src/HOL/Tools/datatype_package.ML
author berghofe
Mon Jan 24 17:59:48 2005 +0100 (2005-01-24)
changeset 15457 1fbd4aba46e3
parent 15444 4f14c151d9f1
child 15531 08c8dad8e399
permissions -rw-r--r--
Adapted to modified interface of PureThy.get_thm(s).
     1 (*  Title:      HOL/Tools/datatype_package.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4 
     5 Datatype package for Isabelle/HOL.
     6 *)
     7 
     8 signature BASIC_DATATYPE_PACKAGE =
     9 sig
    10   val induct_tac : string -> int -> tactic
    11   val induct_thm_tac : thm -> string -> int -> tactic
    12   val case_tac : string -> int -> tactic
    13   val distinct_simproc : simproc
    14 end;
    15 
    16 signature DATATYPE_PACKAGE =
    17 sig
    18   include BASIC_DATATYPE_PACKAGE
    19   val quiet_mode : bool ref
    20   val add_datatype : bool -> string list -> (string list * bstring * mixfix *
    21     (bstring * string list * mixfix) list) list -> theory -> theory *
    22       {distinct : thm list list,
    23        inject : thm list list,
    24        exhaustion : thm list,
    25        rec_thms : thm list,
    26        case_thms : thm list list,
    27        split_thms : (thm * thm) list,
    28        induction : thm,
    29        size : thm list,
    30        simps : thm list}
    31   val add_datatype_i : bool -> bool -> string list -> (string list * bstring * mixfix *
    32     (bstring * typ list * mixfix) list) list -> theory -> theory *
    33       {distinct : thm list list,
    34        inject : thm list list,
    35        exhaustion : thm list,
    36        rec_thms : thm list,
    37        case_thms : thm list list,
    38        split_thms : (thm * thm) list,
    39        induction : thm,
    40        size : thm list,
    41        simps : thm list}
    42   val rep_datatype_i : string list option -> (thm list * theory attribute list) list list ->
    43     (thm list * theory attribute list) list list -> (thm list * theory attribute list) ->
    44     theory -> theory *
    45       {distinct : thm list list,
    46        inject : thm list list,
    47        exhaustion : thm list,
    48        rec_thms : thm list,
    49        case_thms : thm list list,
    50        split_thms : (thm * thm) list,
    51        induction : thm,
    52        size : thm list,
    53        simps : thm list}
    54   val rep_datatype : string list option -> (thmref * Args.src list) list list ->
    55     (thmref * Args.src list) list list -> thmref * Args.src list -> theory -> theory *
    56       {distinct : thm list list,
    57        inject : thm list list,
    58        exhaustion : thm list,
    59        rec_thms : thm list,
    60        case_thms : thm list list,
    61        split_thms : (thm * thm) list,
    62        induction : thm,
    63        size : thm list,
    64        simps : thm list}
    65   val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table
    66   val get_datatypes_sg : Sign.sg -> DatatypeAux.datatype_info Symtab.table
    67   val print_datatypes : theory -> unit
    68   val datatype_info_sg : Sign.sg -> string -> DatatypeAux.datatype_info option
    69   val datatype_info : theory -> string -> DatatypeAux.datatype_info option
    70   val datatype_info_sg_err : Sign.sg -> string -> DatatypeAux.datatype_info
    71   val datatype_info_err : theory -> string -> DatatypeAux.datatype_info
    72   val constrs_of : theory -> string -> term list option
    73   val constrs_of_sg : Sign.sg -> string -> term list option
    74   val case_const_of : theory -> string -> term option
    75   val weak_case_congs_of : theory -> thm list
    76   val weak_case_congs_of_sg : Sign.sg -> thm list
    77   val setup: (theory -> theory) list
    78 end;
    79 
    80 structure DatatypePackage : DATATYPE_PACKAGE =
    81 struct
    82 
    83 open DatatypeAux;
    84 
    85 val quiet_mode = quiet_mode;
    86 
    87 
    88 (* data kind 'HOL/datatypes' *)
    89 
    90 structure DatatypesArgs =
    91 struct
    92   val name = "HOL/datatypes";
    93   type T = datatype_info Symtab.table;
    94 
    95   val empty = Symtab.empty;
    96   val copy = I;
    97   val prep_ext = I;
    98   val merge: T * T -> T = Symtab.merge (K true);
    99 
   100   fun print sg tab =
   101     Pretty.writeln (Pretty.strs ("datatypes:" ::
   102       map #1 (Sign.cond_extern_table sg Sign.typeK tab)));
   103 end;
   104 
   105 structure DatatypesData = TheoryDataFun(DatatypesArgs);
   106 val get_datatypes_sg = DatatypesData.get_sg;
   107 val get_datatypes = DatatypesData.get;
   108 val put_datatypes = DatatypesData.put;
   109 val print_datatypes = DatatypesData.print;
   110 
   111 
   112 (** theory information about datatypes **)
   113 
   114 fun datatype_info_sg sg name = Symtab.lookup (get_datatypes_sg sg, name);
   115 
   116 fun datatype_info_sg_err sg name = (case datatype_info_sg sg name of
   117       Some info => info
   118     | None => error ("Unknown datatype " ^ quote name));
   119 
   120 val datatype_info = datatype_info_sg o Theory.sign_of;
   121 
   122 fun datatype_info_err thy name = (case datatype_info thy name of
   123       Some info => info
   124     | None => error ("Unknown datatype " ^ quote name));
   125 
   126 fun constrs_of_sg sg tname = (case datatype_info_sg sg tname of
   127    Some {index, descr, ...} =>
   128      let val (_, _, constrs) = the (assoc (descr, index))
   129      in Some (map (fn (cname, _) => Const (cname, the (Sign.const_type sg cname))) constrs)
   130      end
   131  | _ => None);
   132 
   133 val constrs_of = constrs_of_sg o Theory.sign_of;
   134 
   135 fun case_const_of thy tname = (case datatype_info thy tname of
   136    Some {case_name, ...} => Some (Const (case_name, the (Sign.const_type
   137      (Theory.sign_of thy) case_name)))
   138  | _ => None);
   139 
   140 val weak_case_congs_of_sg = map (#weak_case_cong o #2) o Symtab.dest o get_datatypes_sg;
   141 val weak_case_congs_of = weak_case_congs_of_sg o Theory.sign_of;
   142 
   143 fun find_tname var Bi =
   144   let val frees = map dest_Free (term_frees Bi)
   145       val params = rename_wrt_term Bi (Logic.strip_params Bi);
   146   in case assoc (frees @ params, var) of
   147        None => error ("No such variable in subgoal: " ^ quote var)
   148      | Some(Type (tn, _)) => tn
   149      | _ => error ("Cannot determine type of " ^ quote var)
   150   end;
   151 
   152 fun infer_tname state i aterm =
   153   let
   154     val sign = Thm.sign_of_thm state;
   155     val (_, _, Bi, _) = Thm.dest_state (state, i)
   156     val params = Logic.strip_params Bi;   (*params of subgoal i*)
   157     val params = rev (rename_wrt_term Bi params);   (*as they are printed*)
   158     val (types, sorts) = types_sorts state;
   159     fun types' (a, ~1) = (case assoc (params, a) of None => types(a, ~1) | sm => sm)
   160       | types' ixn = types ixn;
   161     val (ct, _) = read_def_cterm (sign, types', sorts) [] false (aterm, TypeInfer.logicT);
   162   in case #T (rep_cterm ct) of
   163        Type (tn, _) => tn
   164      | _ => error ("Cannot determine type of " ^ quote aterm)
   165   end;
   166 
   167 (*Warn if the (induction) variable occurs Free among the premises, which
   168   usually signals a mistake.  But calls the tactic either way!*)
   169 fun occs_in_prems tacf vars =
   170   SUBGOAL (fn (Bi, i) =>
   171            (if  exists (fn Free (a, _) => a mem vars)
   172                       (foldr add_term_frees (#2 (strip_context Bi), []))
   173              then warning "Induction variable occurs also among premises!"
   174              else ();
   175             tacf i));
   176 
   177 
   178 (* generic induction tactic for datatypes *)
   179 
   180 local
   181 
   182 fun prep_var (Var (ixn, _), Some x) = Some (ixn, x)
   183   | prep_var _ = None;
   184 
   185 fun prep_inst (concl, xs) =	(*exception LIST*)
   186   let val vs = InductAttrib.vars_of concl
   187   in mapfilter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
   188 
   189 in
   190 
   191 fun gen_induct_tac inst_tac (varss, opt_rule) i state =
   192   let
   193     val (_, _, Bi, _) = Thm.dest_state (state, i);
   194     val {sign, ...} = Thm.rep_thm state;
   195     val (rule, rule_name) =
   196       (case opt_rule of
   197         Some r => (r, "Induction rule")
   198       | None =>
   199           let val tn = find_tname (hd (mapfilter I (flat varss))) Bi
   200           in (#induction (datatype_info_sg_err sign tn), "Induction rule for type " ^ tn) end);
   201 
   202     val concls = HOLogic.dest_concls (Thm.concl_of rule);
   203     val insts = flat (map prep_inst (concls ~~ varss)) handle LIST _ =>
   204       error (rule_name ^ " has different numbers of variables");
   205   in occs_in_prems (inst_tac insts rule) (map #2 insts) i state end;
   206 
   207 fun induct_tac s =
   208   gen_induct_tac Tactic.res_inst_tac'
   209     (map (Library.single o Some) (Syntax.read_idents s), None);
   210 
   211 fun induct_thm_tac th s =
   212   gen_induct_tac Tactic.res_inst_tac'
   213     ([map Some (Syntax.read_idents s)], Some th);
   214 
   215 end;
   216 
   217 
   218 (* generic case tactic for datatypes *)
   219 
   220 fun case_inst_tac inst_tac t rule i state =
   221   let
   222     val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
   223       (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));
   224   in inst_tac [(ixn, t)] rule i state end;
   225 
   226 fun gen_case_tac inst_tac (t, Some rule) i state =
   227       case_inst_tac inst_tac t rule i state
   228   | gen_case_tac inst_tac (t, None) i state =
   229       let val tn = infer_tname state i t in
   230         if tn = HOLogic.boolN then inst_tac [(("P", 0), t)] case_split_thm i state
   231         else case_inst_tac inst_tac t
   232                (#exhaustion (datatype_info_sg_err (Thm.sign_of_thm state) tn))
   233                i state
   234       end handle THM _ => Seq.empty;
   235 
   236 fun case_tac t = gen_case_tac Tactic.res_inst_tac' (t, None);
   237 
   238 
   239 
   240 (** Isar tactic emulations **)
   241 
   242 local
   243 
   244 val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
   245 val opt_rule = Scan.option (rule_spec |-- Attrib.local_thm);
   246 
   247 val varss = Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift Args.name_dummy)));
   248 
   249 val inst_tac = Method.bires_inst_tac false;
   250 
   251 fun induct_meth ctxt (varss, opt_rule) =
   252   gen_induct_tac (inst_tac ctxt) (varss, opt_rule);
   253 fun case_meth ctxt (varss, opt_rule) =
   254   gen_case_tac (inst_tac ctxt) (varss, opt_rule);
   255 
   256 in
   257 
   258 val tactic_emulations =
   259  [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth,
   260     "induct_tac emulation (dynamic instantiation)"),
   261   ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth,
   262     "case_tac emulation (dynamic instantiation)")];
   263 
   264 end;
   265 
   266 
   267 
   268 (** induct method setup **)
   269 
   270 (* case names *)
   271 
   272 local
   273 
   274 fun dt_recs (DtTFree _) = []
   275   | dt_recs (DtType (_, dts)) = flat (map dt_recs dts)
   276   | dt_recs (DtRec i) = [i];
   277 
   278 fun dt_cases (descr: descr) (_, args, constrs) =
   279   let
   280     fun the_bname i = Sign.base_name (#1 (the (assoc (descr, i))));
   281     val bnames = map the_bname (distinct (flat (map dt_recs args)));
   282   in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
   283 
   284 
   285 fun induct_cases descr =
   286   DatatypeProp.indexify_names (flat (map (dt_cases descr) (map #2 descr)));
   287 
   288 fun exhaust_cases descr i = dt_cases descr (the (assoc (descr, i)));
   289 
   290 in
   291 
   292 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
   293 
   294 fun mk_case_names_exhausts descr new =
   295   map (RuleCases.case_names o exhaust_cases descr o #1)
   296     (filter (fn ((_, (name, _, _))) => name mem_string new) descr);
   297 
   298 end;
   299 
   300 fun add_rules simps case_thms size_thms rec_thms inject distinct
   301                   weak_case_congs cong_att =
   302   (#1 o PureThy.add_thmss [(("simps", simps), []),
   303     (("", flat case_thms @ size_thms @ 
   304           flat distinct  @ rec_thms), [Simplifier.simp_add_global]),
   305     (("", size_thms @ rec_thms), [RecfunCodegen.add]),
   306     (("", flat inject),               [iff_add_global]),
   307     (("", flat distinct RL [notE]),   [Classical.safe_elim_global]),
   308     (("", weak_case_congs),           [cong_att])]);
   309 
   310 
   311 (* add_cases_induct *)
   312 
   313 fun add_cases_induct infos induction =
   314   let
   315     val n = length (HOLogic.dest_concls (Thm.concl_of induction));
   316     fun proj i thm =
   317       if n = 1 then thm
   318       else (if i + 1 < n then (fn th => th RS conjunct1) else I)
   319         (Library.funpow i (fn th => th RS conjunct2) thm)
   320         |> Drule.zero_var_indexes
   321         |> RuleCases.save thm;
   322 
   323     fun named_rules (name, {index, exhaustion, ...}: datatype_info) =
   324       [(("", proj index induction), [InductAttrib.induct_type_global name]),
   325        (("", exhaustion), [InductAttrib.cases_type_global name])];
   326     fun unnamed_rule i =
   327       (("", proj i induction), [InductAttrib.induct_type_global ""]);
   328     val rules = flat (map named_rules infos) @ map unnamed_rule (length infos upto n - 1);
   329   in #1 o PureThy.add_thms rules end;
   330 
   331 
   332 
   333 (**** simplification procedure for showing distinctness of constructors ****)
   334 
   335 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
   336   | stripT p = p;
   337 
   338 fun stripC (i, f $ x) = stripC (i + 1, f)
   339   | stripC p = p;
   340 
   341 val distinctN = "constr_distinct";
   342 
   343 exception ConstrDistinct of term;
   344 
   345 fun distinct_proc sg _ (t as Const ("op =", _) $ t1 $ t2) =
   346   (case (stripC (0, t1), stripC (0, t2)) of
   347      ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
   348          (case (stripT (0, T1), stripT (0, T2)) of
   349             ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
   350                 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
   351                    (case (constrs_of_sg sg tname1) of
   352                       Some constrs => let val cnames = map (fst o dest_Const) constrs
   353                         in if cname1 mem cnames andalso cname2 mem cnames then
   354                              let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));
   355                                  val eq_ct = cterm_of sg eq_t;
   356                                  val Datatype_thy = theory "Datatype";
   357                                  val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
   358                                    map (get_thm Datatype_thy o rpair None)
   359                                      ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
   360                              in (case (#distinct (datatype_info_sg_err sg tname1)) of
   361                                  QuickAndDirty => Some (Thm.invoke_oracle
   362                                    Datatype_thy distinctN (sg, ConstrDistinct eq_t))
   363                                | FewConstrs thms => Some (Tactic.prove sg [] [] eq_t (K
   364                                    (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
   365                                     atac 2, resolve_tac thms 1, etac FalseE 1])))
   366                                | ManyConstrs (thm, ss) => Some (Tactic.prove sg [] [] eq_t (K
   367                                    (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
   368                                     full_simp_tac ss 1,
   369                                     REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
   370                                     eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
   371                                     etac FalseE 1]))))
   372                              end
   373                            else None
   374                         end
   375                     | None => None)
   376                 else None
   377           | _ => None)
   378    | _ => None)
   379   | distinct_proc sg _ _ = None;
   380 
   381 val distinct_simproc =
   382   Simplifier.simproc (Theory.sign_of HOL.thy) distinctN ["s = t"] distinct_proc;
   383 
   384 val dist_ss = HOL_ss addsimprocs [distinct_simproc];
   385 
   386 val simproc_setup =
   387   [Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t),
   388    fn thy => (simpset_ref_of thy := simpset_of thy addsimprocs [distinct_simproc]; thy)];
   389 
   390 
   391 (**** translation rules for case ****)
   392 
   393 fun case_tr sg [t, u] =
   394     let
   395       fun case_error s name ts = raise TERM ("Error in case expression" ^
   396         if_none (apsome (curry op ^ " for datatype ") name) "" ^ ":\n" ^ s, ts);
   397       fun dest_case1 (Const ("_case1", _) $ t $ u) = (case strip_comb t of
   398             (Const (s, _), ts) => (Sign.intern_const sg s, ts)
   399           | (Free (s, _), ts) => (Sign.intern_const sg s, ts)
   400           | _ => case_error "Head is not a constructor" None [t, u], u)
   401         | dest_case1 t = raise TERM ("dest_case1", [t]);
   402       fun dest_case2 (Const ("_case2", _) $ t $ u) = t :: dest_case2 u
   403         | dest_case2 t = [t];
   404       val cases as ((cname, _), _) :: _ = map dest_case1 (dest_case2 u);
   405       val tab = Symtab.dest (get_datatypes_sg sg);
   406       val (cases', default) = (case split_last cases of
   407           (cases', (("dummy_pattern", []), t)) => (cases', Some t)
   408         | _ => (cases, None))
   409       fun abstr (Free (x, T), body) = Term.absfree (x, T, body)
   410         | abstr (Const ("_constrain", _) $ Free (x, T) $ tT, body) =
   411             Syntax.const Syntax.constrainAbsC $ Term.absfree (x, T, body) $ tT
   412         | abstr (Const ("Pair", _) $ x $ y, body) =
   413             Syntax.const "split" $ abstr (x, abstr (y, body))
   414         | abstr (t, _) = case_error "Illegal pattern" None [t];
   415     in case find_first (fn (_, {descr, index, ...}) =>
   416       exists (equal cname o fst) (#3 (snd (nth_elem (index, descr))))) tab of
   417         None => case_error ("Not a datatype constructor: " ^ cname) None [u]
   418       | Some (tname, {descr, case_name, index, ...}) =>
   419         let
   420           val _ = if exists (equal "dummy_pattern" o fst o fst) cases' then
   421             case_error "Illegal occurrence of '_' dummy pattern" (Some tname) [u] else ();
   422           val (_, (_, dts, constrs)) = nth_elem (index, descr);
   423           val sorts = map (rpair [] o dest_DtTFree) dts;
   424           fun find_case (cases, (s, dt)) =
   425             (case find_first (equal s o fst o fst) cases' of
   426                None => (case default of
   427                    None => case_error ("No clause for constructor " ^ s) (Some tname) [u]
   428                  | Some t => (cases, list_abs (map (rpair dummyT) (DatatypeProp.make_tnames
   429                      (map (typ_of_dtyp descr sorts) dt)), t)))
   430              | Some (c as ((_, vs), t)) =>
   431                  if length dt <> length vs then
   432                     case_error ("Wrong number of arguments for constructor " ^ s)
   433                       (Some tname) vs
   434                  else (cases \ c, foldr abstr (vs, t)))
   435           val (cases'', fs) = foldl_map find_case (cases', constrs)
   436         in case (cases'', length constrs = length cases', default) of
   437             ([], true, Some _) =>
   438               case_error "Extra '_' dummy pattern" (Some tname) [u]
   439           | (_ :: _, _, _) =>
   440               let val extra = distinct (map (fst o fst) cases'')
   441               in case extra \\ map fst constrs of
   442                   [] => case_error ("More than one clause for constructor(s) " ^
   443                     commas extra) (Some tname) [u]
   444                 | extra' => case_error ("Illegal constructor(s): " ^ commas extra')
   445                     (Some tname) [u]
   446               end
   447           | _ => list_comb (Syntax.const case_name, fs) $ t
   448         end
   449     end
   450   | case_tr sg ts = raise TERM ("case_tr", ts);
   451 
   452 fun case_tr' constrs sg ts =
   453   if length ts <> length constrs + 1 then raise Match else
   454   let
   455     val (fs, x) = split_last ts;
   456     fun strip_abs 0 t = ([], t)
   457       | strip_abs i (Abs p) =
   458         let val (x, u) = Syntax.atomic_abs_tr' p
   459         in apfst (cons x) (strip_abs (i-1) u) end
   460       | strip_abs i (Const ("split", _) $ t) = (case strip_abs (i+1) t of
   461           (v :: v' :: vs, u) => (Syntax.const "Pair" $ v $ v' :: vs, u));
   462     fun is_dependent i t =
   463       let val k = length (strip_abs_vars t) - i
   464       in k < 0 orelse exists (fn j => j >= k)
   465         (loose_bnos (strip_abs_body t))
   466       end;
   467     val cases = map (fn ((cname, dts), t) =>
   468       (Sign.cond_extern sg Sign.constK cname,
   469        strip_abs (length dts) t, is_dependent (length dts) t))
   470       (constrs ~~ fs);
   471     fun count_cases (cs, (_, _, true)) = cs
   472       | count_cases (cs, (cname, (_, body), false)) = (case assoc (cs, body) of
   473           None => (body, [cname]) :: cs
   474         | Some cnames => overwrite (cs, (body, cnames @ [cname])));
   475     val cases' = sort (int_ord o Library.swap o pairself (length o snd))
   476       (foldl count_cases ([], cases));
   477     fun mk_case1 (cname, (vs, body), _) = Syntax.const "_case1" $
   478       list_comb (Syntax.const cname, vs) $ body;
   479   in
   480     Syntax.const "_case_syntax" $ x $
   481       foldr1 (fn (t, u) => Syntax.const "_case2" $ t $ u) (map mk_case1
   482         (case cases' of
   483            [] => cases
   484          | (default, cnames) :: _ =>
   485            if length cnames = 1 then cases
   486            else if length cnames = length constrs then
   487              [hd cases, ("dummy_pattern", ([], default), false)]
   488            else
   489              filter_out (fn (cname, _, _) => cname mem cnames) cases @
   490              [("dummy_pattern", ([], default), false)]))
   491   end;
   492 
   493 fun make_case_tr' case_names descr = flat (map
   494   (fn ((_, (_, _, constrs)), case_name) => map (rpair (case_tr' constrs))
   495     (NameSpace.accesses' case_name)) (descr ~~ case_names));
   496 
   497 val trfun_setup =
   498   [Theory.add_advanced_trfuns ([], [("_case_syntax", case_tr)], [], [])];
   499 
   500 
   501 (* prepare types *)
   502 
   503 fun read_typ sign ((Ts, sorts), str) =
   504   let
   505     val T = Type.no_tvars (Sign.read_typ (sign, (curry assoc)
   506       (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
   507   in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
   508 
   509 fun cert_typ sign ((Ts, sorts), raw_T) =
   510   let
   511     val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
   512       TYPE (msg, _, _) => error msg;
   513     val sorts' = add_typ_tfrees (T, sorts)
   514   in (Ts @ [T],
   515       case duplicates (map fst sorts') of
   516          [] => sorts'
   517        | dups => error ("Inconsistent sort constraints for " ^ commas dups))
   518   end;
   519 
   520 
   521 (**** make datatype info ****)
   522 
   523 fun make_dt_info descr induct reccomb_names rec_thms
   524     (((((((((i, (_, (tname, _, _))), case_name), case_thms),
   525       exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =
   526   (tname,
   527    {index = i,
   528     descr = descr,
   529     rec_names = reccomb_names,
   530     rec_rewrites = rec_thms,
   531     case_name = case_name,
   532     case_rewrites = case_thms,
   533     induction = induct,
   534     exhaustion = exhaustion_thm,
   535     distinct = distinct_thm,
   536     inject = inject,
   537     nchotomy = nchotomy,
   538     case_cong = case_cong,
   539     weak_case_cong = weak_case_cong});
   540 
   541 
   542 (********************* axiomatic introduction of datatypes ********************)
   543 
   544 fun add_and_get_axioms_atts label tnames attss ts thy =
   545   foldr (fn (((tname, atts), t), (thy', axs)) =>
   546     let
   547       val (thy'', [ax]) = thy' |>
   548         Theory.add_path tname |>
   549         PureThy.add_axioms_i [((label, t), atts)];
   550     in (Theory.parent_path thy'', ax::axs)
   551     end) (tnames ~~ attss ~~ ts, (thy, []));
   552 
   553 fun add_and_get_axioms label tnames =
   554   add_and_get_axioms_atts label tnames (replicate (length tnames) []);
   555 
   556 fun add_and_get_axiomss label tnames tss thy =
   557   foldr (fn ((tname, ts), (thy', axss)) =>
   558     let
   559       val (thy'', [axs]) = thy' |>
   560         Theory.add_path tname |>
   561         PureThy.add_axiomss_i [((label, ts), [])];
   562     in (Theory.parent_path thy'', axs::axss)
   563     end) (tnames ~~ tss, (thy, []));
   564 
   565 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   566     case_names_induct case_names_exhausts thy =
   567   let
   568     val descr' = flat descr;
   569     val recTs = get_rec_types descr' sorts;
   570     val used = foldr add_typ_tfree_names (recTs, []);
   571     val newTs = take (length (hd descr), recTs);
   572 
   573     val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
   574       (fn dt => is_rec_type dt andalso not (null (fst (strip_dtyp dt))))
   575         cargs) constrs) descr';
   576 
   577     (**** declare new types and constants ****)
   578 
   579     val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
   580 
   581     val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
   582       map (fn ((_, cargs), (cname, mx)) =>
   583         (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   584           (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
   585 
   586     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   587 
   588     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   589     val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
   590       (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   591         (1 upto (length descr')));
   592 
   593     val size_names = DatatypeProp.indexify_names
   594       (map (fn T => name_of_typ T ^ "_size") (drop (length (hd descr), recTs)));
   595 
   596     val freeT = TFree (variant used "'t", HOLogic.typeS);
   597     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
   598       map (fn (_, cargs) =>
   599         let val Ts = map (typ_of_dtyp descr' sorts) cargs
   600         in Ts ---> freeT end) constrs) (hd descr);
   601 
   602     val case_names = map (fn s => (s ^ "_case")) new_type_names;
   603 
   604     val thy2' = thy |>
   605 
   606       (** new types **)
   607 
   608       curry (foldr (fn (((name, mx), tvs), thy') => thy' |>
   609           TypedefPackage.add_typedecls [(name, tvs, mx)]))
   610         (types_syntax ~~ tyvars) |>
   611       add_path flat_names (space_implode "_" new_type_names) |>
   612 
   613       (** primrec combinators **)
   614 
   615       Theory.add_consts_i (map (fn ((name, T), T') =>
   616         (name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   617           (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
   618 
   619       (** case combinators **)
   620 
   621       Theory.add_consts_i (map (fn ((name, T), Ts) =>
   622         (name, Ts @ [T] ---> freeT, NoSyn))
   623           (case_names ~~ newTs ~~ case_fn_Ts));
   624 
   625     val reccomb_names' = map (Sign.intern_const (Theory.sign_of thy2')) reccomb_names;
   626     val case_names' = map (Sign.intern_const (Theory.sign_of thy2')) case_names;
   627 
   628     val thy2 = thy2' |>
   629 
   630       (** size functions **)
   631 
   632       (if no_size then I else Theory.add_consts_i (map (fn (s, T) =>
   633         (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   634           (size_names ~~ drop (length (hd descr), recTs)))) |>
   635 
   636       (** constructors **)
   637 
   638       parent_path flat_names |>
   639       curry (foldr (fn (((((_, (_, _, constrs)), T), tname),
   640         constr_syntax'), thy') => thy' |>
   641           add_path flat_names tname |>
   642             Theory.add_consts_i (map (fn ((_, cargs), (cname, mx)) =>
   643               (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   644                 (constrs ~~ constr_syntax')) |>
   645           parent_path flat_names))
   646             (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
   647 
   648     (**** introduction of axioms ****)
   649 
   650     val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
   651     val size_axs = if no_size then [] else DatatypeProp.make_size descr sorts thy2;
   652 
   653     val (thy3, (([induct], [rec_thms]), inject)) =
   654       thy2 |>
   655       Theory.add_path (space_implode "_" new_type_names) |>
   656       PureThy.add_axioms_i [(("induct", DatatypeProp.make_ind descr sorts),
   657         [case_names_induct])] |>>>
   658       PureThy.add_axiomss_i [(("recs", rec_axs), [])] |>>
   659       (if no_size then I else #1 o PureThy.add_axiomss_i [(("size", size_axs), [])]) |>>
   660       Theory.parent_path |>>>
   661       add_and_get_axiomss "inject" new_type_names
   662         (DatatypeProp.make_injs descr sorts);
   663     val size_thms = if no_size then [] else get_thms thy3 ("size", None);
   664     val (thy4, distinct) = add_and_get_axiomss "distinct" new_type_names
   665       (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
   666 
   667     val exhaust_ts = DatatypeProp.make_casedists descr sorts;
   668     val (thy5, exhaustion) = add_and_get_axioms_atts "exhaust" new_type_names
   669       (map Library.single case_names_exhausts) exhaust_ts thy4;
   670     val (thy6, case_thms) = add_and_get_axiomss "cases" new_type_names
   671       (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
   672     val (split_ts, split_asm_ts) = ListPair.unzip
   673       (DatatypeProp.make_splits new_type_names descr sorts thy6);
   674     val (thy7, split) = add_and_get_axioms "split" new_type_names split_ts thy6;
   675     val (thy8, split_asm) = add_and_get_axioms "split_asm" new_type_names
   676       split_asm_ts thy7;
   677     val (thy9, nchotomys) = add_and_get_axioms "nchotomy" new_type_names
   678       (DatatypeProp.make_nchotomys descr sorts) thy8;
   679     val (thy10, case_congs) = add_and_get_axioms "case_cong" new_type_names
   680       (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
   681     val (thy11, weak_case_congs) = add_and_get_axioms "weak_case_cong" new_type_names
   682       (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
   683 
   684     val dt_infos = map (make_dt_info descr' induct reccomb_names' rec_thms)
   685       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
   686         exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
   687           nchotomys ~~ case_congs ~~ weak_case_congs);
   688 
   689     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   690     val split_thms = split ~~ split_asm;
   691 
   692     val thy12 = thy11 |>
   693       Theory.add_advanced_trfuns ([], [], make_case_tr' case_names' (hd descr), []) |>
   694       Theory.add_path (space_implode "_" new_type_names) |>
   695       add_rules simps case_thms size_thms rec_thms inject distinct
   696                 weak_case_congs Simplifier.cong_add_global |> 
   697       put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
   698       add_cases_induct dt_infos induct |>
   699       Theory.parent_path |>
   700       (#1 o store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)) |>
   701       DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
   702   in
   703     (thy12,
   704      {distinct = distinct,
   705       inject = inject,
   706       exhaustion = exhaustion,
   707       rec_thms = rec_thms,
   708       case_thms = case_thms,
   709       split_thms = split_thms,
   710       induction = induct,
   711       size = size_thms,
   712       simps = simps})
   713   end;
   714 
   715 
   716 (******************* definitional introduction of datatypes *******************)
   717 
   718 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   719     case_names_induct case_names_exhausts thy =
   720   let
   721     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   722 
   723     val (thy2, inject, distinct, dist_rewrites, simproc_dists, induct) = thy |>
   724       DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
   725         types_syntax constr_syntax case_names_induct;
   726 
   727     val (thy3, casedist_thms) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
   728       sorts induct case_names_exhausts thy2;
   729     val (thy4, (reccomb_names, rec_thms)) = DatatypeAbsProofs.prove_primrec_thms
   730       flat_names new_type_names descr sorts dt_info inject dist_rewrites dist_ss induct thy3;
   731     val (thy6, (case_thms, case_names)) = DatatypeAbsProofs.prove_case_thms
   732       flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
   733     val (thy7, split_thms) = DatatypeAbsProofs.prove_split_thms new_type_names
   734       descr sorts inject dist_rewrites casedist_thms case_thms thy6;
   735     val (thy8, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
   736       descr sorts casedist_thms thy7;
   737     val (thy9, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
   738       descr sorts nchotomys case_thms thy8;
   739     val (thy10, weak_case_congs) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   740       descr sorts thy9;
   741     val (thy11, size_thms) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
   742       descr sorts reccomb_names rec_thms thy10;
   743 
   744     val dt_infos = map (make_dt_info (flat descr) induct reccomb_names rec_thms)
   745       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
   746         casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   747 
   748     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   749 
   750     val thy12 = thy11 |>
   751       Theory.add_advanced_trfuns ([], [], make_case_tr' case_names (hd descr), []) |>
   752       Theory.add_path (space_implode "_" new_type_names) |>
   753       add_rules simps case_thms size_thms rec_thms inject distinct
   754                 weak_case_congs (Simplifier.change_global_ss (op addcongs)) |> 
   755       put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
   756       add_cases_induct dt_infos induct |>
   757       Theory.parent_path |>
   758       (#1 o store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)) |>
   759       DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
   760   in
   761     (thy12,
   762      {distinct = distinct,
   763       inject = inject,
   764       exhaustion = casedist_thms,
   765       rec_thms = rec_thms,
   766       case_thms = case_thms,
   767       split_thms = split_thms,
   768       induction = induct,
   769       size = size_thms,
   770       simps = simps})
   771   end;
   772 
   773 
   774 (*********************** declare existing type as datatype *********************)
   775 
   776 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
   777   let
   778     val _ = Theory.requires thy0 "Inductive" "datatype representations";
   779 
   780     fun app_thmss srcs thy = foldl_map (fn (thy, x) => apply_theorems x thy) (thy, srcs);
   781     fun app_thm src thy = apsnd Library.hd (apply_theorems [src] thy);
   782 
   783     val (((thy1, induction), inject), distinct) = thy0
   784       |> app_thmss raw_distinct
   785       |> apfst (app_thmss raw_inject)
   786       |> apfst (apfst (app_thm raw_induction));
   787     val sign = Theory.sign_of thy1;
   788 
   789     val induction' = freezeT induction;
   790 
   791     fun err t = error ("Ill-formed predicate in induction rule: " ^
   792       Sign.string_of_term sign t);
   793 
   794     fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
   795           ((tname, map dest_TFree Ts) handle TERM _ => err t)
   796       | get_typ t = err t;
   797 
   798     val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
   799     val new_type_names = if_none alt_names (map fst dtnames);
   800 
   801     fun get_constr t = (case Logic.strip_assums_concl t of
   802         _ $ (_ $ t') => (case head_of t' of
   803             Const (cname, cT) => (case strip_type cT of
   804                 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
   805               | _ => err t)
   806           | _ => err t)
   807       | _ => err t);
   808 
   809     fun make_dt_spec [] _ _ = []
   810       | make_dt_spec ((tname, tvs)::dtnames') i constrs =
   811           let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
   812           in (i, (tname, map DtTFree tvs, map snd constrs'))::
   813             (make_dt_spec dtnames' (i + 1) constrs'')
   814           end;
   815 
   816     val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
   817     val sorts = add_term_tfrees (concl_of induction', []);
   818     val dt_info = get_datatypes thy1;
   819 
   820     val case_names_induct = mk_case_names_induct descr;
   821     val case_names_exhausts = mk_case_names_exhausts descr (map #1 dtnames);
   822     
   823 
   824     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   825 
   826     val (thy2, casedist_thms) = thy1 |>
   827       DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
   828         case_names_exhausts;
   829     val (thy3, (reccomb_names, rec_thms)) = DatatypeAbsProofs.prove_primrec_thms
   830       false new_type_names [descr] sorts dt_info inject distinct dist_ss induction thy2;
   831     val (thy4, (case_thms, case_names)) = DatatypeAbsProofs.prove_case_thms false
   832       new_type_names [descr] sorts reccomb_names rec_thms thy3;
   833     val (thy5, split_thms) = DatatypeAbsProofs.prove_split_thms
   834       new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
   835     val (thy6, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
   836       [descr] sorts casedist_thms thy5;
   837     val (thy7, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
   838       [descr] sorts nchotomys case_thms thy6;
   839     val (thy8, weak_case_congs) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   840       [descr] sorts thy7;
   841     val (thy9, size_thms) =
   842       if Sign.exists_stamp "NatArith" (Theory.sign_of thy8) then
   843         DatatypeAbsProofs.prove_size_thms false new_type_names
   844           [descr] sorts reccomb_names rec_thms thy8
   845       else (thy8, []);
   846 
   847     val (thy10, [induction']) = thy9 |>
   848       (#1 o store_thmss "inject" new_type_names inject) |>
   849       (#1 o store_thmss "distinct" new_type_names distinct) |>
   850       Theory.add_path (space_implode "_" new_type_names) |>
   851       PureThy.add_thms [(("induct", induction), [case_names_induct])];
   852 
   853     val dt_infos = map (make_dt_info descr induction' reccomb_names rec_thms)
   854       ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~
   855         map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   856 
   857     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   858 
   859     val thy11 = thy10 |>
   860       Theory.add_advanced_trfuns ([], [], make_case_tr' case_names descr, []) |>
   861       add_rules simps case_thms size_thms rec_thms inject distinct
   862                 weak_case_congs (Simplifier.change_global_ss (op addcongs)) |> 
   863       put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
   864       add_cases_induct dt_infos induction' |>
   865       Theory.parent_path |>
   866       (#1 o store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)) |>
   867       DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
   868   in
   869     (thy11,
   870      {distinct = distinct,
   871       inject = inject,
   872       exhaustion = casedist_thms,
   873       rec_thms = rec_thms,
   874       case_thms = case_thms,
   875       split_thms = split_thms,
   876       induction = induction',
   877       size = size_thms,
   878       simps = simps})
   879   end;
   880 
   881 val rep_datatype = gen_rep_datatype IsarThy.apply_theorems;
   882 val rep_datatype_i = gen_rep_datatype IsarThy.apply_theorems_i;
   883 
   884 
   885 
   886 (******************************** add datatype ********************************)
   887 
   888 fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =
   889   let
   890     val _ = Theory.requires thy "Datatype_Universe" "datatype definitions";
   891 
   892     (* this theory is used just for parsing *)
   893 
   894     val tmp_thy = thy |>
   895       Theory.copy |>
   896       Theory.add_types (map (fn (tvs, tname, mx, _) =>
   897         (tname, length tvs, mx)) dts);
   898 
   899     val sign = Theory.sign_of tmp_thy;
   900 
   901     val (tyvars, _, _, _)::_ = dts;
   902     val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
   903       let val full_tname = Sign.full_name sign (Syntax.type_name tname mx)
   904       in (case duplicates tvs of
   905             [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
   906                   else error ("Mutually recursive datatypes must have same type parameters")
   907           | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
   908               " : " ^ commas dups))
   909       end) dts);
   910 
   911     val _ = (case duplicates (map fst new_dts) @ duplicates new_type_names of
   912       [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
   913 
   914     fun prep_dt_spec ((dts', constr_syntax, sorts, i), (tvs, tname, mx, constrs)) =
   915       let
   916         fun prep_constr ((constrs, constr_syntax', sorts'), (cname, cargs, mx')) =
   917           let
   918             val (cargs', sorts'') = foldl (prep_typ sign) (([], sorts'), cargs);
   919             val _ = (case foldr add_typ_tfree_names (cargs', []) \\ tvs of
   920                 [] => ()
   921               | vs => error ("Extra type variables on rhs: " ^ commas vs))
   922           in (constrs @ [((if flat_names then Sign.full_name sign else
   923                 Sign.full_name_path sign tname) (Syntax.const_name cname mx'),
   924                    map (dtyp_of_typ new_dts) cargs')],
   925               constr_syntax' @ [(cname, mx')], sorts'')
   926           end handle ERROR =>
   927             error ("The error above occured in constructor " ^ cname ^
   928               " of datatype " ^ tname);
   929 
   930         val (constrs', constr_syntax', sorts') =
   931           foldl prep_constr (([], [], sorts), constrs)
   932 
   933       in
   934         case duplicates (map fst constrs') of
   935            [] =>
   936              (dts' @ [(i, (Sign.full_name sign (Syntax.type_name tname mx),
   937                 map DtTFree tvs, constrs'))],
   938               constr_syntax @ [constr_syntax'], sorts', i + 1)
   939          | dups => error ("Duplicate constructors " ^ commas dups ^
   940              " in datatype " ^ tname)
   941       end;
   942 
   943     val (dts', constr_syntax, sorts', i) = foldl prep_dt_spec (([], [], [], 0), dts);
   944     val sorts = sorts' @ (map (rpair (Sign.defaultS sign)) (tyvars \\ map fst sorts'));
   945     val dt_info = get_datatypes thy;
   946     val (descr, _) = unfold_datatypes sign dts' sorts dt_info dts' i;
   947     val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>
   948       if err then error ("Nonemptiness check failed for datatype " ^ s)
   949       else raise exn;
   950 
   951     val descr' = flat descr;
   952     val case_names_induct = mk_case_names_induct descr';
   953     val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
   954   in
   955     (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
   956       flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   957       case_names_induct case_names_exhausts thy
   958   end;
   959 
   960 val add_datatype_i = gen_add_datatype cert_typ;
   961 val add_datatype = gen_add_datatype read_typ true;
   962 
   963 
   964 (** package setup **)
   965 
   966 (* setup theory *)
   967 
   968 val setup = [DatatypesData.init, Method.add_methods tactic_emulations] @ simproc_setup @ trfun_setup;
   969 
   970 
   971 (* outer syntax *)
   972 
   973 local structure P = OuterParse and K = OuterSyntax.Keyword in
   974 
   975 val datatype_decl =
   976   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
   977     (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
   978 
   979 fun mk_datatype args =
   980   let
   981     val names = map (fn ((((None, _), t), _), _) => t | ((((Some t, _), _), _), _) => t) args;
   982     val specs = map (fn ((((_, vs), t), mx), cons) =>
   983       (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
   984   in #1 o add_datatype false names specs end;
   985 
   986 val datatypeP =
   987   OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
   988     (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
   989 
   990 
   991 val rep_datatype_decl =
   992   Scan.option (Scan.repeat1 P.name) --
   993     Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
   994     Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
   995     (P.$$$ "induction" |-- P.!!! P.xthm);
   996 
   997 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #1 o rep_datatype opt_ts dss iss ind;
   998 
   999 val rep_datatypeP =
  1000   OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
  1001     (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
  1002 
  1003 
  1004 val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
  1005 val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
  1006 
  1007 end;
  1008 
  1009 
  1010 end;
  1011 
  1012 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
  1013 open BasicDatatypePackage;