                else SOME (Logic.all v (Logic.mk_implies (prem, concl)))
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   376
              end;
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   377
            val goals = map3 mk_goal ctrs discs selss;
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   378
          in
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   379
            map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
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   380
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
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   381
                mk_collapse_tac ctxt m discD sel_thms))) ms discD_thms sel_thmss goals
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   382
            |> map_filter I
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   383
          end;
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   384
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   385
        val case_eq_thm =
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   386
          let
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   387
            fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels);
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   388
            fun mk_rhs _ [f] [sels] = mk_core f sels
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   389
              | mk_rhs (disc :: discs) (f :: fs) (sels :: selss) =
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   390
                Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $
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   391
                  betapply (disc, v) $ mk_core f sels $ mk_rhs discs fs selss;
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   392
            val goal = mk_Trueprop_eq (caseofB_fs $ v, mk_rhs discs fs selss);
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   393
          in
blanchet@49031
   394
            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49116
   395
              mk_case_eq_tac ctxt exhaust_thm' case_thms disc_thmss' sel_thmss)
blanchet@49031
   396
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49031
   397
          end;
blanchet@49025
   398
blanchet@49033
   399
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   400
          let
blanchet@49032
   401
            fun mk_prem xctr xs f g =
blanchet@49045
   402
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),
blanchet@49032
   403
                mk_Trueprop_eq (f, g)));
blanchet@49033
   404
blanchet@49033
   405
            val v_eq_w = mk_Trueprop_eq (v, w);
blanchet@49043
   406
            val caseof_fs = mk_caseofB_term eta_fs;
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   407
            val caseof_gs = mk_caseofB_term eta_gs;
blanchet@49032
   408
blanchet@49032
   409
            val goal =
blanchet@49033
   410
              Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,
blanchet@49033
   411
                 mk_Trueprop_eq (caseof_fs $ v, caseof_gs $ w));
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   412
            val goal_weak =
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   413
              Logic.mk_implies (v_eq_w, mk_Trueprop_eq (caseof_fs $ v, caseof_fs $ w));
blanchet@49032
   414
          in
blanchet@49049
   415
            (Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms),
blanchet@49033
   416
             Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))
blanchet@49033
   417
            |> pairself (singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   418
          end;
blanchet@49025
   419
blanchet@49044
   420
        val (split_thm, split_asm_thm) =
blanchet@49043
   421
          let
blanchet@49044
   422
            fun mk_conjunct xctr xs f_xs =
blanchet@49043
   423
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));
blanchet@49044
   424
            fun mk_disjunct xctr xs f_xs =
blanchet@49044
   425
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),
blanchet@49044
   426
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   427
blanchet@49044
   428
            val lhs = q $ (mk_caseofB_term eta_fs $ v);
blanchet@49044
   429
blanchet@49043
   430
            val goal =
blanchet@49044
   431
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49044
   432
            val goal_asm =
blanchet@49044
   433
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   434
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   435
blanchet@49044
   436
            val split_thm =
blanchet@49049
   437
              Skip_Proof.prove lthy [] [] goal
blanchet@49052
   438
                (fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss)
blanchet@49044
   439
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49044
   440
            val split_asm_thm =
blanchet@49044
   441
              Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>
blanchet@49044
   442
                mk_split_asm_tac ctxt split_thm)
blanchet@49044
   443
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49043
   444
          in
blanchet@49044
   445
            (split_thm, split_asm_thm)
blanchet@49043
   446
          end;
blanchet@49025
   447
blanchet@49052
   448
        val notes =
blanchet@49052
   449
          [(case_congN, [case_cong_thm]),
blanchet@49116
   450
           (case_eqN, [case_eq_thm]),
blanchet@49052
   451
           (casesN, case_thms),
blanchet@49118
   452
           (collapseN, collapse_thms),
blanchet@49116
   453
           (discsN, disc_thms),
blanchet@49053
   454
           (disc_exclusN, disc_exclus_thms),
blanchet@49116
   455
           (disc_exhaustN, disc_exhaust_thms),
blanchet@49052
   456
           (distinctN, distinct_thms),
blanchet@49052
   457
           (exhaustN, [exhaust_thm]),
blanchet@49052
   458
           (injectN, (flat inject_thmss)),
blanchet@49052
   459
           (nchotomyN, [nchotomy_thm]),
blanchet@49052
   460
           (selsN, (flat sel_thmss)),
blanchet@49052
   461
           (splitN, [split_thm]),
blanchet@49052
   462
           (split_asmN, [split_asm_thm]),
blanchet@49052
   463
           (weak_case_cong_thmsN, [weak_case_cong_thm])]
blanchet@49116
   464
          |> filter_out (null o snd)
blanchet@49052
   465
          |> map (fn (thmN, thms) =>
blanchet@49052
   466
            ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
blanchet@49019
   467
      in
blanchet@49052
   468
        lthy |> Local_Theory.notes notes |> snd
blanchet@49019
   469
      end;
blanchet@49017
   470
  in
blanchet@49025
   471
    (goals, after_qed, lthy')
blanchet@49017
   472
  end;
blanchet@49017
   473
blanchet@49111
   474
fun wrap tacss = (fn (goalss, after_qed, lthy) =>
blanchet@49111
   475
  map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss
blanchet@49111
   476
  |> (fn thms => after_qed thms lthy)) oo
blanchet@49111
   477
  prepare_wrap (singleton o Type_Infer_Context.infer_types)
blanchet@49111
   478
blanchet@49114
   479
val parse_bindings = Parse.$$$ "[" |-- Parse.list Parse.binding --| Parse.$$$ "]";
blanchet@49057
   480
val parse_bindingss = Parse.$$$ "[" |-- Parse.list parse_bindings --| Parse.$$$ "]";
blanchet@49017
   481
blanchet@49074
   482
val wrap_data_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49019
   483
  Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo
blanchet@49074
   484
  prepare_wrap Syntax.read_term;
blanchet@49017
   485
blanchet@49017
   486
val _ =
blanchet@49074
   487
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
blanchet@49023
   488
    (((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term --
blanchet@49057
   489
      Scan.optional (parse_bindings -- Scan.optional parse_bindingss []) ([], []))
blanchet@49074
   490
     >> wrap_data_cmd);
blanchet@49017
   491
blanchet@49017
   492
end;