(* Title: HOL/Tools/Datatype/rep_datatype.ML
Author: Stefan Berghofer, TU Muenchen
Representation of existing types as datatypes.
*)
signature REP_DATATYPE =
sig
val derive_datatype_props : Datatype_Aux.config -> string list -> Datatype_Aux.descr list ->
thm -> thm list list -> thm list list -> theory -> string list * theory
val rep_datatype : Datatype_Aux.config -> (string list -> Proof.context -> Proof.context) ->
term list -> theory -> Proof.state
val rep_datatype_cmd : Datatype_Aux.config -> (string list -> Proof.context -> Proof.context) ->
string list -> theory -> Proof.state
end;
structure Rep_Datatype: REP_DATATYPE =
struct
fun make_dt_info descr induct inducts rec_names rec_rewrites
(index, (((((((((((_, (tname, _, _))), inject), distinct),
exhaust), nchotomy), case_name), case_rewrites), case_cong), weak_case_cong),
(split, split_asm))) =
(tname,
{index = index,
descr = descr,
inject = inject,
distinct = distinct,
induct = induct,
inducts = inducts,
exhaust = exhaust,
nchotomy = nchotomy,
rec_names = rec_names,
rec_rewrites = rec_rewrites,
case_name = case_name,
case_rewrites = case_rewrites,
case_cong = case_cong,
weak_case_cong = weak_case_cong,
split = split,
split_asm = split_asm});
fun derive_datatype_props config dt_names descr induct inject distinct thy1 =
let
val thy2 = thy1 |> Theory.checkpoint;
val flat_descr = flat descr;
val new_type_names = map Long_Name.base_name dt_names;
val _ =
Datatype_Aux.message config
("Deriving properties for datatype(s) " ^ commas_quote new_type_names);
val (exhaust, thy3) = thy2
|> Datatype_Abs_Proofs.prove_casedist_thms config new_type_names
descr induct (Datatype_Data.mk_case_names_exhausts flat_descr dt_names);
val (nchotomys, thy4) = thy3
|> Datatype_Abs_Proofs.prove_nchotomys config new_type_names descr exhaust;
val ((rec_names, rec_rewrites), thy5) = thy4
|> Datatype_Abs_Proofs.prove_primrec_thms
config new_type_names descr (#inject o the o Symtab.lookup (Datatype_Data.get_all thy4))
inject (distinct, Datatype_Data.all_distincts thy2 (Datatype_Aux.get_rec_types flat_descr))
induct;
val ((case_rewrites, case_names), thy6) = thy5
|> Datatype_Abs_Proofs.prove_case_thms config new_type_names descr rec_names rec_rewrites;
val (case_congs, thy7) = thy6
|> Datatype_Abs_Proofs.prove_case_congs new_type_names case_names descr
nchotomys case_rewrites;
val (weak_case_congs, thy8) = thy7
|> Datatype_Abs_Proofs.prove_weak_case_congs new_type_names case_names descr;
val (splits, thy9) = thy8
|> Datatype_Abs_Proofs.prove_split_thms
config new_type_names case_names descr inject distinct exhaust case_rewrites;
val inducts = Project_Rule.projections (Proof_Context.init_global thy2) induct;
val dt_infos =
map_index
(make_dt_info flat_descr induct inducts rec_names rec_rewrites)
(hd descr ~~ inject ~~ distinct ~~ exhaust ~~ nchotomys ~~
case_names ~~ case_rewrites ~~ case_congs ~~ weak_case_congs ~~ splits);
val dt_names = map fst dt_infos;
val prfx = Binding.qualify true (space_implode "_" new_type_names);
val simps = flat (inject @ distinct @ case_rewrites) @ rec_rewrites;
val named_rules = flat (map_index (fn (index, tname) =>
[((Binding.empty, [nth inducts index]), [Induct.induct_type tname]),
((Binding.empty, [nth exhaust index]), [Induct.cases_type tname])]) dt_names);
val unnamed_rules = map (fn induct =>
((Binding.empty, [induct]), [Rule_Cases.inner_rule, Induct.induct_type ""]))
(drop (length dt_names) inducts);
in
thy9
|> Global_Theory.add_thmss ([((prfx (Binding.name "simps"), simps), []),
((prfx (Binding.name "inducts"), inducts), []),
((prfx (Binding.name "splits"), maps (fn (x, y) => [x, y]) splits), []),
((Binding.empty, flat case_rewrites @ flat distinct @ rec_rewrites),
[Simplifier.simp_add]),
((Binding.empty, rec_rewrites), [Code.add_default_eqn_attribute]),
((Binding.empty, flat inject), [iff_add]),
((Binding.empty, map (fn th => th RS notE) (flat distinct)),
[Classical.safe_elim NONE]),
((Binding.empty, weak_case_congs), [Simplifier.cong_add]),
((Binding.empty, flat (distinct @ inject)), [Induct.induct_simp_add])] @
named_rules @ unnamed_rules)
|> snd
|> Datatype_Data.add_case_tr' case_names
|> Datatype_Data.register dt_infos
|> Datatype_Data.interpretation_data (config, dt_names)
|> pair dt_names
end;
(** declare existing type as datatype **)
local
fun prove_rep_datatype config dt_names descr raw_inject half_distinct raw_induct thy1 =
let
val raw_distinct = (map o maps) (fn thm => [thm, thm RS not_sym]) half_distinct;
val new_type_names = map Long_Name.base_name dt_names;
val prfx = Binding.qualify true (space_implode "_" new_type_names);
val (((inject, distinct), [induct]), thy2) =
thy1
|> Datatype_Aux.store_thmss "inject" new_type_names raw_inject
||>> Datatype_Aux.store_thmss "distinct" new_type_names raw_distinct
||>> Global_Theory.add_thms
[((prfx (Binding.name "induct"), raw_induct),
[Datatype_Data.mk_case_names_induct descr])];
in
thy2
|> derive_datatype_props config dt_names [descr] induct inject distinct
end;
fun gen_rep_datatype prep_term config after_qed raw_ts thy =
let
val ctxt = Proof_Context.init_global thy;
fun constr_of_term (Const (c, T)) = (c, T)
| constr_of_term t = error ("Not a constant: " ^ Syntax.string_of_term ctxt t);
fun no_constr (c, T) =
error ("Bad constructor: " ^ Proof_Context.extern_const ctxt c ^ "::" ^
Syntax.string_of_typ ctxt T);
fun type_of_constr (cT as (_, T)) =
let
val frees = Term.add_tfreesT T [];
val (tyco, vs) = (apsnd o map) dest_TFree (dest_Type (body_type T))
handle TYPE _ => no_constr cT
val _ = if has_duplicates (eq_fst (op =)) vs then no_constr cT else ();
val _ = if length frees <> length vs then no_constr cT else ();
in (tyco, (vs, cT)) end;
val raw_cs =
AList.group (op =) (map (type_of_constr o constr_of_term o prep_term thy) raw_ts);
val _ =
(case map_filter (fn (tyco, _) =>
if Symtab.defined (Datatype_Data.get_all thy) tyco then SOME tyco else NONE) raw_cs of
[] => ()
| tycos => error ("Type(s) " ^ commas_quote tycos ^ " already represented inductivly"));
val raw_vss = maps (map (map snd o fst) o snd) raw_cs;
val ms =
(case distinct (op =) (map length raw_vss) of
[n] => 0 upto n - 1
| _ => error "Different types in given constructors");
fun inter_sort m =
map (fn xs => nth xs m) raw_vss
|> foldr1 (Sorts.inter_sort (Sign.classes_of thy));
val sorts = map inter_sort ms;
val vs = Name.invent_names Name.context Name.aT sorts;
fun norm_constr (raw_vs, (c, T)) =
(c, map_atyps
(TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T);
val cs = map (apsnd (map norm_constr)) raw_cs;
val dtyps_of_typ = map (Datatype_Aux.dtyp_of_typ (map (rpair vs o fst) cs)) o binder_types;
val dt_names = map fst cs;
fun mk_spec (i, (tyco, constr)) =
(i, (tyco, map Datatype_Aux.DtTFree vs, (map o apsnd) dtyps_of_typ constr));
val descr = map_index mk_spec cs;
val injs = Datatype_Prop.make_injs [descr];
val half_distincts = Datatype_Prop.make_distincts [descr];
val ind = Datatype_Prop.make_ind [descr];
val rules = (map o map o map) Logic.close_form [[[ind]], injs, half_distincts];
fun after_qed' raw_thms =
let
val [[[raw_induct]], raw_inject, half_distinct] =
unflat rules (map Drule.zero_var_indexes_list raw_thms);
(*FIXME somehow dubious*)
in
Proof_Context.background_theory_result (* FIXME !? *)
(prove_rep_datatype config dt_names descr raw_inject half_distinct raw_induct)
#-> after_qed
end;
in
ctxt
|> Proof.theorem NONE after_qed' ((map o map) (rpair []) (flat rules))
end;
in
val rep_datatype = gen_rep_datatype Sign.cert_term;
val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global;
end;
(* outer syntax *)
val _ =
Outer_Syntax.command "rep_datatype" "represent existing types inductively" Keyword.thy_goal
(Scan.repeat1 Parse.term >> (fn ts =>
Toplevel.print o
Toplevel.theory_to_proof (rep_datatype_cmd Datatype_Aux.default_config (K I) ts)));
end;