src/HOL/Tools/datatype_abs_proofs.ML
author skalberg
Thu Mar 03 12:43:01 2005 +0100 (2005-03-03)
changeset 15570 8d8c70b41bab
parent 15459 16dd63c78049
child 15574 b1d1b5bfc464
permissions -rw-r--r--
Move towards standard functions.
     1 (*  Title:      HOL/Tools/datatype_abs_proofs.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4 
     5 Proofs and defintions independent of concrete representation
     6 of datatypes  (i.e. requiring only abstract properties such as
     7 injectivity / distinctness of constructors and induction)
     8 
     9  - case distinction (exhaustion) theorems
    10  - characteristic equations for primrec combinators
    11  - characteristic equations for case combinators
    12  - equations for splitting "P (case ...)" expressions
    13  - datatype size function
    14  - "nchotomy" and "case_cong" theorems for TFL
    15 
    16 *)
    17 
    18 signature DATATYPE_ABS_PROOFS =
    19 sig
    20   val prove_casedist_thms : string list ->
    21     DatatypeAux.descr list -> (string * sort) list -> thm ->
    22     theory attribute list -> theory -> theory * thm list
    23   val prove_primrec_thms : bool -> string list ->
    24     DatatypeAux.descr list -> (string * sort) list ->
    25       DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list ->
    26         simpset -> thm -> theory -> theory * (string list * thm list)
    27   val prove_case_thms : bool -> string list ->
    28     DatatypeAux.descr list -> (string * sort) list ->
    29       string list -> thm list -> theory -> theory * (thm list list * string list)
    30   val prove_split_thms : string list ->
    31     DatatypeAux.descr list -> (string * sort) list ->
    32       thm list list -> thm list list -> thm list -> thm list list -> theory ->
    33         theory * (thm * thm) list
    34   val prove_size_thms : bool -> string list ->
    35     DatatypeAux.descr list -> (string * sort) list ->
    36       string list -> thm list -> theory -> theory * thm list
    37   val prove_nchotomys : string list -> DatatypeAux.descr list ->
    38     (string * sort) list -> thm list -> theory -> theory * thm list
    39   val prove_weak_case_congs : string list -> DatatypeAux.descr list ->
    40     (string * sort) list -> theory -> theory * thm list
    41   val prove_case_congs : string list ->
    42     DatatypeAux.descr list -> (string * sort) list ->
    43       thm list -> thm list list -> theory -> theory * thm list
    44 end;
    45 
    46 structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
    47 struct
    48 
    49 open DatatypeAux;
    50 
    51 (************************ case distinction theorems ***************************)
    52 
    53 fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy =
    54   let
    55     val _ = message "Proving case distinction theorems ...";
    56 
    57     val descr' = List.concat descr;
    58     val recTs = get_rec_types descr' sorts;
    59     val newTs = Library.take (length (hd descr), recTs);
    60 
    61     val {maxidx, ...} = rep_thm induct;
    62     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
    63 
    64     fun prove_casedist_thm ((i, t), T) =
    65       let
    66         val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
    67           Abs ("z", T', Const ("True", T''))) induct_Ps;
    68         val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
    69           Var (("P", 0), HOLogic.boolT))
    70         val insts = Library.take (i, dummyPs) @ (P::(Library.drop (i + 1, dummyPs)));
    71         val cert = cterm_of (Theory.sign_of thy);
    72         val insts' = (map cert induct_Ps) ~~ (map cert insts);
    73         val induct' = refl RS ((List.nth
    74           (split_conj_thm (cterm_instantiate insts' induct), i)) RSN (2, rev_mp))
    75 
    76       in prove_goalw_cterm [] (cert t) (fn prems =>
    77         [rtac induct' 1,
    78          REPEAT (rtac TrueI 1),
    79          REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
    80          REPEAT (rtac TrueI 1)])
    81       end;
    82 
    83     val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
    84       (DatatypeProp.make_casedists descr sorts) ~~ newTs)
    85   in thy |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms end;
    86 
    87 
    88 (*************************** primrec combinators ******************************)
    89 
    90 fun prove_primrec_thms flat_names new_type_names descr sorts
    91     (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
    92   let
    93     val _ = message "Constructing primrec combinators ...";
    94 
    95     val big_name = space_implode "_" new_type_names;
    96     val thy0 = add_path flat_names big_name thy;
    97 
    98     val descr' = List.concat descr;
    99     val recTs = get_rec_types descr' sorts;
   100     val used = Library.foldr add_typ_tfree_names (recTs, []);
   101     val newTs = Library.take (length (hd descr), recTs);
   102 
   103     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
   104 
   105     val big_rec_name' = big_name ^ "_rec_set";
   106     val rec_set_names = map (Sign.full_name (Theory.sign_of thy0))
   107       (if length descr' = 1 then [big_rec_name'] else
   108         (map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
   109           (1 upto (length descr'))));
   110 
   111     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   112 
   113     val rec_set_Ts = map (fn (T1, T2) => reccomb_fn_Ts ---> HOLogic.mk_setT
   114       (HOLogic.mk_prodT (T1, T2))) (recTs ~~ rec_result_Ts);
   115 
   116     val rec_fns = map (uncurry (mk_Free "f"))
   117       (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
   118     val rec_sets = map (fn c => list_comb (Const c, rec_fns))
   119       (rec_set_names ~~ rec_set_Ts);
   120 
   121     (* introduction rules for graph of primrec function *)
   122 
   123     fun make_rec_intr T set_name ((rec_intr_ts, l), (cname, cargs)) =
   124       let
   125         fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
   126           let val free1 = mk_Free "x" U j
   127           in (case (strip_dtyp dt, strip_type U) of
   128              ((_, DtRec m), (Us, _)) =>
   129                let
   130                  val free2 = mk_Free "y" (Us ---> List.nth (rec_result_Ts, m)) k;
   131                  val i = length Us
   132                in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all
   133                      (map (pair "x") Us, HOLogic.mk_mem (HOLogic.mk_prod
   134                        (app_bnds free1 i, app_bnds free2 i),
   135                          List.nth (rec_sets, m)))) :: prems,
   136                    free1::t1s, free2::t2s)
   137                end
   138            | _ => (j + 1, k, prems, free1::t1s, t2s))
   139           end;
   140 
   141         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   142         val (_, _, prems, t1s, t2s) = Library.foldr mk_prem (cargs ~~ Ts, (1, 1, [], [], []))
   143 
   144       in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop (HOLogic.mk_mem
   145         (HOLogic.mk_prod (list_comb (Const (cname, Ts ---> T), t1s),
   146           list_comb (List.nth (rec_fns, l), t1s @ t2s)), set_name)))], l + 1)
   147       end;
   148 
   149     val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) =>
   150       Library.foldl (make_rec_intr T set_name) (x, #3 (snd d)))
   151         (([], 0), descr' ~~ recTs ~~ rec_sets);
   152 
   153     val (thy1, {intrs = rec_intrs, elims = rec_elims, ...}) =
   154       setmp InductivePackage.quiet_mode (!quiet_mode)
   155         (InductivePackage.add_inductive_i false true big_rec_name' false false true
   156            rec_sets (map (fn x => (("", x), [])) rec_intr_ts) []) thy0;
   157 
   158     (* prove uniqueness and termination of primrec combinators *)
   159 
   160     val _ = message "Proving termination and uniqueness of primrec functions ...";
   161 
   162     fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
   163       let
   164         val distinct_tac = (etac Pair_inject 1) THEN
   165           (if i < length newTs then
   166              full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 1
   167            else full_simp_tac dist_ss 1);
   168 
   169         val inject = map (fn r => r RS iffD1)
   170           (if i < length newTs then List.nth (constr_inject, i)
   171             else #inject (valOf (Symtab.lookup (dt_info, tname))));
   172 
   173         fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
   174           let
   175             val k = length (List.filter is_rec_type cargs)
   176 
   177           in (EVERY [DETERM tac,
   178                 REPEAT (etac ex1E 1), rtac ex1I 1,
   179                 DEPTH_SOLVE_1 (ares_tac [intr] 1),
   180                 REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
   181                 etac elim 1,
   182                 REPEAT_DETERM_N j distinct_tac,
   183                 etac Pair_inject 1, TRY (dresolve_tac inject 1),
   184                 REPEAT (etac conjE 1), hyp_subst_tac 1,
   185                 REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
   186                 TRY (hyp_subst_tac 1),
   187                 rtac refl 1,
   188                 REPEAT_DETERM_N (n - j - 1) distinct_tac],
   189               intrs, j + 1)
   190           end;
   191 
   192         val (tac', intrs', _) = Library.foldl (mk_unique_constr_tac (length constrs))
   193           ((tac, intrs, 0), constrs);
   194 
   195       in (tac', intrs') end;
   196 
   197     val rec_unique_thms =
   198       let
   199         val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
   200           Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
   201             absfree ("y", T2, HOLogic.mk_mem (HOLogic.mk_prod
   202               (mk_Free "x" T1 i, Free ("y", T2)), set_t)))
   203                 (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
   204         val cert = cterm_of (Theory.sign_of thy1)
   205         val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
   206           ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
   207         val induct' = cterm_instantiate ((map cert induct_Ps) ~~
   208           (map cert insts)) induct;
   209         val (tac, _) = Library.foldl mk_unique_tac
   210           (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_tac) 1
   211               THEN rewtac (mk_meta_eq choice_eq), rec_intrs),
   212             descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts);
   213 
   214       in split_conj_thm (prove_goalw_cterm []
   215         (cert (HOLogic.mk_Trueprop (mk_conj rec_unique_ts))) (K [tac]))
   216       end;
   217 
   218     val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
   219 
   220     (* define primrec combinators *)
   221 
   222     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   223     val reccomb_names = map (Sign.full_name (Theory.sign_of thy1))
   224       (if length descr' = 1 then [big_reccomb_name] else
   225         (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   226           (1 upto (length descr'))));
   227     val reccombs = map (fn ((name, T), T') => list_comb
   228       (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
   229         (reccomb_names ~~ recTs ~~ rec_result_Ts);
   230 
   231     val (thy2, reccomb_defs) = thy1 |>
   232       Theory.add_consts_i (map (fn ((name, T), T') =>
   233         (Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   234           (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
   235       (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
   236         ((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
   237            Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
   238              HOLogic.mk_mem (HOLogic.mk_prod (Free ("x", T), Free ("y", T')), set))))))
   239                (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |>>
   240       parent_path flat_names;
   241 
   242 
   243     (* prove characteristic equations for primrec combinators *)
   244 
   245     val _ = message "Proving characteristic theorems for primrec combinators ..."
   246 
   247     val rec_thms = map (fn t => prove_goalw_cterm reccomb_defs
   248       (cterm_of (Theory.sign_of thy2) t) (fn _ =>
   249         [rtac the1_equality 1,
   250          resolve_tac rec_unique_thms 1,
   251          resolve_tac rec_intrs 1,
   252          REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)]))
   253            (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
   254 
   255   in
   256     thy2 |> Theory.add_path (space_implode "_" new_type_names) |>
   257     PureThy.add_thmss [(("recs", rec_thms), [])] |>>
   258     Theory.parent_path |> apsnd (pair reccomb_names o List.concat)
   259   end;
   260 
   261 
   262 (***************************** case combinators *******************************)
   263 
   264 fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   265   let
   266     val _ = message "Proving characteristic theorems for case combinators ...";
   267 
   268     val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
   269 
   270     val descr' = List.concat descr;
   271     val recTs = get_rec_types descr' sorts;
   272     val used = Library.foldr add_typ_tfree_names (recTs, []);
   273     val newTs = Library.take (length (hd descr), recTs);
   274     val T' = TFree (variant used "'t", HOLogic.typeS);
   275 
   276     fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T';
   277 
   278     val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
   279       let
   280         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   281         val Ts' = map mk_dummyT (List.filter is_rec_type cargs)
   282       in Const ("arbitrary", Ts @ Ts' ---> T')
   283       end) constrs) descr';
   284 
   285     val case_names = map (fn s =>
   286       Sign.full_name (Theory.sign_of thy1) (s ^ "_case")) new_type_names;
   287 
   288     (* define case combinators via primrec combinators *)
   289 
   290     val (case_defs, thy2) = Library.foldl (fn ((defs, thy),
   291       ((((i, (_, _, constrs)), T), name), recname)) =>
   292         let
   293           val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
   294             let
   295               val Ts = map (typ_of_dtyp descr' sorts) cargs;
   296               val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs);
   297               val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
   298               val frees = Library.take (length cargs, frees');
   299               val free = mk_Free "f" (Ts ---> T') j
   300             in
   301              (free, list_abs_free (map dest_Free frees',
   302                list_comb (free, frees)))
   303             end) (constrs ~~ (1 upto length constrs)));
   304 
   305           val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
   306           val fns = (List.concat (Library.take (i, case_dummy_fns))) @
   307             fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns)));
   308           val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
   309           val decl = (Sign.base_name name, caseT, NoSyn);
   310           val def = ((Sign.base_name name) ^ "_def",
   311             Logic.mk_equals (list_comb (Const (name, caseT), fns1),
   312               list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @
   313                 fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) )));
   314           val (thy', [def_thm]) = thy |>
   315             Theory.add_consts_i [decl] |> (PureThy.add_defs_i false o map Thm.no_attributes) [def];
   316 
   317         in (defs @ [def_thm], thy')
   318         end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
   319           (Library.take (length newTs, reccomb_names)));
   320 
   321     val case_thms = map (map (fn t => prove_goalw_cterm (case_defs @
   322       (map mk_meta_eq primrec_thms)) (cterm_of (Theory.sign_of thy2) t)
   323         (fn _ => [rtac refl 1])))
   324           (DatatypeProp.make_cases new_type_names descr sorts thy2)
   325 
   326   in
   327     thy2 |>
   328     parent_path flat_names |>
   329     store_thmss "cases" new_type_names case_thms |>
   330     apsnd (rpair case_names)
   331   end;
   332 
   333 
   334 (******************************* case splitting *******************************)
   335 
   336 fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
   337     casedist_thms case_thms thy =
   338   let
   339     val _ = message "Proving equations for case splitting ...";
   340 
   341     val descr' = List.concat descr;
   342     val recTs = get_rec_types descr' sorts;
   343     val newTs = Library.take (length (hd descr), recTs);
   344 
   345     fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
   346         exhaustion), case_thms'), T) =
   347       let
   348         val cert = cterm_of (Theory.sign_of thy);
   349         val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
   350         val exhaustion' = cterm_instantiate
   351           [(cert lhs, cert (Free ("x", T)))] exhaustion;
   352         val tacsf = K [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
   353           (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))]
   354       in
   355         (prove_goalw_cterm [] (cert t1) tacsf,
   356          prove_goalw_cterm [] (cert t2) tacsf)
   357       end;
   358 
   359     val split_thm_pairs = map prove_split_thms
   360       ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
   361         dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
   362 
   363     val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
   364 
   365   in
   366     thy |> store_thms "split" new_type_names split_thms |>>>
   367       store_thms "split_asm" new_type_names split_asm_thms |> apsnd ListPair.zip
   368   end;
   369 
   370 (******************************* size functions *******************************)
   371 
   372 fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   373   if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt =>
   374     is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs)
   375       (List.concat descr)
   376   then
   377     (thy, [])
   378   else
   379   let
   380     val _ = message "Proving equations for size function ...";
   381 
   382     val big_name = space_implode "_" new_type_names;
   383     val thy1 = add_path flat_names big_name thy;
   384 
   385     val descr' = List.concat descr;
   386     val recTs = get_rec_types descr' sorts;
   387 
   388     val size_name = "Nat.size";
   389     val size_names = replicate (length (hd descr)) size_name @
   390       map (Sign.full_name (Theory.sign_of thy1)) (DatatypeProp.indexify_names
   391         (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs))));
   392     val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names
   393       (map (fn T => name_of_typ T ^ "_size") recTs));
   394 
   395     fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2;
   396 
   397     fun make_sizefun (_, cargs) =
   398       let
   399         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   400         val k = length (List.filter is_rec_type cargs);
   401         val t = if k = 0 then HOLogic.zero else
   402           foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.mk_nat 1])
   403       in
   404         Library.foldr (fn (T, t') => Abs ("x", T, t')) (Ts @ replicate k HOLogic.natT, t)
   405       end;
   406 
   407     val fs = List.concat (map (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr');
   408     val fTs = map fastype_of fs;
   409 
   410     val (thy', size_def_thms) = thy1 |>
   411       Theory.add_consts_i (map (fn (s, T) =>
   412         (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   413           (Library.drop (length (hd descr), size_names ~~ recTs))) |>
   414       (PureThy.add_defs_i true o map Thm.no_attributes) (map (fn (((s, T), def_name), rec_name) =>
   415         (def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
   416           list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs))))
   417             (size_names ~~ recTs ~~ def_names ~~ reccomb_names)) |>>
   418       parent_path flat_names;
   419 
   420     val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
   421 
   422     val size_thms = map (fn t => prove_goalw_cterm rewrites
   423       (cterm_of (Theory.sign_of thy') t) (fn _ => [rtac refl 1]))
   424         (DatatypeProp.make_size descr sorts thy')
   425 
   426   in
   427     thy' |> Theory.add_path big_name |>
   428     PureThy.add_thmss [(("size", size_thms), [])] |>>
   429     Theory.parent_path |> apsnd List.concat
   430   end;
   431 
   432 fun prove_weak_case_congs new_type_names descr sorts thy =
   433   let
   434     fun prove_weak_case_cong t =
   435        prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) t)
   436          (fn prems => [rtac ((hd prems) RS arg_cong) 1])
   437 
   438     val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
   439       new_type_names descr sorts thy)
   440 
   441   in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
   442 
   443 (************************* additional theorems for TFL ************************)
   444 
   445 fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
   446   let
   447     val _ = message "Proving additional theorems for TFL ...";
   448 
   449     fun prove_nchotomy (t, exhaustion) =
   450       let
   451         (* For goal i, select the correct disjunct to attack, then prove it *)
   452         fun tac i 0 = EVERY [TRY (rtac disjI1 i),
   453               hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
   454           | tac i n = rtac disjI2 i THEN tac i (n - 1)
   455       in 
   456         prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) t) (fn _ =>
   457           [rtac allI 1,
   458            exh_tac (K exhaustion) 1,
   459            ALLGOALS (fn i => tac i (i-1))])
   460       end;
   461 
   462     val nchotomys =
   463       map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
   464 
   465   in thy |> store_thms "nchotomy" new_type_names nchotomys end;
   466 
   467 fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
   468   let
   469     fun prove_case_cong ((t, nchotomy), case_rewrites) =
   470       let
   471         val (Const ("==>", _) $ tm $ _) = t;
   472         val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
   473         val cert = cterm_of (Theory.sign_of thy);
   474         val nchotomy' = nchotomy RS spec;
   475         val nchotomy'' = cterm_instantiate
   476           [(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy'
   477       in
   478         prove_goalw_cterm [] (cert t) (fn prems => 
   479           let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
   480           in [simp_tac (HOL_ss addsimps [hd prems]) 1,
   481               cut_facts_tac [nchotomy''] 1,
   482               REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
   483               REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
   484           end)
   485       end;
   486 
   487     val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
   488       new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
   489 
   490   in thy |> store_thms "case_cong" new_type_names case_congs end;
   491 
   492 end;