src/HOL/Tools/datatype_abs_proofs.ML
author berghofe
Wed Mar 15 23:36:46 2000 +0100 (2000-03-15)
changeset 8477 17231d71171a
parent 8436 8a87fa482baf
child 8601 8fb3a81b4ccf
permissions -rw-r--r--
- Fixed bug in prove_casedist_thms (proof failed because of
name clashes)
- Now returns theorems with correct names in derivations
     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_case_congs : string list -> (int * (string * DatatypeAux.dtyp list *
    42     (string * DatatypeAux.dtyp list) list)) list 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 val thin = read_instantiate_sg (Theory.sign_of Set.thy) [("V", "?X : ?Y")] thin_rl;
    52 
    53 val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
    54 
    55 (************************ case distinction theorems ***************************)
    56 
    57 fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy =
    58   let
    59     val _ = message "Proving case distinction theorems ...";
    60 
    61     val descr' = flat descr;
    62     val recTs = get_rec_types descr' sorts;
    63     val newTs = take (length (hd descr), recTs);
    64 
    65     val {maxidx, ...} = rep_thm induct;
    66     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
    67 
    68     fun prove_casedist_thm ((i, t), T) =
    69       let
    70         val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
    71           Abs ("z", T', Const ("True", T''))) induct_Ps;
    72         val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
    73           Var (("P", 0), HOLogic.boolT))
    74         val insts = take (i, dummyPs) @ (P::(drop (i + 1, dummyPs)));
    75         val cert = cterm_of (Theory.sign_of thy);
    76         val insts' = (map cert induct_Ps) ~~ (map cert insts);
    77         val induct' = refl RS ((nth_elem (i,
    78           split_conj_thm (cterm_instantiate insts' induct))) RSN (2, rev_mp))
    79 
    80       in prove_goalw_cterm [] (cert t) (fn prems =>
    81         [rtac induct' 1,
    82          REPEAT (rtac TrueI 1),
    83          REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
    84          REPEAT (rtac TrueI 1)])
    85       end;
    86 
    87     val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
    88       (DatatypeProp.make_casedists descr sorts) ~~ newTs)
    89   in thy |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms end;
    90 
    91 
    92 (*************************** primrec combinators ******************************)
    93 
    94 fun prove_primrec_thms flat_names new_type_names descr sorts
    95     (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
    96   let
    97     val _ = message "Constructing primrec combinators ...";
    98 
    99     val fun_rel_comp_name = Sign.intern_const (sign_of Relation.thy) "fun_rel_comp";
   100     val [fun_rel_comp_def, o_def] =
   101       map (get_thm Relation.thy) ["fun_rel_comp_def", "o_def"];
   102 
   103     val big_name = space_implode "_" new_type_names;
   104     val thy0 = add_path flat_names big_name thy;
   105 
   106     val descr' = flat descr;
   107     val recTs = get_rec_types descr' sorts;
   108     val used = foldr add_typ_tfree_names (recTs, []);
   109     val newTs = take (length (hd descr), recTs);
   110 
   111     val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
   112 
   113     val big_rec_name' = big_name ^ "_rec_set";
   114     val rec_set_names = map (Sign.full_name (Theory.sign_of thy0))
   115       (if length descr' = 1 then [big_rec_name'] else
   116         (map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
   117           (1 upto (length descr'))));
   118 
   119     val rec_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~
   120       replicate (length descr') HOLogic.termS);
   121 
   122     val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) =>
   123       map (fn (_, cargs) =>
   124         let
   125           val Ts = map (typ_of_dtyp descr' sorts) cargs;
   126           val recs = filter (is_rec_type o fst) (cargs ~~ Ts);
   127 
   128           fun mk_argT (DtRec k, _) = nth_elem (k, rec_result_Ts)
   129             | mk_argT (DtType ("fun", [_, DtRec k]), Type ("fun", [T, _])) =
   130                T --> nth_elem (k, rec_result_Ts);
   131 
   132           val argTs = Ts @ map mk_argT recs
   133         in argTs ---> nth_elem (i, rec_result_Ts)
   134         end) constrs) descr');
   135 
   136     val rec_set_Ts = map (fn (T1, T2) => reccomb_fn_Ts ---> HOLogic.mk_setT
   137       (HOLogic.mk_prodT (T1, T2))) (recTs ~~ rec_result_Ts);
   138 
   139     val rec_fns = map (uncurry (mk_Free "f"))
   140       (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
   141     val rec_sets = map (fn c => list_comb (Const c, rec_fns))
   142       (rec_set_names ~~ rec_set_Ts);
   143 
   144     (* introduction rules for graph of primrec function *)
   145 
   146     fun make_rec_intr T set_name ((rec_intr_ts, l), (cname, cargs)) =
   147       let
   148         fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
   149           let val free1 = mk_Free "x" U j
   150           in (case (dt, U) of
   151              (DtRec m, _) =>
   152                let val free2 = mk_Free "y" (nth_elem (m, rec_result_Ts)) k
   153                in (j + 1, k + 1, (HOLogic.mk_Trueprop (HOLogic.mk_mem
   154                  (HOLogic.mk_prod (free1, free2), nth_elem (m, rec_sets))))::prems,
   155                    free1::t1s, free2::t2s)
   156                end
   157            | (DtType ("fun", [_, DtRec m]), U' as Type ("fun", [T', _])) =>
   158                let val free2 = mk_Free "y" (T' --> nth_elem (m, rec_result_Ts)) k
   159                in (j + 1, k + 1, (HOLogic.mk_Trueprop (HOLogic.mk_mem (free2,
   160                  Const (fun_rel_comp_name, [U', snd (strip_type (nth_elem (m, rec_set_Ts)))] --->
   161                    HOLogic.mk_setT (T' --> nth_elem (m, rec_result_Ts))) $
   162                      free1 $ nth_elem (m, rec_sets))))::prems, free1::t1s, free2::t2s)
   163                end
   164            | _ => (j + 1, k, prems, free1::t1s, t2s))
   165           end;
   166 
   167         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   168         val (_, _, prems, t1s, t2s) = foldr mk_prem (cargs ~~ Ts, (1, 1, [], [], []))
   169 
   170       in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop (HOLogic.mk_mem
   171         (HOLogic.mk_prod (list_comb (Const (cname, Ts ---> T), t1s),
   172           list_comb (nth_elem (l, rec_fns), t1s @ t2s)), set_name)))], l + 1)
   173       end;
   174 
   175     val (rec_intr_ts, _) = foldl (fn (x, ((d, T), set_name)) =>
   176       foldl (make_rec_intr T set_name) (x, #3 (snd d)))
   177         (([], 0), descr' ~~ recTs ~~ rec_sets);
   178 
   179     val (thy1, {intrs = rec_intrs, elims = rec_elims, ...}) =
   180       setmp InductivePackage.quiet_mode (!quiet_mode)
   181         (InductivePackage.add_inductive_i false true big_rec_name' false false true
   182            rec_sets [] (map (fn x => (("", x), [])) rec_intr_ts) [fun_rel_comp_mono] []) thy0;
   183 
   184     (* prove uniqueness and termination of primrec combinators *)
   185 
   186     val _ = message "Proving termination and uniqueness of primrec functions ...";
   187 
   188     fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
   189       let
   190         val distinct_tac = (etac Pair_inject 1) THEN
   191           (if i < length newTs then
   192              full_simp_tac (HOL_ss addsimps (nth_elem (i, dist_rewrites))) 1
   193            else full_simp_tac dist_ss 1);
   194 
   195         val inject = map (fn r => r RS iffD1)
   196           (if i < length newTs then nth_elem (i, constr_inject)
   197             else #inject (the (Symtab.lookup (dt_info, tname))));
   198 
   199         fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
   200           let
   201             val k = length (filter is_rec_type cargs)
   202 
   203           in (EVERY [DETERM tac,
   204                 REPEAT (dtac fun_rel_comp_unique 1),
   205                 REPEAT (etac ex1E 1), rtac ex1I 1,
   206                 DEPTH_SOLVE_1 (ares_tac [intr] 1),
   207                 REPEAT_DETERM_N k (etac thin 1),
   208                 etac elim 1,
   209                 REPEAT_DETERM_N j distinct_tac,
   210                 etac Pair_inject 1, TRY (dresolve_tac inject 1),
   211                 REPEAT (etac conjE 1), hyp_subst_tac 1,
   212                 REPEAT (etac allE 1),
   213                 REPEAT (dtac mp 1 THEN atac 1),
   214                 TRY (hyp_subst_tac 1),
   215                 rtac refl 1,
   216                 REPEAT_DETERM_N (n - j - 1) distinct_tac],
   217               intrs, j + 1)
   218           end;
   219 
   220         val (tac', intrs', _) = foldl (mk_unique_constr_tac (length constrs))
   221           ((tac, intrs, 0), constrs);
   222 
   223       in (tac', intrs') end;
   224 
   225     val rec_unique_thms =
   226       let
   227         val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
   228           Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
   229             absfree ("y", T2, HOLogic.mk_mem (HOLogic.mk_prod
   230               (mk_Free "x" T1 i, Free ("y", T2)), set_t)))
   231                 (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
   232         val cert = cterm_of (Theory.sign_of thy1)
   233         val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
   234           ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
   235         val induct' = cterm_instantiate ((map cert induct_Ps) ~~
   236           (map cert insts)) induct;
   237         val (tac, _) = foldl mk_unique_tac
   238           ((rtac induct' 1, rec_intrs), descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts)
   239 
   240       in split_conj_thm (prove_goalw_cterm []
   241         (cert (HOLogic.mk_Trueprop (mk_conj rec_unique_ts))) (K [tac]))
   242       end;
   243 
   244     val rec_total_thms = map (fn r =>
   245       r RS ex1_implies_ex RS (select_eq_Ex RS iffD2)) rec_unique_thms;
   246 
   247     (* define primrec combinators *)
   248 
   249     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   250     val reccomb_names = map (Sign.full_name (Theory.sign_of thy1))
   251       (if length descr' = 1 then [big_reccomb_name] else
   252         (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   253           (1 upto (length descr'))));
   254     val reccombs = map (fn ((name, T), T') => list_comb
   255       (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
   256         (reccomb_names ~~ recTs ~~ rec_result_Ts);
   257 
   258     val (thy2, reccomb_defs) = thy1 |>
   259       Theory.add_consts_i (map (fn ((name, T), T') =>
   260         (Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   261           (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
   262       (PureThy.add_defs_i o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
   263         ((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
   264            Const ("Eps", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
   265              HOLogic.mk_mem (HOLogic.mk_prod (Free ("x", T), Free ("y", T')), set))))))
   266                (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |>>
   267       parent_path flat_names;
   268 
   269 
   270     (* prove characteristic equations for primrec combinators *)
   271 
   272     val _ = message "Proving characteristic theorems for primrec combinators ..."
   273 
   274     val rec_thms = map (fn t => prove_goalw_cterm reccomb_defs
   275       (cterm_of (Theory.sign_of thy2) t) (fn _ =>
   276         [rtac select1_equality 1,
   277          resolve_tac rec_unique_thms 1,
   278          resolve_tac rec_intrs 1,
   279          rewrite_goals_tac [o_def, fun_rel_comp_def],
   280          REPEAT ((rtac CollectI 1 THEN rtac allI 1) ORELSE resolve_tac rec_total_thms 1)]))
   281            (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
   282 
   283   in
   284     thy2 |> Theory.add_path (space_implode "_" new_type_names) |>
   285     PureThy.add_thmss [(("recs", rec_thms), [])] |>>
   286     Theory.parent_path |> apsnd (pair reccomb_names o flat)
   287   end;
   288 
   289 
   290 (***************************** case combinators *******************************)
   291 
   292 fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   293   let
   294     val _ = message "Proving characteristic theorems for case combinators ...";
   295 
   296     val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
   297 
   298     val descr' = flat descr;
   299     val recTs = get_rec_types descr' sorts;
   300     val used = foldr add_typ_tfree_names (recTs, []);
   301     val newTs = take (length (hd descr), recTs);
   302     val T' = TFree (variant used "'t", HOLogic.termS);
   303 
   304     fun mk_dummyT (DtRec _) = T'
   305       | mk_dummyT (DtType ("fun", [T, _])) = typ_of_dtyp descr' sorts T --> T'
   306 
   307     val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
   308       let
   309         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   310         val Ts' = map mk_dummyT (filter is_rec_type cargs)
   311       in Const ("arbitrary", Ts @ Ts' ---> T')
   312       end) constrs) descr';
   313 
   314     val case_names = map (fn s =>
   315       Sign.full_name (Theory.sign_of thy1) (s ^ "_case")) new_type_names;
   316 
   317     (* define case combinators via primrec combinators *)
   318 
   319     val (case_defs, thy2) = foldl (fn ((defs, thy),
   320       ((((i, (_, _, constrs)), T), name), recname)) =>
   321         let
   322           val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
   323             let
   324               val Ts = map (typ_of_dtyp descr' sorts) cargs;
   325               val Ts' = Ts @ map mk_dummyT (filter is_rec_type cargs);
   326               val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
   327               val frees = take (length cargs, frees');
   328               val free = mk_Free "f" (Ts ---> T') j
   329             in
   330              (free, list_abs_free (map dest_Free frees',
   331                list_comb (free, frees)))
   332             end) (constrs ~~ (1 upto length constrs)));
   333 
   334           val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
   335           val fns = (flat (take (i, case_dummy_fns))) @
   336             fns2 @ (flat (drop (i + 1, case_dummy_fns)));
   337           val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
   338           val decl = (Sign.base_name name, caseT, NoSyn);
   339           val def = ((Sign.base_name name) ^ "_def",
   340             Logic.mk_equals (list_comb (Const (name, caseT), fns1),
   341               list_comb (reccomb, (flat (take (i, case_dummy_fns))) @
   342                 fns2 @ (flat (drop (i + 1, case_dummy_fns))) )));
   343           val (thy', [def_thm]) = thy |>
   344             Theory.add_consts_i [decl] |> (PureThy.add_defs_i o map Thm.no_attributes) [def];
   345 
   346         in (defs @ [def_thm], thy')
   347         end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
   348           (take (length newTs, reccomb_names)));
   349 
   350     val case_thms = map (map (fn t => prove_goalw_cterm (case_defs @
   351       (map mk_meta_eq primrec_thms)) (cterm_of (Theory.sign_of thy2) t)
   352         (fn _ => [rtac refl 1])))
   353           (DatatypeProp.make_cases new_type_names descr sorts thy2)
   354 
   355   in
   356     thy2 |> Theory.add_trrules_i
   357       (DatatypeProp.make_case_trrules new_type_names descr) |>
   358     parent_path flat_names |>
   359     store_thmss "cases" new_type_names case_thms |>
   360     apsnd (rpair case_names)
   361   end;
   362 
   363 
   364 (******************************* case splitting *******************************)
   365 
   366 fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
   367     casedist_thms case_thms thy =
   368   let
   369     val _ = message "Proving equations for case splitting ...";
   370 
   371     val descr' = flat descr;
   372     val recTs = get_rec_types descr' sorts;
   373     val newTs = take (length (hd descr), recTs);
   374 
   375     fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
   376         exhaustion), case_thms'), T) =
   377       let
   378         val cert = cterm_of (Theory.sign_of thy);
   379         val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
   380         val exhaustion' = cterm_instantiate
   381           [(cert lhs, cert (Free ("x", T)))] exhaustion;
   382         val tacsf = K [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
   383           (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))]
   384       in
   385         (prove_goalw_cterm [] (cert t1) tacsf,
   386          prove_goalw_cterm [] (cert t2) tacsf)
   387       end;
   388 
   389     val split_thm_pairs = map prove_split_thms
   390       ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
   391         dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
   392 
   393     val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
   394 
   395   in
   396     thy |> store_thms "split" new_type_names split_thms |>>>
   397       store_thms "split_asm" new_type_names split_asm_thms |> apsnd ListPair.zip
   398   end;
   399 
   400 (******************************* size functions *******************************)
   401 
   402 fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
   403   if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
   404     (fn (DtType ("fun", [_, DtRec _])) => true | _ => false) cargs) constrs) (flat descr)
   405   then
   406     (thy, [])
   407   else
   408   let
   409     val _ = message "Proving equations for size function ...";
   410 
   411     val big_name = space_implode "_" new_type_names;
   412     val thy1 = add_path flat_names big_name thy;
   413 
   414     val descr' = flat descr;
   415     val recTs = get_rec_types descr' sorts;
   416 
   417     val big_size_name = space_implode "_" new_type_names ^ "_size";
   418     val size_name = Sign.intern_const (Theory.sign_of (theory "Arith")) "size";
   419     val size_names = replicate (length (hd descr)) size_name @
   420       map (Sign.full_name (Theory.sign_of thy1))
   421         (if length (flat (tl descr)) = 1 then [big_size_name] else
   422           map (fn i => big_size_name ^ "_" ^ string_of_int i)
   423             (1 upto length (flat (tl descr))));
   424     val def_names = map (fn i => big_size_name ^ "_def_" ^ string_of_int i)
   425       (1 upto length recTs);
   426 
   427     fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2;
   428 
   429     fun make_sizefun (_, cargs) =
   430       let
   431         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   432         val k = length (filter is_rec_type cargs);
   433         val t = if k = 0 then HOLogic.zero else
   434           foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.mk_nat 1])
   435       in
   436         foldr (fn (T, t') => Abs ("x", T, t')) (Ts @ replicate k HOLogic.natT, t)
   437       end;
   438 
   439     val fs = flat (map (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr');
   440     val fTs = map fastype_of fs;
   441 
   442     val (thy', size_def_thms) = thy1 |>
   443       Theory.add_consts_i (map (fn (s, T) =>
   444         (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   445           (drop (length (hd descr), size_names ~~ recTs))) |>
   446       (PureThy.add_defs_i o map Thm.no_attributes) (map (fn (((s, T), def_name), rec_name) =>
   447         (def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
   448           list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs))))
   449             (size_names ~~ recTs ~~ def_names ~~ reccomb_names)) |>>
   450       parent_path flat_names;
   451 
   452     val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
   453 
   454     val size_thms = map (fn t => prove_goalw_cterm rewrites
   455       (cterm_of (Theory.sign_of thy') t) (fn _ => [rtac refl 1]))
   456         (DatatypeProp.make_size new_type_names descr sorts thy')
   457 
   458   in
   459     thy' |> Theory.add_path big_name |>
   460     PureThy.add_thmss [(("size", size_thms), [])] |>>
   461     Theory.parent_path |> apsnd flat
   462   end;
   463 
   464 
   465 (************************* additional theorems for TFL ************************)
   466 
   467 fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
   468   let
   469     val _ = message "Proving additional theorems for TFL ...";
   470 
   471     fun prove_nchotomy (t, exhaustion) =
   472       let
   473         (* For goal i, select the correct disjunct to attack, then prove it *)
   474         fun tac i 0 = EVERY [TRY (rtac disjI1 i),
   475               hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
   476           | tac i n = rtac disjI2 i THEN tac i (n - 1)
   477       in 
   478         prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) t) (fn _ =>
   479           [rtac allI 1,
   480            exh_tac (K exhaustion) 1,
   481            ALLGOALS (fn i => tac i (i-1))])
   482       end;
   483 
   484     val nchotomys =
   485       map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
   486 
   487   in thy |> store_thms "nchotomy" new_type_names nchotomys end;
   488 
   489 fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
   490   let
   491     fun prove_case_cong ((t, nchotomy), case_rewrites) =
   492       let
   493         val (Const ("==>", _) $ tm $ _) = t;
   494         val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
   495         val cert = cterm_of (Theory.sign_of thy);
   496         val nchotomy' = nchotomy RS spec;
   497         val nchotomy'' = cterm_instantiate
   498           [(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy'
   499       in
   500         prove_goalw_cterm [] (cert t) (fn prems => 
   501           let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
   502           in [simp_tac (HOL_ss addsimps [hd prems]) 1,
   503               cut_facts_tac [nchotomy''] 1,
   504               REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
   505               REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
   506           end)
   507       end;
   508 
   509     val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
   510       new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
   511 
   512   in thy |> store_thms "case_cong" new_type_names case_congs end;
   513 
   514 end;