(* 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 fork_mixfix: bool -> bool -> mixfix -> mixfix * mixfix
val class: bstring -> class list -> Element.context_i Locale.element list -> theory ->
string * Proof.context
val class_cmd: bstring -> string list -> Element.context Locale.element list -> theory ->
string * Proof.context
val instance_arity: arity list -> ((bstring * Attrib.src list) * term) list
-> theory -> Proof.state
val instance_arity_cmd: (bstring * string list * string) list
-> ((bstring * Attrib.src list) * string) list
-> theory -> Proof.state
val prove_instance_arity: tactic -> arity list
-> ((bstring * Attrib.src list) * term) list
-> theory -> theory
val instance_class: class * class -> theory -> Proof.state
val instance_class_cmd: string * string -> theory -> Proof.state
val instance_sort: class * sort -> theory -> Proof.state
val instance_sort_cmd: string * string -> theory -> Proof.state
val prove_instance_sort: tactic -> class * sort -> theory -> theory
val assume_arities_of_sort: theory -> arity list -> typ * sort -> bool
(* experimental class target *)
val class_of_locale: theory -> string -> class option
val add_def_in_class: local_theory -> string
-> (string * Syntax.mixfix) * ((string * Attrib.src list) * (term * thm)) -> theory -> 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
(** auxiliary **)
fun fork_mixfix is_class is_loc mx =
let
val mx' = Syntax.unlocalize_mixfix mx;
val mx1 = if is_class orelse (is_loc andalso mx = mx') then NoSyn else mx';
val mx2 = if is_loc then mx else NoSyn;
in (mx1, mx2) end;
(** AxClasses with implicit parameter handling **)
(* 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 NONE after_qed' ((map (fn t => [(t, [])]) o maps (mk_prop thy)) insts)
end;
in
val axclass_instance_arity =
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.cert_classrel))
AxClass.add_classrel I o single;
end; (* local *)
(* introducing axclasses with implicit parameter handling *)
fun axclass_params (name, raw_superclasses) raw_consts raw_dep_axioms thy =
let
val superclasses = map (Sign.certify_class thy) raw_superclasses;
val consts = (map o apfst o apsnd) (Sign.certify_typ thy) raw_consts;
fun add_const ((c, ty), syn) =
Sign.add_consts_authentic [(c, ty, syn)] #> pair (Sign.full_name thy c, ty);
fun mk_axioms cs thy =
raw_dep_axioms thy cs
|> (map o apsnd o map) (Sign.cert_prop thy)
|> rpair thy;
fun add_constraint class (c, ty) =
Sign.add_const_constraint_i (c, SOME (Term.map_type_tfree (fn (v, _) => TFree (v, [class])) ty));
in
thy
|> fold_map add_const consts
|-> (fn cs => mk_axioms cs
#-> (fn axioms_prop => AxClass.define_class_i (name, superclasses) (map fst cs) axioms_prop
#-> (fn class => `(fn thy => AxClass.get_definition thy class)
#-> (fn {intro, axioms, ...} => fold (add_constraint class) cs
#> pair (class, ((intro, (maps snd axioms_prop, axioms)), cs))))))
end;
(* 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;
(* instances with implicit parameter handling *)
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_cmd thy = gen_read_def thy Attrib.intern_src read_axm;
fun read_def thy = gen_read_def thy (K I) (K I);
fun gen_instance_arity prep_arity read_def do_proof raw_arities raw_defs theory =
let
val arities = map (prep_arity theory) raw_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 super_sort = (Graph.all_succs o #classes o Sorts.rep_algebra o Sign.classes_of) theory
fun get_consts_class tyco ty class =
let
val cs = (these o Option.map snd o try (AxClass.params_of_class theory)) class;
val subst_ty = map_type_tfree (K ty);
in
map (fn (c, ty) => (c, ((tyco, class), subst_ty ty))) cs
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) (super_sort 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, _) = read_defs raw_defs cs
(fold Sign.primitive_arity arities (Theory.copy theory));
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 ((apsnd o map) (Attrib.attribute thy) o snd) defs)
|-> (fn thms => pair (map fst defs ~~ thms));
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, _) => do_proof (after_qed cs) arities)
end;
fun instance_arity_e' do_proof = gen_instance_arity Sign.read_arity read_def_cmd do_proof;
fun instance_arity' do_proof = gen_instance_arity Sign.cert_arity read_def do_proof;
fun tactic_proof tac after_qed arities =
fold (fn arity => AxClass.prove_arity arity tac) arities
#> after_qed;
in
val instance_arity_cmd = instance_arity_e' axclass_instance_arity;
val instance_arity = instance_arity' axclass_instance_arity;
val prove_instance_arity = instance_arity' o tactic_proof;
end; (* local *)
(** combining locales and axclasses **)
(* theory data *)
datatype class_data = ClassData of {
locale: string,
consts: (string * string) list
(*locale parameter ~> toplevel theory constant*),
witness: Element.witness list,
propnames: string list,
(*for ad-hoc instance_in*)
primdefs: thm list
(*for experimental class target*)
};
fun rep_classdata (ClassData c) = c;
fun merge_pair f1 f2 ((x1, y1), (x2, y2)) = (f1 (x1, x2), f2 (y1, y2));
structure ClassData = TheoryDataFun (
struct
val name = "Pure/classes";
type T = class_data Graph.T * class Symtab.table (*locale name ~> class name*);
val empty = (Graph.empty, Symtab.empty);
val copy = I;
val extend = I;
fun merge _ = merge_pair (Graph.merge (K true)) (Symtab.merge (K true));
fun print _ _ = ();
end
);
val _ = Context.add_setup ClassData.init;
(* queries *)
val lookup_class_data = Option.map rep_classdata oo try o Graph.get_node o fst o ClassData.get;
fun class_of_locale thy = Symtab.lookup ((snd o ClassData.get) thy);
fun the_class_data thy class =
case lookup_class_data thy class
of NONE => error ("undeclared class " ^ quote class)
| SOME data => data;
val ancestry = Graph.all_succs o fst o ClassData.get;
fun param_map thy =
let
fun params thy class =
let
val const_typs = (#params o AxClass.get_definition thy) class;
val const_names = (#consts o the_class_data thy) class;
in
(map o apsnd) (fn c => (c, (the o AList.lookup (op =) const_typs) c)) const_names
end;
in maps (params thy) o ancestry thy end;
val the_witness = #witness oo the_class_data;
val the_propnames = #propnames oo the_class_data;
fun print_classes thy =
let
val algebra = Sign.classes_of thy;
val arities =
Symtab.empty
|> Symtab.fold (fn (tyco, arities) => fold (fn (class, _) =>
Symtab.map_default (class, []) (insert (op =) tyco)) arities)
((#arities o Sorts.rep_algebra) algebra);
val the_arities = these o Symtab.lookup arities;
fun mk_arity class tyco =
let
val Ss = Sorts.mg_domain algebra tyco [class];
in Sign.pretty_arity thy (tyco, Ss, [class]) end;
fun mk_param (c, ty) = Pretty.str (Sign.extern_const thy c ^ " :: "
^ setmp show_sorts false (Sign.string_of_typ thy o Type.strip_sorts) ty);
fun mk_entry class = (Pretty.block o Pretty.fbreaks o map_filter I) [
(SOME o Pretty.str) ("class " ^ class ^ ":"),
(SOME o Pretty.block) [Pretty.str "supersort: ",
(Sign.pretty_sort thy o Sign.certify_sort thy o Sign.super_classes thy) class],
Option.map (Pretty.str o prefix "locale: " o #locale) (lookup_class_data thy class),
((fn [] => NONE | ps => (SOME o Pretty.block o Pretty.fbreaks) (Pretty.str "parameters:" :: ps)) o map mk_param
o these o Option.map #params o try (AxClass.get_definition thy)) class,
(SOME o Pretty.block o Pretty.breaks) [
Pretty.str "instances:",
Pretty.list "" "" (map (mk_arity class) (the_arities class))
]
]
in
(Pretty.writeln o Pretty.chunks o separate (Pretty.str "") o map mk_entry o Sorts.all_classes)
algebra
end;
(* updaters *)
fun add_class_data ((class, superclasses), (locale, consts, witness, propnames)) =
ClassData.map (fn (gr, tab) => (
gr
|> Graph.new_node (class, ClassData {
locale = locale,
consts = consts,
witness = witness,
propnames = propnames,
primdefs = []})
|> fold (curry Graph.add_edge class) superclasses,
tab
|> Symtab.update (locale, class)
));
fun add_primdef (class, thm) thy =
(ClassData.map o apfst o Graph.map_node class)
(fn ClassData { locale, consts, witness, propnames, primdefs } => ClassData { locale = locale,
consts = consts, witness = witness, propnames = propnames, primdefs = thm :: primdefs });
(* exporting terms and theorems to global toplevel *)
(*FIXME should also be used when introducing classes*)
fun globalize thy classes =
let
val consts = param_map thy classes;
val constrain_sort = curry (Sorts.inter_sort (Sign.classes_of thy)) classes;
val subst_typ = Term.map_type_tfree (fn var as (v, sort) =>
if v = AxClass.param_tyvarname then TFree (v, constrain_sort sort) else TFree var)
fun subst_aterm (t as Free (v, ty)) = (case AList.lookup (op =) consts v
of SOME (c, _) => Const (c, ty)
| NONE => t)
| subst_aterm t = t;
in (subst_typ, map_types subst_typ #> Term.map_aterms subst_aterm) end;
val global_term = snd oo globalize
(* tactics and methods *)
(*FIXME adjust these when minimal intro rules are at hand*)
fun intro_classes_tac facts st =
let
val thy = Thm.theory_of_thm st;
val ctxt = ProofContext.init thy;
val intro_classes_tac = ALLGOALS
(Method.insert_tac facts THEN' REPEAT_ALL_NEW (resolve_tac (AxClass.class_intros thy)))
THEN Tactic.distinct_subgoals_tac;
val intro_locales_tac = SOMEGOAL (SELECT_GOAL (Locale.intro_locales_tac true ctxt facts))
THEN Tactic.distinct_subgoals_tac;
in
(intro_classes_tac THEN REPEAT (intro_locales_tac ORELSE intro_locales_tac)) st
end;
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")]);
(* tactical interfaces to locale commands *)
fun prove_interpretation tac prfx_atts expr insts thy =
thy
|> Locale.interpretation_i I prfx_atts expr insts
|> Proof.global_terminal_proof (Method.Basic (fn _ => Method.SIMPLE_METHOD tac), NONE)
|> ProofContext.theory_of;
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;
fun instance_sort' do_proof (class, sort) theory =
let
val loc_name = (#locale o the_class_data theory) class;
val loc_expr =
(Locale.Merge o map (Locale.Locale o #locale o the_class_data theory)) sort;
val const_names = (map (NameSpace.base o snd)
o maps (#consts o the_class_data theory)
o ancestry theory) [class];
fun get_thms thy =
ancestry thy sort
|> AList.make (the_propnames thy)
|> map (apsnd (map (NameSpace.append (Logic.const_of_class 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;
val prove_instance_sort = instance_sort' o prove_interpretation_in;
(* classes and instances *)
local
fun add_axclass (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;
fun certify_class thy class =
tap (the_class_data thy) (Sign.certify_class thy class);
fun read_class thy =
certify_class thy o Sign.intern_class thy;
fun gen_class add_locale prep_class bname raw_supclasses raw_elems thy =
let
(*FIXME need proper concept for reading locale statements*)
fun subst_classtyvar (_, _) =
TFree (AxClass.param_tyvarname, [])
| subst_classtyvar (v, sort) =
error ("Sort constraint illegal in type class, for type variable " ^ v ^ "::" ^ Sign.string_of_sort thy sort);
(*val subst_classtyvars = Element.map_ctxt {name = I, var = I, term = I,
typ = Term.map_type_tfree subst_classtyvar, fact = I, attrib = I};*)
val elems = fold_rev (fn Locale.Elem e => cons e | _ => I)
raw_elems []; (*FIXME make include possible here?*)
val supclasses = map (prep_class thy) raw_supclasses;
val supsort =
supclasses
|> Sign.certify_sort thy
|> (fn [] => Sign.defaultS thy | S => S); (*FIXME Why syntax defaultS?*)
val supexpr = Locale.Merge
(map (Locale.Locale o #locale o the_class_data thy) supclasses);
val supparams = (map fst o Locale.parameters_of_expr thy) supexpr;
val supconsts = AList.make
(the o AList.lookup (op =) (param_map thy supclasses)) (map fst supparams);
(*FIXME include proper*)
(*val elems_constrains = map
(Element.Constrains o apsnd (Term.map_type_tfree subst_classtyvar)) supparams;*)
fun extract_params thy name_locale =
let
val params = Locale.parameters_of thy name_locale;
in
(map (fst o fst) params, params
|> (map o apfst o apsnd o Term.map_type_tfree) (K (TFree (AxClass.param_tyvarname, Sign.defaultS thy)))
|> (map o apsnd) (fork_mixfix false true #> fst)
|> chop (length supconsts)
|> snd)
end;
fun extract_assumes name_locale params thy cs =
let
val consts = supconsts @ (map (fst o fst) params ~~ cs);
fun subst (Free (c, ty)) =
Const ((fst o the o AList.lookup (op =) consts) c, ty)
| subst t = t;
fun prep_asm ((name, atts), ts) =
(*FIXME: name handling?*)
((NameSpace.base name, map (Attrib.attribute thy) atts), (map o map_aterms) subst ts);
in
Locale.global_asms_of thy name_locale
|> map prep_asm
end;
fun extract_axiom_names thy name_locale =
name_locale
|> Locale.global_asms_of thy
|> map (NameSpace.base o fst o fst) (*FIXME - is finally dropped*)
fun mk_instT class = Symtab.empty
|> Symtab.update (AxClass.param_tyvarname, TFree (AxClass.param_tyvarname, [class]));
fun mk_inst class param_names cs =
Symtab.empty
|> fold2 (fn v => fn (c, ty) => Symtab.update (v, Const
(c, Term.map_type_tfree (fn (v, _) => TFree (v, [class])) ty))) param_names cs;
fun make_witness t thm = Element.make_witness t (Goal.protect thm);
in
thy
|> add_locale bname supexpr ((*elems_constrains @*) elems)
|-> (fn name_locale => ProofContext.theory_result (
`(fn thy => extract_params thy name_locale)
#-> (fn (param_names, params) =>
axclass_params (bname, supsort) params (extract_assumes name_locale params)
#-> (fn (name_axclass, ((_, (ax_terms, ax_axioms)), consts)) =>
`(fn thy => extract_axiom_names thy name_locale)
#-> (fn axiom_names =>
add_class_data ((name_axclass, supclasses),
(name_locale, map (fst o fst) params ~~ map fst consts,
map2 make_witness ax_terms ax_axioms, axiom_names))
#> prove_interpretation ((ALLGOALS o ProofContext.fact_tac) ax_axioms)
(Logic.const_of_class bname, []) (Locale.Locale name_locale)
(mk_instT name_axclass, mk_inst name_axclass param_names (map snd supconsts @ consts))
#> pair name_axclass
)))))
end;
in
val class_cmd = gen_class (Locale.add_locale true) read_class;
val class = gen_class (Locale.add_locale_i true) certify_class;
end; (*local*)
local
fun gen_instance_sort prep_class prep_sort (raw_class, raw_sort) theory =
let
val class = prep_class theory raw_class;
val sort = prep_sort theory raw_sort;
in
theory
|> instance_sort' (Locale.interpretation_in_locale o ProofContext.theory) (class, sort)
end;
fun gen_instance_class prep_class (raw_class, raw_superclass) theory =
let
val class = prep_class theory raw_class;
val superclass = prep_class theory raw_superclass;
in
theory
|> axclass_instance_sort (class, superclass)
end;
in
val instance_sort_cmd = gen_instance_sort Sign.read_class Sign.read_sort;
val instance_sort = gen_instance_sort Sign.certify_class Sign.certify_sort;
val instance_class_cmd = gen_instance_class Sign.read_class;
val instance_class = gen_instance_class Sign.certify_class;
end; (* local *)
(** experimental class target **)
fun add_def_in_class lthy loc ((c, syn), ((name, atts), (rhs, eq))) thy =
let
val SOME class = class_of_locale thy loc;
val rhs' = global_term thy [class] rhs;
val (syn', _) = fork_mixfix true true syn;
val ty = Term.fastype_of rhs';
fun add_const (c, ty, syn) =
Sign.add_consts_authentic [(c, ty, syn)]
#> pair (Sign.full_name thy c, ty);
fun add_def ((name, atts), prop) thy =
thy
|> PureThy.add_defs_i false [((name, prop), map (Attrib.attribute thy) atts)]
|>> the_single;
(*val _ = Output.info "------ DEF ------";
val _ = Output.info c;
val _ = Output.info name;
val _ = (Output.info o Sign.string_of_term thy) rhs';
val eq' = Morphism.thm (LocalTheory.target_morphism lthy) eq;
val _ = (Output.info o string_of_thm) eq;
val _ = (Output.info o string_of_thm) eq';
val witness = the_witness thy class;
val _ = Output.info "------ WIT ------";
fun print_wit (t, thm) = "(" ^ Sign.string_of_term thy t ^ ", " ^ Display.string_of_thm thm ^ ")"
val _ = (Output.info o cat_lines o map (print_wit o Element.dest_witness)) witness;
val _ = (Output.info o string_of_thm) eq';
val eq'' = Element.satisfy_thm witness eq';
val _ = (Output.info o string_of_thm) eq'';*)
in
thy
(*|> add_const (c, ty, syn')
|-> (fn c => add_def ((name, atts), Logic.mk_equals (Const c, rhs')))
|-> (fn global_def_thm => tap (fn _ => (Output.info o string_of_thm) global_def_thm))*)
end;
end;