(* Title: HOL/Tools/Datatype/datatype_data.ML
Author: Stefan Berghofer, TU Muenchen
Datatype package: bookkeeping; interpretation of existing types as datatypes.
*)
signature DATATYPE_DATA =
sig
include DATATYPE_COMMON
val derive_datatype_props : config -> string list -> descr list ->
thm -> thm list list -> thm list list -> theory -> string list * theory
val rep_datatype : config -> (string list -> Proof.context -> Proof.context) ->
term list -> theory -> Proof.state
val rep_datatype_cmd : config -> (string list -> Proof.context -> Proof.context) ->
string list -> theory -> Proof.state
val get_info : theory -> string -> info option
val the_info : theory -> string -> info
val the_descr : theory -> string list ->
descr * (string * sort) list * string list * string *
(string list * string list) * (typ list * typ list)
val the_spec : theory -> string -> (string * sort) list * (string * typ list) list
val all_distincts : theory -> typ list -> thm list list
val get_constrs : theory -> string -> (string * typ) list option
val get_all : theory -> info Symtab.table
val info_of_constr : theory -> string * typ -> info option
val info_of_constr_permissive : theory -> string * typ -> info option
val info_of_case : theory -> string -> info option
val interpretation : (config -> string list -> theory -> theory) -> theory -> theory
val make_case : Proof.context -> Datatype_Case.config -> string list -> term ->
(term * term) list -> term
val strip_case : Proof.context -> bool -> term -> (term * (term * term) list) option
val mk_case_names_induct: descr -> attribute
val setup: theory -> theory
end;
structure Datatype_Data: DATATYPE_DATA =
struct
(** theory data **)
(* data management *)
structure DatatypesData = Theory_Data
(
type T =
{types: Datatype_Aux.info Symtab.table,
constrs: (string * Datatype_Aux.info) list Symtab.table,
cases: Datatype_Aux.info Symtab.table};
val empty =
{types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty};
val extend = I;
fun merge
({types = types1, constrs = constrs1, cases = cases1},
{types = types2, constrs = constrs2, cases = cases2}) : T =
{types = Symtab.merge (K true) (types1, types2),
constrs = Symtab.join (K (AList.merge (op =) (K true))) (constrs1, constrs2),
cases = Symtab.merge (K true) (cases1, cases2)};
);
val get_all = #types o DatatypesData.get;
val get_info = Symtab.lookup o get_all;
fun the_info thy name =
(case get_info thy name of
SOME info => info
| NONE => error ("Unknown datatype " ^ quote name));
fun info_of_constr thy (c, T) =
let
val tab = Symtab.lookup_list (#constrs (DatatypesData.get thy)) c;
in
(case body_type T of
Type (tyco, _) => AList.lookup (op =) tab tyco
| _ => NONE)
end;
fun info_of_constr_permissive thy (c, T) =
let
val tab = Symtab.lookup_list (#constrs (DatatypesData.get thy)) c;
val hint = (case body_type T of Type (tyco, _) => SOME tyco | _ => NONE);
val default = if null tab then NONE else SOME (snd (List.last tab));
(*conservative wrt. overloaded constructors*)
in
(case hint of
NONE => default
| SOME tyco =>
(case AList.lookup (op =) tab tyco of
NONE => default (*permissive*)
| SOME info => SOME info))
end;
val info_of_case = Symtab.lookup o #cases o DatatypesData.get;
fun register (dt_infos : (string * Datatype_Aux.info) list) =
DatatypesData.map (fn {types, constrs, cases} =>
{types = types |> fold Symtab.update dt_infos,
constrs = constrs |> fold (fn (constr, dtname_info) =>
Symtab.map_default (constr, []) (cons dtname_info))
(maps (fn (dtname, info as {descr, index, ...}) =>
map (rpair (dtname, info) o fst)
(#3 (the (AList.lookup op = descr index)))) dt_infos),
cases = cases |> fold Symtab.update
(map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos)});
(* complex queries *)
fun the_spec thy dtco =
let
val {descr, index, ...} = the_info thy dtco;
val (_, dtys, raw_cos) = the (AList.lookup (op =) descr index);
val args = map Datatype_Aux.dest_DtTFree dtys;
val cos = map (fn (co, tys) => (co, map (Datatype_Aux.typ_of_dtyp descr) tys)) raw_cos;
in (args, cos) end;
fun the_descr thy (raw_tycos as raw_tyco :: _) =
let
val info = the_info thy raw_tyco;
val descr = #descr info;
val (_, dtys, _) = the (AList.lookup (op =) descr (#index info));
val vs = map Datatype_Aux.dest_DtTFree dtys;
fun is_DtTFree (Datatype_Aux.DtTFree _) = true
| is_DtTFree _ = false;
val k = find_index (fn (_, (_, dTs, _)) => not (forall is_DtTFree dTs)) descr;
val protoTs as (dataTs, _) =
chop k descr
|> (pairself o map)
(fn (_, (tyco, dTs, _)) => (tyco, map (Datatype_Aux.typ_of_dtyp descr) dTs));
val tycos = map fst dataTs;
val _ =
if eq_set (op =) (tycos, raw_tycos) then ()
else
error ("Type constructors " ^ commas_quote raw_tycos ^
" do not belong exhaustively to one mutual recursive datatype");
val (Ts, Us) = (pairself o map) Type protoTs;
val names = map Long_Name.base_name tycos;
val (auxnames, _) =
Name.make_context names
|> fold_map (Name.variant o Datatype_Aux.name_of_typ) Us;
val prefix = space_implode "_" names;
in (descr, vs, tycos, prefix, (names, auxnames), (Ts, Us)) end;
fun all_distincts thy Ts =
let
fun add_tycos (Type (tyco, Ts)) = insert (op =) tyco #> fold add_tycos Ts
| add_tycos _ = I;
val tycos = fold add_tycos Ts [];
in map_filter (Option.map #distinct o get_info thy) tycos end;
fun get_constrs thy dtco =
(case try (the_spec thy) dtco of
SOME (args, 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 args);
fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty);
in SOME (map mk_co cos) end
| NONE => NONE);
(** various auxiliary **)
(* case names *)
local
fun dt_recs (Datatype_Aux.DtTFree _) = []
| dt_recs (Datatype_Aux.DtType (_, dts)) = maps dt_recs dts
| dt_recs (Datatype_Aux.DtRec i) = [i];
fun dt_cases (descr: Datatype_Aux.descr) (_, args, constrs) =
let
fun the_bname i = Long_Name.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 "_" (Long_Name.base_name c :: bnames)) constrs end;
fun induct_cases descr =
Datatype_Prop.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 = Rule_Cases.case_names (induct_cases descr);
fun mk_case_names_exhausts descr new =
map (Rule_Cases.case_names o exhaust_cases descr o #1)
(filter (fn ((_, (name, _, _))) => member (op =) new name) descr);
end;
(* translation rules for case *)
fun make_case ctxt =
Datatype_Case.make_case (info_of_constr_permissive (Proof_Context.theory_of ctxt)) ctxt;
fun strip_case ctxt =
Datatype_Case.strip_case (info_of_case (Proof_Context.theory_of ctxt));
fun add_case_tr' case_names thy =
Sign.add_advanced_trfuns ([], [],
map (fn case_name =>
let val case_name' = Lexicon.mark_const case_name in
(case_name', Datatype_Case.case_tr' info_of_case case_name')
end) case_names, []) thy;
val trfun_setup =
Sign.add_advanced_trfuns ([],
[(@{syntax_const "_case_syntax"}, Datatype_Case.case_tr true info_of_constr_permissive)],
[], []);
(** document antiquotation **)
val antiq_setup =
Thy_Output.antiquotation @{binding datatype} (Args.type_name true)
(fn {source = src, context = ctxt, ...} => fn dtco =>
let
val thy = Proof_Context.theory_of ctxt;
val (vs, cos) = the_spec thy dtco;
val ty = Type (dtco, map TFree vs);
val pretty_typ_bracket = Syntax.pretty_typ (Config.put pretty_priority 1001 ctxt);
fun pretty_constr (co, tys) =
Pretty.block (Pretty.breaks
(Syntax.pretty_term ctxt (Const (co, tys ---> ty)) ::
map pretty_typ_bracket tys));
val pretty_datatype =
Pretty.block
(Pretty.command "datatype" :: Pretty.brk 1 ::
Syntax.pretty_typ ctxt ty ::
Pretty.str " =" :: Pretty.brk 1 ::
flat (separate [Pretty.brk 1, Pretty.str "| "] (map (single o pretty_constr) cos)));
in
Thy_Output.output ctxt
(Thy_Output.maybe_pretty_source (K (K pretty_datatype)) ctxt src [()])
end);
(** abstract theory extensions relative to a datatype characterisation **)
structure Datatype_Interpretation = Interpretation
(
type T = Datatype_Aux.config * string list;
val eq: T * T -> bool = eq_snd (op =);
);
fun interpretation f = Datatype_Interpretation.interpretation (uncurry f);
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 (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 (get_all thy4))
inject (distinct, 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
|> add_case_tr' case_names
|> register dt_infos
|> Datatype_Interpretation.data (config, dt_names)
|> pair dt_names
end;
(** declare existing type as datatype **)
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),
[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 (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;
val rep_datatype = gen_rep_datatype Sign.cert_term;
val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global;
(** package setup **)
(* setup theory *)
val setup =
trfun_setup #>
antiq_setup #>
Datatype_Interpretation.init;
(* 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)));
open Datatype_Aux;
end;