src/HOL/Tools/datatype_package.ML
author haftmann
Fri Feb 10 09:09:07 2006 +0100 (2006-02-10)
changeset 19008 14c1b2f5dda4
parent 18988 d6e5fa2ba8b8
child 19046 bc5c6c9b114e
permissions -rw-r--r--
improved code generator devarification
     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 * attribute list) list list ->
    43     (thm list * attribute list) list list -> (thm list * 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 get_datatype : theory -> string -> ((string * sort) list * (string * typ list) list) option
    70   val get_datatype_case_consts : theory -> string list
    71   val get_case_const_data : theory -> string -> (string * int) list option
    72   val get_all_datatype_cons : theory -> (string * string) list
    73   val get_eq_equations: theory -> string -> thm list
    74   val constrs_of : theory -> string -> term list option
    75   val case_const_of : theory -> string -> term option
    76   val weak_case_congs_of : theory -> thm list
    77   val setup: theory -> theory
    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 DatatypesData = TheoryDataFun
    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 extend = I;
    98   fun merge _ tabs : T = Symtab.merge (K true) tabs;
    99 
   100   fun print sg tab =
   101     Pretty.writeln (Pretty.strs ("datatypes:" ::
   102       map #1 (NameSpace.extern_table (Sign.type_space sg, tab))));
   103 end);
   104 
   105 val get_datatypes = DatatypesData.get;
   106 val put_datatypes = DatatypesData.put;
   107 val print_datatypes = DatatypesData.print;
   108 
   109 
   110 (** theory information about datatypes **)
   111 
   112 val datatype_info = Symtab.lookup o get_datatypes;
   113 
   114 fun datatype_info_err thy name = (case datatype_info thy name of
   115       SOME info => info
   116     | NONE => error ("Unknown datatype " ^ quote name));
   117 
   118 fun constrs_of thy tname = (case datatype_info thy tname of
   119    SOME {index, descr, ...} =>
   120      let val (_, _, constrs) = valOf (AList.lookup (op =) descr index)
   121      in SOME (map (fn (cname, _) => Const (cname, Sign.the_const_type thy cname)) constrs)
   122      end
   123  | _ => NONE);
   124 
   125 fun case_const_of thy tname = (case datatype_info thy tname of
   126    SOME {case_name, ...} => SOME (Const (case_name, Sign.the_const_type thy case_name))
   127  | _ => NONE);
   128 
   129 val weak_case_congs_of = map (#weak_case_cong o #2) o Symtab.dest o get_datatypes;
   130 
   131 fun get_datatype thy dtco =
   132   let
   133     fun get_cons descr vs =
   134       apsnd (map (DatatypeAux.typ_of_dtyp descr
   135         ((map (rpair []) o map DatatypeAux.dest_DtTFree) vs)));
   136     fun get_info ({ sorts, descr, ... } : DatatypeAux.datatype_info) =
   137       (sorts,
   138         ((the oo get_first) (fn (_, (dtco', tys, cs)) =>
   139             if dtco = dtco'
   140             then SOME (map (get_cons descr tys) cs)
   141             else NONE) descr));
   142   in case Symtab.lookup (get_datatypes thy) dtco
   143    of SOME info => (SOME o get_info) info
   144     | NONE => NONE
   145   end;
   146 
   147 fun get_datatype_case_consts thy =
   148   Symtab.fold (fn (_, {case_name, ...}) => cons case_name) (get_datatypes thy) [];
   149 
   150 fun get_case_const_data thy c =
   151   case find_first (fn (_, {index, descr, case_name, ...}) =>
   152       case_name = c
   153     ) ((Symtab.dest o get_datatypes) thy)
   154    of NONE => NONE
   155     | SOME (_, {index, descr, ...}) =>
   156         (SOME o map (apsnd length) o #3 o the o AList.lookup (op =) descr) index;
   157 
   158 fun get_all_datatype_cons thy =
   159   Symtab.fold (fn (dtco, _) => fold
   160     (fn (co, _) => cons (co, dtco))
   161       ((snd o the oo get_datatype) thy dtco)) (get_datatypes thy) [];
   162 
   163 fun get_eq_equations thy dtco =
   164   case get_datatype thy dtco
   165    of SOME (vars, cos) =>
   166         let
   167           fun co_inject thm =
   168             ((fst o dest_Const o fst o strip_comb o fst o HOLogic.dest_eq o fst
   169               o HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.prop_of) thm, thm RS HOL.eq_reflection);
   170           val inject = (map co_inject o #inject o the o datatype_info thy) dtco;
   171           fun mk_refl co =
   172             let
   173               fun infer t =
   174                 (fst o Sign.infer_types (Sign.pp thy) thy (Sign.consts_of thy) (K NONE) (K NONE) [] true)
   175                   ([t], Type (dtco, map (fn (v, sort) => TVar ((v, 0), sort)) vars))
   176               val t = (Thm.cterm_of thy o infer) (Const (co, dummyT));
   177             in
   178               HOL.refl 
   179               |> Drule.instantiate' [(SOME o Thm.ctyp_of_term) t] [SOME t]
   180               |> (fn thm => thm RS Eq_TrueI)
   181             end;
   182           fun get_eq co =
   183            case AList.lookup (op =) inject co
   184             of SOME eq => eq
   185              | NONE => mk_refl co;
   186         in map (get_eq o fst) cos end
   187    | NONE => [];
   188 
   189 fun find_tname var Bi =
   190   let val frees = map dest_Free (term_frees Bi)
   191       val params = rename_wrt_term Bi (Logic.strip_params Bi);
   192   in case AList.lookup (op =) (frees @ params) var of
   193        NONE => error ("No such variable in subgoal: " ^ quote var)
   194      | SOME(Type (tn, _)) => tn
   195      | _ => error ("Cannot determine type of " ^ quote var)
   196   end;
   197 
   198 fun infer_tname state i aterm =
   199   let
   200     val sign = Thm.sign_of_thm state;
   201     val (_, _, Bi, _) = Thm.dest_state (state, i)
   202     val params = Logic.strip_params Bi;   (*params of subgoal i*)
   203     val params = rev (rename_wrt_term Bi params);   (*as they are printed*)
   204     val (types, sorts) = types_sorts state;
   205     fun types' (a, ~1) = (case AList.lookup (op =) params a of NONE => types(a, ~1) | sm => sm)
   206       | types' ixn = types ixn;
   207     val (ct, _) = read_def_cterm (sign, types', sorts) [] false (aterm, TypeInfer.logicT);
   208   in case #T (rep_cterm ct) of
   209        Type (tn, _) => tn
   210      | _ => error ("Cannot determine type of " ^ quote aterm)
   211   end;
   212 
   213 (*Warn if the (induction) variable occurs Free among the premises, which
   214   usually signals a mistake.  But calls the tactic either way!*)
   215 fun occs_in_prems tacf vars =
   216   SUBGOAL (fn (Bi, i) =>
   217            (if  exists (fn Free (a, _) => a mem vars)
   218                       (foldr add_term_frees [] (#2 (strip_context Bi)))
   219              then warning "Induction variable occurs also among premises!"
   220              else ();
   221             tacf i));
   222 
   223 
   224 (* generic induction tactic for datatypes *)
   225 
   226 local
   227 
   228 fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x)
   229   | prep_var _ = NONE;
   230 
   231 fun prep_inst (concl, xs) =	(*exception UnequalLengths *)
   232   let val vs = InductAttrib.vars_of concl
   233   in List.mapPartial prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
   234 
   235 in
   236 
   237 fun gen_induct_tac inst_tac (varss, opt_rule) i state = 
   238   SUBGOAL (fn (Bi,_) =>
   239   let
   240     val (rule, rule_name) =
   241       case opt_rule of
   242 	  SOME r => (r, "Induction rule")
   243 	| NONE =>
   244 	    let val tn = find_tname (hd (List.mapPartial I (List.concat varss))) Bi
   245                 val {sign, ...} = Thm.rep_thm state
   246 	    in (#induction (datatype_info_err sign tn), "Induction rule for type " ^ tn) 
   247 	    end
   248     val concls = HOLogic.dest_concls (Thm.concl_of rule);
   249     val insts = List.concat (map prep_inst (concls ~~ varss)) handle UnequalLengths =>
   250       error (rule_name ^ " has different numbers of variables");
   251   in occs_in_prems (inst_tac insts rule) (map #2 insts) i end)
   252   i state;
   253 
   254 fun induct_tac s =
   255   gen_induct_tac Tactic.res_inst_tac'
   256     (map (Library.single o SOME) (Syntax.read_idents s), NONE);
   257 
   258 fun induct_thm_tac th s =
   259   gen_induct_tac Tactic.res_inst_tac'
   260     ([map SOME (Syntax.read_idents s)], SOME th);
   261 
   262 end;
   263 
   264 
   265 (* generic case tactic for datatypes *)
   266 
   267 fun case_inst_tac inst_tac t rule i state =
   268   let
   269     val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
   270       (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));
   271   in inst_tac [(ixn, t)] rule i state end;
   272 
   273 fun gen_case_tac inst_tac (t, SOME rule) i state =
   274       case_inst_tac inst_tac t rule i state
   275   | gen_case_tac inst_tac (t, NONE) i state =
   276       let val tn = infer_tname state i t in
   277         if tn = HOLogic.boolN then inst_tac [(("P", 0), t)] case_split_thm i state
   278         else case_inst_tac inst_tac t
   279                (#exhaustion (datatype_info_err (Thm.sign_of_thm state) tn))
   280                i state
   281       end handle THM _ => Seq.empty;
   282 
   283 fun case_tac t = gen_case_tac Tactic.res_inst_tac' (t, NONE);
   284 
   285 
   286 
   287 (** Isar tactic emulations **)
   288 
   289 local
   290 
   291 val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
   292 val opt_rule = Scan.option (rule_spec |-- Attrib.thm);
   293 
   294 val varss =
   295   Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name))));
   296 
   297 val inst_tac = Method.bires_inst_tac false;
   298 
   299 fun induct_meth ctxt (varss, opt_rule) =
   300   gen_induct_tac (inst_tac ctxt) (varss, opt_rule);
   301 fun case_meth ctxt (varss, opt_rule) =
   302   gen_case_tac (inst_tac ctxt) (varss, opt_rule);
   303 
   304 in
   305 
   306 val tactic_emulations =
   307  [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth,
   308     "induct_tac emulation (dynamic instantiation)"),
   309   ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth,
   310     "case_tac emulation (dynamic instantiation)")];
   311 
   312 end;
   313 
   314 
   315 
   316 (** induct method setup **)
   317 
   318 (* case names *)
   319 
   320 local
   321 
   322 fun dt_recs (DtTFree _) = []
   323   | dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts)
   324   | dt_recs (DtRec i) = [i];
   325 
   326 fun dt_cases (descr: descr) (_, args, constrs) =
   327   let
   328     fun the_bname i = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i)));
   329     val bnames = map the_bname (distinct (List.concat (map dt_recs args)));
   330   in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
   331 
   332 
   333 fun induct_cases descr =
   334   DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr)));
   335 
   336 fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i));
   337 
   338 in
   339 
   340 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
   341 
   342 fun mk_case_names_exhausts descr new =
   343   map (RuleCases.case_names o exhaust_cases descr o #1)
   344     (List.filter (fn ((_, (name, _, _))) => name mem_string new) descr);
   345 
   346 end;
   347 
   348 (*Name management for ATP linkup. The suffix here must agree with the one given
   349   for notE in Clasimp.addIff*)
   350 fun name_notE th =
   351     Thm.name_thm (Thm.name_of_thm th ^ "_iff1", th RS notE);
   352       
   353 fun add_rules simps case_thms size_thms rec_thms inject distinct
   354                   weak_case_congs cong_att =
   355   (snd o PureThy.add_thmss [(("simps", simps), []),
   356     (("", List.concat case_thms @ size_thms @ 
   357           List.concat distinct  @ rec_thms), [Simplifier.simp_add]),
   358     (("", size_thms @ rec_thms),             [RecfunCodegen.add NONE]),
   359     (("", List.concat inject),               [iff_add]),
   360     (("", map name_notE (List.concat distinct)),  [Classical.safe_elim NONE]),
   361     (("", weak_case_congs),                  [cong_att])]);
   362 
   363 
   364 (* add_cases_induct *)
   365 
   366 fun add_cases_induct infos induction =
   367   let
   368     val n = length (HOLogic.dest_concls (Thm.concl_of induction));
   369     fun proj i = ProjectRule.project induction (i + 1);
   370 
   371     fun named_rules (name, {index, exhaustion, ...}: datatype_info) =
   372       [(("", proj index), [InductAttrib.induct_type name]),
   373        (("", exhaustion), [InductAttrib.cases_type name])];
   374     fun unnamed_rule i =
   375       (("", proj i), [PureThy.kind_internal, InductAttrib.induct_type ""]);
   376   in
   377     PureThy.add_thms
   378       (List.concat (map named_rules infos) @
   379         map unnamed_rule (length infos upto n - 1)) #> snd #>
   380     PureThy.add_thmss [(("inducts",
   381       map (proj #> standard #> RuleCases.save induction) (0 upto n - 1)), [])] #> snd
   382   end;
   383 
   384 
   385 
   386 (**** simplification procedure for showing distinctness of constructors ****)
   387 
   388 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
   389   | stripT p = p;
   390 
   391 fun stripC (i, f $ x) = stripC (i + 1, f)
   392   | stripC p = p;
   393 
   394 val distinctN = "constr_distinct";
   395 
   396 exception ConstrDistinct of term;
   397 
   398 fun distinct_proc sg ss (t as Const ("op =", _) $ t1 $ t2) =
   399   (case (stripC (0, t1), stripC (0, t2)) of
   400      ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
   401          (case (stripT (0, T1), stripT (0, T2)) of
   402             ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
   403                 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
   404                    (case (constrs_of sg tname1) of
   405                       SOME constrs => let val cnames = map (fst o dest_Const) constrs
   406                         in if cname1 mem cnames andalso cname2 mem cnames then
   407                              let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));
   408                                  val eq_ct = cterm_of sg eq_t;
   409                                  val Datatype_thy = theory "Datatype";
   410                                  val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
   411                                    map (get_thm Datatype_thy o Name)
   412                                      ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
   413                              in (case (#distinct (datatype_info_err sg tname1)) of
   414                                  QuickAndDirty => SOME (Thm.invoke_oracle
   415                                    Datatype_thy distinctN (sg, ConstrDistinct eq_t))
   416                                | FewConstrs thms => SOME (Goal.prove sg [] [] eq_t (K
   417                                    (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
   418                                     atac 2, resolve_tac thms 1, etac FalseE 1])))
   419                                | ManyConstrs (thm, simpset) => SOME (Goal.prove sg [] [] eq_t (K
   420                                    (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
   421                                     full_simp_tac (Simplifier.inherit_context ss simpset) 1,
   422                                     REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
   423                                     eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
   424                                     etac FalseE 1]))))
   425                              end
   426                            else NONE
   427                         end
   428                     | NONE => NONE)
   429                 else NONE
   430           | _ => NONE)
   431    | _ => NONE)
   432   | distinct_proc sg _ _ = NONE;
   433 
   434 val distinct_simproc =
   435   Simplifier.simproc HOL.thy distinctN ["s = t"] distinct_proc;
   436 
   437 val dist_ss = HOL_ss addsimprocs [distinct_simproc];
   438 
   439 val simproc_setup =
   440   Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t) #>
   441   (fn thy => ((change_simpset_of thy) (fn ss => ss addsimprocs [distinct_simproc]); thy));
   442 
   443 
   444 (**** translation rules for case ****)
   445 
   446 fun find_first f = Library.find_first f;
   447 
   448 fun case_tr context [t, u] =
   449     let
   450       val thy = Context.theory_of context;
   451       fun case_error s name ts = raise TERM ("Error in case expression" ^
   452         getOpt (Option.map (curry op ^ " for datatype ") name, "") ^ ":\n" ^ s, ts);
   453       fun dest_case1 (Const ("_case1", _) $ t $ u) = (case strip_comb t of
   454             (Const (s, _), ts) => (Sign.intern_const thy s, ts)
   455           | (Free (s, _), ts) => (Sign.intern_const thy s, ts)
   456           | _ => case_error "Head is not a constructor" NONE [t, u], u)
   457         | dest_case1 t = raise TERM ("dest_case1", [t]);
   458       fun dest_case2 (Const ("_case2", _) $ t $ u) = t :: dest_case2 u
   459         | dest_case2 t = [t];
   460       val cases as ((cname, _), _) :: _ = map dest_case1 (dest_case2 u);
   461       val tab = Symtab.dest (get_datatypes thy);
   462       val (cases', default) = (case split_last cases of
   463           (cases', (("dummy_pattern", []), t)) => (cases', SOME t)
   464         | _ => (cases, NONE))
   465       fun abstr (Free (x, T), body) = Term.absfree (x, T, body)
   466         | abstr (Const ("_constrain", _) $ Free (x, T) $ tT, body) =
   467             Syntax.const Syntax.constrainAbsC $ Term.absfree (x, T, body) $ tT
   468         | abstr (Const ("Pair", _) $ x $ y, body) =
   469             Syntax.const "split" $ abstr (x, abstr (y, body))
   470         | abstr (t, _) = case_error "Illegal pattern" NONE [t];
   471     in case find_first (fn (_, {descr, index, ...}) =>
   472       exists (equal cname o fst) (#3 (snd (List.nth (descr, index))))) tab of
   473         NONE => case_error ("Not a datatype constructor: " ^ cname) NONE [u]
   474       | SOME (tname, {descr, sorts, case_name, index, ...}) =>
   475         let
   476           val _ = if exists (equal "dummy_pattern" o fst o fst) cases' then
   477             case_error "Illegal occurrence of '_' dummy pattern" (SOME tname) [u] else ();
   478           val (_, (_, dts, constrs)) = List.nth (descr, index);
   479           fun find_case (cases, (s, dt)) =
   480             (case find_first (equal s o fst o fst) cases' of
   481                NONE => (case default of
   482                    NONE => case_error ("No clause for constructor " ^ s) (SOME tname) [u]
   483                  | SOME t => (cases, list_abs (map (rpair dummyT) (DatatypeProp.make_tnames
   484                      (map (typ_of_dtyp descr sorts) dt)), t)))
   485              | SOME (c as ((_, vs), t)) =>
   486                  if length dt <> length vs then
   487                     case_error ("Wrong number of arguments for constructor " ^ s)
   488                       (SOME tname) vs
   489                  else (cases \ c, foldr abstr t vs))
   490           val (cases'', fs) = foldl_map find_case (cases', constrs)
   491         in case (cases'', length constrs = length cases', default) of
   492             ([], true, SOME _) =>
   493               case_error "Extra '_' dummy pattern" (SOME tname) [u]
   494           | (_ :: _, _, _) =>
   495               let val extra = distinct (map (fst o fst) cases'')
   496               in case extra \\ map fst constrs of
   497                   [] => case_error ("More than one clause for constructor(s) " ^
   498                     commas extra) (SOME tname) [u]
   499                 | extra' => case_error ("Illegal constructor(s): " ^ commas extra')
   500                     (SOME tname) [u]
   501               end
   502           | _ => list_comb (Syntax.const case_name, fs) $ t
   503         end
   504     end
   505   | case_tr _ ts = raise TERM ("case_tr", ts);
   506 
   507 fun case_tr' constrs context ts =
   508   if length ts <> length constrs + 1 then raise Match else
   509   let
   510     val (fs, x) = split_last ts;
   511     fun strip_abs 0 t = ([], t)
   512       | strip_abs i (Abs p) =
   513         let val (x, u) = Syntax.atomic_abs_tr' p
   514         in apfst (cons x) (strip_abs (i-1) u) end
   515       | strip_abs i (Const ("split", _) $ t) = (case strip_abs (i+1) t of
   516           (v :: v' :: vs, u) => (Syntax.const "Pair" $ v $ v' :: vs, u));
   517     fun is_dependent i t =
   518       let val k = length (strip_abs_vars t) - i
   519       in k < 0 orelse exists (fn j => j >= k)
   520         (loose_bnos (strip_abs_body t))
   521       end;
   522     val cases = map (fn ((cname, dts), t) =>
   523       (Sign.extern_const (Context.theory_of context) cname,
   524        strip_abs (length dts) t, is_dependent (length dts) t))
   525       (constrs ~~ fs);
   526     fun count_cases (cs, (_, _, true)) = cs
   527       | count_cases (cs, (cname, (_, body), false)) = (case AList.lookup (op =) cs body of
   528           NONE => (body, [cname]) :: cs
   529         | SOME cnames => AList.update (op =) (body, cnames @ [cname]) cs);
   530     val cases' = sort (int_ord o Library.swap o pairself (length o snd))
   531       (Library.foldl count_cases ([], cases));
   532     fun mk_case1 (cname, (vs, body), _) = Syntax.const "_case1" $
   533       list_comb (Syntax.const cname, vs) $ body;
   534   in
   535     Syntax.const "_case_syntax" $ x $
   536       foldr1 (fn (t, u) => Syntax.const "_case2" $ t $ u) (map mk_case1
   537         (case cases' of
   538            [] => cases
   539          | (default, cnames) :: _ =>
   540            if length cnames = 1 then cases
   541            else if length cnames = length constrs then
   542              [hd cases, ("dummy_pattern", ([], default), false)]
   543            else
   544              filter_out (fn (cname, _, _) => cname mem cnames) cases @
   545              [("dummy_pattern", ([], default), false)]))
   546   end;
   547 
   548 fun make_case_tr' case_names descr = List.concat (map
   549   (fn ((_, (_, _, constrs)), case_name) => map (rpair (case_tr' constrs))
   550     (NameSpace.accesses' case_name)) (descr ~~ case_names));
   551 
   552 val trfun_setup =
   553   Theory.add_advanced_trfuns ([], [("_case_syntax", case_tr)], [], []);
   554 
   555 
   556 (* prepare types *)
   557 
   558 fun read_typ sign ((Ts, sorts), str) =
   559   let
   560     val T = Type.no_tvars (Sign.read_typ (sign, AList.lookup (op =)
   561       (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
   562   in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
   563 
   564 fun cert_typ sign ((Ts, sorts), raw_T) =
   565   let
   566     val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
   567       TYPE (msg, _, _) => error msg;
   568     val sorts' = add_typ_tfrees (T, sorts)
   569   in (Ts @ [T],
   570       case duplicates (op =) (map fst sorts') of
   571          [] => sorts'
   572        | dups => error ("Inconsistent sort constraints for " ^ commas dups))
   573   end;
   574 
   575 
   576 (**** make datatype info ****)
   577 
   578 fun make_dt_info descr sorts induct reccomb_names rec_thms
   579     (((((((((i, (_, (tname, _, _))), case_name), case_thms),
   580       exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =
   581   (tname,
   582    {index = i,
   583     descr = descr,
   584     sorts = sorts,
   585     rec_names = reccomb_names,
   586     rec_rewrites = rec_thms,
   587     case_name = case_name,
   588     case_rewrites = case_thms,
   589     induction = induct,
   590     exhaustion = exhaustion_thm,
   591     distinct = distinct_thm,
   592     inject = inject,
   593     nchotomy = nchotomy,
   594     case_cong = case_cong,
   595     weak_case_cong = weak_case_cong});
   596 
   597 
   598 (********************* axiomatic introduction of datatypes ********************)
   599 
   600 fun add_and_get_axioms_atts label tnames attss ts thy =
   601   foldr (fn (((tname, atts), t), (thy', axs)) =>
   602     let
   603       val ([ax], thy'') =
   604         thy'
   605         |> Theory.add_path tname
   606         |> PureThy.add_axioms_i [((label, t), atts)];
   607     in (Theory.parent_path thy'', ax::axs)
   608     end) (thy, []) (tnames ~~ attss ~~ ts) |> swap;
   609 
   610 fun add_and_get_axioms label tnames =
   611   add_and_get_axioms_atts label tnames (replicate (length tnames) []);
   612 
   613 fun add_and_get_axiomss label tnames tss thy =
   614   foldr (fn ((tname, ts), (thy', axss)) =>
   615     let
   616       val ([axs], thy'') =
   617         thy'
   618         |> Theory.add_path tname
   619         |> PureThy.add_axiomss_i [((label, ts), [])];
   620     in (Theory.parent_path thy'', axs::axss)
   621     end) (thy, []) (tnames ~~ tss) |> swap;
   622 
   623 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   624     case_names_induct case_names_exhausts thy =
   625   let
   626     val descr' = List.concat descr;
   627     val recTs = get_rec_types descr' sorts;
   628     val used = foldr add_typ_tfree_names [] recTs;
   629     val newTs = Library.take (length (hd descr), recTs);
   630 
   631     val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
   632       (fn dt => is_rec_type dt andalso not (null (fst (strip_dtyp dt))))
   633         cargs) constrs) descr';
   634 
   635     (**** declare new types and constants ****)
   636 
   637     val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
   638 
   639     val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
   640       map (fn ((_, cargs), (cname, mx)) =>
   641         (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   642           (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
   643 
   644     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   645 
   646     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   647     val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
   648       (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   649         (1 upto (length descr')));
   650 
   651     val size_names = DatatypeProp.indexify_names
   652       (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs)));
   653 
   654     val freeT = TFree (variant used "'t", HOLogic.typeS);
   655     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
   656       map (fn (_, cargs) =>
   657         let val Ts = map (typ_of_dtyp descr' sorts) cargs
   658         in Ts ---> freeT end) constrs) (hd descr);
   659 
   660     val case_names = map (fn s => (s ^ "_case")) new_type_names;
   661 
   662     val thy2' = thy |>
   663 
   664       (** new types **)
   665 
   666       curry (Library.foldr (fn (((name, mx), tvs), thy') => thy' |>
   667           TypedefPackage.add_typedecls [(name, tvs, mx)]))
   668         (types_syntax ~~ tyvars) |>
   669       add_path flat_names (space_implode "_" new_type_names) |>
   670 
   671       (** primrec combinators **)
   672 
   673       Theory.add_consts_i (map (fn ((name, T), T') =>
   674         (name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   675           (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
   676 
   677       (** case combinators **)
   678 
   679       Theory.add_consts_i (map (fn ((name, T), Ts) =>
   680         (name, Ts @ [T] ---> freeT, NoSyn))
   681           (case_names ~~ newTs ~~ case_fn_Ts));
   682 
   683     val reccomb_names' = map (Sign.intern_const thy2') reccomb_names;
   684     val case_names' = map (Sign.intern_const thy2') case_names;
   685 
   686     val thy2 = thy2' |>
   687 
   688       (** size functions **)
   689 
   690       (if no_size then I else Theory.add_consts_i (map (fn (s, T) =>
   691         (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   692           (size_names ~~ Library.drop (length (hd descr), recTs)))) |>
   693 
   694       (** constructors **)
   695 
   696       parent_path flat_names |>
   697       curry (Library.foldr (fn (((((_, (_, _, constrs)), T), tname),
   698         constr_syntax'), thy') => thy' |>
   699           add_path flat_names tname |>
   700             Theory.add_consts_i (map (fn ((_, cargs), (cname, mx)) =>
   701               (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   702                 (constrs ~~ constr_syntax')) |>
   703           parent_path flat_names))
   704             (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
   705 
   706     (**** introduction of axioms ****)
   707 
   708     val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
   709     val size_axs = if no_size then [] else DatatypeProp.make_size descr sorts thy2;
   710 
   711     val ((([induct], [rec_thms]), inject), thy3) =
   712       thy2
   713       |> Theory.add_path (space_implode "_" new_type_names)
   714       |> PureThy.add_axioms_i [(("induct", DatatypeProp.make_ind descr sorts),
   715           [case_names_induct])]
   716       ||>> PureThy.add_axiomss_i [(("recs", rec_axs), [])]
   717       ||> (if no_size then I else snd o PureThy.add_axiomss_i [(("size", size_axs), [])])
   718       ||> Theory.parent_path
   719       ||>> add_and_get_axiomss "inject" new_type_names
   720             (DatatypeProp.make_injs descr sorts);
   721     val size_thms = if no_size then [] else get_thms thy3 (Name "size");
   722     val (distinct, thy4) = add_and_get_axiomss "distinct" new_type_names
   723       (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
   724 
   725     val exhaust_ts = DatatypeProp.make_casedists descr sorts;
   726     val (exhaustion, thy5) = add_and_get_axioms_atts "exhaust" new_type_names
   727       (map Library.single case_names_exhausts) exhaust_ts thy4;
   728     val (case_thms, thy6) = add_and_get_axiomss "cases" new_type_names
   729       (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
   730     val (split_ts, split_asm_ts) = ListPair.unzip
   731       (DatatypeProp.make_splits new_type_names descr sorts thy6);
   732     val (split, thy7) = add_and_get_axioms "split" new_type_names split_ts thy6;
   733     val (split_asm, thy8) = add_and_get_axioms "split_asm" new_type_names
   734       split_asm_ts thy7;
   735     val (nchotomys, thy9) = add_and_get_axioms "nchotomy" new_type_names
   736       (DatatypeProp.make_nchotomys descr sorts) thy8;
   737     val (case_congs, thy10) = add_and_get_axioms "case_cong" new_type_names
   738       (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
   739     val (weak_case_congs, thy11) = add_and_get_axioms "weak_case_cong" new_type_names
   740       (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
   741 
   742     val dt_infos = map (make_dt_info descr' sorts induct reccomb_names' rec_thms)
   743       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
   744         exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
   745           nchotomys ~~ case_congs ~~ weak_case_congs);
   746 
   747     val simps = List.concat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   748     val split_thms = split ~~ split_asm;
   749 
   750     val thy12 =
   751       thy11
   752       |> Theory.add_advanced_trfuns ([], [], make_case_tr' case_names' (hd descr), [])
   753       |> Theory.add_path (space_implode "_" new_type_names)
   754       |> add_rules simps case_thms size_thms rec_thms inject distinct
   755           weak_case_congs Simplifier.cong_add
   756       |> put_datatypes (fold Symtab.update dt_infos dt_info)
   757       |> add_cases_induct dt_infos induct
   758       |> Theory.parent_path
   759       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd
   760       |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
   761       |> fold (CodegenPackage.add_case_const_i get_case_const_data) case_names';
   762   in
   763     ({distinct = distinct,
   764       inject = inject,
   765       exhaustion = exhaustion,
   766       rec_thms = rec_thms,
   767       case_thms = case_thms,
   768       split_thms = split_thms,
   769       induction = induct,
   770       size = size_thms,
   771       simps = simps}, thy12)
   772   end;
   773 
   774 
   775 (******************* definitional introduction of datatypes *******************)
   776 
   777 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   778     case_names_induct case_names_exhausts thy =
   779   let
   780     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   781 
   782     val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |>
   783       DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
   784         types_syntax constr_syntax case_names_induct;
   785 
   786     val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
   787       sorts induct case_names_exhausts thy2;
   788     val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms
   789       flat_names new_type_names descr sorts dt_info inject dist_rewrites dist_ss induct thy3;
   790     val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms
   791       flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
   792     val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names
   793       descr sorts inject dist_rewrites casedist_thms case_thms thy6;
   794     val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names
   795       descr sorts casedist_thms thy7;
   796     val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names
   797       descr sorts nchotomys case_thms thy8;
   798     val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   799       descr sorts thy9;
   800     val (size_thms, thy11) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
   801       descr sorts reccomb_names rec_thms thy10;
   802 
   803     val dt_infos = map (make_dt_info (List.concat descr) sorts induct reccomb_names rec_thms)
   804       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
   805         casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   806 
   807     val simps = List.concat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   808 
   809     val thy12 =
   810       thy11
   811       |> Theory.add_advanced_trfuns ([], [], make_case_tr' case_names (hd descr), [])
   812       |> Theory.add_path (space_implode "_" new_type_names)
   813       |> add_rules simps case_thms size_thms rec_thms inject distinct
   814           weak_case_congs (Simplifier.attrib (op addcongs))
   815       |> put_datatypes (fold Symtab.update dt_infos dt_info)
   816       |> add_cases_induct dt_infos induct
   817       |> Theory.parent_path
   818       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd
   819       |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
   820       |> fold (CodegenPackage.add_case_const_i get_case_const_data) case_names;
   821   in
   822     ({distinct = distinct,
   823       inject = inject,
   824       exhaustion = casedist_thms,
   825       rec_thms = rec_thms,
   826       case_thms = case_thms,
   827       split_thms = split_thms,
   828       induction = induct,
   829       size = size_thms,
   830       simps = simps}, thy12)
   831   end;
   832 
   833 
   834 (*********************** declare existing type as datatype *********************)
   835 
   836 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
   837   let
   838     val _ = Theory.requires thy0 "Inductive" "datatype representations";
   839 
   840     val (((distinct, inject), [induction]), thy1) =
   841       thy0
   842       |> fold_map apply_theorems raw_distinct
   843       ||>> fold_map apply_theorems raw_inject
   844       ||>> apply_theorems [raw_induction];
   845     val sign = Theory.sign_of thy1;
   846 
   847     val induction' = freezeT induction;
   848 
   849     fun err t = error ("Ill-formed predicate in induction rule: " ^
   850       Sign.string_of_term sign t);
   851 
   852     fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
   853           ((tname, map dest_TFree Ts) handle TERM _ => err t)
   854       | get_typ t = err t;
   855 
   856     val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
   857     val new_type_names = getOpt (alt_names, map fst dtnames);
   858 
   859     fun get_constr t = (case Logic.strip_assums_concl t of
   860         _ $ (_ $ t') => (case head_of t' of
   861             Const (cname, cT) => (case strip_type cT of
   862                 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
   863               | _ => err t)
   864           | _ => err t)
   865       | _ => err t);
   866 
   867     fun make_dt_spec [] _ _ = []
   868       | make_dt_spec ((tname, tvs)::dtnames') i constrs =
   869           let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
   870           in (i, (tname, map DtTFree tvs, map snd constrs'))::
   871             (make_dt_spec dtnames' (i + 1) constrs'')
   872           end;
   873 
   874     val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
   875     val sorts = add_term_tfrees (concl_of induction', []);
   876     val dt_info = get_datatypes thy1;
   877 
   878     val case_names_induct = mk_case_names_induct descr;
   879     val case_names_exhausts = mk_case_names_exhausts descr (map #1 dtnames);
   880     
   881 
   882     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   883 
   884     val (casedist_thms, thy2) = thy1 |>
   885       DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
   886         case_names_exhausts;
   887     val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms
   888       false new_type_names [descr] sorts dt_info inject distinct dist_ss induction thy2;
   889     val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false
   890       new_type_names [descr] sorts reccomb_names rec_thms thy3;
   891     val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms
   892       new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
   893     val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names
   894       [descr] sorts casedist_thms thy5;
   895     val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names
   896       [descr] sorts nchotomys case_thms thy6;
   897     val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   898       [descr] sorts thy7;
   899     val (size_thms, thy9) =
   900       if Context.exists_name "NatArith" thy8 then
   901         DatatypeAbsProofs.prove_size_thms false new_type_names
   902           [descr] sorts reccomb_names rec_thms thy8
   903       else ([], thy8);
   904 
   905     val ((_, [induction']), thy10) =
   906       thy9
   907       |> store_thmss "inject" new_type_names inject
   908       ||>> store_thmss "distinct" new_type_names distinct
   909       ||> Theory.add_path (space_implode "_" new_type_names)
   910       ||>> PureThy.add_thms [(("induct", induction), [case_names_induct])];
   911 
   912     val dt_infos = map (make_dt_info descr sorts induction' reccomb_names rec_thms)
   913       ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~
   914         map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   915 
   916     val simps = List.concat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   917 
   918     val thy11 = thy10 |>
   919       Theory.add_advanced_trfuns ([], [], make_case_tr' case_names descr, []) |>
   920       add_rules simps case_thms size_thms rec_thms inject distinct
   921         weak_case_congs (Simplifier.attrib (op addcongs)) |> 
   922       put_datatypes (fold Symtab.update dt_infos dt_info) |>
   923       add_cases_induct dt_infos induction' |>
   924       Theory.parent_path |>
   925       (snd o store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)) |>
   926       DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
   927   in
   928     ({distinct = distinct,
   929       inject = inject,
   930       exhaustion = casedist_thms,
   931       rec_thms = rec_thms,
   932       case_thms = case_thms,
   933       split_thms = split_thms,
   934       induction = induction',
   935       size = size_thms,
   936       simps = simps}, thy11)
   937   end;
   938 
   939 val rep_datatype = gen_rep_datatype IsarThy.apply_theorems;
   940 val rep_datatype_i = gen_rep_datatype IsarThy.apply_theorems_i;
   941 
   942 
   943 
   944 (******************************** add datatype ********************************)
   945 
   946 fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =
   947   let
   948     val _ = Theory.requires thy "Datatype_Universe" "datatype definitions";
   949 
   950     (* this theory is used just for parsing *)
   951 
   952     val tmp_thy = thy |>
   953       Theory.copy |>
   954       Theory.add_types (map (fn (tvs, tname, mx, _) =>
   955         (tname, length tvs, mx)) dts);
   956 
   957     val sign = Theory.sign_of tmp_thy;
   958 
   959     val (tyvars, _, _, _)::_ = dts;
   960     val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
   961       let val full_tname = Sign.full_name sign (Syntax.type_name tname mx)
   962       in (case duplicates (op =) tvs of
   963             [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
   964                   else error ("Mutually recursive datatypes must have same type parameters")
   965           | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
   966               " : " ^ commas dups))
   967       end) dts);
   968 
   969     val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of
   970       [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
   971 
   972     fun prep_dt_spec ((dts', constr_syntax, sorts, i), (tvs, tname, mx, constrs)) =
   973       let
   974         fun prep_constr ((constrs, constr_syntax', sorts'), (cname, cargs, mx')) =
   975           let
   976             val (cargs', sorts'') = Library.foldl (prep_typ sign) (([], sorts'), cargs);
   977             val _ = (case foldr add_typ_tfree_names [] cargs' \\ tvs of
   978                 [] => ()
   979               | vs => error ("Extra type variables on rhs: " ^ commas vs))
   980           in (constrs @ [((if flat_names then Sign.full_name sign else
   981                 Sign.full_name_path sign tname) (Syntax.const_name cname mx'),
   982                    map (dtyp_of_typ new_dts) cargs')],
   983               constr_syntax' @ [(cname, mx')], sorts'')
   984           end handle ERROR msg =>
   985             cat_error msg ("The error above occured in constructor " ^ cname ^
   986               " of datatype " ^ tname);
   987 
   988         val (constrs', constr_syntax', sorts') =
   989           Library.foldl prep_constr (([], [], sorts), constrs)
   990 
   991       in
   992         case duplicates (op =) (map fst constrs') of
   993            [] =>
   994              (dts' @ [(i, (Sign.full_name sign (Syntax.type_name tname mx),
   995                 map DtTFree tvs, constrs'))],
   996               constr_syntax @ [constr_syntax'], sorts', i + 1)
   997          | dups => error ("Duplicate constructors " ^ commas dups ^
   998              " in datatype " ^ tname)
   999       end;
  1000 
  1001     val (dts', constr_syntax, sorts', i) = Library.foldl prep_dt_spec (([], [], [], 0), dts);
  1002     val sorts = sorts' @ (map (rpair (Sign.defaultS sign)) (tyvars \\ map fst sorts'));
  1003     val dt_info = get_datatypes thy;
  1004     val (descr, _) = unfold_datatypes sign dts' sorts dt_info dts' i;
  1005     val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>
  1006       if err then error ("Nonemptiness check failed for datatype " ^ s)
  1007       else raise exn;
  1008 
  1009     val descr' = List.concat descr;
  1010     val case_names_induct = mk_case_names_induct descr';
  1011     val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
  1012   in
  1013     (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
  1014       flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
  1015       case_names_induct case_names_exhausts thy
  1016   end;
  1017 
  1018 val add_datatype_i = gen_add_datatype cert_typ;
  1019 val add_datatype = gen_add_datatype read_typ true;
  1020 
  1021 
  1022 
  1023 (** package setup **)
  1024 
  1025 (* setup theory *)
  1026 
  1027 val setup =
  1028   DatatypesData.init #> Method.add_methods tactic_emulations #> simproc_setup #> trfun_setup;
  1029 
  1030 
  1031 (* outer syntax *)
  1032 
  1033 local structure P = OuterParse and K = OuterKeyword in
  1034 
  1035 val datatype_decl =
  1036   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
  1037     (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
  1038 
  1039 fun mk_datatype args =
  1040   let
  1041     val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
  1042     val specs = map (fn ((((_, vs), t), mx), cons) =>
  1043       (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
  1044   in snd o add_datatype false names specs end;
  1045 
  1046 val datatypeP =
  1047   OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
  1048     (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
  1049 
  1050 
  1051 val rep_datatype_decl =
  1052   Scan.option (Scan.repeat1 P.name) --
  1053     Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
  1054     Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
  1055     (P.$$$ "induction" |-- P.!!! P.xthm);
  1056 
  1057 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #2 o rep_datatype opt_ts dss iss ind;
  1058 
  1059 val rep_datatypeP =
  1060   OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
  1061     (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
  1062 
  1063 
  1064 val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
  1065 val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
  1066 
  1067 end;
  1068 
  1069 
  1070 end;
  1071 
  1072 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
  1073 open BasicDatatypePackage;
  1074