(* Title: HOL/Tools/datatype_package.ML
ID: $Id$
Author: Stefan Berghofer
Copyright 1998 TU Muenchen
Datatype package for Isabelle/HOL
*)
signature DATATYPE_PACKAGE =
sig
val add_datatype : string list -> (string list * bstring * mixfix *
(bstring * mixfix * string list) list) list -> theory -> 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,
size : thm list,
simps : thm list}
val add_datatype_i : string list -> (string list * bstring * mixfix *
(bstring * mixfix * typ list) list) list -> theory -> 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,
size : thm list,
simps : thm list}
val add_rep_datatype : string list option -> thm list list ->
thm list list -> thm -> theory -> 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,
size : thm list,
simps : thm list}
val setup: (theory -> theory) list
val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table
val datatype_info_sg : Sign.sg -> string -> DatatypeAux.datatype_info
val datatype_info : theory -> string -> DatatypeAux.datatype_info
val constrs_of : theory -> string -> term list option
val case_const_of : theory -> string -> term option
val mutual_induct_tac : string list -> int -> tactic
val induct_tac : string -> int -> tactic
val exhaust_tac : string -> int -> tactic
end;
structure DatatypePackage : DATATYPE_PACKAGE =
struct
open DatatypeAux;
(* data kind 'HOL/datatypes' *)
structure DatatypesArgs =
struct
val name = "HOL/datatypes";
type T = datatype_info Symtab.table;
val empty = Symtab.empty;
val prep_ext = I;
val merge: T * T -> T = Symtab.merge (K true);
fun print sg tab =
Pretty.writeln (Pretty.strs ("datatypes:" ::
map (Sign.cond_extern sg Sign.typeK o fst) (Symtab.dest tab)));
end;
structure DatatypesData = TheoryDataFun(DatatypesArgs);
val get_datatypes_sg = DatatypesData.get_sg;
val get_datatypes = DatatypesData.get;
val put_datatypes = DatatypesData.put;
(* setup *)
val setup = [DatatypesData.init];
(** theory information about datatypes **)
fun datatype_info_sg sg name =
(case Symtab.lookup (get_datatypes_sg sg, name) of
Some info => info
| None => error ("Unknown datatype " ^ quote name));
val datatype_info = datatype_info_sg o sign_of;
fun constrs_of thy tname =
let
val {index, descr, ...} = datatype_info thy tname;
val (_, _, constrs) = the (assoc (descr, index))
in
Some (map (fn (cname, _) =>
Const (cname, the (Sign.const_type (sign_of thy) cname))) constrs)
end handle _ => None;
fun case_const_of thy tname =
let
val {case_name, ...} = datatype_info thy tname;
in
Some (Const (case_name, the (Sign.const_type (sign_of thy) case_name)))
end handle _ => None;
fun find_tname var Bi =
let val frees = map dest_Free (term_frees Bi)
val params = Logic.strip_params Bi;
in case assoc (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 sign i aterm =
let
val (_, _, Bi, _) = 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 assoc (params, a) of None => types(a, ~1) | sm => sm)
| types' ixn = types ixn;
val (ct, _) = read_def_cterm (sign, types', sorts) [] false
(aterm, TVar (("", 0), []));
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 Free (a, _) => a mem vars)
(foldr add_term_frees (#2 (strip_context Bi), []))
then warning "Induction variable occurs also among premises!"
else ();
tacf i));
(* generic induction tactic for datatypes *)
fun mutual_induct_tac vars i state =
let
val (_, _, Bi, _) = dest_state (state, i);
val {sign, ...} = rep_thm state;
val tn = find_tname (hd vars) Bi;
val {induction, ...} = datatype_info_sg sign tn;
val ind_vnames = map (fn (_ $ Var (ixn, _)) =>
implode (tl (explode (Syntax.string_of_vname ixn))))
(dest_conj (HOLogic.dest_Trueprop (concl_of induction)));
val insts = (ind_vnames ~~ vars) handle _ =>
error ("Induction rule for type " ^ tn ^ " has different number of variables")
in
occs_in_prems (res_inst_tac insts induction) vars i state
end;
fun induct_tac var = mutual_induct_tac [var];
(* generic exhaustion tactic for datatypes *)
fun exhaust_tac aterm i state =
let
val {sign, ...} = rep_thm state;
val tn = infer_tname state sign i aterm;
val {exhaustion, ...} = datatype_info_sg sign tn;
val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
(hd (Logic.strip_assums_hyp (hd (prems_of exhaustion))));
val exh_vname = implode (tl (explode (Syntax.string_of_vname ixn)))
in
res_inst_tac [(exh_vname, aterm)] exhaustion i state
end;
(* prepare types *)
fun read_typ sign ((Ts, sorts), str) =
let
val T = Type.no_tvars (Sign.read_typ (sign, (curry assoc)
(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 (map fst sorts') of
[] => sorts'
| dups => error ("Inconsistent sort constraints for " ^ commas dups))
end;
(**** make datatype info ****)
fun make_dt_info descr induct reccomb_names rec_thms
((((((((i, (_, (tname, _, _))), case_name), case_thms),
exhaustion_thm), distinct_thm), inject), nchotomy), case_cong) = (tname,
{index = i,
descr = descr,
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});
fun store_clasimp thy (cla, simp) =
(claset_ref_of thy := cla; simpset_ref_of thy := simp);
infix 4 addDistinct;
fun clasimp addDistinct ([], _) = clasimp
| clasimp addDistinct (thms::thmss, (_, (_, _, constrs))::descr) =
if length constrs < DatatypeProp.dtK then
clasimp addIffs thms addDistinct (thmss, descr)
else
clasimp addsimps2 thms addDistinct (thmss, descr);
(********************* axiomatic introduction of datatypes ********************)
fun add_and_get_axioms label tnames ts thy =
foldr (fn ((tname, t), (thy', axs)) =>
let
val thy'' = thy' |>
(if length tnames = 1 then I else Theory.add_path tname) |>
PureThy.add_axioms_i [((label, t), [])];
val ax = get_axiom thy'' label
in (if length tnames = 1 then thy'' else Theory.parent_path thy'', ax::axs)
end) (tnames ~~ ts, (thy, []));
fun add_and_get_axiomss label tnames tss thy =
foldr (fn ((tname, ts), (thy', axss)) =>
let
val thy'' = thy' |>
(if length tnames = 1 then I else Theory.add_path tname) |>
PureThy.add_axiomss_i [((label, ts), [])];
val axs = PureThy.get_thms thy'' label
in (if length tnames = 1 then thy'' else Theory.parent_path thy'', axs::axss)
end) (tnames ~~ tss, (thy, []));
fun add_datatype_axm new_type_names descr sorts types_syntax constr_syntax dt_info thy =
let
val descr' = flat descr;
val recTs = get_rec_types descr' sorts;
val newTs = take (length (hd descr), recTs);
val _ = writeln ("Adding axioms for datatype(s) " ^ commas new_type_names);
(**** 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 = map (fn (i, _) =>
TFree ("'t" ^ (string_of_int (i + 1)), HOLogic.termS)) descr';
val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) =>
map (fn (_, cargs) =>
let
val recs = filter is_rec_type cargs;
val argTs = (map (typ_of_dtyp descr' sorts) cargs) @
(map (fn r => nth_elem (dest_DtRec r, rec_result_Ts)) recs)
in argTs ---> nth_elem (i, rec_result_Ts)
end) constrs) descr');
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 big_size_name = space_implode "_" new_type_names ^ "_size";
val size_names = if length (flat (tl descr)) = 1 then [big_size_name] else
map (fn i => big_size_name ^ "_" ^ string_of_int i)
(1 upto length (flat (tl descr)));
val freeT = TFree ("'t", HOLogic.termS);
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 |>
Theory.add_path (space_implode "_" new_type_names) |>
(** new types **)
curry (foldr (fn (((name, mx), tvs), thy') => thy' |>
PureThy.add_typedecls [(name, tvs, mx)] |>
Theory.add_arities_i
[(Sign.full_name (sign_of thy') (Syntax.type_name name mx),
replicate (length tvs) HOLogic.termS, HOLogic.termS)]))
(types_syntax ~~ tyvars) |>
(** constructors **)
curry (foldr (fn (((((_, (_, _, constrs)), T), tname),
constr_syntax'), thy') => thy' |>
(if length newTs = 1 then I else Theory.add_path tname) |>
Theory.add_consts_i (map (fn ((_, cargs), (cname, mx)) =>
(cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
(constrs ~~ constr_syntax')) |>
(if length newTs = 1 then I else Theory.parent_path)))
(hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax) |>
(** primrec combinators **)
Theory.add_consts_i (map (fn ((name, T), T') =>
(name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
(reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
(** case combinators **)
Theory.add_consts_i (map (fn ((name, T), Ts) =>
(name, Ts @ [T] ---> freeT, NoSyn))
(case_names ~~ newTs ~~ case_fn_Ts)) |>
Theory.add_trrules_i (DatatypeProp.make_case_trrules new_type_names descr) |>
(** t_ord functions **)
Theory.add_consts_i
(foldr (fn ((((_, (_, _, constrs)), tname), T), decls) =>
if length constrs < DatatypeProp.dtK then decls
else (tname ^ "_ord", T --> HOLogic.natT, NoSyn)::decls)
((hd descr) ~~ new_type_names ~~ newTs, [])) |>
(** size functions **)
Theory.add_consts_i (map (fn (s, T) =>
(Sign.base_name s, T --> HOLogic.natT, NoSyn))
(size_names ~~ drop (length (hd descr), recTs)));
(**** introduction of axioms ****)
val (thy3, inject) = thy2 |>
Theory.add_path (space_implode "_" new_type_names) |>
PureThy.add_axioms_i [(("induct", DatatypeProp.make_ind descr sorts), [])] |>
add_and_get_axiomss "inject" new_type_names
(DatatypeProp.make_injs descr sorts);
val (thy4, distinct) = add_and_get_axiomss "distinct" new_type_names
(DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
val induct = get_axiom thy4 "induct";
val (thy5, exhaustion) = add_and_get_axioms "exhaust" new_type_names
(DatatypeProp.make_casedists descr sorts) (PureThy.add_axiomss_i [(("recs",
DatatypeProp.make_primrecs new_type_names descr sorts thy4), [])] thy4);
val rec_thms = get_thms thy5 "recs";
val (thy6, case_thms) = 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 (thy7, split) = add_and_get_axioms "split" new_type_names split_ts thy6;
val (thy8, split_asm) = add_and_get_axioms "split_asm" new_type_names
split_asm_ts thy7;
val (thy9, nchotomys) = add_and_get_axioms "nchotomy" new_type_names
(DatatypeProp.make_nchotomys descr sorts) thy8;
val (thy10, case_congs) = add_and_get_axioms "case_cong" new_type_names
(DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
val thy11 = PureThy.add_axiomss_i [(("size",
DatatypeProp.make_size new_type_names descr sorts thy10), [])] thy10;
val size_thms = get_thms thy11 "size";
val dt_infos = map (make_dt_info descr' induct reccomb_names rec_thms)
((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
exhaustion ~~ distinct ~~ inject ~~ nchotomys ~~ case_congs);
val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
val thy12 = thy11 |>
PureThy.add_tthmss [(("simps", map Attribute.tthm_of simps), [])] |>
put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
Theory.parent_path;
val _ = store_clasimp thy12 ((claset_of thy12, simpset_of thy12)
addsimps2 flat case_thms addsimps2 size_thms addsimps2 rec_thms
addIffs flat inject addDistinct (distinct, hd descr));
in
(thy12,
{distinct = distinct,
inject = inject,
exhaustion = exhaustion,
rec_thms = rec_thms,
case_thms = case_thms,
split_thms = split ~~ split_asm,
induction = induct,
size = size_thms,
simps = simps})
end;
(******************* definitional introduction of datatypes *******************)
fun add_datatype_def new_type_names descr sorts types_syntax constr_syntax dt_info thy =
let
val _ = writeln ("Proofs for datatype(s) " ^ commas new_type_names);
val (thy2, inject, dist_rewrites, induct) = thy |>
Theory.add_path (space_implode "_" new_type_names) |>
DatatypeRepProofs.representation_proofs dt_info new_type_names descr sorts
types_syntax constr_syntax;
val (thy3, casedist_thms) =
DatatypeAbsProofs.prove_casedist_thms new_type_names descr sorts induct thy2;
val (thy4, reccomb_names, rec_thms) = DatatypeAbsProofs.prove_primrec_thms
new_type_names descr sorts dt_info inject dist_rewrites induct thy3;
val (thy5, case_names, case_thms) = DatatypeAbsProofs.prove_case_thms
new_type_names descr sorts reccomb_names rec_thms thy4;
val (thy6, distinct) = DatatypeAbsProofs.prove_distinctness_thms
new_type_names descr sorts dist_rewrites case_thms thy5;
val (thy7, split_thms) = DatatypeAbsProofs.prove_split_thms new_type_names
descr sorts inject dist_rewrites casedist_thms case_thms thy6;
val (thy8, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
descr sorts casedist_thms thy7;
val (thy9, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
descr sorts nchotomys case_thms thy8;
val (thy10, size_thms) = DatatypeAbsProofs.prove_size_thms new_type_names
descr sorts reccomb_names rec_thms thy9;
val dt_infos = map (make_dt_info (flat descr) induct reccomb_names rec_thms)
((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
casedist_thms ~~ distinct ~~ inject ~~ nchotomys ~~ case_congs);
val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
val thy11 = thy10 |>
PureThy.add_tthmss [(("simps", map Attribute.tthm_of simps), [])] |>
put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
Theory.parent_path;
val _ = store_clasimp thy11 ((claset_of thy11, simpset_of thy11)
addsimps2 flat case_thms addsimps2 size_thms addsimps2 rec_thms
addIffs flat inject addDistinct (distinct, hd descr));
in
(thy11,
{distinct = distinct,
inject = inject,
exhaustion = casedist_thms,
rec_thms = rec_thms,
case_thms = case_thms,
split_thms = split_thms,
induction = induct,
size = size_thms,
simps = simps})
end;
(*********************** declare non-datatype as datatype *********************)
fun add_rep_datatype alt_names distinct inject induction thy =
let
val sign = sign_of thy;
val induction' = freezeT induction;
fun err t = error ("Ill-formed predicate in induction rule: " ^
Sign.string_of_term sign t);
fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
((tname, map dest_TFree Ts) handle _ => err t)
| get_typ t = err t;
val dtnames = map get_typ (dest_conj (HOLogic.dest_Trueprop (concl_of induction')));
val new_type_names = if_none 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 thy;
val _ = writeln ("Proofs for datatype(s) " ^ commas new_type_names);
val (thy2, casedist_thms) = thy |>
Theory.add_path (space_implode "_" new_type_names) |>
DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction;
val (thy3, reccomb_names, rec_thms) = DatatypeAbsProofs.prove_primrec_thms
new_type_names [descr] sorts dt_info inject distinct induction thy2;
val (thy4, case_names, case_thms) = DatatypeAbsProofs.prove_case_thms
new_type_names [descr] sorts reccomb_names rec_thms thy3;
val (thy5, split_thms) = DatatypeAbsProofs.prove_split_thms
new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
val (thy6, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
[descr] sorts casedist_thms thy5;
val (thy7, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
[descr] sorts nchotomys case_thms thy6;
val (thy8, size_thms) =
if exists (equal "Arith") (Sign.stamp_names_of (sign_of thy7)) then
DatatypeAbsProofs.prove_size_thms new_type_names
[descr] sorts reccomb_names rec_thms thy7
else (thy7, []);
val dt_infos = map (make_dt_info descr induction reccomb_names rec_thms)
((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~
casedist_thms ~~ distinct ~~ inject ~~ nchotomys ~~ case_congs);
val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
val thy9 = thy8 |>
PureThy.add_tthmss [(("simps", map Attribute.tthm_of simps), [])] |>
put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
Theory.parent_path;
val _ = store_clasimp thy9 ((claset_of thy9, simpset_of thy9)
addsimps2 flat case_thms addsimps2 size_thms addsimps2 rec_thms
addIffs flat inject addDistinct (distinct, descr));
in
(thy9,
{distinct = distinct,
inject = inject,
exhaustion = casedist_thms,
rec_thms = rec_thms,
case_thms = case_thms,
split_thms = split_thms,
induction = induction,
size = size_thms,
simps = simps})
end;
(******************************** add datatype ********************************)
fun gen_add_datatype prep_typ 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.prep_ext |>
Theory.add_path (space_implode "_" new_type_names) |>
Theory.add_types (map (fn (tvs, tname, mx, _) =>
(tname, length tvs, mx)) dts);
val sign = sign_of tmp_thy;
val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
let val full_tname = Sign.full_name sign (Syntax.type_name tname mx)
in (case duplicates tvs of
[] => ((full_tname, tvs), (tname, mx))
| dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
" : " ^ commas dups))
end) dts);
val _ = (case duplicates (map fst new_dts) @ duplicates new_type_names of
[] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
fun prep_dt_spec ((dts', constr_syntax, sorts, i), (tvs, tname, mx, constrs)) =
let
fun prep_constr ((constrs, constr_syntax', sorts'), (cname, mx', cargs)) =
let val (cargs', sorts'') = foldl (prep_typ sign) (([], sorts'), cargs)
in (constrs @ [((if length dts = 1 then Sign.full_name sign
else Sign.full_name_path sign (Sign.base_name tname))
(Syntax.const_name cname mx'),
map (dtyp_of_typ new_dts) cargs')],
constr_syntax' @ [(cname, mx')], sorts'')
end handle ERROR =>
error ("The error above occured in constructor " ^ cname ^
" of datatype " ^ tname);
val (constrs', constr_syntax', sorts') =
foldl prep_constr (([], [], sorts), constrs)
in
case duplicates (map fst constrs') of
[] =>
(dts' @ [(i, (Sign.full_name sign (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) = foldl prep_dt_spec (([], [], [], 0), dts);
val dt_info = get_datatypes thy;
val (descr, _) = unfold_datatypes dt_info dts' i;
val _ = check_nonempty descr;
in
(if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
new_type_names descr sorts types_syntax constr_syntax dt_info thy
end;
val add_datatype_i = gen_add_datatype cert_typ;
val add_datatype = gen_add_datatype read_typ;
end;
val induct_tac = DatatypePackage.induct_tac;
val mutual_induct_tac = DatatypePackage.mutual_induct_tac;
val exhaust_tac = DatatypePackage.exhaust_tac;