src/HOL/Tools/datatype_package.ML
author haftmann
Fri Dec 16 09:00:11 2005 +0100 (2005-12-16)
changeset 18418 bf448d999b7e
parent 18377 0e1d025d57b3
child 18451 5ff0244e25e8
permissions -rw-r--r--
re-arranged tuples (theory * 'a) to ('a * theory) in Pure
     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 ->
    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} * theory
    31   val add_datatype_i : bool -> bool -> string list -> (string list * bstring * mixfix *
    32     (bstring * typ list * mixfix) list) list -> 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} * theory
    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 ->
    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} * theory
    54   val rep_datatype : string list option -> (thmref * Attrib.src list) list list ->
    55     (thmref * Attrib.src list) list list -> thmref * Attrib.src list -> 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} * theory
    65   val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table
    66   val print_datatypes : theory -> unit
    67   val datatype_info : theory -> string -> DatatypeAux.datatype_info option
    68   val datatype_info_err : theory -> string -> DatatypeAux.datatype_info
    69   val constrs_of : theory -> string -> term list option
    70   val case_const_of : theory -> string -> term option
    71   val weak_case_congs_of : theory -> thm list
    72   val setup: (theory -> theory) list
    73 end;
    74 
    75 structure DatatypePackage : DATATYPE_PACKAGE =
    76 struct
    77 
    78 open DatatypeAux;
    79 
    80 val quiet_mode = quiet_mode;
    81 
    82 
    83 (* data kind 'HOL/datatypes' *)
    84 
    85 structure DatatypesData = TheoryDataFun
    86 (struct
    87   val name = "HOL/datatypes";
    88   type T = datatype_info Symtab.table;
    89 
    90   val empty = Symtab.empty;
    91   val copy = I;
    92   val extend = I;
    93   fun merge _ tabs : T = Symtab.merge (K true) tabs;
    94 
    95   fun print sg tab =
    96     Pretty.writeln (Pretty.strs ("datatypes:" ::
    97       map #1 (NameSpace.extern_table (Sign.type_space sg, tab))));
    98 end);
    99 
   100 val get_datatypes = DatatypesData.get;
   101 val put_datatypes = DatatypesData.put;
   102 val print_datatypes = DatatypesData.print;
   103 
   104 
   105 (** theory information about datatypes **)
   106 
   107 val datatype_info = Symtab.lookup o get_datatypes;
   108 
   109 fun datatype_info_err thy name = (case datatype_info thy name of
   110       SOME info => info
   111     | NONE => error ("Unknown datatype " ^ quote name));
   112 
   113 fun constrs_of thy tname = (case datatype_info thy tname of
   114    SOME {index, descr, ...} =>
   115      let val (_, _, constrs) = valOf (AList.lookup (op =) descr index)
   116      in SOME (map (fn (cname, _) => Const (cname, Sign.the_const_type thy cname)) constrs)
   117      end
   118  | _ => NONE);
   119 
   120 fun case_const_of thy tname = (case datatype_info thy tname of
   121    SOME {case_name, ...} => SOME (Const (case_name, Sign.the_const_type thy case_name))
   122  | _ => NONE);
   123 
   124 val weak_case_congs_of = map (#weak_case_cong o #2) o Symtab.dest o get_datatypes;
   125 
   126 fun find_tname var Bi =
   127   let val frees = map dest_Free (term_frees Bi)
   128       val params = rename_wrt_term Bi (Logic.strip_params Bi);
   129   in case AList.lookup (op =) (frees @ params) var of
   130        NONE => error ("No such variable in subgoal: " ^ quote var)
   131      | SOME(Type (tn, _)) => tn
   132      | _ => error ("Cannot determine type of " ^ quote var)
   133   end;
   134 
   135 fun infer_tname state i aterm =
   136   let
   137     val sign = Thm.sign_of_thm state;
   138     val (_, _, Bi, _) = Thm.dest_state (state, i)
   139     val params = Logic.strip_params Bi;   (*params of subgoal i*)
   140     val params = rev (rename_wrt_term Bi params);   (*as they are printed*)
   141     val (types, sorts) = types_sorts state;
   142     fun types' (a, ~1) = (case AList.lookup (op =) params a of NONE => types(a, ~1) | sm => sm)
   143       | types' ixn = types ixn;
   144     val (ct, _) = read_def_cterm (sign, types', sorts) [] false (aterm, TypeInfer.logicT);
   145   in case #T (rep_cterm ct) of
   146        Type (tn, _) => tn
   147      | _ => error ("Cannot determine type of " ^ quote aterm)
   148   end;
   149 
   150 (*Warn if the (induction) variable occurs Free among the premises, which
   151   usually signals a mistake.  But calls the tactic either way!*)
   152 fun occs_in_prems tacf vars =
   153   SUBGOAL (fn (Bi, i) =>
   154            (if  exists (fn Free (a, _) => a mem vars)
   155                       (foldr add_term_frees [] (#2 (strip_context Bi)))
   156              then warning "Induction variable occurs also among premises!"
   157              else ();
   158             tacf i));
   159 
   160 
   161 (* generic induction tactic for datatypes *)
   162 
   163 local
   164 
   165 fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x)
   166   | prep_var _ = NONE;
   167 
   168 fun prep_inst (concl, xs) =	(*exception UnequalLengths *)
   169   let val vs = InductAttrib.vars_of concl
   170   in List.mapPartial prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
   171 
   172 in
   173 
   174 fun gen_induct_tac inst_tac (varss, opt_rule) i state =
   175   let
   176     val (_, _, Bi, _) = Thm.dest_state (state, i);
   177     val {sign, ...} = Thm.rep_thm state;
   178     val (rule, rule_name) =
   179       (case opt_rule of
   180         SOME r => (r, "Induction rule")
   181       | NONE =>
   182           let val tn = find_tname (hd (List.mapPartial I (List.concat varss))) Bi
   183           in (#induction (datatype_info_err sign tn), "Induction rule for type " ^ tn) end);
   184 
   185     val concls = HOLogic.dest_concls (Thm.concl_of rule);
   186     val insts = List.concat (map prep_inst (concls ~~ varss)) handle UnequalLengths =>
   187       error (rule_name ^ " has different numbers of variables");
   188   in occs_in_prems (inst_tac insts rule) (map #2 insts) i state end;
   189 
   190 fun induct_tac s =
   191   gen_induct_tac Tactic.res_inst_tac'
   192     (map (Library.single o SOME) (Syntax.read_idents s), NONE);
   193 
   194 fun induct_thm_tac th s =
   195   gen_induct_tac Tactic.res_inst_tac'
   196     ([map SOME (Syntax.read_idents s)], SOME th);
   197 
   198 end;
   199 
   200 
   201 (* generic case tactic for datatypes *)
   202 
   203 fun case_inst_tac inst_tac t rule i state =
   204   let
   205     val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
   206       (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));
   207   in inst_tac [(ixn, t)] rule i state end;
   208 
   209 fun gen_case_tac inst_tac (t, SOME rule) i state =
   210       case_inst_tac inst_tac t rule i state
   211   | gen_case_tac inst_tac (t, NONE) i state =
   212       let val tn = infer_tname state i t in
   213         if tn = HOLogic.boolN then inst_tac [(("P", 0), t)] case_split_thm i state
   214         else case_inst_tac inst_tac t
   215                (#exhaustion (datatype_info_err (Thm.sign_of_thm state) tn))
   216                i state
   217       end handle THM _ => Seq.empty;
   218 
   219 fun case_tac t = gen_case_tac Tactic.res_inst_tac' (t, NONE);
   220 
   221 
   222 
   223 (** Isar tactic emulations **)
   224 
   225 local
   226 
   227 val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
   228 val opt_rule = Scan.option (rule_spec |-- Attrib.local_thm);
   229 
   230 val varss =
   231   Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name))));
   232 
   233 val inst_tac = Method.bires_inst_tac false;
   234 
   235 fun induct_meth ctxt (varss, opt_rule) =
   236   gen_induct_tac (inst_tac ctxt) (varss, opt_rule);
   237 fun case_meth ctxt (varss, opt_rule) =
   238   gen_case_tac (inst_tac ctxt) (varss, opt_rule);
   239 
   240 in
   241 
   242 val tactic_emulations =
   243  [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth,
   244     "induct_tac emulation (dynamic instantiation)"),
   245   ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth,
   246     "case_tac emulation (dynamic instantiation)")];
   247 
   248 end;
   249 
   250 
   251 
   252 (** induct method setup **)
   253 
   254 (* case names *)
   255 
   256 local
   257 
   258 fun dt_recs (DtTFree _) = []
   259   | dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts)
   260   | dt_recs (DtRec i) = [i];
   261 
   262 fun dt_cases (descr: descr) (_, args, constrs) =
   263   let
   264     fun the_bname i = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i)));
   265     val bnames = map the_bname (distinct (List.concat (map dt_recs args)));
   266   in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
   267 
   268 
   269 fun induct_cases descr =
   270   DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr)));
   271 
   272 fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i));
   273 
   274 in
   275 
   276 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
   277 
   278 fun mk_case_names_exhausts descr new =
   279   map (RuleCases.case_names o exhaust_cases descr o #1)
   280     (List.filter (fn ((_, (name, _, _))) => name mem_string new) descr);
   281 
   282 end;
   283 
   284 fun name_notE th =
   285     Thm.name_thm (Thm.name_of_thm th ^ "_E", th RS notE);
   286       
   287 fun add_rules simps case_thms size_thms rec_thms inject distinct
   288                   weak_case_congs cong_att =
   289   (snd o PureThy.add_thmss [(("simps", simps), []),
   290     (("", List.concat case_thms @ size_thms @ 
   291           List.concat distinct  @ rec_thms), [Simplifier.simp_add_global]),
   292     (("", size_thms @ rec_thms),             [RecfunCodegen.add NONE]),
   293     (("", List.concat inject),               [iff_add_global]),
   294     (("", map name_notE (List.concat distinct)),  [Classical.safe_elim_global]),
   295     (("", weak_case_congs),                  [cong_att])]);
   296 
   297 
   298 (* add_cases_induct *)
   299 
   300 fun add_cases_induct infos induction =
   301   let
   302     val n = length (HOLogic.dest_concls (Thm.concl_of induction));
   303     fun proj i thm =
   304       if n = 1 then thm
   305       else (if i + 1 < n then (fn th => th RS conjunct1) else I)
   306         (Library.funpow i (fn th => th RS conjunct2) thm)
   307         |> Drule.zero_var_indexes
   308         |> RuleCases.save thm;
   309 
   310     fun named_rules (name, {index, exhaustion, ...}: datatype_info) =
   311       [(("", proj index induction), [InductAttrib.induct_type_global name]),
   312        (("", exhaustion), [InductAttrib.cases_type_global name])];
   313     fun unnamed_rule i =
   314       (("", proj i induction), [InductAttrib.induct_type_global ""]);
   315     val rules = List.concat (map named_rules infos) @ map unnamed_rule (length infos upto n - 1);
   316   in snd o PureThy.add_thms rules end;
   317 
   318 
   319 
   320 (**** simplification procedure for showing distinctness of constructors ****)
   321 
   322 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
   323   | stripT p = p;
   324 
   325 fun stripC (i, f $ x) = stripC (i + 1, f)
   326   | stripC p = p;
   327 
   328 val distinctN = "constr_distinct";
   329 
   330 exception ConstrDistinct of term;
   331 
   332 fun distinct_proc sg ss (t as Const ("op =", _) $ t1 $ t2) =
   333   (case (stripC (0, t1), stripC (0, t2)) of
   334      ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
   335          (case (stripT (0, T1), stripT (0, T2)) of
   336             ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
   337                 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
   338                    (case (constrs_of sg tname1) of
   339                       SOME constrs => let val cnames = map (fst o dest_Const) constrs
   340                         in if cname1 mem cnames andalso cname2 mem cnames then
   341                              let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));
   342                                  val eq_ct = cterm_of sg eq_t;
   343                                  val Datatype_thy = theory "Datatype";
   344                                  val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
   345                                    map (get_thm Datatype_thy o Name)
   346                                      ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
   347                              in (case (#distinct (datatype_info_err sg tname1)) of
   348                                  QuickAndDirty => SOME (Thm.invoke_oracle
   349                                    Datatype_thy distinctN (sg, ConstrDistinct eq_t))
   350                                | FewConstrs thms => SOME (Goal.prove sg [] [] eq_t (K
   351                                    (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
   352                                     atac 2, resolve_tac thms 1, etac FalseE 1])))
   353                                | ManyConstrs (thm, simpset) => SOME (Goal.prove sg [] [] eq_t (K
   354                                    (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
   355                                     full_simp_tac (Simplifier.inherit_context ss simpset) 1,
   356                                     REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
   357                                     eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
   358                                     etac FalseE 1]))))
   359                              end
   360                            else NONE
   361                         end
   362                     | NONE => NONE)
   363                 else NONE
   364           | _ => NONE)
   365    | _ => NONE)
   366   | distinct_proc sg _ _ = NONE;
   367 
   368 val distinct_simproc =
   369   Simplifier.simproc HOL.thy distinctN ["s = t"] distinct_proc;
   370 
   371 val dist_ss = HOL_ss addsimprocs [distinct_simproc];
   372 
   373 val simproc_setup =
   374   [Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t),
   375    fn thy => ((change_simpset_of thy) (fn ss => ss addsimprocs [distinct_simproc]); thy)];
   376 
   377 
   378 (**** translation rules for case ****)
   379 
   380 fun find_first f = Library.find_first f;
   381 
   382 fun case_tr sg [t, u] =
   383     let
   384       fun case_error s name ts = raise TERM ("Error in case expression" ^
   385         getOpt (Option.map (curry op ^ " for datatype ") name, "") ^ ":\n" ^ s, ts);
   386       fun dest_case1 (Const ("_case1", _) $ t $ u) = (case strip_comb t of
   387             (Const (s, _), ts) => (Sign.intern_const sg s, ts)
   388           | (Free (s, _), ts) => (Sign.intern_const sg s, ts)
   389           | _ => case_error "Head is not a constructor" NONE [t, u], u)
   390         | dest_case1 t = raise TERM ("dest_case1", [t]);
   391       fun dest_case2 (Const ("_case2", _) $ t $ u) = t :: dest_case2 u
   392         | dest_case2 t = [t];
   393       val cases as ((cname, _), _) :: _ = map dest_case1 (dest_case2 u);
   394       val tab = Symtab.dest (get_datatypes sg);
   395       val (cases', default) = (case split_last cases of
   396           (cases', (("dummy_pattern", []), t)) => (cases', SOME t)
   397         | _ => (cases, NONE))
   398       fun abstr (Free (x, T), body) = Term.absfree (x, T, body)
   399         | abstr (Const ("_constrain", _) $ Free (x, T) $ tT, body) =
   400             Syntax.const Syntax.constrainAbsC $ Term.absfree (x, T, body) $ tT
   401         | abstr (Const ("Pair", _) $ x $ y, body) =
   402             Syntax.const "split" $ abstr (x, abstr (y, body))
   403         | abstr (t, _) = case_error "Illegal pattern" NONE [t];
   404     in case find_first (fn (_, {descr, index, ...}) =>
   405       exists (equal cname o fst) (#3 (snd (List.nth (descr, index))))) tab of
   406         NONE => case_error ("Not a datatype constructor: " ^ cname) NONE [u]
   407       | SOME (tname, {descr, sorts, case_name, index, ...}) =>
   408         let
   409           val _ = if exists (equal "dummy_pattern" o fst o fst) cases' then
   410             case_error "Illegal occurrence of '_' dummy pattern" (SOME tname) [u] else ();
   411           val (_, (_, dts, constrs)) = List.nth (descr, index);
   412           fun find_case (cases, (s, dt)) =
   413             (case find_first (equal s o fst o fst) cases' of
   414                NONE => (case default of
   415                    NONE => case_error ("No clause for constructor " ^ s) (SOME tname) [u]
   416                  | SOME t => (cases, list_abs (map (rpair dummyT) (DatatypeProp.make_tnames
   417                      (map (typ_of_dtyp descr sorts) dt)), t)))
   418              | SOME (c as ((_, vs), t)) =>
   419                  if length dt <> length vs then
   420                     case_error ("Wrong number of arguments for constructor " ^ s)
   421                       (SOME tname) vs
   422                  else (cases \ c, foldr abstr t vs))
   423           val (cases'', fs) = foldl_map find_case (cases', constrs)
   424         in case (cases'', length constrs = length cases', default) of
   425             ([], true, SOME _) =>
   426               case_error "Extra '_' dummy pattern" (SOME tname) [u]
   427           | (_ :: _, _, _) =>
   428               let val extra = distinct (map (fst o fst) cases'')
   429               in case extra \\ map fst constrs of
   430                   [] => case_error ("More than one clause for constructor(s) " ^
   431                     commas extra) (SOME tname) [u]
   432                 | extra' => case_error ("Illegal constructor(s): " ^ commas extra')
   433                     (SOME tname) [u]
   434               end
   435           | _ => list_comb (Syntax.const case_name, fs) $ t
   436         end
   437     end
   438   | case_tr sg ts = raise TERM ("case_tr", ts);
   439 
   440 fun case_tr' constrs sg ts =
   441   if length ts <> length constrs + 1 then raise Match else
   442   let
   443     val (fs, x) = split_last ts;
   444     fun strip_abs 0 t = ([], t)
   445       | strip_abs i (Abs p) =
   446         let val (x, u) = Syntax.atomic_abs_tr' p
   447         in apfst (cons x) (strip_abs (i-1) u) end
   448       | strip_abs i (Const ("split", _) $ t) = (case strip_abs (i+1) t of
   449           (v :: v' :: vs, u) => (Syntax.const "Pair" $ v $ v' :: vs, u));
   450     fun is_dependent i t =
   451       let val k = length (strip_abs_vars t) - i
   452       in k < 0 orelse exists (fn j => j >= k)
   453         (loose_bnos (strip_abs_body t))
   454       end;
   455     val cases = map (fn ((cname, dts), t) =>
   456       (Sign.extern_const sg cname,
   457        strip_abs (length dts) t, is_dependent (length dts) t))
   458       (constrs ~~ fs);
   459     fun count_cases (cs, (_, _, true)) = cs
   460       | count_cases (cs, (cname, (_, body), false)) = (case AList.lookup (op =) cs body of
   461           NONE => (body, [cname]) :: cs
   462         | SOME cnames => AList.update (op =) (body, cnames @ [cname]) cs);
   463     val cases' = sort (int_ord o Library.swap o pairself (length o snd))
   464       (Library.foldl count_cases ([], cases));
   465     fun mk_case1 (cname, (vs, body), _) = Syntax.const "_case1" $
   466       list_comb (Syntax.const cname, vs) $ body;
   467   in
   468     Syntax.const "_case_syntax" $ x $
   469       foldr1 (fn (t, u) => Syntax.const "_case2" $ t $ u) (map mk_case1
   470         (case cases' of
   471            [] => cases
   472          | (default, cnames) :: _ =>
   473            if length cnames = 1 then cases
   474            else if length cnames = length constrs then
   475              [hd cases, ("dummy_pattern", ([], default), false)]
   476            else
   477              filter_out (fn (cname, _, _) => cname mem cnames) cases @
   478              [("dummy_pattern", ([], default), false)]))
   479   end;
   480 
   481 fun make_case_tr' case_names descr = List.concat (map
   482   (fn ((_, (_, _, constrs)), case_name) => map (rpair (case_tr' constrs))
   483     (NameSpace.accesses' case_name)) (descr ~~ case_names));
   484 
   485 val trfun_setup =
   486   [Theory.add_advanced_trfuns ([], [("_case_syntax", case_tr)], [], [])];
   487 
   488 
   489 (* prepare types *)
   490 
   491 fun read_typ sign ((Ts, sorts), str) =
   492   let
   493     val T = Type.no_tvars (Sign.read_typ (sign, AList.lookup (op =)
   494       (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
   495   in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
   496 
   497 fun cert_typ sign ((Ts, sorts), raw_T) =
   498   let
   499     val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
   500       TYPE (msg, _, _) => error msg;
   501     val sorts' = add_typ_tfrees (T, sorts)
   502   in (Ts @ [T],
   503       case duplicates (map fst sorts') of
   504          [] => sorts'
   505        | dups => error ("Inconsistent sort constraints for " ^ commas dups))
   506   end;
   507 
   508 
   509 (**** make datatype info ****)
   510 
   511 fun make_dt_info descr sorts induct reccomb_names rec_thms
   512     (((((((((i, (_, (tname, _, _))), case_name), case_thms),
   513       exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =
   514   (tname,
   515    {index = i,
   516     descr = descr,
   517     sorts = sorts,
   518     rec_names = reccomb_names,
   519     rec_rewrites = rec_thms,
   520     case_name = case_name,
   521     case_rewrites = case_thms,
   522     induction = induct,
   523     exhaustion = exhaustion_thm,
   524     distinct = distinct_thm,
   525     inject = inject,
   526     nchotomy = nchotomy,
   527     case_cong = case_cong,
   528     weak_case_cong = weak_case_cong});
   529 
   530 
   531 (********************* axiomatic introduction of datatypes ********************)
   532 
   533 fun add_and_get_axioms_atts label tnames attss ts thy =
   534   foldr (fn (((tname, atts), t), (thy', axs)) =>
   535     let
   536       val ([ax], thy'') =
   537         thy'
   538         |> Theory.add_path tname
   539         |> PureThy.add_axioms_i [((label, t), atts)];
   540     in (Theory.parent_path thy'', ax::axs)
   541     end) (thy, []) (tnames ~~ attss ~~ ts) |> swap;
   542 
   543 fun add_and_get_axioms label tnames =
   544   add_and_get_axioms_atts label tnames (replicate (length tnames) []);
   545 
   546 fun add_and_get_axiomss label tnames tss thy =
   547   foldr (fn ((tname, ts), (thy', axss)) =>
   548     let
   549       val ([axs], thy'') =
   550         thy'
   551         |> Theory.add_path tname
   552         |> PureThy.add_axiomss_i [((label, ts), [])];
   553     in (Theory.parent_path thy'', axs::axss)
   554     end) (thy, []) (tnames ~~ tss) |> swap;
   555 
   556 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   557     case_names_induct case_names_exhausts thy =
   558   let
   559     val descr' = List.concat descr;
   560     val recTs = get_rec_types descr' sorts;
   561     val used = foldr add_typ_tfree_names [] recTs;
   562     val newTs = Library.take (length (hd descr), recTs);
   563 
   564     val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
   565       (fn dt => is_rec_type dt andalso not (null (fst (strip_dtyp dt))))
   566         cargs) constrs) descr';
   567 
   568     (**** declare new types and constants ****)
   569 
   570     val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
   571 
   572     val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
   573       map (fn ((_, cargs), (cname, mx)) =>
   574         (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   575           (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
   576 
   577     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   578 
   579     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   580     val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
   581       (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   582         (1 upto (length descr')));
   583 
   584     val size_names = DatatypeProp.indexify_names
   585       (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs)));
   586 
   587     val freeT = TFree (variant used "'t", HOLogic.typeS);
   588     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
   589       map (fn (_, cargs) =>
   590         let val Ts = map (typ_of_dtyp descr' sorts) cargs
   591         in Ts ---> freeT end) constrs) (hd descr);
   592 
   593     val case_names = map (fn s => (s ^ "_case")) new_type_names;
   594 
   595     val thy2' = thy |>
   596 
   597       (** new types **)
   598 
   599       curry (Library.foldr (fn (((name, mx), tvs), thy') => thy' |>
   600           TypedefPackage.add_typedecls [(name, tvs, mx)]))
   601         (types_syntax ~~ tyvars) |>
   602       add_path flat_names (space_implode "_" new_type_names) |>
   603 
   604       (** primrec combinators **)
   605 
   606       Theory.add_consts_i (map (fn ((name, T), T') =>
   607         (name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   608           (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
   609 
   610       (** case combinators **)
   611 
   612       Theory.add_consts_i (map (fn ((name, T), Ts) =>
   613         (name, Ts @ [T] ---> freeT, NoSyn))
   614           (case_names ~~ newTs ~~ case_fn_Ts));
   615 
   616     val reccomb_names' = map (Sign.intern_const thy2') reccomb_names;
   617     val case_names' = map (Sign.intern_const thy2') case_names;
   618 
   619     val thy2 = thy2' |>
   620 
   621       (** size functions **)
   622 
   623       (if no_size then I else Theory.add_consts_i (map (fn (s, T) =>
   624         (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   625           (size_names ~~ Library.drop (length (hd descr), recTs)))) |>
   626 
   627       (** constructors **)
   628 
   629       parent_path flat_names |>
   630       curry (Library.foldr (fn (((((_, (_, _, constrs)), T), tname),
   631         constr_syntax'), thy') => thy' |>
   632           add_path flat_names tname |>
   633             Theory.add_consts_i (map (fn ((_, cargs), (cname, mx)) =>
   634               (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   635                 (constrs ~~ constr_syntax')) |>
   636           parent_path flat_names))
   637             (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
   638 
   639     (**** introduction of axioms ****)
   640 
   641     val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
   642     val size_axs = if no_size then [] else DatatypeProp.make_size descr sorts thy2;
   643 
   644     val ((([induct], [rec_thms]), inject), thy3) =
   645       thy2
   646       |> Theory.add_path (space_implode "_" new_type_names)
   647       |> PureThy.add_axioms_i [(("induct", DatatypeProp.make_ind descr sorts),
   648           [case_names_induct])]
   649       ||>> PureThy.add_axiomss_i [(("recs", rec_axs), [])]
   650       ||> (if no_size then I else snd o PureThy.add_axiomss_i [(("size", size_axs), [])])
   651       ||> Theory.parent_path
   652       ||>> add_and_get_axiomss "inject" new_type_names
   653             (DatatypeProp.make_injs descr sorts);
   654     val size_thms = if no_size then [] else get_thms thy3 (Name "size");
   655     val (distinct, thy4) = add_and_get_axiomss "distinct" new_type_names
   656       (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
   657 
   658     val exhaust_ts = DatatypeProp.make_casedists descr sorts;
   659     val (exhaustion, thy5) = add_and_get_axioms_atts "exhaust" new_type_names
   660       (map Library.single case_names_exhausts) exhaust_ts thy4;
   661     val (case_thms, thy6) = add_and_get_axiomss "cases" new_type_names
   662       (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
   663     val (split_ts, split_asm_ts) = ListPair.unzip
   664       (DatatypeProp.make_splits new_type_names descr sorts thy6);
   665     val (split, thy7) = add_and_get_axioms "split" new_type_names split_ts thy6;
   666     val (split_asm, thy8) = add_and_get_axioms "split_asm" new_type_names
   667       split_asm_ts thy7;
   668     val (nchotomys, thy9) = add_and_get_axioms "nchotomy" new_type_names
   669       (DatatypeProp.make_nchotomys descr sorts) thy8;
   670     val (case_congs, thy10) = add_and_get_axioms "case_cong" new_type_names
   671       (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
   672     val (weak_case_congs, thy11) = add_and_get_axioms "weak_case_cong" new_type_names
   673       (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
   674 
   675     val dt_infos = map (make_dt_info descr' sorts induct reccomb_names' rec_thms)
   676       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
   677         exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
   678           nchotomys ~~ case_congs ~~ weak_case_congs);
   679 
   680     val simps = List.concat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   681     val split_thms = split ~~ split_asm;
   682 
   683     val thy12 = thy11 |>
   684       Theory.add_advanced_trfuns ([], [], make_case_tr' case_names' (hd descr), []) |>
   685       Theory.add_path (space_implode "_" new_type_names) |>
   686       add_rules simps case_thms size_thms rec_thms inject distinct
   687                 weak_case_congs Simplifier.cong_add_global |> 
   688       put_datatypes (fold Symtab.update dt_infos dt_info) |>
   689       add_cases_induct dt_infos induct |>
   690       Theory.parent_path |>
   691       store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd |>
   692       DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
   693   in
   694     ({distinct = distinct,
   695       inject = inject,
   696       exhaustion = exhaustion,
   697       rec_thms = rec_thms,
   698       case_thms = case_thms,
   699       split_thms = split_thms,
   700       induction = induct,
   701       size = size_thms,
   702       simps = simps}, thy12)
   703   end;
   704 
   705 
   706 (******************* definitional introduction of datatypes *******************)
   707 
   708 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   709     case_names_induct case_names_exhausts thy =
   710   let
   711     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   712 
   713     val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |>
   714       DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
   715         types_syntax constr_syntax case_names_induct;
   716 
   717     val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
   718       sorts induct case_names_exhausts thy2;
   719     val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms
   720       flat_names new_type_names descr sorts dt_info inject dist_rewrites dist_ss induct thy3;
   721     val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms
   722       flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
   723     val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names
   724       descr sorts inject dist_rewrites casedist_thms case_thms thy6;
   725     val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names
   726       descr sorts casedist_thms thy7;
   727     val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names
   728       descr sorts nchotomys case_thms thy8;
   729     val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   730       descr sorts thy9;
   731     val (size_thms, thy11) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
   732       descr sorts reccomb_names rec_thms thy10;
   733 
   734     val dt_infos = map (make_dt_info (List.concat descr) sorts induct reccomb_names rec_thms)
   735       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
   736         casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   737 
   738     val simps = List.concat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   739 
   740     val thy12 = thy11 |>
   741       Theory.add_advanced_trfuns ([], [], make_case_tr' case_names (hd descr), []) |>
   742       Theory.add_path (space_implode "_" new_type_names) |>
   743       add_rules simps case_thms size_thms rec_thms inject distinct
   744                 weak_case_congs (Simplifier.change_global_ss (op addcongs)) |> 
   745       put_datatypes (fold Symtab.update dt_infos dt_info) |>
   746       add_cases_induct dt_infos induct |>
   747       Theory.parent_path |>
   748       store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd |>
   749       DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
   750   in
   751     ({distinct = distinct,
   752       inject = inject,
   753       exhaustion = casedist_thms,
   754       rec_thms = rec_thms,
   755       case_thms = case_thms,
   756       split_thms = split_thms,
   757       induction = induct,
   758       size = size_thms,
   759       simps = simps}, thy12)
   760   end;
   761 
   762 
   763 (*********************** declare existing type as datatype *********************)
   764 
   765 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
   766   let
   767     val _ = Theory.requires thy0 "Inductive" "datatype representations";
   768 
   769     val (((distinct, inject), [induction]), thy1) =
   770       thy0
   771       |> fold_map apply_theorems raw_distinct
   772       ||>> fold_map apply_theorems raw_inject
   773       ||>> apply_theorems [raw_induction];
   774     val sign = Theory.sign_of thy1;
   775 
   776     val induction' = freezeT induction;
   777 
   778     fun err t = error ("Ill-formed predicate in induction rule: " ^
   779       Sign.string_of_term sign t);
   780 
   781     fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
   782           ((tname, map dest_TFree Ts) handle TERM _ => err t)
   783       | get_typ t = err t;
   784 
   785     val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
   786     val new_type_names = getOpt (alt_names, map fst dtnames);
   787 
   788     fun get_constr t = (case Logic.strip_assums_concl t of
   789         _ $ (_ $ t') => (case head_of t' of
   790             Const (cname, cT) => (case strip_type cT of
   791                 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
   792               | _ => err t)
   793           | _ => err t)
   794       | _ => err t);
   795 
   796     fun make_dt_spec [] _ _ = []
   797       | make_dt_spec ((tname, tvs)::dtnames') i constrs =
   798           let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
   799           in (i, (tname, map DtTFree tvs, map snd constrs'))::
   800             (make_dt_spec dtnames' (i + 1) constrs'')
   801           end;
   802 
   803     val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
   804     val sorts = add_term_tfrees (concl_of induction', []);
   805     val dt_info = get_datatypes thy1;
   806 
   807     val case_names_induct = mk_case_names_induct descr;
   808     val case_names_exhausts = mk_case_names_exhausts descr (map #1 dtnames);
   809     
   810 
   811     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   812 
   813     val (casedist_thms, thy2) = thy1 |>
   814       DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
   815         case_names_exhausts;
   816     val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms
   817       false new_type_names [descr] sorts dt_info inject distinct dist_ss induction thy2;
   818     val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false
   819       new_type_names [descr] sorts reccomb_names rec_thms thy3;
   820     val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms
   821       new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
   822     val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names
   823       [descr] sorts casedist_thms thy5;
   824     val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names
   825       [descr] sorts nchotomys case_thms thy6;
   826     val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   827       [descr] sorts thy7;
   828     val (size_thms, thy9) =
   829       if Context.exists_name "NatArith" thy8 then
   830         DatatypeAbsProofs.prove_size_thms false new_type_names
   831           [descr] sorts reccomb_names rec_thms thy8
   832       else ([], thy8);
   833 
   834     val ((_, [induction']), thy10) =
   835       thy9
   836       |> store_thmss "inject" new_type_names inject
   837       ||>> store_thmss "distinct" new_type_names distinct
   838       ||> Theory.add_path (space_implode "_" new_type_names)
   839       ||>> PureThy.add_thms [(("induct", induction), [case_names_induct])];
   840 
   841     val dt_infos = map (make_dt_info descr sorts induction' reccomb_names rec_thms)
   842       ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~
   843         map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   844 
   845     val simps = List.concat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   846 
   847     val thy11 = thy10 |>
   848       Theory.add_advanced_trfuns ([], [], make_case_tr' case_names descr, []) |>
   849       add_rules simps case_thms size_thms rec_thms inject distinct
   850                 weak_case_congs (Simplifier.change_global_ss (op addcongs)) |> 
   851       put_datatypes (fold Symtab.update dt_infos dt_info) |>
   852       add_cases_induct dt_infos induction' |>
   853       Theory.parent_path |>
   854       (snd o store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)) |>
   855       DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
   856   in
   857     ({distinct = distinct,
   858       inject = inject,
   859       exhaustion = casedist_thms,
   860       rec_thms = rec_thms,
   861       case_thms = case_thms,
   862       split_thms = split_thms,
   863       induction = induction',
   864       size = size_thms,
   865       simps = simps}, thy11)
   866   end;
   867 
   868 val rep_datatype = gen_rep_datatype IsarThy.apply_theorems;
   869 val rep_datatype_i = gen_rep_datatype IsarThy.apply_theorems_i;
   870 
   871 
   872 
   873 (******************************** add datatype ********************************)
   874 
   875 fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =
   876   let
   877     val _ = Theory.requires thy "Datatype_Universe" "datatype definitions";
   878 
   879     (* this theory is used just for parsing *)
   880 
   881     val tmp_thy = thy |>
   882       Theory.copy |>
   883       Theory.add_types (map (fn (tvs, tname, mx, _) =>
   884         (tname, length tvs, mx)) dts);
   885 
   886     val sign = Theory.sign_of tmp_thy;
   887 
   888     val (tyvars, _, _, _)::_ = dts;
   889     val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
   890       let val full_tname = Sign.full_name sign (Syntax.type_name tname mx)
   891       in (case duplicates tvs of
   892             [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
   893                   else error ("Mutually recursive datatypes must have same type parameters")
   894           | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
   895               " : " ^ commas dups))
   896       end) dts);
   897 
   898     val _ = (case duplicates (map fst new_dts) @ duplicates new_type_names of
   899       [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
   900 
   901     fun prep_dt_spec ((dts', constr_syntax, sorts, i), (tvs, tname, mx, constrs)) =
   902       let
   903         fun prep_constr ((constrs, constr_syntax', sorts'), (cname, cargs, mx')) =
   904           let
   905             val (cargs', sorts'') = Library.foldl (prep_typ sign) (([], sorts'), cargs);
   906             val _ = (case foldr add_typ_tfree_names [] cargs' \\ tvs of
   907                 [] => ()
   908               | vs => error ("Extra type variables on rhs: " ^ commas vs))
   909           in (constrs @ [((if flat_names then Sign.full_name sign else
   910                 Sign.full_name_path sign tname) (Syntax.const_name cname mx'),
   911                    map (dtyp_of_typ new_dts) cargs')],
   912               constr_syntax' @ [(cname, mx')], sorts'')
   913           end handle ERROR =>
   914             error ("The error above occured in constructor " ^ cname ^
   915               " of datatype " ^ tname);
   916 
   917         val (constrs', constr_syntax', sorts') =
   918           Library.foldl prep_constr (([], [], sorts), constrs)
   919 
   920       in
   921         case duplicates (map fst constrs') of
   922            [] =>
   923              (dts' @ [(i, (Sign.full_name sign (Syntax.type_name tname mx),
   924                 map DtTFree tvs, constrs'))],
   925               constr_syntax @ [constr_syntax'], sorts', i + 1)
   926          | dups => error ("Duplicate constructors " ^ commas dups ^
   927              " in datatype " ^ tname)
   928       end;
   929 
   930     val (dts', constr_syntax, sorts', i) = Library.foldl prep_dt_spec (([], [], [], 0), dts);
   931     val sorts = sorts' @ (map (rpair (Sign.defaultS sign)) (tyvars \\ map fst sorts'));
   932     val dt_info = get_datatypes thy;
   933     val (descr, _) = unfold_datatypes sign dts' sorts dt_info dts' i;
   934     val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>
   935       if err then error ("Nonemptiness check failed for datatype " ^ s)
   936       else raise exn;
   937 
   938     val descr' = List.concat descr;
   939     val case_names_induct = mk_case_names_induct descr';
   940     val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
   941   in
   942     (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
   943       flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   944       case_names_induct case_names_exhausts thy
   945   end;
   946 
   947 val add_datatype_i = gen_add_datatype cert_typ;
   948 val add_datatype = gen_add_datatype read_typ true;
   949 
   950 
   951 (** package setup **)
   952 
   953 (* setup theory *)
   954 
   955 val setup = [DatatypesData.init, Method.add_methods tactic_emulations] @ simproc_setup @ trfun_setup;
   956 
   957 
   958 (* outer syntax *)
   959 
   960 local structure P = OuterParse and K = OuterKeyword in
   961 
   962 val datatype_decl =
   963   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
   964     (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
   965 
   966 fun mk_datatype args =
   967   let
   968     val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
   969     val specs = map (fn ((((_, vs), t), mx), cons) =>
   970       (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
   971   in snd o add_datatype false names specs end;
   972 
   973 val datatypeP =
   974   OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
   975     (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
   976 
   977 
   978 val rep_datatype_decl =
   979   Scan.option (Scan.repeat1 P.name) --
   980     Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
   981     Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
   982     (P.$$$ "induction" |-- P.!!! P.xthm);
   983 
   984 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #2 o rep_datatype opt_ts dss iss ind;
   985 
   986 val rep_datatypeP =
   987   OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
   988     (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
   989 
   990 
   991 val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
   992 val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
   993 
   994 end;
   995 
   996 
   997 end;
   998 
   999 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
  1000 open BasicDatatypePackage;
  1001