src/HOL/Tools/datatype_package.ML
author haftmann
Tue Sep 18 07:46:00 2007 +0200 (2007-09-18)
changeset 24626 85eceef2edc7
parent 24624 b8383b1bbae3
child 24699 c6674504103f
permissions -rw-r--r--
introduced generic concepts for theory interpretators
     1 (*  Title:      HOL/Tools/datatype_package.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4 
     5 Datatype package for Isabelle/HOL.
     6 *)
     7 
     8 signature BASIC_DATATYPE_PACKAGE =
     9 sig
    10   val induct_tac : string -> int -> tactic
    11   val induct_thm_tac : thm -> string -> int -> tactic
    12   val case_tac : string -> int -> tactic
    13   val distinct_simproc : simproc
    14 end;
    15 
    16 signature DATATYPE_PACKAGE =
    17 sig
    18   include BASIC_DATATYPE_PACKAGE
    19   val quiet_mode : bool ref
    20   val add_datatype : bool -> string list -> (string list * bstring * mixfix *
    21     (bstring * string list * mixfix) list) list -> theory ->
    22       {distinct : thm list list,
    23        inject : thm list list,
    24        exhaustion : thm list,
    25        rec_thms : thm list,
    26        case_thms : thm list list,
    27        split_thms : (thm * thm) list,
    28        induction : thm,
    29        size : thm list,
    30        simps : thm list} * theory
    31   val add_datatype_i : bool -> bool -> string list -> (string list * bstring * mixfix *
    32     (bstring * typ list * mixfix) list) list -> theory ->
    33       {distinct : thm list list,
    34        inject : thm list list,
    35        exhaustion : thm list,
    36        rec_thms : thm list,
    37        case_thms : thm list list,
    38        split_thms : (thm * thm) list,
    39        induction : thm,
    40        size : thm list,
    41        simps : thm list} * theory
    42   val rep_datatype_i : string list option -> (thm list * attribute list) list list ->
    43     (thm list * attribute list) list list -> (thm list * attribute list) ->
    44     theory ->
    45       {distinct : thm list list,
    46        inject : thm list list,
    47        exhaustion : thm list,
    48        rec_thms : thm list,
    49        case_thms : thm list list,
    50        split_thms : (thm * thm) list,
    51        induction : thm,
    52        size : thm list,
    53        simps : thm list} * theory
    54   val rep_datatype : string list option -> (thmref * Attrib.src list) list list ->
    55     (thmref * Attrib.src list) list list -> thmref * Attrib.src list -> theory ->
    56       {distinct : thm list list,
    57        inject : thm list list,
    58        exhaustion : thm list,
    59        rec_thms : thm list,
    60        case_thms : thm list list,
    61        split_thms : (thm * thm) list,
    62        induction : thm,
    63        size : thm list,
    64        simps : thm list} * theory
    65   val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table
    66   val get_datatype : theory -> string -> DatatypeAux.datatype_info option
    67   val the_datatype : theory -> string -> DatatypeAux.datatype_info
    68   val datatype_of_constr : theory -> string -> DatatypeAux.datatype_info option
    69   val datatype_of_case : theory -> string -> DatatypeAux.datatype_info option
    70   val get_datatype_spec : theory -> string -> ((string * sort) list * (string * typ list) list) option
    71   val get_datatype_constrs : theory -> string -> (string * typ) list option
    72   val add_interpretator: (string list -> theory -> theory) -> theory -> theory
    73   val print_datatypes : theory -> unit
    74   val make_case :  Proof.context -> bool -> string list -> term ->
    75     (term * term) list -> term * (term * (int * bool)) list
    76   val strip_case: Proof.context -> bool ->
    77     term -> (term * (term * term) list) option
    78   val setup: theory -> theory
    79 end;
    80 
    81 structure DatatypePackage : DATATYPE_PACKAGE =
    82 struct
    83 
    84 open DatatypeAux;
    85 
    86 val quiet_mode = quiet_mode;
    87 
    88 
    89 (* theory data *)
    90 
    91 structure DatatypesData = TheoryDataFun
    92 (
    93   type T =
    94     {types: datatype_info Symtab.table,
    95      constrs: datatype_info Symtab.table,
    96      cases: datatype_info Symtab.table};
    97 
    98   val empty =
    99     {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty};
   100   val copy = I;
   101   val extend = I;
   102   fun merge _
   103     ({types = types1, constrs = constrs1, cases = cases1},
   104      {types = types2, constrs = constrs2, cases = cases2}) =
   105     {types = Symtab.merge (K true) (types1, types2),
   106      constrs = Symtab.merge (K true) (constrs1, constrs2),
   107      cases = Symtab.merge (K true) (cases1, cases2)};
   108 );
   109 
   110 val get_datatypes = #types o DatatypesData.get;
   111 val map_datatypes = DatatypesData.map;
   112 
   113 fun print_datatypes thy =
   114   Pretty.writeln (Pretty.strs ("datatypes:" ::
   115     map #1 (NameSpace.extern_table (Sign.type_space thy, get_datatypes thy))));
   116 
   117 
   118 (** theory information about datatypes **)
   119 
   120 fun put_dt_infos (dt_infos : (string * datatype_info) list) =
   121   map_datatypes (fn {types, constrs, cases} =>
   122     {types = fold Symtab.update dt_infos types,
   123      constrs = fold Symtab.update
   124        (maps (fn (_, info as {descr, index, ...}) => map (rpair info o fst)
   125           (#3 (the (AList.lookup op = descr index)))) dt_infos) constrs,
   126      cases = fold Symtab.update
   127        (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos)
   128        cases});
   129 
   130 val get_datatype = Symtab.lookup o get_datatypes;
   131 
   132 fun the_datatype thy name = (case get_datatype thy name of
   133       SOME info => info
   134     | NONE => error ("Unknown datatype " ^ quote name));
   135 
   136 val datatype_of_constr = Symtab.lookup o #constrs o DatatypesData.get;
   137 val datatype_of_case = Symtab.lookup o #cases o DatatypesData.get;
   138 
   139 fun get_datatype_descr thy dtco =
   140   get_datatype thy dtco
   141   |> Option.map (fn info as { descr, index, ... } => 
   142        (info, (((fn SOME (_, dtys, cos) => (dtys, cos)) o AList.lookup (op =) descr) index)));
   143 
   144 fun get_datatype_spec thy dtco =
   145   let
   146     fun mk_cons typ_of_dtyp (co, tys) =
   147       (co, map typ_of_dtyp tys);
   148     fun mk_dtyp ({ sorts = raw_sorts, descr, ... } : DatatypeAux.datatype_info, (dtys, cos)) =
   149       let
   150         val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v))
   151           o DatatypeAux.dest_DtTFree) dtys;
   152         val typ_of_dtyp = DatatypeAux.typ_of_dtyp descr sorts;
   153         val tys = map typ_of_dtyp dtys;
   154       in (sorts, map (mk_cons typ_of_dtyp) cos) end;
   155   in Option.map mk_dtyp (get_datatype_descr thy dtco) end;
   156 
   157 fun get_datatype_constrs thy dtco =
   158   case get_datatype_spec thy dtco
   159    of SOME (sorts, cos) =>
   160         let
   161           fun subst (v, sort) = TVar ((v, 0), sort);
   162           fun subst_ty (TFree v) = subst v
   163             | subst_ty ty = ty;
   164           val dty = Type (dtco, map subst sorts);
   165           fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty);
   166         in SOME (map mk_co cos) end
   167     | NONE => NONE;
   168 
   169 fun find_tname var Bi =
   170   let val frees = map dest_Free (term_frees Bi)
   171       val params = rename_wrt_term Bi (Logic.strip_params Bi);
   172   in case AList.lookup (op =) (frees @ params) var of
   173        NONE => error ("No such variable in subgoal: " ^ quote var)
   174      | SOME(Type (tn, _)) => tn
   175      | _ => error ("Cannot determine type of " ^ quote var)
   176   end;
   177 
   178 fun infer_tname state i aterm =
   179   let
   180     val sign = Thm.theory_of_thm state;
   181     val (_, _, Bi, _) = Thm.dest_state (state, i)
   182     val params = Logic.strip_params Bi;   (*params of subgoal i*)
   183     val params = rev (rename_wrt_term Bi params);   (*as they are printed*)
   184     val (types, sorts) = types_sorts state;
   185     fun types' (a, ~1) = (case AList.lookup (op =) params a of NONE => types(a, ~1) | sm => sm)
   186       | types' ixn = types ixn;
   187     val ([ct], _) = Thm.read_def_cterms (sign, types', sorts) [] false [(aterm, dummyT)];
   188   in case #T (rep_cterm ct) of
   189        Type (tn, _) => tn
   190      | _ => error ("Cannot determine type of " ^ quote aterm)
   191   end;
   192 
   193 (*Warn if the (induction) variable occurs Free among the premises, which
   194   usually signals a mistake.  But calls the tactic either way!*)
   195 fun occs_in_prems tacf vars =
   196   SUBGOAL (fn (Bi, i) =>
   197            (if exists (fn (a, _) => member (op =) vars a)
   198                       (fold Term.add_frees (#2 (strip_context Bi)) [])
   199              then warning "Induction variable occurs also among premises!"
   200              else ();
   201             tacf i));
   202 
   203 
   204 (* generic induction tactic for datatypes *)
   205 
   206 local
   207 
   208 fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x)
   209   | prep_var _ = NONE;
   210 
   211 fun prep_inst (concl, xs) = (*exception Library.UnequalLengths*)
   212   let val vs = InductAttrib.vars_of concl
   213   in map_filter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
   214 
   215 in
   216 
   217 fun gen_induct_tac inst_tac (varss, opt_rule) i state = 
   218   SUBGOAL (fn (Bi,_) =>
   219   let
   220     val (rule, rule_name) =
   221       case opt_rule of
   222           SOME r => (r, "Induction rule")
   223         | NONE =>
   224             let val tn = find_tname (hd (map_filter I (flat varss))) Bi
   225                 val thy = Thm.theory_of_thm state
   226             in (#induction (the_datatype thy tn), "Induction rule for type " ^ tn) 
   227             end
   228     val concls = HOLogic.dest_concls (Thm.concl_of rule);
   229     val insts = maps prep_inst (concls ~~ varss) handle Library.UnequalLengths =>
   230       error (rule_name ^ " has different numbers of variables");
   231   in occs_in_prems (inst_tac insts rule) (map #2 insts) i end)
   232   i state;
   233 
   234 fun induct_tac s =
   235   gen_induct_tac Tactic.res_inst_tac'
   236     (map (single o SOME) (Syntax.read_idents s), NONE);
   237 
   238 fun induct_thm_tac th s =
   239   gen_induct_tac Tactic.res_inst_tac'
   240     ([map SOME (Syntax.read_idents s)], SOME th);
   241 
   242 end;
   243 
   244 
   245 (* generic case tactic for datatypes *)
   246 
   247 fun case_inst_tac inst_tac t rule i state =
   248   let
   249     val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
   250       (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));
   251   in inst_tac [(ixn, t)] rule i state end;
   252 
   253 fun gen_case_tac inst_tac (t, SOME rule) i state =
   254       case_inst_tac inst_tac t rule i state
   255   | gen_case_tac inst_tac (t, NONE) i state =
   256       let val tn = infer_tname state i t in
   257         if tn = HOLogic.boolN then inst_tac [(("P", 0), t)] case_split_thm i state
   258         else case_inst_tac inst_tac t
   259                (#exhaustion (the_datatype (Thm.theory_of_thm state) tn))
   260                i state
   261       end handle THM _ => Seq.empty;
   262 
   263 fun case_tac t = gen_case_tac Tactic.res_inst_tac' (t, NONE);
   264 
   265 
   266 
   267 (** Isar tactic emulations **)
   268 
   269 local
   270 
   271 val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
   272 val opt_rule = Scan.option (rule_spec |-- Attrib.thm);
   273 
   274 val varss =
   275   Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name))));
   276 
   277 val inst_tac = RuleInsts.bires_inst_tac false;
   278 
   279 fun induct_meth ctxt (varss, opt_rule) =
   280   gen_induct_tac (inst_tac ctxt) (varss, opt_rule);
   281 fun case_meth ctxt (varss, opt_rule) =
   282   gen_case_tac (inst_tac ctxt) (varss, opt_rule);
   283 
   284 in
   285 
   286 val tactic_emulations =
   287  [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth,
   288     "induct_tac emulation (dynamic instantiation)"),
   289   ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth,
   290     "case_tac emulation (dynamic instantiation)")];
   291 
   292 end;
   293 
   294 
   295 
   296 (** induct method setup **)
   297 
   298 (* case names *)
   299 
   300 local
   301 
   302 fun dt_recs (DtTFree _) = []
   303   | dt_recs (DtType (_, dts)) = maps dt_recs dts
   304   | dt_recs (DtRec i) = [i];
   305 
   306 fun dt_cases (descr: descr) (_, args, constrs) =
   307   let
   308     fun the_bname i = Sign.base_name (#1 (the (AList.lookup (op =) descr i)));
   309     val bnames = map the_bname (distinct (op =) (maps dt_recs args));
   310   in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
   311 
   312 
   313 fun induct_cases descr =
   314   DatatypeProp.indexify_names (maps (dt_cases descr) (map #2 descr));
   315 
   316 fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i));
   317 
   318 in
   319 
   320 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
   321 
   322 fun mk_case_names_exhausts descr new =
   323   map (RuleCases.case_names o exhaust_cases descr o #1)
   324     (filter (fn ((_, (name, _, _))) => member (op =) new name) descr);
   325 
   326 end;
   327 
   328 fun add_rules simps case_thms size_thms rec_thms inject distinct
   329                   weak_case_congs cong_att =
   330   PureThy.add_thmss [(("simps", simps), []),
   331     (("", flat case_thms @ size_thms @ 
   332           flat distinct @ rec_thms), [Simplifier.simp_add]),
   333     (("", size_thms @ rec_thms), [RecfunCodegen.add_default]),
   334     (("", flat inject), [iff_add]),
   335     (("", map (fn th => th RS notE) (flat distinct)), [Classical.safe_elim NONE]),
   336     (("", weak_case_congs), [cong_att])]
   337   #> snd;
   338 
   339 
   340 (* add_cases_induct *)
   341 
   342 fun add_cases_induct infos induction thy =
   343   let
   344     val inducts = ProjectRule.projections (ProofContext.init thy) induction;
   345 
   346     fun named_rules (name, {index, exhaustion, ...}: datatype_info) =
   347       [(("", nth inducts index), [InductAttrib.induct_type name]),
   348        (("", exhaustion), [InductAttrib.cases_type name])];
   349     fun unnamed_rule i =
   350       (("", nth inducts i), [PureThy.kind_internal, InductAttrib.induct_type ""]);
   351   in
   352     thy |> PureThy.add_thms
   353       (maps named_rules infos @
   354         map unnamed_rule (length infos upto length inducts - 1)) |> snd
   355     |> PureThy.add_thmss [(("inducts", inducts), [])] |> snd
   356   end;
   357 
   358 
   359 
   360 (**** simplification procedure for showing distinctness of constructors ****)
   361 
   362 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
   363   | stripT p = p;
   364 
   365 fun stripC (i, f $ x) = stripC (i + 1, f)
   366   | stripC p = p;
   367 
   368 val distinctN = "constr_distinct";
   369 
   370 exception ConstrDistinct of term;
   371 
   372 fun distinct_proc thy ss (t as Const ("op =", _) $ t1 $ t2) =
   373   (case (stripC (0, t1), stripC (0, t2)) of
   374      ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
   375          (case (stripT (0, T1), stripT (0, T2)) of
   376             ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
   377                 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
   378                    (case (get_datatype_descr thy) tname1 of
   379                       SOME (_, (_, constrs)) => let val cnames = map fst constrs
   380                         in if cname1 mem cnames andalso cname2 mem cnames then
   381                              let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));
   382                                  val eq_ct = cterm_of thy eq_t;
   383                                  val Datatype_thy = ThyInfo.the_theory "Datatype" thy;
   384                                  val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
   385                                    map (get_thm Datatype_thy o Name)
   386                                      ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
   387                              in (case (#distinct (the_datatype thy tname1)) of
   388                                  QuickAndDirty => SOME (Thm.invoke_oracle
   389                                    Datatype_thy distinctN (thy, ConstrDistinct eq_t))
   390                                | FewConstrs thms =>
   391                                    SOME (Goal.prove (Simplifier.the_context ss) [] [] eq_t (K
   392                                      (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
   393                                        atac 2, resolve_tac thms 1, etac FalseE 1])))
   394                                | ManyConstrs (thm, simpset) =>
   395                                    SOME (Goal.prove (Simplifier.the_context ss) [] [] eq_t (K
   396                                      (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
   397                                       full_simp_tac (Simplifier.inherit_context ss simpset) 1,
   398                                       REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
   399                                       eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
   400                                       etac FalseE 1]))))
   401                              end
   402                            else NONE
   403                         end
   404                     | NONE => NONE)
   405                 else NONE
   406           | _ => NONE)
   407    | _ => NONE)
   408   | distinct_proc _ _ _ = NONE;
   409 
   410 val distinct_simproc =
   411   Simplifier.simproc HOL.thy distinctN ["s = t"] distinct_proc;
   412 
   413 val dist_ss = HOL_ss addsimprocs [distinct_simproc];
   414 
   415 val simproc_setup =
   416   Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t) #>
   417   (fn thy => ((change_simpset_of thy) (fn ss => ss addsimprocs [distinct_simproc]); thy));
   418 
   419 
   420 (**** translation rules for case ****)
   421 
   422 fun make_case ctxt = DatatypeCase.make_case
   423   (datatype_of_constr (ProofContext.theory_of ctxt)) ctxt;
   424 
   425 fun strip_case ctxt = DatatypeCase.strip_case
   426   (datatype_of_case (ProofContext.theory_of ctxt));
   427 
   428 fun add_case_tr' case_names thy =
   429   Theory.add_advanced_trfuns ([], [],
   430     map (fn case_name => 
   431       let val case_name' = Sign.const_syntax_name thy case_name
   432       in (case_name', DatatypeCase.case_tr' datatype_of_case case_name')
   433       end) case_names, []) thy;
   434 
   435 val trfun_setup =
   436   Theory.add_advanced_trfuns ([],
   437     [("_case_syntax", DatatypeCase.case_tr true datatype_of_constr)],
   438     [], []);
   439 
   440 
   441 (* prepare types *)
   442 
   443 fun read_typ sign ((Ts, sorts), str) =
   444   let
   445     val T = Type.no_tvars (Sign.read_def_typ (sign, AList.lookup (op =)
   446       (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
   447   in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
   448 
   449 fun cert_typ sign ((Ts, sorts), raw_T) =
   450   let
   451     val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
   452       TYPE (msg, _, _) => error msg;
   453     val sorts' = add_typ_tfrees (T, sorts)
   454   in (Ts @ [T],
   455       case duplicates (op =) (map fst sorts') of
   456          [] => sorts'
   457        | dups => error ("Inconsistent sort constraints for " ^ commas dups))
   458   end;
   459 
   460 
   461 (**** make datatype info ****)
   462 
   463 fun make_dt_info descr sorts induct reccomb_names rec_thms
   464     (((((((((i, (_, (tname, _, _))), case_name), case_thms),
   465       exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =
   466   (tname,
   467    {index = i,
   468     descr = descr,
   469     sorts = sorts,
   470     rec_names = reccomb_names,
   471     rec_rewrites = rec_thms,
   472     case_name = case_name,
   473     case_rewrites = case_thms,
   474     induction = induct,
   475     exhaustion = exhaustion_thm,
   476     distinct = distinct_thm,
   477     inject = inject,
   478     nchotomy = nchotomy,
   479     case_cong = case_cong,
   480     weak_case_cong = weak_case_cong});
   481 
   482 
   483 (********************* axiomatic introduction of datatypes ********************)
   484 
   485 fun add_axiom label t atts thy =
   486   thy
   487   |> PureThy.add_axioms_i [((label, t), atts)];
   488 
   489 fun add_axioms label ts atts thy =
   490   thy
   491   |> PureThy.add_axiomss_i [((label, ts), atts)];
   492 
   493 fun add_and_get_axioms_atts label tnames ts attss =
   494   fold_map (fn (tname, (atts, t)) => fn thy =>
   495     thy
   496     |> Theory.add_path tname
   497     |> add_axiom label t atts
   498     ||> Theory.parent_path
   499     |-> (fn [ax] => pair ax)) (tnames ~~ (attss ~~ ts));
   500 
   501 fun add_and_get_axioms label tnames ts =
   502   add_and_get_axioms_atts label tnames ts (replicate (length tnames) []);
   503 
   504 fun add_and_get_axiomss label tnames tss =
   505   fold_map (fn (tname, ts) => fn thy =>
   506     thy
   507     |> Theory.add_path tname
   508     |> add_axioms label ts []
   509     ||> Theory.parent_path
   510     |-> (fn [ax] => pair ax)) (tnames ~~ tss);
   511 
   512 fun gen_specify_consts add args thy =
   513   let
   514     val specs = map (fn (c, T, mx) =>
   515       Const (Sign.full_name thy (Syntax.const_name c mx), T)) args;
   516   in
   517     thy
   518     |> add args
   519     |> Theory.add_finals_i false specs
   520   end;
   521 
   522 val specify_consts = gen_specify_consts Sign.add_consts_i;
   523 val specify_consts_authentic = gen_specify_consts Sign.add_consts_authentic;
   524 
   525 structure DatatypeInterpretator = TheoryInterpretatorFun(struct type T = string; val eq = op = end);
   526 
   527 fun add_interpretator interpretator = DatatypeInterpretator.add_interpretator interpretator;
   528 
   529 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   530     case_names_induct case_names_exhausts thy =
   531   let
   532     val descr' = flat descr;
   533     val recTs = get_rec_types descr' sorts;
   534     val used = map fst (fold Term.add_tfreesT recTs []);
   535     val newTs = Library.take (length (hd descr), recTs);
   536 
   537     val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
   538       (fn dt => is_rec_type dt andalso not (null (fst (strip_dtyp dt))))
   539         cargs) constrs) descr';
   540 
   541     (**** declare new types and constants ****)
   542 
   543     val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
   544 
   545     val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
   546       map (fn ((_, cargs), (cname, mx)) =>
   547         (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   548           (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
   549 
   550     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   551 
   552     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   553     val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
   554       (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   555         (1 upto (length descr')));
   556 
   557     val size_names = DatatypeProp.indexify_names
   558       (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs)));
   559 
   560     val freeT = TFree (Name.variant used "'t", HOLogic.typeS);
   561     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
   562       map (fn (_, cargs) =>
   563         let val Ts = map (typ_of_dtyp descr' sorts) cargs
   564         in Ts ---> freeT end) constrs) (hd descr);
   565 
   566     val case_names = map (fn s => (s ^ "_case")) new_type_names;
   567 
   568     fun instance_size_class tyco thy =
   569       let
   570         val n = Sign.arity_number thy tyco;
   571       in
   572         thy
   573         |> Class.prove_instance (Class.intro_classes_tac [])
   574             [(tyco, replicate n HOLogic.typeS, [HOLogic.class_size])] []
   575         |> snd
   576       end
   577 
   578     val thy2' = thy
   579 
   580       (** new types **)
   581       |> fold2 (fn (name, mx) => fn tvs => TypedefPackage.add_typedecls [(name, tvs, mx)])
   582            types_syntax tyvars
   583       |> fold (fn (_, (name, _, _)) => instance_size_class name) descr'
   584       |> add_path flat_names (space_implode "_" new_type_names)
   585 
   586       (** primrec combinators **)
   587 
   588       |> specify_consts (map (fn ((name, T), T') =>
   589            (name, reccomb_fn_Ts @ [T] ---> T', NoSyn)) (reccomb_names ~~ recTs ~~ rec_result_Ts))
   590 
   591       (** case combinators **)
   592 
   593       |> specify_consts_authentic (map (fn ((name, T), Ts) =>
   594            (name, Ts @ [T] ---> freeT, NoSyn)) (case_names ~~ newTs ~~ case_fn_Ts));
   595 
   596     val reccomb_names' = map (Sign.full_name thy2') reccomb_names;
   597     val case_names' = map (Sign.full_name thy2') case_names;
   598 
   599     val thy2 = thy2'
   600 
   601       (** size functions **)
   602 
   603       |> (if no_size then I else specify_consts (map (fn (s, T) =>
   604         (Sign.base_name s, T --> HOLogic.natT, NoSyn))
   605           (size_names ~~ Library.drop (length (hd descr), recTs))))
   606 
   607       (** constructors **)
   608 
   609       |> parent_path flat_names
   610       |> fold (fn ((((_, (_, _, constrs)), T), tname),
   611         constr_syntax') =>
   612           add_path flat_names tname #>
   613             specify_consts (map (fn ((_, cargs), (cname, mx)) =>
   614               (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   615                 (constrs ~~ constr_syntax')) #>
   616           parent_path flat_names)
   617             (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
   618 
   619     (**** introduction of axioms ****)
   620 
   621     val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
   622     val size_axs = if no_size then [] else DatatypeProp.make_size descr sorts thy2;
   623 
   624     val ((([induct], [rec_thms]), inject), thy3) =
   625       thy2
   626       |> Theory.add_path (space_implode "_" new_type_names)
   627       |> add_axiom "induct" (DatatypeProp.make_ind descr sorts) [case_names_induct]
   628       ||>> add_axioms "recs" rec_axs []
   629       ||> (if no_size then I else add_axioms "size" size_axs [] #> snd)
   630       ||> Theory.parent_path
   631       ||>> add_and_get_axiomss "inject" new_type_names
   632             (DatatypeProp.make_injs descr sorts);
   633     val size_thms = if no_size then [] else get_thms thy3 (Name "size");
   634     val (distinct, thy4) = add_and_get_axiomss "distinct" new_type_names
   635       (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
   636 
   637     val exhaust_ts = DatatypeProp.make_casedists descr sorts;
   638     val (exhaustion, thy5) = add_and_get_axioms_atts "exhaust" new_type_names
   639       exhaust_ts (map single case_names_exhausts) thy4;
   640     val (case_thms, thy6) = add_and_get_axiomss "cases" new_type_names
   641       (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
   642     val (split_ts, split_asm_ts) = ListPair.unzip
   643       (DatatypeProp.make_splits new_type_names descr sorts thy6);
   644     val (split, thy7) = add_and_get_axioms "split" new_type_names split_ts thy6;
   645     val (split_asm, thy8) = add_and_get_axioms "split_asm" new_type_names
   646       split_asm_ts thy7;
   647     val (nchotomys, thy9) = add_and_get_axioms "nchotomy" new_type_names
   648       (DatatypeProp.make_nchotomys descr sorts) thy8;
   649     val (case_congs, thy10) = add_and_get_axioms "case_cong" new_type_names
   650       (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
   651     val (weak_case_congs, thy11) = add_and_get_axioms "weak_case_cong" new_type_names
   652       (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
   653 
   654     val dt_infos = map (make_dt_info descr' sorts induct reccomb_names' rec_thms)
   655       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
   656         exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
   657           nchotomys ~~ case_congs ~~ weak_case_congs);
   658 
   659     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   660     val split_thms = split ~~ split_asm;
   661 
   662     val thy12 =
   663       thy11
   664       |> add_case_tr' case_names'
   665       |> Theory.add_path (space_implode "_" new_type_names)
   666       |> add_rules simps case_thms size_thms rec_thms inject distinct
   667           weak_case_congs Simplifier.cong_add
   668       |> put_dt_infos dt_infos
   669       |> add_cases_induct dt_infos induct
   670       |> Theory.parent_path
   671       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)
   672       |> snd
   673       |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
   674       |> DatatypeInterpretator.add_those (map fst dt_infos);
   675   in
   676     ({distinct = distinct,
   677       inject = inject,
   678       exhaustion = exhaustion,
   679       rec_thms = rec_thms,
   680       case_thms = case_thms,
   681       split_thms = split_thms,
   682       induction = induct,
   683       size = size_thms,
   684       simps = simps}, thy12)
   685   end;
   686 
   687 
   688 (******************* definitional introduction of datatypes *******************)
   689 
   690 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   691     case_names_induct case_names_exhausts thy =
   692   let
   693     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   694 
   695     val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |>
   696       DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
   697         types_syntax constr_syntax case_names_induct;
   698 
   699     val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
   700       sorts induct case_names_exhausts thy2;
   701     val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms
   702       flat_names new_type_names descr sorts dt_info inject dist_rewrites
   703       (Simplifier.theory_context thy3 dist_ss) induct thy3;
   704     val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms
   705       flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
   706     val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names
   707       descr sorts inject dist_rewrites casedist_thms case_thms thy6;
   708     val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names
   709       descr sorts casedist_thms thy7;
   710     val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names
   711       descr sorts nchotomys case_thms thy8;
   712     val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   713       descr sorts thy9;
   714     val (size_thms, thy11) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
   715       descr sorts reccomb_names rec_thms thy10;
   716 
   717     val dt_infos = map (make_dt_info (flat descr) sorts induct reccomb_names rec_thms)
   718       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
   719         casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   720 
   721     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   722 
   723     val thy12 =
   724       thy11
   725       |> add_case_tr' case_names
   726       |> Theory.add_path (space_implode "_" new_type_names)
   727       |> add_rules simps case_thms size_thms rec_thms inject distinct
   728           weak_case_congs (Simplifier.attrib (op addcongs))
   729       |> put_dt_infos dt_infos
   730       |> add_cases_induct dt_infos induct
   731       |> Theory.parent_path
   732       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd
   733       |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
   734       |> DatatypeInterpretator.add_those (map fst dt_infos);
   735   in
   736     ({distinct = distinct,
   737       inject = inject,
   738       exhaustion = casedist_thms,
   739       rec_thms = rec_thms,
   740       case_thms = case_thms,
   741       split_thms = split_thms,
   742       induction = induct,
   743       size = size_thms,
   744       simps = simps}, thy12)
   745   end;
   746 
   747 
   748 (*********************** declare existing type as datatype *********************)
   749 
   750 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
   751   let
   752     val (((distinct, inject), [induction]), thy1) =
   753       thy0
   754       |> fold_map apply_theorems raw_distinct
   755       ||>> fold_map apply_theorems raw_inject
   756       ||>> apply_theorems [raw_induction];
   757 
   758     val ((_, [induction']), _) =
   759       Variable.importT_thms [induction] (Variable.thm_context induction);
   760 
   761     fun err t = error ("Ill-formed predicate in induction rule: " ^
   762       Sign.string_of_term thy1 t);
   763 
   764     fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
   765           ((tname, map dest_TFree Ts) handle TERM _ => err t)
   766       | get_typ t = err t;
   767 
   768     val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
   769     val new_type_names = getOpt (alt_names, map fst dtnames);
   770 
   771     fun get_constr t = (case Logic.strip_assums_concl t of
   772         _ $ (_ $ t') => (case head_of t' of
   773             Const (cname, cT) => (case strip_type cT of
   774                 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
   775               | _ => err t)
   776           | _ => err t)
   777       | _ => err t);
   778 
   779     fun make_dt_spec [] _ _ = []
   780       | make_dt_spec ((tname, tvs)::dtnames') i constrs =
   781           let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
   782           in (i, (tname, map DtTFree tvs, map snd constrs'))::
   783             (make_dt_spec dtnames' (i + 1) constrs'')
   784           end;
   785 
   786     val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
   787     val sorts = add_term_tfrees (concl_of induction', []);
   788     val dt_info = get_datatypes thy1;
   789 
   790     val (case_names_induct, case_names_exhausts) =
   791       (mk_case_names_induct descr, mk_case_names_exhausts descr (map #1 dtnames));
   792 
   793     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   794 
   795     val (casedist_thms, thy2) = thy1 |>
   796       DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
   797         case_names_exhausts;
   798     val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms
   799       false new_type_names [descr] sorts dt_info inject distinct
   800       (Simplifier.theory_context thy2 dist_ss) induction thy2;
   801     val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false
   802       new_type_names [descr] sorts reccomb_names rec_thms thy3;
   803     val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms
   804       new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
   805     val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names
   806       [descr] sorts casedist_thms thy5;
   807     val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names
   808       [descr] sorts nchotomys case_thms thy6;
   809     val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   810       [descr] sorts thy7;
   811     val (size_thms, thy9) =
   812       DatatypeAbsProofs.prove_size_thms false new_type_names
   813         [descr] sorts reccomb_names rec_thms thy8;
   814 
   815     val ((_, [induction']), thy10) =
   816       thy9
   817       |> store_thmss "inject" new_type_names inject
   818       ||>> store_thmss "distinct" new_type_names distinct
   819       ||> Theory.add_path (space_implode "_" new_type_names)
   820       ||>> PureThy.add_thms [(("induct", induction), [case_names_induct])];
   821 
   822     val dt_infos = map (make_dt_info descr sorts induction' reccomb_names rec_thms)
   823       ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~
   824         map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   825 
   826     val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
   827 
   828     val thy11 =
   829       thy10
   830       |> add_case_tr' case_names
   831       |> add_rules simps case_thms size_thms rec_thms inject distinct
   832            weak_case_congs (Simplifier.attrib (op addcongs))
   833       |> put_dt_infos dt_infos
   834       |> add_cases_induct dt_infos induction'
   835       |> Theory.parent_path
   836       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)
   837       |> snd
   838       |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
   839       |> DatatypeInterpretator.add_those (map fst dt_infos);
   840   in
   841     ({distinct = distinct,
   842       inject = inject,
   843       exhaustion = casedist_thms,
   844       rec_thms = rec_thms,
   845       case_thms = case_thms,
   846       split_thms = split_thms,
   847       induction = induction',
   848       size = size_thms,
   849       simps = simps}, thy11)
   850   end;
   851 
   852 val rep_datatype = gen_rep_datatype IsarCmd.apply_theorems;
   853 val rep_datatype_i = gen_rep_datatype IsarCmd.apply_theorems_i;
   854 
   855 
   856 
   857 (******************************** add datatype ********************************)
   858 
   859 fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =
   860   let
   861     val _ = Theory.requires thy "Datatype" "datatype definitions";
   862 
   863     (* this theory is used just for parsing *)
   864 
   865     val tmp_thy = thy |>
   866       Theory.copy |>
   867       Theory.add_types (map (fn (tvs, tname, mx, _) =>
   868         (tname, length tvs, mx)) dts);
   869 
   870     val (tyvars, _, _, _)::_ = dts;
   871     val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
   872       let val full_tname = Sign.full_name tmp_thy (Syntax.type_name tname mx)
   873       in (case duplicates (op =) tvs of
   874             [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
   875                   else error ("Mutually recursive datatypes must have same type parameters")
   876           | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
   877               " : " ^ commas dups))
   878       end) dts);
   879 
   880     val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of
   881       [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
   882 
   883     fun prep_dt_spec (tvs, tname, mx, constrs) (dts', constr_syntax, sorts, i) =
   884       let
   885         fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') =
   886           let
   887             val (cargs', sorts'') = Library.foldl (prep_typ tmp_thy) (([], sorts'), cargs);
   888             val _ = (case fold (curry add_typ_tfree_names) cargs' [] \\ tvs of
   889                 [] => ()
   890               | vs => error ("Extra type variables on rhs: " ^ commas vs))
   891           in (constrs @ [((if flat_names then Sign.full_name tmp_thy else
   892                 Sign.full_name_path tmp_thy tname) (Syntax.const_name cname mx'),
   893                    map (dtyp_of_typ new_dts) cargs')],
   894               constr_syntax' @ [(cname, mx')], sorts'')
   895           end handle ERROR msg =>
   896             cat_error msg ("The error above occured in constructor " ^ cname ^
   897               " of datatype " ^ tname);
   898 
   899         val (constrs', constr_syntax', sorts') =
   900           fold prep_constr constrs ([], [], sorts)
   901 
   902       in
   903         case duplicates (op =) (map fst constrs') of
   904            [] =>
   905              (dts' @ [(i, (Sign.full_name tmp_thy (Syntax.type_name tname mx),
   906                 map DtTFree tvs, constrs'))],
   907               constr_syntax @ [constr_syntax'], sorts', i + 1)
   908          | dups => error ("Duplicate constructors " ^ commas dups ^
   909              " in datatype " ^ tname)
   910       end;
   911 
   912     val (dts', constr_syntax, sorts', i) = fold prep_dt_spec dts ([], [], [], 0);
   913     val sorts = sorts' @ (map (rpair (Sign.defaultS tmp_thy)) (tyvars \\ map fst sorts'));
   914     val dt_info = get_datatypes thy;
   915     val (descr, _) = unfold_datatypes tmp_thy dts' sorts dt_info dts' i;
   916     val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>
   917       if err then error ("Nonemptiness check failed for datatype " ^ s)
   918       else raise exn;
   919 
   920     val descr' = flat descr;
   921     val case_names_induct = mk_case_names_induct descr';
   922     val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
   923   in
   924     (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
   925       flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   926       case_names_induct case_names_exhausts thy
   927   end;
   928 
   929 val add_datatype_i = gen_add_datatype cert_typ;
   930 val add_datatype = gen_add_datatype read_typ true;
   931 
   932 
   933 
   934 (** package setup **)
   935 
   936 (* setup theory *)
   937 
   938 val setup =
   939   DatatypeProp.distinctness_limit_setup #>
   940   Method.add_methods tactic_emulations #>
   941   simproc_setup #>
   942   trfun_setup #>
   943   DatatypeInterpretator.init;
   944 
   945 
   946 (* outer syntax *)
   947 
   948 local structure P = OuterParse and K = OuterKeyword in
   949 
   950 val datatype_decl =
   951   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
   952     (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
   953 
   954 fun mk_datatype args =
   955   let
   956     val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
   957     val specs = map (fn ((((_, vs), t), mx), cons) =>
   958       (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
   959   in snd o add_datatype false names specs end;
   960 
   961 val datatypeP =
   962   OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
   963     (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
   964 
   965 
   966 val rep_datatype_decl =
   967   Scan.option (Scan.repeat1 P.name) --
   968     Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] --
   969     Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] --
   970     (P.$$$ "induction" |-- P.!!! SpecParse.xthm);
   971 
   972 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #2 o rep_datatype opt_ts dss iss ind;
   973 
   974 val rep_datatypeP =
   975   OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
   976     (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
   977 
   978 
   979 val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
   980 val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
   981 
   982 end;
   983 
   984 
   985 end;
   986 
   987 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
   988 open BasicDatatypePackage;
   989