src/HOL/Tools/datatype_abs_proofs.ML
author krauss
Fri Nov 24 13:44:51 2006 +0100 (2006-11-24)
changeset 21512 3786eb1b69d6
parent 21419 809e7520234a
child 21525 1b18b5892dc4
permissions -rw-r--r--
Lemma "fundef_default_value" uses predicate instead of set.
     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     attribute list -> theory -> thm list * theory
    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 -> (string list * thm list) * theory
    27   val prove_case_thms : bool -> string list ->
    28     DatatypeAux.descr list -> (string * sort) list ->
    29       string list -> thm list -> theory -> (thm list list * string list) * theory
    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         (thm * thm) list * theory
    34   val prove_size_thms : bool -> string list ->
    35     DatatypeAux.descr list -> (string * sort) list ->
    36       string list -> thm list -> theory -> thm list * theory
    37   val prove_nchotomys : string list -> DatatypeAux.descr list ->
    38     (string * sort) list -> thm list -> theory -> thm list * theory
    39   val prove_weak_case_congs : string list -> DatatypeAux.descr list ->
    40     (string * sort) list -> theory -> thm list * theory
    41   val prove_case_congs : string list ->
    42     DatatypeAux.descr list -> (string * sort) list ->
    43       thm list -> thm list list -> theory -> thm list * theory
    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 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
    77         Goal.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
    78           (fn prems => EVERY
    79             [rtac induct' 1,
    80              REPEAT (rtac TrueI 1),
    81              REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
    82              REPEAT (rtac TrueI 1)])
    83       end;
    84 
    85     val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
    86       (DatatypeProp.make_casedists descr sorts) ~~ newTs)
    87   in
    88     thy
    89     |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms
    90   end;
    91 
    92 
    93 (*************************** primrec combinators ******************************)
    94 
    95 fun prove_primrec_thms flat_names new_type_names descr sorts
    96     (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
    97   let
    98     val _ = message "Constructing primrec combinators ...";
    99 
   100     val big_name = space_implode "_" new_type_names;
   101     val thy0 = add_path flat_names big_name thy;
   102 
   103     val descr' = List.concat descr;
   104     val recTs = get_rec_types descr' sorts;
   105     val used = foldr add_typ_tfree_names [] recTs;
   106     val newTs = Library.take (length (hd descr), recTs);
   107 
   108     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
   109 
   110     val big_rec_name' = big_name ^ "_rec_set";
   111     val rec_set_names' =
   112       if length descr' = 1 then [big_rec_name'] else
   113         map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
   114           (1 upto (length descr'));
   115     val rec_set_names = map (Sign.full_name (Theory.sign_of thy0)) rec_set_names';
   116 
   117     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   118 
   119     val rec_set_Ts = map (fn (T1, T2) =>
   120       reccomb_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
   121 
   122     val rec_fns = map (uncurry (mk_Free "f"))
   123       (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
   124     val rec_sets' = map (fn c => list_comb (Free c, rec_fns))
   125       (rec_set_names' ~~ rec_set_Ts);
   126     val rec_sets = map (fn c => list_comb (Const c, rec_fns))
   127       (rec_set_names ~~ rec_set_Ts);
   128 
   129     (* introduction rules for graph of primrec function *)
   130 
   131     fun make_rec_intr T rec_set ((rec_intr_ts, l), (cname, cargs)) =
   132       let
   133         fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
   134           let val free1 = mk_Free "x" U j
   135           in (case (strip_dtyp dt, strip_type U) of
   136              ((_, DtRec m), (Us, _)) =>
   137                let
   138                  val free2 = mk_Free "y" (Us ---> List.nth (rec_result_Ts, m)) k;
   139                  val i = length Us
   140                in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all
   141                      (map (pair "x") Us, List.nth (rec_sets', m) $
   142                        app_bnds free1 i $ app_bnds free2 i)) :: prems,
   143                    free1::t1s, free2::t2s)
   144                end
   145            | _ => (j + 1, k, prems, free1::t1s, t2s))
   146           end;
   147 
   148         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   149         val (_, _, prems, t1s, t2s) = foldr mk_prem (1, 1, [], [], []) (cargs ~~ Ts)
   150 
   151       in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop
   152         (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $
   153           list_comb (List.nth (rec_fns, l), t1s @ t2s)))], l + 1)
   154       end;
   155 
   156     val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) =>
   157       Library.foldl (make_rec_intr T set_name) (x, #3 (snd d)))
   158         (([], 0), descr' ~~ recTs ~~ rec_sets');
   159 
   160     val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) =
   161       setmp InductivePackage.quiet_mode (!quiet_mode)
   162         (TheoryTarget.init NONE #>
   163          InductivePackage.add_inductive_i false big_rec_name' false false true
   164            (map (fn (s, T) => (s, SOME T, NoSyn)) (rec_set_names' ~~ rec_set_Ts))
   165            (map (apsnd SOME o dest_Free) rec_fns)
   166            (map (fn x => (("", []), x)) rec_intr_ts) [] #>
   167          apsnd (ProofContext.theory_of o LocalTheory.exit)) thy0;
   168 
   169     (* prove uniqueness and termination of primrec combinators *)
   170 
   171     val _ = message "Proving termination and uniqueness of primrec functions ...";
   172 
   173     fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
   174       let
   175         val distinct_tac =
   176           (if i < length newTs then
   177              full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 1
   178            else full_simp_tac dist_ss 1);
   179 
   180         val inject = map (fn r => r RS iffD1)
   181           (if i < length newTs then List.nth (constr_inject, i)
   182             else #inject (the (Symtab.lookup dt_info tname)));
   183 
   184         fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
   185           let
   186             val k = length (List.filter is_rec_type cargs)
   187 
   188           in (EVERY [DETERM tac,
   189                 REPEAT (etac ex1E 1), rtac ex1I 1,
   190                 DEPTH_SOLVE_1 (ares_tac [intr] 1),
   191                 REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
   192                 etac elim 1,
   193                 REPEAT_DETERM_N j distinct_tac,
   194                 TRY (dresolve_tac inject 1),
   195                 REPEAT (etac conjE 1), hyp_subst_tac 1,
   196                 REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
   197                 TRY (hyp_subst_tac 1),
   198                 rtac refl 1,
   199                 REPEAT_DETERM_N (n - j - 1) distinct_tac],
   200               intrs, j + 1)
   201           end;
   202 
   203         val (tac', intrs', _) = Library.foldl (mk_unique_constr_tac (length constrs))
   204           ((tac, intrs, 0), constrs);
   205 
   206       in (tac', intrs') end;
   207 
   208     val rec_unique_thms =
   209       let
   210         val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
   211           Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
   212             absfree ("y", T2, set_t $ mk_Free "x" T1 i $ Free ("y", T2)))
   213               (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
   214         val cert = cterm_of thy1
   215         val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
   216           ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
   217         val induct' = cterm_instantiate ((map cert induct_Ps) ~~
   218           (map cert insts)) induct;
   219         val (tac, _) = Library.foldl mk_unique_tac
   220           (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_tac) 1
   221               THEN rewtac (mk_meta_eq choice_eq), rec_intrs),
   222             descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts);
   223 
   224       in split_conj_thm (Goal.prove_global thy1 [] []
   225         (HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac))
   226       end;
   227 
   228     val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
   229 
   230     (* define primrec combinators *)
   231 
   232     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   233     val reccomb_names = map (Sign.full_name (Theory.sign_of thy1))
   234       (if length descr' = 1 then [big_reccomb_name] else
   235         (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   236           (1 upto (length descr'))));
   237     val reccombs = map (fn ((name, T), T') => list_comb
   238       (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
   239         (reccomb_names ~~ recTs ~~ rec_result_Ts);
   240 
   241     val (reccomb_defs, thy2) =
   242       thy1
   243       |> Theory.add_consts_i (map (fn ((name, T), T') =>
   244           (Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   245           (reccomb_names ~~ recTs ~~ rec_result_Ts))
   246       |> (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
   247           ((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
   248            Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
   249              set $ Free ("x", T) $ Free ("y", T'))))))
   250                (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
   251       ||> parent_path flat_names;
   252 
   253 
   254     (* prove characteristic equations for primrec combinators *)
   255 
   256     val _ = message "Proving characteristic theorems for primrec combinators ..."
   257 
   258     val rec_thms = map (fn t => Goal.prove_global thy2 [] [] t
   259       (fn _ => EVERY
   260         [rewrite_goals_tac reccomb_defs,
   261          rtac the1_equality 1,
   262          resolve_tac rec_unique_thms 1,
   263          resolve_tac rec_intrs 1,
   264          REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)]))
   265            (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
   266 
   267   in
   268     thy2
   269     |> Theory.add_path (space_implode "_" new_type_names)
   270     |> PureThy.add_thmss [(("recs", rec_thms), [])]
   271     ||> Theory.parent_path
   272     |-> (fn thms => pair (reccomb_names, Library.flat thms))
   273   end;
   274 
   275 
   276 (***************************** case combinators *******************************)
   277 
   278 fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   279   let
   280     val _ = message "Proving characteristic theorems for case combinators ...";
   281 
   282     val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
   283 
   284     val descr' = List.concat descr;
   285     val recTs = get_rec_types descr' sorts;
   286     val used = foldr add_typ_tfree_names [] recTs;
   287     val newTs = Library.take (length (hd descr), recTs);
   288     val T' = TFree (Name.variant used "'t", HOLogic.typeS);
   289 
   290     fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T';
   291 
   292     val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
   293       let
   294         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   295         val Ts' = map mk_dummyT (List.filter is_rec_type cargs)
   296       in Const ("arbitrary", Ts @ Ts' ---> T')
   297       end) constrs) descr';
   298 
   299     val case_names = map (fn s =>
   300       Sign.full_name (Theory.sign_of thy1) (s ^ "_case")) new_type_names;
   301 
   302     (* define case combinators via primrec combinators *)
   303 
   304     val (case_defs, thy2) = Library.foldl (fn ((defs, thy),
   305       ((((i, (_, _, constrs)), T), name), recname)) =>
   306         let
   307           val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
   308             let
   309               val Ts = map (typ_of_dtyp descr' sorts) cargs;
   310               val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs);
   311               val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
   312               val frees = Library.take (length cargs, frees');
   313               val free = mk_Free "f" (Ts ---> T') j
   314             in
   315              (free, list_abs_free (map dest_Free frees',
   316                list_comb (free, frees)))
   317             end) (constrs ~~ (1 upto length constrs)));
   318 
   319           val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
   320           val fns = (List.concat (Library.take (i, case_dummy_fns))) @
   321             fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns)));
   322           val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
   323           val decl = (Sign.base_name name, caseT, NoSyn);
   324           val def = ((Sign.base_name name) ^ "_def",
   325             Logic.mk_equals (list_comb (Const (name, caseT), fns1),
   326               list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @
   327                 fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) )));
   328           val ([def_thm], thy') =
   329             thy
   330             |> Theory.add_consts_i [decl]
   331             |> (PureThy.add_defs_i false o map Thm.no_attributes) [def];
   332 
   333         in (defs @ [def_thm], thy')
   334         end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
   335           (Library.take (length newTs, reccomb_names)));
   336 
   337     val case_thms = map (map (fn t => Goal.prove_global thy2 [] [] t
   338       (fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1])))
   339           (DatatypeProp.make_cases new_type_names descr sorts thy2)
   340 
   341   in
   342     thy2
   343     |> parent_path flat_names
   344     |> store_thmss "cases" new_type_names case_thms
   345     |-> (fn thmss => pair (thmss, case_names))
   346   end;
   347 
   348 
   349 (******************************* case splitting *******************************)
   350 
   351 fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
   352     casedist_thms case_thms thy =
   353   let
   354     val _ = message "Proving equations for case splitting ...";
   355 
   356     val descr' = List.concat descr;
   357     val recTs = get_rec_types descr' sorts;
   358     val newTs = Library.take (length (hd descr), recTs);
   359 
   360     fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
   361         exhaustion), case_thms'), T) =
   362       let
   363         val cert = cterm_of thy;
   364         val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
   365         val exhaustion' = cterm_instantiate
   366           [(cert lhs, cert (Free ("x", T)))] exhaustion;
   367         val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
   368           (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))])
   369       in
   370         (Goal.prove_global thy [] [] t1 tacf,
   371          Goal.prove_global thy [] [] t2 tacf)
   372       end;
   373 
   374     val split_thm_pairs = map prove_split_thms
   375       ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
   376         dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
   377 
   378     val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
   379 
   380   in
   381     thy
   382     |> store_thms "split" new_type_names split_thms
   383     ||>> store_thms "split_asm" new_type_names split_asm_thms
   384     |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
   385   end;
   386 
   387 (******************************* size functions *******************************)
   388 
   389 fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   390   if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt =>
   391     is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs)
   392       (List.concat descr)
   393   then
   394     ([], thy)
   395   else
   396   let
   397     val _ = message "Proving equations for size function ...";
   398 
   399     val big_name = space_implode "_" new_type_names;
   400     val thy1 = add_path flat_names big_name thy;
   401 
   402     val descr' = flat descr;
   403     val recTs = get_rec_types descr' sorts;
   404 
   405     val size_name = "Nat.size";
   406     val size_names = replicate (length (hd descr)) size_name @
   407       map (Sign.full_name (Theory.sign_of thy1)) (DatatypeProp.indexify_names
   408         (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs))));
   409     val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names
   410       (map (fn T => name_of_typ T ^ "_size") recTs));
   411 
   412     fun plus (t1, t2) = Const ("HOL.plus", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2;
   413 
   414     fun make_sizefun (_, cargs) =
   415       let
   416         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   417         val k = length (filter is_rec_type cargs);
   418         val t = if k = 0 then HOLogic.zero else
   419           foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.mk_nat 1])
   420       in
   421         foldr (fn (T, t') => Abs ("x", T, t')) t (Ts @ replicate k HOLogic.natT)
   422       end;
   423 
   424     val fs = maps (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr';
   425     val fTs = map fastype_of fs;
   426 
   427     fun instance_size_class tyco thy =
   428       let
   429         val size_sort = ["Nat.size"];
   430         val n = Sign.arity_number thy tyco;
   431       in
   432         thy
   433         |> AxClass.prove_arity (tyco, replicate n HOLogic.typeS, size_sort)
   434              (ClassPackage.intro_classes_tac [])
   435       end
   436 
   437     val (size_def_thms, thy') =
   438       thy1
   439       |> Theory.add_consts_i (map (fn (s, T) =>
   440            (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   441            (Library.drop (length (hd descr), size_names ~~ recTs)))
   442       |> fold (fn (_, (name, _, _)) => instance_size_class name) descr'
   443       |> PureThy.add_defs_i true (map (Thm.no_attributes o (fn (((s, T), def_name), rec_name) =>
   444            (def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
   445             list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs)))))
   446             (size_names ~~ recTs ~~ def_names ~~ reccomb_names))
   447       ||> parent_path flat_names;
   448 
   449     val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
   450 
   451     val size_thms = map (fn t => Goal.prove_global thy' [] [] t
   452       (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1]))
   453         (DatatypeProp.make_size descr sorts thy')
   454 
   455   in
   456     thy'
   457     |> Theory.add_path big_name
   458     |> PureThy.add_thmss [(("size", size_thms), [])]
   459     ||> Theory.parent_path
   460     |-> (fn thmss => pair (flat thmss))
   461   end;
   462 
   463 fun prove_weak_case_congs new_type_names descr sorts thy =
   464   let
   465     fun prove_weak_case_cong t =
   466        Goal.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
   467          (fn prems => EVERY [rtac ((hd prems) RS arg_cong) 1])
   468 
   469     val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
   470       new_type_names descr sorts thy)
   471 
   472   in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
   473 
   474 (************************* additional theorems for TFL ************************)
   475 
   476 fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
   477   let
   478     val _ = message "Proving additional theorems for TFL ...";
   479 
   480     fun prove_nchotomy (t, exhaustion) =
   481       let
   482         (* For goal i, select the correct disjunct to attack, then prove it *)
   483         fun tac i 0 = EVERY [TRY (rtac disjI1 i),
   484               hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
   485           | tac i n = rtac disjI2 i THEN tac i (n - 1)
   486       in 
   487         Goal.prove_global thy [] [] t (fn _ =>
   488           EVERY [rtac allI 1,
   489            exh_tac (K exhaustion) 1,
   490            ALLGOALS (fn i => tac i (i-1))])
   491       end;
   492 
   493     val nchotomys =
   494       map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
   495 
   496   in thy |> store_thms "nchotomy" new_type_names nchotomys end;
   497 
   498 fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
   499   let
   500     fun prove_case_cong ((t, nchotomy), case_rewrites) =
   501       let
   502         val (Const ("==>", _) $ tm $ _) = t;
   503         val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
   504         val cert = cterm_of (Theory.sign_of thy);
   505         val nchotomy' = nchotomy RS spec;
   506         val nchotomy'' = cterm_instantiate
   507           [(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy'
   508       in
   509         Goal.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
   510           (fn prems => 
   511             let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
   512             in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1,
   513                 cut_facts_tac [nchotomy''] 1,
   514                 REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
   515                 REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
   516             end)
   517       end;
   518 
   519     val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
   520       new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
   521 
   522   in thy |> store_thms "case_cong" new_type_names case_congs end;
   523 
   524 end;