src/HOL/Tools/datatype_package.ML
author nipkow
Tue Mar 28 17:32:24 2000 +0200 (2000-03-28)
changeset 8601 8fb3a81b4ccf
parent 8541 b0d2002f9f04
child 8645 40036a2ab646
permissions -rw-r--r--
added weak_case_cong feature
     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 (* generic induction tactic for datatypes *)
   171 
   172 fun induct_tac s i state =
   173   let
   174     val vars = Syntax.read_idents s;
   175     val (_, _, Bi, _) = dest_state (state, i);
   176     val {sign, ...} = rep_thm state;
   177     val tn = find_tname (hd vars) Bi;
   178     val {induction, ...} = datatype_info_sg_err sign tn;
   179     val ind_vnames = map (fn (_ $ Var (ixn, _)) =>
   180       implode (tl (explode (Syntax.string_of_vname ixn))))
   181         (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induction)));
   182     val insts = (ind_vnames ~~ vars) handle LIST _ =>
   183       error ("Induction rule for type " ^ tn ^ " has different number of variables")
   184   in
   185     occs_in_prems (res_inst_tac insts induction) vars i state
   186   end;
   187 
   188 
   189 (* generic case tactic for datatypes *)
   190 
   191 fun case_tac aterm i state =
   192   let val name = infer_tname state i aterm in
   193     if name = HOLogic.boolN then res_inst_tac [("P", aterm)] case_split_thm i state
   194     else
   195       let
   196         val {exhaustion, ...} = datatype_info_sg_err (Thm.sign_of_thm state) name;
   197         val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
   198           (hd (Logic.strip_assums_hyp (hd (prems_of exhaustion))));
   199         val exh_vname = implode (tl (explode (Syntax.string_of_vname ixn)))
   200       in res_inst_tac [(exh_vname, aterm)] exhaustion i state end
   201   end;
   202 
   203 
   204 (** Isar tactic emulations **)
   205 
   206 fun tactic_syntax tac = #2 oo Method.syntax (Args.goal_spec HEADGOAL -- Scan.lift Args.name >>
   207   (fn (quant, s) => Method.METHOD (fn facts => quant (Method.insert_tac facts THEN' tac s))));
   208 
   209 val tactic_emulations =
   210  [("induct_tac", tactic_syntax induct_tac, "induct_tac emulation (dynamic instantiation!)"),
   211   ("case_tac", tactic_syntax case_tac, "case_tac emulation (dynamic instantiation!)")];
   212 
   213 
   214 
   215 (** induct method setup **)
   216 
   217 (* case names *)
   218 
   219 local
   220 
   221 fun dt_recs (DtTFree _) = []
   222   | dt_recs (DtType (_, dts)) = flat (map dt_recs dts)
   223   | dt_recs (DtRec i) = [i];
   224 
   225 fun dt_cases (descr: descr) (_, args, constrs) =
   226   let
   227     fun the_bname i = Sign.base_name (#1 (the (assoc (descr, i))));
   228     val bnames = map the_bname (distinct (flat (map dt_recs args)));
   229   in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
   230 
   231 
   232 fun induct_cases descr =
   233   DatatypeProp.indexify_names (flat (map (dt_cases descr) (map #2 descr)));
   234 
   235 fun exhaust_cases descr i = dt_cases descr (the (assoc (descr, i)));
   236 
   237 in
   238 
   239 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
   240 
   241 fun mk_case_names_exhausts descr new =
   242   map (RuleCases.case_names o exhaust_cases descr o #1)
   243     (filter (fn ((_, (name, _, _))) => name mem_string new) descr);
   244 
   245 end;
   246 
   247 
   248 (* add_cases_induct *)
   249 
   250 fun add_cases_induct infos =
   251   let
   252     fun proj _ 1 thm = thm
   253       | proj i n thm =
   254           (if i + 1 < n then (fn th => th RS conjunct1) else I)
   255             (Library.funpow i (fn th => th RS conjunct2) thm)
   256           |> Drule.standard;
   257 
   258     fun add (ths, (name, {index, descr, induction, exhaustion, ...}: datatype_info)) =
   259       (("", proj index (length descr) induction), [InductMethod.induct_type_global name]) ::
   260       (("", exhaustion), [InductMethod.cases_type_global name]) :: ths;
   261   in #1 o PureThy.add_thms (foldl add ([], infos)) end;
   262 
   263 
   264 
   265 (**** simplification procedure for showing distinctness of constructors ****)
   266 
   267 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
   268   | stripT p = p;
   269 
   270 fun stripC (i, f $ x) = stripC (i + 1, f)
   271   | stripC p = p;
   272 
   273 val distinctN = "constr_distinct";
   274 
   275 exception ConstrDistinct of term;
   276 
   277 fun distinct_proc sg _ (t as Const ("op =", _) $ t1 $ t2) =
   278   (case (stripC (0, t1), stripC (0, t2)) of
   279      ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
   280          (case (stripT (0, T1), stripT (0, T2)) of
   281             ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
   282                 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
   283                    (case (constrs_of_sg sg tname1) of
   284                       Some constrs => let val cnames = map (fst o dest_Const) constrs
   285                         in if cname1 mem cnames andalso cname2 mem cnames then
   286                              let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));
   287                                  val eq_ct = cterm_of sg eq_t;
   288                                  val Datatype_thy = theory "Datatype";
   289                                  val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
   290                                    map (get_thm Datatype_thy)
   291                                      ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
   292                              in (case (#distinct (datatype_info_sg_err sg tname1)) of
   293                                  QuickAndDirty => Some (Thm.invoke_oracle
   294                                    Datatype_thy distinctN (sg, ConstrDistinct eq_t))
   295                                | FewConstrs thms => Some (prove_goalw_cterm [] eq_ct (K
   296                                    [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
   297                                     atac 2, resolve_tac thms 1, etac FalseE 1]))
   298                                | ManyConstrs (thm, ss) => Some (prove_goalw_cterm [] eq_ct (K
   299                                    [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
   300                                     full_simp_tac ss 1,
   301                                     REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
   302                                     eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
   303                                     etac FalseE 1])))
   304                              end
   305                            else None
   306                         end
   307                     | None => None)
   308                 else None
   309           | _ => None)
   310    | _ => None)
   311   | distinct_proc sg _ _ = None;
   312 
   313 val distinct_pats = [Thm.read_cterm (Theory.sign_of HOL.thy) ("s = t", HOLogic.termT)];
   314 val distinct_simproc = mk_simproc distinctN distinct_pats distinct_proc;
   315 
   316 val dist_ss = HOL_ss addsimprocs [distinct_simproc];
   317 
   318 val simproc_setup =
   319   [Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t),
   320    fn thy => (simpset_ref_of thy := simpset_of thy addsimprocs [distinct_simproc]; thy)];
   321 
   322 
   323 (* prepare types *)
   324 
   325 fun read_typ sign ((Ts, sorts), str) =
   326   let
   327     val T = Type.no_tvars (Sign.read_typ (sign, (curry assoc)
   328       (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
   329   in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
   330 
   331 fun cert_typ sign ((Ts, sorts), raw_T) =
   332   let
   333     val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
   334       TYPE (msg, _, _) => error msg;
   335     val sorts' = add_typ_tfrees (T, sorts)
   336   in (Ts @ [T],
   337       case duplicates (map fst sorts') of
   338          [] => sorts'
   339        | dups => error ("Inconsistent sort constraints for " ^ commas dups))
   340   end;
   341 
   342 
   343 (**** make datatype info ****)
   344 
   345 fun make_dt_info descr induct reccomb_names rec_thms
   346   ((((((((i, (_, (tname, _, _))), case_name), case_thms),
   347     exhaustion_thm), distinct_thm), inject), nchotomy), case_cong) = (tname,
   348       {index = i,
   349        descr = descr,
   350        rec_names = reccomb_names,
   351        rec_rewrites = rec_thms,
   352        case_name = case_name,
   353        case_rewrites = case_thms,
   354        induction = induct,
   355        exhaustion = exhaustion_thm,
   356        distinct = distinct_thm,
   357        inject = inject,
   358        nchotomy = nchotomy,
   359        case_cong = case_cong});
   360 
   361 
   362 (********************* axiomatic introduction of datatypes ********************)
   363 
   364 fun add_and_get_axioms_atts label tnames attss ts thy =
   365   foldr (fn (((tname, atts), t), (thy', axs)) =>
   366     let
   367       val (thy'', [ax]) = thy' |>
   368         Theory.add_path tname |>
   369         PureThy.add_axioms_i [((label, t), atts)];
   370     in (Theory.parent_path thy'', ax::axs)
   371     end) (tnames ~~ attss ~~ ts, (thy, []));
   372 
   373 fun add_and_get_axioms label tnames =
   374   add_and_get_axioms_atts label tnames (replicate (length tnames) []);
   375 
   376 fun add_and_get_axiomss label tnames tss thy =
   377   foldr (fn ((tname, ts), (thy', axss)) =>
   378     let
   379       val (thy'', [axs]) = thy' |>
   380         Theory.add_path tname |>
   381         PureThy.add_axiomss_i [((label, ts), [])];
   382     in (Theory.parent_path thy'', axs::axss)
   383     end) (tnames ~~ tss, (thy, []));
   384 
   385 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   386     case_names_induct case_names_exhausts thy =
   387   let
   388     val descr' = flat descr;
   389     val recTs = get_rec_types descr' sorts;
   390     val used = foldr add_typ_tfree_names (recTs, []);
   391     val newTs = take (length (hd descr), recTs);
   392 
   393     val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
   394       (fn (DtType ("fun", [_, DtRec _])) => true | _ => false) cargs) constrs) descr';
   395 
   396     (**** declare new types and constants ****)
   397 
   398     val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
   399 
   400     val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
   401       map (fn ((_, cargs), (cname, mx)) =>
   402         (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   403           (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
   404 
   405     val rec_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~
   406       replicate (length descr') HOLogic.termS);
   407 
   408     val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) =>
   409       map (fn (_, cargs) =>
   410         let
   411           val Ts = map (typ_of_dtyp descr' sorts) cargs;
   412           val recs = filter (is_rec_type o fst) (cargs ~~ Ts);
   413 
   414           fun mk_argT (DtRec k, _) = nth_elem (k, rec_result_Ts)
   415             | mk_argT (DtType ("fun", [_, DtRec k]), Type ("fun", [T, _])) =
   416                T --> nth_elem (k, rec_result_Ts);
   417 
   418           val argTs = Ts @ map mk_argT recs
   419         in argTs ---> nth_elem (i, rec_result_Ts)
   420         end) constrs) descr');
   421 
   422     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   423     val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
   424       (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   425         (1 upto (length descr')));
   426 
   427     val big_size_name = space_implode "_" new_type_names ^ "_size";
   428     val size_names = if length (flat (tl descr)) = 1 then [big_size_name] else
   429       map (fn i => big_size_name ^ "_" ^ string_of_int i)
   430         (1 upto length (flat (tl descr)));
   431 
   432     val freeT = TFree (variant used "'t", HOLogic.termS);
   433     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
   434       map (fn (_, cargs) =>
   435         let val Ts = map (typ_of_dtyp descr' sorts) cargs
   436         in Ts ---> freeT end) constrs) (hd descr);
   437 
   438     val case_names = map (fn s => (s ^ "_case")) new_type_names;
   439 
   440     val thy2' = thy |>
   441 
   442       (** new types **)
   443 
   444       curry (foldr (fn (((name, mx), tvs), thy') => thy' |>
   445           TypedefPackage.add_typedecls [(name, tvs, mx)]))
   446         (types_syntax ~~ tyvars) |>
   447       add_path flat_names (space_implode "_" new_type_names) |>
   448 
   449       (** primrec combinators **)
   450 
   451       Theory.add_consts_i (map (fn ((name, T), T') =>
   452         (name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
   453           (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
   454 
   455       (** case combinators **)
   456 
   457       Theory.add_consts_i (map (fn ((name, T), Ts) =>
   458         (name, Ts @ [T] ---> freeT, NoSyn))
   459           (case_names ~~ newTs ~~ case_fn_Ts)) |>
   460       Theory.add_trrules_i (DatatypeProp.make_case_trrules new_type_names descr);
   461 
   462     val reccomb_names' = map (Sign.intern_const (Theory.sign_of thy2')) reccomb_names;
   463     val case_names' = map (Sign.intern_const (Theory.sign_of thy2')) case_names;
   464 
   465     val thy2 = thy2' |>
   466 
   467       (** size functions **)
   468 
   469       (if no_size then I else Theory.add_consts_i (map (fn (s, T) =>
   470         (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   471           (size_names ~~ drop (length (hd descr), recTs)))) |>
   472 
   473       (** constructors **)
   474 
   475       parent_path flat_names |>
   476       curry (foldr (fn (((((_, (_, _, constrs)), T), tname),
   477         constr_syntax'), thy') => thy' |>
   478           add_path flat_names tname |>
   479             Theory.add_consts_i (map (fn ((_, cargs), (cname, mx)) =>
   480               (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   481                 (constrs ~~ constr_syntax')) |>
   482           parent_path flat_names))
   483             (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
   484 
   485     (**** introduction of axioms ****)
   486 
   487     val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
   488     val size_axs = if no_size then [] else DatatypeProp.make_size new_type_names descr sorts thy2;
   489 
   490     val (thy3, (([induct], [rec_thms]), inject)) =
   491       thy2 |>
   492       Theory.add_path (space_implode "_" new_type_names) |>
   493       PureThy.add_axioms_i [(("induct", DatatypeProp.make_ind descr sorts), [case_names_induct])] |>>>
   494       PureThy.add_axiomss_i [(("recs", rec_axs), [])] |>>
   495       (if no_size then I else #1 o PureThy.add_axiomss_i [(("size", size_axs), [])]) |>>
   496       Theory.parent_path |>>>
   497       add_and_get_axiomss "inject" new_type_names
   498         (DatatypeProp.make_injs descr sorts);
   499     val size_thms = if no_size then [] else get_thms thy3 "size";
   500     val (thy4, distinct) = add_and_get_axiomss "distinct" new_type_names
   501       (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
   502 
   503     val exhaust_ts = DatatypeProp.make_casedists descr sorts;
   504     val (thy5, exhaustion) = add_and_get_axioms_atts "exhaust" new_type_names
   505       (map Library.single case_names_exhausts) exhaust_ts thy4;
   506     val (thy6, case_thms) = add_and_get_axiomss "cases" new_type_names
   507       (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
   508     val (split_ts, split_asm_ts) = ListPair.unzip
   509       (DatatypeProp.make_splits new_type_names descr sorts thy6);
   510     val (thy7, split) = add_and_get_axioms "split" new_type_names split_ts thy6;
   511     val (thy8, split_asm) = add_and_get_axioms "split_asm" new_type_names
   512       split_asm_ts thy7;
   513     val (thy9, nchotomys) = add_and_get_axioms "nchotomy" new_type_names
   514       (DatatypeProp.make_nchotomys descr sorts) thy8;
   515     val (thy10, case_congs) = add_and_get_axioms "case_cong" new_type_names
   516       (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
   517     val (thy11, weak_case_congs) = add_and_get_axioms "weak_case_cong" new_type_names
   518       (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
   519 
   520     val dt_infos = map (make_dt_info descr' induct reccomb_names' rec_thms)
   521       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
   522         exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
   523           nchotomys ~~ case_congs);
   524 
   525     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   526 
   527     val thy12 = thy11 |>
   528       Theory.add_path (space_implode "_" new_type_names) |>
   529       (#1 o PureThy.add_thmss [(("simps", simps), []),
   530         (("", flat case_thms @ size_thms @ rec_thms), [Simplifier.simp_add_global]),
   531         (("", flat (inject @ distinct)), [iff_add_global]),
   532         (("", weak_case_congs), [Simplifier.change_global_ss (op addcongs)])]) |>
   533       put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
   534       add_cases_induct dt_infos |>
   535       Theory.parent_path;
   536 
   537   in
   538     (thy12,
   539      {distinct = distinct,
   540       inject = inject,
   541       exhaustion = exhaustion,
   542       rec_thms = rec_thms,
   543       case_thms = case_thms,
   544       split_thms = split ~~ split_asm,
   545       induction = induct,
   546       size = size_thms,
   547       simps = simps})
   548   end;
   549 
   550 
   551 (******************* definitional introduction of datatypes *******************)
   552 
   553 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   554     case_names_induct case_names_exhausts thy =
   555   let
   556     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   557 
   558     val (thy2, inject, distinct, dist_rewrites, simproc_dists, induct) = thy |>
   559       DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
   560         types_syntax constr_syntax case_names_induct;
   561 
   562     val (thy3, casedist_thms) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
   563       sorts induct case_names_exhausts thy2;
   564     val (thy4, (reccomb_names, rec_thms)) = DatatypeAbsProofs.prove_primrec_thms
   565       flat_names new_type_names descr sorts dt_info inject dist_rewrites dist_ss induct thy3;
   566     val (thy6, (case_thms, case_names)) = DatatypeAbsProofs.prove_case_thms
   567       flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
   568     val (thy7, split_thms) = DatatypeAbsProofs.prove_split_thms new_type_names
   569       descr sorts inject dist_rewrites casedist_thms case_thms thy6;
   570     val (thy8, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
   571       descr sorts casedist_thms thy7;
   572     val (thy9, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
   573       descr sorts nchotomys case_thms thy8;
   574     val (thy10, weak_case_congs) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   575       descr sorts thy9;
   576     val (thy11, size_thms) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
   577       descr sorts reccomb_names rec_thms thy10;
   578 
   579     val dt_infos = map (make_dt_info (flat descr) induct reccomb_names rec_thms)
   580       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
   581         casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs);
   582 
   583     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   584 
   585     val thy12 = thy11 |>
   586       Theory.add_path (space_implode "_" new_type_names) |>
   587       (#1 o PureThy.add_thmss [(("simps", simps), []),
   588         (("", flat case_thms @ size_thms @ rec_thms), [Simplifier.simp_add_global]),
   589         (("", flat (inject @ distinct)), [iff_add_global]),
   590         (("", weak_case_congs), [Simplifier.change_global_ss (op addcongs)])]) |>
   591       put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
   592       add_cases_induct dt_infos |>
   593       Theory.parent_path;
   594 
   595   in
   596     (thy12,
   597      {distinct = distinct,
   598       inject = inject,
   599       exhaustion = casedist_thms,
   600       rec_thms = rec_thms,
   601       case_thms = case_thms,
   602       split_thms = split_thms,
   603       induction = induct,
   604       size = size_thms,
   605       simps = simps})
   606   end;
   607 
   608 
   609 (*********************** declare existing type as datatype *********************)
   610 
   611 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
   612   let
   613     fun app_thmss srcs thy = foldl_map (fn (thy, x) => apply_theorems x thy) (thy, srcs);
   614     fun app_thm src thy = apsnd Library.hd (apply_theorems [src] thy);
   615 
   616     val (((thy1, induction), inject), distinct) = thy0
   617       |> app_thmss raw_distinct
   618       |> apfst (app_thmss raw_inject)
   619       |> apfst (apfst (app_thm raw_induction));
   620     val sign = Theory.sign_of thy1;
   621 
   622     val induction' = freezeT induction;
   623 
   624     fun err t = error ("Ill-formed predicate in induction rule: " ^
   625       Sign.string_of_term sign t);
   626 
   627     fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
   628           ((tname, map dest_TFree Ts) handle TERM _ => err t)
   629       | get_typ t = err t;
   630 
   631     val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
   632     val new_type_names = if_none alt_names (map fst dtnames);
   633 
   634     fun get_constr t = (case Logic.strip_assums_concl t of
   635         _ $ (_ $ t') => (case head_of t' of
   636             Const (cname, cT) => (case strip_type cT of
   637                 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
   638               | _ => err t)
   639           | _ => err t)
   640       | _ => err t);
   641 
   642     fun make_dt_spec [] _ _ = []
   643       | make_dt_spec ((tname, tvs)::dtnames') i constrs =
   644           let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
   645           in (i, (tname, map DtTFree tvs, map snd constrs'))::
   646             (make_dt_spec dtnames' (i + 1) constrs'')
   647           end;
   648 
   649     val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
   650     val sorts = add_term_tfrees (concl_of induction', []);
   651     val dt_info = get_datatypes thy1;
   652 
   653     val case_names_induct = mk_case_names_induct descr;
   654     val case_names_exhausts = mk_case_names_exhausts descr (map #1 dtnames);
   655     
   656 
   657     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   658 
   659     val (thy2, casedist_thms) = thy1 |>
   660       DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
   661         case_names_exhausts;
   662     val (thy3, (reccomb_names, rec_thms)) = DatatypeAbsProofs.prove_primrec_thms
   663       false new_type_names [descr] sorts dt_info inject distinct dist_ss induction thy2;
   664     val (thy4, (case_thms, case_names)) = DatatypeAbsProofs.prove_case_thms false
   665       new_type_names [descr] sorts reccomb_names rec_thms thy3;
   666     val (thy5, split_thms) = DatatypeAbsProofs.prove_split_thms
   667       new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
   668     val (thy6, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
   669       [descr] sorts casedist_thms thy5;
   670     val (thy7, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
   671       [descr] sorts nchotomys case_thms thy6;
   672     val (thy8, weak_case_congs) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   673       [descr] sorts thy7;
   674     val (thy9, size_thms) =
   675       if exists (equal "Arith") (Sign.stamp_names_of (Theory.sign_of thy8)) then
   676         DatatypeAbsProofs.prove_size_thms false new_type_names
   677           [descr] sorts reccomb_names rec_thms thy8
   678       else (thy8, []);
   679 
   680     val dt_infos = map (make_dt_info descr induction reccomb_names rec_thms)
   681       ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~
   682         casedist_thms ~~ map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs);
   683 
   684     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   685 
   686     val (thy10, [induction']) = thy9 |>
   687       (#1 o store_thmss "inject" new_type_names inject) |>
   688       (#1 o store_thmss "distinct" new_type_names distinct) |>
   689       Theory.add_path (space_implode "_" new_type_names) |>
   690       PureThy.add_thms [(("induct", induction), [case_names_induct])] |>>
   691       (#1 o PureThy.add_thmss [(("simps", simps), []),
   692         (("", flat case_thms @ size_thms @ rec_thms), [Simplifier.simp_add_global]),
   693         (("", flat (inject @ distinct)), [iff_add_global]),
   694         (("", weak_case_congs), [Simplifier.change_global_ss (op addcongs)])]) |>>
   695       put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>>
   696       add_cases_induct dt_infos |>>
   697       Theory.parent_path;
   698 
   699   in
   700     (thy10,
   701      {distinct = distinct,
   702       inject = inject,
   703       exhaustion = casedist_thms,
   704       rec_thms = rec_thms,
   705       case_thms = case_thms,
   706       split_thms = split_thms,
   707       induction = induction',
   708       size = size_thms,
   709       simps = simps})
   710   end;
   711 
   712 val rep_datatype = gen_rep_datatype IsarThy.apply_theorems;
   713 val rep_datatype_i = gen_rep_datatype IsarThy.apply_theorems_i;
   714 
   715 
   716 (******************************** add datatype ********************************)
   717 
   718 fun gen_add_datatype prep_typ flat_names new_type_names dts thy =
   719   let
   720     val _ = Theory.requires thy "Datatype" "datatype definitions";
   721 
   722     (* this theory is used just for parsing *)
   723 
   724     val tmp_thy = thy |>
   725       Theory.copy |>
   726       Theory.add_types (map (fn (tvs, tname, mx, _) =>
   727         (tname, length tvs, mx)) dts);
   728 
   729     val sign = Theory.sign_of tmp_thy;
   730 
   731     val (tyvars, _, _, _)::_ = dts;
   732     val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
   733       let val full_tname = Sign.full_name sign (Syntax.type_name tname mx)
   734       in (case duplicates tvs of
   735             [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
   736                   else error ("Mutually recursive datatypes must have same type parameters")
   737           | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
   738               " : " ^ commas dups))
   739       end) dts);
   740 
   741     val _ = (case duplicates (map fst new_dts) @ duplicates new_type_names of
   742       [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
   743 
   744     fun prep_dt_spec ((dts', constr_syntax, sorts, i), (tvs, tname, mx, constrs)) =
   745       let
   746         fun prep_constr ((constrs, constr_syntax', sorts'), (cname, cargs, mx')) =
   747           let
   748             val (cargs', sorts'') = foldl (prep_typ sign) (([], sorts'), cargs);
   749             val _ = (case foldr add_typ_tfree_names (cargs', []) \\ tvs of
   750                 [] => ()
   751               | vs => error ("Extra type variables on rhs: " ^ commas vs))
   752           in (constrs @ [((if flat_names then Sign.full_name sign else
   753                 Sign.full_name_path sign tname) (Syntax.const_name cname mx'),
   754                    map (dtyp_of_typ new_dts) cargs')],
   755               constr_syntax' @ [(cname, mx')], sorts'')
   756           end handle ERROR =>
   757             error ("The error above occured in constructor " ^ cname ^
   758               " of datatype " ^ tname);
   759 
   760         val (constrs', constr_syntax', sorts') =
   761           foldl prep_constr (([], [], sorts), constrs)
   762 
   763       in
   764         case duplicates (map fst constrs') of
   765            [] =>
   766              (dts' @ [(i, (Sign.full_name sign (Syntax.type_name tname mx),
   767                 map DtTFree tvs, constrs'))],
   768               constr_syntax @ [constr_syntax'], sorts', i + 1)
   769          | dups => error ("Duplicate constructors " ^ commas dups ^
   770              " in datatype " ^ tname)
   771       end;
   772 
   773     val (dts', constr_syntax, sorts', i) = foldl prep_dt_spec (([], [], [], 0), dts);
   774     val sorts = sorts' @ (map (rpair (Sign.defaultS sign)) (tyvars \\ map fst sorts'));
   775     val dt_info = get_datatypes thy;
   776     val (descr, _) = unfold_datatypes sign dts' sorts dt_info dts' i;
   777     val _ = check_nonempty descr;
   778 
   779     val descr' = flat descr;
   780     val case_names_induct = mk_case_names_induct descr';
   781     val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
   782   in
   783     (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
   784       flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   785       case_names_induct case_names_exhausts thy
   786   end;
   787 
   788 val add_datatype_i = gen_add_datatype cert_typ;
   789 val add_datatype = gen_add_datatype read_typ;
   790 
   791 
   792 (** package setup **)
   793 
   794 (* setup theory *)
   795 
   796 val setup = [DatatypesData.init, Method.add_methods tactic_emulations] @ simproc_setup;
   797 
   798 
   799 (* outer syntax *)
   800 
   801 local structure P = OuterParse and K = OuterSyntax.Keyword in
   802 
   803 val datatype_decl =
   804   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
   805     (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix --| P.marg_comment));
   806 
   807 fun mk_datatype args =
   808   let
   809     val names = map (fn ((((None, _), t), _), _) => t | ((((Some t, _), _), _), _) => t) args;
   810     val specs = map (fn ((((_, vs), t), mx), cons) => (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
   811   in #1 o add_datatype false names specs end;
   812 
   813 val datatypeP =
   814   OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
   815     (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
   816 
   817 
   818 val rep_datatype_decl =
   819   Scan.option (Scan.repeat1 P.name) --
   820     Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 P.xthms1)) [] --
   821     Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 P.xthms1)) [] --
   822     (P.$$$ "induction" |-- P.!!! P.xthm);
   823 
   824 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #1 o rep_datatype opt_ts dss iss ind;
   825 
   826 val rep_datatypeP =
   827   OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
   828     (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
   829 
   830 
   831 val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
   832 val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
   833 
   834 end;
   835 
   836 
   837 end;
   838 
   839 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
   840 open BasicDatatypePackage;