src/HOL/Tools/datatype_package.ML
author wenzelm
Wed Apr 12 23:52:50 2000 +0200 (2000-04-12)
changeset 8697 88dafea5955c
parent 8689 a2e82eed6454
child 9149 a126a40cba76
permissions -rw-r--r--
InductMethod.concls_of;
     1 (*  Title:      HOL/Tools/datatype_package.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer
     4     Copyright   1998  TU Muenchen
     5 
     6 Datatype package for Isabelle/HOL.
     7 *)
     8 
     9 signature BASIC_DATATYPE_PACKAGE =
    10 sig
    11   val induct_tac : string -> int -> tactic
    12   val case_tac : string -> int -> tactic
    13   val distinct_simproc : simproc
    14 end;
    15 
    16 signature DATATYPE_PACKAGE =
    17 sig
    18   include BASIC_DATATYPE_PACKAGE
    19   val quiet_mode : bool ref
    20   val add_datatype : bool -> string list -> (string list * bstring * mixfix *
    21     (bstring * string list * mixfix) list) list -> theory -> theory *
    22       {distinct : thm list list,
    23        inject : thm list list,
    24        exhaustion : thm list,
    25        rec_thms : thm list,
    26        case_thms : thm list list,
    27        split_thms : (thm * thm) list,
    28        induction : thm,
    29        size : thm list,
    30        simps : thm list}
    31   val add_datatype_i : bool -> string list -> (string list * bstring * mixfix *
    32     (bstring * typ list * mixfix) list) list -> theory -> theory *
    33       {distinct : thm list list,
    34        inject : thm list list,
    35        exhaustion : thm list,
    36        rec_thms : thm list,
    37        case_thms : thm list list,
    38        split_thms : (thm * thm) list,
    39        induction : thm,
    40        size : thm list,
    41        simps : thm list}
    42   val rep_datatype_i : string list option -> (thm * theory attribute list) list list ->
    43     (thm * theory attribute list) list list -> (thm * theory attribute list) -> theory -> theory *
    44       {distinct : thm list list,
    45        inject : thm list list,
    46        exhaustion : thm list,
    47        rec_thms : thm list,
    48        case_thms : thm list list,
    49        split_thms : (thm * thm) list,
    50        induction : thm,
    51        size : thm list,
    52        simps : thm list}
    53   val rep_datatype : string list option -> (xstring * Args.src list) list list ->
    54     (xstring * Args.src list) list list -> xstring * Args.src list -> theory -> theory *
    55       {distinct : thm list list,
    56        inject : thm list list,
    57        exhaustion : thm list,
    58        rec_thms : thm list,
    59        case_thms : thm list list,
    60        split_thms : (thm * thm) list,
    61        induction : thm,
    62        size : thm list,
    63        simps : thm list}
    64   val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table
    65   val print_datatypes : theory -> unit
    66   val datatype_info_sg : Sign.sg -> string -> DatatypeAux.datatype_info option
    67   val datatype_info : theory -> string -> DatatypeAux.datatype_info option
    68   val datatype_info_sg_err : Sign.sg -> string -> DatatypeAux.datatype_info
    69   val datatype_info_err : theory -> string -> DatatypeAux.datatype_info
    70   val constrs_of : theory -> string -> term list option
    71   val constrs_of_sg : Sign.sg -> string -> term list option
    72   val case_const_of : theory -> string -> term option
    73   val setup: (theory -> theory) list
    74 end;
    75 
    76 structure DatatypePackage : DATATYPE_PACKAGE =
    77 struct
    78 
    79 open DatatypeAux;
    80 
    81 val quiet_mode = quiet_mode;
    82 
    83 
    84 (* data kind 'HOL/datatypes' *)
    85 
    86 structure DatatypesArgs =
    87 struct
    88   val name = "HOL/datatypes";
    89   type T = datatype_info Symtab.table;
    90 
    91   val empty = Symtab.empty;
    92   val copy = I;
    93   val prep_ext = I;
    94   val merge: T * T -> T = Symtab.merge (K true);
    95 
    96   fun print sg tab =
    97     Pretty.writeln (Pretty.strs ("datatypes:" ::
    98       map #1 (Sign.cond_extern_table sg Sign.typeK tab)));
    99 end;
   100 
   101 structure DatatypesData = TheoryDataFun(DatatypesArgs);
   102 val get_datatypes_sg = DatatypesData.get_sg;
   103 val get_datatypes = DatatypesData.get;
   104 val put_datatypes = DatatypesData.put;
   105 val print_datatypes = DatatypesData.print;
   106 
   107 
   108 (** theory information about datatypes **)
   109 
   110 fun datatype_info_sg sg name = Symtab.lookup (get_datatypes_sg sg, name);
   111 
   112 fun datatype_info_sg_err sg name = (case datatype_info_sg sg name of
   113       Some info => info
   114     | None => error ("Unknown datatype " ^ quote name));
   115 
   116 val datatype_info = datatype_info_sg o Theory.sign_of;
   117 
   118 fun datatype_info_err thy name = (case datatype_info thy name of
   119       Some info => info
   120     | None => error ("Unknown datatype " ^ quote name));
   121 
   122 fun constrs_of_sg sg tname = (case datatype_info_sg sg tname of
   123    Some {index, descr, ...} =>
   124      let val (_, _, constrs) = the (assoc (descr, index))
   125      in Some (map (fn (cname, _) => Const (cname, the (Sign.const_type sg cname))) constrs)
   126      end
   127  | _ => None);
   128 
   129 val constrs_of = constrs_of_sg o Theory.sign_of;
   130 
   131 fun case_const_of thy tname = (case datatype_info thy tname of
   132    Some {case_name, ...} => Some (Const (case_name, the (Sign.const_type
   133      (Theory.sign_of thy) case_name)))
   134  | _ => None);
   135 
   136 fun find_tname var Bi =
   137   let val frees = map dest_Free (term_frees Bi)
   138       val params = Logic.strip_params Bi;
   139   in case assoc (frees @ params, var) of
   140        None => error ("No such variable in subgoal: " ^ quote var)
   141      | Some(Type (tn, _)) => tn
   142      | _ => error ("Cannot determine type of " ^ quote var)
   143   end;
   144 
   145 fun infer_tname state i aterm =
   146   let
   147     val sign = Thm.sign_of_thm state;
   148     val (_, _, Bi, _) = Thm.dest_state (state, i)
   149     val params = Logic.strip_params Bi;   (*params of subgoal i*)
   150     val params = rev (rename_wrt_term Bi params);   (*as they are printed*)
   151     val (types, sorts) = types_sorts state;
   152     fun types' (a, ~1) = (case assoc (params, a) of None => types(a, ~1) | sm => sm)
   153       | types' ixn = types ixn;
   154     val (ct, _) = read_def_cterm (sign, types', sorts) [] false (aterm, TypeInfer.logicT);
   155   in case #T (rep_cterm ct) of
   156        Type (tn, _) => tn
   157      | _ => error ("Cannot determine type of " ^ quote aterm)
   158   end;
   159 
   160 (*Warn if the (induction) variable occurs Free among the premises, which
   161   usually signals a mistake.  But calls the tactic either way!*)
   162 fun occs_in_prems tacf vars =
   163   SUBGOAL (fn (Bi, i) =>
   164            (if  exists (fn Free (a, _) => a mem vars)
   165                       (foldr add_term_frees (#2 (strip_context Bi), []))
   166              then warning "Induction variable occurs also among premises!"
   167              else ();
   168             tacf i));
   169 
   170 
   171 (* generic induction tactic for datatypes *)
   172 
   173 local
   174 
   175 fun prep_var (Var (ixn, _), Some x) = Some (implode (tl (explode (Syntax.string_of_vname ixn))), x)
   176   | prep_var _ = None;
   177 
   178 fun prep_inst (concl, xs) =	(*exception LIST*)
   179   let val vs = InductMethod.vars_of concl
   180   in mapfilter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
   181 
   182 in
   183 
   184 fun gen_induct_tac (varss, opt_rule) i state =
   185   let
   186     val (_, _, Bi, _) = Thm.dest_state (state, i);
   187     val {sign, ...} = Thm.rep_thm state;
   188     val (rule, rule_name) =
   189       (case opt_rule of
   190         Some r => (r, "Induction rule")
   191       | None =>
   192           let val tn = find_tname (hd (mapfilter I (flat varss))) Bi
   193           in (#induction (datatype_info_sg_err sign tn), "Induction rule for type " ^ tn) end);
   194 
   195     val concls = InductMethod.concls_of rule;
   196     val insts = flat (map prep_inst (concls ~~ varss)) handle LIST _ =>
   197       error (rule_name ^ " has different numbers of variables");
   198   in occs_in_prems (Tactic.res_inst_tac insts rule) (map #2 insts) i state end;
   199 
   200 fun induct_tac s = gen_induct_tac (map (Library.single o Some) (Syntax.read_idents s), None);
   201 
   202 end;
   203 
   204 
   205 (* generic case tactic for datatypes *)
   206 
   207 fun case_inst_tac t rule i state =
   208   let
   209     val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
   210       (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));
   211     val exh_vname = implode (tl (explode (Syntax.string_of_vname ixn)));
   212   in Tactic.res_inst_tac [(exh_vname, t)] rule i state end;
   213 
   214 fun gen_case_tac (t, Some rule) i state = case_inst_tac t rule i state
   215   | gen_case_tac (t, None) i state =
   216       let val tn = infer_tname state i t in
   217         if tn = HOLogic.boolN then Tactic.res_inst_tac [("P", t)] case_split_thm i state
   218         else case_inst_tac t (#exhaustion (datatype_info_sg_err (Thm.sign_of_thm state) tn)) i state
   219       end;
   220 
   221 fun case_tac t = gen_case_tac (t, None);
   222 
   223 
   224 
   225 (** Isar tactic emulations **)
   226 
   227 local
   228 
   229 val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
   230 val opt_rule = Scan.option (rule_spec |-- Attrib.local_thm);
   231 
   232 val varss = Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift Args.name_dummy)));
   233 
   234 fun tactic_syntax args tac =
   235   #2 oo Method.syntax (Args.goal_spec HEADGOAL -- (args -- opt_rule) >>
   236     (fn (quant, x) => Method.METHOD (fn facts => quant (Method.insert_tac facts THEN' tac x))));
   237 
   238 in
   239 
   240 val tactic_emulations =
   241  [("induct_tac", tactic_syntax varss gen_induct_tac,
   242     "induct_tac emulation (dynamic instantiation!)"),
   243   ("case_tac", tactic_syntax (Scan.lift Args.name) gen_case_tac,
   244     "case_tac emulation (dynamic instantiation!)")];
   245 
   246 end;
   247 
   248 
   249 
   250 (** induct method setup **)
   251 
   252 (* case names *)
   253 
   254 local
   255 
   256 fun dt_recs (DtTFree _) = []
   257   | dt_recs (DtType (_, dts)) = flat (map dt_recs dts)
   258   | dt_recs (DtRec i) = [i];
   259 
   260 fun dt_cases (descr: descr) (_, args, constrs) =
   261   let
   262     fun the_bname i = Sign.base_name (#1 (the (assoc (descr, i))));
   263     val bnames = map the_bname (distinct (flat (map dt_recs args)));
   264   in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
   265 
   266 
   267 fun induct_cases descr =
   268   DatatypeProp.indexify_names (flat (map (dt_cases descr) (map #2 descr)));
   269 
   270 fun exhaust_cases descr i = dt_cases descr (the (assoc (descr, i)));
   271 
   272 in
   273 
   274 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
   275 
   276 fun mk_case_names_exhausts descr new =
   277   map (RuleCases.case_names o exhaust_cases descr o #1)
   278     (filter (fn ((_, (name, _, _))) => name mem_string new) descr);
   279 
   280 end;
   281 
   282 
   283 (* add_cases_induct *)
   284 
   285 fun add_cases_induct infos =
   286   let
   287     fun proj _ 1 thm = thm
   288       | proj i n thm =
   289           (if i + 1 < n then (fn th => th RS conjunct1) else I)
   290             (Library.funpow i (fn th => th RS conjunct2) thm)
   291           |> Drule.standard
   292           |> RuleCases.name (RuleCases.get thm);
   293 
   294     fun add (ths, (name, {index, descr, induction, exhaustion, ...}: datatype_info)) =
   295       (("", proj index (length descr) induction), [InductMethod.induct_type_global name]) ::
   296       (("", exhaustion), [InductMethod.cases_type_global name]) :: ths;
   297   in #1 o PureThy.add_thms (foldl add ([], infos)) end;
   298 
   299 
   300 
   301 (**** simplification procedure for showing distinctness of constructors ****)
   302 
   303 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
   304   | stripT p = p;
   305 
   306 fun stripC (i, f $ x) = stripC (i + 1, f)
   307   | stripC p = p;
   308 
   309 val distinctN = "constr_distinct";
   310 
   311 exception ConstrDistinct of term;
   312 
   313 fun distinct_proc sg _ (t as Const ("op =", _) $ t1 $ t2) =
   314   (case (stripC (0, t1), stripC (0, t2)) of
   315      ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
   316          (case (stripT (0, T1), stripT (0, T2)) of
   317             ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
   318                 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
   319                    (case (constrs_of_sg sg tname1) of
   320                       Some constrs => let val cnames = map (fst o dest_Const) constrs
   321                         in if cname1 mem cnames andalso cname2 mem cnames then
   322                              let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));
   323                                  val eq_ct = cterm_of sg eq_t;
   324                                  val Datatype_thy = theory "Datatype";
   325                                  val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
   326                                    map (get_thm Datatype_thy)
   327                                      ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
   328                              in (case (#distinct (datatype_info_sg_err sg tname1)) of
   329                                  QuickAndDirty => Some (Thm.invoke_oracle
   330                                    Datatype_thy distinctN (sg, ConstrDistinct eq_t))
   331                                | FewConstrs thms => Some (prove_goalw_cterm [] eq_ct (K
   332                                    [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
   333                                     atac 2, resolve_tac thms 1, etac FalseE 1]))
   334                                | ManyConstrs (thm, ss) => Some (prove_goalw_cterm [] eq_ct (K
   335                                    [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
   336                                     full_simp_tac ss 1,
   337                                     REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
   338                                     eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
   339                                     etac FalseE 1])))
   340                              end
   341                            else None
   342                         end
   343                     | None => None)
   344                 else None
   345           | _ => None)
   346    | _ => None)
   347   | distinct_proc sg _ _ = None;
   348 
   349 val distinct_pats = [Thm.read_cterm (Theory.sign_of HOL.thy) ("s = t", HOLogic.termT)];
   350 val distinct_simproc = mk_simproc distinctN distinct_pats distinct_proc;
   351 
   352 val dist_ss = HOL_ss addsimprocs [distinct_simproc];
   353 
   354 val simproc_setup =
   355   [Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t),
   356    fn thy => (simpset_ref_of thy := simpset_of thy addsimprocs [distinct_simproc]; thy)];
   357 
   358 
   359 (* prepare types *)
   360 
   361 fun read_typ sign ((Ts, sorts), str) =
   362   let
   363     val T = Type.no_tvars (Sign.read_typ (sign, (curry assoc)
   364       (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
   365   in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
   366 
   367 fun cert_typ sign ((Ts, sorts), raw_T) =
   368   let
   369     val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
   370       TYPE (msg, _, _) => error msg;
   371     val sorts' = add_typ_tfrees (T, sorts)
   372   in (Ts @ [T],
   373       case duplicates (map fst sorts') of
   374          [] => sorts'
   375        | dups => error ("Inconsistent sort constraints for " ^ commas dups))
   376   end;
   377 
   378 
   379 (**** make datatype info ****)
   380 
   381 fun make_dt_info descr induct reccomb_names rec_thms
   382   ((((((((i, (_, (tname, _, _))), case_name), case_thms),
   383     exhaustion_thm), distinct_thm), inject), nchotomy), case_cong) = (tname,
   384       {index = i,
   385        descr = descr,
   386        rec_names = reccomb_names,
   387        rec_rewrites = rec_thms,
   388        case_name = case_name,
   389        case_rewrites = case_thms,
   390        induction = induct,
   391        exhaustion = exhaustion_thm,
   392        distinct = distinct_thm,
   393        inject = inject,
   394        nchotomy = nchotomy,
   395        case_cong = case_cong});
   396 
   397 
   398 (********************* axiomatic introduction of datatypes ********************)
   399 
   400 fun add_and_get_axioms_atts label tnames attss ts thy =
   401   foldr (fn (((tname, atts), t), (thy', axs)) =>
   402     let
   403       val (thy'', [ax]) = thy' |>
   404         Theory.add_path tname |>
   405         PureThy.add_axioms_i [((label, t), atts)];
   406     in (Theory.parent_path thy'', ax::axs)
   407     end) (tnames ~~ attss ~~ ts, (thy, []));
   408 
   409 fun add_and_get_axioms label tnames =
   410   add_and_get_axioms_atts label tnames (replicate (length tnames) []);
   411 
   412 fun add_and_get_axiomss label tnames tss thy =
   413   foldr (fn ((tname, ts), (thy', axss)) =>
   414     let
   415       val (thy'', [axs]) = thy' |>
   416         Theory.add_path tname |>
   417         PureThy.add_axiomss_i [((label, ts), [])];
   418     in (Theory.parent_path thy'', axs::axss)
   419     end) (tnames ~~ tss, (thy, []));
   420 
   421 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   422     case_names_induct case_names_exhausts thy =
   423   let
   424     val descr' = flat descr;
   425     val recTs = get_rec_types descr' sorts;
   426     val used = foldr add_typ_tfree_names (recTs, []);
   427     val newTs = take (length (hd descr), recTs);
   428 
   429     val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
   430       (fn (DtType ("fun", [_, DtRec _])) => true | _ => false) cargs) constrs) descr';
   431 
   432     (**** declare new types and constants ****)
   433 
   434     val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
   435 
   436     val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
   437       map (fn ((_, cargs), (cname, mx)) =>
   438         (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   439           (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
   440 
   441     val rec_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~
   442       replicate (length descr') HOLogic.termS);
   443 
   444     val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) =>
   445       map (fn (_, cargs) =>
   446         let
   447           val Ts = map (typ_of_dtyp descr' sorts) cargs;
   448           val recs = filter (is_rec_type o fst) (cargs ~~ Ts);
   449 
   450           fun mk_argT (DtRec k, _) = nth_elem (k, rec_result_Ts)
   451             | mk_argT (DtType ("fun", [_, DtRec k]), Type ("fun", [T, _])) =
   452                T --> nth_elem (k, rec_result_Ts);
   453 
   454           val argTs = Ts @ map mk_argT recs
   455         in argTs ---> nth_elem (i, rec_result_Ts)
   456         end) constrs) descr');
   457 
   458     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   459     val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
   460       (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   461         (1 upto (length descr')));
   462 
   463     val big_size_name = space_implode "_" new_type_names ^ "_size";
   464     val size_names = if length (flat (tl descr)) = 1 then [big_size_name] else
   465       map (fn i => big_size_name ^ "_" ^ string_of_int i)
   466         (1 upto length (flat (tl descr)));
   467 
   468     val freeT = TFree (variant used "'t", HOLogic.termS);
   469     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
   470       map (fn (_, cargs) =>
   471         let val Ts = map (typ_of_dtyp descr' sorts) cargs
   472         in Ts ---> freeT end) constrs) (hd descr);
   473 
   474     val case_names = map (fn s => (s ^ "_case")) new_type_names;
   475 
   476     val thy2' = thy |>
   477 
   478       (** new types **)
   479 
   480       curry (foldr (fn (((name, mx), tvs), thy') => thy' |>
   481           TypedefPackage.add_typedecls [(name, tvs, mx)]))
   482         (types_syntax ~~ tyvars) |>
   483       add_path flat_names (space_implode "_" new_type_names) |>
   484 
   485       (** primrec combinators **)
   486 
   487       Theory.add_consts_i (map (fn ((name, T), T') =>
   488         (name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   489           (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
   490 
   491       (** case combinators **)
   492 
   493       Theory.add_consts_i (map (fn ((name, T), Ts) =>
   494         (name, Ts @ [T] ---> freeT, NoSyn))
   495           (case_names ~~ newTs ~~ case_fn_Ts)) |>
   496       Theory.add_trrules_i (DatatypeProp.make_case_trrules new_type_names descr);
   497 
   498     val reccomb_names' = map (Sign.intern_const (Theory.sign_of thy2')) reccomb_names;
   499     val case_names' = map (Sign.intern_const (Theory.sign_of thy2')) case_names;
   500 
   501     val thy2 = thy2' |>
   502 
   503       (** size functions **)
   504 
   505       (if no_size then I else Theory.add_consts_i (map (fn (s, T) =>
   506         (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   507           (size_names ~~ drop (length (hd descr), recTs)))) |>
   508 
   509       (** constructors **)
   510 
   511       parent_path flat_names |>
   512       curry (foldr (fn (((((_, (_, _, constrs)), T), tname),
   513         constr_syntax'), thy') => thy' |>
   514           add_path flat_names tname |>
   515             Theory.add_consts_i (map (fn ((_, cargs), (cname, mx)) =>
   516               (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   517                 (constrs ~~ constr_syntax')) |>
   518           parent_path flat_names))
   519             (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
   520 
   521     (**** introduction of axioms ****)
   522 
   523     val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
   524     val size_axs = if no_size then [] else DatatypeProp.make_size new_type_names descr sorts thy2;
   525 
   526     val (thy3, (([induct], [rec_thms]), inject)) =
   527       thy2 |>
   528       Theory.add_path (space_implode "_" new_type_names) |>
   529       PureThy.add_axioms_i [(("induct", DatatypeProp.make_ind descr sorts), [case_names_induct])] |>>>
   530       PureThy.add_axiomss_i [(("recs", rec_axs), [])] |>>
   531       (if no_size then I else #1 o PureThy.add_axiomss_i [(("size", size_axs), [])]) |>>
   532       Theory.parent_path |>>>
   533       add_and_get_axiomss "inject" new_type_names
   534         (DatatypeProp.make_injs descr sorts);
   535     val size_thms = if no_size then [] else get_thms thy3 "size";
   536     val (thy4, distinct) = add_and_get_axiomss "distinct" new_type_names
   537       (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
   538 
   539     val exhaust_ts = DatatypeProp.make_casedists descr sorts;
   540     val (thy5, exhaustion) = add_and_get_axioms_atts "exhaust" new_type_names
   541       (map Library.single case_names_exhausts) exhaust_ts thy4;
   542     val (thy6, case_thms) = add_and_get_axiomss "cases" new_type_names
   543       (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
   544     val (split_ts, split_asm_ts) = ListPair.unzip
   545       (DatatypeProp.make_splits new_type_names descr sorts thy6);
   546     val (thy7, split) = add_and_get_axioms "split" new_type_names split_ts thy6;
   547     val (thy8, split_asm) = add_and_get_axioms "split_asm" new_type_names
   548       split_asm_ts thy7;
   549     val (thy9, nchotomys) = add_and_get_axioms "nchotomy" new_type_names
   550       (DatatypeProp.make_nchotomys descr sorts) thy8;
   551     val (thy10, case_congs) = add_and_get_axioms "case_cong" new_type_names
   552       (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
   553     val (thy11, weak_case_congs) = add_and_get_axioms "weak_case_cong" new_type_names
   554       (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
   555 
   556     val dt_infos = map (make_dt_info descr' induct reccomb_names' rec_thms)
   557       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
   558         exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
   559           nchotomys ~~ case_congs);
   560 
   561     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   562 
   563     val thy12 = thy11 |>
   564       Theory.add_path (space_implode "_" new_type_names) |>
   565       (#1 o PureThy.add_thmss [(("simps", simps), []),
   566         (("", flat case_thms @ size_thms @ rec_thms), [Simplifier.simp_add_global]),
   567         (("", flat (inject @ distinct)), [iff_add_global]),
   568         (("", weak_case_congs), [cong_add_global])]) |>
   569       put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
   570       add_cases_induct dt_infos |>
   571       Theory.parent_path;
   572 
   573   in
   574     (thy12,
   575      {distinct = distinct,
   576       inject = inject,
   577       exhaustion = exhaustion,
   578       rec_thms = rec_thms,
   579       case_thms = case_thms,
   580       split_thms = split ~~ split_asm,
   581       induction = induct,
   582       size = size_thms,
   583       simps = simps})
   584   end;
   585 
   586 
   587 (******************* definitional introduction of datatypes *******************)
   588 
   589 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   590     case_names_induct case_names_exhausts thy =
   591   let
   592     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   593 
   594     val (thy2, inject, distinct, dist_rewrites, simproc_dists, induct) = thy |>
   595       DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
   596         types_syntax constr_syntax case_names_induct;
   597 
   598     val (thy3, casedist_thms) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
   599       sorts induct case_names_exhausts thy2;
   600     val (thy4, (reccomb_names, rec_thms)) = DatatypeAbsProofs.prove_primrec_thms
   601       flat_names new_type_names descr sorts dt_info inject dist_rewrites dist_ss induct thy3;
   602     val (thy6, (case_thms, case_names)) = DatatypeAbsProofs.prove_case_thms
   603       flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
   604     val (thy7, split_thms) = DatatypeAbsProofs.prove_split_thms new_type_names
   605       descr sorts inject dist_rewrites casedist_thms case_thms thy6;
   606     val (thy8, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
   607       descr sorts casedist_thms thy7;
   608     val (thy9, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
   609       descr sorts nchotomys case_thms thy8;
   610     val (thy10, weak_case_congs) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   611       descr sorts thy9;
   612     val (thy11, size_thms) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
   613       descr sorts reccomb_names rec_thms thy10;
   614 
   615     val dt_infos = map (make_dt_info (flat descr) induct reccomb_names rec_thms)
   616       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
   617         casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs);
   618 
   619     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   620 
   621     val thy12 = thy11 |>
   622       Theory.add_path (space_implode "_" new_type_names) |>
   623       (#1 o PureThy.add_thmss [(("simps", simps), []),
   624         (("", flat case_thms @ size_thms @ rec_thms), [Simplifier.simp_add_global]),
   625         (("", flat (inject @ distinct)), [iff_add_global]),
   626         (("", weak_case_congs), [Simplifier.change_global_ss (op addcongs)])]) |>
   627       put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
   628       add_cases_induct dt_infos |>
   629       Theory.parent_path;
   630 
   631   in
   632     (thy12,
   633      {distinct = distinct,
   634       inject = inject,
   635       exhaustion = casedist_thms,
   636       rec_thms = rec_thms,
   637       case_thms = case_thms,
   638       split_thms = split_thms,
   639       induction = induct,
   640       size = size_thms,
   641       simps = simps})
   642   end;
   643 
   644 
   645 (*********************** declare existing type as datatype *********************)
   646 
   647 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
   648   let
   649     fun app_thmss srcs thy = foldl_map (fn (thy, x) => apply_theorems x thy) (thy, srcs);
   650     fun app_thm src thy = apsnd Library.hd (apply_theorems [src] thy);
   651 
   652     val (((thy1, induction), inject), distinct) = thy0
   653       |> app_thmss raw_distinct
   654       |> apfst (app_thmss raw_inject)
   655       |> apfst (apfst (app_thm raw_induction));
   656     val sign = Theory.sign_of thy1;
   657 
   658     val induction' = freezeT induction;
   659 
   660     fun err t = error ("Ill-formed predicate in induction rule: " ^
   661       Sign.string_of_term sign t);
   662 
   663     fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
   664           ((tname, map dest_TFree Ts) handle TERM _ => err t)
   665       | get_typ t = err t;
   666 
   667     val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
   668     val new_type_names = if_none alt_names (map fst dtnames);
   669 
   670     fun get_constr t = (case Logic.strip_assums_concl t of
   671         _ $ (_ $ t') => (case head_of t' of
   672             Const (cname, cT) => (case strip_type cT of
   673                 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
   674               | _ => err t)
   675           | _ => err t)
   676       | _ => err t);
   677 
   678     fun make_dt_spec [] _ _ = []
   679       | make_dt_spec ((tname, tvs)::dtnames') i constrs =
   680           let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
   681           in (i, (tname, map DtTFree tvs, map snd constrs'))::
   682             (make_dt_spec dtnames' (i + 1) constrs'')
   683           end;
   684 
   685     val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
   686     val sorts = add_term_tfrees (concl_of induction', []);
   687     val dt_info = get_datatypes thy1;
   688 
   689     val case_names_induct = mk_case_names_induct descr;
   690     val case_names_exhausts = mk_case_names_exhausts descr (map #1 dtnames);
   691     
   692 
   693     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   694 
   695     val (thy2, casedist_thms) = thy1 |>
   696       DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
   697         case_names_exhausts;
   698     val (thy3, (reccomb_names, rec_thms)) = DatatypeAbsProofs.prove_primrec_thms
   699       false new_type_names [descr] sorts dt_info inject distinct dist_ss induction thy2;
   700     val (thy4, (case_thms, case_names)) = DatatypeAbsProofs.prove_case_thms false
   701       new_type_names [descr] sorts reccomb_names rec_thms thy3;
   702     val (thy5, split_thms) = DatatypeAbsProofs.prove_split_thms
   703       new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
   704     val (thy6, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
   705       [descr] sorts casedist_thms thy5;
   706     val (thy7, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
   707       [descr] sorts nchotomys case_thms thy6;
   708     val (thy8, weak_case_congs) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   709       [descr] sorts thy7;
   710     val (thy9, size_thms) =
   711       if exists (equal "Arith") (Sign.stamp_names_of (Theory.sign_of thy8)) then
   712         DatatypeAbsProofs.prove_size_thms false new_type_names
   713           [descr] sorts reccomb_names rec_thms thy8
   714       else (thy8, []);
   715 
   716     val dt_infos = map (make_dt_info descr induction reccomb_names rec_thms)
   717       ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~
   718         casedist_thms ~~ map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs);
   719 
   720     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   721 
   722     val (thy10, [induction']) = thy9 |>
   723       (#1 o store_thmss "inject" new_type_names inject) |>
   724       (#1 o store_thmss "distinct" new_type_names distinct) |>
   725       Theory.add_path (space_implode "_" new_type_names) |>
   726       PureThy.add_thms [(("induct", induction), [case_names_induct])] |>>
   727       (#1 o PureThy.add_thmss [(("simps", simps), []),
   728         (("", flat case_thms @ size_thms @ rec_thms), [Simplifier.simp_add_global]),
   729         (("", flat (inject @ distinct)), [iff_add_global]),
   730         (("", weak_case_congs), [Simplifier.change_global_ss (op addcongs)])]) |>>
   731       put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>>
   732       add_cases_induct dt_infos |>>
   733       Theory.parent_path;
   734 
   735   in
   736     (thy10,
   737      {distinct = distinct,
   738       inject = inject,
   739       exhaustion = casedist_thms,
   740       rec_thms = rec_thms,
   741       case_thms = case_thms,
   742       split_thms = split_thms,
   743       induction = induction',
   744       size = size_thms,
   745       simps = simps})
   746   end;
   747 
   748 val rep_datatype = gen_rep_datatype IsarThy.apply_theorems;
   749 val rep_datatype_i = gen_rep_datatype IsarThy.apply_theorems_i;
   750 
   751 
   752 (******************************** add datatype ********************************)
   753 
   754 fun gen_add_datatype prep_typ flat_names new_type_names dts thy =
   755   let
   756     val _ = Theory.requires thy "Datatype" "datatype definitions";
   757 
   758     (* this theory is used just for parsing *)
   759 
   760     val tmp_thy = thy |>
   761       Theory.copy |>
   762       Theory.add_types (map (fn (tvs, tname, mx, _) =>
   763         (tname, length tvs, mx)) dts);
   764 
   765     val sign = Theory.sign_of tmp_thy;
   766 
   767     val (tyvars, _, _, _)::_ = dts;
   768     val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
   769       let val full_tname = Sign.full_name sign (Syntax.type_name tname mx)
   770       in (case duplicates tvs of
   771             [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
   772                   else error ("Mutually recursive datatypes must have same type parameters")
   773           | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
   774               " : " ^ commas dups))
   775       end) dts);
   776 
   777     val _ = (case duplicates (map fst new_dts) @ duplicates new_type_names of
   778       [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
   779 
   780     fun prep_dt_spec ((dts', constr_syntax, sorts, i), (tvs, tname, mx, constrs)) =
   781       let
   782         fun prep_constr ((constrs, constr_syntax', sorts'), (cname, cargs, mx')) =
   783           let
   784             val (cargs', sorts'') = foldl (prep_typ sign) (([], sorts'), cargs);
   785             val _ = (case foldr add_typ_tfree_names (cargs', []) \\ tvs of
   786                 [] => ()
   787               | vs => error ("Extra type variables on rhs: " ^ commas vs))
   788           in (constrs @ [((if flat_names then Sign.full_name sign else
   789                 Sign.full_name_path sign tname) (Syntax.const_name cname mx'),
   790                    map (dtyp_of_typ new_dts) cargs')],
   791               constr_syntax' @ [(cname, mx')], sorts'')
   792           end handle ERROR =>
   793             error ("The error above occured in constructor " ^ cname ^
   794               " of datatype " ^ tname);
   795 
   796         val (constrs', constr_syntax', sorts') =
   797           foldl prep_constr (([], [], sorts), constrs)
   798 
   799       in
   800         case duplicates (map fst constrs') of
   801            [] =>
   802              (dts' @ [(i, (Sign.full_name sign (Syntax.type_name tname mx),
   803                 map DtTFree tvs, constrs'))],
   804               constr_syntax @ [constr_syntax'], sorts', i + 1)
   805          | dups => error ("Duplicate constructors " ^ commas dups ^
   806              " in datatype " ^ tname)
   807       end;
   808 
   809     val (dts', constr_syntax, sorts', i) = foldl prep_dt_spec (([], [], [], 0), dts);
   810     val sorts = sorts' @ (map (rpair (Sign.defaultS sign)) (tyvars \\ map fst sorts'));
   811     val dt_info = get_datatypes thy;
   812     val (descr, _) = unfold_datatypes sign dts' sorts dt_info dts' i;
   813     val _ = check_nonempty descr;
   814 
   815     val descr' = flat descr;
   816     val case_names_induct = mk_case_names_induct descr';
   817     val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
   818   in
   819     (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
   820       flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   821       case_names_induct case_names_exhausts thy
   822   end;
   823 
   824 val add_datatype_i = gen_add_datatype cert_typ;
   825 val add_datatype = gen_add_datatype read_typ;
   826 
   827 
   828 (** package setup **)
   829 
   830 (* setup theory *)
   831 
   832 val setup = [DatatypesData.init, Method.add_methods tactic_emulations] @ simproc_setup;
   833 
   834 
   835 (* outer syntax *)
   836 
   837 local structure P = OuterParse and K = OuterSyntax.Keyword in
   838 
   839 val datatype_decl =
   840   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
   841     (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix --| P.marg_comment));
   842 
   843 fun mk_datatype args =
   844   let
   845     val names = map (fn ((((None, _), t), _), _) => t | ((((Some t, _), _), _), _) => t) args;
   846     val specs = map (fn ((((_, vs), t), mx), cons) => (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
   847   in #1 o add_datatype false names specs end;
   848 
   849 val datatypeP =
   850   OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
   851     (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
   852 
   853 
   854 val rep_datatype_decl =
   855   Scan.option (Scan.repeat1 P.name) --
   856     Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 P.xthms1)) [] --
   857     Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 P.xthms1)) [] --
   858     (P.$$$ "induction" |-- P.!!! P.xthm);
   859 
   860 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #1 o rep_datatype opt_ts dss iss ind;
   861 
   862 val rep_datatypeP =
   863   OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
   864     (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
   865 
   866 
   867 val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
   868 val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
   869 
   870 end;
   871 
   872 
   873 end;
   874 
   875 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
   876 open BasicDatatypePackage;