(* Title: Pure/Tools/class_package.ML
ID: $Id$
Author: Florian Haftmann, TU Muenchen
Type classes derived from primitive axclasses and locales.
*)
signature CLASS_PACKAGE =
sig
val class: bstring -> class list -> Element.context Locale.element list -> theory ->
string * Proof.context
val class_i: bstring -> class list -> Element.context_i Locale.element list -> theory ->
string * Proof.context
val instance_arity: ((bstring * string list) * string) list
-> bstring * Attrib.src list -> ((bstring * Attrib.src list) * string) list
-> theory -> Proof.state
val instance_arity_i: ((bstring * sort list) * sort) list
-> bstring * attribute list -> ((bstring * attribute list) * term) list
-> theory -> Proof.state
val prove_instance_arity: (thm list -> tactic) -> ((string * sort list) * sort) list
-> bstring * attribute list -> ((bstring * attribute list) * term) list
-> theory -> theory
val instance_sort: string * string -> theory -> Proof.state
val instance_sort_i: class * sort -> theory -> Proof.state
val prove_instance_sort: tactic -> class * sort -> theory -> theory
val certify_class: theory -> class -> class
val certify_sort: theory -> sort -> sort
val read_class: theory -> xstring -> class
val read_sort: theory -> string -> sort
val operational_algebra: theory -> (sort -> sort) * Sorts.algebra
val the_consts_sign: theory -> class -> string * (string * typ) list
val the_inst_sign: theory -> class * string -> (string * sort) list * (string * typ) list
val assume_arities_of_sort: theory -> ((string * sort list) * sort) list -> typ * sort -> bool
val assume_arities_thy: theory -> ((string * sort list) * sort) list -> (theory -> 'a) -> 'a
(*'a must not keep any reference to theory*)
val print_classes: theory -> unit
val intro_classes_tac: thm list -> tactic
val default_intro_classes_tac: thm list -> tactic
end;
structure ClassPackage : CLASS_PACKAGE =
struct
(** theory data **)
datatype class_data = ClassData of {
name_locale: string,
name_axclass: string,
var: string,
consts: (string * (string * typ)) list
(*locale parameter ~> toplevel theory constant*),
operational: bool (* == at least one class operation,
or at least two operational superclasses *),
propnames: string list
} * thm list Symtab.table;
fun rep_classdata (ClassData c) = c;
structure ClassData = TheoryDataFun (
struct
val name = "Pure/classes";
type T = class_data Symtab.table;
val empty = Symtab.empty;
val copy = I;
val extend = I;
fun merge _ = Symtab.join (fn _ => fn (ClassData (classd, instd1), ClassData (_, instd2)) =>
(ClassData (classd, Symtab.merge (K true) (instd1, instd2))));
fun print thy data =
let
fun pretty_class (name, ClassData ({name_locale, name_axclass, var, consts, ...}, _)) =
(Pretty.block o Pretty.fbreaks) [
Pretty.str ("class " ^ name ^ ":"),
Pretty.str ("locale: " ^ name_locale),
Pretty.str ("axclass: " ^ name_axclass),
Pretty.str ("class variable: " ^ var),
(Pretty.block o Pretty.fbreaks) (
Pretty.str "constants: "
:: map (fn (_, (c, ty)) => Pretty.str (c ^ " :: " ^ Sign.string_of_typ thy ty)) consts
)
]
in
(Pretty.writeln o Pretty.chunks o map pretty_class o Symtab.dest) data
end;
end
);
val _ = Context.add_setup ClassData.init;
val print_classes = ClassData.print;
(* queries *)
val lookup_class_data = Option.map rep_classdata oo Symtab.lookup o ClassData.get;
fun the_class_data thy class =
case lookup_class_data thy class
of NONE => error ("undeclared constructive class " ^ quote class)
| SOME data => data;
fun the_ancestry thy classes =
let
fun proj_class class =
if is_some (lookup_class_data thy class)
then [class]
else (Sign.certify_sort thy o maps proj_class o Sign.super_classes thy) class;
fun ancestry class anc =
anc
|> insert (op =) class
|> fold ancestry ((maps proj_class o Sign.super_classes thy) class);
in fold ancestry classes [] end;
val the_parm_map = #consts o fst oo the_class_data;
val the_propnames = #propnames o fst oo the_class_data;
fun subst_clsvar v ty_subst =
map_type_tfree (fn u as (w, _) =>
if w = v then ty_subst else TFree u);
(* updaters *)
fun add_class_data (class, (name_locale, name_axclass, var, consts, operational, propnames)) =
ClassData.map (
Symtab.update_new (class, ClassData ({
name_locale = name_locale,
name_axclass = name_axclass,
var = var,
consts = consts,
operational = operational,
propnames = propnames}, Symtab.empty))
);
fun add_inst_def ((class, tyco), thm) =
ClassData.map (
Symtab.map_entry class (fn ClassData (classd, instd) =>
ClassData (classd, Symtab.insert_list eq_thm (tyco, thm) instd))
);
(* certification and reading *)
fun certify_class thy class =
(fn class => (the_class_data thy class; class)) (Sign.certify_class thy class);
fun certify_sort thy sort =
map (fn class => (the_class_data thy class; class)) (Sign.certify_sort thy sort);
fun read_class thy =
certify_class thy o Sign.intern_class thy;
fun read_sort thy =
certify_sort thy o Sign.read_sort thy;
(** contexts with arity assumptions **)
fun assume_arities_of_sort thy arities ty_sort =
let
val pp = Sign.pp thy;
val algebra = Sign.classes_of thy
|> fold (fn ((tyco, asorts), sort) =>
Sorts.add_arities pp (tyco, map (fn class => (class, asorts)) sort)) arities;
in Sorts.of_sort algebra ty_sort end;
fun assume_arities_thy thy arities f =
let
val thy_read = (fold (fn ((tyco, asorts), sort)
=> Sign.primitive_arity (tyco, asorts, sort)) arities o Theory.copy) thy
in f thy_read end;
(** tactics and methods **)
fun intro_classes_tac facts st =
(ALLGOALS (Method.insert_tac facts THEN'
REPEAT_ALL_NEW (resolve_tac (AxClass.class_intros (Thm.theory_of_thm st))))
THEN Tactic.distinct_subgoals_tac) st;
fun default_intro_classes_tac [] = intro_classes_tac []
| default_intro_classes_tac _ = Tactical.no_tac; (*no error message!*)
fun default_tac rules ctxt facts =
HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE
default_intro_classes_tac facts;
val _ = Context.add_setup (Method.add_methods
[("intro_classes", Method.no_args (Method.METHOD intro_classes_tac),
"back-chain introduction rules of classes"),
("default", Method.thms_ctxt_args (Method.METHOD oo default_tac),
"apply some intro/elim rule")]);
(** axclass instances **)
local
fun gen_instance mk_prop add_thm after_qed insts thy =
let
fun after_qed' results =
ProofContext.theory ((fold o fold) add_thm results #> after_qed);
in
thy
|> ProofContext.init
|> Proof.theorem_i PureThy.internalK NONE after_qed' NONE ("", [])
((map (fn t => (("", []), [(t, [])])) o maps (mk_prop thy)) insts)
end;
in
val axclass_instance_arity =
gen_instance (Logic.mk_arities oo Sign.read_arity) AxClass.add_arity;
val axclass_instance_arity_i =
gen_instance (Logic.mk_arities oo Sign.cert_arity) AxClass.add_arity;
val axclass_instance_sort =
gen_instance (single oo (Logic.mk_classrel oo AxClass.read_classrel)) AxClass.add_classrel I o single;
end;
(** classes and instances **)
local
fun add_axclass_i (name, supsort) params axs thy =
let
val (c, thy') = thy
|> AxClass.define_class_i (name, supsort) params axs;
val {intro, axioms, ...} = AxClass.get_definition thy' c;
in ((c, (intro, axioms)), thy') end;
(*FIXME proper locale interface*)
fun prove_interpretation_i (prfx, atts) expr insts tac thy =
let
fun ad_hoc_term (Const (c, ty)) =
let
val p = setmp show_types true (setmp show_sorts true (setmp print_mode [] (Sign.pretty_typ thy))) ty;
val s = c ^ "::" ^ Pretty.output p;
in s end
| ad_hoc_term t =
let
val p = setmp show_types true (setmp show_sorts true (setmp print_mode [] (Sign.pretty_term thy))) t;
val s = Pretty.output p;
in s end;
in
thy
|> Locale.interpretation I (prfx, atts) expr (map (Option.map ad_hoc_term) insts)
|> Proof.global_terminal_proof (Method.Basic (fn _ => Method.SIMPLE_METHOD tac), NONE)
|> ProofContext.theory_of
end;
fun gen_class add_locale prep_class bname raw_supclasses raw_elems thy =
let
val (elems, exprs) = fold_rev (fn Locale.Elem e => apfst (cons e)
| Locale.Expr e => apsnd (cons e))
raw_elems ([], []);
val supclasses = map (prep_class thy) raw_supclasses;
val supsort =
supclasses
|> map (#name_axclass o fst o the_class_data thy)
|> Sign.certify_sort thy
|> null ? K (Sign.defaultS thy);
val expr_supclasses = Locale.Merge
(map (Locale.Locale o #name_locale o fst o the_class_data thy) supclasses);
val expr = Locale.Merge (map (Locale.Locale o #name_locale o fst o the_class_data thy) supclasses
@ exprs);
val mapp_sup = AList.make
(the o AList.lookup (op =) ((flat o map (the_parm_map thy) o the_ancestry thy) supclasses))
((map (fst o fst) o Locale.parameters_of_expr thy) expr_supclasses);
fun extract_tyvar_consts thy name_locale =
let
fun extract_classvar ((c, ty), _) w =
(case Term.add_tfreesT ty []
of [(v, _)] => (case w
of SOME u => if u = v then w else error ("Additonal type variable in type signature of constant " ^ quote c)
| NONE => SOME v)
| [] => error ("No type variable in type signature of constant " ^ quote c)
| _ => error ("More than one type variable in type signature of constant " ^ quote c));
val consts1 =
Locale.parameters_of thy name_locale
|> map (apsnd (Syntax.unlocalize_mixfix true))
val SOME v = fold extract_classvar consts1 NONE;
val consts2 = map ((apfst o apsnd) (subst_clsvar v (TFree (v, [])))) consts1;
in (v, chop (length mapp_sup) consts2) end;
fun add_consts v raw_cs_sup raw_cs_this thy =
let
fun add_global_const ((c, ty), syn) thy =
((c, (Sign.full_name thy c, ty)),
thy
|> Sign.add_consts_authentic [(c, ty |> subst_clsvar v (TFree (v, Sign.defaultS thy)), syn)]);
in
thy
|> fold_map add_global_const raw_cs_this
end;
fun extract_assumes thy name_locale cs_mapp =
let
val subst_assume =
map_aterms (fn Free (c, ty) => Const ((fst o the o AList.lookup (op =) cs_mapp) c, ty)
| t => t)
fun prep_asm ((name, atts), ts) =
((NameSpace.base name, map (Attrib.attribute thy) atts), map subst_assume ts)
in
(map prep_asm o Locale.local_asms_of thy) name_locale
end;
fun add_global_constraint v class (_, (c, ty)) thy =
thy
|> Sign.add_const_constraint_i (c, SOME (subst_clsvar v (TFree (v, [class])) ty));
fun mk_const thy class v (c, ty) =
Const (c, subst_clsvar v (TFree (v, [class])) ty);
fun is_operational thy mapp_this =
length mapp_this > 0 orelse
length (filter (#operational o fst o the o lookup_class_data thy) supclasses) > 1;
in
thy
|> add_locale bname expr elems
|-> (fn name_locale => ProofContext.theory
(`(fn thy => extract_tyvar_consts thy name_locale)
#-> (fn (v, (raw_cs_sup, raw_cs_this)) =>
add_consts v raw_cs_sup raw_cs_this
#-> (fn mapp_this =>
`(fn thy => extract_assumes thy name_locale (mapp_sup @ mapp_this))
#-> (fn loc_axioms =>
add_axclass_i (bname, supsort) (map (fst o snd) mapp_this) loc_axioms
#-> (fn (name_axclass, (_, ax_axioms)) =>
fold (add_global_constraint v name_axclass) mapp_this
#> `(fn thy => is_operational thy mapp_this)
#-> (fn operational => add_class_data (name_locale, (name_locale, name_axclass, v, mapp_this,
operational, map (fst o fst) loc_axioms)))
#> prove_interpretation_i (bname, [])
(Locale.Locale name_locale) (map (SOME o mk_const thy name_axclass v) (map snd (mapp_sup @ mapp_this)))
((ALLGOALS o ProofContext.fact_tac) ax_axioms)
))))) #> pair name_locale)
end;
in
val class = gen_class (Locale.add_locale false) read_class;
val class_i = gen_class (Locale.add_locale_i false) certify_class;
end; (*local*)
local
fun gen_read_def thy prep_att read_def ((raw_name, raw_atts), raw_t) =
let
val (_, t) = read_def thy (raw_name, raw_t);
val ((c, ty), _) = Sign.cert_def (Sign.pp thy) t;
val atts = map (prep_att thy) raw_atts;
val insts = (Consts.typargs (Sign.consts_of thy) (c, ty))
val name = case raw_name
of "" => NONE
| _ => SOME raw_name;
in (c, (insts, ((name, t), atts))) end;
fun read_def thy = gen_read_def thy Attrib.attribute read_axm;
fun read_def_i thy = gen_read_def thy (K I) (K I);
fun gen_instance_arity prep_arity prep_att read_def do_proof raw_arities (raw_name, raw_atts) raw_defs theory =
let
fun prep_arity' ((tyco, asorts), sort) = prep_arity theory (tyco, asorts, sort);
val arities = map prep_arity' raw_arities;
val arities_pair = map (fn (tyco, asorts, sort) => ((tyco, asorts), sort)) arities;
val _ = if null arities then error "at least one arity must be given" else ();
val _ = case (duplicates (op =) o map #1) arities
of [] => ()
| dupl_tycos => error ("type constructors occur more than once in arities: "
^ (commas o map quote) dupl_tycos);
val (bind_always, name) = case raw_name
of "" => (false, Thm.def_name ((space_implode "_" o map NameSpace.base)
(maps (fn (tyco, _, sort) => sort @ [tyco])
(sort (fn ((tyco1, _, _), (tyco2, _, _)) => string_ord (tyco1, tyco2)) arities))))
| _ => (true, raw_name);
val atts = map (prep_att theory) raw_atts;
fun already_defined (c, ty_inst) =
is_some (find_first (fn (_, { lhs = [ty_inst'], ...}) =>
Sign.typ_instance theory (ty_inst', ty_inst) orelse Sign.typ_instance theory (ty_inst, ty_inst'))
(Defs.specifications_of (Theory.defs_of theory) c));
fun get_consts_class tyco ty class =
let
val data = (fst o the_class_data theory) class;
val subst_ty = map_type_tfree (fn (v, sort) =>
if #var data = v then ty else TVar ((v, 0), sort));
in
(map_filter (fn (_, (c, ty)) =>
if already_defined (c, ty)
then NONE else SOME ((c, ((tyco, class), subst_ty ty)))) o #consts) data
end;
fun get_consts_sort (tyco, asorts, sort) =
let
val ty = Type (tyco, map (fn (v, sort) => TVar ((v, 0), sort)) (Name.names Name.context "'a" asorts))
in maps (get_consts_class tyco ty) (the_ancestry theory sort) end;
val cs = maps get_consts_sort arities;
fun mk_typnorm thy (ty, ty_sc) =
case try (Sign.typ_match thy (Logic.varifyT ty_sc, ty)) Vartab.empty
of SOME env => SOME (Logic.varifyT #> Envir.typ_subst_TVars env #> Logic.unvarifyT)
| NONE => NONE;
fun read_defs defs cs thy_read =
let
fun read raw_def cs =
let
val (c, (inst, ((name_opt, t), atts))) = read_def thy_read raw_def;
val ty = Consts.instance (Sign.consts_of thy_read) (c, inst);
val ((tyco, class), ty') = case AList.lookup (op =) cs c
of NONE => error ("superfluous definition for constant " ^ quote c)
| SOME class_ty => class_ty;
val name = case name_opt
of NONE => Thm.def_name (Logic.name_arity (tyco, [], c))
| SOME name => name;
val t' = case mk_typnorm thy_read (ty', ty)
of NONE => error ("superfluous definition for constant " ^
quote c ^ "::" ^ Sign.string_of_typ thy_read ty)
| SOME norm => map_types norm t
in (((class, tyco), ((name, t'), atts)), AList.delete (op =) c cs) end;
in fold_map read defs cs end;
val (defs, _) = assume_arities_thy theory arities_pair (read_defs raw_defs cs);
fun get_remove_contraint c thy =
let
val ty = Sign.the_const_constraint thy c;
in
thy
|> Sign.add_const_constraint_i (c, NONE)
|> pair (c, Logic.unvarifyT ty)
end;
fun add_defs defs thy =
thy
|> PureThy.add_defs_i true (map snd defs)
|-> (fn thms => pair (map fst defs ~~ thms));
fun note_all thy =
(*FIXME: should avoid binding duplicated names*)
let
val bind = bind_always orelse not (can (PureThy.get_thms thy) (Name name));
val thms = maps (fn (tyco, _, sort) => maps (fn class =>
Symtab.lookup_list
((snd o the_class_data thy) class) tyco) (the_ancestry thy sort)) arities;
in if bind then
thy
|> PureThy.note_thmss_i (*qualified*) PureThy.internalK [((name, atts), [(thms, [])])]
|> snd
else
thy
end;
fun after_qed cs thy =
thy
|> fold Sign.add_const_constraint_i (map (apsnd SOME) cs);
in
theory
|> fold_map get_remove_contraint (map fst cs |> distinct (op =))
||>> add_defs defs
|-> (fn (cs, def_thms) =>
fold add_inst_def def_thms
#> note_all
#> do_proof (map snd def_thms) (after_qed cs) arities)
end;
fun instance_arity' do_proof = gen_instance_arity Sign.read_arity Attrib.attribute
read_def do_proof;
fun instance_arity_i' do_proof = gen_instance_arity Sign.cert_arity (K I)
read_def_i do_proof;
fun tactic_proof tac def_thms after_qed arities =
fold (fn arity => AxClass.prove_arity arity (tac def_thms)) arities
#> after_qed;
in
val instance_arity = instance_arity' (K axclass_instance_arity_i);
val instance_arity_i = instance_arity_i' (K axclass_instance_arity_i);
val prove_instance_arity = instance_arity_i' o tactic_proof;
end; (*local*)
local
fun prove_interpretation_in tac after_qed (name, expr) thy =
thy
|> Locale.interpretation_in_locale (ProofContext.theory after_qed) (name, expr)
|> Proof.global_terminal_proof (Method.Basic (fn _ => Method.SIMPLE_METHOD tac), NONE)
|> ProofContext.theory_of;
(*FIXME very ad-hoc, needs proper locale interface*)
fun gen_instance_sort prep_class prep_sort do_proof (raw_class, raw_sort) theory =
let
val class = prep_class theory raw_class;
val sort = prep_sort theory raw_sort;
val loc_name = (#name_locale o fst o the_class_data theory) class;
val loc_expr =
(Locale.Merge o map (Locale.Locale o #name_locale o fst o the_class_data theory)) sort;
val const_names = (map (NameSpace.base o fst o snd)
o maps (#consts o fst o the_class_data theory)
o the_ancestry theory) [class];
fun get_thms thy =
the_ancestry thy sort
|> AList.make (the_propnames thy)
|> map (apsnd (map (NameSpace.append (loc_name))))
|> map_filter (fn (superclass, thm_names) =>
case map_filter (try (PureThy.get_thm thy o Name)) thm_names
of [] => NONE
| thms => SOME (superclass, thms));
fun after_qed thy =
thy
|> `get_thms
|-> fold (fn (supclass, thms) => I
AxClass.prove_classrel (class, supclass)
(ALLGOALS (K (intro_classes_tac [])) THEN
(ALLGOALS o ProofContext.fact_tac) thms))
in
theory
|> do_proof after_qed (loc_name, loc_expr)
end;
fun instance_sort' do_proof = gen_instance_sort read_class read_sort do_proof;
fun instance_sort_i' do_proof = gen_instance_sort certify_class certify_sort do_proof;
val setup_proof = Locale.interpretation_in_locale o ProofContext.theory;
val tactic_proof = prove_interpretation_in;
in
val instance_sort = instance_sort' setup_proof;
val instance_sort_i = instance_sort_i' setup_proof;
val prove_instance_sort = instance_sort_i' o tactic_proof;
end; (* local *)
(** code generation view **)
fun is_operational_class thy class =
the_default false ((Option.map (#operational o fst) o lookup_class_data thy) class);
fun operational_algebra thy =
Sorts.project_algebra (Sign.pp thy)
(is_operational_class thy) (Sign.classes_of thy);
fun the_consts_sign thy class =
let
val _ = if is_operational_class thy class then () else error ("no operational class: " ^ quote class);
val data = (fst o the_class_data thy) class
in (#var data, (map snd o #consts) data) end;
fun the_inst_sign thy (class, tyco) =
let
val _ = if is_operational_class thy class then () else error ("no operational class: " ^ quote class);
val asorts = Sign.arity_sorts thy tyco [class];
val (clsvar, const_sign) = the_consts_sign thy class;
fun add_var sort used =
let val v = hd (Name.invents used "'a" 1);
in ((v, sort), Name.declare v used) end;
val (vsorts, _) =
Name.context
|> Name.declare clsvar
|> fold (fn (_, ty) => fold Name.declare
((map (fst o fst) o typ_tvars) ty @ map fst (Term.add_tfreesT ty []))) const_sign
|> fold_map add_var asorts;
val ty_inst = Type (tyco, map TFree vsorts);
val inst_signs = map (apsnd (subst_clsvar clsvar ty_inst)) const_sign;
in (vsorts, inst_signs) end;
(** toplevel interface **)
local
structure P = OuterParse
and K = OuterKeyword
in
val (classK, instanceK, print_classesK) = ("class", "instance", "print_classes")
fun wrap_add_instance_sort (class, sort) thy =
(if forall (is_some o lookup_class_data thy) (Sign.read_sort thy sort)
then instance_sort else axclass_instance_sort) (class, sort) thy;
val class_subP = P.name -- Scan.repeat (P.$$$ "+" |-- P.name) >> (op ::);
val class_bodyP = P.!!! (Scan.repeat1 P.locale_element);
val parse_arity =
(P.xname --| P.$$$ "::" -- P.!!! P.arity)
>> (fn (tyco, (asorts, sort)) => ((tyco, asorts), sort));
val classP =
OuterSyntax.command classK "define operational type class" K.thy_decl (
P.name --| P.$$$ "="
-- (
class_subP --| P.$$$ "+" -- class_bodyP
|| class_subP >> rpair []
|| class_bodyP >> pair [])
-- P.opt_begin
>> (fn ((bname, (supclasses, elems)), begin) =>
Toplevel.begin_local_theory begin (class bname supclasses elems #-> TheoryTarget.begin)));
val instanceP =
OuterSyntax.command instanceK "prove type arity or subclass relation" K.thy_goal ((
P.xname -- ((P.$$$ "\\<subseteq>" || P.$$$ "<") |-- P.!!! P.xname) >> wrap_add_instance_sort
|| P.opt_thm_name ":" -- (P.and_list1 parse_arity -- Scan.repeat (P.opt_thm_name ":" -- P.prop))
>> (fn (("", []), ([((tyco, asorts), sort)], [])) => axclass_instance_arity I [(tyco, asorts, sort)]
| (natts, (arities, defs)) => instance_arity arities natts defs)
) >> (Toplevel.print oo Toplevel.theory_to_proof));
val print_classesP =
OuterSyntax.improper_command print_classesK "print classes of this theory" K.diag
(Scan.succeed (Toplevel.no_timing o Toplevel.unknown_theory
o Toplevel.keep (print_classes o Toplevel.theory_of)));
val _ = OuterSyntax.add_parsers [classP, instanceP, print_classesP];
end; (*local*)
end;