(*  Title:      HOL/Tools/datatype_package.ML

     ID:         $Id$

     Author:     Stefan Berghofer, TU Muenchen

 Datatype package for Isabelle/HOL.

 *)

 signature BASIC_DATATYPE_PACKAGE =

 sig

   val induct_tac : string -> int -> tactic

   val induct_thm_tac : thm -> string -> int -> tactic

   val case_tac : string -> int -> tactic

   val distinct_simproc : simproc

 end;

 signature DATATYPE_PACKAGE =

 sig

   include BASIC_DATATYPE_PACKAGE

   val quiet_mode : bool ref

   val add_datatype_i : bool -> bool -> string list -> (string list * bstring * mixfix *

     (bstring * typ list * mixfix) list) list -> theory ->

       {distinct : thm list list,

        inject : thm list list,

        exhaustion : thm list,

        rec_thms : thm list,

        case_thms : thm list list,

        split_thms : (thm * thm) list,

        induction : thm,

        simps : thm list} * theory

   val add_datatype : bool -> string list -> (string list * bstring * mixfix *

     (bstring * string list * mixfix) list) list -> theory ->

       {distinct : thm list list,

        inject : thm list list,

        exhaustion : thm list,

        rec_thms : thm list,

        case_thms : thm list list,

        split_thms : (thm * thm) list,

        induction : thm,

        simps : thm list} * theory

   val rep_datatype_i : string list option -> (thm list * attribute list) list list ->

     (thm list * attribute list) list list -> (thm list * attribute list) ->

     theory ->

       {distinct : thm list list,

        inject : thm list list,

        exhaustion : thm list,

        rec_thms : thm list,

        case_thms : thm list list,

        split_thms : (thm * thm) list,

        induction : thm,

        simps : thm list} * theory

   val rep_datatype : string list option -> (thmref * Attrib.src list) list list ->

     (thmref * Attrib.src list) list list -> thmref * Attrib.src list -> theory ->

       {distinct : thm list list,

        inject : thm list list,

        exhaustion : thm list,

        rec_thms : thm list,

        case_thms : thm list list,

        split_thms : (thm * thm) list,

        induction : thm,

        simps : thm list} * theory

   val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table

   val get_datatype : theory -> string -> DatatypeAux.datatype_info option

   val the_datatype : theory -> string -> DatatypeAux.datatype_info

   val datatype_of_constr : theory -> string -> DatatypeAux.datatype_info option

   val datatype_of_case : theory -> string -> DatatypeAux.datatype_info option

   val get_datatype_spec : theory -> string -> ((string * sort) list * (string * typ list) list) option

   val get_datatype_constrs : theory -> string -> (string * typ) list option

   val interpretation: (string list -> theory -> theory) -> theory -> theory

   val print_datatypes : theory -> unit

   val make_case :  Proof.context -> bool -> string list -> term ->

     (term * term) list -> term * (term * (int * bool)) list

   val strip_case: Proof.context -> bool ->

     term -> (term * (term * term) list) option

   val setup: theory -> theory

 end;

 structure DatatypePackage : DATATYPE_PACKAGE =

 struct

 open DatatypeAux;

 val quiet_mode = quiet_mode;

 (* theory data *)

 structure DatatypesData = TheoryDataFun

 (

   type T =

     {types: datatype_info Symtab.table,

      constrs: datatype_info Symtab.table,

      cases: datatype_info Symtab.table};

   val empty =

     {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty};

   val copy = I;

   val extend = I;

   fun merge _

     ({types = types1, constrs = constrs1, cases = cases1},

      {types = types2, constrs = constrs2, cases = cases2}) =

     {types = Symtab.merge (K true) (types1, types2),

      constrs = Symtab.merge (K true) (constrs1, constrs2),

      cases = Symtab.merge (K true) (cases1, cases2)};

 );

 val get_datatypes = #types o DatatypesData.get;

 val map_datatypes = DatatypesData.map;

 fun print_datatypes thy =

   Pretty.writeln (Pretty.strs ("datatypes:" ::

     map #1 (NameSpace.extern_table (Sign.type_space thy, get_datatypes thy))));

 (** theory information about datatypes **)

 fun put_dt_infos (dt_infos : (string * datatype_info) list) =

   map_datatypes (fn {types, constrs, cases} =>

     {types = fold Symtab.update dt_infos types,

      constrs = fold Symtab.update

        (maps (fn (_, info as {descr, index, ...}) => map (rpair info o fst)

           (#3 (the (AList.lookup op = descr index)))) dt_infos) constrs,

      cases = fold Symtab.update

        (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos)

        cases});

 val get_datatype = Symtab.lookup o get_datatypes;

 fun the_datatype thy name = (case get_datatype thy name of

       SOME info => info

     | NONE => error ("Unknown datatype " ^ quote name));

 val datatype_of_constr = Symtab.lookup o #constrs o DatatypesData.get;

 val datatype_of_case = Symtab.lookup o #cases o DatatypesData.get;

 fun get_datatype_descr thy dtco =

   get_datatype thy dtco

   |> Option.map (fn info as { descr, index, ... } =>

        (info, (((fn SOME (_, dtys, cos) => (dtys, cos)) o AList.lookup (op =) descr) index)));

 fun get_datatype_spec thy dtco =

   let

     fun mk_cons typ_of_dtyp (co, tys) =

       (co, map typ_of_dtyp tys);

     fun mk_dtyp ({ sorts = raw_sorts, descr, ... } : DatatypeAux.datatype_info, (dtys, cos)) =

       let

         val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v))

           o DatatypeAux.dest_DtTFree) dtys;

         val typ_of_dtyp = DatatypeAux.typ_of_dtyp descr sorts;

         val tys = map typ_of_dtyp dtys;

       in (sorts, map (mk_cons typ_of_dtyp) cos) end;

   in Option.map mk_dtyp (get_datatype_descr thy dtco) end;

 fun get_datatype_constrs thy dtco =

   case get_datatype_spec thy dtco

    of SOME (sorts, cos) =>

         let

           fun subst (v, sort) = TVar ((v, 0), sort);

           fun subst_ty (TFree v) = subst v

             | subst_ty ty = ty;

           val dty = Type (dtco, map subst sorts);

           fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty);

         in SOME (map mk_co cos) end

     | NONE => NONE;

 fun find_tname var Bi =

   let val frees = map dest_Free (term_frees Bi)

       val params = rename_wrt_term Bi (Logic.strip_params Bi);

   in case AList.lookup (op =) (frees @ params) var of

        NONE => error ("No such variable in subgoal: " ^ quote var)

      | SOME(Type (tn, _)) => tn

      | _ => error ("Cannot determine type of " ^ quote var)

   end;

 fun infer_tname state i aterm =

   let

     val sign = Thm.theory_of_thm state;

     val (_, _, Bi, _) = Thm.dest_state (state, i)

     val params = Logic.strip_params Bi;   (*params of subgoal i*)

     val params = rev (rename_wrt_term Bi params);   (*as they are printed*)

     val (types, sorts) = types_sorts state;

     fun types' (a, ~1) = (case AList.lookup (op =) params a of NONE => types(a, ~1) | sm => sm)

       | types' ixn = types ixn;

     val ([ct], _) = Thm.read_def_cterms (sign, types', sorts) [] false [(aterm, dummyT)];

   in case #T (rep_cterm ct) of

        Type (tn, _) => tn

      | _ => error ("Cannot determine type of " ^ quote aterm)

   end;

 (*Warn if the (induction) variable occurs Free among the premises, which

   usually signals a mistake.  But calls the tactic either way!*)

 fun occs_in_prems tacf vars =

   SUBGOAL (fn (Bi, i) =>

            (if exists (fn (a, _) => member (op =) vars a)

                       (fold Term.add_frees (#2 (strip_context Bi)) [])

              then warning "Induction variable occurs also among premises!"

              else ();

             tacf i));

 (* generic induction tactic for datatypes *)

 local

 fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x)

   | prep_var _ = NONE;

 fun prep_inst (concl, xs) = (*exception Library.UnequalLengths*)

   let val vs = Induct.vars_of concl

   in map_filter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;

 in

 fun gen_induct_tac inst_tac (varss, opt_rule) i state =

   SUBGOAL (fn (Bi,_) =>

   let

     val (rule, rule_name) =

       case opt_rule of

           SOME r => (r, "Induction rule")

         | NONE =>

             let val tn = find_tname (hd (map_filter I (flat varss))) Bi

                 val thy = Thm.theory_of_thm state

             in (#induction (the_datatype thy tn), "Induction rule for type " ^ tn)

             end

     val concls = HOLogic.dest_concls (Thm.concl_of rule);

     val insts = maps prep_inst (concls ~~ varss) handle Library.UnequalLengths =>

       error (rule_name ^ " has different numbers of variables");

   in occs_in_prems (inst_tac insts rule) (map #2 insts) i end)

   i state;

 fun induct_tac s =

   gen_induct_tac Tactic.res_inst_tac'

     (map (single o SOME) (Syntax.read_idents s), NONE);

 fun induct_thm_tac th s =

   gen_induct_tac Tactic.res_inst_tac'

     ([map SOME (Syntax.read_idents s)], SOME th);

 end;

 (* generic case tactic for datatypes *)

 fun case_inst_tac inst_tac t rule i state =

   let

     val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop

       (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));

   in inst_tac [(ixn, t)] rule i state end;

 fun gen_case_tac inst_tac (t, SOME rule) i state =

       case_inst_tac inst_tac t rule i state

   | gen_case_tac inst_tac (t, NONE) i state =

       let val tn = infer_tname state i t in

         if tn = HOLogic.boolN then inst_tac [(("P", 0), t)] case_split_thm i state

         else case_inst_tac inst_tac t

                (#exhaustion (the_datatype (Thm.theory_of_thm state) tn))

                i state

       end handle THM _ => Seq.empty;

 fun case_tac t = gen_case_tac Tactic.res_inst_tac' (t, NONE);

 (** Isar tactic emulations **)

 local

 val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");

 val opt_rule = Scan.option (rule_spec |-- Attrib.thm);

 val varss =

   Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name))));

 val inst_tac = RuleInsts.bires_inst_tac false;

 fun induct_meth ctxt (varss, opt_rule) =

   gen_induct_tac (inst_tac ctxt) (varss, opt_rule);

 fun case_meth ctxt (varss, opt_rule) =

   gen_case_tac (inst_tac ctxt) (varss, opt_rule);

 in

 val tactic_emulations =

  [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth,

     "induct_tac emulation (dynamic instantiation)"),

   ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth,

     "case_tac emulation (dynamic instantiation)")];

 end;

 (** induct method setup **)

 (* case names *)

 local

 fun dt_recs (DtTFree _) = []

   | dt_recs (DtType (_, dts)) = maps dt_recs dts

   | dt_recs (DtRec i) = [i];

 fun dt_cases (descr: descr) (_, args, constrs) =

   let

     fun the_bname i = Sign.base_name (#1 (the (AList.lookup (op =) descr i)));

     val bnames = map the_bname (distinct (op =) (maps dt_recs args));

   in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;

 fun induct_cases descr =

   DatatypeProp.indexify_names (maps (dt_cases descr) (map #2 descr));

 fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i));

 in

 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);

 fun mk_case_names_exhausts descr new =

   map (RuleCases.case_names o exhaust_cases descr o #1)

     (filter (fn ((_, (name, _, _))) => member (op =) new name) descr);

 end;

 fun add_rules simps case_thms rec_thms inject distinct

                   weak_case_congs cong_att =

   PureThy.add_thmss [(("simps", simps), []),

     (("", flat case_thms @

           flat distinct @ rec_thms), [Simplifier.simp_add]),

     (("", rec_thms), [RecfunCodegen.add_default]),

     (("", flat inject), [iff_add]),

     (("", map (fn th => th RS notE) (flat distinct)), [Classical.safe_elim NONE]),

     (("", weak_case_congs), [cong_att])]

   #> snd;

 (* add_cases_induct *)

 fun add_cases_induct infos induction thy =

   let

     val inducts = ProjectRule.projections (ProofContext.init thy) induction;

     fun named_rules (name, {index, exhaustion, ...}: datatype_info) =

       [(("", nth inducts index), [Induct.induct_type name]),

        (("", exhaustion), [Induct.cases_type name])];

     fun unnamed_rule i =

       (("", nth inducts i), [PureThy.kind_internal, Induct.induct_type ""]);

   in

     thy |> PureThy.add_thms

       (maps named_rules infos @

         map unnamed_rule (length infos upto length inducts - 1)) |> snd

     |> PureThy.add_thmss [(("inducts", inducts), [])] |> snd

   end;

 (**** simplification procedure for showing distinctness of constructors ****)

 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)

   | stripT p = p;

 fun stripC (i, f $ x) = stripC (i + 1, f)

   | stripC p = p;

 val distinctN = "constr_distinct";

 exception ConstrDistinct of term;

 fun distinct_proc thy ss (t as Const ("op =", _) $ t1 $ t2) =

   (case (stripC (0, t1), stripC (0, t2)) of

      ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>

          (case (stripT (0, T1), stripT (0, T2)) of

             ((i', Type (tname1, _)), (j', Type (tname2, _))) =>

                 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then

                    (case (get_datatype_descr thy) tname1 of

                       SOME (_, (_, constrs)) => let val cnames = map fst constrs

                         in if cname1 mem cnames andalso cname2 mem cnames then

                              let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));

                                  val eq_ct = cterm_of thy eq_t;

                                  val Datatype_thy = ThyInfo.the_theory "Datatype" thy;

                                  val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =

                                    map (get_thm Datatype_thy o Name)

                                      ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]

                              in (case (#distinct (the_datatype thy tname1)) of

                                  QuickAndDirty => SOME (Thm.invoke_oracle

                                    Datatype_thy distinctN (thy, ConstrDistinct eq_t))

                                | FewConstrs thms =>

                                    SOME (Goal.prove (Simplifier.the_context ss) [] [] eq_t (K

                                      (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,

                                        atac 2, resolve_tac thms 1, etac FalseE 1])))

                                | ManyConstrs (thm, simpset) =>

                                    SOME (Goal.prove (Simplifier.the_context ss) [] [] eq_t (K

                                      (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,

                                       full_simp_tac (Simplifier.inherit_context ss simpset) 1,

                                       REPEAT (dresolve_tac [In0_inject, In1_inject] 1),

                                       eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,

                                       etac FalseE 1]))))

                              end

                            else NONE

                         end

                     | NONE => NONE)

                 else NONE

           | _ => NONE)

    | _ => NONE)

   | distinct_proc _ _ _ = NONE;

 val distinct_simproc =

   Simplifier.simproc HOL.thy distinctN ["s = t"] distinct_proc;

 val dist_ss = HOL_ss addsimprocs [distinct_simproc];

 val simproc_setup =

   Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t) #>

   (fn thy => ((change_simpset_of thy) (fn ss => ss addsimprocs [distinct_simproc]); thy));

 (**** translation rules for case ****)

 fun make_case ctxt = DatatypeCase.make_case

   (datatype_of_constr (ProofContext.theory_of ctxt)) ctxt;

 fun strip_case ctxt = DatatypeCase.strip_case

   (datatype_of_case (ProofContext.theory_of ctxt));

 fun add_case_tr' case_names thy =

   Sign.add_advanced_trfuns ([], [],

     map (fn case_name =>

       let val case_name' = Sign.const_syntax_name thy case_name

       in (case_name', DatatypeCase.case_tr' datatype_of_case case_name')

       end) case_names, []) thy;

 val trfun_setup =

   Sign.add_advanced_trfuns ([],

     [("_case_syntax", DatatypeCase.case_tr true datatype_of_constr)],

     [], []);

 (* prepare types *)

 fun read_typ sign ((Ts, sorts), str) =

   let

     val T = Type.no_tvars (Sign.read_def_typ (sign, AList.lookup (op =)

       (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg

   in (Ts @ [T], add_typ_tfrees (T, sorts)) end;

 fun cert_typ sign ((Ts, sorts), raw_T) =

   let

     val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle

       TYPE (msg, _, _) => error msg;

     val sorts' = add_typ_tfrees (T, sorts)

   in (Ts @ [T],

       case duplicates (op =) (map fst sorts') of

          [] => sorts'

        | dups => error ("Inconsistent sort constraints for " ^ commas dups))

   end;

 (**** make datatype info ****)

 fun make_dt_info head_len descr sorts induct reccomb_names rec_thms

     (((((((((i, (_, (tname, _, _))), case_name), case_thms),

       exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =

   (tname,

    {index = i,

     head_len = head_len,

     descr = descr,

     sorts = sorts,

     rec_names = reccomb_names,

     rec_rewrites = rec_thms,

     case_name = case_name,

     case_rewrites = case_thms,

     induction = induct,

     exhaustion = exhaustion_thm,

     distinct = distinct_thm,

     inject = inject,

     nchotomy = nchotomy,

     case_cong = case_cong,

     weak_case_cong = weak_case_cong});

 (********************* axiomatic introduction of datatypes ********************)

 fun add_axiom label t atts thy =

   thy

   |> PureThy.add_axioms_i [((label, t), atts)];

 fun add_axioms label ts atts thy =

   thy

   |> PureThy.add_axiomss_i [((label, ts), atts)];

 fun add_and_get_axioms_atts label tnames ts attss =

   fold_map (fn (tname, (atts, t)) => fn thy =>

     thy

     |> Sign.add_path tname

     |> add_axiom label t atts

     ||> Sign.parent_path

     |-> (fn [ax] => pair ax)) (tnames ~~ (attss ~~ ts));

 fun add_and_get_axioms label tnames ts =

   add_and_get_axioms_atts label tnames ts (replicate (length tnames) []);

 fun add_and_get_axiomss label tnames tss =

   fold_map (fn (tname, ts) => fn thy =>

     thy

     |> Sign.add_path tname

     |> add_axioms label ts []

     ||> Sign.parent_path

     |-> (fn [ax] => pair ax)) (tnames ~~ tss);

 fun gen_specify_consts add args thy =

   let

     val specs = map (fn (c, T, mx) =>

       Const (Sign.full_name thy (Syntax.const_name c mx), T)) args;

   in

     thy

     |> add args

     |> Theory.add_finals_i false specs

   end;

 val specify_consts = gen_specify_consts Sign.add_consts_i;

 val specify_consts_authentic = gen_specify_consts (Sign.add_consts_authentic []);

 structure DatatypeInterpretation = InterpretationFun(type T = string list val eq = op =);

 val interpretation = DatatypeInterpretation.interpretation;

 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info

     case_names_induct case_names_exhausts thy =

   let

     val descr' = flat descr;

     val recTs = get_rec_types descr' sorts;

     val used = map fst (fold Term.add_tfreesT recTs []);

     val newTs = Library.take (length (hd descr), recTs);

     (**** declare new types and constants ****)

     val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);

     val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>

       map (fn ((_, cargs), (cname, mx)) =>

         (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))

           (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);

     val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;

     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";

     val reccomb_names = if length descr' = 1 then [big_reccomb_name] else

       (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)

         (1 upto (length descr')));

     val freeT = TFree (Name.variant used "'t", HOLogic.typeS);

     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>

       map (fn (_, cargs) =>

         let val Ts = map (typ_of_dtyp descr' sorts) cargs

         in Ts ---> freeT end) constrs) (hd descr);

     val case_names = map (fn s => (s ^ "_case")) new_type_names;

     val thy2' = thy

       (** new types **)

       |> fold2 (fn (name, mx) => fn tvs => TypedefPackage.add_typedecls [(name, tvs, mx)])

            types_syntax tyvars

       |> add_path flat_names (space_implode "_" new_type_names)

       (** primrec combinators **)

       |> specify_consts (map (fn ((name, T), T') =>

            (name, reccomb_fn_Ts @ [T] ---> T', NoSyn)) (reccomb_names ~~ recTs ~~ rec_result_Ts))

       (** case combinators **)

       |> specify_consts_authentic (map (fn ((name, T), Ts) =>

            (name, Ts @ [T] ---> freeT, NoSyn)) (case_names ~~ newTs ~~ case_fn_Ts));

     val reccomb_names' = map (Sign.full_name thy2') reccomb_names;

     val case_names' = map (Sign.full_name thy2') case_names;

     val thy2 = thy2'

       (** constructors **)

       |> parent_path flat_names

       |> fold (fn ((((_, (_, _, constrs)), T), tname),

         constr_syntax') =>

           add_path flat_names tname #>

             specify_consts (map (fn ((_, cargs), (cname, mx)) =>

               (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))

                 (constrs ~~ constr_syntax')) #>

           parent_path flat_names)

             (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);

     (**** introduction of axioms ****)

     val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;

     val ((([induct], [rec_thms]), inject), thy3) =

       thy2

       |> Sign.add_path (space_implode "_" new_type_names)

       |> add_axiom "induct" (DatatypeProp.make_ind descr sorts) [case_names_induct]

       ||>> add_axioms "recs" rec_axs []

       ||> Sign.parent_path

       ||>> add_and_get_axiomss "inject" new_type_names

             (DatatypeProp.make_injs descr sorts);

     val (distinct, thy4) = add_and_get_axiomss "distinct" new_type_names

       (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;

     val exhaust_ts = DatatypeProp.make_casedists descr sorts;

     val (exhaustion, thy5) = add_and_get_axioms_atts "exhaust" new_type_names

       exhaust_ts (map single case_names_exhausts) thy4;

     val (case_thms, thy6) = add_and_get_axiomss "cases" new_type_names

       (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;

     val (split_ts, split_asm_ts) = ListPair.unzip

       (DatatypeProp.make_splits new_type_names descr sorts thy6);

     val (split, thy7) = add_and_get_axioms "split" new_type_names split_ts thy6;

     val (split_asm, thy8) = add_and_get_axioms "split_asm" new_type_names

       split_asm_ts thy7;

     val (nchotomys, thy9) = add_and_get_axioms "nchotomy" new_type_names

       (DatatypeProp.make_nchotomys descr sorts) thy8;

     val (case_congs, thy10) = add_and_get_axioms "case_cong" new_type_names

       (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;

     val (weak_case_congs, thy11) = add_and_get_axioms "weak_case_cong" new_type_names

       (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;

     val dt_infos = map (make_dt_info (length (hd descr)) descr' sorts induct

         reccomb_names' rec_thms)

       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~

         exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~

           nchotomys ~~ case_congs ~~ weak_case_congs);

     val simps = flat (distinct @ inject @ case_thms) @ rec_thms;

     val split_thms = split ~~ split_asm;

     val thy12 =

       thy11

       |> add_case_tr' case_names'

       |> Sign.add_path (space_implode "_" new_type_names)

       |> add_rules simps case_thms rec_thms inject distinct

           weak_case_congs Simplifier.cong_add

       |> put_dt_infos dt_infos

       |> add_cases_induct dt_infos induct

       |> Sign.parent_path

       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)

       |> snd

       |> DatatypeInterpretation.data (map fst dt_infos);

   in

     ({distinct = distinct,

       inject = inject,

       exhaustion = exhaustion,

       rec_thms = rec_thms,

       case_thms = case_thms,

       split_thms = split_thms,

       induction = induct,

       simps = simps}, thy12)

   end;

 (******************* definitional introduction of datatypes *******************)

 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info

     case_names_induct case_names_exhausts thy =

   let

     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);

     val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |>

       DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts

         types_syntax constr_syntax case_names_induct;

     val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr

       sorts induct case_names_exhausts thy2;

     val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms

       flat_names new_type_names descr sorts dt_info inject dist_rewrites

       (Simplifier.theory_context thy3 dist_ss) induct thy3;

     val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms

       flat_names new_type_names descr sorts reccomb_names rec_thms thy4;

     val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names

       descr sorts inject dist_rewrites casedist_thms case_thms thy6;

     val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names

       descr sorts casedist_thms thy7;

     val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names

       descr sorts nchotomys case_thms thy8;

     val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names

       descr sorts thy9;

     val dt_infos = map (make_dt_info (length (hd descr)) (flat descr) sorts induct

         reccomb_names rec_thms)

       ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~

         casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);

     val simps = flat (distinct @ inject @ case_thms) @ rec_thms;

     val thy12 =

       thy10

       |> add_case_tr' case_names

       |> Sign.add_path (space_implode "_" new_type_names)

       |> add_rules simps case_thms rec_thms inject distinct

           weak_case_congs (Simplifier.attrib (op addcongs))

       |> put_dt_infos dt_infos

       |> add_cases_induct dt_infos induct

       |> Sign.parent_path

       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd

       |> DatatypeInterpretation.data (map fst dt_infos);

   in

     ({distinct = distinct,

       inject = inject,

       exhaustion = casedist_thms,

       rec_thms = rec_thms,

       case_thms = case_thms,

       split_thms = split_thms,

       induction = induct,

       simps = simps}, thy12)

   end;

 (*********************** declare existing type as datatype *********************)

 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =

   let

     val (((distinct, inject), [induction]), thy1) =

       thy0

       |> fold_map apply_theorems raw_distinct

       ||>> fold_map apply_theorems raw_inject

       ||>> apply_theorems [raw_induction];

     val ((_, [induction']), _) =

       Variable.importT_thms [induction] (Variable.thm_context induction);

     fun err t = error ("Ill-formed predicate in induction rule: " ^

       Sign.string_of_term thy1 t);

     fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =

           ((tname, map dest_TFree Ts) handle TERM _ => err t)

       | get_typ t = err t;

     val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));

     val new_type_names = getOpt (alt_names, map fst dtnames);

     fun get_constr t = (case Logic.strip_assums_concl t of

         _ $ (_ $ t') => (case head_of t' of

             Const (cname, cT) => (case strip_type cT of

                 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))

               | _ => err t)

           | _ => err t)

       | _ => err t);

     fun make_dt_spec [] _ _ = []

       | make_dt_spec ((tname, tvs)::dtnames') i constrs =

           let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs

           in (i, (tname, map DtTFree tvs, map snd constrs'))::

             (make_dt_spec dtnames' (i + 1) constrs'')

           end;

     val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));

     val sorts = add_term_tfrees (concl_of induction', []);

     val dt_info = get_datatypes thy1;

     val (case_names_induct, case_names_exhausts) =

       (mk_case_names_induct descr, mk_case_names_exhausts descr (map #1 dtnames));

     val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);

     val (casedist_thms, thy2) = thy1 |>

       DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction

         case_names_exhausts;

     val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms

       false new_type_names [descr] sorts dt_info inject distinct

       (Simplifier.theory_context thy2 dist_ss) induction thy2;

     val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false

       new_type_names [descr] sorts reccomb_names rec_thms thy3;

     val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms

       new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;

     val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names

       [descr] sorts casedist_thms thy5;

     val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names

       [descr] sorts nchotomys case_thms thy6;

     val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names

       [descr] sorts thy7;

     val ((_, [induction']), thy10) =

       thy8

       |> store_thmss "inject" new_type_names inject

       ||>> store_thmss "distinct" new_type_names distinct

       ||> Sign.add_path (space_implode "_" new_type_names)

       ||>> PureThy.add_thms [(("induct", induction), [case_names_induct])];

     val dt_infos = map (make_dt_info (length descr) descr sorts induction'

         reccomb_names rec_thms)

       ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~

         map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);

     val simps = flat (distinct @ inject @ case_thms) @ rec_thms;

     val thy11 =

       thy10

       |> add_case_tr' case_names

       |> add_rules simps case_thms rec_thms inject distinct

            weak_case_congs (Simplifier.attrib (op addcongs))

       |> put_dt_infos dt_infos

       |> add_cases_induct dt_infos induction'

       |> Sign.parent_path

       |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)

       |> snd

       |> DatatypeInterpretation.data (map fst dt_infos);

   in

     ({distinct = distinct,

       inject = inject,

       exhaustion = casedist_thms,

       rec_thms = rec_thms,

       case_thms = case_thms,

       split_thms = split_thms,

       induction = induction',

       simps = simps}, thy11)

   end;

 val rep_datatype = gen_rep_datatype IsarCmd.apply_theorems;

 val rep_datatype_i = gen_rep_datatype IsarCmd.apply_theorems_i;

 (******************************** add datatype ********************************)

 fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =

   let

     val _ = Theory.requires thy "Datatype" "datatype definitions";

     (* this theory is used just for parsing *)

     val tmp_thy = thy |>

       Theory.copy |>

       Sign.add_types (map (fn (tvs, tname, mx, _) =>

         (tname, length tvs, mx)) dts);

     val (tyvars, _, _, _)::_ = dts;

     val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>

       let val full_tname = Sign.full_name tmp_thy (Syntax.type_name tname mx)

       in (case duplicates (op =) tvs of

             [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))

                   else error ("Mutually recursive datatypes must have same type parameters")

           | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^

               " : " ^ commas dups))

       end) dts);

     val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of

       [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));

     fun prep_dt_spec (tvs, tname, mx, constrs) (dts', constr_syntax, sorts, i) =

       let

         fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') =

           let

             val (cargs', sorts'') = Library.foldl (prep_typ tmp_thy) (([], sorts'), cargs);

             val _ = (case fold (curry add_typ_tfree_names) cargs' [] \\ tvs of

                 [] => ()

               | vs => error ("Extra type variables on rhs: " ^ commas vs))

           in (constrs @ [((if flat_names then Sign.full_name tmp_thy else

                 Sign.full_name_path tmp_thy tname) (Syntax.const_name cname mx'),

                    map (dtyp_of_typ new_dts) cargs')],

               constr_syntax' @ [(cname, mx')], sorts'')

           end handle ERROR msg =>

             cat_error msg ("The error above occured in constructor " ^ cname ^

               " of datatype " ^ tname);

         val (constrs', constr_syntax', sorts') =

           fold prep_constr constrs ([], [], sorts)

       in

         case duplicates (op =) (map fst constrs') of

            [] =>

              (dts' @ [(i, (Sign.full_name tmp_thy (Syntax.type_name tname mx),

                 map DtTFree tvs, constrs'))],

               constr_syntax @ [constr_syntax'], sorts', i + 1)

          | dups => error ("Duplicate constructors " ^ commas dups ^

              " in datatype " ^ tname)

       end;

     val (dts', constr_syntax, sorts', i) = fold prep_dt_spec dts ([], [], [], 0);

     val sorts = sorts' @ (map (rpair (Sign.defaultS tmp_thy)) (tyvars \\ map fst sorts'));

     val dt_info = get_datatypes thy;

     val (descr, _) = unfold_datatypes tmp_thy dts' sorts dt_info dts' i;

     val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>

       if err then error ("Nonemptiness check failed for datatype " ^ s)

       else raise exn;

     val descr' = flat descr;

     val case_names_induct = mk_case_names_induct descr';

     val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);

   in

     (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)

       flat_names new_type_names descr sorts types_syntax constr_syntax dt_info

       case_names_induct case_names_exhausts thy

   end;

 val add_datatype_i = gen_add_datatype cert_typ;

 val add_datatype = gen_add_datatype read_typ true;

 (** package setup **)

 (* setup theory *)

 val setup =

   DatatypeProp.distinctness_limit_setup #>

   Method.add_methods tactic_emulations #>

   simproc_setup #>

   trfun_setup #>

   DatatypeInterpretation.init;

 (* outer syntax *)

 local structure P = OuterParse and K = OuterKeyword in

 val _ = OuterSyntax.keywords ["distinct", "inject", "induction"];

 val datatype_decl =

   Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --

     (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));

 fun mk_datatype args =

   let

     val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;

     val specs = map (fn ((((_, vs), t), mx), cons) =>

       (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;

   in snd o add_datatype false names specs end;

 val _ =

   OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl

     (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));

 val rep_datatype_decl =

   Scan.option (Scan.repeat1 P.name) --

     Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] --

     Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 SpecParse.xthms1)) [[]] --

     (P.$$$ "induction" |-- P.!!! SpecParse.xthm);

 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #2 o rep_datatype opt_ts dss iss ind;

 val _ =

   OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl

     (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));

 end;

 end;

 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;

 open BasicDatatypePackage;