src/HOL/Tools/datatype_package.ML
author wenzelm
Thu Mar 27 14:41:09 2008 +0100 (2008-03-27)
changeset 26424 a6cad32a27b0
parent 26343 0dd2eab7b296
child 26496 49ae9456eba9
permissions -rw-r--r--
eliminated theory ProtoPure;
     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 -> (Facts.ref * Attrib.src list) list list ->
    52     (Facts.ref * Attrib.src list) list list -> Facts.ref * 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 construction_interpretation: theory
    69     -> { atom: typ -> 'a, dtyp: string -> 'a, rtyp: string -> 'a list -> 'a }
    70     -> (string * Term.sort) list -> string list
    71     -> (string * (string * 'a list) list) list
    72   val interpretation: (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 the_datatype_spec thy dtco =
   145   let
   146     val info as { descr, index, sorts = raw_sorts, ... } = the_datatype thy dtco;
   147     val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr index;
   148     val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v))
   149       o DatatypeAux.dest_DtTFree) dtys;
   150     val cos = map
   151       (fn (co, tys) => (co, map (DatatypeAux.typ_of_dtyp descr sorts) tys)) raw_cos;
   152   in (sorts, cos) end;
   153 
   154 fun get_datatype_constrs thy dtco =
   155   case try (the_datatype_spec thy) dtco
   156    of SOME (sorts, cos) =>
   157         let
   158           fun subst (v, sort) = TVar ((v, 0), sort);
   159           fun subst_ty (TFree v) = subst v
   160             | subst_ty ty = ty;
   161           val dty = Type (dtco, map subst sorts);
   162           fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty);
   163         in SOME (map mk_co cos) end
   164     | NONE => NONE;
   165 
   166 fun construction_interpretation thy { atom, dtyp, rtyp } sorts tycos =
   167   let
   168     val descr = (#descr o the_datatype thy o hd) tycos;
   169     val k = length tycos;
   170     val descr_of = the o AList.lookup (op =) descr;
   171     fun interpT (T as DtTFree _) = atom (typ_of_dtyp descr sorts T)
   172       | interpT (T as DtType (tyco, Ts)) = if is_rec_type T
   173           then rtyp tyco (map interpT Ts)
   174           else atom (typ_of_dtyp descr sorts T)
   175       | interpT (DtRec l) = if l < k then (dtyp o #1 o descr_of) l
   176           else let val (tyco, Ts, _) = descr_of l
   177           in rtyp tyco (map interpT Ts) end;
   178     fun interpC (c, Ts) = (c, map interpT Ts);
   179     fun interpK (_, (tyco, _, cs)) = (tyco, map interpC cs);
   180   in map interpK (Library.take (k, descr)) end;
   181 
   182 fun find_tname var Bi =
   183   let val frees = map dest_Free (term_frees Bi)
   184       val params = rename_wrt_term Bi (Logic.strip_params Bi);
   185   in case AList.lookup (op =) (frees @ params) var of
   186        NONE => error ("No such variable in subgoal: " ^ quote var)
   187      | SOME(Type (tn, _)) => tn
   188      | _ => error ("Cannot determine type of " ^ quote var)
   189   end;
   190 
   191 fun infer_tname state i aterm =
   192   let
   193     val sign = Thm.theory_of_thm state;
   194     val (_, _, Bi, _) = Thm.dest_state (state, i)
   195     val params = Logic.strip_params Bi;   (*params of subgoal i*)
   196     val params = rev (rename_wrt_term Bi params);   (*as they are printed*)
   197     val (types, sorts) = types_sorts state;
   198     fun types' (a, ~1) = (case AList.lookup (op =) params a of NONE => types(a, ~1) | sm => sm)
   199       | types' ixn = types ixn;
   200     val ([ct], _) = Thm.read_def_cterms (sign, types', sorts) [] false [(aterm, dummyT)];
   201   in case #T (rep_cterm ct) of
   202        Type (tn, _) => tn
   203      | _ => error ("Cannot determine type of " ^ quote aterm)
   204   end;
   205 
   206 (*Warn if the (induction) variable occurs Free among the premises, which
   207   usually signals a mistake.  But calls the tactic either way!*)
   208 fun occs_in_prems tacf vars =
   209   SUBGOAL (fn (Bi, i) =>
   210            (if exists (fn (a, _) => member (op =) vars a)
   211                       (fold Term.add_frees (#2 (strip_context Bi)) [])
   212              then warning "Induction variable occurs also among premises!"
   213              else ();
   214             tacf i));
   215 
   216 
   217 (* generic induction tactic for datatypes *)
   218 
   219 local
   220 
   221 fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x)
   222   | prep_var _ = NONE;
   223 
   224 fun prep_inst (concl, xs) = (*exception Library.UnequalLengths*)
   225   let val vs = Induct.vars_of concl
   226   in map_filter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
   227 
   228 in
   229 
   230 fun gen_induct_tac inst_tac (varss, opt_rule) i state =
   231   SUBGOAL (fn (Bi,_) =>
   232   let
   233     val (rule, rule_name) =
   234       case opt_rule of
   235           SOME r => (r, "Induction rule")
   236         | NONE =>
   237             let val tn = find_tname (hd (map_filter I (flat varss))) Bi
   238                 val thy = Thm.theory_of_thm state
   239             in (#induction (the_datatype thy tn), "Induction rule for type " ^ tn)
   240             end
   241     val concls = HOLogic.dest_concls (Thm.concl_of rule);
   242     val insts = maps prep_inst (concls ~~ varss) handle Library.UnequalLengths =>
   243       error (rule_name ^ " has different numbers of variables");
   244   in occs_in_prems (inst_tac insts rule) (map #2 insts) i end)
   245   i state;
   246 
   247 fun induct_tac s =
   248   gen_induct_tac Tactic.res_inst_tac'
   249     (map (single o SOME) (Syntax.read_idents s), NONE);
   250 
   251 fun induct_thm_tac th s =
   252   gen_induct_tac Tactic.res_inst_tac'
   253     ([map SOME (Syntax.read_idents s)], SOME th);
   254 
   255 end;
   256 
   257 
   258 (* generic case tactic for datatypes *)
   259 
   260 fun case_inst_tac inst_tac t rule i state =
   261   let
   262     val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
   263       (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));
   264   in inst_tac [(ixn, t)] rule i state end;
   265 
   266 fun gen_case_tac inst_tac (t, SOME rule) i state =
   267       case_inst_tac inst_tac t rule i state
   268   | gen_case_tac inst_tac (t, NONE) i state =
   269       let val tn = infer_tname state i t in
   270         if tn = HOLogic.boolN then inst_tac [(("P", 0), t)] case_split_thm i state
   271         else case_inst_tac inst_tac t
   272                (#exhaustion (the_datatype (Thm.theory_of_thm state) tn))
   273                i state
   274       end handle THM _ => Seq.empty;
   275 
   276 fun case_tac t = gen_case_tac Tactic.res_inst_tac' (t, NONE);
   277 
   278 
   279 
   280 (** Isar tactic emulations **)
   281 
   282 local
   283 
   284 val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
   285 val opt_rule = Scan.option (rule_spec |-- Attrib.thm);
   286 
   287 val varss =
   288   Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name))));
   289 
   290 val inst_tac = RuleInsts.bires_inst_tac false;
   291 
   292 fun induct_meth ctxt (varss, opt_rule) =
   293   gen_induct_tac (inst_tac ctxt) (varss, opt_rule);
   294 fun case_meth ctxt (varss, opt_rule) =
   295   gen_case_tac (inst_tac ctxt) (varss, opt_rule);
   296 
   297 in
   298 
   299 val tactic_emulations =
   300  [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth,
   301     "induct_tac emulation (dynamic instantiation)"),
   302   ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth,
   303     "case_tac emulation (dynamic instantiation)")];
   304 
   305 end;
   306 
   307 
   308 
   309 (** induct method setup **)
   310 
   311 (* case names *)
   312 
   313 local
   314 
   315 fun dt_recs (DtTFree _) = []
   316   | dt_recs (DtType (_, dts)) = maps dt_recs dts
   317   | dt_recs (DtRec i) = [i];
   318 
   319 fun dt_cases (descr: descr) (_, args, constrs) =
   320   let
   321     fun the_bname i = Sign.base_name (#1 (the (AList.lookup (op =) descr i)));
   322     val bnames = map the_bname (distinct (op =) (maps dt_recs args));
   323   in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
   324 
   325 
   326 fun induct_cases descr =
   327   DatatypeProp.indexify_names (maps (dt_cases descr) (map #2 descr));
   328 
   329 fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i));
   330 
   331 in
   332 
   333 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
   334 
   335 fun mk_case_names_exhausts descr new =
   336   map (RuleCases.case_names o exhaust_cases descr o #1)
   337     (filter (fn ((_, (name, _, _))) => member (op =) new name) descr);
   338 
   339 end;
   340 
   341 fun add_rules simps case_thms rec_thms inject distinct
   342                   weak_case_congs cong_att =
   343   PureThy.add_thmss [(("simps", simps), []),
   344     (("", flat case_thms @
   345           flat distinct @ rec_thms), [Simplifier.simp_add]),
   346     (("", rec_thms), [RecfunCodegen.add_default]),
   347     (("", flat inject), [iff_add]),
   348     (("", map (fn th => th RS notE) (flat distinct)), [Classical.safe_elim NONE]),
   349     (("", weak_case_congs), [cong_att])]
   350   #> snd;
   351 
   352 
   353 (* add_cases_induct *)
   354 
   355 fun add_cases_induct infos induction thy =
   356   let
   357     val inducts = ProjectRule.projections (ProofContext.init thy) induction;
   358 
   359     fun named_rules (name, {index, exhaustion, ...}: datatype_info) =
   360       [(("", nth inducts index), [Induct.induct_type name]),
   361        (("", exhaustion), [Induct.cases_type name])];
   362     fun unnamed_rule i =
   363       (("", nth inducts i), [PureThy.kind_internal, Induct.induct_type ""]);
   364   in
   365     thy |> PureThy.add_thms
   366       (maps named_rules infos @
   367         map unnamed_rule (length infos upto length inducts - 1)) |> snd
   368     |> PureThy.add_thmss [(("inducts", inducts), [])] |> snd
   369   end;
   370 
   371 
   372 
   373 (**** simplification procedure for showing distinctness of constructors ****)
   374 
   375 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
   376   | stripT p = p;
   377 
   378 fun stripC (i, f $ x) = stripC (i + 1, f)
   379   | stripC p = p;
   380 
   381 val distinctN = "constr_distinct";
   382 
   383 exception ConstrDistinct of term;
   384 
   385 fun distinct_rule thy ss tname eq_t = case #distinct (the_datatype thy tname) of
   386     QuickAndDirty => Thm.invoke_oracle
   387       (ThyInfo.the_theory "Datatype" thy) distinctN (thy, ConstrDistinct eq_t)
   388   | FewConstrs thms => Goal.prove (Simplifier.the_context ss) [] [] eq_t (K
   389       (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
   390         atac 2, resolve_tac thms 1, etac FalseE 1]))
   391   | ManyConstrs (thm, simpset) =>
   392       let
   393         val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
   394           map (PureThy.get_thm (ThyInfo.the_theory "Datatype" thy))
   395             ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"];
   396       in
   397         Goal.prove (Simplifier.the_context ss) [] [] eq_t (K
   398         (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
   399           full_simp_tac (Simplifier.inherit_context ss simpset) 1,
   400           REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
   401           eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
   402           etac FalseE 1]))
   403       end;
   404 
   405 fun distinct_proc thy ss (t as Const ("op =", _) $ t1 $ t2) =
   406   (case (stripC (0, t1), stripC (0, t2)) of
   407      ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
   408          (case (stripT (0, T1), stripT (0, T2)) of
   409             ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
   410                 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
   411                    (case (get_datatype_descr thy) tname1 of
   412                       SOME (_, (_, constrs)) => let val cnames = map fst constrs
   413                         in if cname1 mem cnames andalso cname2 mem cnames then
   414                              SOME (distinct_rule thy ss tname1
   415                                (Logic.mk_equals (t, Const ("False", HOLogic.boolT))))
   416                            else NONE
   417                         end
   418                     | NONE => NONE)
   419                 else NONE
   420           | _ => NONE)
   421    | _ => NONE)
   422   | distinct_proc _ _ _ = NONE;
   423 
   424 val distinct_simproc =
   425   Simplifier.simproc HOL.thy distinctN ["s = t"] distinct_proc;
   426 
   427 val dist_ss = HOL_ss addsimprocs [distinct_simproc];
   428 
   429 val simproc_setup =
   430   Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t) #>
   431   (fn thy => ((change_simpset_of thy) (fn ss => ss addsimprocs [distinct_simproc]); thy));
   432 
   433 
   434 (**** translation rules for case ****)
   435 
   436 fun make_case ctxt = DatatypeCase.make_case
   437   (datatype_of_constr (ProofContext.theory_of ctxt)) ctxt;
   438 
   439 fun strip_case ctxt = DatatypeCase.strip_case
   440   (datatype_of_case (ProofContext.theory_of ctxt));
   441 
   442 fun add_case_tr' case_names thy =
   443   Sign.add_advanced_trfuns ([], [],
   444     map (fn case_name =>
   445       let val case_name' = Sign.const_syntax_name thy case_name
   446       in (case_name', DatatypeCase.case_tr' datatype_of_case case_name')
   447       end) case_names, []) thy;
   448 
   449 val trfun_setup =
   450   Sign.add_advanced_trfuns ([],
   451     [("_case_syntax", DatatypeCase.case_tr true datatype_of_constr)],
   452     [], []);
   453 
   454 
   455 (* prepare types *)
   456 
   457 fun read_typ sign ((Ts, sorts), str) =
   458   let
   459     val T = Type.no_tvars (Sign.read_def_typ (sign, AList.lookup (op =)
   460       (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
   461   in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
   462 
   463 fun cert_typ sign ((Ts, sorts), raw_T) =
   464   let
   465     val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
   466       TYPE (msg, _, _) => error msg;
   467     val sorts' = add_typ_tfrees (T, sorts)
   468   in (Ts @ [T],
   469       case duplicates (op =) (map fst sorts') of
   470          [] => sorts'
   471        | dups => error ("Inconsistent sort constraints for " ^ commas dups))
   472   end;
   473 
   474 
   475 (**** make datatype info ****)
   476 
   477 fun make_dt_info alt_names descr sorts induct reccomb_names rec_thms
   478     (((((((((i, (_, (tname, _, _))), case_name), case_thms),
   479       exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =
   480   (tname,
   481    {index = i,
   482     alt_names = alt_names,
   483     descr = descr,
   484     sorts = sorts,
   485     rec_names = reccomb_names,
   486     rec_rewrites = rec_thms,
   487     case_name = case_name,
   488     case_rewrites = case_thms,
   489     induction = induct,
   490     exhaustion = exhaustion_thm,
   491     distinct = distinct_thm,
   492     inject = inject,
   493     nchotomy = nchotomy,
   494     case_cong = case_cong,
   495     weak_case_cong = weak_case_cong});
   496 
   497 
   498 (********************* axiomatic introduction of datatypes ********************)
   499 
   500 fun add_axiom label t atts thy =
   501   thy
   502   |> PureThy.add_axioms_i [((label, t), atts)];
   503 
   504 fun add_axioms label ts atts thy =
   505   thy
   506   |> PureThy.add_axiomss_i [((label, ts), atts)];
   507 
   508 fun add_and_get_axioms_atts label tnames ts attss =
   509   fold_map (fn (tname, (atts, t)) => fn thy =>
   510     thy
   511     |> Sign.add_path tname
   512     |> add_axiom label t atts
   513     ||> Sign.parent_path
   514     |-> (fn [ax] => pair ax)) (tnames ~~ (attss ~~ ts));
   515 
   516 fun add_and_get_axioms label tnames ts =
   517   add_and_get_axioms_atts label tnames ts (replicate (length tnames) []);
   518 
   519 fun add_and_get_axiomss label tnames tss =
   520   fold_map (fn (tname, ts) => fn thy =>
   521     thy
   522     |> Sign.add_path tname
   523     |> add_axioms label ts []
   524     ||> Sign.parent_path
   525     |-> (fn [ax] => pair ax)) (tnames ~~ tss);
   526 
   527 fun gen_specify_consts add args thy =
   528   let
   529     val specs = map (fn (c, T, mx) =>
   530       Const (Sign.full_name thy (Syntax.const_name c mx), T)) args;
   531   in
   532     thy
   533     |> add args
   534     |> Theory.add_finals_i false specs
   535   end;
   536 
   537 val specify_consts = gen_specify_consts Sign.add_consts_i;
   538 val specify_consts_authentic = gen_specify_consts (fold (snd oo Sign.declare_const []));
   539 
   540 structure DatatypeInterpretation = InterpretationFun(type T = string list val eq = op =);
   541 val interpretation = DatatypeInterpretation.interpretation;
   542 
   543 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   544     case_names_induct case_names_exhausts thy =
   545   let
   546     val descr' = flat descr;
   547     val recTs = get_rec_types descr' sorts;
   548     val used = map fst (fold Term.add_tfreesT recTs []);
   549     val newTs = Library.take (length (hd descr), recTs);
   550 
   551     (**** declare new types and constants ****)
   552 
   553     val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
   554 
   555     val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
   556       map (fn ((_, cargs), (cname, mx)) =>
   557         (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   558           (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
   559 
   560     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
   561 
   562     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   563     val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
   564       (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   565         (1 upto (length descr')));
   566 
   567     val freeT = TFree (Name.variant used "'t", HOLogic.typeS);
   568     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
   569       map (fn (_, cargs) =>
   570         let val Ts = map (typ_of_dtyp descr' sorts) cargs
   571         in Ts ---> freeT end) constrs) (hd descr);
   572 
   573     val case_names = map (fn s => (s ^ "_case")) new_type_names;
   574 
   575     val thy2' = thy
   576 
   577       (** new types **)
   578       |> fold2 (fn (name, mx) => fn tvs => ObjectLogic.typedecl (name, tvs, mx) #> snd)
   579            types_syntax tyvars
   580       |> add_path flat_names (space_implode "_" new_type_names)
   581 
   582       (** primrec combinators **)
   583 
   584       |> specify_consts (map (fn ((name, T), T') =>
   585            (name, reccomb_fn_Ts @ [T] ---> T', NoSyn)) (reccomb_names ~~ recTs ~~ rec_result_Ts))
   586 
   587       (** case combinators **)
   588 
   589       |> specify_consts_authentic (map (fn ((name, T), Ts) =>
   590            (name, Ts @ [T] ---> freeT, NoSyn)) (case_names ~~ newTs ~~ case_fn_Ts));
   591 
   592     val reccomb_names' = map (Sign.full_name thy2') reccomb_names;
   593     val case_names' = map (Sign.full_name thy2') case_names;
   594 
   595     val thy2 = thy2'
   596 
   597       (** constructors **)
   598 
   599       |> parent_path flat_names
   600       |> fold (fn ((((_, (_, _, constrs)), T), tname),
   601         constr_syntax') =>
   602           add_path flat_names tname #>
   603             specify_consts (map (fn ((_, cargs), (cname, mx)) =>
   604               (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
   605                 (constrs ~~ constr_syntax')) #>
   606           parent_path flat_names)
   607             (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
   608 
   609     (**** introduction of axioms ****)
   610 
   611     val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
   612 
   613     val ((([induct], [rec_thms]), inject), thy3) =
   614       thy2
   615       |> Sign.add_path (space_implode "_" new_type_names)
   616       |> add_axiom "induct" (DatatypeProp.make_ind descr sorts) [case_names_induct]
   617       ||>> add_axioms "recs" rec_axs []
   618       ||> Sign.parent_path
   619       ||>> add_and_get_axiomss "inject" new_type_names
   620             (DatatypeProp.make_injs descr sorts);
   621     val (distinct, thy4) = add_and_get_axiomss "distinct" new_type_names
   622       (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
   623 
   624     val exhaust_ts = DatatypeProp.make_casedists descr sorts;
   625     val (exhaustion, thy5) = add_and_get_axioms_atts "exhaust" new_type_names
   626       exhaust_ts (map single case_names_exhausts) thy4;
   627     val (case_thms, thy6) = add_and_get_axiomss "cases" new_type_names
   628       (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
   629     val (split_ts, split_asm_ts) = ListPair.unzip
   630       (DatatypeProp.make_splits new_type_names descr sorts thy6);
   631     val (split, thy7) = add_and_get_axioms "split" new_type_names split_ts thy6;
   632     val (split_asm, thy8) = add_and_get_axioms "split_asm" new_type_names
   633       split_asm_ts thy7;
   634     val (nchotomys, thy9) = add_and_get_axioms "nchotomy" new_type_names
   635       (DatatypeProp.make_nchotomys descr sorts) thy8;
   636     val (case_congs, thy10) = add_and_get_axioms "case_cong" new_type_names
   637       (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
   638     val (weak_case_congs, thy11) = add_and_get_axioms "weak_case_cong" new_type_names
   639       (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
   640 
   641     val dt_infos = map (make_dt_info NONE descr' sorts induct reccomb_names' rec_thms)
   642       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
   643         exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
   644           nchotomys ~~ case_congs ~~ weak_case_congs);
   645 
   646     val simps = flat (distinct @ inject @ case_thms) @ rec_thms;
   647     val split_thms = split ~~ split_asm;
   648 
   649     val thy12 =
   650       thy11
   651       |> add_case_tr' case_names'
   652       |> Sign.add_path (space_implode "_" new_type_names)
   653       |> add_rules simps case_thms rec_thms inject distinct
   654           weak_case_congs Simplifier.cong_add
   655       |> put_dt_infos dt_infos
   656       |> add_cases_induct dt_infos induct
   657       |> Sign.parent_path
   658       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)
   659       |> snd
   660       |> DatatypeInterpretation.data (map fst dt_infos);
   661   in
   662     ({distinct = distinct,
   663       inject = inject,
   664       exhaustion = exhaustion,
   665       rec_thms = rec_thms,
   666       case_thms = case_thms,
   667       split_thms = split_thms,
   668       induction = induct,
   669       simps = simps}, thy12)
   670   end;
   671 
   672 
   673 (******************* definitional introduction of datatypes *******************)
   674 
   675 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   676     case_names_induct case_names_exhausts thy =
   677   let
   678     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   679 
   680     val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |>
   681       DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
   682         types_syntax constr_syntax case_names_induct;
   683 
   684     val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
   685       sorts induct case_names_exhausts thy2;
   686     val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms
   687       flat_names new_type_names descr sorts dt_info inject dist_rewrites
   688       (Simplifier.theory_context thy3 dist_ss) induct thy3;
   689     val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms
   690       flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
   691     val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names
   692       descr sorts inject dist_rewrites casedist_thms case_thms thy6;
   693     val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names
   694       descr sorts casedist_thms thy7;
   695     val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names
   696       descr sorts nchotomys case_thms thy8;
   697     val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   698       descr sorts thy9;
   699 
   700     val dt_infos = map (make_dt_info NONE (flat descr) sorts induct reccomb_names rec_thms)
   701       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
   702         casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   703 
   704     val simps = flat (distinct @ inject @ case_thms) @ rec_thms;
   705 
   706     val thy12 =
   707       thy10
   708       |> add_case_tr' case_names
   709       |> Sign.add_path (space_implode "_" new_type_names)
   710       |> add_rules simps case_thms rec_thms inject distinct
   711           weak_case_congs (Simplifier.attrib (op addcongs))
   712       |> put_dt_infos dt_infos
   713       |> add_cases_induct dt_infos induct
   714       |> Sign.parent_path
   715       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd
   716       |> DatatypeInterpretation.data (map fst dt_infos);
   717   in
   718     ({distinct = distinct,
   719       inject = inject,
   720       exhaustion = casedist_thms,
   721       rec_thms = rec_thms,
   722       case_thms = case_thms,
   723       split_thms = split_thms,
   724       induction = induct,
   725       simps = simps}, thy12)
   726   end;
   727 
   728 
   729 (*********************** declare existing type as datatype *********************)
   730 
   731 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
   732   let
   733     val (((distinct, inject), [induction]), thy1) =
   734       thy0
   735       |> fold_map apply_theorems raw_distinct
   736       ||>> fold_map apply_theorems raw_inject
   737       ||>> apply_theorems [raw_induction];
   738 
   739     val ((_, [induction']), _) =
   740       Variable.importT_thms [induction] (Variable.thm_context induction);
   741 
   742     fun err t = error ("Ill-formed predicate in induction rule: " ^
   743       Sign.string_of_term thy1 t);
   744 
   745     fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
   746           ((tname, map (fst o dest_TFree) Ts) handle TERM _ => err t)
   747       | get_typ t = err t;
   748 
   749     val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
   750     val new_type_names = getOpt (alt_names, map fst dtnames);
   751 
   752     fun get_constr t = (case Logic.strip_assums_concl t of
   753         _ $ (_ $ t') => (case head_of t' of
   754             Const (cname, cT) => (case strip_type cT of
   755                 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
   756               | _ => err t)
   757           | _ => err t)
   758       | _ => err t);
   759 
   760     fun make_dt_spec [] _ _ = []
   761       | make_dt_spec ((tname, tvs)::dtnames') i constrs =
   762           let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
   763           in (i, (tname, map DtTFree tvs, map snd constrs'))::
   764             (make_dt_spec dtnames' (i + 1) constrs'')
   765           end;
   766 
   767     val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
   768     val sorts = add_term_tfrees (concl_of induction', []);
   769     val dt_info = get_datatypes thy1;
   770 
   771     val (case_names_induct, case_names_exhausts) =
   772       (mk_case_names_induct descr, mk_case_names_exhausts descr (map #1 dtnames));
   773 
   774     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
   775 
   776     val (casedist_thms, thy2) = thy1 |>
   777       DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
   778         case_names_exhausts;
   779     val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms
   780       false new_type_names [descr] sorts dt_info inject distinct
   781       (Simplifier.theory_context thy2 dist_ss) induction thy2;
   782     val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false
   783       new_type_names [descr] sorts reccomb_names rec_thms thy3;
   784     val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms
   785       new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
   786     val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names
   787       [descr] sorts casedist_thms thy5;
   788     val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names
   789       [descr] sorts nchotomys case_thms thy6;
   790     val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
   791       [descr] sorts thy7;
   792 
   793     val ((_, [induction']), thy10) =
   794       thy8
   795       |> store_thmss "inject" new_type_names inject
   796       ||>> store_thmss "distinct" new_type_names distinct
   797       ||> Sign.add_path (space_implode "_" new_type_names)
   798       ||>> PureThy.add_thms [(("induct", induction), [case_names_induct])];
   799 
   800     val dt_infos = map (make_dt_info alt_names descr sorts induction' reccomb_names rec_thms)
   801       ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~
   802         map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
   803 
   804     val simps = flat (distinct @ inject @ case_thms) @ rec_thms;
   805 
   806     val thy11 =
   807       thy10
   808       |> add_case_tr' case_names
   809       |> add_rules simps case_thms rec_thms inject distinct
   810            weak_case_congs (Simplifier.attrib (op addcongs))
   811       |> put_dt_infos dt_infos
   812       |> add_cases_induct dt_infos induction'
   813       |> Sign.parent_path
   814       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)
   815       |> snd
   816       |> DatatypeInterpretation.data (map fst dt_infos);
   817   in
   818     ({distinct = distinct,
   819       inject = inject,
   820       exhaustion = casedist_thms,
   821       rec_thms = rec_thms,
   822       case_thms = case_thms,
   823       split_thms = split_thms,
   824       induction = induction',
   825       simps = simps}, thy11)
   826   end;
   827 
   828 val rep_datatype = gen_rep_datatype IsarCmd.apply_theorems;
   829 val rep_datatype_i = gen_rep_datatype IsarCmd.apply_theorems_i;
   830 
   831 
   832 
   833 (******************************** add datatype ********************************)
   834 
   835 fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =
   836   let
   837     val _ = Theory.requires thy "Datatype" "datatype definitions";
   838 
   839     (* this theory is used just for parsing *)
   840 
   841     val tmp_thy = thy |>
   842       Theory.copy |>
   843       Sign.add_types (map (fn (tvs, tname, mx, _) =>
   844         (tname, length tvs, mx)) dts);
   845 
   846     val (tyvars, _, _, _)::_ = dts;
   847     val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
   848       let val full_tname = Sign.full_name tmp_thy (Syntax.type_name tname mx)
   849       in (case duplicates (op =) tvs of
   850             [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
   851                   else error ("Mutually recursive datatypes must have same type parameters")
   852           | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
   853               " : " ^ commas dups))
   854       end) dts);
   855 
   856     val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of
   857       [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
   858 
   859     fun prep_dt_spec (tvs, tname, mx, constrs) (dts', constr_syntax, sorts, i) =
   860       let
   861         fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') =
   862           let
   863             val (cargs', sorts'') = Library.foldl (prep_typ tmp_thy) (([], sorts'), cargs);
   864             val _ = (case fold (curry add_typ_tfree_names) cargs' [] \\ tvs of
   865                 [] => ()
   866               | vs => error ("Extra type variables on rhs: " ^ commas vs))
   867           in (constrs @ [((if flat_names then Sign.full_name tmp_thy else
   868                 Sign.full_name_path tmp_thy tname) (Syntax.const_name cname mx'),
   869                    map (dtyp_of_typ new_dts) cargs')],
   870               constr_syntax' @ [(cname, mx')], sorts'')
   871           end handle ERROR msg =>
   872             cat_error msg ("The error above occured in constructor " ^ cname ^
   873               " of datatype " ^ tname);
   874 
   875         val (constrs', constr_syntax', sorts') =
   876           fold prep_constr constrs ([], [], sorts)
   877 
   878       in
   879         case duplicates (op =) (map fst constrs') of
   880            [] =>
   881              (dts' @ [(i, (Sign.full_name tmp_thy (Syntax.type_name tname mx),
   882                 map DtTFree tvs, constrs'))],
   883               constr_syntax @ [constr_syntax'], sorts', i + 1)
   884          | dups => error ("Duplicate constructors " ^ commas dups ^
   885              " in datatype " ^ tname)
   886       end;
   887 
   888     val (dts', constr_syntax, sorts', i) = fold prep_dt_spec dts ([], [], [], 0);
   889     val sorts = sorts' @ (map (rpair (Sign.defaultS tmp_thy)) (tyvars \\ map fst sorts'));
   890     val dt_info = get_datatypes thy;
   891     val (descr, _) = unfold_datatypes tmp_thy dts' sorts dt_info dts' i;
   892     val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>
   893       if err then error ("Nonemptiness check failed for datatype " ^ s)
   894       else raise exn;
   895 
   896     val descr' = flat descr;
   897     val case_names_induct = mk_case_names_induct descr';
   898     val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
   899   in
   900     (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
   901       flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
   902       case_names_induct case_names_exhausts thy
   903   end;
   904 
   905 val add_datatype_i = gen_add_datatype cert_typ;
   906 val add_datatype = gen_add_datatype read_typ true;
   907 
   908 
   909 (** a datatype antiquotation **)
   910 
   911 local
   912 
   913 val sym_datatype = Pretty.str "\\isacommand{datatype}";
   914 val sym_binder = Pretty.str "{\\isacharequal}";
   915 val sym_of = Pretty.str "of";
   916 val sym_sep = Pretty.str "{\\isacharbar}";
   917 
   918 in
   919 
   920 fun args_datatype (ctxt, args) =
   921   let
   922     val (tyco, (ctxt', args')) = Args.tyname (ctxt, args);
   923     val thy = Context.theory_of ctxt';
   924     val spec = the_datatype_spec thy tyco;
   925   in ((tyco, spec), (ctxt', args')) end;
   926 
   927 fun pretty_datatype ctxt (dtco, (vs, cos)) =
   928   let
   929     val ty = Type (dtco, map TFree vs);
   930     fun pretty_typ_br ty =
   931       let
   932         val p = Syntax.pretty_typ ctxt ty;
   933         val s = explode (Pretty.str_of p);
   934       in if member (op =) s " " then Pretty.enclose "(" ")" [p]
   935         else p
   936       end;
   937     fun pretty_constr (co, []) =
   938           Syntax.pretty_term ctxt (Const (co, ty))
   939       | pretty_constr (co, [ty']) =
   940           (Pretty.block o Pretty.breaks)
   941             [Syntax.pretty_term ctxt (Const (co, ty' --> ty)),
   942               sym_of, Syntax.pretty_typ ctxt ty']
   943       | pretty_constr (co, tys) =
   944           (Pretty.block o Pretty.breaks)
   945             (Syntax.pretty_term ctxt (Const (co, tys ---> ty)) ::
   946               sym_of :: map pretty_typ_br tys);
   947   in (Pretty.block o Pretty.breaks) (
   948     sym_datatype
   949     :: Syntax.pretty_typ ctxt ty
   950     :: sym_binder
   951     :: separate sym_sep (map pretty_constr cos)
   952   ) end
   953 
   954 end;
   955 
   956 (** package setup **)
   957 
   958 (* setup theory *)
   959 
   960 val setup =
   961   DatatypeProp.distinctness_limit_setup #>
   962   Method.add_methods tactic_emulations #>
   963   simproc_setup #>
   964   trfun_setup #>
   965   DatatypeInterpretation.init;
   966 
   967 
   968 (* outer syntax *)
   969 
   970 local structure P = OuterParse and K = OuterKeyword in
   971 
   972 val _ = OuterSyntax.keywords ["distinct", "inject", "induction"];
   973 
   974 val datatype_decl =
   975   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
   976     (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
   977 
   978 fun mk_datatype args =
   979   let
   980     val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
   981     val specs = map (fn ((((_, vs), t), mx), cons) =>
   982       (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
   983   in snd o add_datatype false names specs end;
   984 
   985 val _ =
   986   OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
   987     (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
   988 
   989 
   990 val rep_datatype_decl =
   991   Scan.option (Scan.repeat1 P.name) --
   992     Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] --
   993     Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] --
   994     (P.$$$ "induction" |-- P.!!! SpecParse.xthm);
   995 
   996 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #2 o rep_datatype opt_ts dss iss ind;
   997 
   998 val _ =
   999   OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
  1000     (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
  1001 
  1002 val _ =
  1003   ThyOutput.add_commands [("datatype",
  1004     ThyOutput.args args_datatype (ThyOutput.output pretty_datatype))];
  1005 
  1006 end;
  1007 
  1008 
  1009 end;
  1010 
  1011 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
  1012 open BasicDatatypePackage;
  1013