src/HOL/Tools/datatype_abs_proofs.ML
author berghofe
Mon Jan 29 13:26:04 2001 +0100 (2001-01-29 ago)
changeset 10988 e0016a009c17
parent 10911 eb5721204b38
child 11435 bd1a7f53c11b
permissions -rw-r--r--
Splitting of arguments of product types in induction rules is now less
aggressive.
     1 (*  Title:      HOL/Tools/datatype_abs_proofs.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer
     4     Copyright   1998  TU Muenchen
     5 
     6 Proofs and defintions independent of concrete representation
     7 of datatypes  (i.e. requiring only abstract properties such as
     8 injectivity / distinctness of constructors and induction)
     9 
    10  - case distinction (exhaustion) theorems
    11  - characteristic equations for primrec combinators
    12  - characteristic equations for case combinators
    13  - equations for splitting "P (case ...)" expressions
    14  - datatype size function
    15  - "nchotomy" and "case_cong" theorems for TFL
    16 
    17 *)
    18 
    19 signature DATATYPE_ABS_PROOFS =
    20 sig
    21   val prove_casedist_thms : string list -> (int * (string * DatatypeAux.dtyp list *
    22     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    23       thm -> theory attribute list -> theory -> theory * thm list
    24   val prove_primrec_thms : bool -> string list -> (int * (string * DatatypeAux.dtyp list *
    25     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    26       DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list ->
    27         simpset -> thm -> theory -> theory * (string list * thm list)
    28   val prove_case_thms : bool -> string list -> (int * (string * DatatypeAux.dtyp list *
    29     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    30       string list -> thm list -> theory -> theory * (thm list list * string list)
    31   val prove_split_thms : string list -> (int * (string * DatatypeAux.dtyp list *
    32     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    33       thm list list -> thm list list -> thm list -> thm list list -> theory ->
    34         theory * (thm * thm) list
    35   val prove_size_thms : bool -> string list -> (int * (string * DatatypeAux.dtyp list *
    36     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    37       string list -> thm list -> theory -> theory * thm list
    38   val prove_nchotomys : string list -> (int * (string * DatatypeAux.dtyp list *
    39     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    40       thm list -> theory -> theory * thm list
    41   val prove_weak_case_congs : string list -> (int * (string * DatatypeAux.dtyp list *
    42     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    43       theory -> theory * thm list
    44   val prove_case_congs : string list -> (int * (string * DatatypeAux.dtyp list *
    45     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    46       thm list -> thm list list -> theory -> theory * thm list
    47 end;
    48 
    49 structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
    50 struct
    51 
    52 open DatatypeAux;
    53 
    54 val thin = read_instantiate_sg (Theory.sign_of Set.thy) [("V", "?X : ?Y")] thin_rl;
    55 
    56 val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
    57 
    58 (************************ case distinction theorems ***************************)
    59 
    60 fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy =
    61   let
    62     val _ = message "Proving case distinction theorems ...";
    63 
    64     val descr' = flat descr;
    65     val recTs = get_rec_types descr' sorts;
    66     val newTs = take (length (hd descr), recTs);
    67 
    68     val {maxidx, ...} = rep_thm induct;
    69     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
    70 
    71     fun prove_casedist_thm ((i, t), T) =
    72       let
    73         val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
    74           Abs ("z", T', Const ("True", T''))) induct_Ps;
    75         val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
    76           Var (("P", 0), HOLogic.boolT))
    77         val insts = take (i, dummyPs) @ (P::(drop (i + 1, dummyPs)));
    78         val cert = cterm_of (Theory.sign_of thy);
    79         val insts' = (map cert induct_Ps) ~~ (map cert insts);
    80         val induct' = refl RS ((nth_elem (i,
    81           split_conj_thm (cterm_instantiate insts' induct))) RSN (2, rev_mp))
    82 
    83       in prove_goalw_cterm [] (cert t) (fn prems =>
    84         [rtac induct' 1,
    85          REPEAT (rtac TrueI 1),
    86          REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
    87          REPEAT (rtac TrueI 1)])
    88       end;
    89 
    90     val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
    91       (DatatypeProp.make_casedists descr sorts) ~~ newTs)
    92   in thy |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms end;
    93 
    94 
    95 (*************************** primrec combinators ******************************)
    96 
    97 fun prove_primrec_thms flat_names new_type_names descr sorts
    98     (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
    99   let
   100     val _ = message "Constructing primrec combinators ...";
   101 
   102     val fun_rel_comp_name = Sign.intern_const (sign_of Relation.thy) "fun_rel_comp";
   103     val [fun_rel_comp_def, o_def] =
   104       map (get_thm Relation.thy) ["fun_rel_comp_def", "o_def"];
   105 
   106     val big_name = space_implode "_" new_type_names;
   107     val thy0 = add_path flat_names big_name thy;
   108 
   109     val descr' = flat descr;
   110     val recTs = get_rec_types descr' sorts;
   111     val used = foldr add_typ_tfree_names (recTs, []);
   112     val newTs = take (length (hd descr), recTs);
   113 
   114     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
   115 
   116     val big_rec_name' = big_name ^ "_rec_set";
   117     val rec_set_names = map (Sign.full_name (Theory.sign_of thy0))
   118       (if length descr' = 1 then [big_rec_name'] else
   119         (map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
   120           (1 upto (length descr'))));
   121 
   122     val rec_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~
   123       replicate (length descr') HOLogic.termS);
   124 
   125     val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) =>
   126       map (fn (_, cargs) =>
   127         let
   128           val Ts = map (typ_of_dtyp descr' sorts) cargs;
   129           val recs = filter (is_rec_type o fst) (cargs ~~ Ts);
   130 
   131           fun mk_argT (DtRec k, _) = nth_elem (k, rec_result_Ts)
   132             | mk_argT (DtType ("fun", [_, DtRec k]), Type ("fun", [T, _])) =
   133                T --> nth_elem (k, rec_result_Ts);
   134 
   135           val argTs = Ts @ map mk_argT recs
   136         in argTs ---> nth_elem (i, rec_result_Ts)
   137         end) constrs) descr');
   138 
   139     val rec_set_Ts = map (fn (T1, T2) => reccomb_fn_Ts ---> HOLogic.mk_setT
   140       (HOLogic.mk_prodT (T1, T2))) (recTs ~~ rec_result_Ts);
   141 
   142     val rec_fns = map (uncurry (mk_Free "f"))
   143       (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
   144     val rec_sets = map (fn c => list_comb (Const c, rec_fns))
   145       (rec_set_names ~~ rec_set_Ts);
   146 
   147     (* introduction rules for graph of primrec function *)
   148 
   149     fun make_rec_intr T set_name ((rec_intr_ts, l), (cname, cargs)) =
   150       let
   151         fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
   152           let val free1 = mk_Free "x" U j
   153           in (case (dt, U) of
   154              (DtRec m, _) =>
   155                let val free2 = mk_Free "y" (nth_elem (m, rec_result_Ts)) k
   156                in (j + 1, k + 1, (HOLogic.mk_Trueprop (HOLogic.mk_mem
   157                  (HOLogic.mk_prod (free1, free2), nth_elem (m, rec_sets))))::prems,
   158                    free1::t1s, free2::t2s)
   159                end
   160            | (DtType ("fun", [_, DtRec m]), U' as Type ("fun", [T', _])) =>
   161                let val free2 = mk_Free "y" (T' --> nth_elem (m, rec_result_Ts)) k
   162                in (j + 1, k + 1, (HOLogic.mk_Trueprop (HOLogic.mk_mem (free2,
   163                  Const (fun_rel_comp_name, [U', snd (strip_type (nth_elem (m, rec_set_Ts)))] --->
   164                    HOLogic.mk_setT (T' --> nth_elem (m, rec_result_Ts))) $
   165                      free1 $ nth_elem (m, rec_sets))))::prems, free1::t1s, free2::t2s)
   166                end
   167            | _ => (j + 1, k, prems, free1::t1s, t2s))
   168           end;
   169 
   170         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   171         val (_, _, prems, t1s, t2s) = foldr mk_prem (cargs ~~ Ts, (1, 1, [], [], []))
   172 
   173       in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop (HOLogic.mk_mem
   174         (HOLogic.mk_prod (list_comb (Const (cname, Ts ---> T), t1s),
   175           list_comb (nth_elem (l, rec_fns), t1s @ t2s)), set_name)))], l + 1)
   176       end;
   177 
   178     val (rec_intr_ts, _) = foldl (fn (x, ((d, T), set_name)) =>
   179       foldl (make_rec_intr T set_name) (x, #3 (snd d)))
   180         (([], 0), descr' ~~ recTs ~~ rec_sets);
   181 
   182     val (thy1, {intrs = rec_intrs, elims = rec_elims, ...}) =
   183       setmp InductivePackage.quiet_mode (!quiet_mode)
   184         (InductivePackage.add_inductive_i false true big_rec_name' false false true
   185            rec_sets [] (map (fn x => (("", x), [])) rec_intr_ts) [fun_rel_comp_mono] []) thy0;
   186 
   187     (* prove uniqueness and termination of primrec combinators *)
   188 
   189     val _ = message "Proving termination and uniqueness of primrec functions ...";
   190 
   191     fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
   192       let
   193         val distinct_tac = (etac Pair_inject 1) THEN
   194           (if i < length newTs then
   195              full_simp_tac (HOL_ss addsimps (nth_elem (i, dist_rewrites))) 1
   196            else full_simp_tac dist_ss 1);
   197 
   198         val inject = map (fn r => r RS iffD1)
   199           (if i < length newTs then nth_elem (i, constr_inject)
   200             else #inject (the (Symtab.lookup (dt_info, tname))));
   201 
   202         fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
   203           let
   204             val k = length (filter is_rec_type cargs)
   205 
   206           in (EVERY [DETERM tac,
   207                 REPEAT (dtac fun_rel_comp_unique 1),
   208                 REPEAT (etac ex1E 1), rtac ex1I 1,
   209                 DEPTH_SOLVE_1 (ares_tac [intr] 1),
   210                 REPEAT_DETERM_N k (etac thin 1),
   211                 etac elim 1,
   212                 REPEAT_DETERM_N j distinct_tac,
   213                 etac Pair_inject 1, TRY (dresolve_tac inject 1),
   214                 REPEAT (etac conjE 1), hyp_subst_tac 1,
   215                 REPEAT (etac allE 1),
   216                 REPEAT (dtac mp 1 THEN atac 1),
   217                 TRY (hyp_subst_tac 1),
   218                 rtac refl 1,
   219                 REPEAT_DETERM_N (n - j - 1) distinct_tac],
   220               intrs, j + 1)
   221           end;
   222 
   223         val (tac', intrs', _) = foldl (mk_unique_constr_tac (length constrs))
   224           ((tac, intrs, 0), constrs);
   225 
   226       in (tac', intrs') end;
   227 
   228     val rec_unique_thms =
   229       let
   230         val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
   231           Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
   232             absfree ("y", T2, HOLogic.mk_mem (HOLogic.mk_prod
   233               (mk_Free "x" T1 i, Free ("y", T2)), set_t)))
   234                 (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
   235         val cert = cterm_of (Theory.sign_of thy1)
   236         val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
   237           ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
   238         val induct' = cterm_instantiate ((map cert induct_Ps) ~~
   239           (map cert insts)) induct;
   240         val (tac, _) = foldl mk_unique_tac
   241           (((rtac induct' THEN_ALL_NEW atomize_strip_tac) 1, rec_intrs),
   242             descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts);
   243 
   244       in split_conj_thm (prove_goalw_cterm []
   245         (cert (HOLogic.mk_Trueprop (mk_conj rec_unique_ts))) (K [tac]))
   246       end;
   247 
   248     val rec_total_thms = map (fn r =>
   249       r RS ex1_implies_ex RS (some_eq_ex RS iffD2)) rec_unique_thms;
   250 
   251     (* define primrec combinators *)
   252 
   253     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   254     val reccomb_names = map (Sign.full_name (Theory.sign_of thy1))
   255       (if length descr' = 1 then [big_reccomb_name] else
   256         (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   257           (1 upto (length descr'))));
   258     val reccombs = map (fn ((name, T), T') => list_comb
   259       (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
   260         (reccomb_names ~~ recTs ~~ rec_result_Ts);
   261 
   262     val (thy2, reccomb_defs) = thy1 |>
   263       Theory.add_consts_i (map (fn ((name, T), T') =>
   264         (Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   265           (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
   266       (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
   267         ((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
   268            Const ("Eps", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
   269              HOLogic.mk_mem (HOLogic.mk_prod (Free ("x", T), Free ("y", T')), set))))))
   270                (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |>>
   271       parent_path flat_names;
   272 
   273 
   274     (* prove characteristic equations for primrec combinators *)
   275 
   276     val _ = message "Proving characteristic theorems for primrec combinators ..."
   277 
   278     val rec_thms = map (fn t => prove_goalw_cterm reccomb_defs
   279       (cterm_of (Theory.sign_of thy2) t) (fn _ =>
   280         [rtac some1_equality 1,
   281          resolve_tac rec_unique_thms 1,
   282          resolve_tac rec_intrs 1,
   283          rewrite_goals_tac [o_def, fun_rel_comp_def],
   284          REPEAT ((rtac CollectI 1 THEN rtac allI 1) ORELSE resolve_tac rec_total_thms 1)]))
   285            (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
   286 
   287   in
   288     thy2 |> Theory.add_path (space_implode "_" new_type_names) |>
   289     PureThy.add_thmss [(("recs", rec_thms), [])] |>>
   290     Theory.parent_path |> apsnd (pair reccomb_names o flat)
   291   end;
   292 
   293 
   294 (***************************** case combinators *******************************)
   295 
   296 fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   297   let
   298     val _ = message "Proving characteristic theorems for case combinators ...";
   299 
   300     val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
   301 
   302     val descr' = flat descr;
   303     val recTs = get_rec_types descr' sorts;
   304     val used = foldr add_typ_tfree_names (recTs, []);
   305     val newTs = take (length (hd descr), recTs);
   306     val T' = TFree (variant used "'t", HOLogic.termS);
   307 
   308     fun mk_dummyT (DtRec _) = T'
   309       | mk_dummyT (DtType ("fun", [T, _])) = typ_of_dtyp descr' sorts T --> T'
   310 
   311     val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
   312       let
   313         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   314         val Ts' = map mk_dummyT (filter is_rec_type cargs)
   315       in Const ("arbitrary", Ts @ Ts' ---> T')
   316       end) constrs) descr';
   317 
   318     val case_names = map (fn s =>
   319       Sign.full_name (Theory.sign_of thy1) (s ^ "_case")) new_type_names;
   320 
   321     (* define case combinators via primrec combinators *)
   322 
   323     val (case_defs, thy2) = foldl (fn ((defs, thy),
   324       ((((i, (_, _, constrs)), T), name), recname)) =>
   325         let
   326           val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
   327             let
   328               val Ts = map (typ_of_dtyp descr' sorts) cargs;
   329               val Ts' = Ts @ map mk_dummyT (filter is_rec_type cargs);
   330               val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
   331               val frees = take (length cargs, frees');
   332               val free = mk_Free "f" (Ts ---> T') j
   333             in
   334              (free, list_abs_free (map dest_Free frees',
   335                list_comb (free, frees)))
   336             end) (constrs ~~ (1 upto length constrs)));
   337 
   338           val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
   339           val fns = (flat (take (i, case_dummy_fns))) @
   340             fns2 @ (flat (drop (i + 1, case_dummy_fns)));
   341           val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
   342           val decl = (Sign.base_name name, caseT, NoSyn);
   343           val def = ((Sign.base_name name) ^ "_def",
   344             Logic.mk_equals (list_comb (Const (name, caseT), fns1),
   345               list_comb (reccomb, (flat (take (i, case_dummy_fns))) @
   346                 fns2 @ (flat (drop (i + 1, case_dummy_fns))) )));
   347           val (thy', [def_thm]) = thy |>
   348             Theory.add_consts_i [decl] |> (PureThy.add_defs_i false o map Thm.no_attributes) [def];
   349 
   350         in (defs @ [def_thm], thy')
   351         end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
   352           (take (length newTs, reccomb_names)));
   353 
   354     val case_thms = map (map (fn t => prove_goalw_cterm (case_defs @
   355       (map mk_meta_eq primrec_thms)) (cterm_of (Theory.sign_of thy2) t)
   356         (fn _ => [rtac refl 1])))
   357           (DatatypeProp.make_cases new_type_names descr sorts thy2)
   358 
   359   in
   360     thy2 |> Theory.add_trrules_i
   361       (DatatypeProp.make_case_trrules new_type_names descr) |>
   362     parent_path flat_names |>
   363     store_thmss "cases" new_type_names case_thms |>
   364     apsnd (rpair case_names)
   365   end;
   366 
   367 
   368 (******************************* case splitting *******************************)
   369 
   370 fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
   371     casedist_thms case_thms thy =
   372   let
   373     val _ = message "Proving equations for case splitting ...";
   374 
   375     val descr' = flat descr;
   376     val recTs = get_rec_types descr' sorts;
   377     val newTs = take (length (hd descr), recTs);
   378 
   379     fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
   380         exhaustion), case_thms'), T) =
   381       let
   382         val cert = cterm_of (Theory.sign_of thy);
   383         val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
   384         val exhaustion' = cterm_instantiate
   385           [(cert lhs, cert (Free ("x", T)))] exhaustion;
   386         val tacsf = K [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
   387           (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))]
   388       in
   389         (prove_goalw_cterm [] (cert t1) tacsf,
   390          prove_goalw_cterm [] (cert t2) tacsf)
   391       end;
   392 
   393     val split_thm_pairs = map prove_split_thms
   394       ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
   395         dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
   396 
   397     val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
   398 
   399   in
   400     thy |> store_thms "split" new_type_names split_thms |>>>
   401       store_thms "split_asm" new_type_names split_asm_thms |> apsnd ListPair.zip
   402   end;
   403 
   404 (******************************* size functions *******************************)
   405 
   406 fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   407   if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
   408     (fn (DtType ("fun", [_, DtRec _])) => true | _ => false) cargs) constrs) (flat descr)
   409   then
   410     (thy, [])
   411   else
   412   let
   413     val _ = message "Proving equations for size function ...";
   414 
   415     val big_name = space_implode "_" new_type_names;
   416     val thy1 = add_path flat_names big_name thy;
   417 
   418     val descr' = flat descr;
   419     val recTs = get_rec_types descr' sorts;
   420 
   421     val size_name = Sign.intern_const (Theory.sign_of (theory "NatArith")) "size";
   422     val size_names = replicate (length (hd descr)) size_name @
   423       map (Sign.full_name (Theory.sign_of thy1)) (DatatypeProp.indexify_names
   424         (map (fn T => name_of_typ T ^ "_size") (drop (length (hd descr), recTs))));
   425     val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names
   426       (map (fn T => name_of_typ T ^ "_size") recTs));
   427 
   428     fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2;
   429 
   430     fun make_sizefun (_, cargs) =
   431       let
   432         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   433         val k = length (filter is_rec_type cargs);
   434         val t = if k = 0 then HOLogic.zero else
   435           foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.mk_nat 1])
   436       in
   437         foldr (fn (T, t') => Abs ("x", T, t')) (Ts @ replicate k HOLogic.natT, t)
   438       end;
   439 
   440     val fs = flat (map (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr');
   441     val fTs = map fastype_of fs;
   442 
   443     val (thy', size_def_thms) = thy1 |>
   444       Theory.add_consts_i (map (fn (s, T) =>
   445         (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   446           (drop (length (hd descr), size_names ~~ recTs))) |>
   447       (PureThy.add_defs_i true o map Thm.no_attributes) (map (fn (((s, T), def_name), rec_name) =>
   448         (def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
   449           list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs))))
   450             (size_names ~~ recTs ~~ def_names ~~ reccomb_names)) |>>
   451       parent_path flat_names;
   452 
   453     val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
   454 
   455     val size_thms = map (fn t => prove_goalw_cterm rewrites
   456       (cterm_of (Theory.sign_of thy') t) (fn _ => [rtac refl 1]))
   457         (DatatypeProp.make_size descr sorts thy')
   458 
   459   in
   460     thy' |> Theory.add_path big_name |>
   461     PureThy.add_thmss [(("size", size_thms), [])] |>>
   462     Theory.parent_path |> apsnd flat
   463   end;
   464 
   465 fun prove_weak_case_congs new_type_names descr sorts thy =
   466   let
   467     fun prove_weak_case_cong t =
   468        prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) t)
   469          (fn prems => [rtac ((hd prems) RS arg_cong) 1])
   470 
   471     val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
   472       new_type_names descr sorts thy)
   473 
   474   in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
   475 
   476 (************************* additional theorems for TFL ************************)
   477 
   478 fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
   479   let
   480     val _ = message "Proving additional theorems for TFL ...";
   481 
   482     fun prove_nchotomy (t, exhaustion) =
   483       let
   484         (* For goal i, select the correct disjunct to attack, then prove it *)
   485         fun tac i 0 = EVERY [TRY (rtac disjI1 i),
   486               hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
   487           | tac i n = rtac disjI2 i THEN tac i (n - 1)
   488       in 
   489         prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) t) (fn _ =>
   490           [rtac allI 1,
   491            exh_tac (K exhaustion) 1,
   492            ALLGOALS (fn i => tac i (i-1))])
   493       end;
   494 
   495     val nchotomys =
   496       map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
   497 
   498   in thy |> store_thms "nchotomy" new_type_names nchotomys end;
   499 
   500 fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
   501   let
   502     fun prove_case_cong ((t, nchotomy), case_rewrites) =
   503       let
   504         val (Const ("==>", _) $ tm $ _) = t;
   505         val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
   506         val cert = cterm_of (Theory.sign_of thy);
   507         val nchotomy' = nchotomy RS spec;
   508         val nchotomy'' = cterm_instantiate
   509           [(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy'
   510       in
   511         prove_goalw_cterm [] (cert t) (fn prems => 
   512           let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
   513           in [simp_tac (HOL_ss addsimps [hd prems]) 1,
   514               cut_facts_tac [nchotomy''] 1,
   515               REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
   516               REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
   517           end)
   518       end;
   519 
   520     val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
   521       new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
   522 
   523   in thy |> store_thms "case_cong" new_type_names case_congs end;
   524 
   525 end;