src/HOL/Tools/datatype_package.ML
author haftmann
Mon Feb 18 22:56:53 2008 +0100 (2008-02-18)
changeset 26093 51e8d37b4e7b
parent 25888 48cc198b9ac5
child 26111 91e0999b075f
permissions -rw-r--r--
tuned
     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_i : bool -> bool -> string list -> (string list * bstring * mixfix *
    21     (bstring * typ 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        simps : thm list} * theory
    30   val add_datatype : bool -> string list -> (string list * bstring * mixfix *
    31     (bstring * string list * mixfix) list) list -> theory ->
    32       {distinct : thm list list,
    33        inject : thm list list,
    34        exhaustion : thm list,
    35        rec_thms : thm list,
    36        case_thms : thm list list,
    37        split_thms : (thm * thm) list,
    38        induction : thm,
    39        simps : thm list} * theory
    40   val rep_datatype_i : string list option -> (thm list * attribute list) list list ->
    41     (thm list * attribute list) list list -> (thm list * attribute list) ->
    42     theory ->
    43       {distinct : thm list list,
    44        inject : thm list list,
    45        exhaustion : thm list,
    46        rec_thms : thm list,
    47        case_thms : thm list list,
    48        split_thms : (thm * thm) list,
    49        induction : thm,
    50        simps : thm list} * theory
    51   val rep_datatype : string list option -> (thmref * Attrib.src list) list list ->
    52     (thmref * Attrib.src list) list list -> thmref * Attrib.src list -> theory ->
    53       {distinct : thm list list,
    54        inject : thm list list,
    55        exhaustion : thm list,
    56        rec_thms : thm list,
    57        case_thms : thm list list,
    58        split_thms : (thm * thm) list,
    59        induction : thm,
    60        simps : thm list} * theory
    61   val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table
    62   val get_datatype : theory -> string -> DatatypeAux.datatype_info option
    63   val the_datatype : theory -> string -> DatatypeAux.datatype_info
    64   val the_datatype_spec : theory -> string -> (string * sort) list * (string * typ list) list
    65   val datatype_of_constr : theory -> string -> DatatypeAux.datatype_info option
    66   val datatype_of_case : theory -> string -> DatatypeAux.datatype_info option
    67   val get_datatype_constrs : theory -> string -> (string * typ) list option
    68   val interpretation: (string list -> theory -> theory) -> theory -> theory
    69   val print_datatypes : theory -> unit
    70   val make_case :  Proof.context -> bool -> string list -> term ->
    71     (term * term) list -> term * (term * (int * bool)) list
    72   val strip_case: Proof.context -> bool ->
    73     term -> (term * (term * term) list) option
    74   val setup: theory -> theory
    75 end;
    76 
    77 structure DatatypePackage : DATATYPE_PACKAGE =
    78 struct
    79 
    80 open DatatypeAux;
    81 
    82 val quiet_mode = quiet_mode;
    83 
    84 
    85 (* theory data *)
    86 
    87 structure DatatypesData = TheoryDataFun
    88 (
    89   type T =
    90     {types: datatype_info Symtab.table,
    91      constrs: datatype_info Symtab.table,
    92      cases: datatype_info Symtab.table};
    93 
    94   val empty =
    95     {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty};
    96   val copy = I;
    97   val extend = I;
    98   fun merge _
    99     ({types = types1, constrs = constrs1, cases = cases1},
   100      {types = types2, constrs = constrs2, cases = cases2}) =
   101     {types = Symtab.merge (K true) (types1, types2),
   102      constrs = Symtab.merge (K true) (constrs1, constrs2),
   103      cases = Symtab.merge (K true) (cases1, cases2)};
   104 );
   105 
   106 val get_datatypes = #types o DatatypesData.get;
   107 val map_datatypes = DatatypesData.map;
   108 
   109 fun print_datatypes thy =
   110   Pretty.writeln (Pretty.strs ("datatypes:" ::
   111     map #1 (NameSpace.extern_table (Sign.type_space thy, get_datatypes thy))));
   112 
   113 
   114 (** theory information about datatypes **)
   115 
   116 fun put_dt_infos (dt_infos : (string * datatype_info) list) =
   117   map_datatypes (fn {types, constrs, cases} =>
   118     {types = fold Symtab.update dt_infos types,
   119      constrs = fold Symtab.update
   120        (maps (fn (_, info as {descr, index, ...}) => map (rpair info o fst)
   121           (#3 (the (AList.lookup op = descr index)))) dt_infos) constrs,
   122      cases = fold Symtab.update
   123        (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos)
   124        cases});
   125 
   126 val get_datatype = Symtab.lookup o get_datatypes;
   127 
   128 fun the_datatype thy name = (case get_datatype thy name of
   129       SOME info => info
   130     | NONE => error ("Unknown datatype " ^ quote name));
   131 
   132 val datatype_of_constr = Symtab.lookup o #constrs o DatatypesData.get;
   133 val datatype_of_case = Symtab.lookup o #cases o DatatypesData.get;
   134 
   135 fun get_datatype_descr thy dtco =
   136   get_datatype thy dtco
   137   |> Option.map (fn info as { descr, index, ... } =>
   138        (info, (((fn SOME (_, dtys, cos) => (dtys, cos)) o AList.lookup (op =) descr) index)));
   139 
   140 fun the_datatype_spec thy dtco =
   141   let
   142     val info as { descr, index, sorts = raw_sorts, ... } = the_datatype thy dtco;
   143     val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr index;
   144     val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v))
   145       o DatatypeAux.dest_DtTFree) dtys;
   146     val cos = map
   147       (fn (co, tys) => (co, map (DatatypeAux.typ_of_dtyp descr sorts) tys)) raw_cos;
   148   in (sorts, cos) end;
   149 
   150 fun get_datatype_constrs thy dtco =
   151   case try (the_datatype_spec thy) dtco
   152    of SOME (sorts, cos) =>
   153         let
   154           fun subst (v, sort) = TVar ((v, 0), sort);
   155           fun subst_ty (TFree v) = subst v
   156             | subst_ty ty = ty;
   157           val dty = Type (dtco, map subst sorts);
   158           fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty);
   159         in SOME (map mk_co cos) end
   160     | NONE => NONE;
   161 
   162 fun find_tname var Bi =
   163   let val frees = map dest_Free (term_frees Bi)
   164       val params = rename_wrt_term Bi (Logic.strip_params Bi);
   165   in case AList.lookup (op =) (frees @ params) var of
   166        NONE => error ("No such variable in subgoal: " ^ quote var)
   167      | SOME(Type (tn, _)) => tn
   168      | _ => error ("Cannot determine type of " ^ quote var)
   169   end;
   170 
   171 fun infer_tname state i aterm =
   172   let
   173     val sign = Thm.theory_of_thm state;
   174     val (_, _, Bi, _) = Thm.dest_state (state, i)
   175     val params = Logic.strip_params Bi;   (*params of subgoal i*)
   176     val params = rev (rename_wrt_term Bi params);   (*as they are printed*)
   177     val (types, sorts) = types_sorts state;
   178     fun types' (a, ~1) = (case AList.lookup (op =) params a of NONE => types(a, ~1) | sm => sm)
   179       | types' ixn = types ixn;
   180     val ([ct], _) = Thm.read_def_cterms (sign, types', sorts) [] false [(aterm, dummyT)];
   181   in case #T (rep_cterm ct) of
   182        Type (tn, _) => tn
   183      | _ => error ("Cannot determine type of " ^ quote aterm)
   184   end;
   185 
   186 (*Warn if the (induction) variable occurs Free among the premises, which
   187   usually signals a mistake.  But calls the tactic either way!*)
   188 fun occs_in_prems tacf vars =
   189   SUBGOAL (fn (Bi, i) =>
   190            (if exists (fn (a, _) => member (op =) vars a)
   191                       (fold Term.add_frees (#2 (strip_context Bi)) [])
   192              then warning "Induction variable occurs also among premises!"
   193              else ();
   194             tacf i));
   195 
   196 
   197 (* generic induction tactic for datatypes *)
   198 
   199 local
   200 
   201 fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x)
   202   | prep_var _ = NONE;
   203 
   204 fun prep_inst (concl, xs) = (*exception Library.UnequalLengths*)
   205   let val vs = Induct.vars_of concl
   206   in map_filter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
   207 
   208 in
   209 
   210 fun gen_induct_tac inst_tac (varss, opt_rule) i state =
   211   SUBGOAL (fn (Bi,_) =>
   212   let
   213     val (rule, rule_name) =
   214       case opt_rule of
   215           SOME r => (r, "Induction rule")
   216         | NONE =>
   217             let val tn = find_tname (hd (map_filter I (flat varss))) Bi
   218                 val thy = Thm.theory_of_thm state
   219             in (#induction (the_datatype thy tn), "Induction rule for type " ^ tn)
   220             end
   221     val concls = HOLogic.dest_concls (Thm.concl_of rule);
   222     val insts = maps prep_inst (concls ~~ varss) handle Library.UnequalLengths =>
   223       error (rule_name ^ " has different numbers of variables");
   224   in occs_in_prems (inst_tac insts rule) (map #2 insts) i end)
   225   i state;
   226 
   227 fun induct_tac s =
   228   gen_induct_tac Tactic.res_inst_tac'
   229     (map (single o SOME) (Syntax.read_idents s), NONE);
   230 
   231 fun induct_thm_tac th s =
   232   gen_induct_tac Tactic.res_inst_tac'
   233     ([map SOME (Syntax.read_idents s)], SOME th);
   234 
   235 end;
   236 
   237 
   238 (* generic case tactic for datatypes *)
   239 
   240 fun case_inst_tac inst_tac t rule i state =
   241   let
   242     val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
   243       (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));
   244   in inst_tac [(ixn, t)] rule i state end;
   245 
   246 fun gen_case_tac inst_tac (t, SOME rule) i state =
   247       case_inst_tac inst_tac t rule i state
   248   | gen_case_tac inst_tac (t, NONE) i state =
   249       let val tn = infer_tname state i t in
   250         if tn = HOLogic.boolN then inst_tac [(("P", 0), t)] case_split_thm i state
   251         else case_inst_tac inst_tac t
   252                (#exhaustion (the_datatype (Thm.theory_of_thm state) tn))
   253                i state
   254       end handle THM _ => Seq.empty;
   255 
   256 fun case_tac t = gen_case_tac Tactic.res_inst_tac' (t, NONE);
   257 
   258 
   259 
   260 (** Isar tactic emulations **)
   261 
   262 local
   263 
   264 val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
   265 val opt_rule = Scan.option (rule_spec |-- Attrib.thm);
   266 
   267 val varss =
   268   Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name))));
   269 
   270 val inst_tac = RuleInsts.bires_inst_tac false;
   271 
   272 fun induct_meth ctxt (varss, opt_rule) =
   273   gen_induct_tac (inst_tac ctxt) (varss, opt_rule);
   274 fun case_meth ctxt (varss, opt_rule) =
   275   gen_case_tac (inst_tac ctxt) (varss, opt_rule);
   276 
   277 in
   278 
   279 val tactic_emulations =
   280  [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth,
   281     "induct_tac emulation (dynamic instantiation)"),
   282   ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth,
   283     "case_tac emulation (dynamic instantiation)")];
   284 
   285 end;
   286 
   287 
   288 
   289 (** induct method setup **)
   290 
   291 (* case names *)
   292 
   293 local
   294 
   295 fun dt_recs (DtTFree _) = []
   296   | dt_recs (DtType (_, dts)) = maps dt_recs dts
   297   | dt_recs (DtRec i) = [i];
   298 
   299 fun dt_cases (descr: descr) (_, args, constrs) =
   300   let
   301     fun the_bname i = Sign.base_name (#1 (the (AList.lookup (op =) descr i)));
   302     val bnames = map the_bname (distinct (op =) (maps dt_recs args));
   303   in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
   304 
   305 
   306 fun induct_cases descr =
   307   DatatypeProp.indexify_names (maps (dt_cases descr) (map #2 descr));
   308 
   309 fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i));
   310 
   311 in
   312 
   313 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
   314 
   315 fun mk_case_names_exhausts descr new =
   316   map (RuleCases.case_names o exhaust_cases descr o #1)
   317     (filter (fn ((_, (name, _, _))) => member (op =) new name) descr);
   318 
   319 end;
   320 
   321 fun add_rules simps case_thms rec_thms inject distinct
   322                   weak_case_congs cong_att =
   323   PureThy.add_thmss [(("simps", simps), []),
   324     (("", flat case_thms @
   325           flat distinct @ rec_thms), [Simplifier.simp_add]),
   326     (("", rec_thms), [RecfunCodegen.add_default]),
   327     (("", flat inject), [iff_add]),
   328     (("", map (fn th => th RS notE) (flat distinct)), [Classical.safe_elim NONE]),
   329     (("", weak_case_congs), [cong_att])]
   330   #> snd;
   331 
   332 
   333 (* add_cases_induct *)
   334 
   335 fun add_cases_induct infos induction thy =
   336   let
   337     val inducts = ProjectRule.projections (ProofContext.init thy) induction;
   338 
   339     fun named_rules (name, {index, exhaustion, ...}: datatype_info) =
   340       [(("", nth inducts index), [Induct.induct_type name]),
   341        (("", exhaustion), [Induct.cases_type name])];
   342     fun unnamed_rule i =
   343       (("", nth inducts i), [PureThy.kind_internal, Induct.induct_type ""]);
   344   in
   345     thy |> PureThy.add_thms
   346       (maps named_rules infos @
   347         map unnamed_rule (length infos upto length inducts - 1)) |> snd
   348     |> PureThy.add_thmss [(("inducts", inducts), [])] |> snd
   349   end;
   350 
   351 
   352 
   353 (**** simplification procedure for showing distinctness of constructors ****)
   354 
   355 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
   356   | stripT p = p;
   357 
   358 fun stripC (i, f $ x) = stripC (i + 1, f)
   359   | stripC p = p;
   360 
   361 val distinctN = "constr_distinct";
   362 
   363 exception ConstrDistinct of term;
   364 
   365 fun distinct_rule thy ss tname eq_t = case #distinct (the_datatype thy tname) of
   366     QuickAndDirty => Thm.invoke_oracle
   367       (ThyInfo.the_theory "Datatype" thy) distinctN (thy, ConstrDistinct eq_t)
   368   | FewConstrs thms => Goal.prove (Simplifier.the_context ss) [] [] eq_t (K
   369       (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
   370         atac 2, resolve_tac thms 1, etac FalseE 1]))
   371   | ManyConstrs (thm, simpset) =>
   372       let
   373         val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
   374           map (get_thm (ThyInfo.the_theory "Datatype" thy) o Name)
   375             ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"];
   376       in
   377         Goal.prove (Simplifier.the_context ss) [] [] eq_t (K
   378         (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
   379           full_simp_tac (Simplifier.inherit_context ss simpset) 1,
   380           REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
   381           eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
   382           etac FalseE 1]))
   383       end;
   384 
   385 fun distinct_proc thy ss (t as Const ("op =", _) $ t1 $ t2) =
   386   (case (stripC (0, t1), stripC (0, t2)) of
   387      ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
   388          (case (stripT (0, T1), stripT (0, T2)) of
   389             ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
   390                 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
   391                    (case (get_datatype_descr thy) tname1 of
   392                       SOME (_, (_, constrs)) => let val cnames = map fst constrs
   393                         in if cname1 mem cnames andalso cname2 mem cnames then
   394                              SOME (distinct_rule thy ss tname1
   395                                (Logic.mk_equals (t, Const ("False", HOLogic.boolT))))
   396                            else NONE
   397                         end
   398                     | NONE => NONE)
   399                 else NONE
   400           | _ => NONE)
   401    | _ => NONE)
   402   | distinct_proc _ _ _ = NONE;
   403 
   404 val distinct_simproc =
   405   Simplifier.simproc HOL.thy distinctN ["s = t"] distinct_proc;
   406 
   407 val dist_ss = HOL_ss addsimprocs [distinct_simproc];
   408 
   409 val simproc_setup =
   410   Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t) #>
   411   (fn thy => ((change_simpset_of thy) (fn ss => ss addsimprocs [distinct_simproc]); thy));
   412 
   413 
   414 (**** translation rules for case ****)
   415 
   416 fun make_case ctxt = DatatypeCase.make_case
   417   (datatype_of_constr (ProofContext.theory_of ctxt)) ctxt;
   418 
   419 fun strip_case ctxt = DatatypeCase.strip_case
   420   (datatype_of_case (ProofContext.theory_of ctxt));
   421 
   422 fun add_case_tr' case_names thy =
   423   Sign.add_advanced_trfuns ([], [],
   424     map (fn case_name =>
   425       let val case_name' = Sign.const_syntax_name thy case_name
   426       in (case_name', DatatypeCase.case_tr' datatype_of_case case_name')
   427       end) case_names, []) thy;
   428 
   429 val trfun_setup =
   430   Sign.add_advanced_trfuns ([],
   431     [("_case_syntax", DatatypeCase.case_tr true datatype_of_constr)],
   432     [], []);
   433 
   434 
   435 (* prepare types *)
   436 
   437 fun read_typ sign ((Ts, sorts), str) =
   438   let
   439     val T = Type.no_tvars (Sign.read_def_typ (sign, AList.lookup (op =)
   440       (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
   441   in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
   442 
   443 fun cert_typ sign ((Ts, sorts), raw_T) =
   444   let
   445     val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
   446       TYPE (msg, _, _) => error msg;
   447     val sorts' = add_typ_tfrees (T, sorts)
   448   in (Ts @ [T],
   449       case duplicates (op =) (map fst sorts') of
   450          [] => sorts'
   451        | dups => error ("Inconsistent sort constraints for " ^ commas dups))
   452   end;
   453 
   454 
   455 (**** make datatype info ****)
   456 
   457 fun make_dt_info alt_names descr sorts induct reccomb_names rec_thms
   458     (((((((((i, (_, (tname, _, _))), case_name), case_thms),
   459       exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =
   460   (tname,
   461    {index = i,
   462     alt_names = alt_names,
   463     descr = descr,
   464     sorts = sorts,
   465     rec_names = reccomb_names,
   466     rec_rewrites = rec_thms,
   467     case_name = case_name,
   468     case_rewrites = case_thms,
   469     induction = induct,
   470     exhaustion = exhaustion_thm,
   471     distinct = distinct_thm,
   472     inject = inject,
   473     nchotomy = nchotomy,
   474     case_cong = case_cong,
   475     weak_case_cong = weak_case_cong});
   476 
   477 
   478 (********************* axiomatic introduction of datatypes ********************)
   479 
   480 fun add_axiom label t atts thy =
   481   thy
   482   |> PureThy.add_axioms_i [((label, t), atts)];
   483 
   484 fun add_axioms label ts atts thy =
   485   thy
   486   |> PureThy.add_axiomss_i [((label, ts), atts)];
   487 
   488 fun add_and_get_axioms_atts label tnames ts attss =
   489   fold_map (fn (tname, (atts, t)) => fn thy =>
   490     thy
   491     |> Sign.add_path tname
   492     |> add_axiom label t atts
   493     ||> Sign.parent_path
   494     |-> (fn [ax] => pair ax)) (tnames ~~ (attss ~~ ts));
   495 
   496 fun add_and_get_axioms label tnames ts =
   497   add_and_get_axioms_atts label tnames ts (replicate (length tnames) []);
   498 
   499 fun add_and_get_axiomss label tnames tss =
   500   fold_map (fn (tname, ts) => fn thy =>
   501     thy
   502     |> Sign.add_path tname
   503     |> add_axioms label ts []
   504     ||> Sign.parent_path
   505     |-> (fn [ax] => pair ax)) (tnames ~~ tss);
   506 
   507 fun gen_specify_consts add args thy =
   508   let
   509     val specs = map (fn (c, T, mx) =>
   510       Const (Sign.full_name thy (Syntax.const_name c mx), T)) args;
   511   in
   512     thy
   513     |> add args
   514     |> Theory.add_finals_i false specs
   515   end;
   516 
   517 val specify_consts = gen_specify_consts Sign.add_consts_i;
   518 val specify_consts_authentic = gen_specify_consts (fold (snd oo Sign.declare_const []));
   519 
   520 structure DatatypeInterpretation = InterpretationFun(type T = string list val eq = op =);
   521 val interpretation = DatatypeInterpretation.interpretation;
   522 
   523 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   524     case_names_induct case_names_exhausts thy =
   525   let
   526     val descr' = flat descr;
   527     val recTs = get_rec_types descr' sorts;
   528     val used = map fst (fold Term.add_tfreesT recTs []);
   529     val newTs = Library.take (length (hd descr), recTs);
   530 
   531     (**** declare new types and constants ****)
   532 
   533     val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
   534 
   535     val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
   536       map (fn ((_, cargs), (cname, mx)) =>
   537         (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   538           (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
   539 
   540     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   541 
   542     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   543     val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
   544       (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   545         (1 upto (length descr')));
   546 
   547     val freeT = TFree (Name.variant used "'t", HOLogic.typeS);
   548     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
   549       map (fn (_, cargs) =>
   550         let val Ts = map (typ_of_dtyp descr' sorts) cargs
   551         in Ts ---> freeT end) constrs) (hd descr);
   552 
   553     val case_names = map (fn s => (s ^ "_case")) new_type_names;
   554 
   555     val thy2' = thy
   556 
   557       (** new types **)
   558       |> fold2 (fn (name, mx) => fn tvs => ObjectLogic.typedecl (name, tvs, mx) #> snd)
   559            types_syntax tyvars
   560       |> add_path flat_names (space_implode "_" new_type_names)
   561 
   562       (** primrec combinators **)
   563 
   564       |> specify_consts (map (fn ((name, T), T') =>
   565            (name, reccomb_fn_Ts @ [T] ---> T', NoSyn)) (reccomb_names ~~ recTs ~~ rec_result_Ts))
   566 
   567       (** case combinators **)
   568 
   569       |> specify_consts_authentic (map (fn ((name, T), Ts) =>
   570            (name, Ts @ [T] ---> freeT, NoSyn)) (case_names ~~ newTs ~~ case_fn_Ts));
   571 
   572     val reccomb_names' = map (Sign.full_name thy2') reccomb_names;
   573     val case_names' = map (Sign.full_name thy2') case_names;
   574 
   575     val thy2 = thy2'
   576 
   577       (** constructors **)
   578 
   579       |> parent_path flat_names
   580       |> fold (fn ((((_, (_, _, constrs)), T), tname),
   581         constr_syntax') =>
   582           add_path flat_names tname #>
   583             specify_consts (map (fn ((_, cargs), (cname, mx)) =>
   584               (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   585                 (constrs ~~ constr_syntax')) #>
   586           parent_path flat_names)
   587             (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
   588 
   589     (**** introduction of axioms ****)
   590 
   591     val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
   592 
   593     val ((([induct], [rec_thms]), inject), thy3) =
   594       thy2
   595       |> Sign.add_path (space_implode "_" new_type_names)
   596       |> add_axiom "induct" (DatatypeProp.make_ind descr sorts) [case_names_induct]
   597       ||>> add_axioms "recs" rec_axs []
   598       ||> Sign.parent_path
   599       ||>> add_and_get_axiomss "inject" new_type_names
   600             (DatatypeProp.make_injs descr sorts);
   601     val (distinct, thy4) = add_and_get_axiomss "distinct" new_type_names
   602       (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
   603 
   604     val exhaust_ts = DatatypeProp.make_casedists descr sorts;
   605     val (exhaustion, thy5) = add_and_get_axioms_atts "exhaust" new_type_names
   606       exhaust_ts (map single case_names_exhausts) thy4;
   607     val (case_thms, thy6) = add_and_get_axiomss "cases" new_type_names
   608       (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
   609     val (split_ts, split_asm_ts) = ListPair.unzip
   610       (DatatypeProp.make_splits new_type_names descr sorts thy6);
   611     val (split, thy7) = add_and_get_axioms "split" new_type_names split_ts thy6;
   612     val (split_asm, thy8) = add_and_get_axioms "split_asm" new_type_names
   613       split_asm_ts thy7;
   614     val (nchotomys, thy9) = add_and_get_axioms "nchotomy" new_type_names
   615       (DatatypeProp.make_nchotomys descr sorts) thy8;
   616     val (case_congs, thy10) = add_and_get_axioms "case_cong" new_type_names
   617       (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
   618     val (weak_case_congs, thy11) = add_and_get_axioms "weak_case_cong" new_type_names
   619       (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
   620 
   621     val dt_infos = map (make_dt_info NONE descr' sorts induct reccomb_names' rec_thms)
   622       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
   623         exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
   624           nchotomys ~~ case_congs ~~ weak_case_congs);
   625 
   626     val simps = flat (distinct @ inject @ case_thms) @ rec_thms;
   627     val split_thms = split ~~ split_asm;
   628 
   629     val thy12 =
   630       thy11
   631       |> add_case_tr' case_names'
   632       |> Sign.add_path (space_implode "_" new_type_names)
   633       |> add_rules simps case_thms rec_thms inject distinct
   634           weak_case_congs Simplifier.cong_add
   635       |> put_dt_infos dt_infos
   636       |> add_cases_induct dt_infos induct
   637       |> Sign.parent_path
   638       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)
   639       |> snd
   640       |> DatatypeInterpretation.data (map fst dt_infos);
   641   in
   642     ({distinct = distinct,
   643       inject = inject,
   644       exhaustion = exhaustion,
   645       rec_thms = rec_thms,
   646       case_thms = case_thms,
   647       split_thms = split_thms,
   648       induction = induct,
   649       simps = simps}, thy12)
   650   end;
   651 
   652 
   653 (******************* definitional introduction of datatypes *******************)
   654 
   655 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   656     case_names_induct case_names_exhausts thy =
   657   let
   658     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   659 
   660     val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |>
   661       DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
   662         types_syntax constr_syntax case_names_induct;
   663 
   664     val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
   665       sorts induct case_names_exhausts thy2;
   666     val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms
   667       flat_names new_type_names descr sorts dt_info inject dist_rewrites
   668       (Simplifier.theory_context thy3 dist_ss) induct thy3;
   669     val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms
   670       flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
   671     val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names
   672       descr sorts inject dist_rewrites casedist_thms case_thms thy6;
   673     val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names
   674       descr sorts casedist_thms thy7;
   675     val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names
   676       descr sorts nchotomys case_thms thy8;
   677     val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   678       descr sorts thy9;
   679 
   680     val dt_infos = map (make_dt_info NONE (flat descr) sorts induct reccomb_names rec_thms)
   681       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
   682         casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   683 
   684     val simps = flat (distinct @ inject @ case_thms) @ rec_thms;
   685 
   686     val thy12 =
   687       thy10
   688       |> add_case_tr' case_names
   689       |> Sign.add_path (space_implode "_" new_type_names)
   690       |> add_rules simps case_thms rec_thms inject distinct
   691           weak_case_congs (Simplifier.attrib (op addcongs))
   692       |> put_dt_infos dt_infos
   693       |> add_cases_induct dt_infos induct
   694       |> Sign.parent_path
   695       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd
   696       |> DatatypeInterpretation.data (map fst dt_infos);
   697   in
   698     ({distinct = distinct,
   699       inject = inject,
   700       exhaustion = casedist_thms,
   701       rec_thms = rec_thms,
   702       case_thms = case_thms,
   703       split_thms = split_thms,
   704       induction = induct,
   705       simps = simps}, thy12)
   706   end;
   707 
   708 
   709 (*********************** declare existing type as datatype *********************)
   710 
   711 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
   712   let
   713     val (((distinct, inject), [induction]), thy1) =
   714       thy0
   715       |> fold_map apply_theorems raw_distinct
   716       ||>> fold_map apply_theorems raw_inject
   717       ||>> apply_theorems [raw_induction];
   718 
   719     val ((_, [induction']), _) =
   720       Variable.importT_thms [induction] (Variable.thm_context induction);
   721 
   722     fun err t = error ("Ill-formed predicate in induction rule: " ^
   723       Sign.string_of_term thy1 t);
   724 
   725     fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
   726           ((tname, map (fst o dest_TFree) Ts) handle TERM _ => err t)
   727       | get_typ t = err t;
   728 
   729     val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
   730     val new_type_names = getOpt (alt_names, map fst dtnames);
   731 
   732     fun get_constr t = (case Logic.strip_assums_concl t of
   733         _ $ (_ $ t') => (case head_of t' of
   734             Const (cname, cT) => (case strip_type cT of
   735                 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
   736               | _ => err t)
   737           | _ => err t)
   738       | _ => err t);
   739 
   740     fun make_dt_spec [] _ _ = []
   741       | make_dt_spec ((tname, tvs)::dtnames') i constrs =
   742           let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
   743           in (i, (tname, map DtTFree tvs, map snd constrs'))::
   744             (make_dt_spec dtnames' (i + 1) constrs'')
   745           end;
   746 
   747     val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
   748     val sorts = add_term_tfrees (concl_of induction', []);
   749     val dt_info = get_datatypes thy1;
   750 
   751     val (case_names_induct, case_names_exhausts) =
   752       (mk_case_names_induct descr, mk_case_names_exhausts descr (map #1 dtnames));
   753 
   754     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   755 
   756     val (casedist_thms, thy2) = thy1 |>
   757       DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
   758         case_names_exhausts;
   759     val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms
   760       false new_type_names [descr] sorts dt_info inject distinct
   761       (Simplifier.theory_context thy2 dist_ss) induction thy2;
   762     val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false
   763       new_type_names [descr] sorts reccomb_names rec_thms thy3;
   764     val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms
   765       new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
   766     val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names
   767       [descr] sorts casedist_thms thy5;
   768     val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names
   769       [descr] sorts nchotomys case_thms thy6;
   770     val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   771       [descr] sorts thy7;
   772 
   773     val ((_, [induction']), thy10) =
   774       thy8
   775       |> store_thmss "inject" new_type_names inject
   776       ||>> store_thmss "distinct" new_type_names distinct
   777       ||> Sign.add_path (space_implode "_" new_type_names)
   778       ||>> PureThy.add_thms [(("induct", induction), [case_names_induct])];
   779 
   780     val dt_infos = map (make_dt_info alt_names descr sorts induction' reccomb_names rec_thms)
   781       ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~
   782         map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   783 
   784     val simps = flat (distinct @ inject @ case_thms) @ rec_thms;
   785 
   786     val thy11 =
   787       thy10
   788       |> add_case_tr' case_names
   789       |> add_rules simps case_thms rec_thms inject distinct
   790            weak_case_congs (Simplifier.attrib (op addcongs))
   791       |> put_dt_infos dt_infos
   792       |> add_cases_induct dt_infos induction'
   793       |> Sign.parent_path
   794       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)
   795       |> snd
   796       |> DatatypeInterpretation.data (map fst dt_infos);
   797   in
   798     ({distinct = distinct,
   799       inject = inject,
   800       exhaustion = casedist_thms,
   801       rec_thms = rec_thms,
   802       case_thms = case_thms,
   803       split_thms = split_thms,
   804       induction = induction',
   805       simps = simps}, thy11)
   806   end;
   807 
   808 val rep_datatype = gen_rep_datatype IsarCmd.apply_theorems;
   809 val rep_datatype_i = gen_rep_datatype IsarCmd.apply_theorems_i;
   810 
   811 
   812 
   813 (******************************** add datatype ********************************)
   814 
   815 fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =
   816   let
   817     val _ = Theory.requires thy "Datatype" "datatype definitions";
   818 
   819     (* this theory is used just for parsing *)
   820 
   821     val tmp_thy = thy |>
   822       Theory.copy |>
   823       Sign.add_types (map (fn (tvs, tname, mx, _) =>
   824         (tname, length tvs, mx)) dts);
   825 
   826     val (tyvars, _, _, _)::_ = dts;
   827     val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
   828       let val full_tname = Sign.full_name tmp_thy (Syntax.type_name tname mx)
   829       in (case duplicates (op =) tvs of
   830             [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
   831                   else error ("Mutually recursive datatypes must have same type parameters")
   832           | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
   833               " : " ^ commas dups))
   834       end) dts);
   835 
   836     val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of
   837       [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
   838 
   839     fun prep_dt_spec (tvs, tname, mx, constrs) (dts', constr_syntax, sorts, i) =
   840       let
   841         fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') =
   842           let
   843             val (cargs', sorts'') = Library.foldl (prep_typ tmp_thy) (([], sorts'), cargs);
   844             val _ = (case fold (curry add_typ_tfree_names) cargs' [] \\ tvs of
   845                 [] => ()
   846               | vs => error ("Extra type variables on rhs: " ^ commas vs))
   847           in (constrs @ [((if flat_names then Sign.full_name tmp_thy else
   848                 Sign.full_name_path tmp_thy tname) (Syntax.const_name cname mx'),
   849                    map (dtyp_of_typ new_dts) cargs')],
   850               constr_syntax' @ [(cname, mx')], sorts'')
   851           end handle ERROR msg =>
   852             cat_error msg ("The error above occured in constructor " ^ cname ^
   853               " of datatype " ^ tname);
   854 
   855         val (constrs', constr_syntax', sorts') =
   856           fold prep_constr constrs ([], [], sorts)
   857 
   858       in
   859         case duplicates (op =) (map fst constrs') of
   860            [] =>
   861              (dts' @ [(i, (Sign.full_name tmp_thy (Syntax.type_name tname mx),
   862                 map DtTFree tvs, constrs'))],
   863               constr_syntax @ [constr_syntax'], sorts', i + 1)
   864          | dups => error ("Duplicate constructors " ^ commas dups ^
   865              " in datatype " ^ tname)
   866       end;
   867 
   868     val (dts', constr_syntax, sorts', i) = fold prep_dt_spec dts ([], [], [], 0);
   869     val sorts = sorts' @ (map (rpair (Sign.defaultS tmp_thy)) (tyvars \\ map fst sorts'));
   870     val dt_info = get_datatypes thy;
   871     val (descr, _) = unfold_datatypes tmp_thy dts' sorts dt_info dts' i;
   872     val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>
   873       if err then error ("Nonemptiness check failed for datatype " ^ s)
   874       else raise exn;
   875 
   876     val descr' = flat descr;
   877     val case_names_induct = mk_case_names_induct descr';
   878     val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
   879   in
   880     (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
   881       flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   882       case_names_induct case_names_exhausts thy
   883   end;
   884 
   885 val add_datatype_i = gen_add_datatype cert_typ;
   886 val add_datatype = gen_add_datatype read_typ true;
   887 
   888 
   889 
   890 (** package setup **)
   891 
   892 (* setup theory *)
   893 
   894 val setup =
   895   DatatypeProp.distinctness_limit_setup #>
   896   Method.add_methods tactic_emulations #>
   897   simproc_setup #>
   898   trfun_setup #>
   899   DatatypeInterpretation.init;
   900 
   901 
   902 (* outer syntax *)
   903 
   904 local structure P = OuterParse and K = OuterKeyword in
   905 
   906 val _ = OuterSyntax.keywords ["distinct", "inject", "induction"];
   907 
   908 val datatype_decl =
   909   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
   910     (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
   911 
   912 fun mk_datatype args =
   913   let
   914     val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
   915     val specs = map (fn ((((_, vs), t), mx), cons) =>
   916       (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
   917   in snd o add_datatype false names specs end;
   918 
   919 val _ =
   920   OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
   921     (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
   922 
   923 
   924 val rep_datatype_decl =
   925   Scan.option (Scan.repeat1 P.name) --
   926     Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] --
   927     Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] --
   928     (P.$$$ "induction" |-- P.!!! SpecParse.xthm);
   929 
   930 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #2 o rep_datatype opt_ts dss iss ind;
   931 
   932 val _ =
   933   OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
   934     (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
   935 
   936 end;
   937 
   938 
   939 end;
   940 
   941 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
   942 open BasicDatatypePackage;
   943