src/HOL/Codatatype/Tools/bnf_wrap.ML
author blanchet
Sat Sep 08 21:04:26 2012 +0200 (2012-09-08)
changeset 49199 7c9a3c67c55d
parent 49174 41790d616f63
child 49201 c69c2c18dccb
permissions -rw-r--r--
added high-level recursor, not yet curried
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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 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 -> 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_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 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 eta_expand_case_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_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 (T_name, As0) = 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 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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    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_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 is_N 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_un_N 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 caseB = mk_case As B;
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    val caseB_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
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    fun mk_caseB_term eta_fs = Term.list_comb (caseB, 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" caseB_Ts
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      ||>> mk_Frees "g" caseB_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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    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 caseB_fs = Term.list_comb (caseB, 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_case_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 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 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_case As T', mk_sel_case_args k xs x 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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    (* TODO: Allow use of same selector for several constructors *)
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    (* TODO: Allow use of same name for datatype and for constructor, e.g. "data L = L" *)
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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 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_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_binderss 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 (Term.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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        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, t), (xs', t')) =
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          fold_rev Logic.all (xs @ xs')
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            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (t, t'))));
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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 (caseB_fs $ 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;
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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_case_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;
blanchet@49028
   303
            fun mk_thms k xs goal_case case_thm sel_defs =
blanchet@49140
   304
              map2 (mk_thm k xs (strip_all_body goal_case) case_thm) xs sel_defs;
blanchet@49025
   305
          in
blanchet@49030
   306
            map5 mk_thms ks xss goal_cases case_thms sel_defss
blanchet@49025
   307
          end;
blanchet@49025
   308
blanchet@49157
   309
        fun mk_unique_disc_def () =
blanchet@49137
   310
          let
blanchet@49137
   311
            val m = the_single ms;
blanchet@49137
   312
            val goal = mk_Trueprop_eq (mk_v_eq_v (), the_single exist_xs_v_eq_ctrs);
blanchet@49137
   313
          in
blanchet@49137
   314
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_unique_disc_def_tac m exhaust_thm')
blanchet@49137
   315
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49137
   316
            |> Thm.close_derivation
blanchet@49137
   317
          end;
blanchet@49137
   318
blanchet@49137
   319
        fun mk_alternate_disc_def k =
blanchet@49116
   320
          let
blanchet@49116
   321
            val goal =
blanchet@49152
   322
              mk_Trueprop_eq (Morphism.term phi (alternate_disc_lhs (3 - k)),
blanchet@49116
   323
                nth exist_xs_v_eq_ctrs (k - 1));
blanchet@49116
   324
          in
blanchet@49116
   325
            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49148
   326
              mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k)) (nth distinct_thms (2 - k))
blanchet@49116
   327
                exhaust_thm')
blanchet@49116
   328
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49125
   329
            |> Thm.close_derivation
blanchet@49116
   330
          end;
blanchet@49116
   331
blanchet@49137
   332
        val has_alternate_disc_def =
blanchet@49137
   333
          exists (fn def => Thm.eq_thm_prop (def, missing_alternate_disc_def)) disc_defs;
blanchet@49116
   334
blanchet@49116
   335
        val disc_defs' =
blanchet@49116
   336
          map2 (fn k => fn def =>
blanchet@49157
   337
            if Thm.eq_thm_prop (def, missing_unique_disc_def) then mk_unique_disc_def ()
blanchet@49137
   338
            else if Thm.eq_thm_prop (def, missing_alternate_disc_def) then mk_alternate_disc_def k
blanchet@49137
   339
            else def)
blanchet@49116
   340
          ks disc_defs;
blanchet@49116
   341
blanchet@49116
   342
        val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49028
   343
        val discI_thms =
blanchet@49116
   344
          map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs';
blanchet@49137
   345
        val not_discI_thms =
blanchet@49030
   346
          map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49116
   347
            (Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49116
   348
          ms disc_defs';
blanchet@49028
   349
blanchet@49050
   350
        val (disc_thmss', disc_thmss) =
blanchet@49027
   351
          let
blanchet@49048
   352
            fun mk_thm discI _ [] = refl RS discI
blanchet@49137
   353
              | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49137
   354
            fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49027
   355
          in
blanchet@49137
   356
            map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49027
   357
          end;
blanchet@49025
   358
blanchet@49116
   359
        val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss);
blanchet@49116
   360
blanchet@49122
   361
        val disc_exclude_thms =
blanchet@49137
   362
          if has_alternate_disc_def then
blanchet@49116
   363
            []
blanchet@49116
   364
          else
blanchet@49116
   365
            let
blanchet@49116
   366
              fun mk_goal [] = []
blanchet@49116
   367
                | mk_goal [((_, true), (_, true))] = []
blanchet@49116
   368
                | mk_goal [(((_, disc), _), ((_, disc'), _))] =
blanchet@49116
   369
                  [Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (betapply (disc, v)),
blanchet@49116
   370
                     HOLogic.mk_Trueprop (HOLogic.mk_not (betapply (disc', v)))))];
blanchet@49116
   371
              fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
blanchet@49028
   372
blanchet@49116
   373
              val bundles = ms ~~ discD_thms ~~ discs ~~ no_discs;
blanchet@49116
   374
              val half_pairss = mk_half_pairss bundles;
blanchet@49028
   375
blanchet@49116
   376
              val goal_halvess = map mk_goal half_pairss;
blanchet@49116
   377
              val half_thmss =
blanchet@49116
   378
                map3 (fn [] => K (K []) | [goal] => fn [((((m, discD), _), _), _)] => fn disc_thm =>
blanchet@49122
   379
                  [prove (mk_half_disc_exclude_tac m discD disc_thm) goal])
blanchet@49116
   380
                goal_halvess half_pairss (flat disc_thmss');
blanchet@49028
   381
blanchet@49116
   382
              val goal_other_halvess = map (mk_goal o map swap) half_pairss;
blanchet@49116
   383
              val other_half_thmss =
blanchet@49122
   384
                map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss goal_other_halvess;
blanchet@49116
   385
            in
blanchet@49116
   386
              interleave (flat half_thmss) (flat other_half_thmss)
blanchet@49116
   387
            end;
blanchet@49025
   388
blanchet@49116
   389
        val disc_exhaust_thms =
blanchet@49137
   390
          if has_alternate_disc_def orelse no_discs_at_all then
blanchet@49116
   391
            []
blanchet@49116
   392
          else
blanchet@49116
   393
            let
blanchet@49116
   394
              fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (betapply (disc, v))];
blanchet@49121
   395
              val goal = fold_rev Logic.all [p, v] (mk_imp_p (map mk_prem discs));
blanchet@49116
   396
            in
blanchet@49116
   397
              [Skip_Proof.prove lthy [] [] goal (fn _ =>
blanchet@49116
   398
                 mk_disc_exhaust_tac n exhaust_thm discI_thms)]
blanchet@49116
   399
            end;
blanchet@49025
   400
blanchet@49118
   401
        val collapse_thms =
blanchet@49030
   402
          let
blanchet@49030
   403
            fun mk_goal ctr disc sels =
blanchet@49114
   404
              let
blanchet@49114
   405
                val prem = HOLogic.mk_Trueprop (betapply (disc, v));
blanchet@49114
   406
                val concl =
blanchet@49114
   407
                  mk_Trueprop_eq ((null sels ? swap)
blanchet@49114
   408
                    (Term.list_comb (ctr, map (fn sel => sel $ v) sels), v));
blanchet@49114
   409
              in
blanchet@49114
   410
                if prem aconv concl then NONE
blanchet@49114
   411
                else SOME (Logic.all v (Logic.mk_implies (prem, concl)))
blanchet@49114
   412
              end;
blanchet@49030
   413
            val goals = map3 mk_goal ctrs discs selss;
blanchet@49030
   414
          in
blanchet@49114
   415
            map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
blanchet@49030
   416
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49137
   417
                mk_collapse_tac ctxt m discD sel_thms)
blanchet@49137
   418
              |> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals
blanchet@49114
   419
            |> map_filter I
blanchet@49030
   420
          end;
blanchet@49025
   421
blanchet@49116
   422
        val case_eq_thm =
blanchet@49031
   423
          let
blanchet@49031
   424
            fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels);
blanchet@49031
   425
            fun mk_rhs _ [f] [sels] = mk_core f sels
blanchet@49031
   426
              | mk_rhs (disc :: discs) (f :: fs) (sels :: selss) =
blanchet@49031
   427
                Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $
blanchet@49114
   428
                  betapply (disc, v) $ mk_core f sels $ mk_rhs discs fs selss;
blanchet@49130
   429
            val goal = mk_Trueprop_eq (caseB_fs $ v, mk_rhs discs fs selss);
blanchet@49031
   430
          in
blanchet@49031
   431
            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49153
   432
              mk_case_eq_tac ctxt n exhaust_thm' case_thms disc_thmss' sel_thmss)
blanchet@49031
   433
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49031
   434
          end;
blanchet@49025
   435
blanchet@49033
   436
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   437
          let
blanchet@49032
   438
            fun mk_prem xctr xs f g =
blanchet@49045
   439
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),
blanchet@49032
   440
                mk_Trueprop_eq (f, g)));
blanchet@49033
   441
blanchet@49033
   442
            val v_eq_w = mk_Trueprop_eq (v, w);
blanchet@49130
   443
            val case_fs = mk_caseB_term eta_fs;
blanchet@49130
   444
            val case_gs = mk_caseB_term eta_gs;
blanchet@49032
   445
blanchet@49032
   446
            val goal =
blanchet@49033
   447
              Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,
blanchet@49130
   448
                 mk_Trueprop_eq (case_fs $ v, case_gs $ w));
blanchet@49130
   449
            val goal_weak = Logic.mk_implies (v_eq_w, mk_Trueprop_eq (case_fs $ v, case_fs $ w));
blanchet@49032
   450
          in
blanchet@49049
   451
            (Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms),
blanchet@49033
   452
             Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))
blanchet@49033
   453
            |> pairself (singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   454
          end;
blanchet@49025
   455
blanchet@49044
   456
        val (split_thm, split_asm_thm) =
blanchet@49043
   457
          let
blanchet@49044
   458
            fun mk_conjunct xctr xs f_xs =
blanchet@49043
   459
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));
blanchet@49044
   460
            fun mk_disjunct xctr xs f_xs =
blanchet@49044
   461
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),
blanchet@49044
   462
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   463
blanchet@49130
   464
            val lhs = q $ (mk_caseB_term eta_fs $ v);
blanchet@49044
   465
blanchet@49043
   466
            val goal =
blanchet@49044
   467
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49044
   468
            val goal_asm =
blanchet@49044
   469
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   470
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   471
blanchet@49044
   472
            val split_thm =
blanchet@49049
   473
              Skip_Proof.prove lthy [] [] goal
blanchet@49052
   474
                (fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss)
blanchet@49044
   475
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49044
   476
            val split_asm_thm =
blanchet@49044
   477
              Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>
blanchet@49044
   478
                mk_split_asm_tac ctxt split_thm)
blanchet@49044
   479
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49043
   480
          in
blanchet@49044
   481
            (split_thm, split_asm_thm)
blanchet@49043
   482
          end;
blanchet@49025
   483
blanchet@49052
   484
        val notes =
blanchet@49052
   485
          [(case_congN, [case_cong_thm]),
blanchet@49116
   486
           (case_eqN, [case_eq_thm]),
blanchet@49052
   487
           (casesN, case_thms),
blanchet@49118
   488
           (collapseN, collapse_thms),
blanchet@49116
   489
           (discsN, disc_thms),
blanchet@49122
   490
           (disc_excludeN, disc_exclude_thms),
blanchet@49116
   491
           (disc_exhaustN, disc_exhaust_thms),
blanchet@49052
   492
           (distinctN, distinct_thms),
blanchet@49052
   493
           (exhaustN, [exhaust_thm]),
blanchet@49121
   494
           (injectN, flat inject_thmss),
blanchet@49052
   495
           (nchotomyN, [nchotomy_thm]),
blanchet@49121
   496
           (selsN, flat sel_thmss),
blanchet@49052
   497
           (splitN, [split_thm]),
blanchet@49052
   498
           (split_asmN, [split_asm_thm]),
blanchet@49052
   499
           (weak_case_cong_thmsN, [weak_case_cong_thm])]
blanchet@49116
   500
          |> filter_out (null o snd)
blanchet@49052
   501
          |> map (fn (thmN, thms) =>
blanchet@49052
   502
            ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
blanchet@49019
   503
      in
blanchet@49052
   504
        lthy |> Local_Theory.notes notes |> snd
blanchet@49019
   505
      end;
blanchet@49017
   506
  in
blanchet@49121
   507
    (goalss, after_qed, lthy')
blanchet@49017
   508
  end;
blanchet@49017
   509
blanchet@49199
   510
fun wrap_datatype tacss = (fn (goalss, after_qed, lthy) =>
blanchet@49111
   511
  map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss
blanchet@49111
   512
  |> (fn thms => after_qed thms lthy)) oo
blanchet@49199
   513
  prepare_wrap_datatype (K I) (* FIXME? (singleton o Type_Infer_Context.infer_types) *)
blanchet@49111
   514
blanchet@49114
   515
val parse_bindings = Parse.$$$ "[" |-- Parse.list Parse.binding --| Parse.$$$ "]";
blanchet@49057
   516
val parse_bindingss = Parse.$$$ "[" |-- Parse.list parse_bindings --| Parse.$$$ "]";
blanchet@49017
   517
blanchet@49199
   518
val wrap_datatype_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49019
   519
  Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo
blanchet@49199
   520
  prepare_wrap_datatype Syntax.read_term;
blanchet@49017
   521
blanchet@49017
   522
val _ =
blanchet@49074
   523
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
blanchet@49023
   524
    (((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term --
blanchet@49057
   525
      Scan.optional (parse_bindings -- Scan.optional parse_bindingss []) ([], []))
blanchet@49199
   526
     >> wrap_datatype_cmd);
blanchet@49017
   527
blanchet@49017
   528
end;